History of Jacobi sums of pairs of Dirichlet characters modulo a prime

who	what
2026-09-05 03:54	bmatschke with assisted by an agent	the Jacobi sums that are Gaussian integers now say so, rather than being written as a hundred digits of an integer	current reviewed
2026-09-05 03:54	bmatschke	checking that this table can be written to
2026-09-04 14:25	bmatschke	who asked for a table is not a fact about the mathematics; the issue is answered in the issue
2026-09-03 13:53	zeta3	the parameter titles lose an in-page HREF that the site turned into a "no entry CL" warning; the three parameter comments, which the page never shows, become a comment on what is listed and why; the four entries at p=5 are all in the degree-2 table, so two gain their equals and comment (14) says fou
2026-09-03 13:25	zeta3 with Claude Code, table-build@8390298,	Jacobi sums of every pair of nontrivial characters modulo the primes up to 19 with nontrivial product, summed in ball arithmetic from Conrey's definition of the characters and checked against Sage's exact Jacobi sum
2026-09-03 13:25	zeta3	checking that this table can be written to
2026-09-03 13:25	zeta3 with Claude Code, table-build@8390298, run 20260903T130444Z	draft: Jacobi sums of pairs of Dirichlet characters modulo a prime, proposal 2 of BATCH-2026-09-03T1011
from line 206 (2865 lines, 2862 more than before) @@ -206,3 +206,2865 @@
 Display properties:   number-header: $J(\chi_p(m,\cdot),\chi_p(n,\cdot))$-Numbers: []+Numbers:+- params:+    p: '5'+    m: '2'+    n: '2'+  number: -1 + i * -2+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=-1 - 2i$+  equals: HREF{Algebraic_numbers_of_degree_2#1,2,5,1}[$-1-2i$]+- params:+    p: '5'+    m: '2'+    n: '4'+  number: 1 + i * 2+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2i$+  equals: HREF{Algebraic_numbers_of_degree_2#1,-2,5,2}[$1+2i$]+- params:+    p: '5'+    m: '3'+    n: '3'+  number: -1 + i * 2+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=-1 + 2i$+  equals: HREF{Algebraic_numbers_of_degree_2#1,2,5,2}[$-1+2i$]+- params:+    p: '5'+    m: '3'+    n: '4'+  number: 1 + i * -2+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 2i$+  equals: HREF{Algebraic_numbers_of_degree_2#1,-2,5,1}[$1-2i$]+- params:+    p: '7'+    m: '2'+    n: '2'+  number: 0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=-1 - 3\zeta_{3}$+- params:+    p: '7'+    m: '2'+    n: '3'+  number: 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=1 + 2\zeta_{6}$+- params:+    p: '7'+    m: '2'+    n: '5'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=-2 - \zeta_{6}$+- params:+    p: '7'+    m: '2'+    n: '6'+  number: 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2\zeta_{6}$+- params:+    p: '7'+    m: '3'+    n: '3'+  number: 2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=3 - \zeta_{6}$+- params:+    p: '7'+    m: '3'+    n: '4'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $3$; $J(\chi,\psi)=-3 + \zeta_{6}$+- params:+    p: '7'+    m: '3'+    n: '6'+  number: -2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{6}$+- params:+    p: '7'+    m: '4'+    n: '4'+  number: 0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=2 + 3\zeta_{3}$+- params:+    p: '7'+    m: '4'+    n: '5'+  number: 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=3 - 2\zeta_{6}$+- params:+    p: '7'+    m: '4'+    n: '6'+  number: 2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{6}$+- params:+    p: '7'+    m: '5'+    n: '5'+  number: 2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=2 + \zeta_{6}$+- params:+    p: '7'+    m: '5'+    n: '6'+  number: -2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=-3 + 2\zeta_{6}$+- params:+    p: '11'+    m: '2'+    n: '2'+  number: -3.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602094695569+    + i * 0.2245139882897926862209725758987633937896062411605417596972393170844037782395104132982152887546712902+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-4 + 2\zeta_{10}+    - 2\zeta_{10}^{2} + \zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '3'+  number: 3.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602094695569+    + i * -0.2245139882897926862209725758987633937896062411605417596972393170844037782395104132982152887546712902+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=4 - 2\zeta_{10}+    + 2\zeta_{10}^{2} - \zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '4'+  number: 0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=\zeta_{10} - 2\zeta_{10}^{2}+    - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '5'+  number: 1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=-1 + 2\zeta_{10}+    + 2\zeta_{10}^{2}$+- params:+    p: '11'+    m: '2'+    n: '7'+  number: -0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-\zeta_{10} ++    2\zeta_{10}^{2} + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '8'+  number: 0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=2 - 4\zeta_{10}+    + 2\zeta_{10}^{2} - 3\zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '9'+  number: -0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=-2 + 4\zeta_{10}+    - 2\zeta_{10}^{2} + 3\zeta_{10}^{3}$+- params:+    p: '11'+    m: '2'+    n: '10'+  number: -1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $10$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 2\zeta_{10}+    - 2\zeta_{10}^{2}$+- params:+    p: '11'+    m: '3'+    n: '3'+  number: 3.045084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * -1.314327780297834015064172712119691518213744830608354453822338808103027866008035045929081572078881427+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=-2 - 2\zeta_{5}+    - 3\zeta_{5}^{2} - 4\zeta_{5}^{3}$+- params:+    p: '11'+    m: '3'+    n: '5'+  number: 3.045084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * -1.314327780297834015064172712119691518213744830608354453822338808103027866008035045929081572078881427+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=-2 - 2\zeta_{5}+    - 3\zeta_{5}^{2} - 4\zeta_{5}^{3}$+- params:+    p: '11'+    m: '3'+    n: '6'+  number: 0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=1 - \zeta_{10}+    + 3\zeta_{10}^{2} + \zeta_{10}^{3}$+- params:+    p: '11'+    m: '3'+    n: '7'+  number: -3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=-3 + 2\zeta_{10}+    - 4\zeta_{10}^{2} + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '3'+    n: '8'+  number: 0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=1 - \zeta_{10}+    + 3\zeta_{10}^{2} + \zeta_{10}^{3}$+- params:+    p: '11'+    m: '3'+    n: '9'+  number: -2.545084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * -2.126627020880099830453851242657527680601003509412042204591850605944710118409897416735800910696294054+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=1 - \zeta_{5} ++    \zeta_{5}^{2} + 3\zeta_{5}^{3}$+- params:+    p: '11'+    m: '3'+    n: '10'+  number: -3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $5$, $\psi$ of order $2$; $J(\chi,\psi)=-3 + 2\zeta_{10}+    - 4\zeta_{10}^{2} + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '4'+    n: '4'+  number: 3.045084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * 1.314327780297834015064172712119691518213744830608354453822338808103027866008035045929081572078881427+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=2\zeta_{5} - 2\zeta_{5}^{2}+    - \zeta_{5}^{3}$+- params:+    p: '11'+    m: '4'+    n: '5'+  number: -2.545084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * 2.126627020880099830453851242657527680601003509412042204591850605944710118409897416735800910696294054+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=2 + \zeta_{5} ++    4\zeta_{5}^{2} + 2\zeta_{5}^{3}$+- params:+    p: '11'+    m: '4'+    n: '6'+  number: 3.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602094695569+    + i * 0.2245139882897926862209725758987633937896062411605417596972393170844037782395104132982152887546712902+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=2 + 2\zeta_{10}+    - \zeta_{10}^{2}$+- params:+    p: '11'+    m: '4'+    n: '7'+  number: 0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=\zeta_{10} - 2\zeta_{10}^{2}+    - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '4'+    n: '8'+  number: -3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=-1 - 2\zeta_{10}+    + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '4'+    n: '9'+  number: 3.045084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * 1.314327780297834015064172712119691518213744830608354453822338808103027866008035045929081572078881427+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=2\zeta_{5} - 2\zeta_{5}^{2}+    - \zeta_{5}^{3}$+- params:+    p: '11'+    m: '4'+    n: '10'+  number: -3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $5$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{10}+    + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '5'+    n: '5'+  number: -2.545084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * 2.126627020880099830453851242657527680601003509412042204591850605944710118409897416735800910696294054+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=2 + \zeta_{5} ++    4\zeta_{5}^{2} + 2\zeta_{5}^{3}$+- params:+    p: '11'+    m: '5'+    n: '6'+  number: -0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=2 - 4\zeta_{10}+    + \zeta_{10}^{2} - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '5'+    n: '7'+  number: -0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=2 - 4\zeta_{10}+    + \zeta_{10}^{2} - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '5'+    n: '8'+  number: 2.190983005625052575897706582817180941139845410097118568932275688647369768590548775146396397905304431+    + i * -2.489898284882780273401584621397837055409049705894646435966883769617584814332738960946089671804364099+  comment: $\chi$ of order $5$, $\psi$ of order $10$; $J(\chi,\psi)=3 - \zeta_{10}+    - \zeta_{10}^{2} - \zeta_{10}^{3}$+- params:+    p: '11'+    m: '5'+    n: '10'+  number: 1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $5$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{10}+    + 2\zeta_{10}^{2}$+- params:+    p: '11'+    m: '6'+    n: '6'+  number: -3.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602094695569+    + i * -0.2245139882897926862209725758987633937896062411605417596972393170844037782395104132982152887546712902+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-2 - 2\zeta_{10}+    + \zeta_{10}^{2}$+- params:+    p: '11'+    m: '6'+    n: '7'+  number: 0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-2 + 4\zeta_{10}+    - \zeta_{10}^{2} + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '6'+    n: '8'+  number: -0.8090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * -3.216440812888141159297051378878455805025142098859854898716950096963334206178422049366667194020504191+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-1 + \zeta_{10}+    - 3\zeta_{10}^{2} - \zeta_{10}^{3}$+- params:+    p: '11'+    m: '6'+    n: '9'+  number: 1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=1 - 2\zeta_{10}+    + 2\zeta_{10}^{2} - 4\zeta_{10}^{3}$+- params:+    p: '11'+    m: '6'+    n: '10'+  number: -1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $10$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{10}+    - 2\zeta_{10}^{2} + 4\zeta_{10}^{3}$+- params:+    p: '11'+    m: '7'+    n: '7'+  number: -2.190983005625052575897706582817180941139845410097118568932275688647369768590548775146396397905304431+    + i * -2.489898284882780273401584621397837055409049705894646435966883769617584814332738960946089671804364099+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-2 - \zeta_{10}+    - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '7'+    n: '9'+  number: 2.190983005625052575897706582817180941139845410097118568932275688647369768590548775146396397905304431+    + i * 2.489898284882780273401584621397837055409049705894646435966883769617584814332738960946089671804364099+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=2 + \zeta_{10}+    + 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '7'+    n: '10'+  number: 3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * 0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $10$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{10}+    + 4\zeta_{10}^{2} - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '8'+    n: '8'+  number: -2.190983005625052575897706582817180941139845410097118568932275688647369768590548775146396397905304431+    + i * 2.489898284882780273401584621397837055409049705894646435966883769617584814332738960946089671804364099+  comment: $\chi$ of order $10$, $\psi$ of order $10$; $J(\chi,\psi)=-3 + \zeta_{10}+    + \zeta_{10}^{2} + \zeta_{10}^{3}$+- params:+    p: '11'+    m: '8'+    n: '9'+  number: -0.3090169943749474241022934171828190588601545899028814310677243113526302314094512248536036020946955687+    + i * 3.302197525465046088791263151935673217796308384698334186736395567459267066734601331752809010421776726+  comment: $\chi$ of order $10$, $\psi$ of order $5$; $J(\chi,\psi)=-2 + 4\zeta_{10}+    - 2\zeta_{10}^{2} + 3\zeta_{10}^{3}$+- params:+    p: '11'+    m: '8'+    n: '10'+  number: 3.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -0.7265425280053608858954667574806187496160923929652084627500663273457493918456830884205775222161400914+  comment: $\chi$ of order $10$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2\zeta_{10}+    - 2\zeta_{10}^{3}$+- params:+    p: '11'+    m: '9'+    n: '9'+  number: -2.545084971874737120511467085914095294300772949514407155338621556763151157047256124268018010473477844+    + i * -2.126627020880099830453851242657527680601003509412042204591850605944710118409897416735800910696294054+  comment: $\chi$ of order $5$, $\psi$ of order $5$; $J(\chi,\psi)=1 - \zeta_{5} ++    \zeta_{5}^{2} + 3\zeta_{5}^{3}$+- params:+    p: '11'+    m: '9'+    n: '10'+  number: 1.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275+    + i * -3.077683537175253402570290576036909824006702143537792427039156250374863288495090918454593721667105435+  comment: $\chi$ of order $5$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 2\zeta_{10}+    + 2\zeta_{10}^{2} - 4\zeta_{10}^{3}$+- params:+    p: '13'+    m: '2'+    n: '2'+  number: -0.2320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485757+    + i * -3.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=3 - 2\zeta_{12}+    - 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '2'+    n: '3'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $3$; $J(\chi,\psi)=-1 - 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '2'+    n: '4'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $12$, $\psi$ of order $6$; $J(\chi,\psi)=4\zeta_{12} -+    \zeta_{12}^{3}$+- params:+    p: '13'+    m: '2'+    n: '5'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $12$, $\psi$ of order $4$; $J(\chi,\psi)=-4\zeta_{12} ++    \zeta_{12}^{3}$+- params:+    p: '13'+    m: '2'+    n: '6'+  number: -3 + i * 2+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=-3 + 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '2'+    n: '8'+  number: -2 + i * -3+  comment: $\chi$ of order $12$, $\psi$ of order $4$; $J(\chi,\psi)=-2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '2'+    n: '9'+  number: 2 + i * 3+  comment: $\chi$ of order $12$, $\psi$ of order $3$; $J(\chi,\psi)=2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '2'+    n: '10'+  number: 0.2320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485757+    + i * 3.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $6$; $J(\chi,\psi)=-3 + 2\zeta_{12}+    + 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '2'+    n: '11'+  number: 2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=1 + 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '2'+    n: '12'+  number: 3 + i * -2+  comment: $\chi$ of order $12$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '3'+    n: '3'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=-4 - 3\zeta_{3}$+- params:+    p: '13'+    m: '3'+    n: '4'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=-3 + 4\zeta_{6}$+- params:+    p: '13'+    m: '3'+    n: '5'+  number: 2 + i * -3+  comment: $\chi$ of order $3$, $\psi$ of order $4$; $J(\chi,\psi)=2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '3'+    n: '6'+  number: 2 + i * 3+  comment: $\chi$ of order $3$, $\psi$ of order $12$; $J(\chi,\psi)=2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '3'+    n: '7'+  number: 2 + i * -3+  comment: $\chi$ of order $3$, $\psi$ of order $12$; $J(\chi,\psi)=2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '3'+    n: '8'+  number: 2 + i * 3+  comment: $\chi$ of order $3$, $\psi$ of order $4$; $J(\chi,\psi)=2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '3'+    n: '10'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=3 + \zeta_{6}$+- params:+    p: '13'+    m: '3'+    n: '11'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $12$; $J(\chi,\psi)=-1 - 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '3'+    n: '12'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=-3 + 4\zeta_{6}$+- params:+    p: '13'+    m: '4'+    n: '4'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=4 - \zeta_{6}$+- params:+    p: '13'+    m: '4'+    n: '5'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $6$, $\psi$ of order $4$; $J(\chi,\psi)=4\zeta_{12} - \zeta_{12}^{3}$+- params:+    p: '13'+    m: '4'+    n: '6'+  number: -3.232050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+    + i * -1.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $6$, $\psi$ of order $12$; $J(\chi,\psi)=-2\zeta_{12} -+    3\zeta_{12}^{2} + 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '4'+    n: '7'+  number: 0.2320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485757+    + i * -3.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $6$, $\psi$ of order $12$; $J(\chi,\psi)=2\zeta_{12} -+    3\zeta_{12}^{2} - 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '4'+    n: '8'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $6$, $\psi$ of order $4$; $J(\chi,\psi)=-4\zeta_{12} ++    \zeta_{12}^{3}$+- params:+    p: '13'+    m: '4'+    n: '9'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $3$; $J(\chi,\psi)=4 - \zeta_{6}$+- params:+    p: '13'+    m: '4'+    n: '11'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $6$, $\psi$ of order $12$; $J(\chi,\psi)=-4\zeta_{12} ++    \zeta_{12}^{3}$+- params:+    p: '13'+    m: '4'+    n: '12'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=-3 + 4\zeta_{6}$+- params:+    p: '13'+    m: '5'+    n: '5'+  number: 3 + i * 2+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=3 + 2i$+- params:+    p: '13'+    m: '5'+    n: '6'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $4$, $\psi$ of order $12$; $J(\chi,\psi)=4\zeta_{12} -+    3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '5'+    n: '7'+  number: -2 + i * 3+  comment: $\chi$ of order $4$, $\psi$ of order $12$; $J(\chi,\psi)=-2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '5'+    n: '9'+  number: 2 + i * -3+  comment: $\chi$ of order $4$, $\psi$ of order $3$; $J(\chi,\psi)=2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '5'+    n: '10'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $4$, $\psi$ of order $6$; $J(\chi,\psi)=-4\zeta_{12} ++    3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '5'+    n: '11'+  number: -2 + i * 3+  comment: $\chi$ of order $4$, $\psi$ of order $12$; $J(\chi,\psi)=-2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '5'+    n: '12'+  number: -3 + i * -2+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=-3 - 2i$+- params:+    p: '13'+    m: '6'+    n: '6'+  number: 3.232050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+    + i * 1.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=2\zeta_{12} ++    3\zeta_{12}^{2} - 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '6'+    n: '7'+  number: 2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=4 - 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '6'+    n: '8'+  number: -2 + i * -3+  comment: $\chi$ of order $12$, $\psi$ of order $4$; $J(\chi,\psi)=-2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '6'+    n: '9'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $3$; $J(\chi,\psi)=-4 + 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '6'+    n: '10'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $12$, $\psi$ of order $6$; $J(\chi,\psi)=-4\zeta_{12} ++    3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '6'+    n: '12'+  number: 3 + i * -2+  comment: $\chi$ of order $12$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '7'+    n: '7'+  number: -0.2320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485757+    + i * 3.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=-2\zeta_{12}+    + 3\zeta_{12}^{2} + 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '7'+    n: '8'+  number: -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $12$, $\psi$ of order $4$; $J(\chi,\psi)=-4\zeta_{12} ++    3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '7'+    n: '9'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $3$; $J(\chi,\psi)=-4 + 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '7'+    n: '10'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $12$, $\psi$ of order $6$; $J(\chi,\psi)=4\zeta_{12} -+    3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '7'+    n: '11'+  number: -3 + i * -2+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=-3 - 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '7'+    n: '12'+  number: 3 + i * 2+  comment: $\chi$ of order $12$, $\psi$ of order $2$; $J(\chi,\psi)=3 + 2\zeta_{12}^{3}$+- params:+    p: '13'+    m: '8'+    n: '8'+  number: 3 + i * -2+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=3 - 2i$+- params:+    p: '13'+    m: '8'+    n: '9'+  number: 2 + i * 3+  comment: $\chi$ of order $4$, $\psi$ of order $3$; $J(\chi,\psi)=2 + 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '8'+    n: '10'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $4$, $\psi$ of order $6$; $J(\chi,\psi)=4\zeta_{12} - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '8'+    n: '11'+  number: 3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+    + i * 1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $4$, $\psi$ of order $12$; $J(\chi,\psi)=4\zeta_{12} -+    \zeta_{12}^{3}$+- params:+    p: '13'+    m: '8'+    n: '12'+  number: -3 + i * 2+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=-3 + 2i$+- params:+    p: '13'+    m: '9'+    n: '9'+  number: -2.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=-1 + 3\zeta_{3}$+- params:+    p: '13'+    m: '9'+    n: '10'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=1 - 4\zeta_{6}$+- params:+    p: '13'+    m: '9'+    n: '11'+  number: 2 + i * -3+  comment: $\chi$ of order $3$, $\psi$ of order $12$; $J(\chi,\psi)=2 - 3\zeta_{12}^{3}$+- params:+    p: '13'+    m: '9'+    n: '12'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 4\zeta_{6}$+- params:+    p: '13'+    m: '10'+    n: '10'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 0.8660254037844386467637231707529361834714026269051903140279034897259665084544000185405730933786242878+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=3 + \zeta_{6}$+- params:+    p: '13'+    m: '10'+    n: '11'+  number: -3.232050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+    + i * 1.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $6$, $\psi$ of order $12$; $J(\chi,\psi)=-3 - 2\zeta_{12}+    + 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '10'+    n: '12'+  number: -1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 4\zeta_{6}$+- params:+    p: '13'+    m: '11'+    n: '11'+  number: 3.232050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+    + i * -1.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $12$, $\psi$ of order $12$; $J(\chi,\psi)=3 + 2\zeta_{12}+    - 3\zeta_{12}^{2}$+- params:+    p: '13'+    m: '11'+    n: '12'+  number: 3 + i * 2+  comment: $\chi$ of order $12$, $\psi$ of order $2$; $J(\chi,\psi)=3 + 2\zeta_{12}^{3}$+- params:+    p: '17'+    m: '2'+    n: '2'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=-3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '2'+    n: '3'+  number: 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16} -+    2\zeta_{16}^{2} + \zeta_{16}^{4} - 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '4'+  number: 1 + i * 4+  comment: $\chi$ of order $8$, $\psi$ of order $4$; $J(\chi,\psi)=1 + 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '2'+    n: '5'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '2'+    n: '6'+  number: 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * 4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} ++    2\zeta_{16}^{2} + 3\zeta_{16}^{3} - \zeta_{16}^{4} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '7'+  number: 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * -3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} + 2\zeta_{16}^{2}+    - 3\zeta_{16}^{3} - \zeta_{16}^{4} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '8'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '2'+    n: '10'+  number: 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * 4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} ++    2\zeta_{16}^{2} + 3\zeta_{16}^{3} - \zeta_{16}^{4} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '11'+  number: 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * -3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} + 2\zeta_{16}^{2}+    - 3\zeta_{16}^{3} - \zeta_{16}^{4} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '12'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '2'+    n: '13'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $4$; $J(\chi,\psi)=-3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '2'+    n: '14'+  number: -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16} -+    2\zeta_{16}^{2} + \zeta_{16}^{4} - 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '2'+    n: '15'+  number: 1 + i * 4+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=1 + 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '2'+    n: '16'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '3'+    n: '3'+  number: -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}+    + 2\zeta_{16}^{2} - \zeta_{16}^{4} + 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '4'+  number: 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 - \zeta_{16}+    - 3\zeta_{16}^{3} + \zeta_{16}^{5} - 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '5'+  number: -1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * -3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-3\zeta_{16}+    - \zeta_{16}^{3} - \zeta_{16}^{4} + \zeta_{16}^{5} - 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '7'+  number: 4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 + 3\zeta_{16}+    + 2\zeta_{16}^{2} - \zeta_{16}^{3} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '8'+  number: 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=3\zeta_{16} ++    \zeta_{16}^{3} + \zeta_{16}^{4} - \zeta_{16}^{5} + 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '9'+  number: 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=-\zeta_{16} -+    \zeta_{16}^{3} + \zeta_{16}^{4} - 3\zeta_{16}^{5} - 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '10'+  number: -0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * 4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 + \zeta_{16}+    + 3\zeta_{16}^{3} - \zeta_{16}^{5} + 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '11'+  number: -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=1 - 2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} - 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '3'+    n: '12'+  number: -0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * 4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} ++    \zeta_{16}^{3} - \zeta_{16}^{4} + 3\zeta_{16}^{5} + 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '13'+  number: -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * -0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 - 3\zeta_{16}+    - 2\zeta_{16}^{2} + \zeta_{16}^{3} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '3'+    n: '14'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '3'+    n: '15'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '3'+    n: '16'+  number: 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} + 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '4'+    n: '4'+  number: -1 + i * -4+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=-1 - 4i$+- params:+    p: '17'+    m: '4'+    n: '5'+  number: -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 - \zeta_{16}+    - \zeta_{16}^{3} - \zeta_{16}^{5} + 2\zeta_{16}^{6} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '6'+  number: -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 - \zeta_{16}+    - \zeta_{16}^{3} - \zeta_{16}^{5} + 2\zeta_{16}^{6} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '7'+  number: 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 + \zeta_{16}+    + 3\zeta_{16}^{3} - \zeta_{16}^{5} - 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '8'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $4$, $\psi$ of order $8$; $J(\chi,\psi)=-3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '4'+    n: '9'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $4$, $\psi$ of order $8$; $J(\chi,\psi)=-3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '4'+    n: '10'+  number: 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 - \zeta_{16}+    - 3\zeta_{16}^{3} + \zeta_{16}^{5} - 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '11'+  number: 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 + \zeta_{16}+    + \zeta_{16}^{3} + \zeta_{16}^{5} + 2\zeta_{16}^{6} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '12'+  number: 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 + \zeta_{16}+    + \zeta_{16}^{3} + \zeta_{16}^{5} + 2\zeta_{16}^{6} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '14'+  number: 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 + \zeta_{16}+    + 3\zeta_{16}^{3} - \zeta_{16}^{5} - 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '4'+    n: '15'+  number: 1 + i * 4+  comment: $\chi$ of order $4$, $\psi$ of order $8$; $J(\chi,\psi)=1 + 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '4'+    n: '16'+  number: -1 + i * -4+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 4i$+- params:+    p: '17'+    m: '5'+    n: '5'+  number: 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} - \zeta_{16}^{4} - 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '5'+    n: '6'+  number: 4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * -0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 + \zeta_{16}+    + \zeta_{16}^{3} + \zeta_{16}^{5} - 2\zeta_{16}^{6} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '8'+  number: 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=3\zeta_{16} ++    \zeta_{16}^{3} + \zeta_{16}^{4} - \zeta_{16}^{5} + 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '9'+  number: 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=\zeta_{16} + \zeta_{16}^{3}+    + \zeta_{16}^{4} + 3\zeta_{16}^{5} - 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '10'+  number: 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=1 + 2\zeta_{16}+    + 2\zeta_{16}^{2} - 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '11'+  number: -3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 + \zeta_{16}+    - 2\zeta_{16}^{2} - \zeta_{16}^{3} + 3\zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '12'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '5'+    n: '13'+  number: 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * -1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 - \zeta_{16}+    + 2\zeta_{16}^{2} + \zeta_{16}^{3} - 3\zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '14'+  number: -2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * -3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} -+    \zeta_{16}^{3} - \zeta_{16}^{4} - 3\zeta_{16}^{5} + 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '5'+    n: '15'+  number: -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} + \zeta_{16}^{4} + 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '5'+    n: '16'+  number: -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{16}+    - 2\zeta_{16}^{2} + 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '6'+  number: -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}+    - 2\zeta_{16}^{2} + \zeta_{16}^{4} - 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '7'+  number: -1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} ++    2\zeta_{16}^{2} - \zeta_{16}^{3} + \zeta_{16}^{4} + \zeta_{16}^{5} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '8'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '6'+    n: '9'+  number: 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16} ++    2\zeta_{16}^{2} - \zeta_{16}^{4} + 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '10'+  number: -0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} -+    2\zeta_{16}^{2} - 3\zeta_{16}^{3} + \zeta_{16}^{4} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '11'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '6'+    n: '12'+  number: -0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 - \zeta_{16}+    - 2\zeta_{16}^{2} + \zeta_{16}^{3} - 3\zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '13'+  number: 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * 4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 + \zeta_{16}+    + 2\zeta_{16}^{2} - \zeta_{16}^{3} + 3\zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '14'+  number: -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=1 - 2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} + 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '6'+    n: '15'+  number: 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * -3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=-\zeta_{16} -+    2\zeta_{16}^{2} + \zeta_{16}^{3} - \zeta_{16}^{4} - \zeta_{16}^{5} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '6'+    n: '16'+  number: 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} - 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '7'+    n: '7'+  number: 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} + \zeta_{16}^{4} - 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '7'+    n: '8'+  number: -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} - \zeta_{16}^{4} + 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '7'+    n: '9'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '7'+    n: '10'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '7'+    n: '11'+  number: -2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} -+    2\zeta_{16}^{2} + 3\zeta_{16}^{3} + \zeta_{16}^{4} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '7'+    n: '12'+  number: 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=1 - 2\zeta_{16}+    + 2\zeta_{16}^{2} - 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '7'+    n: '13'+  number: -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+    + i * -0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 - 3\zeta_{16}+    - 2\zeta_{16}^{2} + \zeta_{16}^{3} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '7'+    n: '14'+  number: -3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * -1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 - \zeta_{16}+    - 3\zeta_{16}^{3} + \zeta_{16}^{5} + 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '7'+    n: '15'+  number: 1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+    + i * -3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=-\zeta_{16} -+    2\zeta_{16}^{2} + \zeta_{16}^{3} - \zeta_{16}^{4} - \zeta_{16}^{5} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '7'+    n: '16'+  number: -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}+    - 2\zeta_{16}^{2} + 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '8'+    n: '8'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=-3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '8'+    n: '9'+  number: 1 + i * -4+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=1 - 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '8'+    n: '10'+  number: 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} - \zeta_{16}^{4} - 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '8'+    n: '11'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '8'+    n: '12'+  number: -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-3\zeta_{16} -+    \zeta_{16}^{3} + \zeta_{16}^{4} + \zeta_{16}^{5} + 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '8'+    n: '13'+  number: 1 + i * -4+  comment: $\chi$ of order $8$, $\psi$ of order $4$; $J(\chi,\psi)=1 - 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '8'+    n: '14'+  number: -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-3\zeta_{16} -+    \zeta_{16}^{3} + \zeta_{16}^{4} + \zeta_{16}^{5} + 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '8'+    n: '16'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $2$; $J(\chi,\psi)=3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '9'+    n: '9'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=-3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '9'+    n: '10'+  number: -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    + 3\zeta_{16}^{4} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '9'+    n: '11'+  number: -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16} ++    2\zeta_{16}^{2} - \zeta_{16}^{4} + 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '9'+    n: '12'+  number: 0.3318213620807010800022423134769192384475277486209171838140855466847545313800817058947352353115194748+    + i * -4.109731692418242073314421481796851225859338378831518017637070663112872508466516473709747273729019957+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} -+    \zeta_{16}^{3} + \zeta_{16}^{4} - 3\zeta_{16}^{5} - 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '9'+    n: '13'+  number: 1 + i * -4+  comment: $\chi$ of order $8$, $\psi$ of order $4$; $J(\chi,\psi)=1 - 4\zeta_{8}^{2}$+- params:+    p: '17'+    m: '9'+    n: '14'+  number: 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+    + i * 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+  comment: $\chi$ of order $8$, $\psi$ of order $16$; $J(\chi,\psi)=\zeta_{16} + \zeta_{16}^{3}+    + \zeta_{16}^{4} + 3\zeta_{16}^{5} - 2\zeta_{16}^{6} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '9'+    n: '15'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '9'+    n: '16'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $2$; $J(\chi,\psi)=3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '10'+    n: '10'+  number: -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} + \zeta_{16}^{4} + 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '10'+    n: '11'+  number: 4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-\zeta_{16} ++    2\zeta_{16}^{2} + \zeta_{16}^{3} + \zeta_{16}^{4} - \zeta_{16}^{5} - 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '10'+    n: '13'+  number: 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * -2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 + 3\zeta_{16}+    - 2\zeta_{16}^{2} - \zeta_{16}^{3} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '10'+    n: '14'+  number: -3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * 2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 - 3\zeta_{16}+    + 2\zeta_{16}^{2} + \zeta_{16}^{3} + \zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '10'+    n: '15'+  number: -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * -0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=\zeta_{16} - 2\zeta_{16}^{2}+    - \zeta_{16}^{3} - \zeta_{16}^{4} + \zeta_{16}^{5} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '10'+    n: '16'+  number: -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{16}+    - 2\zeta_{16}^{2} + 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '11'+    n: '11'+  number: 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * -1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16} -+    2\zeta_{16}^{2} + \zeta_{16}^{4} - 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '11'+    n: '12'+  number: -3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * -2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-1 - \zeta_{16}+    - \zeta_{16}^{3} - \zeta_{16}^{5} - 2\zeta_{16}^{6} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '11'+    n: '13'+  number: 3.944947291833454135715528660331293545615050125319456238911882280500916614302465807798442675696775761+    + i * -1.198912367379658006911597622644676228597850501321590981921116995825429604460277063053319906057614714+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 - \zeta_{16}+    + 2\zeta_{16}^{2} + \zeta_{16}^{3} - 3\zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '11'+    n: '15'+  number: -4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * -0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=\zeta_{16} - 2\zeta_{16}^{2}+    - \zeta_{16}^{3} - \zeta_{16}^{4} + \zeta_{16}^{5} + 3\zeta_{16}^{7}$+- params:+    p: '17'+    m: '11'+    n: '16'+  number: 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} + 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '12'+    n: '12'+  number: -1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=-2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} - \zeta_{16}^{4} + 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '12'+    n: '13'+  number: 0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+    + i * 4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+  comment: $\chi$ of order $16$, $\psi$ of order $4$; $J(\chi,\psi)=1 + \zeta_{16}+    + 2\zeta_{16}^{2} - \zeta_{16}^{3} + 3\zeta_{16}^{5} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '12'+    n: '14'+  number: 4.027339492125848104514975071064072385737194252075487128274476471806894561384491140754094974712897859+    + i * -0.8834798329127359618878487880881026115242936254344399074414771954805483426217482699023323929585073841+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=3\zeta_{16} ++    \zeta_{16}^{3} - \zeta_{16}^{4} - \zeta_{16}^{5} - 2\zeta_{16}^{6} + \zeta_{16}^{7}$+- params:+    p: '17'+    m: '12'+    n: '15'+  number: 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+    + i * 3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16}^{2}+    + 2\zeta_{16}^{3} + \zeta_{16}^{4} - 2\zeta_{16}^{5} + 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '12'+    n: '16'+  number: -3.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * 1.530733729460359086913839936121595467045378249942508165735202542510184135840358768948055141369134189+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}+    - 2\zeta_{16}^{2} + 2\zeta_{16}^{6} + 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '13'+    n: '13'+  number: -1 + i * 4+  comment: $\chi$ of order $4$, $\psi$ of order $4$; $J(\chi,\psi)=-1 + 4i$+- params:+    p: '17'+    m: '13'+    n: '14'+  number: 3.281304567672051975711044033377455068719994628077621871283711187131407551542302396008972205073736812+    + i * -2.496605762665489017601135134942476918691816002132978962539273929296710425544132371806039833343763671+  comment: $\chi$ of order $4$, $\psi$ of order $16$; $J(\chi,\psi)=1 + 3\zeta_{16}+    - 2\zeta_{16}^{2} - \zeta_{16}^{3} - \zeta_{16}^{5} - \zeta_{16}^{7}$+- params:+    p: '17'+    m: '13'+    n: '15'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $4$, $\psi$ of order $8$; $J(\chi,\psi)=-3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '13'+    n: '16'+  number: -1 + i * 4+  comment: $\chi$ of order $4$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 4i$+- params:+    p: '17'+    m: '14'+    n: '14'+  number: 3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+    + i * 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $16$, $\psi$ of order $16$; $J(\chi,\psi)=2\zeta_{16} ++    2\zeta_{16}^{2} - \zeta_{16}^{4} + 2\zeta_{16}^{6} - 2\zeta_{16}^{7}$+- params:+    p: '17'+    m: '14'+    n: '15'+  number: 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+  comment: $\chi$ of order $16$, $\psi$ of order $8$; $J(\chi,\psi)=2\zeta_{16}^{2}+    - 3\zeta_{16}^{4} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '14'+    n: '16'+  number: 1.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+    + i * -3.695518130045147024512732757587153147289666503454569944460390925122140030004409434859359739401378384+  comment: $\chi$ of order $16$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{16}^{2}+    - 2\zeta_{16}^{3} - 2\zeta_{16}^{5} - 2\zeta_{16}^{6}$+- params:+    p: '17'+    m: '15'+    n: '15'+  number: -3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $8$; $J(\chi,\psi)=-3 - 2\zeta_{8}+    - 2\zeta_{8}^{3}$+- params:+    p: '17'+    m: '15'+    n: '16'+  number: 3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145+  comment: $\chi$ of order $8$, $\psi$ of order $2$; $J(\chi,\psi)=3 + 2\zeta_{8}+    + 2\zeta_{8}^{3}$+- params:+    p: '19'+    m: '2'+    n: '2'+  number: -1.460637153786699430609259157632675857937335165816672794799010797170418677412933665214295729310146789+    + i * 4.106889224824293913377536092919008166793170391826443046436591213574978870058558713872780601232091503+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - \zeta_{18}+    + 4\zeta_{18}^{3} - \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '3'+  number: 4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * -0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=4 - \zeta_{18}+    + 2\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '4'+  number: 2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * -3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=4 - 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '5'+  number: 1.460637153786699430609259157632675857937335165816672794799010797170418677412933665214295729310146789+    + i * -4.106889224824293913377536092919008166793170391826443046436591213574978870058558713872780601232091503+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{18}+    - 4\zeta_{18}^{3} + \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '6'+  number: 3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * 2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=3\zeta_{18} ++    2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '2'+    n: '7'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * 0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $18$, $\psi$ of order $3$; $J(\chi,\psi)=2 + 4\zeta_{18}+    - \zeta_{18}^{2} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '8'+  number: -3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * -2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $18$, $\psi$ of order $6$; $J(\chi,\psi)=-3\zeta_{18} -+    2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '2'+    n: '9'+  number: 3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * -2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-1 + 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '11'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * 4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $18$, $\psi$ of order $3$; $J(\chi,\psi)=2 - \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{4} + 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '12'+  number: -2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * 3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $18$, $\psi$ of order $6$; $J(\chi,\psi)=-4 + 2\zeta_{18}+    - \zeta_{18}^{2} + 2\zeta_{18}^{3} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '13'+  number: 0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * -4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + \zeta_{18}+    + 2\zeta_{18}^{2} - 2\zeta_{18}^{4} - 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '14'+  number: 0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * -4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=4 - \zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - \zeta_{18}^{4}$+- params:+    p: '19'+    m: '2'+    n: '15'+  number: -4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * -0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 4\zeta_{18}+    + \zeta_{18}^{2} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '16'+  number: -4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * 0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-4 + \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '2'+    n: '17'+  number: -0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * 4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-4 + \zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4}$+- params:+    p: '19'+    m: '2'+    n: '18'+  number: -3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * 2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '3'+  number: -2.124485151690003756755461324896935225807121694057116350325894475794400344431609435163171216884245906+    + i * 3.806121758463423320098992297694004314648693875134921884576662456588580797519677673726482555853022699+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - \zeta_{18}+    - 2\zeta_{18}^{2} + 4\zeta_{18}^{3} + 2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '3'+    n: '4'+  number: 1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * -4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2\zeta_{18} -+    5\zeta_{18}^{4}$+- params:+    p: '19'+    m: '3'+    n: '5'+  number: -4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * 0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-4 - 2\zeta_{18}+    + 2\zeta_{18}^{3} + \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '6'+  number: -0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * 4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-1 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '7'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * -4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $18$, $\psi$ of order $3$; $J(\chi,\psi)=2 - 2\zeta_{18}+    - \zeta_{18}^{2} - 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '8'+  number: -1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * 4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $18$, $\psi$ of order $6$; $J(\chi,\psi)=-2\zeta_{18} ++    5\zeta_{18}^{4}$+- params:+    p: '19'+    m: '3'+    n: '9'+  number: 3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * 1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=4 + \zeta_{18}^{2}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '10'+  number: 0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * 4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    + \zeta_{18}^{2} + 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '11'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * -3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $18$, $\psi$ of order $3$; $J(\chi,\psi)=2 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '12'+  number: -3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * -1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $18$, $\psi$ of order $6$; $J(\chi,\psi)=-4 - \zeta_{18}^{2}+    + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '14'+  number: 4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * -0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=4 + 2\zeta_{18}+    - 2\zeta_{18}^{3} - \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '15'+  number: -2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * 3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '16'+  number: -4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * 0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-4 + \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '3'+    n: '17'+  number: 2.124485151690003756755461324896935225807121694057116350325894475794400344431609435163171216884245906+    + i * -3.806121758463423320098992297694004314648693875134921884576662456588580797519677673726482555853022699+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{18}+    + 2\zeta_{18}^{2} - 4\zeta_{18}^{3} - 2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '3'+    n: '18'+  number: 0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * -4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '4'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * 3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{9} ++    4\zeta_{9}^{2} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '6'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * 3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{9} ++    4\zeta_{9}^{2} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '7'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * 0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} + 2\zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '8'+  number: 1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * -4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=2\zeta_{18} - 5\zeta_{18}^{4}$+- params:+    p: '19'+    m: '4'+    n: '9'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * 0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{9} -+    2\zeta_{9}^{2} + 2\zeta_{9}^{4} - 4\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '10'+  number: 1.460637153786699430609259157632675857937335165816672794799010797170418677412933665214295729310146789+    + i * 4.106889224824293913377536092919008166793170391826443046436591213574978870058558713872780601232091503+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + \zeta_{18}^{2}+    + 4\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '11'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * -1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} - 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '12'+  number: 2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * -3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=4 - 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '13'+  number: -4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * -0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}^{2}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '14'+  number: -3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * 3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-1 - 4\zeta_{18}^{2}+    + 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '15'+  number: -4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * -0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}^{2}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '4'+    n: '16'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * -1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} - 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '17'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * 0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} + 2\zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '4'+    n: '18'+  number: -3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * 3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 4\zeta_{18}^{2}+    + 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '5'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * -3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 4\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{4} - 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '6'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * 1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} - 4\zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '7'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * 1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} - 4\zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '8'+  number: 2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * 3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=2 + \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '9'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * -0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} + 4\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '10'+  number: 2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * 3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=2 + \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '11'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * -0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} + 4\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '12'+  number: 1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * 4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=2\zeta_{18}^{2}+    + 3\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '13'+  number: 1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * 4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=2\zeta_{18}^{2}+    + 3\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '14'+  number: -4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * 0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-4 - 2\zeta_{18}+    + 2\zeta_{18}^{3} + \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '15'+  number: -3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * -3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=1 - 4\zeta_{18}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '5'+    n: '16'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * -3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 4\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{4} - 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '17'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * -0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '5'+    n: '18'+  number: -3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * -3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=1 - 4\zeta_{18}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '6'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * -4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 2\zeta_{9}+    - 2\zeta_{9}^{2} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '6'+    n: '7'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * 1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} - 4\zeta_{9}^{5}$+- params:+    p: '19'+    m: '6'+    n: '8'+  number: 3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * 2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=3\zeta_{18} + 2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '6'+    n: '9'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * -4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 2\zeta_{9}+    - 2\zeta_{9}^{2} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '6'+    n: '10'+  number: -4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * -0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '11'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * -3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=-2 - 4\zeta_{9}+    + 2\zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '6'+    n: '12'+  number: 2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * -3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=4 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '13'+  number: -4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * -0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '14'+  number: 2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * -3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=4 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '15'+  number: -3.585122305476703187364720482529611083744456859873789145124905272964819021844543100377466946194392696+    + i * 2.479293862125546527688149658422221720214967255900918837321588206548038433874563834887613963458377252+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - 2\zeta_{18}+    - 2\zeta_{18}^{2} + 4\zeta_{18}^{3} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '6'+    n: '17'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * -3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=-2 - 4\zeta_{9}+    + 2\zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '6'+    n: '18'+  number: -0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * 4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '7'+    n: '7'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=2 - 3\zeta_{3}$+- params:+    p: '19'+    m: '7'+    n: '8'+  number: -4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=-3 - 2\zeta_{6}$+- params:+    p: '19'+    m: '7'+    n: '9'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * 3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $3$, $\psi$ of order $9$; $J(\chi,\psi)=-2\zeta_{9} + 4\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '7'+    n: '10'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * -4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 - 2\zeta_{18}+    - \zeta_{18}^{2} - 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '7'+    n: '12'+  number: 0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -4.330127018922193233818615853764680917357013134525951570139517448629832542272000092702865466893121439+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=3 - 5\zeta_{6}$+- params:+    p: '19'+    m: '7'+    n: '13'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * 3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 4\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '7'+    n: '14'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * 3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 4\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '7'+    n: '15'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * 0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 + 4\zeta_{18}+    - \zeta_{18}^{2} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '7'+    n: '16'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * 3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $3$, $\psi$ of order $9$; $J(\chi,\psi)=-2\zeta_{9} + 4\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '7'+    n: '17'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * 0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $3$, $\psi$ of order $9$; $J(\chi,\psi)=\zeta_{9} - 2\zeta_{9}^{2}+    + 2\zeta_{9}^{3} + 2\zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '7'+    n: '18'+  number: -4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=-3 - 2\zeta_{6}$+- params:+    p: '19'+    m: '8'+    n: '8'+  number: -0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -4.330127018922193233818615853764680917357013134525951570139517448629832542272000092702865466893121439+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=2 - 5\zeta_{6}$+- params:+    p: '19'+    m: '8'+    n: '9'+  number: -4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * 1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $6$, $\psi$ of order $9$; $J(\chi,\psi)=-5\zeta_{18} ++    3\zeta_{18}^{4}$+- params:+    p: '19'+    m: '8'+    n: '10'+  number: -2.233955556881021964797607349444583326064167542919604754145954715357844611143125276471770723319451507+    + i * -3.742918990558091552026488210142174122902698608072704932240978224861904907958069075048395143828945117+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - \zeta_{18}+    + 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '8'+    n: '11'+  number: 0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 4.330127018922193233818615853764680917357013134525951570139517448629832542272000092702865466893121439+  comment: $\chi$ of order $6$, $\psi$ of order $3$; $J(\chi,\psi)=-2 + 5\zeta_{6}$+- params:+    p: '19'+    m: '8'+    n: '13'+  number: -3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * 1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=-2 - \zeta_{18}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '8'+    n: '14'+  number: 4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * -1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=5\zeta_{18} -+    3\zeta_{18}^{4}$+- params:+    p: '19'+    m: '8'+    n: '15'+  number: -2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * -3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - \zeta_{18}^{4}$+- params:+    p: '19'+    m: '8'+    n: '16'+  number: 2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * 3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $6$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4}$+- params:+    p: '19'+    m: '8'+    n: '17'+  number: 3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * -1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $6$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{18}+    + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '8'+    n: '18'+  number: 4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=3 + 2\zeta_{6}$+- params:+    p: '19'+    m: '9'+    n: '9'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * 0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{9} -+    2\zeta_{9}^{2} + 2\zeta_{9}^{4} - 4\zeta_{9}^{5}$+- params:+    p: '19'+    m: '9'+    n: '10'+  number: -0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * -4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '9'+    n: '11'+  number: -4.340022395358516198717477712282138797809751434345602060979584122718861099404712583113787508986042924+    + i * -0.4052229112310005011166037022340897725090786345763775808007327294113906532636861982422775943626031290+  comment: $\chi$ of order $9$, $\psi$ of order $3$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} + 4\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '9'+    n: '12'+  number: 3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * 1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $9$, $\psi$ of order $6$; $J(\chi,\psi)=4 + \zeta_{18}^{2}+    - 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '9'+    n: '13'+  number: 2.124485151690003756755461324896935225807121694057116350325894475794400344431609435163171216884245906+    + i * 3.806121758463423320098992297694004314648693875134921884576662456588580797519677673726482555853022699+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    + \zeta_{18}^{2} + 4\zeta_{18}^{3} - 2\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '9'+    n: '14'+  number: -4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * 1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-5\zeta_{18} ++    3\zeta_{18}^{4}$+- params:+    p: '19'+    m: '9'+    n: '15'+  number: -0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * -4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $9$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    + \zeta_{18}^{2} - 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '9'+    n: '16'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * 3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=-2\zeta_{9} + 4\zeta_{9}^{2}+    + 2\zeta_{9}^{3} - \zeta_{9}^{4} + 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '9'+    n: '18'+  number: 3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * -2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '10'+  number: -1.460637153786699430609259157632675857937335165816672794799010797170418677412933665214295729310146789+    + i * -4.106889224824293913377536092919008166793170391826443046436591213574978870058558713872780601232091503+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 - \zeta_{18}^{2}+    - 4\zeta_{18}^{3} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '11'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * -0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $18$, $\psi$ of order $3$; $J(\chi,\psi)=2 - \zeta_{18}+    + 4\zeta_{18}^{2} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '12'+  number: -3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * 2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $18$, $\psi$ of order $6$; $J(\chi,\psi)=-3\zeta_{18}^{2}+    + 5\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '13'+  number: 4.286988976119769081757542530863361061936959488632603407562769419038352855273918929792779116152747215+    + i * 0.7884957315214673739262591363736050818907688529131776758709009677944221081289603572243599136605854200+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 + 2\zeta_{18}+    - \zeta_{18}^{2} + 2\zeta_{18}^{3} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '14'+  number: -4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * 0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + \zeta_{18}+    - 4\zeta_{18}^{2} + \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '15'+  number: 0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * 4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 - 2\zeta_{18}+    - \zeta_{18}^{2} + 2\zeta_{18}^{3} + 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '16'+  number: 3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * -2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=3\zeta_{18}^{2}+    - 5\zeta_{18}^{5}$+- params:+    p: '19'+    m: '10'+    n: '17'+  number: 3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * 2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=1 + 2\zeta_{18}+    + 2\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '10'+    n: '18'+  number: -3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * -2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{3} - 2\zeta_{18}^{4}$+- params:+    p: '19'+    m: '11'+    n: '11'+  number: 3.500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 2.598076211353315940291169512258808550414207880715570942083710469177899525363200055621719280135872864+  comment: $\chi$ of order $3$, $\psi$ of order $3$; $J(\chi,\psi)=5 + 3\zeta_{3}$+- params:+    p: '19'+    m: '11'+    n: '12'+  number: -4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $6$; $J(\chi,\psi)=-5 + 2\zeta_{6}$+- params:+    p: '19'+    m: '11'+    n: '13'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * 4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 - \zeta_{18}+    - 2\zeta_{18}^{2} + 2\zeta_{18}^{4} + 4\zeta_{18}^{5}$+- params:+    p: '19'+    m: '11'+    n: '14'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * -0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 - \zeta_{18}+    + 4\zeta_{18}^{2} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '11'+    n: '15'+  number: 2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * -3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $3$, $\psi$ of order $18$; $J(\chi,\psi)=2 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '11'+    n: '16'+  number: 4.117211191714659257769505783640444431616121774034579636832995842249129799558292547433925499555489683+    + i * -1.431283341208006700248902546280868514798328737118859466195878222465534944369918996934848141378179772+  comment: $\chi$ of order $3$, $\psi$ of order $9$; $J(\chi,\psi)=-2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} - 2\zeta_{9}^{5}$+- params:+    p: '19'+    m: '11'+    n: '17'+  number: -2.777188796356143059052028071358305633806370339688977575853411719530268700153579964320137990569446758+    + i * -3.359646170267624679216832776002658813521008389735904837170809986478873453092794916066312824530962826+  comment: $\chi$ of order $3$, $\psi$ of order $9$; $J(\chi,\psi)=-2 - 4\zeta_{9}+    + 2\zeta_{9}^{2} - 2\zeta_{9}^{3} - 2\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '11'+    n: '18'+  number: -4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $3$, $\psi$ of order $2$; $J(\chi,\psi)=-5 + 2\zeta_{6}$+- params:+    p: '19'+    m: '12'+    n: '12'+  number: -0.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * 4.330127018922193233818615853764680917357013134525951570139517448629832542272000092702865466893121439+  comment: $\chi$ of order $6$, $\psi$ of order $6$; $J(\chi,\psi)=-3 + 5\zeta_{6}$+- params:+    p: '19'+    m: '12'+    n: '13'+  number: -1.011144353237165023849635420802888959870537882608582329999366434888113311296705240791908713888898265+    + i * -4.239998478409702830745515893583095906827049523570890837020031766409708472311025997245011685603548401+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=-2\zeta_{18}^{2}+    - 3\zeta_{18}^{5}$+- params:+    p: '19'+    m: '12'+    n: '14'+  number: -2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * 3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=-4 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '12'+    n: '15'+  number: 4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * 1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $6$, $\psi$ of order $18$; $J(\chi,\psi)=5\zeta_{18}^{2}+    - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '12'+    n: '16'+  number: 3.166374217691585849865761085512824001809375757161532673743342744586795277265697847692270895828643350+    + i * -2.995675936001422317865784893225824769630536605982166722975196997765799490992305277241927367127816441+  comment: $\chi$ of order $6$, $\psi$ of order $9$; $J(\chi,\psi)=3\zeta_{18}^{2}+    - 5\zeta_{18}^{5}$+- params:+    p: '19'+    m: '12'+    n: '17'+  number: -4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * -1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $6$, $\psi$ of order $9$; $J(\chi,\psi)=-5\zeta_{18}^{2}+    + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '12'+    n: '18'+  number: 4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+    + i * -1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576+  comment: $\chi$ of order $6$, $\psi$ of order $2$; $J(\chi,\psi)=5 - 2\zeta_{6}$+- params:+    p: '19'+    m: '13'+    n: '13'+  number: -2.124485151690003756755461324896935225807121694057116350325894475794400344431609435163171216884245906+    + i * -3.806121758463423320098992297694004314648693875134921884576662456588580797519677673726482555853022699+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 - 2\zeta_{18}+    - \zeta_{18}^{2} - 4\zeta_{18}^{3} + 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '13'+    n: '14'+  number: -2.520944533000791046555149880307944388001127031552208161708724134396197466417044206264549839472198722+    + i * -3.555958191758365364657316664218576745300882788542569580089934771040278944906870798116631320926497306+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 4\zeta_{18}^{4} + \zeta_{18}^{5}$+- params:+    p: '19'+    m: '13'+    n: '15'+  number: 4.358440708571025721553068674341518551871289236976721104471849191152244955574734711634941940203697413+    + i * 0.06320276790533176807250408755183019174599526706221695233568423172667588956160859867808741202407758143+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 + 2\zeta_{18}^{2}+    + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '13'+    n: '16'+  number: -0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * -4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=1 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 4\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '13'+    n: '17'+  number: 3.939692620785908384054109277324731469936208134264464633090286662774221210995889458949745889837948067+    + i * -1.865160061154286210895426142169960106976684385554828418639247532286662619161267320453377271128705473+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2 + \zeta_{18}+    + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '13'+    n: '18'+  number: 0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * 4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=-1 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + 4\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '14'+    n: '14'+  number: 3.585122305476703187364720482529611083744456859873789145124905272964819021844543100377466946194392696+    + i * 2.479293862125546527688149658422221720214967255900918837321588206548038433874563834887613963458377252+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=-2 + 2\zeta_{18}+    + 2\zeta_{18}^{2} + 4\zeta_{18}^{3} - \zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '14'+    n: '16'+  number: -3.585122305476703187364720482529611083744456859873789145124905272964819021844543100377466946194392696+    + i * -2.479293862125546527688149658422221720214967255900918837321588206548038433874563834887613963458377252+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 2\zeta_{18}+    - 2\zeta_{18}^{2} - 4\zeta_{18}^{3} + \zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '14'+    n: '17'+  number: -0.3545703153092051966893887947951203861917512743906754879653813898094021891513463585722789436435553716+    + i * 4.344453923279832738583575800592181827191651641455747255960835738834701053035831155340991234587082726+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-4 + \zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4}$+- params:+    p: '19'+    m: '14'+    n: '18'+  number: 3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * -3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 4\zeta_{18}^{2}+    - 2\zeta_{18}^{3} - 2\zeta_{18}^{4} - 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '15'+    n: '15'+  number: 3.585122305476703187364720482529611083744456859873789145124905272964819021844543100377466946194392696+    + i * -2.479293862125546527688149658422221720214967255900918837321588206548038433874563834887613963458377252+  comment: $\chi$ of order $18$, $\psi$ of order $18$; $J(\chi,\psi)=2 + 2\zeta_{18}+    + 2\zeta_{18}^{2} - 4\zeta_{18}^{3} - \zeta_{18}^{5}$+- params:+    p: '19'+    m: '15'+    n: '16'+  number: 2.826351822333069651148283373230685203999624322815930612763758621867934177860985264578483386842600426+    + i * 3.318393493302826539451276956545403084902401538913265370565690245780556761929598356648420687571506083+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=2 - 2\zeta_{18}+    + 2\zeta_{18}^{2} + 2\zeta_{18}^{3} + \zeta_{18}^{4}$+- params:+    p: '19'+    m: '15'+    n: '17'+  number: -4.177518570928750873715396506315712961679913639770115003742709179474908588562403088484179609717541615+    + i * -1.244322542408280512879731000357271137196512917588724114044834768643908981318720720003084318475731960+  comment: $\chi$ of order $18$, $\psi$ of order $9$; $J(\chi,\psi)=-5\zeta_{18}^{2}+    + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '15'+    n: '18'+  number: 3.064177772475912140809570602221666695743329828321580983416181138568621555427498894112917106722193974+    + i * 3.100131380871552225703844800234910689995138723867023141916000970190792071717110435337906916111350766+  comment: $\chi$ of order $18$, $\psi$ of order $2$; $J(\chi,\psi)=-1 + 4\zeta_{18}+    + 2\zeta_{18}^{3} - 2\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '16'+    n: '16'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * 4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + 2\zeta_{9}+    + 2\zeta_{9}^{2} + 4\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '16'+    n: '17'+  number: -0.8190778623577251521623278319741944098086244027933938992708599883226636329876683768492376695138442024+    + i * 4.281251155374500970511071713040351635445656374393530303625151507108025163474222556662903822563005144+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + 2\zeta_{9}+    + 2\zeta_{9}^{2} + 4\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '16'+    n: '18'+  number: -0.6945927106677213954068665070772591840015027087362775489449655125282632885560589416860664526295982960+    + i * -4.303201246315034598818019981134926098573044790633107789355715998136384361872634595923099097627625982+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2\zeta_{18}+    - 2\zeta_{18}^{2} - 2\zeta_{18}^{3} - 4\zeta_{18}^{4} + 2\zeta_{18}^{5}$+- params:+    p: '19'+    m: '17'+    n: '17'+  number: 4.298133329356934105607177951666250021807497371241185737562135853926466166570624170584687830041645480+    + i * -0.7252929636161356058537550488217748901447735858509607235352167360677462185673517585462725016365078385+  comment: $\chi$ of order $9$, $\psi$ of order $9$; $J(\chi,\psi)=2 + 2\zeta_{9}+    - \zeta_{9}^{2} - 2\zeta_{9}^{4} + \zeta_{9}^{5}$+- params:+    p: '19'+    m: '17'+    n: '18'+  number: 3.758770483143633536216437109298925879744832537057858532361146651096884843983557835798983559351792270+    + i * 2.207180204479954943939525756852219687739767753068989047104296029971377382863344920017567453467231021+  comment: $\chi$ of order $9$, $\psi$ of order $2$; $J(\chi,\psi)=1 + 2\zeta_{18}+    + 2\zeta_{18}^{2} - 2\zeta_{18}^{3} + 2\zeta_{18}^{4}$
History of Jacobi sums of pairs of Dirichlet characters modulo a prime

What changed between 2026-09-05 03:54 and 2026-09-05 03:54
