History of Fourier coefficients of Maass forms of level 1

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when	who	what
2026-09-11 19:11	bmatschke with assisted by an agent	republished on the grid the generator now describes	current reviewed
2026-09-11 11:42	zeta3	define the Maass spectral parameter and Hecke normalization; remove the zeta-zero similarity; leave the audited tag set clean
2026-09-11 11:39	zeta3	define the Maass spectral parameter and Hecke normalization; remove the zeta-zero similarity; add the modular form tag
2026-09-11 11:19	zeta3	state Maass coefficient interval widening
2026-09-11 11:15	zeta3	state Maass coefficient interval widening
2026-09-11 11:15	zeta3 with Codex CLI, table-build	widen Maass coefficient balls for displayed center rounding
2026-09-11 11:10	zeta3 with Codex CLI, table-build	Maass form prime coefficients from LMFDB source intervals
2026-09-11 11:10	zeta3	draft Maass form coefficient table

What changed between 2026-09-11 11:10 and 2026-09-11 11:15

from line 121 (5 lines) @@ -121,5 +121,5 @@

     R: '9.533'     p: '2'-  number: -1.06833355122357080666928622627694936009954418855042731123159 +/- 7.42e-68+  number: -1.06833355122357080666928622627694936009954418855042731123159 +/- 1.00e-59   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.1}[1.0.1.1.1]     has odd symmetry and Fricke sign $+1$.

from line 127 (61 lines) @@ -127,61 +127,61 @@

     R: '9.533'     p: '3'-  number: -0.456197354506118383993146932026287174769667991907802558455934 +/- 7.42e-68-- params:-    R: '9.533'-    p: '5'-  number: -0.290672554985070175688117486718684866515616326895321600724241 +/- 7.42e-68-- params:-    R: '9.533'-    p: '7'-  number: -0.744941612147579895111694931328246048135008462597099829011756 +/- 7.42e-68-- params:-    R: '9.533'-    p: '11'-  number: 0.166163596614439771585386447968304032987695532334476291913951 +/- 7.42e-68-- params:-    R: '9.533'-    p: '13'-  number: -0.586688527862709130835898730215107840213448937034907568807196 +/- 7.42e-68-- params:-    R: '9.533'-    p: '17'-  number: 0.570695802472205582381752261531683984454477413915946074923643 +/- 7.42e-68-- params:-    R: '9.533'-    p: '19'-  number: -0.981938586511859209084291380562289853364673620031835987864457 +/- 7.42e-68-- params:-    R: '9.533'-    p: '23'-  number: 0.662968958592475655673792389148721601842942331351712999941227 +/- 7.42e-68-- params:-    R: '9.533'-    p: '29'-  number: -1.04868856398186295141183502810455002240156175042313273981364 +/- 7.42e-68-- params:-    R: '9.533'-    p: '31'-  number: 0.786268441383978014188203086046187113763304943112590796359269 +/- 7.42e-68-- params:-    R: '9.533'-    p: '37'-  number: -0.448198119911044556540808842127413069868282639714950558425852 +/- 7.42e-68-- params:-    R: '9.533'-    p: '41'-  number: -1.19825263816603552393517797200711968391725727869496490338287 +/- 7.42e-68-- params:-    R: '9.533'-    p: '43'-  number: 1.56203091638302357285528069262766845581640542849755016669681 +/- 7.42e-68-- params:-    R: '9.533'-    p: '47'-  number: -0.603152239500140299510836534225618595333360174431911573891611 +/- 7.42e-68-- params:-    R: '12.17'-    p: '2'-  number: 0.289251871462399267773269780310234658693451892185490584912430 +/- 7.42e-68+  number: -0.456197354506118383993146932026287174769667991907802558455934 +/- 1.00e-60+- params:+    R: '9.533'+    p: '5'+  number: -0.290672554985070175688117486718684866515616326895321600724241 +/- 1.00e-60+- params:+    R: '9.533'+    p: '7'+  number: -0.744941612147579895111694931328246048135008462597099829011756 +/- 1.00e-60+- params:+    R: '9.533'+    p: '11'+  number: 0.166163596614439771585386447968304032987695532334476291913951 +/- 1.00e-60+- params:+    R: '9.533'+    p: '13'+  number: -0.586688527862709130835898730215107840213448937034907568807196 +/- 1.00e-60+- params:+    R: '9.533'+    p: '17'+  number: 0.570695802472205582381752261531683984454477413915946074923643 +/- 1.00e-60+- params:+    R: '9.533'+    p: '19'+  number: -0.981938586511859209084291380562289853364673620031835987864457 +/- 1.00e-60+- params:+    R: '9.533'+    p: '23'+  number: 0.662968958592475655673792389148721601842942331351712999941227 +/- 1.00e-60+- params:+    R: '9.533'+    p: '29'+  number: -1.04868856398186295141183502810455002240156175042313273981364 +/- 1.00e-59+- params:+    R: '9.533'+    p: '31'+  number: 0.786268441383978014188203086046187113763304943112590796359269 +/- 1.00e-60+- params:+    R: '9.533'+    p: '37'+  number: -0.448198119911044556540808842127413069868282639714950558425852 +/- 1.00e-60+- params:+    R: '9.533'+    p: '41'+  number: -1.19825263816603552393517797200711968391725727869496490338287 +/- 1.00e-59+- params:+    R: '9.533'+    p: '43'+  number: 1.56203091638302357285528069262766845581640542849755016669681 +/- 1.00e-59+- params:+    R: '9.533'+    p: '47'+  number: -0.603152239500140299510836534225618595333360174431911573891611 +/- 1.00e-60+- params:+    R: '12.17'+    p: '2'+  number: 0.289251871462399267773269780310234658693451892185490584912430 +/- 1.00e-60   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.2}[1.0.1.2.1]     has odd symmetry and Fricke sign $+1$.

from line 189 (61 lines) @@ -189,61 +189,61 @@

     R: '12.17'     p: '3'-  number: -1.20185876101181356357202808486615429883297966139415813778368 +/- 7.42e-68-- params:-    R: '12.17'-    p: '5'-  number: 0.0395527072874140832754340690889726126636625500926284405228757 +/- 7.42e-68-- params:-    R: '12.17'-    p: '7'-  number: 0.448133104491298844785265657009447836619057771693539411885904 +/- 7.42e-68-- params:-    R: '12.17'-    p: '11'-  number: -0.691450783394931735373487088545189033574002169557381773602656 +/- 7.42e-68-- params:-    R: '12.17'-    p: '13'-  number: -0.802780003332336260758681160546378902337301290802991167409919 +/- 7.42e-68-- params:-    R: '12.17'-    p: '17'-  number: -1.03767537346331747877021673795120727847211798380936877361944 +/- 7.42e-68-- params:-    R: '12.17'-    p: '19'-  number: 0.637178807167946560284741083224594483817780191468836240234850 +/- 7.42e-68-- params:-    R: '12.17'-    p: '23'-  number: 0.508798692369429706459050548164928906329556721279043300414745 +/- 7.42e-68-- params:-    R: '12.17'-    p: '29'-  number: 0.779996881214532090387175327811582179979550963549276684790299 +/- 7.42e-68-- params:-    R: '12.17'-    p: '31'-  number: -1.59801358370870288050212349971523533991733587735512032670003 +/- 7.42e-68-- params:-    R: '12.17'-    p: '37'-  number: -0.429215160956814643573655197048060009815842493648404176242214 +/- 7.42e-68-- params:-    R: '12.17'-    p: '41'-  number: -0.548524187705905343287633852332195229106935462862420712070673 +/- 7.42e-68-- params:-    R: '12.17'-    p: '43'-  number: -0.489355022263905723678071904981036531818433664152700313271513 +/- 7.42e-68-- params:-    R: '12.17'-    p: '47'-  number: 0.816868005896020044944221262925190684709350238762314939034228 +/- 7.42e-68-- params:-    R: '13.77'-    p: '2'-  number: 1.54930447794129622450746926287076707892155702885038788148649 +/- 7.42e-68+  number: -1.20185876101181356357202808486615429883297966139415813778368 +/- 1.00e-59+- params:+    R: '12.17'+    p: '5'+  number: 0.0395527072874140832754340690889726126636625500926284405228757 +/- 1.00e-61+- params:+    R: '12.17'+    p: '7'+  number: 0.448133104491298844785265657009447836619057771693539411885904 +/- 1.00e-60+- params:+    R: '12.17'+    p: '11'+  number: -0.691450783394931735373487088545189033574002169557381773602656 +/- 1.00e-60+- params:+    R: '12.17'+    p: '13'+  number: -0.802780003332336260758681160546378902337301290802991167409919 +/- 1.00e-60+- params:+    R: '12.17'+    p: '17'+  number: -1.03767537346331747877021673795120727847211798380936877361944 +/- 1.00e-59+- params:+    R: '12.17'+    p: '19'+  number: 0.637178807167946560284741083224594483817780191468836240234850 +/- 1.00e-60+- params:+    R: '12.17'+    p: '23'+  number: 0.508798692369429706459050548164928906329556721279043300414745 +/- 1.00e-60+- params:+    R: '12.17'+    p: '29'+  number: 0.779996881214532090387175327811582179979550963549276684790299 +/- 1.00e-60+- params:+    R: '12.17'+    p: '31'+  number: -1.59801358370870288050212349971523533991733587735512032670003 +/- 1.00e-59+- params:+    R: '12.17'+    p: '37'+  number: -0.429215160956814643573655197048060009815842493648404176242214 +/- 1.00e-60+- params:+    R: '12.17'+    p: '41'+  number: -0.548524187705905343287633852332195229106935462862420712070673 +/- 1.00e-60+- params:+    R: '12.17'+    p: '43'+  number: -0.489355022263905723678071904981036531818433664152700313271513 +/- 1.00e-60+- params:+    R: '12.17'+    p: '47'+  number: 0.816868005896020044944221262925190684709350238762314939034228 +/- 1.00e-60+- params:+    R: '13.77'+    p: '2'+  number: 1.54930447794129622450746926287076707892155702885038788148649 +/- 1.00e-59   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.3}[1.0.1.3.1]     has even symmetry and Fricke sign $+1$.

from line 251 (61 lines) @@ -251,61 +251,61 @@

     R: '13.77'     p: '3'-  number: 0.246899772453980898011441050996101949008024809807106402817698 +/- 7.42e-68-- params:-    R: '13.77'-    p: '5'-  number: 0.737060385348301086378778483390181480763698381648229361735816 +/- 7.42e-68-- params:-    R: '13.77'-    p: '7'-  number: -0.261420075765216142299887246426986520625437198055093758344859 +/- 7.42e-68-- params:-    R: '13.77'-    p: '11'-  number: -0.953564652617777476767573709662167965971573715654626906491413 +/- 7.42e-68-- params:-    R: '13.77'-    p: '13'-  number: 0.278827029162325172187570322224228144409225388953957618475497 +/- 7.42e-68-- params:-    R: '13.77'-    p: '17'-  number: 1.30734171453365862411595596765660813299770850418110837425285 +/- 7.42e-68-- params:-    R: '13.77'-    p: '19'-  number: 0.0925585825082122607636913236432938192295256204387983752391964 +/- 7.42e-68-- params:-    R: '13.77'-    p: '23'-  number: 1.13806852140661122544474802155062440477757729388459877156367 +/- 7.42e-68-- params:-    R: '13.77'-    p: '29'-  number: 0.752113845466087521270009548145857214895821037078724175929672 +/- 7.42e-68-- params:-    R: '13.77'-    p: '31'-  number: 0.0248519535131855197887868849912016520790990962282749248721339 +/- 7.42e-68-- params:-    R: '13.77'-    p: '37'-  number: 0.199265655590814182604966191824380295916530411633798020800361 +/- 7.42e-68-- params:-    R: '13.77'-    p: '41'-  number: -0.304032996755827813139735322907195321727236849987783805579593 +/- 7.42e-68-- params:-    R: '13.77'-    p: '43'-  number: 0.783239363516272674070507223803234924489484029232860728069681 +/- 7.42e-68-- params:-    R: '13.77'-    p: '47'-  number: 0.360568410494812125778218879725751456700509835277241637354386 +/- 7.42e-68-- params:-    R: '14.35'-    p: '2'-  number: -0.230915191201460703714219380031419467998184746865180273751158 +/- 7.42e-68+  number: 0.246899772453980898011441050996101949008024809807106402817698 +/- 1.00e-60+- params:+    R: '13.77'+    p: '5'+  number: 0.737060385348301086378778483390181480763698381648229361735816 +/- 1.00e-60+- params:+    R: '13.77'+    p: '7'+  number: -0.261420075765216142299887246426986520625437198055093758344859 +/- 1.00e-60+- params:+    R: '13.77'+    p: '11'+  number: -0.953564652617777476767573709662167965971573715654626906491413 +/- 1.00e-60+- params:+    R: '13.77'+    p: '13'+  number: 0.278827029162325172187570322224228144409225388953957618475497 +/- 1.00e-60+- params:+    R: '13.77'+    p: '17'+  number: 1.30734171453365862411595596765660813299770850418110837425285 +/- 1.00e-59+- params:+    R: '13.77'+    p: '19'+  number: 0.0925585825082122607636913236432938192295256204387983752391964 +/- 1.00e-61+- params:+    R: '13.77'+    p: '23'+  number: 1.13806852140661122544474802155062440477757729388459877156367 +/- 1.00e-59+- params:+    R: '13.77'+    p: '29'+  number: 0.752113845466087521270009548145857214895821037078724175929672 +/- 1.00e-60+- params:+    R: '13.77'+    p: '31'+  number: 0.0248519535131855197887868849912016520790990962282749248721339 +/- 1.00e-61+- params:+    R: '13.77'+    p: '37'+  number: 0.199265655590814182604966191824380295916530411633798020800361 +/- 1.00e-60+- params:+    R: '13.77'+    p: '41'+  number: -0.304032996755827813139735322907195321727236849987783805579593 +/- 1.00e-60+- params:+    R: '13.77'+    p: '43'+  number: 0.783239363516272674070507223803234924489484029232860728069681 +/- 1.00e-60+- params:+    R: '13.77'+    p: '47'+  number: 0.360568410494812125778218879725751456700509835277241637354386 +/- 1.00e-60+- params:+    R: '14.35'+    p: '2'+  number: -0.230915191201460703714219380031419467998184746865180273751158 +/- 1.00e-60   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.4}[1.0.1.4.1]     has odd symmetry and Fricke sign $+1$.

from line 313 (61 lines) @@ -313,61 +313,61 @@

     R: '14.35'     p: '3'-  number: 0.695594986264415169582285355831973449300553444578082058519561 +/- 7.42e-68-- params:-    R: '14.35'-    p: '5'-  number: -1.29828459887189402076614369307268461468644684122963645878746 +/- 7.42e-68-- params:-    R: '14.35'-    p: '7'-  number: -0.483281981773519835241510123784720196989212137702711094845189 +/- 7.42e-68-- params:-    R: '14.35'-    p: '11'-  number: 0.177498072885612436225956568336028494067180663724899061587674 +/- 7.42e-68-- params:-    R: '14.35'-    p: '13'-  number: 0.625443542219883620988066338264907650732458772674612142024968 +/- 7.42e-68-- params:-    R: '14.35'-    p: '17'-  number: -0.151559498933736667055111870064224525152787966742362272180137 +/- 7.42e-68-- params:-    R: '14.35'-    p: '19'-  number: -0.980264796515567681143509716998581587205529399284366646013737 +/- 7.42e-68-- params:-    R: '14.35'-    p: '23'-  number: -0.568015293731010164173103974436305572552132392832247233932676 +/- 7.42e-68-- params:-    R: '14.35'-    p: '29'-  number: 0.381344552453384028477469277827224518951719843625501856826225 +/- 7.42e-68-- params:-    R: '14.35'-    p: '31'-  number: -0.129584231192542045515350456984080528539151895363638858710699 +/- 7.42e-68-- params:-    R: '14.35'-    p: '37'-  number: -1.48602367503192007961749666097179788857436682672811183929467 +/- 7.42e-68-- params:-    R: '14.35'-    p: '41'-  number: 1.29363735890056729559784457202826040819820162954992077503552 +/- 7.42e-68-- params:-    R: '14.35'-    p: '43'-  number: -1.38886997288110025535460592840702471664901059592938559269398 +/- 7.42e-68-- params:-    R: '14.35'-    p: '47'-  number: 0.0531024292757065501235441199939858202655397919240983259583507 +/- 7.42e-68-- params:-    R: '16.13'-    p: '2'-  number: 1.16185559241585099379817152285831454241338534663731538102900 +/- 7.42e-68+  number: 0.695594986264415169582285355831973449300553444578082058519561 +/- 1.00e-60+- params:+    R: '14.35'+    p: '5'+  number: -1.29828459887189402076614369307268461468644684122963645878746 +/- 1.00e-59+- params:+    R: '14.35'+    p: '7'+  number: -0.483281981773519835241510123784720196989212137702711094845189 +/- 1.00e-60+- params:+    R: '14.35'+    p: '11'+  number: 0.177498072885612436225956568336028494067180663724899061587674 +/- 1.00e-60+- params:+    R: '14.35'+    p: '13'+  number: 0.625443542219883620988066338264907650732458772674612142024968 +/- 1.00e-60+- params:+    R: '14.35'+    p: '17'+  number: -0.151559498933736667055111870064224525152787966742362272180137 +/- 1.00e-60+- params:+    R: '14.35'+    p: '19'+  number: -0.980264796515567681143509716998581587205529399284366646013737 +/- 1.00e-60+- params:+    R: '14.35'+    p: '23'+  number: -0.568015293731010164173103974436305572552132392832247233932676 +/- 1.00e-60+- params:+    R: '14.35'+    p: '29'+  number: 0.381344552453384028477469277827224518951719843625501856826225 +/- 1.00e-60+- params:+    R: '14.35'+    p: '31'+  number: -0.129584231192542045515350456984080528539151895363638858710699 +/- 1.00e-60+- params:+    R: '14.35'+    p: '37'+  number: -1.48602367503192007961749666097179788857436682672811183929467 +/- 1.00e-59+- params:+    R: '14.35'+    p: '41'+  number: 1.29363735890056729559784457202826040819820162954992077503552 +/- 1.00e-59+- params:+    R: '14.35'+    p: '43'+  number: -1.38886997288110025535460592840702471664901059592938559269398 +/- 1.00e-59+- params:+    R: '14.35'+    p: '47'+  number: 0.0531024292757065501235441199939858202655397919240983259583507 +/- 1.00e-61+- params:+    R: '16.13'+    p: '2'+  number: 1.16185559241585099379817152285831454241338534663731538102900 +/- 1.00e-59   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.5}[1.0.1.5.1]     has odd symmetry and Fricke sign $+1$.

from line 375 (61 lines) @@ -375,61 +375,61 @@

     R: '16.13'     p: '3'-  number: -1.28197256115333231232245321313240977705062096148593711868574 +/- 7.42e-68-- params:-    R: '16.13'-    p: '5'-  number: -0.756806413858300196301334598261889959803210123538774192667933 +/- 7.42e-68-- params:-    R: '16.13'-    p: '7'-  number: -0.298519116597898187128739770296986502428960140838277552941216 +/- 7.42e-68-- params:-    R: '16.13'-    p: '11'-  number: 0.764090704453398061637191894065979429490696872767281358929118 +/- 7.42e-68-- params:-    R: '16.13'-    p: '13'-  number: 0.162602317648074694793336968904842716998684390290153412712501 +/- 7.42e-68-- params:-    R: '16.13'-    p: '17'-  number: 0.416417432526531905797701049311209308405735818985970864616366 +/- 7.42e-68-- params:-    R: '16.13'-    p: '19'-  number: -0.755676384083098730418142448214050374605690739831545055063358 +/- 7.42e-68-- params:-    R: '16.13'-    p: '23'-  number: -1.60164448770225523811303078658724153865551022100834089233288 +/- 7.42e-68-- params:-    R: '16.13'-    p: '29'-  number: -1.48437213108248775789838860479264225231710924519356088809970 +/- 7.42e-68-- params:-    R: '16.13'-    p: '31'-  number: 0.959375991064966610390554587135569339178951502616606359482592 +/- 7.42e-68-- params:-    R: '16.13'-    p: '37'-  number: 0.400473807470319149259948775445736168558271915669044579803854 +/- 7.42e-68-- params:-    R: '16.13'-    p: '41'-  number: -0.390411275673835267717993314382221652648665885763084845851321 +/- 7.42e-68-- params:-    R: '16.13'-    p: '43'-  number: 0.158052512803159740362051786522180303279384321488395884376627 +/- 7.42e-68-- params:-    R: '16.13'-    p: '47'-  number: 1.56173288212153212944309166560681124753039565162752620900846 +/- 7.42e-68-- params:-    R: '16.64'-    p: '2'-  number: -1.54022782571692169738175161393975255182569862497982844833735 +/- 7.42e-68+  number: -1.28197256115333231232245321313240977705062096148593711868574 +/- 1.00e-59+- params:+    R: '16.13'+    p: '5'+  number: -0.756806413858300196301334598261889959803210123538774192667933 +/- 1.00e-60+- params:+    R: '16.13'+    p: '7'+  number: -0.298519116597898187128739770296986502428960140838277552941216 +/- 1.00e-60+- params:+    R: '16.13'+    p: '11'+  number: 0.764090704453398061637191894065979429490696872767281358929118 +/- 1.00e-60+- params:+    R: '16.13'+    p: '13'+  number: 0.162602317648074694793336968904842716998684390290153412712501 +/- 1.00e-60+- params:+    R: '16.13'+    p: '17'+  number: 0.416417432526531905797701049311209308405735818985970864616366 +/- 1.00e-60+- params:+    R: '16.13'+    p: '19'+  number: -0.755676384083098730418142448214050374605690739831545055063358 +/- 1.00e-60+- params:+    R: '16.13'+    p: '23'+  number: -1.60164448770225523811303078658724153865551022100834089233288 +/- 1.00e-59+- params:+    R: '16.13'+    p: '29'+  number: -1.48437213108248775789838860479264225231710924519356088809970 +/- 1.00e-59+- params:+    R: '16.13'+    p: '31'+  number: 0.959375991064966610390554587135569339178951502616606359482592 +/- 1.00e-60+- params:+    R: '16.13'+    p: '37'+  number: 0.400473807470319149259948775445736168558271915669044579803854 +/- 1.00e-60+- params:+    R: '16.13'+    p: '41'+  number: -0.390411275673835267717993314382221652648665885763084845851321 +/- 1.00e-60+- params:+    R: '16.13'+    p: '43'+  number: 0.158052512803159740362051786522180303279384321488395884376627 +/- 1.00e-60+- params:+    R: '16.13'+    p: '47'+  number: 1.56173288212153212944309166560681124753039565162752620900846 +/- 1.00e-59+- params:+    R: '16.64'+    p: '2'+  number: -1.54022782571692169738175161393975255182569862497982844833735 +/- 1.00e-59   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.6}[1.0.1.6.1]     has odd symmetry and Fricke sign $+1$.

from line 437 (61 lines) @@ -437,61 +437,61 @@

     R: '16.64'     p: '3'-  number: 0.977492591468552530610844247610894347575947500710024355345131 +/- 7.42e-68-- params:-    R: '16.64'-    p: '5'-  number: -0.105242362627703347431924530777387201480587523498272463418029 +/- 7.42e-68-- params:-    R: '16.64'-    p: '7'-  number: -0.692640859085130185371412024291218228414985184214417581153535 +/- 7.42e-68-- params:-    R: '16.64'-    p: '11'-  number: -0.760201275952541655532440225974553786821791343447324603571268 +/- 7.42e-68-- params:-    R: '16.64'-    p: '13'-  number: -1.57043706204610679575024811139751153504485057265428826309386 +/- 7.42e-68-- params:-    R: '16.64'-    p: '17'-  number: 0.281889822617368166549468046278075604209498542582427494630839 +/- 7.42e-68-- params:-    R: '16.64'-    p: '19'-  number: 0.104046090515609362887713962042986127561340097155882295098315 +/- 7.42e-68-- params:-    R: '16.64'-    p: '23'-  number: -0.143879470635166273762064766274397666353932773088377434591526 +/- 7.42e-68-- params:-    R: '16.64'-    p: '29'-  number: 0.791244081318887885937458808257215498523413819123700534029791 +/- 7.42e-68-- params:-    R: '16.64'-    p: '31'-  number: -0.757175513640587194526344263717219492460846904180997191082308 +/- 7.42e-68-- params:-    R: '16.64'-    p: '37'-  number: 1.27255986412066140583463447660484222891878340984426750380809 +/- 7.42e-68-- params:-    R: '16.64'-    p: '41'-  number: 0.547489986132042028333467663595051148103741400427464647182744 +/- 7.42e-68-- params:-    R: '16.64'-    p: '43'-  number: -0.235422983086000779021874246223026690756874592919953705791540 +/- 7.42e-68-- params:-    R: '16.64'-    p: '47'-  number: 0.565743802161055015483656964405766101010454680856719873925731 +/- 7.42e-68-- params:-    R: '17.73'-    p: '2'-  number: -0.765458056600338169232569663961409982938579592871925273098483 +/- 7.42e-68+  number: 0.977492591468552530610844247610894347575947500710024355345131 +/- 1.00e-60+- params:+    R: '16.64'+    p: '5'+  number: -0.105242362627703347431924530777387201480587523498272463418029 +/- 1.00e-60+- params:+    R: '16.64'+    p: '7'+  number: -0.692640859085130185371412024291218228414985184214417581153535 +/- 1.00e-60+- params:+    R: '16.64'+    p: '11'+  number: -0.760201275952541655532440225974553786821791343447324603571268 +/- 1.00e-60+- params:+    R: '16.64'+    p: '13'+  number: -1.57043706204610679575024811139751153504485057265428826309386 +/- 1.00e-59+- params:+    R: '16.64'+    p: '17'+  number: 0.281889822617368166549468046278075604209498542582427494630839 +/- 1.00e-60+- params:+    R: '16.64'+    p: '19'+  number: 0.104046090515609362887713962042986127561340097155882295098315 +/- 1.00e-60+- params:+    R: '16.64'+    p: '23'+  number: -0.143879470635166273762064766274397666353932773088377434591526 +/- 1.00e-60+- params:+    R: '16.64'+    p: '29'+  number: 0.791244081318887885937458808257215498523413819123700534029791 +/- 1.00e-60+- params:+    R: '16.64'+    p: '31'+  number: -0.757175513640587194526344263717219492460846904180997191082308 +/- 1.00e-60+- params:+    R: '16.64'+    p: '37'+  number: 1.27255986412066140583463447660484222891878340984426750380809 +/- 1.00e-59+- params:+    R: '16.64'+    p: '41'+  number: 0.547489986132042028333467663595051148103741400427464647182744 +/- 1.00e-60+- params:+    R: '16.64'+    p: '43'+  number: -0.235422983086000779021874246223026690756874592919953705791540 +/- 1.00e-60+- params:+    R: '16.64'+    p: '47'+  number: 0.565743802161055015483656964405766101010454680856719873925731 +/- 1.00e-60+- params:+    R: '17.73'+    p: '2'+  number: -0.765458056600338169232569663961409982938579592871925273098483 +/- 1.00e-60   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.7}[1.0.1.7.1]     has even symmetry and Fricke sign $+1$.

from line 499 (61 lines) @@ -499,61 +499,61 @@

     R: '17.73'     p: '3'-  number: -0.977778907476143038108505126097599028250952337282040616453347 +/- 7.42e-68-- params:-    R: '17.73'-    p: '5'-  number: -1.01527352252591962089585339876253691779699142053593206860790 +/- 7.42e-68-- params:-    R: '17.73'-    p: '7'-  number: 1.18082083560596529908218157175346820158639223552255103654182 +/- 7.42e-68-- params:-    R: '17.73'-    p: '11'-  number: -0.620487726175120683745403033500669330015041779960111686462280 +/- 7.42e-68-- params:-    R: '17.73'-    p: '13'-  number: 0.265288698930324604489652744242185639538822112403365128774322 +/- 7.42e-68-- params:-    R: '17.73'-    p: '17'-  number: -0.135740408678224741059574072457953220248281378278873978812382 +/- 7.42e-68-- params:-    R: '17.73'-    p: '19'-  number: 0.176971040950302581561411386949557921570831268224465391954195 +/- 7.42e-68-- params:-    R: '17.73'-    p: '23'-  number: 1.00137335555581933892385885351285820896917999927543972371321 +/- 7.42e-68-- params:-    R: '17.73'-    p: '29'-  number: -0.110159954199412400021615301947054275996911143176116385951615 +/- 7.42e-68-- params:-    R: '17.73'-    p: '31'-  number: 1.27586848869693077124960974081053581953967429760073201774104 +/- 7.42e-68-- params:-    R: '17.73'-    p: '37'-  number: 1.39231869851857213272617510666407298689714294255204734215960 +/- 7.42e-68-- params:-    R: '17.73'-    p: '41'-  number: 0.344716239254896724339895664377084108793022990419085104879970 +/- 7.42e-68-- params:-    R: '17.73'-    p: '43'-  number: -0.351234617154737725457447011683306972680180656687410490376021 +/- 7.42e-68-- params:-    R: '17.73'-    p: '47'-  number: -0.133377451643331393648208088077335679879073988002658363417809 +/- 7.42e-68-- params:-    R: '18.18'-    p: '2'-  number: 0.374063346723585885896186666580354106185941324258920737616185 +/- 7.42e-68+  number: -0.977778907476143038108505126097599028250952337282040616453347 +/- 1.00e-60+- params:+    R: '17.73'+    p: '5'+  number: -1.01527352252591962089585339876253691779699142053593206860790 +/- 1.00e-59+- params:+    R: '17.73'+    p: '7'+  number: 1.18082083560596529908218157175346820158639223552255103654182 +/- 1.00e-59+- params:+    R: '17.73'+    p: '11'+  number: -0.620487726175120683745403033500669330015041779960111686462280 +/- 1.00e-60+- params:+    R: '17.73'+    p: '13'+  number: 0.265288698930324604489652744242185639538822112403365128774322 +/- 1.00e-60+- params:+    R: '17.73'+    p: '17'+  number: -0.135740408678224741059574072457953220248281378278873978812382 +/- 1.00e-60+- params:+    R: '17.73'+    p: '19'+  number: 0.176971040950302581561411386949557921570831268224465391954195 +/- 1.00e-60+- params:+    R: '17.73'+    p: '23'+  number: 1.00137335555581933892385885351285820896917999927543972371321 +/- 1.00e-59+- params:+    R: '17.73'+    p: '29'+  number: -0.110159954199412400021615301947054275996911143176116385951615 +/- 1.00e-60+- params:+    R: '17.73'+    p: '31'+  number: 1.27586848869693077124960974081053581953967429760073201774104 +/- 1.00e-59+- params:+    R: '17.73'+    p: '37'+  number: 1.39231869851857213272617510666407298689714294255204734215960 +/- 1.00e-59+- params:+    R: '17.73'+    p: '41'+  number: 0.344716239254896724339895664377084108793022990419085104879970 +/- 1.00e-60+- params:+    R: '17.73'+    p: '43'+  number: -0.351234617154737725457447011683306972680180656687410490376021 +/- 1.00e-60+- params:+    R: '17.73'+    p: '47'+  number: -0.133377451643331393648208088077335679879073988002658363417809 +/- 1.00e-60+- params:+    R: '18.18'+    p: '2'+  number: 0.374063346723585885896186666580354106185941324258920737616185 +/- 1.00e-60   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.8}[1.0.1.8.1]     has odd symmetry and Fricke sign $+1$.

from line 561 (61 lines) @@ -561,61 +561,61 @@

     R: '18.18'     p: '3'-  number: 0.101958697619578543890683140077602061541379466770343404583023 +/- 7.42e-68-- params:-    R: '18.18'-    p: '5'-  number: 0.637330829346188125587886179211258479652642686893568816548189 +/- 7.42e-68-- params:-    R: '18.18'-    p: '7'-  number: -1.54209922327203811999685297331223491992749452997057636653159 +/- 7.42e-68-- params:-    R: '18.18'-    p: '11'-  number: -0.411715706793125351318538225984060447926627747542642831042342 +/- 7.42e-68-- params:-    R: '18.18'-    p: '13'-  number: 0.478703729678757544989076202424533360698708781788906237701897 +/- 7.42e-68-- params:-    R: '18.18'-    p: '17'-  number: -0.548557414997243980166512746907587928248159405961850426403915 +/- 7.42e-68-- params:-    R: '18.18'-    p: '19'-  number: 1.03098415798997397319802878877472696889972700382211182819126 +/- 7.42e-68-- params:-    R: '18.18'-    p: '23'-  number: 0.663425770592332908206882468447076922788273667238637256373154 +/- 7.42e-68-- params:-    R: '18.18'-    p: '29'-  number: -1.27082249594460181407342380179019602217228427743351406143287 +/- 7.42e-68-- params:-    R: '18.18'-    p: '31'-  number: -0.223968759910987289454952532648142535237479086409934751422932 +/- 7.42e-68-- params:-    R: '18.18'-    p: '37'-  number: -0.108741556504690245537426237813768621616840019079181951444056 +/- 7.42e-68-- params:-    R: '18.18'-    p: '41'-  number: -0.419097539782316388445303264114538717121480787954445520018410 +/- 7.42e-68-- params:-    R: '18.18'-    p: '43'-  number: 0.848150865377788848344458369007768952451475620411662301652555 +/- 7.42e-68-- params:-    R: '18.18'-    p: '47'-  number: -1.08630166641434424977181521719827775481911268379711135546293 +/- 7.42e-68-- params:-    R: '19.42'-    p: '2'-  number: -0.692761976402402506264953793147383620381616394008946345628856 +/- 7.42e-68+  number: 0.101958697619578543890683140077602061541379466770343404583023 +/- 1.00e-60+- params:+    R: '18.18'+    p: '5'+  number: 0.637330829346188125587886179211258479652642686893568816548189 +/- 1.00e-60+- params:+    R: '18.18'+    p: '7'+  number: -1.54209922327203811999685297331223491992749452997057636653159 +/- 1.00e-59+- params:+    R: '18.18'+    p: '11'+  number: -0.411715706793125351318538225984060447926627747542642831042342 +/- 1.00e-60+- params:+    R: '18.18'+    p: '13'+  number: 0.478703729678757544989076202424533360698708781788906237701897 +/- 1.00e-60+- params:+    R: '18.18'+    p: '17'+  number: -0.548557414997243980166512746907587928248159405961850426403915 +/- 1.00e-60+- params:+    R: '18.18'+    p: '19'+  number: 1.03098415798997397319802878877472696889972700382211182819126 +/- 1.00e-59+- params:+    R: '18.18'+    p: '23'+  number: 0.663425770592332908206882468447076922788273667238637256373154 +/- 1.00e-60+- params:+    R: '18.18'+    p: '29'+  number: -1.27082249594460181407342380179019602217228427743351406143287 +/- 1.00e-59+- params:+    R: '18.18'+    p: '31'+  number: -0.223968759910987289454952532648142535237479086409934751422932 +/- 1.00e-60+- params:+    R: '18.18'+    p: '37'+  number: -0.108741556504690245537426237813768621616840019079181951444056 +/- 1.00e-60+- params:+    R: '18.18'+    p: '41'+  number: -0.419097539782316388445303264114538717121480787954445520018410 +/- 1.00e-60+- params:+    R: '18.18'+    p: '43'+  number: 0.848150865377788848344458369007768952451475620411662301652555 +/- 1.00e-60+- params:+    R: '18.18'+    p: '47'+  number: -1.08630166641434424977181521719827775481911268379711135546293 +/- 1.00e-59+- params:+    R: '19.42'+    p: '2'+  number: -0.692761976402402506264953793147383620381616394008946345628856 +/- 1.00e-60   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.9}[1.0.1.9.1]     has even symmetry and Fricke sign $+1$.

from line 623 (61 lines) @@ -623,61 +623,61 @@

     R: '19.42'     p: '3'-  number: 1.56235430211493697839681908280502808033801825458456774517253 +/- 7.42e-68-- params:-    R: '19.42'-    p: '5'-  number: -0.0384116982264217210898341144484874919418588162027556457533250 +/- 7.42e-68-- params:-    R: '19.42'-    p: '7'-  number: 0.312952980696207723881742441770757671167258593279737212858554 +/- 7.42e-68-- params:-    R: '19.42'-    p: '11'-  number: 1.15363355448408073411142073354386113546506756759165980216048 +/- 7.42e-68-- params:-    R: '19.42'-    p: '13'-  number: 0.758971425656586365322627747695746843010434150610261078796188 +/- 7.42e-68-- params:-    R: '19.42'-    p: '17'-  number: 0.844381009819172111193884741196629570979211105841107440953398 +/- 7.42e-68-- params:-    R: '19.42'-    p: '19'-  number: 0.393212896981308540029842023580893254353310956922038426802876 +/- 7.42e-68-- params:-    R: '19.42'-    p: '23'-  number: -0.357998742809567882901673063652251058382799251625793873575064 +/- 7.42e-68-- params:-    R: '19.42'-    p: '29'-  number: 0.224703571863084688010867005940517362316130625884889008871410 +/- 7.42e-68-- params:-    R: '19.42'-    p: '31'-  number: -0.330286117042824988806262922378667409352744302170318081537122 +/- 7.42e-68-- params:-    R: '19.42'-    p: '37'-  number: 0.403965397731231376874005539667587197186774743340794507167797 +/- 7.42e-68-- params:-    R: '19.42'-    p: '41'-  number: -1.37981522486067187800364334196680844089583714395282022752715 +/- 7.42e-68-- params:-    R: '19.42'-    p: '43'-  number: 1.64472447191254960234943625796663002976798647996693136697577 +/- 7.42e-68-- params:-    R: '19.42'-    p: '47'-  number: -0.0183959469393231111696238987205566235391709377406621143740430 +/- 7.42e-68-- params:-    R: '19.48'-    p: '2'-  number: -1.70018803236937520494757001211438294728825341606771734815813 +/- 7.42e-68+  number: 1.56235430211493697839681908280502808033801825458456774517253 +/- 1.00e-59+- params:+    R: '19.42'+    p: '5'+  number: -0.0384116982264217210898341144484874919418588162027556457533250 +/- 1.00e-61+- params:+    R: '19.42'+    p: '7'+  number: 0.312952980696207723881742441770757671167258593279737212858554 +/- 1.00e-60+- params:+    R: '19.42'+    p: '11'+  number: 1.15363355448408073411142073354386113546506756759165980216048 +/- 1.00e-59+- params:+    R: '19.42'+    p: '13'+  number: 0.758971425656586365322627747695746843010434150610261078796188 +/- 1.00e-60+- params:+    R: '19.42'+    p: '17'+  number: 0.844381009819172111193884741196629570979211105841107440953398 +/- 1.00e-60+- params:+    R: '19.42'+    p: '19'+  number: 0.393212896981308540029842023580893254353310956922038426802876 +/- 1.00e-60+- params:+    R: '19.42'+    p: '23'+  number: -0.357998742809567882901673063652251058382799251625793873575064 +/- 1.00e-60+- params:+    R: '19.42'+    p: '29'+  number: 0.224703571863084688010867005940517362316130625884889008871410 +/- 1.00e-60+- params:+    R: '19.42'+    p: '31'+  number: -0.330286117042824988806262922378667409352744302170318081537122 +/- 1.00e-60+- params:+    R: '19.42'+    p: '37'+  number: 0.403965397731231376874005539667587197186774743340794507167797 +/- 1.00e-60+- params:+    R: '19.42'+    p: '41'+  number: -1.37981522486067187800364334196680844089583714395282022752715 +/- 1.00e-59+- params:+    R: '19.42'+    p: '43'+  number: 1.64472447191254960234943625796663002976798647996693136697577 +/- 1.00e-59+- params:+    R: '19.42'+    p: '47'+  number: -0.0183959469393231111696238987205566235391709377406621143740430 +/- 1.00e-61+- params:+    R: '19.48'+    p: '2'+  number: -1.70018803236937520494757001211438294728825341606771734815813 +/- 1.00e-59   comment: LMFDB form HREF{https://www.lmfdb.org/ModularForm/GL2/Q/Maass/1.10}[1.0.1.10.1]     has odd symmetry and Fricke sign $+1$.

from line 685 (55 lines) @@ -685,55 +685,55 @@

     R: '19.48'     p: '3'-  number: -0.614565376587703532221370711422105332968204292647336684599260 +/- 7.42e-68-- params:-    R: '19.48'-    p: '5'-  number: 0.819825344160936972665932369755175601419669726579637915908160 +/- 7.42e-68-- params:-    R: '19.48'-    p: '7'-  number: 0.0635689937509351771246421256077566564582643460743268386888142 +/- 7.42e-68-- params:-    R: '19.48'-    p: '11'-  number: 0.659736423647445393813525401364875205625679863179875834770262 +/- 7.42e-68-- params:-    R: '19.48'-    p: '13'-  number: 0.662330122479272354619867770138719504705406186122152980295927 +/- 7.42e-68-- params:-    R: '19.48'-    p: '17'-  number: -0.677781119632414933981489902774046788306670441887658834959182 +/- 7.42e-68-- params:-    R: '19.48'-    p: '19'-  number: -1.73440748458416285377349958885307197519335242077928618669111 +/- 7.42e-68-- params:-    R: '19.48'-    p: '23'-  number: 0.334160762688498295988574433198154970749399699046441227922608 +/- 7.42e-68-- params:-    R: '19.48'-    p: '29'-  number: -0.585623950702460345708476565632075547279530034968137717401191 +/- 7.42e-68-- params:-    R: '19.48'-    p: '31'-  number: -0.988659933153983979006888155451320132430365500900407486404572 +/- 7.42e-68-- params:-    R: '19.48'-    p: '37'-  number: -1.28098080805126155036580513926216356255709370603579498644218 +/- 7.42e-68-- params:-    R: '19.48'-    p: '41'-  number: 0.239150190588673651300287708573707521698209380099887002175250 +/- 7.42e-68-- params:-    R: '19.48'-    p: '43'-  number: -0.429138221315136325423035251081345257085726256900478812482727 +/- 7.42e-68-- params:-    R: '19.48'-    p: '47'-  number: 0.907515236334520573845616423107515390812294263240302412686264 +/- 7.42e-68+  number: -0.614565376587703532221370711422105332968204292647336684599260 +/- 1.00e-60+- params:+    R: '19.48'+    p: '5'+  number: 0.819825344160936972665932369755175601419669726579637915908160 +/- 1.00e-60+- params:+    R: '19.48'+    p: '7'+  number: 0.0635689937509351771246421256077566564582643460743268386888142 +/- 1.00e-61+- params:+    R: '19.48'+    p: '11'+  number: 0.659736423647445393813525401364875205625679863179875834770262 +/- 1.00e-60+- params:+    R: '19.48'+    p: '13'+  number: 0.662330122479272354619867770138719504705406186122152980295927 +/- 1.00e-60+- params:+    R: '19.48'+    p: '17'+  number: -0.677781119632414933981489902774046788306670441887658834959182 +/- 1.00e-60+- params:+    R: '19.48'+    p: '19'+  number: -1.73440748458416285377349958885307197519335242077928618669111 +/- 1.00e-59+- params:+    R: '19.48'+    p: '23'+  number: 0.334160762688498295988574433198154970749399699046441227922608 +/- 1.00e-60+- params:+    R: '19.48'+    p: '29'+  number: -0.585623950702460345708476565632075547279530034968137717401191 +/- 1.00e-60+- params:+    R: '19.48'+    p: '31'+  number: -0.988659933153983979006888155451320132430365500900407486404572 +/- 1.00e-60+- params:+    R: '19.48'+    p: '37'+  number: -1.28098080805126155036580513926216356255709370603579498644218 +/- 1.00e-59+- params:+    R: '19.48'+    p: '41'+  number: 0.239150190588673651300287708573707521698209380099887002175250 +/- 1.00e-60+- params:+    R: '19.48'+    p: '43'+  number: -0.429138221315136325423035251081345257085726256900478812482727 +/- 1.00e-60+- params:+    R: '19.48'+    p: '47'+  number: 0.907515236334520573845616423107515390812294263240302412686264 +/- 1.00e-60