History of Zeros of Dirichlet L-series

+Title: Zeros of Dirichlet L-series+Definition: The list contains the first few imaginary parts of zeros of the first+  few Dirichlet L-functions $L(\chi,s)$ on the critical line.+Parameters:+  q:+    title: conductor of $\chi$+    type: Z+    constraints: $q \geq 1$+  n:+    title: HREF{#CL}[Conrey index] of $\chi$+    type: Z+    constraints: $1 \leq n \leq \max(q-1,1)$+    comments: The pair $(q,n)$ uniquely determines the Dirichlet character $\chi$.+  k:+    title: Index of the zero+    type: Z+    constraints: $k \neq 0$+    comments: The positive imaginary parts are labelled $k = 1, 2, 3, \ldots$,  the+      negative ones are labelled $k = -1, -2, -3, \ldots$, and the index $k = 0$ is+      skipped.+Comments:+  comment_0: Let $\chi$ be a Dirichlet character. The associated L-function $\zeta(\chi,s)$+    is the  meromorphic continuation of the Dirichlet series  $\sum_{n=0}^\infty \chi(n)+    n^{-s}, \Re(s) > 0$.+  comment_1: 'Its so-called trivial zeros lie on the negative $x$-axis, which are+    therefore not listed.++    All known non-trivial zeros lie on the line $\Re(s) = 1/2$. If $\chi$ is real,+    their imaginary parts are symmetric about 0,  in which case we only list the positive+    ones.'+Formulas: {}+Programs: {}+References:+  Pl11:+    bib: David J. Platt, "Computing degree 1 L-functions rigorously",  PhD thesis,+      University of Bristol, 2011.+Links:+  Wiki:+    title: 'Wikipedia: Dirichlet L-function'+    url: https://en.wikipedia.org/wiki/Dirichlet_L-function+  LMFDB:+    title: 'LMFDB: Degree-1 L-functions'+    url: https://www.lmfdb.org/L/degree1/+  CL:+    title: 'LMFDB knowl: Conrey label'+    url: https://www.lmfdb.org/knowledge/show/character.dirichlet.conrey+Similar tables: ''+Keywords:+- GRH+Tags:+- zero+- L-function+Data properties:+  type: R+  complete: 'no'+  relative precision: 1e-28+  sources:+  - CITE{Pl11}+  - CITE{LMFDB}+Display properties:+  layout: nested lists+  group parameters:+  - - q+    - n+  - - k+Numbers:+  1,1:+    equals: HREF{Zeros_of_the_Riemann_zeta_function}+    comment: $\chi = 1$+  3,2:+    both signs: 'yes'+    numbers:+      '1': '8.03973715568146668171362321417'+      '2': '11.24920620777293524970502567886'+      '3': '15.70461917672162556516555088043'+      '4': '18.26199749569312756892441409359'+      '5': '20.45577080774249285344502583131'+      '6': '24.05941485649345077459305359321'+      '7': '26.57786873577458531458435093753'+      '8': '28.21816450623338609318302976031'+      '9': '30.74504026138249573780824181050'+      '10': '33.89738892725941901767787403300'+      '11': '35.60841265393863465481291012803'+      '12': '37.55179655636462701986044645770'+      '13': '39.48520726092935076736629266003'+      '14': '42.6163792261575675743228068514'+      '15': '44.12057291207220244202440459309'+      '16': '46.27411802351314008510487166014'+      '17': '47.5141045101173221149363569968'+      '18': '50.375138650636265982821917341449'+      '19': '52.4967495990607536672882221717'+      '20': '54.19384310155191357860186830353'+      '21': '55.6425587002162213738564033666'+      '22': '57.58405636044918378148658948822'+      '23': '60.02685745671590223526149077217'+      '24': '62.20607812228213648686964588013'+      '25': '63.17699276733910829118311838811'+    url: https://www.lmfdb.org/Character/Dirichlet/3/2+  4,3:+    both signs: 'yes'+    numbers:+      '1': '6.02094890469759665490251152161'+      '2': '10.2437703041665545521377574791'+      '3': '12.98809801231242250745310978956'+      '4': '16.34260710458722219497686148345'+      '5': '18.29199319612353483852600427759'+      '6': '21.45061134398346049720094838629'+      '7': '23.27837652045953153181955888634'+      '8': '25.728756425088727567265088674277'+      '9': '28.35963434302532778565160794178'+      '10': '29.65638401459315272180990696821'+      '11': '32.59218652711715513081519404895'+      '12': '34.19995750921314691304479547000'+      '13': '36.14288045830313783056581447010'+      '14': '38.511923141718691293776504688065'+      '15': '40.32267406669054418034439436231'+      '16': '41.80708462000456233715752189724'+      '17': '44.6178910586623033934820457250'+      '18': '45.59958439679156674593770229335'+      '19': '47.74156228093914125078134734303'+      '20': '49.723129323782586066569570880970'+      '21': '51.68609345287052843953381111031'+      '22': '52.76882076780472926503507657877'+      '23': '55.267543584699224846718259656915'+      '24': '56.934374055202296886801711961125'+      '25': '58.1167071106739179772623675469'+    url: https://www.lmfdb.org/Character/Dirichlet/4/3+  5,2:+    both signs: 'no'+    numbers:+      '-25': '-55.53255063917714331177635885562'+      '-24': '-53.75667308835424588804456665093'+      '-23': '-51.08998804633721267564942694432'+      '-22': '-49.5201121831721842836352461905'+      '-21': '-48.47765991878316956160896236195'+      '-20': '-46.26641381346456449258634989372'+      '-19': '-45.08582264962074326882242881556'+      '-18': '-43.12543488567473830905726366337'+      '-17': '-40.508934445122041603749872022008'+      '-16': '-39.0916158639927091132955773909'+      '-15': '-37.84761841624699497844836046640'+      '-14': '-36.09652653725364935231283520536'+      '-13': '-33.30774552092450944486851535240'+      '-12': '-31.714038216978378088676011094547'+      '-11': '-29.70278103479729044076360156773'+      '-10': '-27.81247022179307495811051208168'+      '-9': '-26.47278891481336832795849047572'+      '-8': '-22.9655764347914803808601277723'+      '-7': '-21.2830471577778699486763506284'+      '-6': '-19.72905478631162605830813598374'+      '-5': '-16.99590394259028444664793427768'+      '-4': '-14.11546426656964617536066631834'+      '-3': '-11.2828964415816001332254807924'+      '-2': '-9.44293112972850911710026212431'+      '-1': '-4.13290370521285159500191933156'+      '1': '6.18357819545085391437751730970'+      '2': '8.45722917442323072160535286274'+      '3': '12.67494641701135578048229914508'+      '4': '14.82502557032842825143025217404'+      '5': '17.33780210685303969091451014241'+      '6': '18.9985880416861449287245250119'+      '7': '22.48758458302875002505567290925'+      '8': '24.36527977540229805651909575745'+      '9': '25.531186800433429601457551452466'+      '10': '27.982756935693594324451001091893'+      '11': '30.46364068840366112797004484191'+      '12': '32.195159688892272026544832306389'+      '13': '34.45722878527839758405756301004'+      '14': '35.49089317885139349790895129816'+      '15': '37.27195057455605008724509915557'+      '16': '40.39611485175259003483748872182'+      '17': '41.53645675792969665969385524901'+      '18': '42.99208544275153854582429789755'+      '19': '44.82617597081092363119666478355'+      '20': '46.59016101776473881831044964340'+      '21': '48.4778466442218740132847945792'+      '22': '50.66421039080575037299754421231'+      '23': '51.977053467572707629124054585044'+      '24': '53.442232173354543204000399997353'+      '25': '54.48544238876467911470039917979'+    url: https://www.lmfdb.org/Character/Dirichlet/5/2+  5,3:+    both signs: 'no'+    numbers:+      '-25': '-54.48544238876467911470039917979'+      '-24': '-53.442232173354543204000399997353'+      '-23': '-51.977053467572707629124054585044'+      '-22': '-50.66421039080575037299754421231'+      '-21': '-48.4778466442218740132847945792'+      '-20': '-46.59016101776473881831044964340'+      '-19': '-44.82617597081092363119666478355'+      '-18': '-42.99208544275153854582429789755'+      '-17': '-41.53645675792969665969385524901'+      '-16': '-40.39611485175259003483748872182'+      '-15': '-37.27195057455605008724509915557'+      '-14': '-35.49089317885139349790895129816'+      '-13': '-34.45722878527839758405756301004'+      '-12': '-32.195159688892272026544832306389'+      '-11': '-30.46364068840366112797004484191'+      '-10': '-27.982756935693594324451001091893'+      '-9': '-25.531186800433429601457551452466'+      '-8': '-24.36527977540229805651909575745'+      '-7': '-22.48758458302875002505567290925'+      '-6': '-18.9985880416861449287245250119'+      '-5': '-17.33780210685303969091451014241'+      '-4': '-14.82502557032842825143025217404'+      '-3': '-12.67494641701135578048229914508'+      '-2': '-8.45722917442323072160535286274'+      '-1': '-6.18357819545085391437751730970'+      '1': '4.13290370521285159500191933156'+      '2': '9.44293112972850911710026212431'+      '3': '11.2828964415816001332254807924'+      '4': '14.11546426656964617536066631834'+      '5': '16.99590394259028444664793427768'+      '6': '19.72905478631162605830813598374'+      '7': '21.2830471577778699486763506284'+      '8': '22.9655764347914803808601277723'+      '9': '26.47278891481336832795849047572'+      '10': '27.81247022179307495811051208168'+      '11': '29.70278103479729044076360156773'+      '12': '31.714038216978378088676011094547'+      '13': '33.30774552092450944486851535240'+      '14': '36.09652653725364935231283520536'+      '15': '37.84761841624699497844836046640'+      '16': '39.0916158639927091132955773909'+      '17': '40.508934445122041603749872022008'+      '18': '43.12543488567473830905726366337'+      '19': '45.08582264962074326882242881556'+      '20': '46.26641381346456449258634989372'+      '21': '48.47765991878316956160896236195'+      '22': '49.5201121831721842836352461905'+      '23': '51.08998804633721267564942694432'+      '24': '53.75667308835424588804456665093'+      '25': '55.53255063917714331177635885562'+    url: https://www.lmfdb.org/Character/Dirichlet/5/3+  5,4:+    both signs: 'yes'+    numbers:+      '1': '6.64845334472771471612327845997'+      '2': '9.831444432886669616348321347458'+      '3': '11.95884562608351453026565868826'+      '4': '16.03382112838423567459325378224'+      '5': '17.566994292325555202701595268144'+      '6': '19.54073262278475025037869002299'+      '7': '22.227405454459410911877624963081'+      '8': '24.58846621740819520765626997608'+      '9': '26.77609594800414011652357496527'+      '10': '28.46103510017752247518697827232'+      '11': '29.70790935048096556923098651865'+      '12': '33.00045600687051436794975917721'+      '13': '34.728812978904808674143729833981'+      '14': '35.86863837181227459459504863887'+      '15': '38.12918472143653185015141827037'+      '16': '39.56057294640318170505509505995'+      '17': '41.84243854579169430850930688531'+      '18': '44.03129006144169504470090805842'+      '19': '45.4273000827822893888415619096'+      '20': '46.49272715949140534533919935167'+      '21': '48.34566182106784617654820130449'+      '22': '51.08775192674649135525825720413'+      '23': '52.1259022313169741886041306959'+      '24': '53.83044519544216335105426902233'+      '25': '55.58928033540481015096458899849'+    url: https://www.lmfdb.org/Character/Dirichlet/5/4