L(s) = 1 | + (0.695 − 0.718i)2-s + (−0.946 + 0.323i)3-s + (−0.0319 − 0.999i)4-s + (−0.825 − 0.564i)5-s + (−0.425 + 0.904i)6-s + (−0.936 − 0.351i)7-s + (−0.740 − 0.672i)8-s + (0.790 − 0.612i)9-s + (−0.979 + 0.200i)10-s + (0.0466 + 0.998i)11-s + (0.353 + 0.935i)12-s + (0.974 + 0.224i)13-s + (−0.903 + 0.428i)14-s + (0.963 + 0.267i)15-s + (−0.997 + 0.0638i)16-s + (0.958 + 0.286i)17-s + ⋯ |
L(s) = 1 | + (0.695 − 0.718i)2-s + (−0.946 + 0.323i)3-s + (−0.0319 − 0.999i)4-s + (−0.825 − 0.564i)5-s + (−0.425 + 0.904i)6-s + (−0.936 − 0.351i)7-s + (−0.740 − 0.672i)8-s + (0.790 − 0.612i)9-s + (−0.979 + 0.200i)10-s + (0.0466 + 0.998i)11-s + (0.353 + 0.935i)12-s + (0.974 + 0.224i)13-s + (−0.903 + 0.428i)14-s + (0.963 + 0.267i)15-s + (−0.997 + 0.0638i)16-s + (0.958 + 0.286i)17-s + ⋯ |
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.151+0.988i)Λ(1−s)
Λ(s)=(=(2557s/2ΓR(s)L(s)(0.151+0.988i)Λ(1−s)
Degree: |
1 |
Conductor: |
2557
|
Sign: |
0.151+0.988i
|
Analytic conductor: |
11.8746 |
Root analytic conductor: |
11.8746 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2557(1034,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2557, (0: ), 0.151+0.988i)
|
Particular Values
L(21) |
≈ |
−0.07820509164−0.06716394735i |
L(21) |
≈ |
−0.07820509164−0.06716394735i |
L(1) |
≈ |
0.6225364305−0.4114366382i |
L(1) |
≈ |
0.6225364305−0.4114366382i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2557 | 1 |
good | 2 | 1+(0.695−0.718i)T |
| 3 | 1+(−0.946+0.323i)T |
| 5 | 1+(−0.825−0.564i)T |
| 7 | 1+(−0.936−0.351i)T |
| 11 | 1+(0.0466+0.998i)T |
| 13 | 1+(0.974+0.224i)T |
| 17 | 1+(0.958+0.286i)T |
| 19 | 1+(−0.430−0.902i)T |
| 23 | 1+(−0.674−0.738i)T |
| 29 | 1+(−0.0908−0.995i)T |
| 31 | 1+(−0.221−0.975i)T |
| 37 | 1+(−0.508−0.861i)T |
| 41 | 1+(−0.962+0.271i)T |
| 43 | 1+(0.558−0.829i)T |
| 47 | 1+(−0.974+0.224i)T |
| 53 | 1+(0.814+0.580i)T |
| 59 | 1+(−0.999+0.0245i)T |
| 61 | 1+(−0.197−0.980i)T |
| 67 | 1+(−0.362−0.931i)T |
| 71 | 1+(−0.637+0.770i)T |
| 73 | 1+(−0.188−0.982i)T |
| 79 | 1+(−0.699+0.714i)T |
| 83 | 1+(0.159−0.987i)T |
| 89 | 1+(−0.478+0.878i)T |
| 97 | 1+(0.0368+0.999i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.80933913762024019679674315408, −18.99292988870775212926648088966, −18.46561746422557078660415376996, −17.89485321473953952815517331416, −16.70818675486890859652891204170, −16.27547762753435715877677133406, −15.92945074776168899745753214383, −15.129959303990223790640218465878, −14.21254366090364260814753438685, −13.51528278357305817708226424523, −12.76737413704779947192947219299, −12.07303190440125697697498338807, −11.62659131160510620363044026429, −10.76990637194917030608720448702, −10.02012900502560591679485737317, −8.65885462013733053098370918528, −8.112516264208784896976036837523, −7.196297243926243808219778506881, −6.62226955126046912975731936677, −5.85464298581735299453496459648, −5.51086854145726204888268240428, −4.28964851062563512800571074013, −3.3786886507666156984384789376, −3.12815813026173932744778310548, −1.45896176954983561695551791525,
0.037505492918069948147297064251, 0.905128660609760188233229585528, 1.95451588869059564812679227957, 3.28003539071409804633851505190, 4.05933850911675479633051843408, 4.353582988015033071529060340422, 5.31898189209789263316218644090, 6.141129478792029903331724396913, 6.75258377064796205102910475752, 7.69029479669954162174713302229, 8.99727953107347334215294563119, 9.62513848189963342185169820615, 10.39713460904495270706300210977, 10.95667073368487514890316531751, 11.876344100749289739471900824746, 12.24561492285665994323907528586, 12.94764256459146660133509124053, 13.49035610447833167511088687953, 14.68756228950109747185668362819, 15.461947381741203774160641721925, 15.845083027075956653555552908327, 16.64461013006323834184846201906, 17.301751849081182015746018811941, 18.40690229175499150354835309317, 18.91984791162526076799656724051