L(s) = 1 | + (−1.36 − 0.385i)2-s + 0.423i·3-s + (1.70 + 1.04i)4-s + (−1.74 + 1.39i)5-s + (0.163 − 0.576i)6-s + (−1.91 − 2.08i)8-s + 2.82·9-s + (2.91 − 1.23i)10-s − 4.89i·11-s + (−0.443 + 0.721i)12-s − 2.54·13-s + (−0.591 − 0.738i)15-s + (1.80 + 3.57i)16-s + 5.11·17-s + (−3.83 − 1.08i)18-s − 6.26·19-s + ⋯ |
L(s) = 1 | + (−0.962 − 0.272i)2-s + 0.244i·3-s + (0.851 + 0.524i)4-s + (−0.780 + 0.625i)5-s + (0.0665 − 0.235i)6-s + (−0.676 − 0.736i)8-s + 0.940·9-s + (0.921 − 0.388i)10-s − 1.47i·11-s + (−0.128 + 0.208i)12-s − 0.706·13-s + (−0.152 − 0.190i)15-s + (0.450 + 0.892i)16-s + 1.24·17-s + (−0.904 − 0.256i)18-s − 1.43·19-s + ⋯ |
Λ(s)=(=(980s/2ΓC(s)L(s)(0.277+0.960i)Λ(2−s)
Λ(s)=(=(980s/2ΓC(s+1/2)L(s)(0.277+0.960i)Λ(1−s)
Degree: |
2 |
Conductor: |
980
= 22⋅5⋅72
|
Sign: |
0.277+0.960i
|
Analytic conductor: |
7.82533 |
Root analytic conductor: |
2.79738 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ980(979,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 980, ( :1/2), 0.277+0.960i)
|
Particular Values
L(1) |
≈ |
0.544129−0.409334i |
L(21) |
≈ |
0.544129−0.409334i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.36+0.385i)T |
| 5 | 1+(1.74−1.39i)T |
| 7 | 1 |
good | 3 | 1−0.423iT−3T2 |
| 11 | 1+4.89iT−11T2 |
| 13 | 1+2.54T+13T2 |
| 17 | 1−5.11T+17T2 |
| 19 | 1+6.26T+19T2 |
| 23 | 1+4.63T+23T2 |
| 29 | 1+1.88T+29T2 |
| 31 | 1−1.47T+31T2 |
| 37 | 1+2.35iT−37T2 |
| 41 | 1+7.05iT−41T2 |
| 43 | 1−10.7T+43T2 |
| 47 | 1+12.2iT−47T2 |
| 53 | 1+2.23iT−53T2 |
| 59 | 1−5.68T+59T2 |
| 61 | 1−3.87iT−61T2 |
| 67 | 1+0.889T+67T2 |
| 71 | 1+14.3iT−71T2 |
| 73 | 1−7.87T+73T2 |
| 79 | 1+4.63iT−79T2 |
| 83 | 1−4.32iT−83T2 |
| 89 | 1+2.18iT−89T2 |
| 97 | 1+3.42T+97T2 |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.04081128400024297605089400328, −8.977826709125875115199842046999, −8.157086377408563965289590255794, −7.52535347202671296701170832955, −6.70299907196099508331374890128, −5.73239694653302311297990095911, −4.08786647449685797695103002394, −3.43243088101486807484913663598, −2.20998014045916134004057994940, −0.47754250680285151547833910002,
1.22703849621438465423137230664, 2.34442292278684794566963064703, 4.09638739652273207096865611077, 4.89098561961929100151483351360, 6.16117970127656949502883840054, 7.18370266724588254408904266406, 7.66643037994739798608417070383, 8.310656328198516145698969602987, 9.522155546706164107948301508100, 9.866929588527376311037673980069