L(s) = 1 | + (0.5 − 0.866i)2-s + (0.664 − 1.15i)3-s + (−0.499 − 0.866i)4-s + (−0.664 − 1.15i)6-s + 2.32·7-s − 0.999·8-s + (0.616 + 1.06i)9-s + 6.39·11-s − 1.32·12-s + (0.429 + 0.743i)13-s + (1.16 − 2.01i)14-s + (−0.5 + 0.866i)16-s + (−2.34 + 4.06i)17-s + 1.23·18-s + (3.75 − 2.21i)19-s + ⋯ |
L(s) = 1 | + (0.353 − 0.612i)2-s + (0.383 − 0.664i)3-s + (−0.249 − 0.433i)4-s + (−0.271 − 0.469i)6-s + 0.880·7-s − 0.353·8-s + (0.205 + 0.355i)9-s + 1.92·11-s − 0.383·12-s + (0.119 + 0.206i)13-s + (0.311 − 0.539i)14-s + (−0.125 + 0.216i)16-s + (−0.568 + 0.985i)17-s + 0.290·18-s + (0.860 − 0.509i)19-s + ⋯ |
Λ(s)=(=(950s/2ΓC(s)L(s)(0.221+0.975i)Λ(2−s)
Λ(s)=(=(950s/2ΓC(s+1/2)L(s)(0.221+0.975i)Λ(1−s)
Degree: |
2 |
Conductor: |
950
= 2⋅52⋅19
|
Sign: |
0.221+0.975i
|
Analytic conductor: |
7.58578 |
Root analytic conductor: |
2.75423 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ950(201,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 950, ( :1/2), 0.221+0.975i)
|
Particular Values
L(1) |
≈ |
2.01216−1.60634i |
L(21) |
≈ |
2.01216−1.60634i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.5+0.866i)T |
| 5 | 1 |
| 19 | 1+(−3.75+2.21i)T |
good | 3 | 1+(−0.664+1.15i)T+(−1.5−2.59i)T2 |
| 7 | 1−2.32T+7T2 |
| 11 | 1−6.39T+11T2 |
| 13 | 1+(−0.429−0.743i)T+(−6.5+11.2i)T2 |
| 17 | 1+(2.34−4.06i)T+(−8.5−14.7i)T2 |
| 23 | 1+(1.73+3.00i)T+(−11.5+19.9i)T2 |
| 29 | 1+(−2.21−3.82i)T+(−14.5+25.1i)T2 |
| 31 | 1+8.25T+31T2 |
| 37 | 1+9.76T+37T2 |
| 41 | 1+(1.84−3.19i)T+(−20.5−35.5i)T2 |
| 43 | 1+(−3.56+6.17i)T+(−21.5−37.2i)T2 |
| 47 | 1+(3.59+6.22i)T+(−23.5+40.7i)T2 |
| 53 | 1+(3.10+5.37i)T+(−26.5+45.8i)T2 |
| 59 | 1+(−3.09+5.35i)T+(−29.5−51.0i)T2 |
| 61 | 1+(−4.01−6.94i)T+(−30.5+52.8i)T2 |
| 67 | 1+(2.45+4.24i)T+(−33.5+58.0i)T2 |
| 71 | 1+(1.10−1.90i)T+(−35.5−61.4i)T2 |
| 73 | 1+(2.32−4.03i)T+(−36.5−63.2i)T2 |
| 79 | 1+(5.79−10.0i)T+(−39.5−68.4i)T2 |
| 83 | 1+6.07T+83T2 |
| 89 | 1+(5.64+9.78i)T+(−44.5+77.0i)T2 |
| 97 | 1+(5.67−9.82i)T+(−48.5−84.0i)T2 |
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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
−9.942426319338394921548003957492, −8.816844303690172395916834701507, −8.482513944518071658262909427277, −7.16970606853695673957843703370, −6.61336321418382467141739162368, −5.34216392398065583932203364259, −4.36544867130133885585811870202, −3.50397597573142819098099045350, −1.96595759283898213887532636994, −1.41123166081409293411567953934,
1.47483832602227039304648821405, 3.29061187106906006373359409763, 4.05059036568680158179108688892, 4.81821699422194481113673298727, 5.88526795394336365702027705385, 6.85164382955672137152257095800, 7.60619945614018153056356869345, 8.708769626162057522615074803112, 9.234328811828112258183545514316, 9.912988399368212399420982013094