L(s) = 1 | + (−0.337 − 0.941i)2-s + (−0.637 − 0.770i)3-s + (−0.772 + 0.635i)4-s + (−0.741 + 0.670i)5-s + (−0.510 + 0.859i)6-s + (−0.570 − 0.821i)7-s + (0.858 + 0.512i)8-s + (−0.188 + 0.982i)9-s + (0.881 + 0.472i)10-s + (0.999 − 0.0393i)11-s + (0.981 + 0.190i)12-s + (0.867 + 0.497i)13-s + (−0.580 + 0.814i)14-s + (0.989 + 0.144i)15-s + (0.192 − 0.981i)16-s + (0.947 + 0.321i)17-s + ⋯ |
L(s) = 1 | + (−0.337 − 0.941i)2-s + (−0.637 − 0.770i)3-s + (−0.772 + 0.635i)4-s + (−0.741 + 0.670i)5-s + (−0.510 + 0.859i)6-s + (−0.570 − 0.821i)7-s + (0.858 + 0.512i)8-s + (−0.188 + 0.982i)9-s + (0.881 + 0.472i)10-s + (0.999 − 0.0393i)11-s + (0.981 + 0.190i)12-s + (0.867 + 0.497i)13-s + (−0.580 + 0.814i)14-s + (0.989 + 0.144i)15-s + (0.192 − 0.981i)16-s + (0.947 + 0.321i)17-s + ⋯ |
Λ(s)=(=(2557s/2ΓR(s+1)L(s)(−0.297−0.954i)Λ(1−s)
Λ(s)=(=(2557s/2ΓR(s+1)L(s)(−0.297−0.954i)Λ(1−s)
Degree: |
1 |
Conductor: |
2557
|
Sign: |
−0.297−0.954i
|
Analytic conductor: |
274.787 |
Root analytic conductor: |
274.787 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2557(78,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2557, (1: ), −0.297−0.954i)
|
Particular Values
L(21) |
≈ |
0.8044086381−1.093077132i |
L(21) |
≈ |
0.8044086381−1.093077132i |
L(1) |
≈ |
0.5873803487−0.4081111737i |
L(1) |
≈ |
0.5873803487−0.4081111737i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2557 | 1 |
good | 2 | 1+(−0.337−0.941i)T |
| 3 | 1+(−0.637−0.770i)T |
| 5 | 1+(−0.741+0.670i)T |
| 7 | 1+(−0.570−0.821i)T |
| 11 | 1+(0.999−0.0393i)T |
| 13 | 1+(0.867+0.497i)T |
| 17 | 1+(0.947+0.321i)T |
| 19 | 1+(0.202−0.979i)T |
| 23 | 1+(−0.578+0.815i)T |
| 29 | 1+(0.330−0.943i)T |
| 31 | 1+(0.994−0.105i)T |
| 37 | 1+(0.817−0.576i)T |
| 41 | 1+(0.560−0.828i)T |
| 43 | 1+(0.916−0.399i)T |
| 47 | 1+(−0.497−0.867i)T |
| 53 | 1+(0.525+0.850i)T |
| 59 | 1+(−0.529+0.848i)T |
| 61 | 1+(−0.787+0.616i)T |
| 67 | 1+(0.994+0.100i)T |
| 71 | 1+(0.478−0.878i)T |
| 73 | 1+(0.541+0.840i)T |
| 79 | 1+(0.467−0.883i)T |
| 83 | 1+(0.295−0.955i)T |
| 89 | 1+(0.882−0.469i)T |
| 97 | 1+(0.0515−0.998i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.318561408715562783555390671401, −18.51626709653053259590660682462, −17.97912388872301325495531069088, −16.98991505592642800623287928890, −16.39309632664700342020730363920, −16.09775013320268884716426141825, −15.445390913506892141269533132244, −14.70551430202397174939826498670, −14.08983438059346401562160408842, −12.7521000563024716639022655803, −12.333532237971758734732745673802, −11.53878688407728663623694648879, −10.647722665717380994782329585327, −9.63835991767327475893467354308, −9.390054399849074891214209333276, −8.36231895438381776389557713763, −8.01826286557689454791960472633, −6.62384191603226914003760670707, −6.16472871895847928520286539656, −5.43598285502016130934306280376, −4.685993400922121703083313144494, −3.88836768186830788154181758096, −3.20614587153284766505996563952, −1.24813576066025755995709667785, −0.65520208909955017303887440372,
0.59449746557562890739644874166, 0.99198484840582949565740950956, 2.11873145322191264144981261101, 3.11698221735581985385223126793, 3.91032981573309891985773147062, 4.41877371699100985806416318771, 5.85703962798614539929317739654, 6.571961612806886154235871642334, 7.40163970392398614794044998945, 7.85763236486868591710759374557, 8.87879545046304527582977118947, 9.7715661260712343251862999359, 10.60602625257569761605997429860, 11.1027913360583934575365194960, 11.907195112497814734037969683598, 12.1247635149052702832679091894, 13.304269599456432358860675376228, 13.72790313993820654866594192877, 14.38028002378510694255540667763, 15.7090231758426002854030595912, 16.40587721085373372020223353146, 17.16002229995333477480257079183, 17.64660331844894337718649335087, 18.56686550398657649004035841405, 19.030156062123462639269197278