L(s) = 1 | + (0.222 − 0.974i)2-s + (−0.900 − 0.433i)4-s + (−0.110 + 0.482i)5-s + (−2.82 + 1.36i)7-s + (−0.623 + 0.781i)8-s + (0.445 + 0.214i)10-s + (−0.870 − 1.09i)11-s + (−3.56 − 4.46i)13-s + (0.698 + 3.05i)14-s + (0.623 + 0.781i)16-s − 5.31·17-s + (−4.47 − 2.15i)19-s + (0.308 − 0.386i)20-s + (−1.25 + 0.606i)22-s + (−0.181 − 0.793i)23-s + ⋯ |
L(s) = 1 | + (0.157 − 0.689i)2-s + (−0.450 − 0.216i)4-s + (−0.0492 + 0.215i)5-s + (−1.06 + 0.514i)7-s + (−0.220 + 0.276i)8-s + (0.140 + 0.0678i)10-s + (−0.262 − 0.329i)11-s + (−0.988 − 1.23i)13-s + (0.186 + 0.817i)14-s + (0.155 + 0.195i)16-s − 1.28·17-s + (−1.02 − 0.494i)19-s + (0.0689 − 0.0864i)20-s + (−0.268 + 0.129i)22-s + (−0.0377 − 0.165i)23-s + ⋯ |
Λ(s)=(=(522s/2ΓC(s)L(s)(−0.905−0.423i)Λ(2−s)
Λ(s)=(=(522s/2ΓC(s+1/2)L(s)(−0.905−0.423i)Λ(1−s)
Degree: |
2 |
Conductor: |
522
= 2⋅32⋅29
|
Sign: |
−0.905−0.423i
|
Analytic conductor: |
4.16819 |
Root analytic conductor: |
2.04161 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ522(199,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 522, ( :1/2), −0.905−0.423i)
|
Particular Values
L(1) |
≈ |
0.0484768+0.218208i |
L(21) |
≈ |
0.0484768+0.218208i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.222+0.974i)T |
| 3 | 1 |
| 29 | 1+(5.38−0.0414i)T |
good | 5 | 1+(0.110−0.482i)T+(−4.50−2.16i)T2 |
| 7 | 1+(2.82−1.36i)T+(4.36−5.47i)T2 |
| 11 | 1+(0.870+1.09i)T+(−2.44+10.7i)T2 |
| 13 | 1+(3.56+4.46i)T+(−2.89+12.6i)T2 |
| 17 | 1+5.31T+17T2 |
| 19 | 1+(4.47+2.15i)T+(11.8+14.8i)T2 |
| 23 | 1+(0.181+0.793i)T+(−20.7+9.97i)T2 |
| 31 | 1+(1.41−6.20i)T+(−27.9−13.4i)T2 |
| 37 | 1+(−5.56+6.97i)T+(−8.23−36.0i)T2 |
| 41 | 1−4.01T+41T2 |
| 43 | 1+(−0.310−1.36i)T+(−38.7+18.6i)T2 |
| 47 | 1+(−6.42−8.05i)T+(−10.4+45.8i)T2 |
| 53 | 1+(−0.944+4.13i)T+(−47.7−22.9i)T2 |
| 59 | 1+11.1T+59T2 |
| 61 | 1+(4.38−2.11i)T+(38.0−47.6i)T2 |
| 67 | 1+(−4.45+5.58i)T+(−14.9−65.3i)T2 |
| 71 | 1+(3.76+4.72i)T+(−15.7+69.2i)T2 |
| 73 | 1+(2.73+11.9i)T+(−65.7+31.6i)T2 |
| 79 | 1+(5.86−7.35i)T+(−17.5−77.0i)T2 |
| 83 | 1+(−11.4−5.51i)T+(51.7+64.8i)T2 |
| 89 | 1+(−0.398+1.74i)T+(−80.1−38.6i)T2 |
| 97 | 1+(3.42+1.64i)T+(60.4+75.8i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.71587912225879834247094726678, −9.435550884786242042487610187577, −8.952882992718297403858396311560, −7.69111753651128390067772431282, −6.56650057541530579645271122287, −5.62044833438314532497024401419, −4.51123322372680052612577950311, −3.14736503818121022309888496059, −2.43174931719043622804303630478, −0.11469088845825167069727013470,
2.37233655266475913954876742828, 4.00735830828999201012627153299, 4.65004033058177301051120052051, 6.07938331748716522764141869595, 6.81246586935018057291091831924, 7.53207468492190732353879145972, 8.773794919880636393677592204241, 9.467859598669375575608209325789, 10.28537491651074004640096240601, 11.40807592521721833379575859043