L(s) = 1 | + (0.973 + 0.230i)2-s + (1.70 + 0.290i)3-s + (0.893 + 0.448i)4-s + (0.537 − 0.721i)5-s + (1.59 + 0.676i)6-s + (−3.95 − 2.60i)7-s + (0.766 + 0.642i)8-s + (2.83 + 0.992i)9-s + (0.689 − 0.578i)10-s + (−4.21 + 0.492i)11-s + (1.39 + 1.02i)12-s + (−1.75 + 5.86i)13-s + (−3.24 − 3.44i)14-s + (1.12 − 1.07i)15-s + (0.597 + 0.802i)16-s + (−0.432 − 2.45i)17-s + ⋯ |
L(s) = 1 | + (0.688 + 0.163i)2-s + (0.985 + 0.167i)3-s + (0.446 + 0.224i)4-s + (0.240 − 0.322i)5-s + (0.650 + 0.276i)6-s + (−1.49 − 0.983i)7-s + (0.270 + 0.227i)8-s + (0.943 + 0.330i)9-s + (0.217 − 0.182i)10-s + (−1.26 + 0.148i)11-s + (0.402 + 0.296i)12-s + (−0.487 + 1.62i)13-s + (−0.868 − 0.920i)14-s + (0.291 − 0.277i)15-s + (0.149 + 0.200i)16-s + (−0.104 − 0.594i)17-s + ⋯ |
Λ(s)=(=(162s/2ΓC(s)L(s)(0.984−0.177i)Λ(2−s)
Λ(s)=(=(162s/2ΓC(s+1/2)L(s)(0.984−0.177i)Λ(1−s)
Degree: |
2 |
Conductor: |
162
= 2⋅34
|
Sign: |
0.984−0.177i
|
Analytic conductor: |
1.29357 |
Root analytic conductor: |
1.13735 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ162(97,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 162, ( :1/2), 0.984−0.177i)
|
Particular Values
L(1) |
≈ |
1.91919+0.171820i |
L(21) |
≈ |
1.91919+0.171820i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.973−0.230i)T |
| 3 | 1+(−1.70−0.290i)T |
good | 5 | 1+(−0.537+0.721i)T+(−1.43−4.78i)T2 |
| 7 | 1+(3.95+2.60i)T+(2.77+6.42i)T2 |
| 11 | 1+(4.21−0.492i)T+(10.7−2.53i)T2 |
| 13 | 1+(1.75−5.86i)T+(−10.8−7.14i)T2 |
| 17 | 1+(0.432+2.45i)T+(−15.9+5.81i)T2 |
| 19 | 1+(0.284−1.61i)T+(−17.8−6.49i)T2 |
| 23 | 1+(−6.35+4.17i)T+(9.10−21.1i)T2 |
| 29 | 1+(−2.09+2.21i)T+(−1.68−28.9i)T2 |
| 31 | 1+(0.107+1.84i)T+(−30.7+3.59i)T2 |
| 37 | 1+(8.42+3.06i)T+(28.3+23.7i)T2 |
| 41 | 1+(−5.04+1.19i)T+(36.6−18.4i)T2 |
| 43 | 1+(−1.06+2.46i)T+(−29.5−31.2i)T2 |
| 47 | 1+(−0.486+8.35i)T+(−46.6−5.45i)T2 |
| 53 | 1+(1.11+1.93i)T+(−26.5+45.8i)T2 |
| 59 | 1+(3.71+0.433i)T+(57.4+13.6i)T2 |
| 61 | 1+(−2.81+1.41i)T+(36.4−48.9i)T2 |
| 67 | 1+(−3.28−3.48i)T+(−3.89+66.8i)T2 |
| 71 | 1+(3.18−2.67i)T+(12.3−69.9i)T2 |
| 73 | 1+(−1.09−0.922i)T+(12.6+71.8i)T2 |
| 79 | 1+(5.03+1.19i)T+(70.5+35.4i)T2 |
| 83 | 1+(2.63+0.624i)T+(74.1+37.2i)T2 |
| 89 | 1+(−12.5−10.5i)T+(15.4+87.6i)T2 |
| 97 | 1+(−2.79−3.75i)T+(−27.8+92.9i)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
−13.19134611871119355281362995050, −12.39165404853972178686072889063, −10.71897108539107005664582091102, −9.802519275269370745863797597508, −8.923740243562694930650066007403, −7.35911102685172985824918700081, −6.76930066405254153411832754788, −4.95543185954429229297530967145, −3.80400254564471347820740126459, −2.54352155780279284700628637825,
2.76745412678928797247351510067, 3.10460446898260012657750010895, 5.20912162212214439184039484586, 6.34470074635749085602795074163, 7.54684454753043927427250536867, 8.777445811289761209946368885212, 9.922171153356912434171272250920, 10.63531137735042718010294738982, 12.52773176027738623641992322486, 12.79463850023032950976361596949