L(s) = 1 | + (0.909 + 0.415i)3-s + (0.540 + 0.841i)7-s + (0.654 + 0.755i)9-s + (−0.142 + 0.989i)11-s + (0.540 − 0.841i)13-s + (−0.281 + 0.959i)17-s + (0.959 − 0.281i)19-s + (0.142 + 0.989i)21-s + (0.281 + 0.959i)27-s + (−0.959 − 0.281i)29-s + (−0.415 − 0.909i)31-s + (−0.540 + 0.841i)33-s + (0.755 − 0.654i)37-s + (0.841 − 0.540i)39-s + (−0.654 + 0.755i)41-s + ⋯ |
L(s) = 1 | + (0.909 + 0.415i)3-s + (0.540 + 0.841i)7-s + (0.654 + 0.755i)9-s + (−0.142 + 0.989i)11-s + (0.540 − 0.841i)13-s + (−0.281 + 0.959i)17-s + (0.959 − 0.281i)19-s + (0.142 + 0.989i)21-s + (0.281 + 0.959i)27-s + (−0.959 − 0.281i)29-s + (−0.415 − 0.909i)31-s + (−0.540 + 0.841i)33-s + (0.755 − 0.654i)37-s + (0.841 − 0.540i)39-s + (−0.654 + 0.755i)41-s + ⋯ |
Λ(s)=(=(920s/2ΓR(s)L(s)(0.276+0.961i)Λ(1−s)
Λ(s)=(=(920s/2ΓR(s)L(s)(0.276+0.961i)Λ(1−s)
Degree: |
1 |
Conductor: |
920
= 23⋅5⋅23
|
Sign: |
0.276+0.961i
|
Analytic conductor: |
4.27246 |
Root analytic conductor: |
4.27246 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ920(683,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 920, (0: ), 0.276+0.961i)
|
Particular Values
L(21) |
≈ |
1.793909025+1.351106112i |
L(21) |
≈ |
1.793909025+1.351106112i |
L(1) |
≈ |
1.466677188+0.5078856391i |
L(1) |
≈ |
1.466677188+0.5078856391i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 23 | 1 |
good | 3 | 1+(0.909+0.415i)T |
| 7 | 1+(0.540+0.841i)T |
| 11 | 1+(−0.142+0.989i)T |
| 13 | 1+(0.540−0.841i)T |
| 17 | 1+(−0.281+0.959i)T |
| 19 | 1+(0.959−0.281i)T |
| 29 | 1+(−0.959−0.281i)T |
| 31 | 1+(−0.415−0.909i)T |
| 37 | 1+(0.755−0.654i)T |
| 41 | 1+(−0.654+0.755i)T |
| 43 | 1+(0.909+0.415i)T |
| 47 | 1−iT |
| 53 | 1+(−0.540−0.841i)T |
| 59 | 1+(−0.841−0.540i)T |
| 61 | 1+(−0.415−0.909i)T |
| 67 | 1+(−0.989+0.142i)T |
| 71 | 1+(0.142+0.989i)T |
| 73 | 1+(−0.281−0.959i)T |
| 79 | 1+(0.841+0.540i)T |
| 83 | 1+(0.755−0.654i)T |
| 89 | 1+(−0.415+0.909i)T |
| 97 | 1+(0.755+0.654i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−21.49465932217547204510342916645, −20.747297579706414826017590541514, −20.24359727119216193555202456353, −19.41079026043855262084582921696, −18.45781076203359160523631290482, −18.150652523197135845815564130619, −16.84647920655242635729635086656, −16.19815392205733369513713131537, −15.270339488236272059380360202737, −14.130457846592803937141664228317, −13.89516820235116762930201980016, −13.22254407635936027796600919934, −11.999132052957877301378260364590, −11.2531341734570839953005872804, −10.33943158125301498721902928462, −9.21253216702008984261700309009, −8.67965739070328443173231496825, −7.60478726113721429837362626492, −7.13991109156406040572789425045, −6.03536724049604310752666034690, −4.813947742202994180329761003741, −3.7855391059529413584482566297, −3.08624045715004311112256698215, −1.8246684742316543208474005819, −0.937511104183572619123201558314,
1.56477551151466920285606448301, 2.37374260391729114209951926369, 3.349706835713283224352313001134, 4.35553758257124977454636176483, 5.21450103866311048427731440426, 6.17567215444127178383229302685, 7.67160974213303513335366514810, 7.94975501401511297276331143795, 9.09501817374698840386786467996, 9.603053210136638379053064393946, 10.65323468295295886343270520243, 11.42455607455268977364452228288, 12.66483072050728952782434305221, 13.122679746161307701950209427022, 14.25403574288948477865434307545, 15.044050343161128837195714494656, 15.37508201442439552868806082970, 16.25153573304112241768800481043, 17.467910328265810885853729357911, 18.15071079431482603473132455094, 18.89863913612703235054008110834, 19.88556972430603544756478126285, 20.49218787047570826422640151641, 21.08800967863263769932136818561, 22.027750795354639500408044038031