L(s) = 1 | + (0.866 + 0.5i)2-s + (0.5 + 0.866i)4-s + (−0.965 − 0.258i)5-s + (0.965 − 0.258i)7-s + i·8-s + (−0.707 − 0.707i)10-s + (0.965 − 0.258i)11-s + (0.5 + 0.866i)13-s + (0.965 + 0.258i)14-s + (−0.5 + 0.866i)16-s + i·19-s + (−0.258 − 0.965i)20-s + (0.965 + 0.258i)22-s + (−0.258 + 0.965i)23-s + (0.866 + 0.5i)25-s + i·26-s + ⋯ |
L(s) = 1 | + (0.866 + 0.5i)2-s + (0.5 + 0.866i)4-s + (−0.965 − 0.258i)5-s + (0.965 − 0.258i)7-s + i·8-s + (−0.707 − 0.707i)10-s + (0.965 − 0.258i)11-s + (0.5 + 0.866i)13-s + (0.965 + 0.258i)14-s + (−0.5 + 0.866i)16-s + i·19-s + (−0.258 − 0.965i)20-s + (0.965 + 0.258i)22-s + (−0.258 + 0.965i)23-s + (0.866 + 0.5i)25-s + i·26-s + ⋯ |
Λ(s)=(=(153s/2ΓR(s+1)L(s)(0.133+0.991i)Λ(1−s)
Λ(s)=(=(153s/2ΓR(s+1)L(s)(0.133+0.991i)Λ(1−s)
Degree: |
1 |
Conductor: |
153
= 32⋅17
|
Sign: |
0.133+0.991i
|
Analytic conductor: |
16.4421 |
Root analytic conductor: |
16.4421 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ153(104,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 153, (1: ), 0.133+0.991i)
|
Particular Values
L(21) |
≈ |
2.212266218+1.934443494i |
L(21) |
≈ |
2.212266218+1.934443494i |
L(1) |
≈ |
1.620936543+0.7207802631i |
L(1) |
≈ |
1.620936543+0.7207802631i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 17 | 1 |
good | 2 | 1+(0.866+0.5i)T |
| 5 | 1+(−0.965−0.258i)T |
| 7 | 1+(0.965−0.258i)T |
| 11 | 1+(0.965−0.258i)T |
| 13 | 1+(0.5+0.866i)T |
| 19 | 1+iT |
| 23 | 1+(−0.258+0.965i)T |
| 29 | 1+(0.258+0.965i)T |
| 31 | 1+(−0.965−0.258i)T |
| 37 | 1+(0.707−0.707i)T |
| 41 | 1+(0.258−0.965i)T |
| 43 | 1+(0.866+0.5i)T |
| 47 | 1+(−0.5+0.866i)T |
| 53 | 1−iT |
| 59 | 1+(0.866−0.5i)T |
| 61 | 1+(0.965−0.258i)T |
| 67 | 1+(−0.5−0.866i)T |
| 71 | 1+(−0.707+0.707i)T |
| 73 | 1+(−0.707+0.707i)T |
| 79 | 1+(−0.965+0.258i)T |
| 83 | 1+(0.866+0.5i)T |
| 89 | 1+T |
| 97 | 1+(−0.258−0.965i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−27.79879663863715783887894097643, −26.86489281787507494010424200312, −25.25509623502611436525607620561, −24.36184073459540247515914319509, −23.51728123241874873390198374828, −22.589641639745033466068804590431, −21.79993957670440535113527325331, −20.5216718201839889224307415435, −19.924187426890430932003845449680, −18.83531363406225120079900979787, −17.75842006843718802214660967330, −16.16661287333566998382996772798, −15.0631082179336011853221162088, −14.59997900311599543653835682487, −13.24965903589167821202132970506, −12.03529990268774483222276887132, −11.39607860786312450875825484509, −10.45228504515983200150616680990, −8.80542535521314255906904474936, −7.501579288627620838848828563512, −6.23892357889258505652053277778, −4.81367818506680757380820608441, −3.92150926059061505608007007310, −2.57378017092832365170150701060, −0.941544432252174846541596478642,
1.57811761314141607038018843056, 3.65665658595157164399827898339, 4.28807041628245694974749295453, 5.615073648967271889409299597578, 7.00076322547200261611861619707, 7.94220192611283077665258609079, 8.9430365901961284818897905497, 11.128433035818366691190593735741, 11.65702159103913906331897808541, 12.73024935141601208901072241864, 14.17240858968253655051935182375, 14.630588642769430325310806469635, 15.98126738402049672616496530197, 16.63284577615338912319497342969, 17.78660676670954314860419795006, 19.251680267741497819801832496006, 20.33054450243347006833477507778, 21.17112183500569401665047788891, 22.22491038270832260302040843386, 23.3617690593912335574606300448, 23.92530307798550989904602110704, 24.75221821800092080021113774250, 25.888527472903000995198820240075, 27.09405859057722759998659092174, 27.65930762894801043299514850089