L(s) = 1 | + (−0.398 − 0.398i)2-s + (1.60 − 0.654i)3-s − 1.68i·4-s − 5-s + (−0.899 − 0.378i)6-s − 4.31·7-s + (−1.46 + 1.46i)8-s + (2.14 − 2.10i)9-s + (0.398 + 0.398i)10-s + (0.656 + 0.656i)11-s + (−1.10 − 2.69i)12-s − 2.82i·13-s + (1.72 + 1.72i)14-s + (−1.60 + 0.654i)15-s − 2.19·16-s + (−4.74 − 4.74i)17-s + ⋯ |
L(s) = 1 | + (−0.281 − 0.281i)2-s + (0.925 − 0.378i)3-s − 0.841i·4-s − 0.447·5-s + (−0.367 − 0.154i)6-s − 1.63·7-s + (−0.518 + 0.518i)8-s + (0.714 − 0.700i)9-s + (0.126 + 0.126i)10-s + (0.197 + 0.197i)11-s + (−0.318 − 0.778i)12-s − 0.782i·13-s + (0.459 + 0.459i)14-s + (−0.414 + 0.169i)15-s − 0.548·16-s + (−1.15 − 1.15i)17-s + ⋯ |
Λ(s)=(=(435s/2ΓC(s)L(s)(−0.907+0.419i)Λ(2−s)
Λ(s)=(=(435s/2ΓC(s+1/2)L(s)(−0.907+0.419i)Λ(1−s)
Degree: |
2 |
Conductor: |
435
= 3⋅5⋅29
|
Sign: |
−0.907+0.419i
|
Analytic conductor: |
3.47349 |
Root analytic conductor: |
1.86373 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ435(191,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 435, ( :1/2), −0.907+0.419i)
|
Particular Values
L(1) |
≈ |
0.206488−0.939530i |
L(21) |
≈ |
0.206488−0.939530i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(−1.60+0.654i)T |
| 5 | 1+T |
| 29 | 1+(−1.25−5.23i)T |
good | 2 | 1+(0.398+0.398i)T+2iT2 |
| 7 | 1+4.31T+7T2 |
| 11 | 1+(−0.656−0.656i)T+11iT2 |
| 13 | 1+2.82iT−13T2 |
| 17 | 1+(4.74+4.74i)T+17iT2 |
| 19 | 1+(−1.21+1.21i)T−19iT2 |
| 23 | 1+1.96iT−23T2 |
| 31 | 1+(−2.91+2.91i)T−31iT2 |
| 37 | 1+(−3.89−3.89i)T+37iT2 |
| 41 | 1+(2.91−2.91i)T−41iT2 |
| 43 | 1+(−4.82+4.82i)T−43iT2 |
| 47 | 1+(6.22−6.22i)T−47iT2 |
| 53 | 1+7.97iT−53T2 |
| 59 | 1+7.91iT−59T2 |
| 61 | 1+(−2.74+2.74i)T−61iT2 |
| 67 | 1+9.91iT−67T2 |
| 71 | 1−5.70T+71T2 |
| 73 | 1+(−6.98−6.98i)T+73iT2 |
| 79 | 1+(−3.13+3.13i)T−79iT2 |
| 83 | 1+13.0iT−83T2 |
| 89 | 1+(−10.5−10.5i)T+89iT2 |
| 97 | 1+(−8.43−8.43i)T+97iT2 |
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L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.54274565737729405946614624313, −9.586075396366748543401558962089, −9.264862823963704990858305669188, −8.169441458158182282392680641084, −6.88836444394377207711988958775, −6.39841912757927267486063808855, −4.83333617533309138276278790309, −3.34977790511709480759962802085, −2.48001595111949212245978587177, −0.57653764907458312612450611667,
2.56944487035404553322893166443, 3.64875092992432578470904675151, 4.20555639468303337190024256276, 6.28067519112364642074708171616, 7.01229647705078325842356520437, 8.009626494648711770495081116960, 8.870306130735585470384664323679, 9.413949458518641815189666863169, 10.35756335658400694111719373736, 11.59384941028493842808588311835