L(s) = 1 | − 0.549i·2-s + (−1.68 − 0.420i)3-s + 1.69·4-s + 3.60·5-s + (−0.230 + 0.922i)6-s + (1.38 − 2.25i)7-s − 2.03i·8-s + (2.64 + 1.41i)9-s − 1.98i·10-s + 5.41i·11-s + (−2.85 − 0.714i)12-s − 1.72i·13-s + (−1.23 − 0.761i)14-s + (−6.06 − 1.51i)15-s + 2.28·16-s − 4.50·17-s + ⋯ |
L(s) = 1 | − 0.388i·2-s + (−0.970 − 0.242i)3-s + 0.849·4-s + 1.61·5-s + (−0.0942 + 0.376i)6-s + (0.524 − 0.851i)7-s − 0.717i·8-s + (0.882 + 0.471i)9-s − 0.626i·10-s + 1.63i·11-s + (−0.823 − 0.206i)12-s − 0.479i·13-s + (−0.330 − 0.203i)14-s + (−1.56 − 0.391i)15-s + 0.570·16-s − 1.09·17-s + ⋯ |
Λ(s)=(=(483s/2ΓC(s)L(s)(0.698+0.715i)Λ(2−s)
Λ(s)=(=(483s/2ΓC(s+1/2)L(s)(0.698+0.715i)Λ(1−s)
Degree: |
2 |
Conductor: |
483
= 3⋅7⋅23
|
Sign: |
0.698+0.715i
|
Analytic conductor: |
3.85677 |
Root analytic conductor: |
1.96386 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ483(461,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 483, ( :1/2), 0.698+0.715i)
|
Particular Values
L(1) |
≈ |
1.61601−0.680581i |
L(21) |
≈ |
1.61601−0.680581i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(1.68+0.420i)T |
| 7 | 1+(−1.38+2.25i)T |
| 23 | 1−iT |
good | 2 | 1+0.549iT−2T2 |
| 5 | 1−3.60T+5T2 |
| 11 | 1−5.41iT−11T2 |
| 13 | 1+1.72iT−13T2 |
| 17 | 1+4.50T+17T2 |
| 19 | 1−6.73iT−19T2 |
| 29 | 1+9.24iT−29T2 |
| 31 | 1−0.592iT−31T2 |
| 37 | 1+8.23T+37T2 |
| 41 | 1−6.44T+41T2 |
| 43 | 1+5.11T+43T2 |
| 47 | 1+2.58T+47T2 |
| 53 | 1−1.00iT−53T2 |
| 59 | 1+0.599T+59T2 |
| 61 | 1+6.29iT−61T2 |
| 67 | 1+0.526T+67T2 |
| 71 | 1+1.86iT−71T2 |
| 73 | 1−9.34iT−73T2 |
| 79 | 1−1.25T+79T2 |
| 83 | 1+11.0T+83T2 |
| 89 | 1+3.79T+89T2 |
| 97 | 1+2.14iT−97T2 |
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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
−10.73043192207660263130910269829, −10.11668044621392011721694380150, −9.744646979446037706933236367828, −7.85129628469602358437362851160, −6.96381681932576988818126219352, −6.27554956802020706666691415411, −5.33896641934297270985873842075, −4.20367892848128214176888641841, −2.14026669410574435975753370052, −1.54526339670181378802748391092,
1.63745797618162007873238832418, 2.82383610713710024731591953522, 4.97711383365327071270585020302, 5.59349208696769222275683787405, 6.35430491568380921826973145294, 6.92807928478217261991598769746, 8.675347529029794600985510146112, 9.165947636251288286736931909305, 10.52896569646446892798003414729, 11.05562974514670455376249964693