L(s) = 1 | + (−2.08 − 1.66i)2-s + (0.222 − 0.974i)3-s + (1.14 + 5.00i)4-s + (−0.847 − 2.06i)5-s + (−2.08 + 1.66i)6-s + (2.44 − 1.53i)7-s + (3.63 − 7.54i)8-s + (−0.900 − 0.433i)9-s + (−1.67 + 5.73i)10-s + (5.75 + 2.01i)11-s + 5.13·12-s + (5.07 + 1.77i)13-s + (−7.67 − 0.865i)14-s + (−2.20 + 0.366i)15-s + (−10.9 + 5.25i)16-s − 1.01i·17-s + ⋯ |
L(s) = 1 | + (−1.47 − 1.17i)2-s + (0.128 − 0.562i)3-s + (0.571 + 2.50i)4-s + (−0.379 − 0.925i)5-s + (−0.852 + 0.679i)6-s + (0.925 − 0.581i)7-s + (1.28 − 2.66i)8-s + (−0.300 − 0.144i)9-s + (−0.529 + 1.81i)10-s + (1.73 + 0.607i)11-s + 1.48·12-s + (1.40 + 0.492i)13-s + (−2.05 − 0.231i)14-s + (−0.569 + 0.0945i)15-s + (−2.72 + 1.31i)16-s − 0.246i·17-s + ⋯ |
Λ(s)=(=(435s/2ΓC(s)L(s)(−0.676+0.736i)Λ(2−s)
Λ(s)=(=(435s/2ΓC(s+1/2)L(s)(−0.676+0.736i)Λ(1−s)
Degree: |
2 |
Conductor: |
435
= 3⋅5⋅29
|
Sign: |
−0.676+0.736i
|
Analytic conductor: |
3.47349 |
Root analytic conductor: |
1.86373 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ435(247,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 435, ( :1/2), −0.676+0.736i)
|
Particular Values
L(1) |
≈ |
0.337799−0.769660i |
L(21) |
≈ |
0.337799−0.769660i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1+(−0.222+0.974i)T |
| 5 | 1+(0.847+2.06i)T |
| 29 | 1+(3.41+4.16i)T |
good | 2 | 1+(2.08+1.66i)T+(0.445+1.94i)T2 |
| 7 | 1+(−2.44+1.53i)T+(3.03−6.30i)T2 |
| 11 | 1+(−5.75−2.01i)T+(8.60+6.85i)T2 |
| 13 | 1+(−5.07−1.77i)T+(10.1+8.10i)T2 |
| 17 | 1+1.01iT−17T2 |
| 19 | 1+(−0.508−0.319i)T+(8.24+17.1i)T2 |
| 23 | 1+(−5.33−0.600i)T+(22.4+5.11i)T2 |
| 31 | 1+(−6.69+0.753i)T+(30.2−6.89i)T2 |
| 37 | 1+(2.41+1.16i)T+(23.0+28.9i)T2 |
| 41 | 1+(6.09−6.09i)T−41iT2 |
| 43 | 1+(6.57+8.24i)T+(−9.56+41.9i)T2 |
| 47 | 1+(6.94−3.34i)T+(29.3−36.7i)T2 |
| 53 | 1+(−0.344−3.05i)T+(−51.6+11.7i)T2 |
| 59 | 1−7.34iT−59T2 |
| 61 | 1+(0.588−0.369i)T+(26.4−54.9i)T2 |
| 67 | 1+(2.74−0.959i)T+(52.3−41.7i)T2 |
| 71 | 1+(0.234+0.486i)T+(−44.2+55.5i)T2 |
| 73 | 1+(−4.42+3.52i)T+(16.2−71.1i)T2 |
| 79 | 1+(1.59−0.558i)T+(61.7−49.2i)T2 |
| 83 | 1+(−2.95−1.85i)T+(36.0+74.7i)T2 |
| 89 | 1+(1.32+11.7i)T+(−86.7+19.8i)T2 |
| 97 | 1+(0.130+0.569i)T+(−87.3+42.0i)T2 |
show more | |
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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
−10.99877065323691766202805253149, −9.738668743525330571805875736755, −8.934314199299727533391801202851, −8.431707911991903820988028785361, −7.55130329006897372706751296496, −6.62955866136781156962087999665, −4.45828241763287052153386121838, −3.57012302284836541778241711647, −1.62102420853638248537544124704, −1.14005598311501528702387411409,
1.42941678427147307244596696210, 3.48800151802092460477035845316, 5.14746502317943757710848452808, 6.26986593718361710671783370246, 6.82447551355085537637320343260, 8.204846411898008576923084276594, 8.530574173602201844300389718136, 9.368828276884017160802107608821, 10.43442161789557722117965322691, 11.17870537299501751259765331099