L(s) = 1 | + (0.893 + 1.09i)2-s + (2.27 − 0.737i)3-s + (−0.402 + 1.95i)4-s + (−0.809 − 0.587i)5-s + (2.83 + 1.82i)6-s + (0.461 − 1.42i)7-s + (−2.50 + 1.30i)8-s + (2.18 − 1.58i)9-s + (−0.0788 − 1.41i)10-s + (1.72 + 2.83i)11-s + (0.531 + 4.74i)12-s + (−1.61 − 2.22i)13-s + (1.97 − 0.764i)14-s + (−2.27 − 0.737i)15-s + (−3.67 − 1.57i)16-s + (−3.56 + 4.90i)17-s + ⋯ |
L(s) = 1 | + (0.631 + 0.774i)2-s + (1.31 − 0.425i)3-s + (−0.201 + 0.979i)4-s + (−0.361 − 0.262i)5-s + (1.15 + 0.746i)6-s + (0.174 − 0.537i)7-s + (−0.886 + 0.463i)8-s + (0.728 − 0.529i)9-s + (−0.0249 − 0.446i)10-s + (0.519 + 0.854i)11-s + (0.153 + 1.36i)12-s + (−0.447 − 0.616i)13-s + (0.526 − 0.204i)14-s + (−0.586 − 0.190i)15-s + (−0.919 − 0.394i)16-s + (−0.863 + 1.18i)17-s + ⋯ |
Λ(s)=(=(220s/2ΓC(s)L(s)(0.746−0.665i)Λ(2−s)
Λ(s)=(=(220s/2ΓC(s+1/2)L(s)(0.746−0.665i)Λ(1−s)
Degree: |
2 |
Conductor: |
220
= 22⋅5⋅11
|
Sign: |
0.746−0.665i
|
Analytic conductor: |
1.75670 |
Root analytic conductor: |
1.32540 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ220(151,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 220, ( :1/2), 0.746−0.665i)
|
Particular Values
L(1) |
≈ |
2.01851+0.768486i |
L(21) |
≈ |
2.01851+0.768486i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.893−1.09i)T |
| 5 | 1+(0.809+0.587i)T |
| 11 | 1+(−1.72−2.83i)T |
good | 3 | 1+(−2.27+0.737i)T+(2.42−1.76i)T2 |
| 7 | 1+(−0.461+1.42i)T+(−5.66−4.11i)T2 |
| 13 | 1+(1.61+2.22i)T+(−4.01+12.3i)T2 |
| 17 | 1+(3.56−4.90i)T+(−5.25−16.1i)T2 |
| 19 | 1+(1.25+3.85i)T+(−15.3+11.1i)T2 |
| 23 | 1+7.20iT−23T2 |
| 29 | 1+(−1.78−0.578i)T+(23.4+17.0i)T2 |
| 31 | 1+(0.545+0.751i)T+(−9.57+29.4i)T2 |
| 37 | 1+(2.08−6.40i)T+(−29.9−21.7i)T2 |
| 41 | 1+(3.96−1.28i)T+(33.1−24.0i)T2 |
| 43 | 1+5.04T+43T2 |
| 47 | 1+(−8.50+2.76i)T+(38.0−27.6i)T2 |
| 53 | 1+(−6.02+4.37i)T+(16.3−50.4i)T2 |
| 59 | 1+(−11.1−3.63i)T+(47.7+34.6i)T2 |
| 61 | 1+(−1.84+2.53i)T+(−18.8−58.0i)T2 |
| 67 | 1+11.6iT−67T2 |
| 71 | 1+(7.69−10.5i)T+(−21.9−67.5i)T2 |
| 73 | 1+(7.42+2.41i)T+(59.0+42.9i)T2 |
| 79 | 1+(3.96−2.88i)T+(24.4−75.1i)T2 |
| 83 | 1+(−2.82−2.05i)T+(25.6+78.9i)T2 |
| 89 | 1−4.08T+89T2 |
| 97 | 1+(−12.0+8.75i)T+(29.9−92.2i)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
−12.87250293402601501564922460819, −11.86336410381016509867990708171, −10.35096565558050644678209629313, −8.853893103958396148266818526512, −8.375325644023398136072169008532, −7.35404997138492164983875170470, −6.60823978476092676391294750357, −4.77397112409260330968221995088, −3.85168176640926824190319936368, −2.41866844405229758441029428160,
2.19770431297163853221125012536, 3.32130574402360206839307107485, 4.22796137827155187892698610369, 5.65932232363909633408555937214, 7.16747016770166219517407273424, 8.675812665762617874096793976444, 9.187161928373647135536523553349, 10.20325136289352966408789711045, 11.46930108813690124170895233197, 11.96029278129249837027573865131