L(s) = 1 | + 2.23i·3-s − 4.47i·7-s − 2.00·9-s − 2.23·11-s − 4i·13-s − 7i·17-s − 6.70·19-s + 10.0·21-s − 4.47i·23-s + 2.23i·27-s − 4.47·31-s − 5.00i·33-s + 2i·37-s + 8.94·39-s + 5·41-s + ⋯ |
L(s) = 1 | + 1.29i·3-s − 1.69i·7-s − 0.666·9-s − 0.674·11-s − 1.10i·13-s − 1.69i·17-s − 1.53·19-s + 2.18·21-s − 0.932i·23-s + 0.430i·27-s − 0.803·31-s − 0.870i·33-s + 0.328i·37-s + 1.43·39-s + 0.780·41-s + ⋯ |
Λ(s)=(=(800s/2ΓC(s)L(s)(0.447+0.894i)Λ(2−s)
Λ(s)=(=(800s/2ΓC(s+1/2)L(s)(0.447+0.894i)Λ(1−s)
Degree: |
2 |
Conductor: |
800
= 25⋅52
|
Sign: |
0.447+0.894i
|
Analytic conductor: |
6.38803 |
Root analytic conductor: |
2.52745 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ800(449,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 800, ( :1/2), 0.447+0.894i)
|
Particular Values
L(1) |
≈ |
0.891694−0.551097i |
L(21) |
≈ |
0.891694−0.551097i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
good | 3 | 1−2.23iT−3T2 |
| 7 | 1+4.47iT−7T2 |
| 11 | 1+2.23T+11T2 |
| 13 | 1+4iT−13T2 |
| 17 | 1+7iT−17T2 |
| 19 | 1+6.70T+19T2 |
| 23 | 1+4.47iT−23T2 |
| 29 | 1+29T2 |
| 31 | 1+4.47T+31T2 |
| 37 | 1−2iT−37T2 |
| 41 | 1−5T+41T2 |
| 43 | 1−43T2 |
| 47 | 1−8.94iT−47T2 |
| 53 | 1+6iT−53T2 |
| 59 | 1−8.94T+59T2 |
| 61 | 1−10T+61T2 |
| 67 | 1−2.23iT−67T2 |
| 71 | 1−8.94T+71T2 |
| 73 | 1−9iT−73T2 |
| 79 | 1+4.47T+79T2 |
| 83 | 1+11.1iT−83T2 |
| 89 | 1−5T+89T2 |
| 97 | 1−2iT−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
−10.22126893401987219877113284521, −9.584141881149224723783467051629, −8.469176036014149012714456319255, −7.56745687713949154328048309048, −6.74252003028005576873378520665, −5.34854868382741696583165440957, −4.57272530213011923377055113525, −3.85967026668060147693194313413, −2.75877629512651577296731893493, −0.50057434318881295746733251681,
1.85793490824930887371118267577, 2.30465757592091406978958476340, 3.95401355288388500054661419207, 5.41618953321174318252451866652, 6.13917781042818966015678213445, 6.84081540251077787635520578612, 7.971796019656869401796858542685, 8.552610306597801414122356193401, 9.305065441663806047337678323255, 10.53520457198126335357522580774