L(s) = 1 | + (−0.459 + 0.413i)2-s + (−0.0646 + 0.614i)4-s + (−0.743 − 0.669i)5-s + (−0.309 + 0.535i)7-s + (−0.587 − 0.809i)8-s + 0.618·10-s + (0.743 − 0.669i)11-s + (−0.0794 − 0.373i)14-s + (0.587 + 0.809i)17-s + (0.809 − 0.587i)19-s + (0.459 − 0.413i)20-s + (−0.0646 + 0.614i)22-s + (0.207 + 0.978i)23-s + (0.104 + 0.994i)25-s + (−0.309 − 0.224i)28-s + (−0.658 − 1.47i)29-s + ⋯ |
L(s) = 1 | + (−0.459 + 0.413i)2-s + (−0.0646 + 0.614i)4-s + (−0.743 − 0.669i)5-s + (−0.309 + 0.535i)7-s + (−0.587 − 0.809i)8-s + 0.618·10-s + (0.743 − 0.669i)11-s + (−0.0794 − 0.373i)14-s + (0.587 + 0.809i)17-s + (0.809 − 0.587i)19-s + (0.459 − 0.413i)20-s + (−0.0646 + 0.614i)22-s + (0.207 + 0.978i)23-s + (0.104 + 0.994i)25-s + (−0.309 − 0.224i)28-s + (−0.658 − 1.47i)29-s + ⋯ |
Λ(s)=(=(2025s/2ΓC(s)L(s)(0.432−0.901i)Λ(1−s)
Λ(s)=(=(2025s/2ΓC(s)L(s)(0.432−0.901i)Λ(1−s)
Degree: |
2 |
Conductor: |
2025
= 34⋅52
|
Sign: |
0.432−0.901i
|
Analytic conductor: |
1.01060 |
Root analytic conductor: |
1.00528 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2025(1646,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 2025, ( :0), 0.432−0.901i)
|
Particular Values
L(21) |
≈ |
0.7478213715 |
L(21) |
≈ |
0.7478213715 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 5 | 1+(0.743+0.669i)T |
good | 2 | 1+(0.459−0.413i)T+(0.104−0.994i)T2 |
| 7 | 1+(0.309−0.535i)T+(−0.5−0.866i)T2 |
| 11 | 1+(−0.743+0.669i)T+(0.104−0.994i)T2 |
| 13 | 1+(−0.104−0.994i)T2 |
| 17 | 1+(−0.587−0.809i)T+(−0.309+0.951i)T2 |
| 19 | 1+(−0.809+0.587i)T+(0.309−0.951i)T2 |
| 23 | 1+(−0.207−0.978i)T+(−0.913+0.406i)T2 |
| 29 | 1+(0.658+1.47i)T+(−0.669+0.743i)T2 |
| 31 | 1+(0.669+0.743i)T2 |
| 37 | 1+(−0.5−1.53i)T+(−0.809+0.587i)T2 |
| 41 | 1+(−0.743−0.669i)T+(0.104+0.994i)T2 |
| 43 | 1+(−0.5−0.866i)T2 |
| 47 | 1+(−0.658−1.47i)T+(−0.669+0.743i)T2 |
| 53 | 1+(−0.363+0.5i)T+(−0.309−0.951i)T2 |
| 59 | 1+(0.104+0.994i)T2 |
| 61 | 1+(0.669+0.743i)T+(−0.104+0.994i)T2 |
| 67 | 1+(−0.564−0.251i)T+(0.669+0.743i)T2 |
| 71 | 1+(0.951−1.30i)T+(−0.309−0.951i)T2 |
| 73 | 1+(−0.809−0.587i)T2 |
| 79 | 1+(−1.47+0.658i)T+(0.669−0.743i)T2 |
| 83 | 1+(0.614−0.0646i)T+(0.978−0.207i)T2 |
| 89 | 1+(0.951+0.309i)T+(0.809+0.587i)T2 |
| 97 | 1+(−0.913+0.406i)T+(0.669−0.743i)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
−9.309244999148642232511590786198, −8.640408559550704426187333559223, −7.916721242263277598640020760354, −7.45592589382914959748508356035, −6.35029170978153427157918742635, −5.70154971532837151137747251170, −4.47770103010308932400639739405, −3.67245820294498941245492625176, −2.92867718632348906129502072146, −1.08400043211464697062822940920,
0.816459609364607724552658043149, 2.17808236767767896473866573445, 3.29215037107903319855970567139, 4.12540859854794156419175221802, 5.17789684325368895422988463833, 6.09412751138016942186837549920, 7.15489814993628706706910706983, 7.37993170183307506425902439429, 8.639428462234207713911909929002, 9.310114014570906467371382051734