L(s) = 1 | + (−1.38 + 0.305i)2-s + (1.81 − 0.844i)4-s − 1.41i·7-s + (−2.24 + 1.71i)8-s + 0.191i·11-s − 2.63i·13-s + (0.432 + 1.95i)14-s + (2.57 − 3.06i)16-s + 6.20i·17-s − 1.52·19-s + (−0.0585 − 0.264i)22-s + 5.25·23-s + (0.806 + 3.64i)26-s + (−1.19 − 2.56i)28-s − 0.270·29-s + ⋯ |
L(s) = 1 | + (−0.976 + 0.216i)2-s + (0.906 − 0.422i)4-s − 0.534i·7-s + (−0.793 + 0.608i)8-s + 0.0577i·11-s − 0.731i·13-s + (0.115 + 0.521i)14-s + (0.643 − 0.765i)16-s + 1.50i·17-s − 0.349·19-s + (−0.0124 − 0.0563i)22-s + 1.09·23-s + (0.158 + 0.714i)26-s + (−0.225 − 0.484i)28-s − 0.0502·29-s + ⋯ |
Λ(s)=(=(1800s/2ΓC(s)L(s)(0.954+0.297i)Λ(2−s)
Λ(s)=(=(1800s/2ΓC(s+1/2)L(s)(0.954+0.297i)Λ(1−s)
Degree: |
2 |
Conductor: |
1800
= 23⋅32⋅52
|
Sign: |
0.954+0.297i
|
Analytic conductor: |
14.3730 |
Root analytic conductor: |
3.79118 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1800(251,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1800, ( :1/2), 0.954+0.297i)
|
Particular Values
L(1) |
≈ |
1.058716574 |
L(21) |
≈ |
1.058716574 |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.38−0.305i)T |
| 3 | 1 |
| 5 | 1 |
good | 7 | 1+1.41iT−7T2 |
| 11 | 1−0.191iT−11T2 |
| 13 | 1+2.63iT−13T2 |
| 17 | 1−6.20iT−17T2 |
| 19 | 1+1.52T+19T2 |
| 23 | 1−5.25T+23T2 |
| 29 | 1+0.270T+29T2 |
| 31 | 1−6.20iT−31T2 |
| 37 | 1+7.61iT−37T2 |
| 41 | 1+9.22iT−41T2 |
| 43 | 1−12.7T+43T2 |
| 47 | 1+3.79T+47T2 |
| 53 | 1−8.77T+53T2 |
| 59 | 1−10.4iT−59T2 |
| 61 | 1+0.382iT−61T2 |
| 67 | 1+1.72T+67T2 |
| 71 | 1+9.72T+71T2 |
| 73 | 1−5.45T+73T2 |
| 79 | 1+14.3iT−79T2 |
| 83 | 1+15.2iT−83T2 |
| 89 | 1+3.56iT−89T2 |
| 97 | 1+7.31T+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
−8.906208235403378820946964114598, −8.714305705600110987858196407511, −7.54081616340834718696273838092, −7.20230832698193488416180677730, −6.10947526156611301792449766726, −5.49724362420598410412853268554, −4.20072494481432589299795844667, −3.12704117521793972498201720410, −1.93302806043394279273300634174, −0.73332656158974230656505223619,
0.913408531030874371717806414364, 2.28394101357306519360971580781, 2.98919996431091715463861459722, 4.27375885373632938695910722368, 5.36009155388023317818321265896, 6.38934339636538907592208870346, 7.04516604477080666824923618472, 7.85099736576917650745274683535, 8.681480567114023326118374284944, 9.372034202460861425007610273112