L(s) = 1 | + (−1.38 + 0.295i)2-s + (−1.64 − 0.531i)3-s + (1.82 − 0.817i)4-s + (2.43 + 0.247i)6-s + (−2.08 + 3.61i)7-s + (−2.28 + 1.67i)8-s + (2.43 + 1.75i)9-s + (−3.22 + 5.57i)11-s + (−3.44 + 0.378i)12-s + (1.53 − 0.887i)13-s + (1.81 − 5.61i)14-s + (2.66 − 2.98i)16-s + 0.950·17-s + (−3.88 − 1.70i)18-s − 2.19i·19-s + ⋯ |
L(s) = 1 | + (−0.977 + 0.209i)2-s + (−0.951 − 0.306i)3-s + (0.912 − 0.408i)4-s + (0.994 + 0.101i)6-s + (−0.788 + 1.36i)7-s + (−0.806 + 0.590i)8-s + (0.811 + 0.584i)9-s + (−0.971 + 1.68i)11-s + (−0.994 + 0.109i)12-s + (0.426 − 0.246i)13-s + (0.485 − 1.49i)14-s + (0.665 − 0.746i)16-s + 0.230·17-s + (−0.915 − 0.401i)18-s − 0.503i·19-s + ⋯ |
Λ(s)=(=(900s/2ΓC(s)L(s)(−0.819+0.573i)Λ(2−s)
Λ(s)=(=(900s/2ΓC(s+1/2)L(s)(−0.819+0.573i)Λ(1−s)
Degree: |
2 |
Conductor: |
900
= 22⋅32⋅52
|
Sign: |
−0.819+0.573i
|
Analytic conductor: |
7.18653 |
Root analytic conductor: |
2.68077 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ900(299,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 900, ( :1/2), −0.819+0.573i)
|
Particular Values
L(1) |
≈ |
0.0227332−0.0721774i |
L(21) |
≈ |
0.0227332−0.0721774i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.38−0.295i)T |
| 3 | 1+(1.64+0.531i)T |
| 5 | 1 |
good | 7 | 1+(2.08−3.61i)T+(−3.5−6.06i)T2 |
| 11 | 1+(3.22−5.57i)T+(−5.5−9.52i)T2 |
| 13 | 1+(−1.53+0.887i)T+(6.5−11.2i)T2 |
| 17 | 1−0.950T+17T2 |
| 19 | 1+2.19iT−19T2 |
| 23 | 1+(−1.74+1.01i)T+(11.5−19.9i)T2 |
| 29 | 1+(5.65+3.26i)T+(14.5+25.1i)T2 |
| 31 | 1+(−2.46+1.42i)T+(15.5−26.8i)T2 |
| 37 | 1−5.83iT−37T2 |
| 41 | 1+(6.16−3.55i)T+(20.5−35.5i)T2 |
| 43 | 1+(−2.65+4.59i)T+(−21.5−37.2i)T2 |
| 47 | 1+(0.349+0.201i)T+(23.5+40.7i)T2 |
| 53 | 1+4.87T+53T2 |
| 59 | 1+(−1.34−2.32i)T+(−29.5+51.0i)T2 |
| 61 | 1+(2.04−3.54i)T+(−30.5−52.8i)T2 |
| 67 | 1+(5.44+9.43i)T+(−33.5+58.0i)T2 |
| 71 | 1+2.23T+71T2 |
| 73 | 1+1.74iT−73T2 |
| 79 | 1+(0.214+0.123i)T+(39.5+68.4i)T2 |
| 83 | 1+(10.1+5.83i)T+(41.5+71.8i)T2 |
| 89 | 1+6.13iT−89T2 |
| 97 | 1+(−15.7−9.08i)T+(48.5+84.0i)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
−10.36265773578019029178792621409, −9.853252984327107190919732442079, −9.064395312540465964366297951978, −7.994905009010870658175189302232, −7.21731104582358157175839459894, −6.39553639295459336010379023433, −5.64950169595843359210450618847, −4.83161989047987755089299683268, −2.80169313632431834242878374529, −1.83485039388050321110250940379,
0.06288348438562582030974291662, 1.14427857683208484313900950333, 3.20596671888702095242000964035, 3.87759972531138006674528060837, 5.48396599439314403067804666702, 6.26880400088140472775013522000, 7.09007382237209152218451003489, 7.88839247246327611809660087927, 8.935646905849912559751750184383, 9.830893479801243539900519193255