L(s) = 1 | + (−1.38 + 0.262i)2-s + (1.86 − 0.730i)4-s + (−1.64 − 1.51i)5-s + (1.86 + 1.86i)7-s + (−2.39 + 1.50i)8-s + (2.68 + 1.67i)10-s + (1.78 + 2.45i)11-s + (−0.962 − 6.07i)13-s + (−3.07 − 2.09i)14-s + (2.93 − 2.72i)16-s + (0.217 + 0.110i)17-s + (2.00 + 6.17i)19-s + (−4.17 − 1.61i)20-s + (−3.12 − 2.94i)22-s + (0.523 − 3.30i)23-s + ⋯ |
L(s) = 1 | + (−0.982 + 0.185i)2-s + (0.930 − 0.365i)4-s + (−0.735 − 0.676i)5-s + (0.704 + 0.704i)7-s + (−0.846 + 0.532i)8-s + (0.849 + 0.528i)10-s + (0.537 + 0.739i)11-s + (−0.266 − 1.68i)13-s + (−0.823 − 0.561i)14-s + (0.732 − 0.680i)16-s + (0.0526 + 0.0268i)17-s + (0.460 + 1.41i)19-s + (−0.932 − 0.361i)20-s + (−0.665 − 0.627i)22-s + (0.109 − 0.688i)23-s + ⋯ |
Λ(s)=(=(900s/2ΓC(s)L(s)(0.998+0.0451i)Λ(2−s)
Λ(s)=(=(900s/2ΓC(s+1/2)L(s)(0.998+0.0451i)Λ(1−s)
Degree: |
2 |
Conductor: |
900
= 22⋅32⋅52
|
Sign: |
0.998+0.0451i
|
Analytic conductor: |
7.18653 |
Root analytic conductor: |
2.68077 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ900(523,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 900, ( :1/2), 0.998+0.0451i)
|
Particular Values
L(1) |
≈ |
0.966271−0.0218157i |
L(21) |
≈ |
0.966271−0.0218157i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(1.38−0.262i)T |
| 3 | 1 |
| 5 | 1+(1.64+1.51i)T |
good | 7 | 1+(−1.86−1.86i)T+7iT2 |
| 11 | 1+(−1.78−2.45i)T+(−3.39+10.4i)T2 |
| 13 | 1+(0.962+6.07i)T+(−12.3+4.01i)T2 |
| 17 | 1+(−0.217−0.110i)T+(9.99+13.7i)T2 |
| 19 | 1+(−2.00−6.17i)T+(−15.3+11.1i)T2 |
| 23 | 1+(−0.523+3.30i)T+(−21.8−7.10i)T2 |
| 29 | 1+(−2.54−0.827i)T+(23.4+17.0i)T2 |
| 31 | 1+(2.58−0.838i)T+(25.0−18.2i)T2 |
| 37 | 1+(−4.97+0.787i)T+(35.1−11.4i)T2 |
| 41 | 1+(1.92+1.39i)T+(12.6+38.9i)T2 |
| 43 | 1+(0.914−0.914i)T−43iT2 |
| 47 | 1+(−10.2+5.22i)T+(27.6−38.0i)T2 |
| 53 | 1+(−4.36+2.22i)T+(31.1−42.8i)T2 |
| 59 | 1+(−5.24−3.80i)T+(18.2+56.1i)T2 |
| 61 | 1+(−10.7+7.84i)T+(18.8−58.0i)T2 |
| 67 | 1+(−4.31+8.47i)T+(−39.3−54.2i)T2 |
| 71 | 1+(−2.81−0.914i)T+(57.4+41.7i)T2 |
| 73 | 1+(6.76+1.07i)T+(69.4+22.5i)T2 |
| 79 | 1+(2.50−7.72i)T+(−63.9−46.4i)T2 |
| 83 | 1+(−6.29−3.20i)T+(48.7+67.1i)T2 |
| 89 | 1+(−10.2−14.0i)T+(−27.5+84.6i)T2 |
| 97 | 1+(−1.60−3.15i)T+(−57.0+78.4i)T2 |
show more | |
show less | |
L(s)=p∏ j=1∏2(1−αj,pp−s)−1
Imaginary part of the first few zeros on the critical line
−10.03050908895239313108867585038, −9.134522851035322842342280892944, −8.248540773912681179183970386644, −7.944276123143210370927112719931, −6.99189272630317674236373177297, −5.68942089884464070319731025395, −5.07899706154149297901166404169, −3.64569919641303120007407370857, −2.23106252435629148023811563569, −0.910070674727749709971003436745,
0.956427664716119760589079567813, 2.42145382921263304647904302546, 3.63499176339953054024332661735, 4.52171399839902748116645647576, 6.17579442263768232579069355161, 7.15276497149678747534552984457, 7.40063292039675397122257441615, 8.563507848424284870647813093308, 9.176059349727462290902855834731, 10.14382577749952698812806513125