L(s) = 1 | + (−0.120 + 1.14i)2-s + (0.662 + 0.140i)4-s + (−0.408 − 3.88i)5-s + (3.06 − 3.40i)7-s + (−0.951 + 2.92i)8-s + 4.49·10-s + (−3.04 + 1.32i)11-s + (−0.533 + 0.237i)13-s + (3.53 + 3.92i)14-s + (−1.99 − 0.889i)16-s + (1.01 − 0.736i)17-s + (−0.681 + 2.09i)19-s + (0.276 − 2.63i)20-s + (−1.15 − 3.63i)22-s + (3.65 − 6.32i)23-s + ⋯ |
L(s) = 1 | + (−0.0850 + 0.808i)2-s + (0.331 + 0.0704i)4-s + (−0.182 − 1.73i)5-s + (1.16 − 1.28i)7-s + (−0.336 + 1.03i)8-s + 1.42·10-s + (−0.916 + 0.399i)11-s + (−0.147 + 0.0658i)13-s + (0.943 + 1.04i)14-s + (−0.499 − 0.222i)16-s + (0.245 − 0.178i)17-s + (−0.156 + 0.481i)19-s + (0.0619 − 0.589i)20-s + (−0.245 − 0.775i)22-s + (0.761 − 1.31i)23-s + ⋯ |
Λ(s)=(=(891s/2ΓC(s)L(s)(0.797+0.602i)Λ(2−s)
Λ(s)=(=(891s/2ΓC(s+1/2)L(s)(0.797+0.602i)Λ(1−s)
Degree: |
2 |
Conductor: |
891
= 34⋅11
|
Sign: |
0.797+0.602i
|
Analytic conductor: |
7.11467 |
Root analytic conductor: |
2.66733 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ891(433,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 891, ( :1/2), 0.797+0.602i)
|
Particular Values
L(1) |
≈ |
1.60681−0.538839i |
L(21) |
≈ |
1.60681−0.538839i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 11 | 1+(3.04−1.32i)T |
good | 2 | 1+(0.120−1.14i)T+(−1.95−0.415i)T2 |
| 5 | 1+(0.408+3.88i)T+(−4.89+1.03i)T2 |
| 7 | 1+(−3.06+3.40i)T+(−0.731−6.96i)T2 |
| 13 | 1+(0.533−0.237i)T+(8.69−9.66i)T2 |
| 17 | 1+(−1.01+0.736i)T+(5.25−16.1i)T2 |
| 19 | 1+(0.681−2.09i)T+(−15.3−11.1i)T2 |
| 23 | 1+(−3.65+6.32i)T+(−11.5−19.9i)T2 |
| 29 | 1+(−0.832+0.924i)T+(−3.03−28.8i)T2 |
| 31 | 1+(−7.92+3.52i)T+(20.7−23.0i)T2 |
| 37 | 1+(2.36+7.26i)T+(−29.9+21.7i)T2 |
| 41 | 1+(1.10+1.22i)T+(−4.28+40.7i)T2 |
| 43 | 1+(2.89+5.01i)T+(−21.5+37.2i)T2 |
| 47 | 1+(0.516−0.109i)T+(42.9−19.1i)T2 |
| 53 | 1+(1.07+0.782i)T+(16.3+50.4i)T2 |
| 59 | 1+(0.543+0.115i)T+(53.8+23.9i)T2 |
| 61 | 1+(−10.2−4.55i)T+(40.8+45.3i)T2 |
| 67 | 1+(3.73−6.46i)T+(−33.5−58.0i)T2 |
| 71 | 1+(−4.14+3.00i)T+(21.9−67.5i)T2 |
| 73 | 1+(−0.117−0.361i)T+(−59.0+42.9i)T2 |
| 79 | 1+(1.42−13.5i)T+(−77.2−16.4i)T2 |
| 83 | 1+(−0.912−0.406i)T+(55.5+61.6i)T2 |
| 89 | 1−3.33T+89T2 |
| 97 | 1+(1.64−15.6i)T+(−94.8−20.1i)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
−10.04786092611326164043988473712, −8.763052374080551201244359445474, −8.158311193521608164421331967942, −7.69321922819917590812101720809, −6.81976160819412178079430825706, −5.45505434194267567824241007910, −4.88289187216579821036327320991, −4.13495362934067372893914568036, −2.18920080349328549357891927547, −0.840337189161243563326908813157,
1.76830143833905369756116534044, 2.81870094865350572881589750434, 3.17749633794413612679445715085, 4.91377145411466062937528497666, 5.93863188774478899874855599763, 6.78881280794298169673014002806, 7.69113504935028577293387514964, 8.497434035106849201232143485131, 9.734081451471609600685279907171, 10.43038561129589446867503529082