L(s) = 1 | + (0.707 − 0.707i)2-s + (−0.292 − 1.70i)3-s − 1.00i·4-s + (−0.489 + 2.18i)5-s + (−1.41 − 0.999i)6-s + (−0.474 − 0.474i)7-s + (−0.707 − 0.707i)8-s + (−2.82 + i)9-s + (1.19 + 1.88i)10-s + 4.08i·11-s + (−1.70 + 0.292i)12-s + (−3.10 + 3.10i)13-s − 0.671·14-s + (3.86 + 0.196i)15-s − 1.00·16-s + (−4.06 + 4.06i)17-s + ⋯ |
L(s) = 1 | + (0.499 − 0.499i)2-s + (−0.169 − 0.985i)3-s − 0.500i·4-s + (−0.218 + 0.975i)5-s + (−0.577 − 0.408i)6-s + (−0.179 − 0.179i)7-s + (−0.250 − 0.250i)8-s + (−0.942 + 0.333i)9-s + (0.378 + 0.597i)10-s + 1.23i·11-s + (−0.492 + 0.0845i)12-s + (−0.861 + 0.861i)13-s − 0.179·14-s + (0.998 + 0.0507i)15-s − 0.250·16-s + (−0.985 + 0.985i)17-s + ⋯ |
Λ(s)=(=(930s/2ΓC(s)L(s)(0.278−0.960i)Λ(2−s)
Λ(s)=(=(930s/2ΓC(s+1/2)L(s)(0.278−0.960i)Λ(1−s)
Degree: |
2 |
Conductor: |
930
= 2⋅3⋅5⋅31
|
Sign: |
0.278−0.960i
|
Analytic conductor: |
7.42608 |
Root analytic conductor: |
2.72508 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ930(497,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 930, ( :1/2), 0.278−0.960i)
|
Particular Values
L(1) |
≈ |
0.571907+0.429457i |
L(21) |
≈ |
0.571907+0.429457i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.707+0.707i)T |
| 3 | 1+(0.292+1.70i)T |
| 5 | 1+(0.489−2.18i)T |
| 31 | 1−T |
good | 7 | 1+(0.474+0.474i)T+7iT2 |
| 11 | 1−4.08iT−11T2 |
| 13 | 1+(3.10−3.10i)T−13iT2 |
| 17 | 1+(4.06−4.06i)T−17iT2 |
| 19 | 1+1.57iT−19T2 |
| 23 | 1+(1.06+1.06i)T+23iT2 |
| 29 | 1+1.87T+29T2 |
| 37 | 1+(2+2i)T+37iT2 |
| 41 | 1−7.26iT−41T2 |
| 43 | 1+(−1.16+1.16i)T−43iT2 |
| 47 | 1+(0.520−0.520i)T−47iT2 |
| 53 | 1+(2.48+2.48i)T+53iT2 |
| 59 | 1−4.40T+59T2 |
| 61 | 1−11.2T+61T2 |
| 67 | 1+(5.37+5.37i)T+67iT2 |
| 71 | 1−4.42iT−71T2 |
| 73 | 1+(7.86−7.86i)T−73iT2 |
| 79 | 1−9.12iT−79T2 |
| 83 | 1+(8.35+8.35i)T+83iT2 |
| 89 | 1−5.69T+89T2 |
| 97 | 1+(−8.34−8.34i)T+97iT2 |
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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
−10.38065925707056542785814891930, −9.659762612144430905401963276751, −8.487295859475516452958426080178, −7.31777358561120146716565335177, −6.87030656021301716596957363684, −6.15008660348775559105891526187, −4.85071754308855974134270111697, −3.89459038795344976961591592598, −2.52876465515745990889822937007, −1.89743625596477068033474476882,
0.26941786097721548168154628210, 2.76425803474612312926511452961, 3.76251143522893554252333932214, 4.72621020712984179988137246974, 5.40680039015041144996047589666, 6.07305664488126583064772813964, 7.40902807999662342555545872806, 8.377404164023938352431786949111, 8.964227722967320513707883633321, 9.741226516539289495562994281776