L(s) = 1 | − i·2-s + (2.31 + 2.31i)3-s − 4-s + (2.31 − 2.31i)6-s + (3.26 − 3.26i)7-s + i·8-s + 7.68i·9-s + (−1.82 + 1.82i)11-s + (−2.31 − 2.31i)12-s + 0.145·13-s + (−3.26 − 3.26i)14-s + 16-s + (3.31 + 2.45i)17-s + 7.68·18-s − 2.06i·19-s + ⋯ |
L(s) = 1 | − 0.707i·2-s + (1.33 + 1.33i)3-s − 0.5·4-s + (0.943 − 0.943i)6-s + (1.23 − 1.23i)7-s + 0.353i·8-s + 2.56i·9-s + (−0.551 + 0.551i)11-s + (−0.667 − 0.667i)12-s + 0.0404·13-s + (−0.873 − 0.873i)14-s + 0.250·16-s + (0.803 + 0.595i)17-s + 1.81·18-s − 0.472i·19-s + ⋯ |
Λ(s)=(=(850s/2ΓC(s)L(s)(0.963−0.266i)Λ(2−s)
Λ(s)=(=(850s/2ΓC(s+1/2)L(s)(0.963−0.266i)Λ(1−s)
Degree: |
2 |
Conductor: |
850
= 2⋅52⋅17
|
Sign: |
0.963−0.266i
|
Analytic conductor: |
6.78728 |
Root analytic conductor: |
2.60524 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ850(251,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 850, ( :1/2), 0.963−0.266i)
|
Particular Values
L(1) |
≈ |
2.54635+0.345233i |
L(21) |
≈ |
2.54635+0.345233i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+iT |
| 5 | 1 |
| 17 | 1+(−3.31−2.45i)T |
good | 3 | 1+(−2.31−2.31i)T+3iT2 |
| 7 | 1+(−3.26+3.26i)T−7iT2 |
| 11 | 1+(1.82−1.82i)T−11iT2 |
| 13 | 1−0.145T+13T2 |
| 19 | 1+2.06iT−19T2 |
| 23 | 1+(−3.41+3.41i)T−23iT2 |
| 29 | 1+(−2.10−2.10i)T+29iT2 |
| 31 | 1+(2.78+2.78i)T+31iT2 |
| 37 | 1+(−2.44−2.44i)T+37iT2 |
| 41 | 1+(5.53−5.53i)T−41iT2 |
| 43 | 1+0.622iT−43T2 |
| 47 | 1+8.47T+47T2 |
| 53 | 1+6.68iT−53T2 |
| 59 | 1−5.71iT−59T2 |
| 61 | 1+(−2.63+2.63i)T−61iT2 |
| 67 | 1+1.58T+67T2 |
| 71 | 1+(−1.83−1.83i)T+71iT2 |
| 73 | 1+(−5.82−5.82i)T+73iT2 |
| 79 | 1+(−3.29+3.29i)T−79iT2 |
| 83 | 1+8.91iT−83T2 |
| 89 | 1+15.9T+89T2 |
| 97 | 1+(12.5+12.5i)T+97iT2 |
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
−10.15976179752424282608791789004, −9.677802728409923846196669978714, −8.485439407081151665654407286568, −8.126907817065276586493589386143, −7.21662609269066891607117631893, −5.10505174051850921781931328043, −4.60803122990648269219789936444, −3.81117219140134024895014239570, −2.85681274026975509876065877358, −1.64082146433733557784162174913,
1.34157374814247450900026558976, 2.47034490802670404638749481459, 3.45120159183274146684320412711, 5.11777002247425183365249151999, 5.87466675140136841831611926738, 6.98238946568047282764662768809, 7.82829240219325790931736557960, 8.224638802041945354705203512479, 8.887940120268604737110526368303, 9.632777179800772761198634076360