L(s) = 1 | + (−0.540 + 0.841i)2-s + (0.989 − 0.142i)3-s + (−0.415 − 0.909i)4-s + (−0.959 − 0.281i)5-s + (−0.415 + 0.909i)6-s + (0.654 − 0.755i)7-s + (0.989 + 0.142i)8-s + (0.959 − 0.281i)9-s + (0.755 − 0.654i)10-s + (−0.540 − 0.841i)11-s + (−0.540 − 0.841i)12-s + (0.654 + 0.755i)13-s + (0.281 + 0.959i)14-s + (−0.989 − 0.142i)15-s + (−0.654 + 0.755i)16-s + (−0.909 − 0.415i)17-s + ⋯ |
L(s) = 1 | + (−0.540 + 0.841i)2-s + (0.989 − 0.142i)3-s + (−0.415 − 0.909i)4-s + (−0.959 − 0.281i)5-s + (−0.415 + 0.909i)6-s + (0.654 − 0.755i)7-s + (0.989 + 0.142i)8-s + (0.959 − 0.281i)9-s + (0.755 − 0.654i)10-s + (−0.540 − 0.841i)11-s + (−0.540 − 0.841i)12-s + (0.654 + 0.755i)13-s + (0.281 + 0.959i)14-s + (−0.989 − 0.142i)15-s + (−0.654 + 0.755i)16-s + (−0.909 − 0.415i)17-s + ⋯ |
Λ(s)=(=(667s/2ΓR(s)L(s)(0.702−0.711i)Λ(1−s)
Λ(s)=(=(667s/2ΓR(s)L(s)(0.702−0.711i)Λ(1−s)
Degree: |
1 |
Conductor: |
667
= 23⋅29
|
Sign: |
0.702−0.711i
|
Analytic conductor: |
3.09753 |
Root analytic conductor: |
3.09753 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ667(534,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 667, (0: ), 0.702−0.711i)
|
Particular Values
L(21) |
≈ |
1.114087377−0.4657393425i |
L(21) |
≈ |
1.114087377−0.4657393425i |
L(1) |
≈ |
0.9903112962+0.008690875694i |
L(1) |
≈ |
0.9903112962+0.008690875694i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 23 | 1 |
| 29 | 1 |
good | 2 | 1+(−0.540+0.841i)T |
| 3 | 1+(0.989−0.142i)T |
| 5 | 1+(−0.959−0.281i)T |
| 7 | 1+(0.654−0.755i)T |
| 11 | 1+(−0.540−0.841i)T |
| 13 | 1+(0.654+0.755i)T |
| 17 | 1+(−0.909−0.415i)T |
| 19 | 1+(0.909−0.415i)T |
| 31 | 1+(−0.989−0.142i)T |
| 37 | 1+(−0.281−0.959i)T |
| 41 | 1+(−0.281+0.959i)T |
| 43 | 1+(−0.989+0.142i)T |
| 47 | 1−iT |
| 53 | 1+(0.654−0.755i)T |
| 59 | 1+(−0.654−0.755i)T |
| 61 | 1+(0.989+0.142i)T |
| 67 | 1+(0.841+0.540i)T |
| 71 | 1+(−0.841−0.540i)T |
| 73 | 1+(0.909−0.415i)T |
| 79 | 1+(−0.755+0.654i)T |
| 83 | 1+(0.959−0.281i)T |
| 89 | 1+(−0.989+0.142i)T |
| 97 | 1+(0.281−0.959i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−22.589320622409198857922189737656, −21.928240422510163809108464511513, −20.91417838033637271089706405103, −20.28647201549797471157671969671, −19.87010366068007559795011503135, −18.65445953334560433890378874129, −18.435366591421444105807710003068, −17.51503967600000424875358057840, −16.02801794646934940671669423815, −15.460618133013253318237375920571, −14.72371311366357193543692469137, −13.58819209268820554440178845010, −12.70071108027428822843715824088, −11.98595960476366305960973224593, −10.97362286798328176766419013865, −10.30222325567867677333479618457, −9.212023246640317948751565497570, −8.39837760195214796263792858949, −7.893748187175311641525206165304, −7.05936125476591835415699664885, −5.13277206950818913805403619527, −4.16253543588035120139748003121, −3.29695878877662779304533066634, −2.443614401467427197618948423655, −1.46033014886591656611354032619,
0.67323407430103334699519306812, 1.82556395280777123237296008555, 3.45196954339993945152735707328, 4.313350696458225872772450766160, 5.220040062786343499495283130442, 6.80418604113861164797546747433, 7.344272220988379809153225077046, 8.262871624415466715385274429506, 8.67793204445631387096931518863, 9.641744830144150611394602459858, 10.87986093812374640709099885383, 11.47860726508339884290537645210, 13.149847530007280012374913639741, 13.6889295740727019263484699071, 14.47090315459290516533659822221, 15.34394712588480718937441724150, 16.09102065350403280183937197611, 16.60482120195856162473149292463, 18.01284365140667520382152715805, 18.472165407980389065296758589440, 19.43502389078331230166458657580, 20.04407874231517654034106531303, 20.70294015236642828092463978844, 21.82718969577717817944853908365, 23.18925386291448121322305799901