L(s) = 1 | + (−0.365 − 0.930i)2-s + (−0.149 − 1.98i)3-s + (−0.733 + 0.680i)4-s + (−1.79 + 0.865i)6-s + (−0.433 + 0.900i)7-s + (0.900 + 0.433i)8-s + (−2.94 + 0.443i)9-s + (1.84 + 0.277i)11-s + (1.46 + 1.35i)12-s + (−0.455 + 0.571i)13-s + (0.997 + 0.0747i)14-s + (0.0747 − 0.997i)16-s + (0.955 − 0.294i)17-s + (1.48 + 2.57i)18-s + (1.85 + 0.728i)21-s + (−0.414 − 1.81i)22-s + ⋯ |
L(s) = 1 | + (−0.365 − 0.930i)2-s + (−0.149 − 1.98i)3-s + (−0.733 + 0.680i)4-s + (−1.79 + 0.865i)6-s + (−0.433 + 0.900i)7-s + (0.900 + 0.433i)8-s + (−2.94 + 0.443i)9-s + (1.84 + 0.277i)11-s + (1.46 + 1.35i)12-s + (−0.455 + 0.571i)13-s + (0.997 + 0.0747i)14-s + (0.0747 − 0.997i)16-s + (0.955 − 0.294i)17-s + (1.48 + 2.57i)18-s + (1.85 + 0.728i)21-s + (−0.414 − 1.81i)22-s + ⋯ |
Λ(s)=(=(3332s/2ΓC(s)L(s)(−0.481+0.876i)Λ(1−s)
Λ(s)=(=(3332s/2ΓC(s)L(s)(−0.481+0.876i)Λ(1−s)
Degree: |
2 |
Conductor: |
3332
= 22⋅72⋅17
|
Sign: |
−0.481+0.876i
|
Analytic conductor: |
1.66288 |
Root analytic conductor: |
1.28952 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ3332(2515,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 3332, ( :0), −0.481+0.876i)
|
Particular Values
L(21) |
≈ |
0.9249834998 |
L(21) |
≈ |
0.9249834998 |
L(1) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.365+0.930i)T |
| 7 | 1+(0.433−0.900i)T |
| 17 | 1+(−0.955+0.294i)T |
good | 3 | 1+(0.149+1.98i)T+(−0.988+0.149i)T2 |
| 5 | 1+(−0.365+0.930i)T2 |
| 11 | 1+(−1.84−0.277i)T+(0.955+0.294i)T2 |
| 13 | 1+(0.455−0.571i)T+(−0.222−0.974i)T2 |
| 19 | 1+(0.5+0.866i)T2 |
| 23 | 1+(−1.49−0.460i)T+(0.826+0.563i)T2 |
| 29 | 1+(0.900+0.433i)T2 |
| 31 | 1+(−0.433−0.751i)T+(−0.5+0.866i)T2 |
| 37 | 1+(−0.0747−0.997i)T2 |
| 41 | 1+(−0.623−0.781i)T2 |
| 43 | 1+(−0.623+0.781i)T2 |
| 47 | 1+(0.733−0.680i)T2 |
| 53 | 1+(1.21−1.12i)T+(0.0747−0.997i)T2 |
| 59 | 1+(−0.365−0.930i)T2 |
| 61 | 1+(−0.0747−0.997i)T2 |
| 67 | 1+(0.5−0.866i)T2 |
| 71 | 1+(−0.250−1.09i)T+(−0.900+0.433i)T2 |
| 73 | 1+(0.733+0.680i)T2 |
| 79 | 1+(−0.149+0.258i)T+(−0.5−0.866i)T2 |
| 83 | 1+(0.222−0.974i)T2 |
| 89 | 1+(−0.147+0.0222i)T+(0.955−0.294i)T2 |
| 97 | 1−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
−8.754544724297870351345490955772, −7.84738728630060470723852843624, −7.02651647684643329954788268327, −6.60972766400120352272251827049, −5.70803714724611779299667061271, −4.74191036026273193172260542667, −3.31606604418325077881974066859, −2.69026325392106622771774940414, −1.71231673097765192992542225312, −1.03774895530056787745488036532,
0.884543582747539532695854431845, 3.27379726588034037706103030928, 3.72050301161578072520764466380, 4.57284103610135599657559904490, 5.14783706370095813021331311642, 6.05739409530682606607523932561, 6.63020090545962215425442197434, 7.63924988433357425389075627848, 8.556485924309393959996671871375, 9.191474060021538723185689281640