L(s) = 1 | + (−0.995 + 0.0950i)2-s + (0.723 − 0.690i)3-s + (0.981 − 0.189i)4-s + (0.888 + 0.458i)5-s + (−0.654 + 0.755i)6-s + (−0.959 + 0.281i)8-s + (0.0475 − 0.998i)9-s + (−0.928 − 0.371i)10-s + (0.995 + 0.0950i)11-s + (0.580 − 0.814i)12-s + (−0.142 − 0.989i)13-s + (0.959 − 0.281i)15-s + (0.928 − 0.371i)16-s + (0.327 + 0.945i)17-s + (0.0475 + 0.998i)18-s + (0.327 − 0.945i)19-s + ⋯ |
L(s) = 1 | + (−0.995 + 0.0950i)2-s + (0.723 − 0.690i)3-s + (0.981 − 0.189i)4-s + (0.888 + 0.458i)5-s + (−0.654 + 0.755i)6-s + (−0.959 + 0.281i)8-s + (0.0475 − 0.998i)9-s + (−0.928 − 0.371i)10-s + (0.995 + 0.0950i)11-s + (0.580 − 0.814i)12-s + (−0.142 − 0.989i)13-s + (0.959 − 0.281i)15-s + (0.928 − 0.371i)16-s + (0.327 + 0.945i)17-s + (0.0475 + 0.998i)18-s + (0.327 − 0.945i)19-s + ⋯ |
Λ(s)=(=(161s/2ΓR(s+1)L(s)(0.714−0.700i)Λ(1−s)
Λ(s)=(=(161s/2ΓR(s+1)L(s)(0.714−0.700i)Λ(1−s)
Degree: |
1 |
Conductor: |
161
= 7⋅23
|
Sign: |
0.714−0.700i
|
Analytic conductor: |
17.3018 |
Root analytic conductor: |
17.3018 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ161(149,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 161, (1: ), 0.714−0.700i)
|
Particular Values
L(21) |
≈ |
1.757434518−0.7177625577i |
L(21) |
≈ |
1.757434518−0.7177625577i |
L(1) |
≈ |
1.127056423−0.2355427061i |
L(1) |
≈ |
1.127056423−0.2355427061i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 7 | 1 |
| 23 | 1 |
good | 2 | 1+(−0.995+0.0950i)T |
| 3 | 1+(0.723−0.690i)T |
| 5 | 1+(0.888+0.458i)T |
| 11 | 1+(0.995+0.0950i)T |
| 13 | 1+(−0.142−0.989i)T |
| 17 | 1+(0.327+0.945i)T |
| 19 | 1+(0.327−0.945i)T |
| 29 | 1+(−0.654+0.755i)T |
| 31 | 1+(0.235−0.971i)T |
| 37 | 1+(−0.0475+0.998i)T |
| 41 | 1+(0.841−0.540i)T |
| 43 | 1+(0.959+0.281i)T |
| 47 | 1+(−0.5−0.866i)T |
| 53 | 1+(0.786+0.618i)T |
| 59 | 1+(0.928+0.371i)T |
| 61 | 1+(−0.723−0.690i)T |
| 67 | 1+(−0.580−0.814i)T |
| 71 | 1+(0.415−0.909i)T |
| 73 | 1+(0.981−0.189i)T |
| 79 | 1+(0.786−0.618i)T |
| 83 | 1+(−0.841−0.540i)T |
| 89 | 1+(−0.235−0.971i)T |
| 97 | 1+(−0.841+0.540i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−27.521938007656970124525696873535, −26.75013283550055487776321703522, −25.82289495022643093181327949623, −24.97456355193785833411942111602, −24.45716768195814586789806513594, −22.48266787788252809287103326414, −21.287564012939897789243656375700, −20.86035400051187289923943489927, −19.78810324889828231754490081965, −18.94256138332123131616467356664, −17.72027198333294801307486656120, −16.59587568657614306243658725701, −16.172769805368290176325595837167, −14.61611529206196436541594059959, −13.89712273432921729989197174623, −12.30343259010455985401131428010, −11.10388948481505578685578134813, −9.72419347646108267954843841633, −9.40860510255548478016675150683, −8.3932490716367804485488112192, −7.05521847670317042362541526933, −5.65576012010816774821374044279, −4.03033751933920793132153489921, −2.52805097567221832350602757038, −1.36656509777211546382245901035,
1.022724865052365175499209746424, 2.168696010633057559266635771072, 3.3036639313328352683457678366, 5.83111366917314248349978704348, 6.75396174076108712128364613881, 7.7431104200776225051474999365, 8.93523661603215974785717338302, 9.7151340561906281669568438013, 10.869265641848023356233524888276, 12.21873573962539904512370711438, 13.36924100184878939747181216737, 14.60561772804464329758137162537, 15.23116783665997508594141398298, 16.96221958906494125431958757265, 17.657800719812890051918830626408, 18.48450531828723121431343208540, 19.47658556696876849210133028029, 20.21346949765964965434339716105, 21.28290718306835557821687547898, 22.50214164371627480828097152519, 24.109776820017328927439818256339, 24.75181139875802102650959525829, 25.72726235439202299058042104955, 26.09595977676386945739316381304, 27.34023161617452370741752979711