L(s) = 1 | + (0.730 + 1.21i)2-s + (−2.15 − 2.15i)3-s + (−0.931 + 1.76i)4-s + (0.480 − 0.480i)5-s + (1.03 − 4.18i)6-s + 2.39i·7-s + (−2.82 + 0.164i)8-s + 6.27i·9-s + (0.931 + 0.230i)10-s + (2.77 − 2.77i)11-s + (5.81 − 1.80i)12-s + (3.45 + 3.45i)13-s + (−2.90 + 1.75i)14-s − 2.06·15-s + (−2.26 − 3.29i)16-s + 6.32·17-s + ⋯ |
L(s) = 1 | + (0.516 + 0.856i)2-s + (−1.24 − 1.24i)3-s + (−0.465 + 0.884i)4-s + (0.214 − 0.214i)5-s + (0.421 − 1.70i)6-s + 0.905i·7-s + (−0.998 + 0.0582i)8-s + 2.09i·9-s + (0.294 + 0.0728i)10-s + (0.837 − 0.837i)11-s + (1.67 − 0.520i)12-s + (0.957 + 0.957i)13-s + (−0.775 + 0.468i)14-s − 0.533·15-s + (−0.565 − 0.824i)16-s + 1.53·17-s + ⋯ |
Λ(s)=(=(368s/2ΓC(s)L(s)(0.545−0.838i)Λ(2−s)
Λ(s)=(=(368s/2ΓC(s+1/2)L(s)(0.545−0.838i)Λ(1−s)
Degree: |
2 |
Conductor: |
368
= 24⋅23
|
Sign: |
0.545−0.838i
|
Analytic conductor: |
2.93849 |
Root analytic conductor: |
1.71420 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ368(93,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 368, ( :1/2), 0.545−0.838i)
|
Particular Values
L(1) |
≈ |
1.05204+0.570643i |
L(21) |
≈ |
1.05204+0.570643i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.730−1.21i)T |
| 23 | 1+iT |
good | 3 | 1+(2.15+2.15i)T+3iT2 |
| 5 | 1+(−0.480+0.480i)T−5iT2 |
| 7 | 1−2.39iT−7T2 |
| 11 | 1+(−2.77+2.77i)T−11iT2 |
| 13 | 1+(−3.45−3.45i)T+13iT2 |
| 17 | 1−6.32T+17T2 |
| 19 | 1+(−3.50−3.50i)T+19iT2 |
| 29 | 1+(2.24+2.24i)T+29iT2 |
| 31 | 1+6.75T+31T2 |
| 37 | 1+(3.49−3.49i)T−37iT2 |
| 41 | 1−9.37iT−41T2 |
| 43 | 1+(−4.56+4.56i)T−43iT2 |
| 47 | 1+4.24T+47T2 |
| 53 | 1+(−6.78+6.78i)T−53iT2 |
| 59 | 1+(1.90−1.90i)T−59iT2 |
| 61 | 1+(5.55+5.55i)T+61iT2 |
| 67 | 1+(−7.24−7.24i)T+67iT2 |
| 71 | 1+2.27iT−71T2 |
| 73 | 1+12.4iT−73T2 |
| 79 | 1+5.39T+79T2 |
| 83 | 1+(−2.75−2.75i)T+83iT2 |
| 89 | 1−5.62iT−89T2 |
| 97 | 1−1.10T+97T2 |
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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
−11.84669091931449072097622058212, −11.22295747458369207664932377328, −9.446957251994562387659192784224, −8.457313935866802748293992865110, −7.51053117623267288223443123429, −6.50155818616952408305648321215, −5.80878837892000965258830799972, −5.33395611335204659480611331988, −3.56642477865107408090498588831, −1.44912067532206196759076245087,
0.972083666400802943416359132554, 3.44854537667658453260635333742, 4.11939488470847156783891164903, 5.26078663991850001877357198588, 5.91159309720000789146080371022, 7.17465398653656772005904109187, 9.119236655436871050244699676186, 9.900949043723048045383249489036, 10.52579931440410396390103880687, 11.06221400797375856440121354811