L(s) = 1 | + (0.909 + 1.08i)2-s + (1.18 − 3.24i)3-s + (−0.347 + 1.96i)4-s + (4.58 − 1.66i)6-s + (−2.44 + 1.41i)8-s + (−6.83 − 5.73i)9-s + (2.33 + 4.04i)11-s + (5.97 + 3.45i)12-s + (−3.75 − 1.36i)16-s + (−1.45 + 1.22i)17-s − 12.6i·18-s + (4.00 + 1.72i)19-s + (−2.25 + 6.20i)22-s + (1.69 + 9.61i)24-s + (−4.69 + 1.71i)25-s + ⋯ |
L(s) = 1 | + (0.642 + 0.766i)2-s + (0.681 − 1.87i)3-s + (−0.173 + 0.984i)4-s + (1.87 − 0.681i)6-s + (−0.866 + 0.500i)8-s + (−2.27 − 1.91i)9-s + (0.704 + 1.21i)11-s + (1.72 + 0.996i)12-s + (−0.939 − 0.342i)16-s + (−0.352 + 0.296i)17-s − 2.97i·18-s + (0.918 + 0.394i)19-s + (−0.481 + 1.32i)22-s + (0.346 + 1.96i)24-s + (−0.939 + 0.342i)25-s + ⋯ |
Λ(s)=(=(152s/2ΓC(s)L(s)(0.973+0.230i)Λ(2−s)
Λ(s)=(=(152s/2ΓC(s+1/2)L(s)(0.973+0.230i)Λ(1−s)
Degree: |
2 |
Conductor: |
152
= 23⋅19
|
Sign: |
0.973+0.230i
|
Analytic conductor: |
1.21372 |
Root analytic conductor: |
1.10169 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ152(51,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 152, ( :1/2), 0.973+0.230i)
|
Particular Values
L(1) |
≈ |
1.70153−0.198380i |
L(21) |
≈ |
1.70153−0.198380i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.909−1.08i)T |
| 19 | 1+(−4.00−1.72i)T |
good | 3 | 1+(−1.18+3.24i)T+(−2.29−1.92i)T2 |
| 5 | 1+(4.69−1.71i)T2 |
| 7 | 1+(3.5+6.06i)T2 |
| 11 | 1+(−2.33−4.04i)T+(−5.5+9.52i)T2 |
| 13 | 1+(9.95−8.35i)T2 |
| 17 | 1+(1.45−1.22i)T+(2.95−16.7i)T2 |
| 23 | 1+(21.6+7.86i)T2 |
| 29 | 1+(5.03+28.5i)T2 |
| 31 | 1+(−15.5−26.8i)T2 |
| 37 | 1+37T2 |
| 41 | 1+(−1.34+3.70i)T+(−31.4−26.3i)T2 |
| 43 | 1+(2.14+12.1i)T+(−40.4+14.7i)T2 |
| 47 | 1+(−8.16−46.2i)T2 |
| 53 | 1+(−49.8−18.1i)T2 |
| 59 | 1+(−9.86−11.7i)T+(−10.2+58.1i)T2 |
| 61 | 1+(57.3+20.8i)T2 |
| 67 | 1+(−7.91+9.43i)T+(−11.6−65.9i)T2 |
| 71 | 1+(−66.7+24.2i)T2 |
| 73 | 1+(7.22+2.62i)T+(55.9+46.9i)T2 |
| 79 | 1+(60.5+50.7i)T2 |
| 83 | 1+(−0.170+0.294i)T+(−41.5−71.8i)T2 |
| 89 | 1+(−4.36−11.9i)T+(−68.1+57.2i)T2 |
| 97 | 1+(8.22+9.80i)T+(−16.8+95.5i)T2 |
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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
−13.14880359193795375547832457354, −12.20590905229838886927646644991, −11.76390382854928949498166392594, −9.375964422101208504678643954668, −8.365753861823423950510282181136, −7.37457657094967253590996987715, −6.82149037340385372951350959510, −5.66210075499383552096713239828, −3.67489148035696175270220736082, −2.05880234418347244395018623740,
2.86695587920878528688999874646, 3.79912227473024341795502571271, 4.85040987597856448870964717988, 5.96451182560450691026781664244, 8.348823173270527279524169261967, 9.352557615455495874950149151719, 9.932572800734602349222443116711, 11.18382566105165015213552586650, 11.48557251552763405025148352676, 13.35692912592296562357809572104