L(s) = 1 | + (0.327 − 0.945i)2-s + (0.458 + 0.888i)3-s + (−0.786 − 0.618i)4-s + (−0.614 + 0.0586i)5-s + (0.989 − 0.142i)6-s + (2.12 − 1.57i)7-s + (−0.841 + 0.540i)8-s + (−0.580 + 0.814i)9-s + (−0.145 + 0.599i)10-s + (0.580 − 0.200i)11-s + (0.189 − 0.981i)12-s + (−0.399 − 1.36i)13-s + (−0.791 − 2.52i)14-s + (−0.333 − 0.519i)15-s + (0.235 + 0.971i)16-s + (3.61 + 1.44i)17-s + ⋯ |
L(s) = 1 | + (0.231 − 0.668i)2-s + (0.264 + 0.513i)3-s + (−0.393 − 0.309i)4-s + (−0.274 + 0.0262i)5-s + (0.404 − 0.0580i)6-s + (0.803 − 0.594i)7-s + (−0.297 + 0.191i)8-s + (−0.193 + 0.271i)9-s + (−0.0460 + 0.189i)10-s + (0.175 − 0.0605i)11-s + (0.0546 − 0.283i)12-s + (−0.110 − 0.377i)13-s + (−0.211 − 0.674i)14-s + (−0.0861 − 0.134i)15-s + (0.0589 + 0.242i)16-s + (0.877 + 0.351i)17-s + ⋯ |
Λ(s)=(=(966s/2ΓC(s)L(s)(0.484+0.874i)Λ(2−s)
Λ(s)=(=(966s/2ΓC(s+1/2)L(s)(0.484+0.874i)Λ(1−s)
Degree: |
2 |
Conductor: |
966
= 2⋅3⋅7⋅23
|
Sign: |
0.484+0.874i
|
Analytic conductor: |
7.71354 |
Root analytic conductor: |
2.77732 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ966(493,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 966, ( :1/2), 0.484+0.874i)
|
Particular Values
L(1) |
≈ |
1.69146−0.996985i |
L(21) |
≈ |
1.69146−0.996985i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.327+0.945i)T |
| 3 | 1+(−0.458−0.888i)T |
| 7 | 1+(−2.12+1.57i)T |
| 23 | 1+(0.0117+4.79i)T |
good | 5 | 1+(0.614−0.0586i)T+(4.90−0.946i)T2 |
| 11 | 1+(−0.580+0.200i)T+(8.64−6.79i)T2 |
| 13 | 1+(0.399+1.36i)T+(−10.9+7.02i)T2 |
| 17 | 1+(−3.61−1.44i)T+(12.3+11.7i)T2 |
| 19 | 1+(−3.76+1.50i)T+(13.7−13.1i)T2 |
| 29 | 1+(0.716+4.98i)T+(−27.8+8.17i)T2 |
| 31 | 1+(−8.57+0.408i)T+(30.8−2.94i)T2 |
| 37 | 1+(−6.40−4.56i)T+(12.1+34.9i)T2 |
| 41 | 1+(1.48+0.678i)T+(26.8+30.9i)T2 |
| 43 | 1+(−4.17+6.49i)T+(−17.8−39.1i)T2 |
| 47 | 1+(6.20−3.58i)T+(23.5−40.7i)T2 |
| 53 | 1+(−3.49−3.66i)T+(−2.52+52.9i)T2 |
| 59 | 1+(0.698+0.169i)T+(52.4+27.0i)T2 |
| 61 | 1+(3.40+1.75i)T+(35.3+49.6i)T2 |
| 67 | 1+(0.973+5.05i)T+(−62.2+24.9i)T2 |
| 71 | 1+(−6.76−7.80i)T+(−10.1+70.2i)T2 |
| 73 | 1+(−6.98+8.87i)T+(−17.2−70.9i)T2 |
| 79 | 1+(0.242−0.254i)T+(−3.75−78.9i)T2 |
| 83 | 1+(1.67+3.66i)T+(−54.3+62.7i)T2 |
| 89 | 1+(−0.104+2.18i)T+(−88.5−8.45i)T2 |
| 97 | 1+(−2.07+4.55i)T+(−63.5−73.3i)T2 |
show more | |
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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
−10.07782157355422577158025840591, −9.258492126005389025953630529716, −8.113208735533989312005933943513, −7.74061315034808536175763831722, −6.30540121164109649565519228510, −5.19372062513269978108333016882, −4.40369490292293675074955824431, −3.59463875631000137108348435741, −2.49359813794743293688500306550, −0.981374635557093489672544840958,
1.38207249514554758825756372459, 2.83143595071766195964028485479, 3.98694543521718458117067791435, 5.11692912273125224021668650239, 5.82059299405158628190991946949, 6.87009056023487936497040058840, 7.80213125557737709653020209344, 8.105641334512201783530344896946, 9.210000656836977639792311438889, 9.835452582644797288143834550196