L(s) = 1 | + (0.809 + 0.587i)2-s + (0.5 − 1.53i)3-s + (0.309 + 0.951i)4-s + (1.30 − 0.951i)6-s + (0.690 + 2.12i)7-s + (−0.309 + 0.951i)8-s + (0.309 + 0.224i)9-s + (3.23 − 0.726i)11-s + 1.61·12-s + (0.190 + 0.138i)13-s + (−0.690 + 2.12i)14-s + (−0.809 + 0.587i)16-s + (−0.309 + 0.224i)17-s + (0.118 + 0.363i)18-s + (0.809 − 2.48i)19-s + ⋯ |
L(s) = 1 | + (0.572 + 0.415i)2-s + (0.288 − 0.888i)3-s + (0.154 + 0.475i)4-s + (0.534 − 0.388i)6-s + (0.261 + 0.803i)7-s + (−0.109 + 0.336i)8-s + (0.103 + 0.0748i)9-s + (0.975 − 0.219i)11-s + 0.467·12-s + (0.0529 + 0.0384i)13-s + (−0.184 + 0.568i)14-s + (−0.202 + 0.146i)16-s + (−0.0749 + 0.0544i)17-s + (0.0278 + 0.0856i)18-s + (0.185 − 0.571i)19-s + ⋯ |
Λ(s)=(=(550s/2ΓC(s)L(s)(0.970−0.242i)Λ(2−s)
Λ(s)=(=(550s/2ΓC(s+1/2)L(s)(0.970−0.242i)Λ(1−s)
Degree: |
2 |
Conductor: |
550
= 2⋅52⋅11
|
Sign: |
0.970−0.242i
|
Analytic conductor: |
4.39177 |
Root analytic conductor: |
2.09565 |
Motivic weight: |
1 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ550(301,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 550, ( :1/2), 0.970−0.242i)
|
Particular Values
L(1) |
≈ |
2.33946+0.287582i |
L(21) |
≈ |
2.33946+0.287582i |
L(23) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(−0.809−0.587i)T |
| 5 | 1 |
| 11 | 1+(−3.23+0.726i)T |
good | 3 | 1+(−0.5+1.53i)T+(−2.42−1.76i)T2 |
| 7 | 1+(−0.690−2.12i)T+(−5.66+4.11i)T2 |
| 13 | 1+(−0.190−0.138i)T+(4.01+12.3i)T2 |
| 17 | 1+(0.309−0.224i)T+(5.25−16.1i)T2 |
| 19 | 1+(−0.809+2.48i)T+(−15.3−11.1i)T2 |
| 23 | 1+3.85T+23T2 |
| 29 | 1+(0.163+0.502i)T+(−23.4+17.0i)T2 |
| 31 | 1+(−8.28−6.01i)T+(9.57+29.4i)T2 |
| 37 | 1+(2.73+8.42i)T+(−29.9+21.7i)T2 |
| 41 | 1+(1.14−3.52i)T+(−33.1−24.0i)T2 |
| 43 | 1+9.47T+43T2 |
| 47 | 1+(−0.0729+0.224i)T+(−38.0−27.6i)T2 |
| 53 | 1+(1.11+0.812i)T+(16.3+50.4i)T2 |
| 59 | 1+(3.54+10.9i)T+(−47.7+34.6i)T2 |
| 61 | 1+(1.80−1.31i)T+(18.8−58.0i)T2 |
| 67 | 1+9.32T+67T2 |
| 71 | 1+(7.92−5.75i)T+(21.9−67.5i)T2 |
| 73 | 1+(−2.51−7.74i)T+(−59.0+42.9i)T2 |
| 79 | 1+(−9.66−7.02i)T+(24.4+75.1i)T2 |
| 83 | 1+(7.28−5.29i)T+(25.6−78.9i)T2 |
| 89 | 1+13.1T+89T2 |
| 97 | 1+(9.70+7.05i)T+(29.9+92.2i)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
−11.13321964509832851051515312003, −9.823748839916816534096535340990, −8.681749797210188084068191382790, −8.148426609054947401298120110770, −7.01703346470665150888252092779, −6.42774877131851644296201087652, −5.34632524689397124616372472283, −4.23162899185671318961552330918, −2.85716819555706553983343282281, −1.64704053097485234803427798234,
1.44840835629022151443446558423, 3.19717357854908788317891381201, 4.13154587604028447398252618662, 4.64654250736063069771338783213, 6.06023753451115941612270917194, 7.01241332524899192723445514658, 8.197858715340911673854251924115, 9.312947609700835660352450051289, 10.05854996027490666055482008300, 10.56669560627442646699821727631