L(s) = 1 | + 2.53i·3-s − 31.0i·7-s + 20.5·9-s + 11·11-s − 79.1i·13-s − 54.4i·17-s − 105.·19-s + 78.8·21-s − 72.0i·23-s + 120. i·27-s − 228.·29-s + 22.7·31-s + 27.9i·33-s − 140. i·37-s + 201.·39-s + ⋯ |
L(s) = 1 | + 0.488i·3-s − 1.67i·7-s + 0.761·9-s + 0.301·11-s − 1.68i·13-s − 0.776i·17-s − 1.27·19-s + 0.819·21-s − 0.653i·23-s + 0.860i·27-s − 1.46·29-s + 0.132·31-s + 0.147i·33-s − 0.624i·37-s + 0.825·39-s + ⋯ |
Λ(s)=(=(1100s/2ΓC(s)L(s)(−0.894+0.447i)Λ(4−s)
Λ(s)=(=(1100s/2ΓC(s+3/2)L(s)(−0.894+0.447i)Λ(1−s)
Degree: |
2 |
Conductor: |
1100
= 22⋅52⋅11
|
Sign: |
−0.894+0.447i
|
Analytic conductor: |
64.9021 |
Root analytic conductor: |
8.05618 |
Motivic weight: |
3 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ1100(749,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 1100, ( :3/2), −0.894+0.447i)
|
Particular Values
L(2) |
≈ |
1.123775867 |
L(21) |
≈ |
1.123775867 |
L(25) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 5 | 1 |
| 11 | 1−11T |
good | 3 | 1−2.53iT−27T2 |
| 7 | 1+31.0iT−343T2 |
| 13 | 1+79.1iT−2.19e3T2 |
| 17 | 1+54.4iT−4.91e3T2 |
| 19 | 1+105.T+6.85e3T2 |
| 23 | 1+72.0iT−1.21e4T2 |
| 29 | 1+228.T+2.43e4T2 |
| 31 | 1−22.7T+2.97e4T2 |
| 37 | 1+140.iT−5.06e4T2 |
| 41 | 1−62.8T+6.89e4T2 |
| 43 | 1−481.iT−7.95e4T2 |
| 47 | 1−69.1iT−1.03e5T2 |
| 53 | 1−453.iT−1.48e5T2 |
| 59 | 1−225.T+2.05e5T2 |
| 61 | 1+320.T+2.26e5T2 |
| 67 | 1−200.iT−3.00e5T2 |
| 71 | 1+971.T+3.57e5T2 |
| 73 | 1−688.iT−3.89e5T2 |
| 79 | 1−544.T+4.93e5T2 |
| 83 | 1−788.iT−5.71e5T2 |
| 89 | 1+1.11e3T+7.04e5T2 |
| 97 | 1−842.iT−9.12e5T2 |
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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
−9.367317718825131111281809382743, −8.153275531687693652417557338989, −7.45820211613666968506446685197, −6.77688844808574006176416843998, −5.63725468230956603068156520032, −4.47783794696925704564264749556, −4.02093066872797519393076560317, −2.92475755677558875260601969504, −1.28870530319547676419461106603, −0.26932951511772553823108687709,
1.78695922576799862318158775069, 2.07285914302726225534194578209, 3.69116141940300616569805157187, 4.61964148712638756077949145640, 5.78299584389586882416766145959, 6.45094978440253217498998710487, 7.21439202126780774098295157289, 8.336382963774411364187506061180, 8.989705869271898138073016463000, 9.578165058157278552342524502100