L(s) = 1 | + (−0.587 − 0.809i)3-s + (0.951 − 0.309i)5-s + (0.809 + 0.587i)7-s + (−0.309 + 0.951i)9-s + (0.951 + 0.309i)13-s + (−0.809 − 0.587i)15-s + (0.309 + 0.951i)17-s + (−0.587 − 0.809i)19-s − i·21-s − 23-s + (0.809 − 0.587i)25-s + (0.951 − 0.309i)27-s + (0.587 − 0.809i)29-s + (0.309 − 0.951i)31-s + (0.951 + 0.309i)35-s + ⋯ |
L(s) = 1 | + (−0.587 − 0.809i)3-s + (0.951 − 0.309i)5-s + (0.809 + 0.587i)7-s + (−0.309 + 0.951i)9-s + (0.951 + 0.309i)13-s + (−0.809 − 0.587i)15-s + (0.309 + 0.951i)17-s + (−0.587 − 0.809i)19-s − i·21-s − 23-s + (0.809 − 0.587i)25-s + (0.951 − 0.309i)27-s + (0.587 − 0.809i)29-s + (0.309 − 0.951i)31-s + (0.951 + 0.309i)35-s + ⋯ |
Λ(s)=(=(176s/2ΓR(s)L(s)(0.839−0.542i)Λ(1−s)
Λ(s)=(=(176s/2ΓR(s)L(s)(0.839−0.542i)Λ(1−s)
Degree: |
1 |
Conductor: |
176
= 24⋅11
|
Sign: |
0.839−0.542i
|
Analytic conductor: |
0.817340 |
Root analytic conductor: |
0.817340 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ176(157,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 176, (0: ), 0.839−0.542i)
|
Particular Values
L(21) |
≈ |
1.151359617−0.3395421650i |
L(21) |
≈ |
1.151359617−0.3395421650i |
L(1) |
≈ |
1.084269641−0.2229968010i |
L(1) |
≈ |
1.084269641−0.2229968010i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 11 | 1 |
good | 3 | 1+(−0.587−0.809i)T |
| 5 | 1+(0.951−0.309i)T |
| 7 | 1+(0.809+0.587i)T |
| 13 | 1+(0.951+0.309i)T |
| 17 | 1+(0.309+0.951i)T |
| 19 | 1+(−0.587−0.809i)T |
| 23 | 1−T |
| 29 | 1+(0.587−0.809i)T |
| 31 | 1+(0.309−0.951i)T |
| 37 | 1+(−0.587+0.809i)T |
| 41 | 1+(0.809−0.587i)T |
| 43 | 1−iT |
| 47 | 1+(−0.809+0.587i)T |
| 53 | 1+(−0.951−0.309i)T |
| 59 | 1+(−0.587+0.809i)T |
| 61 | 1+(−0.951+0.309i)T |
| 67 | 1+iT |
| 71 | 1+(−0.309−0.951i)T |
| 73 | 1+(0.809+0.587i)T |
| 79 | 1+(0.309−0.951i)T |
| 83 | 1+(−0.951+0.309i)T |
| 89 | 1−T |
| 97 | 1+(0.309−0.951i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−27.53766116384214648278770491828, −26.63481160141652424086714364427, −25.735337140789610488378139919764, −24.703206521472242390919196138850, −23.3557455506331838311502066103, −22.781378210222444238156059614612, −21.492320446833927255726090984464, −21.043902835908273261851905379031, −20.09979828793710112954424928421, −18.24927865911735701069932371454, −17.80748426119096913165566436473, −16.73674798406161690496259568202, −15.875966365327498919323041476098, −14.49602884570148604196307769126, −13.93282213756496101886290608733, −12.43958584494704134565795985785, −11.11525109557949386873667938864, −10.48510832949185301551499363211, −9.525511020457568469191294724515, −8.225695017695942845013601598725, −6.64084139726066347507210367907, −5.638905930232108566269704713717, −4.59922751846235182436760029962, −3.27212816759386222715352038933, −1.440029303350501005614341196252,
1.40812656019102209928066007356, 2.32072053764644670471483501257, 4.533016058229276416312892522881, 5.77825504122755555893440368289, 6.36649040833402979168270842281, 7.98095112394808131512495663725, 8.833822441347579555780186001670, 10.348505479521055386432365643441, 11.38309684347593311298478558890, 12.38124275024979873227964002965, 13.38107902475614448501657715952, 14.18081136126682837273637208607, 15.573276933928883731097155303100, 16.91765789223704557225602705576, 17.59403802620364570639247956183, 18.37120972538441019891119690228, 19.326211060996644877526739899937, 20.7831840498015471612109365440, 21.54696486537547593449692207487, 22.47997192748235887314778667869, 23.85241093583886843720719423597, 24.24604437553900076791816079446, 25.36233368121133173777389335120, 26.03223218163391975764473098355, 27.87876868826721167342094756663