L(s) = 1 | + (−0.573 + 1.91i)2-s + (0.146 − 0.146i)3-s + (−3.34 − 2.19i)4-s + (3.68 − 3.68i)5-s + (0.196 + 0.364i)6-s − 9.66·7-s + (6.12 − 5.14i)8-s + 8.95i·9-s + (4.94 + 9.17i)10-s + (5.51 + 5.51i)11-s + (−0.810 + 0.167i)12-s + (−6.27 − 6.27i)13-s + (5.53 − 18.5i)14-s − 1.07i·15-s + (6.35 + 14.6i)16-s − 6.78·17-s + ⋯ |
L(s) = 1 | + (−0.286 + 0.958i)2-s + (0.0487 − 0.0487i)3-s + (−0.835 − 0.549i)4-s + (0.737 − 0.737i)5-s + (0.0327 + 0.0607i)6-s − 1.38·7-s + (0.765 − 0.643i)8-s + 0.995i·9-s + (0.494 + 0.917i)10-s + (0.501 + 0.501i)11-s + (−0.0675 + 0.0139i)12-s + (−0.482 − 0.482i)13-s + (0.395 − 1.32i)14-s − 0.0719i·15-s + (0.396 + 0.917i)16-s − 0.399·17-s + ⋯ |
Λ(s)=(=(16s/2ΓC(s)L(s)(0.696−0.717i)Λ(3−s)
Λ(s)=(=(16s/2ΓC(s+1)L(s)(0.696−0.717i)Λ(1−s)
Degree: |
2 |
Conductor: |
16
= 24
|
Sign: |
0.696−0.717i
|
Analytic conductor: |
0.435968 |
Root analytic conductor: |
0.660279 |
Motivic weight: |
2 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ16(3,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(2, 16, ( :1), 0.696−0.717i)
|
Particular Values
L(23) |
≈ |
0.638050+0.270074i |
L(21) |
≈ |
0.638050+0.270074i |
L(2) |
|
not available |
L(1) |
|
not available |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1+(0.573−1.91i)T |
good | 3 | 1+(−0.146+0.146i)T−9iT2 |
| 5 | 1+(−3.68+3.68i)T−25iT2 |
| 7 | 1+9.66T+49T2 |
| 11 | 1+(−5.51−5.51i)T+121iT2 |
| 13 | 1+(6.27+6.27i)T+169iT2 |
| 17 | 1+6.78T+289T2 |
| 19 | 1+(−13.5+13.5i)T−361iT2 |
| 23 | 1−17.0T+529T2 |
| 29 | 1+(−4.85−4.85i)T+841iT2 |
| 31 | 1+5.25iT−961T2 |
| 37 | 1+(18.1−18.1i)T−1.36e3iT2 |
| 41 | 1+48.2iT−1.68e3T2 |
| 43 | 1+(54.5+54.5i)T+1.84e3iT2 |
| 47 | 1−40.4iT−2.20e3T2 |
| 53 | 1+(−10.8+10.8i)T−2.80e3iT2 |
| 59 | 1+(−50.8−50.8i)T+3.48e3iT2 |
| 61 | 1+(17.0+17.0i)T+3.72e3iT2 |
| 67 | 1+(−22.9+22.9i)T−4.48e3iT2 |
| 71 | 1+51.6T+5.04e3T2 |
| 73 | 1−78.5iT−5.32e3T2 |
| 79 | 1−108.iT−6.24e3T2 |
| 83 | 1+(−57.3+57.3i)T−6.88e3iT2 |
| 89 | 1−44.1iT−7.92e3T2 |
| 97 | 1−112.T+9.40e3T2 |
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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
−19.05917366499240579387292539661, −17.44809472315373685434368322205, −16.61854860503053858588883402170, −15.48577849509374745221103926577, −13.70565852781556031159673061557, −12.86943297645273560521880912709, −10.06652148021096439654084648890, −8.994231981046499986081599454075, −7.00661769518024865851982438880, −5.23955131995947565398025839100,
3.26337001318846697709200002217, 6.53005724998402159368645936403, 9.230626755154415845242817721063, 10.09800024692954469366961831329, 11.82170795194160262411601729103, 13.20271751375459428613970751030, 14.48541207774191503482784312224, 16.50844412781028768059825791010, 17.85434448226598555919006841803, 18.90176009244069779044019867640