L(s) = 1 | + (−0.988 + 0.149i)2-s + (0.955 − 0.294i)4-s + (−0.900 + 0.433i)5-s + (−0.900 + 0.433i)8-s + (0.826 − 0.563i)10-s + (0.623 + 0.781i)11-s + (−0.988 + 0.149i)13-s + (0.826 − 0.563i)16-s + (0.955 + 0.294i)17-s + (−0.5 − 0.866i)19-s + (−0.733 + 0.680i)20-s + (−0.733 − 0.680i)22-s + (−0.222 + 0.974i)23-s + (0.623 − 0.781i)25-s + (0.955 − 0.294i)26-s + ⋯ |
L(s) = 1 | + (−0.988 + 0.149i)2-s + (0.955 − 0.294i)4-s + (−0.900 + 0.433i)5-s + (−0.900 + 0.433i)8-s + (0.826 − 0.563i)10-s + (0.623 + 0.781i)11-s + (−0.988 + 0.149i)13-s + (0.826 − 0.563i)16-s + (0.955 + 0.294i)17-s + (−0.5 − 0.866i)19-s + (−0.733 + 0.680i)20-s + (−0.733 − 0.680i)22-s + (−0.222 + 0.974i)23-s + (0.623 − 0.781i)25-s + (0.955 − 0.294i)26-s + ⋯ |
Λ(s)=(=(441s/2ΓR(s)L(s)(−0.944+0.328i)Λ(1−s)
Λ(s)=(=(441s/2ΓR(s)L(s)(−0.944+0.328i)Λ(1−s)
Degree: |
1 |
Conductor: |
441
= 32⋅72
|
Sign: |
−0.944+0.328i
|
Analytic conductor: |
2.04799 |
Root analytic conductor: |
2.04799 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ441(331,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 441, (0: ), −0.944+0.328i)
|
Particular Values
L(21) |
≈ |
0.04745373722+0.2808066450i |
L(21) |
≈ |
0.04745373722+0.2808066450i |
L(1) |
≈ |
0.4793672100+0.1414886859i |
L(1) |
≈ |
0.4793672100+0.1414886859i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 7 | 1 |
good | 2 | 1+(−0.988+0.149i)T |
| 5 | 1+(−0.900+0.433i)T |
| 11 | 1+(0.623+0.781i)T |
| 13 | 1+(−0.988+0.149i)T |
| 17 | 1+(0.955+0.294i)T |
| 19 | 1+(−0.5−0.866i)T |
| 23 | 1+(−0.222+0.974i)T |
| 29 | 1+(−0.733+0.680i)T |
| 31 | 1+(−0.5−0.866i)T |
| 37 | 1+(−0.733+0.680i)T |
| 41 | 1+(0.0747−0.997i)T |
| 43 | 1+(0.0747+0.997i)T |
| 47 | 1+(−0.988+0.149i)T |
| 53 | 1+(−0.733−0.680i)T |
| 59 | 1+(0.0747+0.997i)T |
| 61 | 1+(0.955+0.294i)T |
| 67 | 1+(−0.5−0.866i)T |
| 71 | 1+(−0.222+0.974i)T |
| 73 | 1+(0.365+0.930i)T |
| 79 | 1+(−0.5+0.866i)T |
| 83 | 1+(−0.988−0.149i)T |
| 89 | 1+(−0.988−0.149i)T |
| 97 | 1+(−0.5−0.866i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−23.93384051175900444816840880608, −22.87274523662188370726686668119, −21.79924768665563346610160966455, −20.813256975954006113397835828431, −20.111739449403670659637364928757, −19.1522056374930921083647067752, −18.86603567718612194156639824478, −17.56295402260594058130515538375, −16.560237406960438739092561219518, −16.34441454684644902637682857736, −15.07786975493916168167587421338, −14.327968504854425407139630939, −12.62832655919554475018487608138, −12.10326084203571000115793277870, −11.23360878850897224682914801709, −10.256698326265912341877886737770, −9.268687243522395488928862123572, −8.350242944332857498347307592922, −7.687565785447277092213182432541, −6.67190772744381331767052887980, −5.444790467485266746530466438080, −3.986828271384747757132914505498, −3.03742221114446672215858288217, −1.57795649631299633453736377182, −0.226478204665773083664332328433,
1.55259665310733025358229632797, 2.79484078170745703218910835128, 3.98771631239866435477099998805, 5.35688238122113427702908940281, 6.766212325978196415178353245313, 7.31668976401916484947857298870, 8.17007130484121293125444416270, 9.32862638148061156133185327166, 10.04837141705778431348841872732, 11.15283489574639719999021953476, 11.83475882594341428211833531399, 12.68901429423241352488416442951, 14.47501285253101099544680599777, 14.94586919054153881833653638651, 15.7957035778888622372166652570, 16.827719232594079790167632444905, 17.471759022665749604743579313023, 18.47719424957170675646578781823, 19.403609029052873289810553660351, 19.72805711676113773049760933261, 20.74423284196152302585996297119, 21.883779946292572194069449324865, 22.81473318849430039705114401067, 23.86605648353064851749288893398, 24.35760643228993523221782284334