L(s) = 1 | + (−0.5 − 0.866i)5-s + 7-s + (0.5 + 0.866i)11-s + (−0.5 − 0.866i)13-s + (0.5 + 0.866i)17-s + (−0.5 + 0.866i)19-s + (0.5 − 0.866i)23-s + (−0.5 + 0.866i)25-s + (−0.5 − 0.866i)29-s + (0.5 − 0.866i)31-s + (−0.5 − 0.866i)35-s + (−0.5 − 0.866i)41-s + (−0.5 − 0.866i)43-s + (−0.5 − 0.866i)47-s + 49-s + ⋯ |
L(s) = 1 | + (−0.5 − 0.866i)5-s + 7-s + (0.5 + 0.866i)11-s + (−0.5 − 0.866i)13-s + (0.5 + 0.866i)17-s + (−0.5 + 0.866i)19-s + (0.5 − 0.866i)23-s + (−0.5 + 0.866i)25-s + (−0.5 − 0.866i)29-s + (0.5 − 0.866i)31-s + (−0.5 − 0.866i)35-s + (−0.5 − 0.866i)41-s + (−0.5 − 0.866i)43-s + (−0.5 − 0.866i)47-s + 49-s + ⋯ |
Λ(s)=(=(2664s/2ΓR(s)L(s)(0.546−0.837i)Λ(1−s)
Λ(s)=(=(2664s/2ΓR(s)L(s)(0.546−0.837i)Λ(1−s)
Degree: |
1 |
Conductor: |
2664
= 23⋅32⋅37
|
Sign: |
0.546−0.837i
|
Analytic conductor: |
12.3715 |
Root analytic conductor: |
12.3715 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2664(1285,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2664, (0: ), 0.546−0.837i)
|
Particular Values
L(21) |
≈ |
1.457626077−0.7890672285i |
L(21) |
≈ |
1.457626077−0.7890672285i |
L(1) |
≈ |
1.096215256−0.2048777902i |
L(1) |
≈ |
1.096215256−0.2048777902i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 2 | 1 |
| 3 | 1 |
| 37 | 1 |
good | 5 | 1+(−0.5−0.866i)T |
| 7 | 1+T |
| 11 | 1+(0.5+0.866i)T |
| 13 | 1+(−0.5−0.866i)T |
| 17 | 1+(0.5+0.866i)T |
| 19 | 1+(−0.5+0.866i)T |
| 23 | 1+(0.5−0.866i)T |
| 29 | 1+(−0.5−0.866i)T |
| 31 | 1+(0.5−0.866i)T |
| 41 | 1+(−0.5−0.866i)T |
| 43 | 1+(−0.5−0.866i)T |
| 47 | 1+(−0.5−0.866i)T |
| 53 | 1+(0.5+0.866i)T |
| 59 | 1+T |
| 61 | 1+T |
| 67 | 1+(0.5+0.866i)T |
| 71 | 1+(−0.5+0.866i)T |
| 73 | 1+T |
| 79 | 1−T |
| 83 | 1+(0.5−0.866i)T |
| 89 | 1+(0.5+0.866i)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
−19.47410888950860678803480812826, −18.70618881600275075057151380799, −18.10461891154492282900483525813, −17.375950733247536750922878031799, −16.59260703866024542785703825107, −15.90004442626215544135814718876, −15.006000239770370510026622952, −14.44046236891357522853839966686, −14.01361731538217611430883715027, −13.11883473518666955639697869854, −11.94930353022926085965930956341, −11.39794475517774356209289362264, −11.14711001095838568347539321386, −10.121267793986835122647825221509, −9.23455674083039747910069983434, −8.504401229565311918449444184765, −7.69752038227246417754076241636, −6.9837325366079494344040204405, −6.419175028789577480406622698683, −5.20743579672021014682409048373, −4.656529942758767622531234639170, −3.615281535465638204751105923446, −2.959118168338840350904663359266, −1.97531602723750407206100912627, −0.95686974346214562499056117877,
0.63789797373158624707446976709, 1.632906770945987667450552023835, 2.348602837773391860515740699015, 3.8166861655805678064275745860, 4.21853378266099915180718055178, 5.14409497992975977877157437684, 5.68667862091401648041552327232, 6.87074544755388236563791820820, 7.73949641661833404066876097402, 8.23804258292088408052015560647, 8.85302512066659360341024046431, 9.954330218681768039354052004474, 10.43725514848050182485002444256, 11.53624510712038160315748308148, 12.06732592837531866466821898781, 12.67150712767393149183878138909, 13.35264256230506032151043875955, 14.5199732149413899050537341207, 14.9437296763752736084027116965, 15.46647945664166659805866434616, 16.60268254762613048769456512013, 17.2018075699164555370103525767, 17.45476194295152766220231650454, 18.6370079781438830473018195227, 19.164748995222975205759992482