L(s) = 1 | + (0.987 + 0.156i)2-s + (0.951 + 0.309i)4-s + (0.0784 + 0.996i)7-s + (0.891 + 0.453i)8-s + (−0.809 + 0.587i)13-s + (−0.0784 + 0.996i)14-s + (0.809 + 0.587i)16-s + (0.891 + 0.453i)19-s + (0.382 + 0.923i)23-s + (−0.891 + 0.453i)26-s + (−0.233 + 0.972i)28-s + (−0.760 − 0.649i)29-s + (−0.972 + 0.233i)31-s + (0.707 + 0.707i)32-s + (0.760 + 0.649i)37-s + (0.809 + 0.587i)38-s + ⋯ |
L(s) = 1 | + (0.987 + 0.156i)2-s + (0.951 + 0.309i)4-s + (0.0784 + 0.996i)7-s + (0.891 + 0.453i)8-s + (−0.809 + 0.587i)13-s + (−0.0784 + 0.996i)14-s + (0.809 + 0.587i)16-s + (0.891 + 0.453i)19-s + (0.382 + 0.923i)23-s + (−0.891 + 0.453i)26-s + (−0.233 + 0.972i)28-s + (−0.760 − 0.649i)29-s + (−0.972 + 0.233i)31-s + (0.707 + 0.707i)32-s + (0.760 + 0.649i)37-s + (0.809 + 0.587i)38-s + ⋯ |
Λ(s)=(=(2805s/2ΓR(s)L(s)(−0.342+0.939i)Λ(1−s)
Λ(s)=(=(2805s/2ΓR(s)L(s)(−0.342+0.939i)Λ(1−s)
Degree: |
1 |
Conductor: |
2805
= 3⋅5⋅11⋅17
|
Sign: |
−0.342+0.939i
|
Analytic conductor: |
13.0263 |
Root analytic conductor: |
13.0263 |
Motivic weight: |
0 |
Rational: |
no |
Arithmetic: |
yes |
Character: |
χ2805(1238,⋅)
|
Primitive: |
yes
|
Self-dual: |
no
|
Analytic rank: |
0
|
Selberg data: |
(1, 2805, (0: ), −0.342+0.939i)
|
Particular Values
L(21) |
≈ |
1.747612613+2.497592963i |
L(21) |
≈ |
1.747612613+2.497592963i |
L(1) |
≈ |
1.755691987+0.7403848482i |
L(1) |
≈ |
1.755691987+0.7403848482i |
L(s)=p∏Fp(p−s)−1 | p | Fp(T) |
---|
bad | 3 | 1 |
| 5 | 1 |
| 11 | 1 |
| 17 | 1 |
good | 2 | 1+(0.987+0.156i)T |
| 7 | 1+(0.0784+0.996i)T |
| 13 | 1+(−0.809+0.587i)T |
| 19 | 1+(0.891+0.453i)T |
| 23 | 1+(0.382+0.923i)T |
| 29 | 1+(−0.760−0.649i)T |
| 31 | 1+(−0.972+0.233i)T |
| 37 | 1+(0.760+0.649i)T |
| 41 | 1+(−0.760+0.649i)T |
| 43 | 1+(0.707−0.707i)T |
| 47 | 1+(−0.309−0.951i)T |
| 53 | 1+(0.987+0.156i)T |
| 59 | 1+(−0.891+0.453i)T |
| 61 | 1+(0.233−0.972i)T |
| 67 | 1+iT |
| 71 | 1+(−0.522−0.852i)T |
| 73 | 1+(−0.649+0.760i)T |
| 79 | 1+(−0.522+0.852i)T |
| 83 | 1+(0.156+0.987i)T |
| 89 | 1−iT |
| 97 | 1+(−0.972+0.233i)T |
show more | |
show less | |
L(s)=p∏ (1−αpp−s)−1
Imaginary part of the first few zeros on the critical line
−19.29005599143245831947567237066, −18.30133559192630329578693312630, −17.484768374200144597071364888266, −16.646947607608293604358645428660, −16.23311343403678241767293038389, −15.26523134642727058941636989960, −14.57494597277743497573076073062, −14.14661730825170860880124879559, −13.16776755992618267883984997764, −12.843524376000316456899829762407, −11.962121524536453986848493746987, −11.13767490949661541601410357490, −10.609499354769643921824210318393, −9.89157451398277797961719767069, −9.00453064284233793578470443288, −7.54731032106464567337278187417, −7.48278568215130823889557013092, −6.52377342541154874245364012216, −5.59729690956036958108611152695, −4.89921992363889334090914673119, −4.21339848827916130625363895804, −3.352642730192328615779247912274, −2.66088006958059531405158220902, −1.62372994748377228493667104060, −0.61213802723578970963641542671,
1.49651403491684209007917603423, 2.23290540138838999589932592607, 3.05188622076704374659593479936, 3.84022286781422509748826718155, 4.8071599335830228319115550056, 5.45523535174504971398632522914, 6.004305195498494519531107125990, 7.04350249434553022440353541593, 7.56218653761994928146881660496, 8.49810447618871667598682942941, 9.4071961027918653221509279619, 10.091102310576613630048375674728, 11.30944178297334752809808576639, 11.65892875680220954599999323732, 12.32882359642262614020072778658, 13.057491488632453499084006176829, 13.79355093387614589519684593868, 14.54443377652444460663180218587, 15.127467396128349192614782837000, 15.67158655005980929004627275905, 16.56421325346518207030483818876, 17.02877659297445331126598761800, 18.07075508038130769714087016678, 18.76898577293055198256677292180, 19.54484874952542853229609617889