Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(719,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.br (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 719.3 | ||
Character | \(\chi\) | \(=\) | 2160.719 |
Dual form | 2160.2.br.c.1439.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.74305 | + | 1.40063i | −0.779516 | + | 0.626382i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.45766 | + | 4.25679i | 0.928908 | + | 1.60892i | 0.785152 | + | 0.619302i | \(0.212585\pi\) |
0.143755 | + | 0.989613i | \(0.454082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62292 | + | 2.81098i | 0.489329 | + | 0.847542i | 0.999925 | − | 0.0122787i | \(-0.00390852\pi\) |
−0.510596 | + | 0.859821i | \(0.670575\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.94659 | + | 2.27856i | 1.09459 | + | 0.631960i | 0.934794 | − | 0.355191i | \(-0.115584\pi\) |
0.159793 | + | 0.987151i | \(0.448917\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.68147 | 1.13542 | 0.567712 | − | 0.823227i | \(-0.307829\pi\) | ||||
0.567712 | + | 0.823227i | \(0.307829\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.29982i | − | 0.527615i | −0.964575 | − | 0.263807i | \(-0.915022\pi\) | ||
0.964575 | − | 0.263807i | \(-0.0849783\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.41968 | − | 1.39700i | −0.504538 | − | 0.291295i | 0.226048 | − | 0.974116i | \(-0.427419\pi\) |
−0.730585 | + | 0.682821i | \(0.760753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07645 | − | 4.88275i | 0.215290 | − | 0.976550i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.841610 | + | 0.485904i | −0.156283 | + | 0.0902301i | −0.576102 | − | 0.817378i | \(-0.695427\pi\) |
0.419819 | + | 0.907608i | \(0.362094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.33350 | + | 4.81135i | 1.49674 | + | 0.864144i | 0.999993 | − | 0.00375071i | \(-0.00119389\pi\) |
0.496748 | + | 0.867895i | \(0.334527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2460 | − | 3.97752i | −1.73190 | − | 0.672324i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.32167i | 0.381679i | 0.981621 | + | 0.190840i | \(0.0611211\pi\) | ||||
−0.981621 | + | 0.190840i | \(0.938879\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.23509 | − | 4.75453i | −1.28611 | − | 0.742533i | −0.308148 | − | 0.951338i | \(-0.599709\pi\) |
−0.977957 | + | 0.208805i | \(0.933043\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.256227 | − | 0.443798i | −0.0390743 | − | 0.0676786i | 0.845827 | − | 0.533457i | \(-0.179108\pi\) |
−0.884901 | + | 0.465779i | \(0.845774\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.37017 | − | 4.25517i | 1.07505 | − | 0.620680i | 0.145493 | − | 0.989359i | \(-0.453523\pi\) |
0.929557 | + | 0.368679i | \(0.120190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.58018 | + | 14.8613i | −1.22574 | + | 2.12304i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.90660 | −1.36078 | −0.680388 | − | 0.732852i | \(-0.738189\pi\) | ||||
−0.680388 | + | 0.732852i | \(0.738189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.76598 | − | 2.62656i | −0.912325 | − | 0.354166i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.48077 | + | 2.56476i | −0.192779 | + | 0.333904i | −0.946170 | − | 0.323669i | \(-0.895083\pi\) |
0.753391 | + | 0.657573i | \(0.228417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.67840 | + | 2.90707i | 0.214897 | + | 0.372212i | 0.953241 | − | 0.302212i | \(-0.0977252\pi\) |
−0.738344 | + | 0.674424i | \(0.764392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.0705 | + | 1.55607i | −1.24910 | + | 0.193007i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.05210 | − | 7.01844i | 0.495042 | − | 0.857439i | −0.504941 | − | 0.863154i | \(-0.668486\pi\) |
0.999984 | + | 0.00571511i | \(0.00181918\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.66662 | 1.02854 | 0.514270 | − | 0.857629i | \(-0.328063\pi\) | ||||
0.514270 | + | 0.857629i | \(0.328063\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.66953i | 0.429486i | 0.976671 | + | 0.214743i | \(0.0688914\pi\) | ||||
−0.976671 | + | 0.214743i | \(0.931109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.97717 | + | 13.8169i | −0.909083 | + | 1.57458i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.00584899 | + | 0.00337691i | −0.000658062 | + | 0.000379932i | −0.500329 | − | 0.865835i | \(-0.666788\pi\) |
0.499671 | + | 0.866215i | \(0.333454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.41968 | − | 1.39700i | 0.265594 | − | 0.153341i | −0.361290 | − | 0.932454i | \(-0.617663\pi\) |
0.626884 | + | 0.779113i | \(0.284330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.16004 | + | 6.55703i | −0.885081 | + | 0.711210i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.952424i | 0.100957i | 0.998725 | + | 0.0504784i | \(0.0160746\pi\) | ||||
−0.998725 | + | 0.0504784i | \(0.983925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.3997i | 2.34813i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.22120 | + | 4.00870i | 0.330489 | + | 0.411284i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.07057 | + | 1.77279i | −0.311769 | + | 0.180000i | −0.647718 | − | 0.761880i | \(-0.724276\pi\) |
0.335949 | + | 0.941880i | \(0.390943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.59275 | + | 3.22898i | −0.556499 | + | 0.321295i | −0.751739 | − | 0.659460i | \(-0.770785\pi\) |
0.195240 | + | 0.980756i | \(0.437451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.43413 | − | 5.94809i | 0.338375 | − | 0.586083i | −0.645752 | − | 0.763547i | \(-0.723456\pi\) |
0.984127 | + | 0.177464i | \(0.0567894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.35683i | 0.807886i | 0.914784 | + | 0.403943i | \(0.132361\pi\) | ||||
−0.914784 | + | 0.403943i | \(0.867639\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.40624 | −0.805172 | −0.402586 | − | 0.915382i | \(-0.631889\pi\) | ||||
−0.402586 | + | 0.915382i | \(0.631889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.70815 | − | 13.3509i | 0.725121 | − | 1.25595i | −0.233803 | − | 0.972284i | \(-0.575117\pi\) |
0.958924 | − | 0.283663i | \(-0.0915497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.17431 | − | 0.954038i | 0.575757 | − | 0.0889645i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5055 | + | 19.9281i | 1.05470 | + | 1.82680i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.232264 | − | 0.402293i | 0.0211149 | − | 0.0365721i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.96264 | + | 10.0186i | 0.443872 | + | 0.896090i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.57050 | −0.316830 | −0.158415 | − | 0.987373i | \(-0.550638\pi\) | ||||
−0.158415 | + | 0.987373i | \(0.550638\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.63122 | + | 4.55740i | −0.229891 | + | 0.398182i | −0.957775 | − | 0.287517i | \(-0.907170\pi\) |
0.727885 | + | 0.685699i | \(0.240503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.78985 | − | 5.65217i | 0.848888 | − | 0.490105i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.02560 | + | 10.4366i | 0.514802 | + | 0.891663i | 0.999852 | + | 0.0171767i | \(0.00546779\pi\) |
−0.485051 | + | 0.874486i | \(0.661199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.8635 | − | 9.15882i | −1.34553 | − | 0.776841i | −0.357916 | − | 0.933754i | \(-0.616513\pi\) |
−0.987612 | + | 0.156913i | \(0.949846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.7917i | 1.23694i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.786396 | − | 2.02574i | 0.0653066 | − | 0.168229i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.2462 | − | 11.6891i | −1.65863 | − | 0.957612i | −0.973347 | − | 0.229338i | \(-0.926344\pi\) |
−0.685286 | − | 0.728274i | \(-0.740323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4153 | − | 8.90005i | 1.25448 | − | 0.724276i | 0.282486 | − | 0.959272i | \(-0.408841\pi\) |
0.971996 | + | 0.234996i | \(0.0755077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.2647 | + | 3.28576i | −1.70802 | + | 0.263919i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.22723 | − | 1.28589i | −0.177753 | − | 0.102626i | 0.408484 | − | 0.912766i | \(-0.366058\pi\) |
−0.586236 | + | 0.810140i | \(0.699391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.7334i | − | 1.08234i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.61388 | −0.361387 | −0.180694 | − | 0.983539i | \(-0.557834\pi\) | ||||
−0.180694 | + | 0.983539i | \(0.557834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.72157 | + | 2.72600i | 0.365366 | + | 0.210944i | 0.671432 | − | 0.741066i | \(-0.265680\pi\) |
−0.306066 | + | 0.952010i | \(0.599013\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.88370 | + | 6.72677i | 0.298746 | + | 0.517444i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0583 | + | 19.1535i | 0.840746 | + | 1.45621i | 0.889265 | + | 0.457393i | \(0.151217\pi\) |
−0.0485189 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.4304 | − | 7.41792i | 1.77117 | − | 0.560742i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.02225 | 0.674355 | 0.337177 | − | 0.941441i | \(-0.390528\pi\) | ||||
0.337177 | + | 0.941441i | \(0.390528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6415 | −1.01396 | −0.506982 | − | 0.861957i | \(-0.669239\pi\) | ||||
−0.506982 | + | 0.861957i | \(0.669239\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.25180 | − | 4.04678i | −0.239077 | − | 0.297525i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.59766 | + | 13.1595i | 0.555596 | + | 0.962320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.28131 | − | 9.14750i | −0.382142 | − | 0.661890i | 0.609226 | − | 0.792997i | \(-0.291480\pi\) |
−0.991368 | + | 0.131107i | \(0.958147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6860 | − | 7.90162i | −0.985140 | − | 0.568771i | −0.0813222 | − | 0.996688i | \(-0.525914\pi\) |
−0.903818 | + | 0.427917i | \(0.859248\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.0230 | 1.35533 | 0.677666 | − | 0.735370i | \(-0.262992\pi\) | ||||
0.677666 | + | 0.735370i | \(0.262992\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.43855i | − | 0.101976i | −0.998699 | − | 0.0509881i | \(-0.983763\pi\) | ||
0.998699 | − | 0.0509881i | \(-0.0162371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.13678 | − | 2.38837i | −0.290345 | − | 0.167631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0135 | − | 3.24696i | 1.46765 | − | 0.226777i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.46474 | − | 3.73242i | 0.447176 | − | 0.258177i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4153 | − | 8.90005i | −1.06124 | − | 0.612704i | −0.135462 | − | 0.990783i | \(-0.543252\pi\) |
−0.925774 | + | 0.378078i | \(0.876585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.06822 | + | 0.414683i | 0.0728517 | + | 0.0282811i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.2986i | 3.21084i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.4758 | + | 10.6670i | 1.24282 | + | 0.717542i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.772004 | + | 1.33715i | 0.0516972 | + | 0.0895422i | 0.890716 | − | 0.454560i | \(-0.150204\pi\) |
−0.839019 | + | 0.544102i | \(0.816870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.32514 | − | 4.22917i | 0.486187 | − | 0.280700i | −0.236804 | − | 0.971557i | \(-0.576100\pi\) |
0.722991 | + | 0.690857i | \(0.242767\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.13038 | − | 7.15403i | 0.272943 | − | 0.472752i | −0.696671 | − | 0.717391i | \(-0.745336\pi\) |
0.969614 | + | 0.244639i | \(0.0786696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6573 | −0.960229 | −0.480115 | − | 0.877206i | \(-0.659405\pi\) | ||||
−0.480115 | + | 0.877206i | \(0.659405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88665 | + | 17.7399i | −0.449235 | + | 1.15722i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.171965 | + | 0.297852i | −0.0111235 | + | 0.0192664i | −0.871534 | − | 0.490336i | \(-0.836874\pi\) |
0.860410 | + | 0.509602i | \(0.170207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.93539 | + | 8.54834i | 0.317916 | + | 0.550647i | 0.980053 | − | 0.198736i | \(-0.0636836\pi\) |
−0.662137 | + | 0.749383i | \(0.730350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.85956 | − | 37.9217i | −0.374354 | − | 2.42273i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.24028 | − | 9.07644i | 0.333431 | − | 0.577520i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5795 | −1.04649 | −0.523243 | − | 0.852183i | \(-0.675278\pi\) | ||||
−0.523243 | + | 0.852183i | \(0.675278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.06888i | − | 0.570156i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.09105 | + | 12.2821i | −0.442327 | + | 0.766133i | −0.997862 | − | 0.0653601i | \(-0.979180\pi\) |
0.555534 | + | 0.831494i | \(0.312514\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.88284 | + | 5.70586i | −0.614090 | + | 0.354545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.76712 | − | 2.75230i | 0.293953 | − | 0.169714i | −0.345770 | − | 0.938319i | \(-0.612382\pi\) |
0.639723 | + | 0.768605i | \(0.279049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.2677 | − | 13.8755i | 1.06075 | − | 0.852367i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 23.3589i | − | 1.42422i | −0.702069 | − | 0.712109i | \(-0.747740\pi\) | ||
0.702069 | − | 0.712109i | \(-0.252260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.4755i | − | 1.18305i | −0.806287 | − | 0.591525i | \(-0.798526\pi\) | ||
0.806287 | − | 0.591525i | \(-0.201474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4723 | − | 4.89843i | 0.933015 | − | 0.295387i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.4830 | + | 12.4032i | −1.29079 | + | 0.745236i | −0.978794 | − | 0.204848i | \(-0.934330\pi\) |
−0.311994 | + | 0.950084i | \(0.600997\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2519 | + | 12.8471i | −1.32743 | + | 0.766395i | −0.984902 | − | 0.173112i | \(-0.944618\pi\) |
−0.342532 | + | 0.939506i | \(0.611285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.17373 | − | 12.4253i | 0.426434 | − | 0.738605i | −0.570119 | − | 0.821562i | \(-0.693103\pi\) |
0.996553 | + | 0.0829568i | \(0.0264363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 46.7401i | − | 2.75898i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.91619 | 0.289188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.76145 | − | 15.1753i | 0.511849 | − | 0.886549i | −0.488056 | − | 0.872812i | \(-0.662294\pi\) |
0.999906 | − | 0.0137369i | \(-0.00437272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.01124 | − | 6.54452i | −0.0588768 | − | 0.381037i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.36631 | − | 11.0268i | −0.368173 | − | 0.637695i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.25944 | − | 2.18141i | 0.0725928 | − | 0.125734i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.99727 | − | 2.71635i | −0.400663 | − | 0.155538i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.415391 | 0.0237076 | 0.0118538 | − | 0.999930i | \(-0.496227\pi\) | ||||
0.0118538 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8799 | + | 18.8446i | −0.616943 | + | 1.06858i | 0.373097 | + | 0.927792i | \(0.378296\pi\) |
−0.990040 | + | 0.140784i | \(0.955038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.8846 | − | 10.3257i | 1.01090 | − | 0.583641i | 0.0994419 | − | 0.995043i | \(-0.468294\pi\) |
0.911454 | + | 0.411403i | \(0.134961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.28802 | + | 9.15912i | 0.297005 | + | 0.514428i | 0.975449 | − | 0.220224i | \(-0.0706789\pi\) |
−0.678444 | + | 0.734652i | \(0.737346\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73173 | − | 1.57717i | −0.152948 | − | 0.0883044i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.7665i | − | 0.599066i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.3740 | − | 16.8174i | 0.852794 | − | 0.932864i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.2267 | + | 20.9155i | 1.99725 | + | 1.15311i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.59592 | + | 1.49876i | −0.142685 | + | 0.0823791i | −0.569643 | − | 0.821892i | \(-0.692918\pi\) |
0.426958 | + | 0.904271i | \(0.359585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.76725 | + | 17.9090i | 0.151191 | + | 0.978473i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.9848 | − | 14.4250i | −1.36101 | − | 0.785780i | −0.371252 | − | 0.928532i | \(-0.621072\pi\) |
−0.989758 | + | 0.142752i | \(0.954405\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.2337i | 1.69140i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −49.9414 | −2.69658 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.84132 | + | 4.52719i | 0.420944 | + | 0.243032i | 0.695481 | − | 0.718544i | \(-0.255191\pi\) |
−0.274537 | + | 0.961577i | \(0.588525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.32154 | − | 12.6813i | −0.391913 | − | 0.678813i | 0.600789 | − | 0.799408i | \(-0.294853\pi\) |
−0.992702 | + | 0.120595i | \(0.961520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.20672 | − | 9.01831i | −0.277126 | − | 0.479996i | 0.693543 | − | 0.720415i | \(-0.256049\pi\) |
−0.970669 | + | 0.240419i | \(0.922715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1064 | + | 12.1388i | −0.801763 | + | 0.644259i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.0275 | 1.16257 | 0.581283 | − | 0.813701i | \(-0.302551\pi\) | ||||
0.581283 | + | 0.813701i | \(0.302551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7108 | 0.721623 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.13967 | − | 6.39618i | −0.269023 | − | 0.334791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.7698 | + | 30.7782i | 0.927577 | + | 1.60661i | 0.787363 | + | 0.616490i | \(0.211446\pi\) |
0.140214 | + | 0.990121i | \(0.455221\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.3471 | − | 42.1703i | −1.26404 | − | 2.18937i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.66594 | − | 3.27123i | −0.293371 | − | 0.169378i | 0.346090 | − | 0.938201i | \(-0.387509\pi\) |
−0.639461 | + | 0.768823i | \(0.720843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.42865 | −0.228087 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2443i | 0.731682i | 0.930677 | + | 0.365841i | \(0.119219\pi\) | ||||
−0.930677 | + | 0.365841i | \(0.880781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.10979 | − | 4.68219i | −0.414391 | − | 0.239249i | 0.278284 | − | 0.960499i | \(-0.410234\pi\) |
−0.692675 | + | 0.721250i | \(0.743568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.44775 | − | 35.2566i | −0.277643 | − | 1.79684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.64156 | − | 4.41186i | 0.387442 | − | 0.223690i | −0.293609 | − | 0.955926i | \(-0.594856\pi\) |
0.681051 | + | 0.732236i | \(0.261523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3277 | − | 6.54002i | −0.572864 | − | 0.330743i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.00546526 | − | 0.0140784i | 0.000274987 | − | 0.000708362i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.68445i | 0.0845401i | 0.999106 | + | 0.0422700i | \(0.0134590\pi\) | ||||
−0.999106 | + | 0.0422700i | \(0.986541\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.7375 | + | 7.93137i | 0.686020 | + | 0.396074i | 0.802119 | − | 0.597164i | \(-0.203706\pi\) |
−0.116099 | + | 0.993238i | \(0.537039\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.9259 | + | 37.9768i | 1.09221 | + | 1.89176i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.52615 | + | 3.76788i | −0.323489 | + | 0.186767i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0555181 | + | 0.0961601i | −0.00274519 | + | 0.00475481i | −0.867395 | − | 0.497621i | \(-0.834207\pi\) |
0.864650 | + | 0.502376i | \(0.167540\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.5569 | −0.716297 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.26093 | + | 5.82412i | −0.110985 | + | 0.285895i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.66122 | − | 16.7337i | 0.471981 | − | 0.817496i | −0.527505 | − | 0.849552i | \(-0.676872\pi\) |
0.999486 | + | 0.0320563i | \(0.0102056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.4323 | − | 31.9258i | −0.898337 | − | 1.55597i | −0.829619 | − | 0.558330i | \(-0.811442\pi\) |
−0.0687183 | − | 0.997636i | \(-0.521891\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.03937 | − | 22.8585i | 0.244445 | − | 1.10880i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24986 | + | 14.2892i | −0.399239 | + | 0.691502i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5407 | 0.748571 | 0.374286 | − | 0.927313i | \(-0.377888\pi\) | ||||
0.374286 | + | 0.927313i | \(0.377888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.23429i | − | 0.395715i | −0.980231 | − | 0.197857i | \(-0.936602\pi\) | ||
0.980231 | − | 0.197857i | \(-0.0633983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.21285 | + | 5.56482i | −0.153691 | + | 0.266201i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8199 | − | 16.6392i | 1.37550 | − | 0.794145i | 0.383886 | − | 0.923381i | \(-0.374586\pi\) |
0.991614 | + | 0.129235i | \(0.0412523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.6345 | + | 6.71718i | −0.552772 | + | 0.319143i | −0.750239 | − | 0.661167i | \(-0.770062\pi\) |
0.197467 | + | 0.980309i | \(0.436728\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.33400 | − | 1.66012i | −0.0632376 | − | 0.0786974i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4331i | 1.43622i | 0.695927 | + | 0.718112i | \(0.254994\pi\) | ||||
−0.695927 | + | 0.718112i | \(0.745006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 30.8649i | − | 1.45337i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.3738 | − | 39.0439i | −1.47083 | − | 1.83040i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.90969 | − | 3.98931i | 0.323222 | − | 0.186612i | −0.329606 | − | 0.944119i | \(-0.606916\pi\) |
0.652828 | + | 0.757507i | \(0.273583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8613 | − | 13.1990i | 1.06476 | − | 0.614738i | 0.138014 | − | 0.990430i | \(-0.455928\pi\) |
0.926745 | + | 0.375692i | \(0.122595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.473161 | + | 0.819539i | −0.0219896 | + | 0.0380872i | −0.876811 | − | 0.480836i | \(-0.840333\pi\) |
0.854821 | + | 0.518923i | \(0.173667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.4606i | 1.59464i | 0.603554 | + | 0.797322i | \(0.293751\pi\) | ||||
−0.603554 | + | 0.797322i | \(0.706249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.8347 | 1.83940 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.831672 | − | 1.44050i | 0.0382403 | − | 0.0662342i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.2294 | − | 2.47564i | −0.515242 | − | 0.113590i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.07387 | + | 5.32411i | 0.140449 | + | 0.243265i | 0.927666 | − | 0.373412i | \(-0.121812\pi\) |
−0.787217 | + | 0.616676i | \(0.788479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.29006 | + | 9.16265i | −0.241206 | + | 0.417781i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.86912 | − | 7.39081i | 0.130280 | − | 0.335600i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.7766 | 0.896164 | 0.448082 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448082 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.30861 | + | 5.73068i | −0.149316 | + | 0.258622i | −0.930975 | − | 0.365084i | \(-0.881040\pi\) |
0.781659 | + | 0.623706i | \(0.214374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.93998 | + | 2.27475i | −0.177448 | + | 0.102449i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.2996 | + | 36.8920i | 0.955418 | + | 1.65483i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7185 | + | 8.49775i | 0.658892 | + | 0.380412i | 0.791855 | − | 0.610710i | \(-0.209116\pi\) |
−0.132963 | + | 0.991121i | \(0.542449\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.4892i | 0.690631i | 0.938487 | + | 0.345316i | \(0.112228\pi\) | ||||
−0.938487 | + | 0.345316i | \(0.887772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.22583 | − | 13.4617i | 0.232547 | − | 0.599036i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.57111 | + | 4.37118i | 0.335584 | + | 0.193749i | 0.658317 | − | 0.752741i | \(-0.271269\pi\) |
−0.322734 | + | 0.946490i | \(0.604602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.6204 | + | 9.01846i | −0.691007 | + | 0.398953i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.34523 | + | 15.1778i | 0.103343 | + | 0.668813i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.9224 | + | 13.8116i | 1.05211 | + | 0.607433i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 34.5835i | − | 1.51513i | −0.652758 | − | 0.757566i | \(-0.726388\pi\) | ||
0.652758 | − | 0.757566i | \(-0.273612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1425 | 0.443501 | 0.221751 | − | 0.975103i | \(-0.428823\pi\) | ||||
0.221751 | + | 0.975103i | \(0.428823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.0131 | + | 22.5242i | 1.69944 | + | 0.981170i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.59678 | − | 13.1580i | −0.330295 | − | 0.572087i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6670 | − | 37.5284i | −0.938503 | − | 1.62553i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7049 | − | 14.5664i | −0.506045 | − | 0.629760i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −55.6998 | −2.39916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.9906 | 0.945450 | 0.472725 | − | 0.881210i | \(-0.343270\pi\) | ||||
0.472725 | + | 0.881210i | \(0.343270\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.6525 | − | 11.7741i | 0.627645 | − | 0.504346i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.66047 | + | 11.5363i | 0.284781 | + | 0.493256i | 0.972556 | − | 0.232668i | \(-0.0747457\pi\) |
−0.687775 | + | 0.725924i | \(0.741412\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.11749 | + | 1.93555i | 0.0476067 | + | 0.0824573i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0287496 | − | 0.0165986i | −0.00122256 | − | 0.000705845i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.2286 | 0.475771 | 0.237885 | − | 0.971293i | \(-0.423546\pi\) | ||||
0.237885 | + | 0.971293i | \(0.423546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.33532i | − | 0.0987735i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.3748 | − | 15.2275i | −1.11157 | − | 0.641764i | −0.172332 | − | 0.985039i | \(-0.555130\pi\) |
−0.939235 | + | 0.343275i | \(0.888464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.26403 | + | 34.0676i | 0.221460 | + | 1.43323i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2927 | − | 12.2934i | 0.892638 | − | 0.515365i | 0.0178334 | − | 0.999841i | \(-0.494323\pi\) |
0.874804 | + | 0.484476i | \(0.160990\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.86354 | − | 5.69472i | −0.412776 | − | 0.238317i | 0.279206 | − | 0.960231i | \(-0.409929\pi\) |
−0.691982 | + | 0.721915i | \(0.743262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.42587 | + | 10.3109i | −0.393086 | + | 0.429993i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.96503i | − | 0.165066i | −0.996588 | − | 0.0825331i | \(-0.973699\pi\) | ||
0.996588 | − | 0.0825331i | \(-0.0263010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8935 | + | 6.86671i | 0.493425 | + | 0.284879i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.0776 | − | 27.8473i | −0.665867 | − | 1.15332i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.6601 | − | 16.5469i | 1.18293 | − | 0.682965i | 0.226240 | − | 0.974072i | \(-0.427357\pi\) |
0.956691 | + | 0.291106i | \(0.0940233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.0652 | − | 19.1655i | 0.455935 | − | 0.789703i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4391 | 0.839334 | 0.419667 | − | 0.907678i | \(-0.362147\pi\) | ||||
0.419667 | + | 0.907678i | \(0.362147\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.9665 | − | 18.6207i | −1.96644 | − | 0.763373i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8710 | − | 37.8817i | 0.893625 | − | 1.54780i | 0.0581288 | − | 0.998309i | \(-0.481487\pi\) |
0.835497 | − | 0.549496i | \(-0.185180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1919 | − | 19.3850i | −0.456529 | − | 0.790732i | 0.542246 | − | 0.840220i | \(-0.317574\pi\) |
−0.998775 | + | 0.0494884i | \(0.984241\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.158617 | + | 1.02653i | 0.00644871 | + | 0.0417345i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1622 | − | 21.0656i | 0.493649 | − | 0.855025i | −0.506325 | − | 0.862343i | \(-0.668996\pi\) |
0.999973 | + | 0.00731837i | \(0.00232953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.7827 | 1.56898 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7753i | 0.637157i | 0.947896 | + | 0.318579i | \(0.103205\pi\) | ||||
−0.947896 | + | 0.318579i | \(0.896795\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.17947 | − | 5.50700i | 0.128001 | − | 0.221703i | −0.794901 | − | 0.606739i | \(-0.792477\pi\) |
0.922902 | + | 0.385035i | \(0.125811\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.7015 | + | 15.9935i | −1.11342 | + | 0.642832i | −0.939712 | − | 0.341966i | \(-0.888907\pi\) |
−0.173705 | + | 0.984798i | \(0.555574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.05427 | + | 2.34073i | −0.162431 | + | 0.0937795i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6825 | − | 10.5121i | −0.907300 | − | 0.420483i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.8688i | 0.433368i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.8543i | 0.830196i | 0.909777 | + | 0.415098i | \(0.136253\pi\) | ||||
−0.909777 | + | 0.415098i | \(0.863747\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.22356 | − | 5.00096i | 0.246974 | − | 0.198457i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −67.7249 | + | 39.1010i | −2.68336 | + | 1.54924i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5324 | − | 15.3185i | 1.04797 | − | 0.605043i | 0.125886 | − | 0.992045i | \(-0.459823\pi\) |
0.922079 | + | 0.387002i | \(0.126489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.0142 | − | 32.9335i | 0.749846 | − | 1.29877i | −0.198050 | − | 0.980192i | \(-0.563461\pi\) |
0.947896 | − | 0.318580i | \(-0.103206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 28.3431i | − | 1.11428i | −0.830417 | − | 0.557142i | \(-0.811898\pi\) | ||
0.830417 | − | 0.557142i | \(-0.188102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.61266 | −0.377330 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.2134 | − | 19.4221i | 0.438813 | − | 0.760046i | −0.558785 | − | 0.829312i | \(-0.688732\pi\) |
0.997598 | + | 0.0692663i | \(0.0220658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.79691 | − | 11.6292i | −0.0702110 | − | 0.454389i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.01881 | − | 6.96078i | −0.156551 | − | 0.271154i | 0.777072 | − | 0.629412i | \(-0.216704\pi\) |
−0.933623 | + | 0.358258i | \(0.883371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1926 | − | 17.6542i | 0.396448 | − | 0.686668i | −0.596837 | − | 0.802362i | \(-0.703576\pi\) |
0.993285 | + | 0.115695i | \(0.0369095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.14758 | + | 23.5640i | −0.354728 | + | 0.913773i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.71523 | 0.105134 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.44781 | + | 9.43588i | −0.210310 | + | 0.364268i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.6402 | − | 13.6487i | 0.911264 | − | 0.526119i | 0.0304264 | − | 0.999537i | \(-0.490313\pi\) |
0.880838 | + | 0.473418i | \(0.156980\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7854 | + | 32.5373i | 0.721981 | + | 1.25051i | 0.960205 | + | 0.279298i | \(0.0901017\pi\) |
−0.238223 | + | 0.971210i | \(0.576565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0928 | − | 8.71385i | −0.579210 | − | 0.334407i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.779851i | 0.0298402i | 0.999889 | + | 0.0149201i | \(0.00474938\pi\) | ||||
−0.999889 | + | 0.0149201i | \(0.995251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.1208 | − | 9.75194i | −0.959818 | − | 0.372602i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.0973 | − | 22.5728i | −1.48949 | − | 0.859956i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.5980 | + | 13.0469i | −0.859668 | + | 0.496329i | −0.863901 | − | 0.503662i | \(-0.831986\pi\) |
0.00423336 | + | 0.999991i | \(0.498652\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.4791 | − | 6.25473i | 1.53546 | − | 0.237255i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.5524 | − | 22.2582i | −1.46028 | − | 0.843090i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.3745i | − | 0.618458i | −0.950988 | − | 0.309229i | \(-0.899929\pi\) | ||
0.950988 | − | 0.309229i | \(-0.100071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.33941 | 0.201380 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.4901 | − | 15.8714i | −1.03387 | − | 0.596907i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.64926 | + | 16.7130i | 0.362385 | + | 0.627670i | 0.988353 | − | 0.152179i | \(-0.0486291\pi\) |
−0.625968 | + | 0.779849i | \(0.715296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.4429 | − | 23.2838i | −0.503441 | − | 0.871986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.7178 | − | 25.7827i | −0.774800 | − | 0.964218i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.2738 | −1.72572 | −0.862860 | − | 0.505442i | \(-0.831329\pi\) | ||||
−0.862860 | + | 0.505442i | \(0.831329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.7597 | 1.25728 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.46660 | + | 4.63243i | 0.0544680 | + | 0.172044i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.16075 | − | 15.8669i | −0.339753 | − | 0.588470i | 0.644633 | − | 0.764492i | \(-0.277010\pi\) |
−0.984386 | + | 0.176022i | \(0.943677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.19952 | − | 2.07763i | −0.0443659 | − | 0.0768439i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.01463 | + | 2.31785i | 0.148284 | + | 0.0856117i | 0.572306 | − | 0.820040i | \(-0.306049\pi\) |
−0.424022 | + | 0.905652i | \(0.639382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.3049 | 0.968954 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.4405i | − | 0.420844i | −0.977611 | − | 0.210422i | \(-0.932516\pi\) | ||
0.977611 | − | 0.210422i | \(-0.0674839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.6156 | + | 13.6345i | 0.866373 | + | 0.500201i | 0.866141 | − | 0.499799i | \(-0.166593\pi\) |
0.000231838 | 1.00000i | \(0.499926\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.6624 | − | 7.98273i | 1.89276 | − | 0.292465i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.5733 | + | 20.5383i | −1.29982 | + | 0.750451i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9256 | + | 14.3908i | 0.909549 | + | 0.525128i | 0.880286 | − | 0.474443i | \(-0.157351\pi\) |
0.0292631 | + | 0.999572i | \(0.490684\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.4040 | + | 37.1045i | −0.524215 | + | 1.35037i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.6191i | 1.40363i | 0.712357 | + | 0.701817i | \(0.247628\pi\) | ||||
−0.712357 | + | 0.701817i | \(0.752372\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.7901 | − | 6.22969i | −0.391142 | − | 0.225826i | 0.291513 | − | 0.956567i | \(-0.405841\pi\) |
−0.682655 | + | 0.730741i | \(0.739175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.6597 | − | 35.7836i | −0.747931 | − | 1.29545i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.6879 | + | 6.74804i | −0.422027 | + | 0.243658i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7262 | − | 35.8988i | 0.747405 | − | 1.29454i | −0.201657 | − | 0.979456i | \(-0.564633\pi\) |
0.949062 | − | 0.315088i | \(-0.102034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.8158 | 0.460954 | 0.230477 | − | 0.973078i | \(-0.425971\pi\) | ||||
0.230477 | + | 0.973078i | \(0.425971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.4632 | − | 35.5112i | 1.16611 | − | 1.27560i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.9346 | + | 18.9392i | −0.391772 | + | 0.678568i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0652 | + | 24.3617i | 0.503294 | + | 0.871730i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.68325 | − | 0.878161i | 0.202844 | − | 0.0313429i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.29742 | + | 2.24720i | −0.0462481 | + | 0.0801041i | −0.888223 | − | 0.459413i | \(-0.848060\pi\) |
0.841975 | + | 0.539517i | \(0.181393\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 75.7760 | 2.69428 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2973i | 0.543225i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.96403 | − | 3.40180i | 0.0695695 | − | 0.120498i | −0.829142 | − | 0.559038i | \(-0.811171\pi\) |
0.898712 | + | 0.438540i | \(0.144504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5033 | − | 19.9205i | 1.22064 | − | 0.704736i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.3150 | + | 5.95535i | −0.364008 | + | 0.210160i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.2355 | + | 23.9380i | 0.677962 | + | 0.843705i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.6490i | 0.831454i | 0.909489 | + | 0.415727i | \(0.136473\pi\) | ||||
−0.909489 | + | 0.415727i | \(0.863527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.1396i | 1.05834i | 0.848515 | + | 0.529172i | \(0.177497\pi\) | ||||
−0.848515 | + | 0.529172i | \(0.822503\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.04223 | − | 6.46236i | 0.281707 | − | 0.226367i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.02066 | + | 0.589276i | −0.0357082 | + | 0.0206162i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.5981 | + | 16.5111i | −0.998081 | + | 0.576242i | −0.907680 | − | 0.419663i | \(-0.862148\pi\) |
−0.0904010 | + | 0.995905i | \(0.528815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.3286 | + | 47.3345i | −0.952615 | + | 1.64998i | −0.212881 | + | 0.977078i | \(0.568285\pi\) |
−0.739734 | + | 0.672900i | \(0.765049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 7.83653i | − | 0.272503i | −0.990674 | − | 0.136251i | \(-0.956494\pi\) | ||
0.990674 | − | 0.136251i | \(-0.0435055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.3314 | −1.57442 | −0.787211 | − | 0.616683i | \(-0.788476\pi\) | ||||
−0.787211 | + | 0.616683i | \(0.788476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.1679 | + | 69.5728i | −1.39173 | + | 2.41056i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0481 | + | 1.86163i | −0.416940 | + | 0.0644245i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.1201 | − | 20.9926i | −0.418432 | − | 0.724745i | 0.577350 | − | 0.816497i | \(-0.304087\pi\) |
−0.995782 | + | 0.0917514i | \(0.970753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0278 | + | 24.2969i | −0.483717 | + | 0.837823i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.1912 | − | 6.28546i | −0.556995 | − | 0.216226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.28330 | 0.0784552 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.24337 | − | 5.61768i | 0.111181 | − | 0.192572i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.9184 | + | 8.03581i | −0.476558 | + | 0.275141i | −0.718981 | − | 0.695030i | \(-0.755391\pi\) |
0.242423 | + | 0.970171i | \(0.422058\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.14515 | − | 1.98346i | −0.0391177 | − | 0.0677538i | 0.845804 | − | 0.533494i | \(-0.179121\pi\) |
−0.884921 | + | 0.465740i | \(0.845788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.7347 | + | 14.8579i | 0.878056 | + | 0.506946i | 0.870017 | − | 0.493022i | \(-0.164108\pi\) |
0.00803922 | + | 0.999968i | \(0.497441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.7002i | 1.18121i | 0.806961 | + | 0.590605i | \(0.201111\pi\) | ||||
−0.806961 | + | 0.590605i | \(0.798889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.1022 | − | 17.8969i | −1.56752 | − | 0.608514i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.0189849 | − | 0.0109609i | −0.000644018 | − | 0.000371824i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.9839 | − | 18.4659i | 1.08373 | − | 0.625694i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.4506 | + | 45.7472i | −1.02942 | + | 1.54654i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.08267 | + | 2.35713i | 0.137862 | + | 0.0795947i | 0.567345 | − | 0.823480i | \(-0.307971\pi\) |
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.1882i | − | 1.38766i | −0.720136 | − | 0.693832i | \(-0.755921\pi\) | ||
0.720136 | − | 0.693832i | \(-0.244079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9479 | 0.906870 | 0.453435 | − | 0.891289i | \(-0.350198\pi\) | ||||
0.453435 | + | 0.891289i | \(0.350198\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.0614320 | − | 0.0354678i | −0.00206269 | − | 0.00119089i | 0.498968 | − | 0.866620i | \(-0.333712\pi\) |
−0.501031 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.77507 | − | 15.1989i | −0.294306 | − | 0.509753i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.78612 | − | 16.9501i | −0.327480 | − | 0.567212i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.7262 | + | 12.6369i | −0.525670 | + | 0.422404i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.35142 | −0.311887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.3775 | −1.54506 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.7778 | − | 19.1067i | 0.790401 | − | 0.635129i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5017 | + | 32.0459i | 0.614340 | + | 1.06407i | 0.990500 | + | 0.137513i | \(0.0439110\pi\) |
−0.376160 | + | 0.926555i | \(0.622756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.7405 | + | 28.9954i | 0.554637 | + | 0.960660i | 0.997932 | + | 0.0642840i | \(0.0204763\pi\) |
−0.443294 | + | 0.896376i | \(0.646190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.85388 | + | 4.53444i | 0.259926 | + | 0.150068i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.8665 | −0.854189 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.0547i | 1.22232i | 0.791506 | + | 0.611161i | \(0.209297\pi\) | ||||
−0.791506 | + | 0.611161i | \(0.790703\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.2036 | + | 19.7475i | 1.12583 | + | 0.649995i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3361 | + | 2.49916i | 0.372729 | + | 0.0821718i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.32859 | + | 1.92176i | −0.109208 | + | 0.0630510i | −0.553609 | − | 0.832777i | \(-0.686750\pi\) |
0.444401 | + | 0.895828i | \(0.353416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.1783 | + | 19.7329i | 1.12015 | + | 0.646718i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.6748 | − | 12.2962i | −1.03588 | − | 0.402128i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6287i | 0.673912i | 0.941520 | + | 0.336956i | \(0.109397\pi\) | ||||
−0.941520 | + | 0.336956i | \(0.890603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.3168 | + | 12.3072i | 0.694907 | + | 0.401205i | 0.805448 | − | 0.592667i | \(-0.201925\pi\) |
−0.110541 | + | 0.993872i | \(0.535258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2842 | + | 23.0089i | 0.432592 | + | 0.749272i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.4985 | − | 12.9895i | 0.731104 | − | 0.422103i | −0.0877216 | − | 0.996145i | \(-0.527959\pi\) |
0.818826 | + | 0.574042i | \(0.194625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.36126 | + | 14.4821i | −0.271418 | + | 0.470110i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.7615 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.0179 | + | 8.54737i | 0.712482 | + | 0.276586i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.6177 | + | 51.2994i | −0.956407 | + | 1.65655i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.7982 | + | 53.3440i | 0.993490 | + | 1.72077i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.9227 | − | 5.39616i | 1.12420 | − | 0.173709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.5551 | + | 33.8704i | −0.628849 | + | 1.08920i | 0.358934 | + | 0.933363i | \(0.383140\pi\) |
−0.987783 | + | 0.155835i | \(0.950193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5132 | 0.754574 | 0.377287 | − | 0.926096i | \(-0.376857\pi\) | ||||
0.377287 | + | 0.926096i | \(0.376857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 90.0371i | − | 2.88646i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.9499 | + | 34.5542i | −0.638253 | + | 1.10549i | 0.347563 | + | 0.937657i | \(0.387009\pi\) |
−0.985816 | + | 0.167830i | \(0.946324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.67724 | + | 1.54571i | −0.0855651 | + | 0.0494010i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.2536 | + | 24.9725i | −1.37958 | + | 0.796499i | −0.992108 | − | 0.125384i | \(-0.959984\pi\) |
−0.387469 | + | 0.921883i | \(0.626650\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.1580 | + | 26.6442i | −1.05650 | + | 0.848956i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.43180i | 0.0455285i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.3553i | 1.18663i | 0.804971 | + | 0.593315i | \(0.202181\pi\) | ||||
−0.804971 | + | 0.593315i | \(0.797819\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01488 | + | 2.50747i | 0.0638761 | + | 0.0794921i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.6518 | − | 25.7797i | 1.41414 | − | 0.816452i | 0.418361 | − | 0.908281i | \(-0.362605\pi\) |
0.995775 | + | 0.0918294i | \(0.0292714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2160.2.br.c.719.3 | 24 | ||
3.2 | odd | 2 | 720.2.br.d.239.2 | yes | 24 | ||
4.3 | odd | 2 | 2160.2.br.d.719.3 | 24 | |||
5.4 | even | 2 | inner | 2160.2.br.c.719.7 | 24 | ||
9.2 | odd | 6 | 2160.2.br.d.1439.7 | 24 | |||
9.7 | even | 3 | 720.2.br.c.479.2 | yes | 24 | ||
12.11 | even | 2 | 720.2.br.c.239.11 | yes | 24 | ||
15.14 | odd | 2 | 720.2.br.d.239.11 | yes | 24 | ||
20.19 | odd | 2 | 2160.2.br.d.719.7 | 24 | |||
36.7 | odd | 6 | 720.2.br.d.479.11 | yes | 24 | ||
36.11 | even | 6 | inner | 2160.2.br.c.1439.7 | 24 | ||
45.29 | odd | 6 | 2160.2.br.d.1439.3 | 24 | |||
45.34 | even | 6 | 720.2.br.c.479.11 | yes | 24 | ||
60.59 | even | 2 | 720.2.br.c.239.2 | ✓ | 24 | ||
180.79 | odd | 6 | 720.2.br.d.479.2 | yes | 24 | ||
180.119 | even | 6 | inner | 2160.2.br.c.1439.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.br.c.239.2 | ✓ | 24 | 60.59 | even | 2 | ||
720.2.br.c.239.11 | yes | 24 | 12.11 | even | 2 | ||
720.2.br.c.479.2 | yes | 24 | 9.7 | even | 3 | ||
720.2.br.c.479.11 | yes | 24 | 45.34 | even | 6 | ||
720.2.br.d.239.2 | yes | 24 | 3.2 | odd | 2 | ||
720.2.br.d.239.11 | yes | 24 | 15.14 | odd | 2 | ||
720.2.br.d.479.2 | yes | 24 | 180.79 | odd | 6 | ||
720.2.br.d.479.11 | yes | 24 | 36.7 | odd | 6 | ||
2160.2.br.c.719.3 | 24 | 1.1 | even | 1 | trivial | ||
2160.2.br.c.719.7 | 24 | 5.4 | even | 2 | inner | ||
2160.2.br.c.1439.3 | 24 | 180.119 | even | 6 | inner | ||
2160.2.br.c.1439.7 | 24 | 36.11 | even | 6 | inner | ||
2160.2.br.d.719.3 | 24 | 4.3 | odd | 2 | |||
2160.2.br.d.719.7 | 24 | 20.19 | odd | 2 | |||
2160.2.br.d.1439.3 | 24 | 45.29 | odd | 6 | |||
2160.2.br.d.1439.7 | 24 | 9.2 | odd | 6 |