Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(493,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.l (of order \(4\), degree \(2\), 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 28 x^{10} - 64 x^{9} + 236 x^{8} - 420 x^{7} + 946 x^{6} - 1216 x^{5} + 1896 x^{4} + \cdots + 1370 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1557.1 | ||
Root | \(1.24060 + 1.01288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1557 |
Dual form | 1900.2.l.b.493.1 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.25348 | − | 2.25348i | −1.30105 | − | 1.30105i | −0.927687 | − | 0.373359i | \(-0.878206\pi\) |
−0.373359 | − | 0.927687i | \(-0.621794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48119 | + | 1.48119i | 0.559839 | + | 0.559839i | 0.929261 | − | 0.369423i | \(-0.120445\pi\) |
−0.369423 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.15633i | 2.38544i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.806063 | 0.243037 | 0.121519 | − | 0.992589i | \(-0.461224\pi\) | ||||
0.121519 | + | 0.992589i | \(0.461224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.437032 | + | 0.437032i | 0.121211 | + | 0.121211i | 0.765110 | − | 0.643899i | \(-0.222684\pi\) |
−0.643899 | + | 0.765110i | \(0.722684\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.15633 | − | 3.15633i | −0.765521 | − | 0.765521i | 0.211793 | − | 0.977315i | \(-0.432070\pi\) |
−0.977315 | + | 0.211793i | \(0.932070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81645 | + | 3.96239i | 0.416721 | + | 0.909034i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.67568i | − | 1.45675i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.86907 | + | 1.86907i | −0.389728 | + | 0.389728i | −0.874590 | − | 0.484863i | \(-0.838870\pi\) |
0.484863 | + | 0.874590i | \(0.338870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.36619 | − | 9.36619i | 1.80252 | − | 1.80252i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50696 | −0.836921 | −0.418460 | − | 0.908235i | \(-0.637430\pi\) | ||||
−0.418460 | + | 0.908235i | \(0.637430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.67568i | − | 1.19899i | −0.800380 | − | 0.599494i | \(-0.795369\pi\) | ||
0.800380 | − | 0.599494i | \(-0.204631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.81645 | − | 1.81645i | −0.316203 | − | 0.316203i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.29626 | + | 5.29626i | −0.870700 | + | 0.870700i | −0.992549 | − | 0.121848i | \(-0.961118\pi\) |
0.121848 | + | 0.992549i | \(0.461118\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.96968i | − | 0.315402i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.1826i | − | 1.74643i | −0.487332 | − | 0.873217i | \(-0.662030\pi\) | ||
0.487332 | − | 0.873217i | \(-0.337970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.86907 | − | 3.86907i | 0.590027 | − | 0.590027i | −0.347611 | − | 0.937639i | \(-0.613007\pi\) |
0.937639 | + | 0.347611i | \(0.113007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.83146 | − | 6.83146i | −0.996470 | − | 0.996470i | 0.00352351 | − | 0.999994i | \(-0.498878\pi\) |
−0.999994 | + | 0.00352351i | \(0.998878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 2.61213i | − | 0.373161i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.2254i | 1.99196i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.92916 | − | 8.92916i | −1.22651 | − | 1.22651i | −0.965274 | − | 0.261240i | \(-0.915869\pi\) |
−0.261240 | − | 0.965274i | \(-0.584131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.83583 | − | 13.0225i | 0.640522 | − | 1.72487i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9308 | 1.68344 | 0.841721 | − | 0.539913i | \(-0.181543\pi\) | ||||
0.841721 | + | 0.539913i | \(0.181543\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.15633 | −0.276089 | −0.138045 | − | 0.990426i | \(-0.544082\pi\) | ||||
−0.138045 | + | 0.990426i | \(0.544082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.5999 | + | 10.5999i | −1.33546 | + | 1.33546i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.94399 | + | 4.94399i | −0.604004 | + | 0.604004i | −0.941373 | − | 0.337368i | \(-0.890463\pi\) |
0.337368 | + | 0.941373i | \(0.390463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.42380 | 1.01411 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.04278i | 0.361112i | 0.983565 | + | 0.180556i | \(0.0577897\pi\) | ||||
−0.983565 | + | 0.180556i | \(0.942210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.19394 | − | 6.19394i | 0.724945 | − | 0.724945i | −0.244663 | − | 0.969608i | \(-0.578677\pi\) |
0.969608 | + | 0.244663i | \(0.0786773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19394 | + | 1.19394i | 0.136062 | + | 0.136062i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.46417 | −0.164732 | −0.0823660 | − | 0.996602i | \(-0.526248\pi\) | ||||
−0.0823660 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −20.7440 | −2.30489 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.32487 | + | 5.32487i | −0.584480 | + | 0.584480i | −0.936131 | − | 0.351651i | \(-0.885620\pi\) |
0.351651 | + | 0.936131i | \(0.385620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.1563 | + | 10.1563i | 1.08887 | + | 1.08887i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.2254 | −1.50789 | −0.753946 | − | 0.656937i | \(-0.771852\pi\) | ||||
−0.753946 | + | 0.656937i | \(0.771852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29466i | 0.135717i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.0435 | + | 15.0435i | −1.55994 | + | 1.55994i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.46498 | + | 7.46498i | −0.757954 | + | 0.757954i | −0.975950 | − | 0.217995i | \(-0.930048\pi\) |
0.217995 | + | 0.975950i | \(0.430048\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.76845i | 0.579751i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.08110 | 0.406085 | 0.203042 | − | 0.979170i | \(-0.434917\pi\) | ||||
0.203042 | + | 0.979170i | \(0.434917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.31110 | + | 1.31110i | 0.129186 | + | 0.129186i | 0.768743 | − | 0.639557i | \(-0.220882\pi\) |
−0.639557 | + | 0.768743i | \(0.720882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.11271 | + | 7.11271i | −0.687612 | + | 0.687612i | −0.961703 | − | 0.274092i | \(-0.911623\pi\) |
0.274092 | + | 0.961703i | \(0.411623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3225 | −1.85076 | −0.925379 | − | 0.379043i | \(-0.876253\pi\) | ||||
−0.925379 | + | 0.379043i | \(0.876253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.8700 | 2.26564 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.23865 | + | 6.23865i | 0.586882 | + | 0.586882i | 0.936786 | − | 0.349903i | \(-0.113786\pi\) |
−0.349903 | + | 0.936786i | \(0.613786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12754 | + | 3.12754i | −0.289141 | + | 0.289141i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.35026i | − | 0.857137i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3503 | −0.940933 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −25.1998 | + | 25.1998i | −2.27219 | + | 2.27219i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.80322 | − | 9.80322i | 0.869895 | − | 0.869895i | −0.122565 | − | 0.992460i | \(-0.539112\pi\) |
0.992460 | + | 0.122565i | \(0.0391121\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17.4377 | −1.53531 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.14903 | −0.799355 | −0.399677 | − | 0.916656i | \(-0.630878\pi\) | ||||
−0.399677 | + | 0.916656i | \(0.630878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.17856 | + | 8.55958i | −0.275616 | + | 0.742209i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.18664 | − | 3.18664i | −0.272253 | − | 0.272253i | 0.557753 | − | 0.830007i | \(-0.311663\pi\) |
−0.830007 | + | 0.557753i | \(0.811663\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2447i | 1.29304i | 0.762897 | + | 0.646520i | \(0.223776\pi\) | ||||
−0.762897 | + | 0.646520i | \(0.776224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.7891i | 2.59291i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.352275 | + | 0.352275i | 0.0294587 | + | 0.0294587i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.88637 | + | 5.88637i | −0.485500 | + | 0.485500i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 15.3806i | − | 1.26003i | −0.776585 | − | 0.630013i | \(-0.783050\pi\) | ||
0.776585 | − | 0.630013i | \(-0.216950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.21151i | − | 0.424106i | −0.977258 | − | 0.212053i | \(-0.931985\pi\) | ||
0.977258 | − | 0.212053i | \(-0.0680150\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.5877 | − | 22.5877i | 1.82611 | − | 1.82611i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2447 | + | 10.2447i | 0.817618 | + | 0.817618i | 0.985762 | − | 0.168145i | \(-0.0537775\pi\) |
−0.168145 | + | 0.985762i | \(0.553778\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 40.2433i | 3.19150i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.53690 | −0.436369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4133 | − | 10.4133i | 0.815630 | − | 0.815630i | −0.169841 | − | 0.985471i | \(-0.554326\pi\) |
0.985471 | + | 0.169841i | \(0.0543256\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.42220 | − | 4.42220i | 0.342200 | − | 0.342200i | −0.514994 | − | 0.857194i | \(-0.672206\pi\) |
0.857194 | + | 0.514994i | \(0.172206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.6180i | − | 0.970616i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28.3561 | + | 12.9991i | −2.16845 | + | 0.994064i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.06992 | + | 4.06992i | 0.309431 | + | 0.309431i | 0.844689 | − | 0.535258i | \(-0.179786\pi\) |
−0.535258 | + | 0.844689i | \(0.679786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −29.1392 | − | 29.1392i | −2.19024 | − | 2.19024i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.87327 | −0.214758 | −0.107379 | − | 0.994218i | \(-0.534246\pi\) | ||||
−0.107379 | + | 0.994218i | \(0.534246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.0278i | − | 1.34000i | −0.742362 | − | 0.669999i | \(-0.766295\pi\) | ||
0.742362 | − | 0.669999i | \(-0.233705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85923 | + | 4.85923i | 0.359205 | + | 0.359205i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.54420 | − | 2.54420i | −0.186050 | − | 0.186050i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.7463 | 2.01825 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.43866 | −0.321170 | −0.160585 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160585 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.42220 | + | 4.42220i | 0.318317 | + | 0.318317i | 0.848120 | − | 0.529804i | \(-0.177734\pi\) |
−0.529804 | + | 0.848120i | \(0.677734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3806 | − | 10.3806i | −0.739586 | − | 0.739586i | 0.232912 | − | 0.972498i | \(-0.425175\pi\) |
−0.972498 | + | 0.232912i | \(0.925175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.23743i | − | 0.583936i | −0.956428 | − | 0.291968i | \(-0.905690\pi\) | ||
0.956428 | − | 0.291968i | \(-0.0943100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.2823 | 1.57167 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.67568 | − | 6.67568i | −0.468541 | − | 0.468541i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.3757 | − | 13.3757i | −0.929672 | − | 0.929672i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.46417 | + | 3.19394i | 0.101279 | + | 0.220929i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5348i | 1.55136i | 0.631128 | + | 0.775679i | \(0.282592\pi\) | ||||
−0.631128 | + | 0.775679i | \(0.717408\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.85685 | − | 6.85685i | 0.469824 | − | 0.469824i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.88798 | − | 9.88798i | 0.671239 | − | 0.671239i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.9158 | −1.88637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.75883i | − | 0.185579i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4361 | − | 13.4361i | −0.899749 | − | 0.899749i | 0.0956650 | − | 0.995414i | \(-0.469502\pi\) |
−0.995414 | + | 0.0956650i | \(0.969502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.06992 | − | 4.06992i | 0.270130 | − | 0.270130i | −0.559022 | − | 0.829153i | \(-0.688823\pi\) |
0.829153 | + | 0.559022i | \(0.188823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.46898i | 0.295318i | 0.989038 | + | 0.147659i | \(0.0471738\pi\) | ||||
−0.989038 | + | 0.147659i | \(0.952826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 5.38102i | − | 0.354045i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.1114 | − | 11.1114i | 0.727933 | − | 0.727933i | −0.242274 | − | 0.970208i | \(-0.577893\pi\) |
0.970208 | + | 0.242274i | \(0.0778934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.29948 | + | 3.29948i | 0.214324 | + | 0.214324i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.4387i | − | 0.675221i | −0.941286 | − | 0.337610i | \(-0.890381\pi\) | ||
0.941286 | − | 0.337610i | \(-0.109619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.6353i | − | 0.878328i | −0.898407 | − | 0.439164i | \(-0.855275\pi\) | ||
0.898407 | − | 0.439164i | \(-0.144725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.6476 | + | 18.6476i | 1.19625 | + | 1.19625i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.937845 | + | 2.52553i | −0.0596737 | + | 0.160696i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.9989 | 1.52087 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.96239 | 0.565701 | 0.282850 | − | 0.959164i | \(-0.408720\pi\) | ||||
0.282850 | + | 0.959164i | \(0.408720\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.50659 | + | 1.50659i | −0.0947183 | + | 0.0947183i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.76043 | + | 6.76043i | −0.421704 | + | 0.421704i | −0.885790 | − | 0.464086i | \(-0.846383\pi\) |
0.464086 | + | 0.885790i | \(0.346383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.6896 | −0.974904 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 32.2532i | − | 1.99643i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.36248 | − | 4.36248i | 0.269002 | − | 0.269002i | −0.559696 | − | 0.828698i | \(-0.689082\pi\) |
0.828698 | + | 0.559696i | \(0.189082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 32.0567 | + | 32.0567i | 1.96184 | + | 1.96184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.4377 | −1.06320 | −0.531598 | − | 0.846997i | \(-0.678408\pi\) | ||||
−0.531598 | + | 0.846997i | \(0.678408\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.28233 | −0.503116 | −0.251558 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251558 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.91748 | − | 2.91748i | 0.176574 | − | 0.176574i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.80606 | + | 9.80606i | 0.589189 | + | 0.589189i | 0.937412 | − | 0.348223i | \(-0.113215\pi\) |
−0.348223 | + | 0.937412i | \(0.613215\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 47.7733 | 2.86011 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.66498i | 0.337944i | 0.985621 | + | 0.168972i | \(0.0540448\pi\) | ||||
−0.985621 | + | 0.168972i | \(0.945955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.18172 | + | 4.18172i | −0.248577 | + | 0.248577i | −0.820387 | − | 0.571809i | \(-0.806242\pi\) |
0.571809 | + | 0.820387i | \(0.306242\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.5637 | − | 16.5637i | 0.977721 | − | 0.977721i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.92478i | 0.172046i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33.6444 | 1.97227 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.35054 | + | 7.35054i | 0.429423 | + | 0.429423i | 0.888432 | − | 0.459009i | \(-0.151795\pi\) |
−0.459009 | + | 0.888432i | \(0.651795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.54974 | − | 7.54974i | 0.438080 | − | 0.438080i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.63368 | −0.0944784 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4617 | 0.660640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.19667 | − | 9.19667i | −0.528335 | − | 0.528335i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.3924 | + | 23.3924i | −1.33508 | + | 1.33508i | −0.434313 | + | 0.900762i | \(0.643009\pi\) |
−0.900762 | + | 0.434313i | \(0.856991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.90905i | − | 0.336154i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2546 | 0.638188 | 0.319094 | − | 0.947723i | \(-0.396621\pi\) | ||||
0.319094 | + | 0.947723i | \(0.396621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5369 | + | 14.5369i | −0.821674 | + | 0.821674i | −0.986348 | − | 0.164674i | \(-0.947343\pi\) |
0.164674 | + | 0.986348i | \(0.447343\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.87154 | − | 9.87154i | 0.554441 | − | 0.554441i | −0.373279 | − | 0.927719i | \(-0.621766\pi\) |
0.927719 | + | 0.373279i | \(0.121766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63289 | −0.203403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 32.0567 | 1.78923 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.77329 | − | 18.2399i | 0.376876 | − | 1.01489i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43.5428 | + | 43.5428i | 2.40792 | + | 2.40792i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 20.2374i | − | 1.11573i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.3110i | − | 1.11639i | −0.829709 | − | 0.558196i | \(-0.811494\pi\) | ||
0.829709 | − | 0.558196i | \(-0.188506\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −37.9018 | − | 37.9018i | −2.07700 | − | 2.07700i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7892 | + | 11.7892i | −0.642197 | + | 0.642197i | −0.951095 | − | 0.308898i | \(-0.900040\pi\) |
0.308898 | + | 0.951095i | \(0.400040\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 28.1173i | − | 1.52712i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.38102i | − | 0.291399i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2374 | − | 14.2374i | 0.768749 | − | 0.768749i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.6302 | − | 18.6302i | −1.00012 | − | 1.00012i | −1.00000 | 0.000122901i | \(-0.999961\pi\) | |
−0.000122901 | − | 1.00000i | \(-0.500039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 21.0640i | − | 1.12753i | −0.825936 | − | 0.563764i | \(-0.809353\pi\) | ||
0.825936 | − | 0.563764i | \(-0.190647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.18664 | 0.436971 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.99271 | − | 1.99271i | 0.106061 | − | 0.106061i | −0.652085 | − | 0.758146i | \(-0.726105\pi\) |
0.758146 | + | 0.652085i | \(0.226105\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.0706 | + | 21.0706i | −1.11517 | + | 1.11517i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.6458i | 1.51187i | 0.654649 | + | 0.755933i | \(0.272816\pi\) | ||||
−0.654649 | + | 0.755933i | \(0.727184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4010 | + | 14.3949i | −0.652687 | + | 0.757628i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 23.3241 | + | 23.3241i | 1.22420 | + | 1.22420i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.1368 | + | 12.1368i | 0.633536 | + | 0.633536i | 0.948953 | − | 0.315417i | \(-0.102144\pi\) |
−0.315417 | + | 0.948953i | \(0.602144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 80.0266 | 4.16602 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 26.4516i | − | 1.37330i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4789 | − | 16.4789i | −0.853245 | − | 0.853245i | 0.137286 | − | 0.990531i | \(-0.456162\pi\) |
−0.990531 | + | 0.137286i | \(0.956162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.96968 | − | 1.96968i | −0.101444 | − | 0.101444i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.92834 | 0.150419 | 0.0752094 | − | 0.997168i | \(-0.476037\pi\) | ||||
0.0752094 | + | 0.997168i | \(0.476037\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −44.1827 | −2.26355 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.3381 | − | 21.3381i | −1.09033 | − | 1.09033i | −0.995493 | − | 0.0948343i | \(-0.969768\pi\) |
−0.0948343 | − | 0.995493i | \(-0.530232\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.6883 | + | 27.6883i | 1.40748 | + | 1.40748i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.5647i | 1.24548i | 0.782430 | + | 0.622739i | \(0.213980\pi\) | ||||
−0.782430 | + | 0.622739i | \(0.786020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.7988 | 0.596689 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.6171 | + | 20.6171i | 1.04000 | + | 1.04000i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.23155 | + | 5.23155i | 0.262564 | + | 0.262564i | 0.826095 | − | 0.563531i | \(-0.190557\pi\) |
−0.563531 | + | 0.826095i | \(0.690557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.4516 | − | 12.1260i | 1.32424 | − | 0.607060i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.7324i | 0.935450i | 0.883874 | + | 0.467725i | \(0.154926\pi\) | ||||
−0.883874 | + | 0.467725i | \(0.845074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.91748 | − | 2.91748i | 0.145330 | − | 0.145330i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.26912 | + | 4.26912i | −0.211613 | + | 0.211613i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9850 | −0.740962 | −0.370481 | − | 0.928840i | \(-0.620807\pi\) | ||||
−0.370481 | + | 0.928840i | \(0.620807\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.3621i | 0.708428i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.1530 | + | 19.1530i | 0.942456 | + | 0.942456i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.3536 | − | 34.3536i | 1.68231 | − | 1.68231i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 34.2882i | − | 1.67509i | −0.546369 | − | 0.837544i | \(-0.683990\pi\) | ||
0.546369 | − | 0.837544i | \(-0.316010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6056i | 1.05299i | 0.850177 | + | 0.526497i | \(0.176495\pi\) | ||||
−0.850177 | + | 0.526497i | \(0.823505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 48.8881 | − | 48.8881i | 2.37702 | − | 2.37702i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.19394 | − | 3.19394i | −0.154565 | − | 0.154565i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.58769i | − | 0.0766544i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.7431i | − | 0.950990i | −0.879718 | − | 0.475495i | \(-0.842269\pi\) | ||
0.879718 | − | 0.475495i | \(-0.157731\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.0296 | − | 11.0296i | −0.530047 | − | 0.530047i | 0.390539 | − | 0.920586i | \(-0.372288\pi\) |
−0.920586 | + | 0.390539i | \(0.872288\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.8010 | − | 4.01091i | −0.516683 | − | 0.191868i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3628 | 0.590047 | 0.295023 | − | 0.955490i | \(-0.404673\pi\) | ||||
0.295023 | + | 0.955490i | \(0.404673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.6932 | 0.890154 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1744 | + | 11.1744i | −0.530913 | + | 0.530913i | −0.920844 | − | 0.389931i | \(-0.872499\pi\) |
0.389931 | + | 0.920844i | \(0.372499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.6598 | + | 34.6598i | −1.63935 | + | 1.63935i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.90615 | −0.137150 | −0.0685748 | − | 0.997646i | \(-0.521845\pi\) | ||||
−0.0685748 | + | 0.997646i | \(0.521845\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.01391i | − | 0.424449i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.7440 | + | 11.7440i | −0.551782 | + | 0.551782i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.1490 | − | 14.1490i | −0.661864 | − | 0.661864i | 0.293955 | − | 0.955819i | \(-0.405028\pi\) |
−0.955819 | + | 0.293955i | \(0.905028\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.1255 | −2.75974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6859 | −0.870291 | −0.435145 | − | 0.900360i | \(-0.643303\pi\) | ||||
−0.435145 | + | 0.900360i | \(0.643303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.906679 | + | 0.906679i | −0.0421369 | + | 0.0421369i | −0.727861 | − | 0.685724i | \(-0.759486\pi\) |
0.685724 | + | 0.727861i | \(0.259486\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.49437 | − | 8.49437i | −0.393072 | − | 0.393072i | 0.482709 | − | 0.875781i | \(-0.339653\pi\) |
−0.875781 | + | 0.482709i | \(0.839653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6460 | −0.676290 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 46.1725i | − | 2.12752i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.11871 | − | 3.11871i | 0.143399 | − | 0.143399i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 63.8999 | − | 63.8999i | 2.92578 | − | 2.92578i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 15.9307i | − | 0.727890i | −0.931420 | − | 0.363945i | \(-0.881430\pi\) | ||
0.931420 | − | 0.363945i | \(-0.118570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.62927 | −0.211077 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.4773 | + | 12.4773i | 0.567736 | + | 0.567736i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.02714 | + | 1.02714i | −0.0465441 | + | 0.0465441i | −0.729996 | − | 0.683452i | \(-0.760478\pi\) |
0.683452 | + | 0.729996i | \(0.260478\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.9321 | −2.12234 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1866 | −0.730493 | −0.365246 | − | 0.930911i | \(-0.619015\pi\) | ||||
−0.365246 | + | 0.930911i | \(0.619015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.2254 | + | 14.2254i | 0.640681 | + | 0.640681i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.50696 | + | 4.50696i | −0.202165 | + | 0.202165i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0943i | 0.675713i | 0.941198 | + | 0.337856i | \(0.109702\pi\) | ||||
−0.941198 | + | 0.337856i | \(0.890298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.9307 | −0.890436 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.9429 | − | 26.9429i | 1.20132 | − | 1.20132i | 0.227559 | − | 0.973764i | \(-0.426925\pi\) |
0.973764 | − | 0.227559i | \(-0.0730745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.4344 | + | 28.4344i | −1.26282 | + | 1.26282i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6484 | 1.09252 | 0.546261 | − | 0.837615i | \(-0.316051\pi\) | ||||
0.546261 | + | 0.837615i | \(0.316051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.3488 | 0.811705 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 54.1256 | + | 20.0993i | 2.38971 | + | 0.887406i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.50659 | − | 5.50659i | −0.242179 | − | 0.242179i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.3430i | − | 0.805167i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.60481i | 0.333173i | 0.986027 | + | 0.166586i | \(0.0532745\pi\) | ||||
−0.986027 | + | 0.166586i | \(0.946726\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5645 | + | 22.5645i | 0.986675 | + | 0.986675i | 0.999912 | − | 0.0132372i | \(-0.00421365\pi\) |
−0.0132372 | + | 0.999912i | \(0.504214\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.0706 | + | 21.0706i | −0.917850 | + | 0.917850i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0132i | 0.696225i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 92.5367i | 4.01575i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.88717 | − | 4.88717i | 0.211687 | − | 0.211687i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.47486 | + | 6.47486i | 0.279411 | + | 0.279411i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.10554i | − | 0.0906920i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.3331 | 1.56208 | 0.781041 | − | 0.624479i | \(-0.214689\pi\) | ||||
0.781041 | + | 0.624479i | \(0.214689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.6253 | + | 40.6253i | −1.74340 | + | 1.74340i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.18103 | + | 7.18103i | −0.307039 | + | 0.307039i | −0.843760 | − | 0.536721i | \(-0.819663\pi\) |
0.536721 | + | 0.843760i | \(0.319663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 15.4314i | − | 0.658595i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.18664 | − | 17.8583i | −0.348763 | − | 0.760790i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.16872 | − | 2.16872i | −0.0922234 | − | 0.0922234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.3054 | − | 24.3054i | −1.02985 | − | 1.02985i | −0.999541 | − | 0.0303105i | \(-0.990350\pi\) |
−0.0303105 | − | 0.999541i | \(-0.509650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.38181 | 0.143035 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.4666i | 0.484120i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.7743 | + | 15.7743i | 0.664809 | + | 0.664809i | 0.956510 | − | 0.291700i | \(-0.0942210\pi\) |
−0.291700 | + | 0.956510i | \(0.594221\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.7259 | − | 30.7259i | −1.29037 | − | 1.29037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.45189 | −0.186633 | −0.0933164 | − | 0.995637i | \(-0.529747\pi\) | ||||
−0.0933164 | + | 0.995637i | \(0.529747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.6834 | 1.24221 | 0.621105 | − | 0.783727i | \(-0.286684\pi\) | ||||
0.621105 | + | 0.783727i | \(0.286684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0024 | + | 10.0024i | 0.417857 | + | 0.417857i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7235 | + | 12.7235i | 0.529688 | + | 0.529688i | 0.920479 | − | 0.390791i | \(-0.127799\pi\) |
−0.390791 | + | 0.920479i | \(0.627799\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 19.9307i | − | 0.828290i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.7743 | −0.654430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.19747 | − | 7.19747i | −0.298089 | − | 0.298089i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.48849 | − | 2.48849i | −0.102711 | − | 0.102711i | 0.653884 | − | 0.756595i | \(-0.273138\pi\) |
−0.756595 | + | 0.653884i | \(0.773138\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4516 | − | 12.1260i | 1.08992 | − | 0.499643i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.7848i | 1.92447i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.78892 | − | 2.78892i | 0.114527 | − | 0.114527i | −0.647521 | − | 0.762048i | \(-0.724194\pi\) |
0.762048 | + | 0.647521i | \(0.224194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.5629 | + | 18.5629i | −0.759727 | + | 0.759727i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.1947 | −1.88746 | −0.943732 | − | 0.330711i | \(-0.892712\pi\) | ||||
−0.943732 | + | 0.330711i | \(0.892712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.8714i | 1.17769i | 0.808246 | + | 0.588845i | \(0.200417\pi\) | ||||
−0.808246 | + | 0.588845i | \(0.799583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.3808 | − | 35.3808i | −1.44082 | − | 1.44082i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5365 | − | 15.5365i | 0.630608 | − | 0.630608i | −0.317613 | − | 0.948220i | \(-0.602881\pi\) |
0.948220 | + | 0.317613i | \(0.102881\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.0870i | 1.21919i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.97113i | − | 0.241566i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.4241 | + | 23.4241i | −0.946089 | + | 0.946089i | −0.998619 | − | 0.0525301i | \(-0.983271\pi\) |
0.0525301 | + | 0.998619i | \(0.483271\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4558 | + | 16.4558i | 0.662486 | + | 0.662486i | 0.955965 | − | 0.293480i | \(-0.0948133\pi\) |
−0.293480 | + | 0.955965i | \(0.594813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.2711i | 1.65882i | 0.558637 | + | 0.829412i | \(0.311324\pi\) | ||||
−0.558637 | + | 0.829412i | \(0.688676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.0121i | 1.40499i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.0706 | − | 21.0706i | −0.844176 | − | 0.844176i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.89799 | − | 10.4969i | 0.155671 | − | 0.419207i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.4335 | 1.33308 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.1939 | 1.08257 | 0.541287 | − | 0.840838i | \(-0.317937\pi\) | ||||
0.541287 | + | 0.840838i | \(0.317937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50.7816 | − | 50.7816i | 2.01839 | − | 2.01839i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.14158 | − | 1.14158i | 0.0452311 | − | 0.0452311i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.7752 | −0.861412 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.96042i | − | 0.195925i | −0.995190 | − | 0.0979625i | \(-0.968767\pi\) | ||
0.995190 | − | 0.0979625i | \(-0.0312325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.3176 | + | 20.3176i | −0.801247 | + | 0.801247i | −0.983290 | − | 0.182044i | \(-0.941729\pi\) |
0.182044 | + | 0.983290i | \(0.441729\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.16125 | − | 8.16125i | −0.320852 | − | 0.320852i | 0.528242 | − | 0.849094i | \(-0.322851\pi\) |
−0.849094 | + | 0.528242i | \(0.822851\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4230 | 0.409139 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.5647 | −1.74663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.4387 | − | 23.4387i | 0.917226 | − | 0.917226i | −0.0796012 | − | 0.996827i | \(-0.525365\pi\) |
0.996827 | + | 0.0796012i | \(0.0253647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 44.3258 | + | 44.3258i | 1.72932 | + | 1.72932i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.84519 | 0.266651 | 0.133325 | − | 0.991072i | \(-0.457434\pi\) | ||||
0.133325 | + | 0.991072i | \(0.457434\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13.0674i | − | 0.508263i | −0.967170 | − | 0.254131i | \(-0.918210\pi\) | ||
0.967170 | − | 0.254131i | \(-0.0817896\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.21696 | + | 6.21696i | −0.241447 | + | 0.241447i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.42380 | − | 8.42380i | 0.326171 | − | 0.326171i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.5560i | 2.34123i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.73813 | −0.0671000 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.16699 | + | 9.16699i | 0.353361 | + | 0.353361i | 0.861359 | − | 0.507997i | \(-0.169614\pi\) |
−0.507997 | + | 0.861359i | \(0.669614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.13824 | − | 4.13824i | 0.159046 | − | 0.159046i | −0.623098 | − | 0.782144i | \(-0.714126\pi\) |
0.782144 | + | 0.623098i | \(0.214126\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.1142 | −0.848665 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.3430 | −0.702904 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.7907 | + | 34.7907i | 1.33123 | + | 1.33123i | 0.904273 | + | 0.426956i | \(0.140414\pi\) |
0.426956 | + | 0.904273i | \(0.359586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0707 | − | 10.0707i | 0.384223 | − | 0.384223i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.80465i | − | 0.297333i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1939 | 0.425837 | 0.212919 | − | 0.977070i | \(-0.431703\pi\) | ||||
0.212919 | + | 0.977070i | \(0.431703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.54420 | + | 8.54420i | −0.324567 | + | 0.324567i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.2960 | + | 35.2960i | −1.33693 | + | 1.33693i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −50.0787 | −1.89415 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.75386 | −0.0662425 | −0.0331213 | − | 0.999451i | \(-0.510545\pi\) | ||||
−0.0331213 | + | 0.999451i | \(0.510545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.6062 | − | 11.3655i | −1.15434 | − | 0.428657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.04491 | + | 6.04491i | 0.227342 | + | 0.227342i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.4109i | − | 1.02944i | −0.857359 | − | 0.514719i | \(-0.827896\pi\) | ||
0.857359 | − | 0.514719i | \(-0.172104\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.4781i | − | 0.392959i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4773 | + | 12.4773i | 0.467278 | + | 0.467278i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.5233 | + | 23.5233i | −0.878493 | + | 0.878493i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.2170i | 0.679378i | 0.940538 | + | 0.339689i | \(0.110322\pi\) | ||||
−0.940538 | + | 0.339689i | \(0.889678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.88397i | 0.144647i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.7269 | + | 30.7269i | −1.14274 | + | 1.14274i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.28726 | − | 2.28726i | −0.0848297 | − | 0.0848297i | 0.663419 | − | 0.748248i | \(-0.269105\pi\) |
−0.748248 | + | 0.663419i | \(0.769105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 21.8119i | − | 0.807850i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.4241 | −0.903357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8872 | + | 25.8872i | −0.956164 | + | 0.956164i | −0.999079 | − | 0.0429145i | \(-0.986336\pi\) |
0.0429145 | + | 0.999079i | \(0.486336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.98517 | + | 3.98517i | −0.146796 | + | 0.146796i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 48.8021i | − | 1.79521i | −0.440797 | − | 0.897607i | \(-0.645304\pi\) | ||
0.440797 | − | 0.897607i | \(-0.354696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.80465 | − | 3.57782i | 0.286711 | − | 0.131435i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.674864 | + | 0.674864i | 0.0247583 | + | 0.0247583i | 0.719378 | − | 0.694619i | \(-0.244427\pi\) |
−0.694619 | + | 0.719378i | \(0.744427\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38.1065 | − | 38.1065i | −1.39424 | − | 1.39424i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.0706 | −0.769903 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.7727i | − | 0.429593i | −0.976659 | − | 0.214797i | \(-0.931091\pi\) | ||
0.976659 | − | 0.214797i | \(-0.0689089\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.1965 | − | 20.1965i | −0.736003 | − | 0.736003i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0943 | − | 36.0943i | −1.31187 | − | 1.31187i | −0.920037 | − | 0.391832i | \(-0.871841\pi\) |
−0.391832 | − | 0.920037i | \(-0.628159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.79012 | 0.246466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6194 | −0.674953 | −0.337477 | − | 0.941334i | \(-0.609573\pi\) | ||||
−0.337477 | + | 0.941334i | \(0.609573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.6203 | − | 28.6203i | −1.03613 | − | 1.03613i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.65115 | + | 5.65115i | 0.204051 | + | 0.204051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23.5720i | − | 0.850027i | −0.905187 | − | 0.425013i | \(-0.860269\pi\) | ||
0.905187 | − | 0.425013i | \(-0.139731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.4690 | 1.09731 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.7627 | + | 27.7627i | 0.998556 | + | 0.998556i | 0.999999 | − | 0.00144323i | \(-0.000459394\pi\) |
−0.00144323 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.3561 | + | 35.3561i | 1.26839 | + | 1.26839i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.3099 | − | 20.3127i | 1.58757 | − | 0.727776i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.45268i | 0.0877637i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.2130 | + | 42.2130i | −1.50857 | + | 1.50857i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7019 | − | 20.7019i | 0.737943 | − | 0.737943i | −0.234237 | − | 0.972180i | \(-0.575259\pi\) |
0.972180 | + | 0.234237i | \(0.0752591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.6615 | −0.699968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.4813i | 0.657119i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.942383 | − | 0.942383i | −0.0334650 | − | 0.0334650i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.81471 | − | 8.81471i | 0.312233 | − | 0.312233i | −0.533541 | − | 0.845774i | \(-0.679139\pi\) |
0.845774 | + | 0.533541i | \(0.179139\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.1246i | 1.52564i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 101.802i | − | 3.59699i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.99271 | − | 4.99271i | 0.176189 | − | 0.176189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.2955 | + | 39.2955i | 1.38327 | + | 1.38327i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.73672i | − | 0.236850i | −0.992963 | − | 0.118425i | \(-0.962215\pi\) | ||
0.992963 | − | 0.118425i | \(-0.0377846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.29466i | 0.0454616i | 0.999742 | + | 0.0227308i | \(0.00723606\pi\) | ||||
−0.999742 | + | 0.0227308i | \(0.992764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.6641 | + | 18.6641i | 0.654577 | + | 0.654577i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.3587 | + | 8.30280i | 0.782232 | + | 0.290478i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.26499 | −0.323745 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7137 | −0.827614 | −0.413807 | − | 0.910365i | \(-0.635801\pi\) | ||||
−0.413807 | + | 0.910365i | \(0.635801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.15140 | + | 2.15140i | −0.0749931 | + | 0.0749931i | −0.743608 | − | 0.668615i | \(-0.766887\pi\) |
0.668615 | + | 0.743608i | \(0.266887\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4896 | − | 17.4896i | 0.608173 | − | 0.608173i | −0.334295 | − | 0.942468i | \(-0.608498\pi\) |
0.942468 | + | 0.334295i | \(0.108498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7752 | 0.756283 | 0.378141 | − | 0.925748i | \(-0.376563\pi\) | ||||
0.378141 | + | 0.925748i | \(0.376563\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 44.1955i | − | 1.53312i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.24472 | + | 8.24472i | −0.285663 | + | 0.285663i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.5256 | − | 62.5256i | −2.16120 | − | 2.16120i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.6196 | 1.05710 | 0.528552 | − | 0.848901i | \(-0.322735\pi\) | ||||
0.528552 | + | 0.848901i | \(0.322735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.68735 | −0.299564 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.7659 | − | 12.7659i | 0.439681 | − | 0.439681i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.3307 | − | 15.3307i | −0.526771 | − | 0.526771i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.8468 | 0.646821 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 19.7981i | − | 0.678672i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.18664 | − | 7.18664i | 0.246066 | − | 0.246066i | −0.573288 | − | 0.819354i | \(-0.694332\pi\) |
0.819354 | + | 0.573288i | \(0.194332\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.3522 | + | 19.3522i | −0.661057 | + | 0.661057i | −0.955629 | − | 0.294572i | \(-0.904823\pi\) |
0.294572 | + | 0.955629i | \(0.404823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5599i | 1.04269i | 0.853346 | + | 0.521346i | \(0.174570\pi\) | ||||
−0.853346 | + | 0.521346i | \(0.825430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −74.6516 | −2.54412 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.199200 | + | 0.199200i | 0.00678084 | + | 0.00678084i | 0.710489 | − | 0.703708i | \(-0.248474\pi\) |
−0.703708 | + | 0.710489i | \(0.748474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.59092 | − | 6.59092i | 0.223839 | − | 0.223839i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.18021 | −0.0400360 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.32136 | −0.146424 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −53.4219 | − | 53.4219i | −1.80806 | − | 1.80806i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1546 | − | 23.1546i | 0.781874 | − | 0.781874i | −0.198273 | − | 0.980147i | \(-0.563533\pi\) |
0.980147 | + | 0.198273i | \(0.0635331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 33.1286i | − | 1.11740i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.84367 | 0.331642 | 0.165821 | − | 0.986156i | \(-0.446973\pi\) | ||||
0.165821 | + | 0.986156i | \(0.446973\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.71274 | + | 3.71274i | −0.124944 | + | 0.124944i | −0.766814 | − | 0.641870i | \(-0.778159\pi\) |
0.641870 | + | 0.766814i | \(0.278159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.8697 | − | 35.8697i | 1.20439 | − | 1.20439i | 0.231568 | − | 0.972819i | \(-0.425615\pi\) |
0.972819 | − | 0.231568i | \(-0.0743855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.0409 | 0.974002 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7210 | −0.560174 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.6599 | − | 39.4779i | 0.490575 | − | 1.32108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.68147 | + | 3.68147i | 0.122921 | + | 0.122921i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0870i | 1.00346i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.3666i | 1.87784i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.8286 | − | 25.8286i | −0.859523 | − | 0.859523i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.52260 | − | 6.52260i | 0.216579 | − | 0.216579i | −0.590476 | − | 0.807055i | \(-0.701060\pi\) |
0.807055 | + | 0.590476i | \(0.201060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.2057i | 0.968692i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 20.4476i | − | 0.677460i | −0.940884 | − | 0.338730i | \(-0.890003\pi\) | ||
0.940884 | − | 0.338730i | \(-0.109997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.29218 | + | 4.29218i | −0.142051 | + | 0.142051i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5515 | − | 13.5515i | −0.447510 | − | 0.447510i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13.9756i | − | 0.461011i | −0.973071 | − | 0.230506i | \(-0.925962\pi\) | ||
0.973071 | − | 0.230506i | \(-0.0740380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 105.429 | 3.47399 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.32979 | + | 1.32979i | −0.0437707 | + | 0.0437707i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.38262 | + | 9.38262i | −0.308166 | + | 0.308166i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.9478i | 0.752893i | 0.926438 | + | 0.376446i | \(0.122854\pi\) | ||||
−0.926438 | + | 0.376446i | \(0.877146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.3503 | − | 4.74479i | 0.339216 | − | 0.155504i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.3619 | − | 25.3619i | −0.830312 | − | 0.830312i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9076 | + | 11.9076i | 0.389005 | + | 0.389005i | 0.874333 | − | 0.485327i | \(-0.161300\pi\) |
−0.485327 | + | 0.874333i | \(0.661300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.5172 | 2.13807 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 34.1709i | − | 1.11394i | −0.830533 | − | 0.556969i | \(-0.811964\pi\) | ||
0.830533 | − | 0.556969i | \(-0.188036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.9011 | + | 20.9011i | 0.680633 | + | 0.680633i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.00096 | + | 6.00096i | 0.195005 | + | 0.195005i | 0.797855 | − | 0.602850i | \(-0.205968\pi\) |
−0.602850 | + | 0.797855i | \(0.705968\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.41389 | 0.175742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.4906 | −1.44271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0583 | − | 16.0583i | −0.520179 | − | 0.520179i | 0.397446 | − | 0.917626i | \(-0.369897\pi\) |
−0.917626 | + | 0.397446i | \(0.869897\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.18664 | + | 8.18664i | 0.264637 | + | 0.264637i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 9.44007i | − | 0.304836i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5647 | −0.437570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −50.9009 | − | 50.9009i | −1.64026 | − | 1.64026i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6956 | − | 16.6956i | −0.536894 | − | 0.536894i | 0.385721 | − | 0.922615i | \(-0.373953\pi\) |
−0.922615 | + | 0.385721i | \(0.873953\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −56.3666 | + | 25.8397i | −1.81076 | + | 0.830091i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.6476i | 0.341698i | 0.985297 | + | 0.170849i | \(0.0546510\pi\) | ||||
−0.985297 | + | 0.170849i | \(0.945349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5804 | + | 22.5804i | −0.723894 | + | 0.723894i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.3085 | − | 29.3085i | 0.937661 | − | 0.937661i | −0.0605070 | − | 0.998168i | \(-0.519272\pi\) |
0.998168 | + | 0.0605070i | \(0.0192717\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4666 | −0.366474 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 138.278i | − | 4.41488i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.77527 | + | 2.77527i | 0.0885172 | + | 0.0885172i | 0.749979 | − | 0.661462i | \(-0.230064\pi\) |
−0.661462 | + | 0.749979i | \(0.730064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −45.6046 | + | 45.6046i | −1.45161 | + | 1.45161i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.4631i | 0.459900i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.18342i | 0.291721i | 0.989305 | + | 0.145861i | \(0.0465951\pi\) | ||||
−0.989305 | + | 0.145861i | \(0.953405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −45.7704 | + | 45.7704i | −1.45248 | + | 1.45248i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.8773 | + | 37.8773i | 1.19959 | + | 1.19959i | 0.974290 | + | 0.225296i | \(0.0723350\pi\) |
0.225296 | + | 0.974290i | \(0.427665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 99.2116i | 3.13892i |
(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 | 1900.2.l.b.1557.1 | 12 | ||
5.2 | odd | 4 | 380.2.l.b.113.1 | yes | 12 | ||
5.3 | odd | 4 | inner | 1900.2.l.b.493.6 | 12 | ||
5.4 | even | 2 | 380.2.l.b.37.6 | yes | 12 | ||
15.2 | even | 4 | 3420.2.bb.d.2773.6 | 12 | |||
15.14 | odd | 2 | 3420.2.bb.d.37.5 | 12 | |||
19.18 | odd | 2 | inner | 1900.2.l.b.1557.6 | 12 | ||
95.18 | even | 4 | inner | 1900.2.l.b.493.1 | 12 | ||
95.37 | even | 4 | 380.2.l.b.113.6 | yes | 12 | ||
95.94 | odd | 2 | 380.2.l.b.37.1 | ✓ | 12 | ||
285.227 | odd | 4 | 3420.2.bb.d.2773.5 | 12 | |||
285.284 | even | 2 | 3420.2.bb.d.37.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.l.b.37.1 | ✓ | 12 | 95.94 | odd | 2 | ||
380.2.l.b.37.6 | yes | 12 | 5.4 | even | 2 | ||
380.2.l.b.113.1 | yes | 12 | 5.2 | odd | 4 | ||
380.2.l.b.113.6 | yes | 12 | 95.37 | even | 4 | ||
1900.2.l.b.493.1 | 12 | 95.18 | even | 4 | inner | ||
1900.2.l.b.493.6 | 12 | 5.3 | odd | 4 | inner | ||
1900.2.l.b.1557.1 | 12 | 1.1 | even | 1 | trivial | ||
1900.2.l.b.1557.6 | 12 | 19.18 | odd | 2 | inner | ||
3420.2.bb.d.37.5 | 12 | 15.14 | odd | 2 | |||
3420.2.bb.d.37.6 | 12 | 285.284 | even | 2 | |||
3420.2.bb.d.2773.5 | 12 | 285.227 | odd | 4 | |||
3420.2.bb.d.2773.6 | 12 | 15.2 | even | 4 |