Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(369,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.c (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.8 | ||
Root | \(-3.08006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.369 |
Dual form | 460.2.c.a.369.5 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.873449i | 0.504286i | 0.967690 | + | 0.252143i | \(0.0811353\pi\) | ||||
−0.967690 | + | 0.252143i | \(0.918865\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.89824 | − | 1.18182i | −0.848917 | − | 0.528526i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.992530i | 0.375141i | 0.982251 | + | 0.187570i | \(0.0600613\pi\) | ||||
−0.982251 | + | 0.187570i | \(0.939939\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23709 | 0.745696 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.83236 | 0.552478 | 0.276239 | − | 0.961089i | \(-0.410912\pi\) | ||||
0.276239 | + | 0.961089i | \(0.410912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.28666i | 0.911556i | 0.890093 | + | 0.455778i | \(0.150639\pi\) | ||||
−0.890093 | + | 0.455778i | \(0.849361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.03226 | − | 1.65801i | 0.266528 | − | 0.428097i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.63631i | 1.60954i | 0.593586 | + | 0.804770i | \(0.297712\pi\) | ||||
−0.593586 | + | 0.804770i | \(0.702288\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.64378 | 1.29477 | 0.647386 | − | 0.762163i | \(-0.275862\pi\) | ||||
0.647386 | + | 0.762163i | \(0.275862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.866924 | −0.189178 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.20661 | + | 4.48675i | 0.441321 | + | 0.897349i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57433i | 0.880330i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.01596 | −0.374354 | −0.187177 | − | 0.982326i | \(-0.559934\pi\) | ||||
−0.187177 | + | 0.982326i | \(0.559934\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.315080 | −0.0565901 | −0.0282951 | − | 0.999600i | \(-0.509008\pi\) | ||||
−0.0282951 | + | 0.999600i | \(0.509008\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.60047i | 0.278607i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.17299 | − | 1.88406i | 0.198272 | − | 0.318464i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.07470i | 0.505478i | 0.967534 | + | 0.252739i | \(0.0813314\pi\) | ||||
−0.967534 | + | 0.252739i | \(0.918669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.87073 | −0.459685 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.34964 | −0.210779 | −0.105389 | − | 0.994431i | \(-0.533609\pi\) | ||||
−0.105389 | + | 0.994431i | \(0.533609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.97905i | − | 0.911797i | −0.890032 | − | 0.455899i | \(-0.849318\pi\) | ||
0.890032 | − | 0.455899i | \(-0.150682\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.24652 | − | 2.64383i | −0.633034 | − | 0.394119i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.306285i | − | 0.0446762i | −0.999750 | − | 0.0223381i | \(-0.992889\pi\) | ||
0.999750 | − | 0.0223381i | \(-0.00711103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.01489 | 0.859269 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.79647 | −0.811669 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.98500i | − | 0.959464i | −0.877415 | − | 0.479732i | \(-0.840734\pi\) | ||
0.877415 | − | 0.479732i | \(-0.159266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.47826 | − | 2.16552i | −0.469008 | − | 0.291999i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.92955i | 0.652935i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.49533 | −1.23619 | −0.618094 | − | 0.786105i | \(-0.712095\pi\) | ||||
−0.618094 | + | 0.786105i | \(0.712095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.56160 | 0.712090 | 0.356045 | − | 0.934469i | \(-0.384125\pi\) | ||||
0.356045 | + | 0.934469i | \(0.384125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.22038i | 0.279741i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.88424 | − | 6.23887i | 0.481781 | − | 0.773836i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.853521i | − | 0.104274i | −0.998640 | − | 0.0521371i | \(-0.983397\pi\) | ||
0.998640 | − | 0.0521371i | \(-0.0166033\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.873449 | 0.105151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.797419 | 0.0946363 | 0.0473181 | − | 0.998880i | \(-0.484933\pi\) | ||||
0.0473181 | + | 0.998880i | \(0.484933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.67189i | 0.897926i | 0.893550 | + | 0.448963i | \(0.148207\pi\) | ||||
−0.893550 | + | 0.448963i | \(0.851793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.91894 | + | 1.92736i | −0.452521 | + | 0.222552i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.81867i | 0.207257i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.62884 | 0.408276 | 0.204138 | − | 0.978942i | \(-0.434561\pi\) | ||||
0.204138 | + | 0.978942i | \(0.434561\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.71582 | 0.301758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.1966i | − | 1.88757i | −0.330560 | − | 0.943785i | \(-0.607238\pi\) | ||
0.330560 | − | 0.943785i | \(-0.392762\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.84291 | − | 12.5973i | 0.850683 | − | 1.36637i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.76084i | − | 0.188782i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.01565 | 0.743658 | 0.371829 | − | 0.928301i | \(-0.378731\pi\) | ||||
0.371829 | + | 0.928301i | \(0.378731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.26211 | −0.341962 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.275207i | − | 0.0285376i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.7132 | − | 6.66992i | −1.09915 | − | 0.684320i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.5807i | 1.88659i | 0.331958 | + | 0.943294i | \(0.392291\pi\) | ||||
−0.331958 | + | 0.943294i | \(0.607709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.09915 | 0.411980 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.96538 | −0.792585 | −0.396293 | − | 0.918124i | \(-0.629703\pi\) | ||||
−0.396293 | + | 0.918124i | \(0.629703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.8268i | − | 1.65799i | −0.559253 | − | 0.828997i | \(-0.688912\pi\) | ||
0.559253 | − | 0.828997i | \(-0.311088\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64563 | + | 1.02455i | 0.160597 | + | 0.0999856i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.7429i | − | 1.03855i | −0.854606 | − | 0.519276i | \(-0.826202\pi\) | ||
0.854606 | − | 0.519276i | \(-0.173798\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.34117 | −0.798939 | −0.399470 | − | 0.916746i | \(-0.630806\pi\) | ||||
−0.399470 | + | 0.916746i | \(0.630806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.68560 | −0.254906 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.28008i | − | 0.778925i | −0.921042 | − | 0.389462i | \(-0.872661\pi\) | ||
0.921042 | − | 0.389462i | \(-0.127339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.18182 | + | 1.89824i | −0.110205 | + | 0.177012i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.35255i | 0.679744i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.58673 | −0.603805 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.64245 | −0.694768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.17884i | − | 0.106293i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.11386 | − | 11.1247i | 0.0996265 | − | 0.995025i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5531i | 0.936437i | 0.883613 | + | 0.468219i | \(0.155104\pi\) | ||||
−0.883613 | + | 0.468219i | \(0.844896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.22240 | 0.459806 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.84966 | 0.685828 | 0.342914 | − | 0.939367i | \(-0.388586\pi\) | ||||
0.342914 | + | 0.939367i | \(0.388586\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.60161i | 0.485722i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.40603 | − | 8.68316i | 0.465277 | − | 0.747327i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.27261i | − | 0.792213i | −0.918205 | − | 0.396106i | \(-0.870361\pi\) | ||
0.918205 | − | 0.396106i | \(-0.129639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.5293 | −1.57163 | −0.785816 | − | 0.618461i | \(-0.787757\pi\) | ||||
−0.785816 | + | 0.618461i | \(0.787757\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.267524 | 0.0225296 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.02236i | 0.503615i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.82677 | + | 2.38250i | 0.317796 | + | 0.197856i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.25369i | 0.433317i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.6227 | −1.93525 | −0.967624 | − | 0.252395i | \(-0.918782\pi\) | ||||
−0.967624 | + | 0.252395i | \(0.918782\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2472 | −1.56631 | −0.783157 | − | 0.621825i | \(-0.786392\pi\) | ||||
−0.783157 | + | 0.621825i | \(0.786392\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.8460i | 1.20023i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.598097 | + | 0.372368i | 0.0480403 | + | 0.0299093i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.61180i | − | 0.527679i | −0.964567 | − | 0.263840i | \(-0.915011\pi\) | ||
0.964567 | − | 0.263840i | \(-0.0849890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.10104 | 0.483844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.992530 | 0.0782223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.6157i | − | 0.909809i | −0.890540 | − | 0.454905i | \(-0.849673\pi\) | ||
0.890540 | − | 0.454905i | \(-0.150327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.89147 | − | 3.03808i | 0.147251 | − | 0.236514i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.4280i | 1.42600i | 0.701162 | + | 0.713002i | \(0.252665\pi\) | ||||
−0.701162 | + | 0.713002i | \(0.747335\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.19784 | 0.169065 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.6256 | 0.965505 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.51955i | 0.419644i | 0.977740 | + | 0.209822i | \(0.0672884\pi\) | ||||
−0.977740 | + | 0.209822i | \(0.932712\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.45323 | + | 2.19012i | −0.336632 | + | 0.165558i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.29369i | − | 0.623392i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.73640 | 0.727733 | 0.363866 | − | 0.931451i | \(-0.381456\pi\) | ||||
0.363866 | + | 0.931451i | \(0.381456\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8277 | 1.62244 | 0.811220 | − | 0.584741i | \(-0.198804\pi\) | ||||
0.811220 | + | 0.584741i | \(0.198804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.85777i | 0.359097i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.63374 | − | 5.83652i | 0.267158 | − | 0.429109i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.1601i | 0.889235i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.54016 | −0.330248 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4807 | 1.19250 | 0.596251 | − | 0.802798i | \(-0.296656\pi\) | ||||
0.596251 | + | 0.802798i | \(0.296656\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.60541i | 0.331504i | 0.986167 | + | 0.165752i | \(0.0530052\pi\) | ||||
−0.986167 | + | 0.165752i | \(0.946995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.44933 | + | 3.39269i | 0.390235 | + | 0.242955i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.157186i | 0.0111990i | 0.999984 | + | 0.00559951i | \(0.00178239\pi\) | ||||
−0.999984 | + | 0.00559951i | \(0.998218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94253 | 0.137702 | 0.0688511 | − | 0.997627i | \(-0.478067\pi\) | ||||
0.0688511 | + | 0.997627i | \(0.478067\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.745507 | 0.0525840 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2.00090i | − | 0.140436i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.56194 | + | 1.59503i | 0.178934 | + | 0.111402i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.23709i | − | 0.155488i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3414 | 0.715332 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5602 | 1.62195 | 0.810976 | − | 0.585079i | \(-0.198937\pi\) | ||||
0.810976 | + | 0.585079i | \(0.198937\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.696505i | 0.0477237i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.06616 | + | 11.3497i | −0.481908 | + | 0.774040i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.312727i | − | 0.0212293i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.70100 | −0.452812 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.8113 | −1.46719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.59356i | − | 0.642432i | −0.947006 | − | 0.321216i | \(-0.895908\pi\) | ||
0.947006 | − | 0.321216i | \(-0.104092\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.93637 | + | 10.0372i | 0.329091 | + | 0.669149i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.90765i | 0.657594i | 0.944401 | + | 0.328797i | \(0.106643\pi\) | ||||
−0.944401 | + | 0.328797i | \(0.893357\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.90156 | 0.323904 | 0.161952 | − | 0.986799i | \(-0.448221\pi\) | ||||
0.161952 | + | 0.986799i | \(0.448221\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.58852 | −0.104517 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.3123i | 1.00314i | 0.865116 | + | 0.501571i | \(0.167245\pi\) | ||||
−0.865116 | + | 0.501571i | \(0.832755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.361973 | + | 0.581401i | −0.0236125 | + | 0.0379264i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.16960i | 0.205888i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.88065 | 0.251018 | 0.125509 | − | 0.992092i | \(-0.459944\pi\) | ||||
0.125509 | + | 0.992092i | \(0.459944\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.64578 | 0.428092 | 0.214046 | − | 0.976824i | \(-0.431336\pi\) | ||||
0.214046 | + | 0.976824i | \(0.431336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0951i | 1.03250i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.4177 | − | 7.10851i | −0.729449 | − | 0.454146i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5492i | 1.18026i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0203 | 0.951875 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.82636 | 0.367756 | 0.183878 | − | 0.982949i | \(-0.441135\pi\) | ||||
0.183878 | + | 0.982949i | \(0.441135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.83236i | − | 0.115200i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.0031 | + | 6.85038i | 0.689040 | + | 0.428988i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.1979i | − | 1.07278i | −0.843971 | − | 0.536388i | \(-0.819788\pi\) | ||
0.843971 | − | 0.536388i | \(-0.180212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.05173 | −0.189626 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.50988 | −0.279154 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 19.5353i | − | 1.20460i | −0.798269 | − | 0.602301i | \(-0.794251\pi\) | ||
0.798269 | − | 0.602301i | \(-0.205749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.25501 | + | 13.2592i | −0.507101 | + | 0.814506i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.12781i | 0.375016i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.2275 | 1.29426 | 0.647132 | − | 0.762378i | \(-0.275968\pi\) | ||||
0.647132 | + | 0.762378i | \(0.275968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.19621 | 0.558630 | 0.279315 | − | 0.960200i | \(-0.409893\pi\) | ||||
0.279315 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.84929i | − | 0.172447i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.04330 | + | 8.22134i | 0.243820 | + | 0.495765i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.77325i | 0.166628i | 0.996523 | + | 0.0833141i | \(0.0265505\pi\) | ||||
−0.996523 | + | 0.0833141i | \(0.973450\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.704862 | −0.0421990 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.7971 | −1.95651 | −0.978255 | − | 0.207407i | \(-0.933497\pi\) | ||||
−0.978255 | + | 0.207407i | \(0.933497\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 23.6017i | − | 1.40298i | −0.712680 | − | 0.701489i | \(-0.752519\pi\) | ||
0.712680 | − | 0.701489i | \(-0.247481\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.82584 | − | 9.35745i | 0.345093 | − | 0.554288i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.33956i | − | 0.0790717i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.0406 | −1.59062 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.2293 | −0.951380 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.83939i | 0.107458i | 0.998556 | + | 0.0537291i | \(0.0171107\pi\) | ||||
−0.998556 | + | 0.0537291i | \(0.982889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.0244 | + | 11.2218i | 1.04942 | + | 0.653356i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.38182i | 0.486363i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.28666 | 0.190073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.93439 | 0.342052 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6.95735i | − | 0.399690i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.5572 | − | 6.57281i | −0.604506 | − | 0.376358i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3956i | 0.593310i | 0.954985 | + | 0.296655i | \(0.0958711\pi\) | ||||
−0.954985 | + | 0.296655i | \(0.904129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6973 | 0.836103 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2967 | −0.697281 | −0.348640 | − | 0.937257i | \(-0.613357\pi\) | ||||
−0.348640 | + | 0.937257i | \(0.613357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2954i | 0.977592i | 0.872398 | + | 0.488796i | \(0.162564\pi\) | ||||
−0.872398 | + | 0.488796i | \(0.837436\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.62408 | − | 4.21480i | 0.147850 | − | 0.237477i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 33.6362i | − | 1.88920i | −0.328227 | − | 0.944599i | \(-0.606451\pi\) | ||
0.328227 | − | 0.944599i | \(-0.393549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.69397 | −0.206822 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.38335 | 0.523728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 37.4538i | 2.08399i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7464 | + | 7.25237i | −0.817984 | + | 0.402289i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.28559i | − | 0.402894i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.303997 | 0.0167599 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.81704 | −0.539593 | −0.269797 | − | 0.962917i | \(-0.586956\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.87838i | 0.376933i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00871 | + | 1.62018i | −0.0551115 | + | 0.0885201i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.15644i | 0.498783i | 0.968403 | + | 0.249392i | \(0.0802306\pi\) | ||||
−0.968403 | + | 0.249392i | \(0.919769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.23223 | 0.392801 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.577341 | −0.0312648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9177i | 0.697488i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.65801 | − | 1.03226i | −0.0892644 | − | 0.0555749i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 32.5921i | − | 1.74963i | −0.484453 | − | 0.874817i | \(-0.660981\pi\) | ||
0.484453 | − | 0.874817i | \(-0.339019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5701 | 0.833448 | 0.416724 | − | 0.909033i | \(-0.363178\pi\) | ||||
0.416724 | + | 0.909033i | \(0.363178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0343 | −0.802470 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.9313i | 0.581816i | 0.956751 | + | 0.290908i | \(0.0939573\pi\) | ||||
−0.956751 | + | 0.290908i | \(0.906043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.51369 | − | 0.942405i | −0.0803384 | − | 0.0500177i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.75317i | − | 0.304490i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.405120 | −0.0213814 | −0.0106907 | − | 0.999943i | \(-0.503403\pi\) | ||||
−0.0106907 | + | 0.999943i | \(0.503403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.8522 | 0.676432 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.67529i | − | 0.350362i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.06678 | − | 14.5631i | 0.474577 | − | 0.762265i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.26443i | − | 0.379200i | −0.981861 | − | 0.189600i | \(-0.939281\pi\) | ||
0.981861 | − | 0.189600i | \(-0.0607191\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.01927 | −0.157177 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.93282 | 0.359934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.36770i | − | 0.174373i | −0.996192 | − | 0.0871866i | \(-0.972212\pi\) | ||
0.996192 | − | 0.0871866i | \(-0.0277876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.71687 | + | 0.972898i | 0.501777 | + | 0.0502402i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.62578i | − | 0.341245i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.54534 | 0.233478 | 0.116739 | − | 0.993163i | \(-0.462756\pi\) | ||||
0.116739 | + | 0.993163i | \(0.462756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.21760 | −0.472232 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 12.0978i | − | 0.618167i | −0.951035 | − | 0.309084i | \(-0.899978\pi\) | ||
0.951035 | − | 0.309084i | \(-0.100022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.14934 | − | 3.45227i | 0.109541 | − | 0.175944i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 13.3757i | − | 0.679923i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8934 | −1.16074 | −0.580371 | − | 0.814352i | \(-0.697092\pi\) | ||||
−0.580371 | + | 0.814352i | \(0.697092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.63631 | 0.335612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.85627i | 0.345853i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.88839 | − | 4.28863i | −0.346593 | − | 0.215784i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.9748i | − | 1.20326i | −0.798774 | − | 0.601631i | \(-0.794518\pi\) | ||
0.798774 | − | 0.601631i | \(-0.205482\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.89272 | −0.244943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8722 | 1.34193 | 0.670967 | − | 0.741487i | \(-0.265879\pi\) | ||||
0.670967 | + | 0.741487i | \(0.265879\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.03556i | − | 0.0515851i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.15527 | − | 3.20961i | −0.256167 | − | 0.159487i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.63397i | 0.279266i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7840 | −0.780467 | −0.390233 | − | 0.920716i | \(-0.627606\pi\) | ||||
−0.390233 | + | 0.920716i | \(0.627606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.09915 | 0.399502 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.42440i | − | 0.463744i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.3232 | + | 32.6432i | −0.997629 | + | 1.60239i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 16.1844i | − | 0.792552i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.6999 | −0.962402 | −0.481201 | − | 0.876610i | \(-0.659799\pi\) | ||||
−0.481201 | + | 0.876610i | \(0.659799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6913 | −0.764748 | −0.382374 | − | 0.924008i | \(-0.624893\pi\) | ||||
−0.382374 | + | 0.924008i | \(0.624893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.685185i | − | 0.0333149i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.7754 | + | 14.6437i | −1.44432 | + | 0.710325i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.52005i | 0.267134i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.26022 | −0.253966 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.33660 | −0.0643819 | −0.0321909 | − | 0.999482i | \(-0.510248\pi\) | ||||
−0.0321909 | + | 0.999482i | \(0.510248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.26379i | − | 0.204905i | −0.994738 | − | 0.102452i | \(-0.967331\pi\) | ||
0.994738 | − | 0.102452i | \(-0.0326689\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.08099 | + | 3.34249i | −0.0997759 | + | 0.160260i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.64378i | − | 0.269978i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.6899 | 1.56020 | 0.780101 | − | 0.625653i | \(-0.215167\pi\) | ||||
0.780101 | + | 0.625653i | \(0.215167\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.4558 | 0.640753 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8373i | 0.799964i | 0.916523 | + | 0.399982i | \(0.130984\pi\) | ||||
−0.916523 | + | 0.399982i | \(0.869016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.3174 | − | 8.29123i | −0.631304 | − | 0.393042i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 20.6332i | − | 0.975919i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.8502 | −0.606440 | −0.303220 | − | 0.952921i | \(-0.598062\pi\) | ||||
−0.303220 | + | 0.952921i | \(0.598062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.47303 | −0.116451 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 16.8114i | − | 0.789870i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.19226 | + | 3.85522i | 0.290298 | + | 0.180736i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 40.1900i | − | 1.88001i | −0.341161 | − | 0.940005i | \(-0.610820\pi\) | ||
0.341161 | − | 0.940005i | \(-0.389180\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.3566 | −1.41693 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.7208 | −1.61711 | −0.808554 | − | 0.588422i | \(-0.799750\pi\) | ||||
−0.808554 | + | 0.588422i | \(0.799750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.7292i | − | 1.24221i | −0.783727 | − | 0.621106i | \(-0.786684\pi\) | ||
0.783727 | − | 0.621106i | \(-0.213316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.325245 | + | 0.522408i | −0.0150829 | + | 0.0242261i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.6579i | − | 0.817112i | −0.912733 | − | 0.408556i | \(-0.866032\pi\) | ||
0.912733 | − | 0.408556i | \(-0.133968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.847144 | 0.0391175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.77507 | 0.266101 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.9558i | − | 0.503748i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4536 | + | 25.3222i | 0.571410 | + | 1.16186i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 15.6261i | − | 0.715468i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.8085 | 1.72752 | 0.863758 | − | 0.503907i | \(-0.168104\pi\) | ||||
0.863758 | + | 0.503907i | \(0.168104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1055 | −0.460772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.866924i | 0.0394464i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9591 | − | 35.2706i | 0.997110 | − | 1.60156i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.9951i | − | 1.26858i | −0.773096 | − | 0.634289i | \(-0.781293\pi\) | ||
0.773096 | − | 0.634289i | \(-0.218707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.1457 | 0.458804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1212 | 0.456762 | 0.228381 | − | 0.973572i | \(-0.426657\pi\) | ||||
0.228381 | + | 0.973572i | \(0.426657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 13.3785i | − | 0.602538i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.78116 | − | 4.84446i | −0.349737 | − | 0.217742i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.791462i | 0.0355019i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.0240 | 1.65742 | 0.828712 | − | 0.559676i | \(-0.189074\pi\) | ||||
0.828712 | + | 0.559676i | \(0.189074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.0960 | −0.719114 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.5700i | 1.00635i | 0.864185 | + | 0.503174i | \(0.167834\pi\) | ||||
−0.864185 | + | 0.503174i | \(0.832166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.1202 | + | 9.41364i | 0.672839 | + | 0.418902i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.91970i | 0.0852571i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3212 | −1.29964 | −0.649819 | − | 0.760089i | \(-0.725155\pi\) | ||||
−0.649819 | + | 0.760089i | \(0.725155\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.61457 | −0.336849 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.8165i | 1.13983i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.8862 | + | 31.9413i | −0.876292 | + | 1.40750i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.561224i | − | 0.0246826i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.82105 | −0.211620 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.9057 | 0.609220 | 0.304610 | − | 0.952477i | \(-0.401474\pi\) | ||||
0.304610 | + | 0.952477i | \(0.401474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.6591i | − | 1.60299i | −0.598001 | − | 0.801496i | \(-0.704038\pi\) | ||
0.598001 | − | 0.801496i | \(-0.295962\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.91296 | − | 3.88967i | −0.0834884 | − | 0.169759i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.09097i | − | 0.0910841i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.2419 | −0.921819 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.43582i | − | 0.192137i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.6961 | + | 20.3925i | −0.548902 | + | 0.881645i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.50425i | 0.366986i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0214 | 0.474727 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8082 | 0.679647 | 0.339823 | − | 0.940489i | \(-0.389633\pi\) | ||||
0.339823 | + | 0.940489i | \(0.389633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.0654i | 0.818174i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.8335 | + | 9.85776i | 0.678233 | + | 0.422260i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.6129i | 1.09513i | 0.836764 | + | 0.547563i | \(0.184444\pi\) | ||||
−0.836764 | + | 0.547563i | \(0.815556\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.4418 | 0.531003 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.3776 | −0.484703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.60173i | 0.153161i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.09790 | + | 3.17389i | 0.216394 | + | 0.134724i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.9292i | 0.929172i | 0.885528 | + | 0.464586i | \(0.153797\pi\) | ||||
−0.885528 | + | 0.464586i | \(0.846203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.6511 | 0.831154 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6212 | −0.448429 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.2718i | 1.44439i | 0.691692 | + | 0.722193i | \(0.256866\pi\) | ||||
−0.691692 | + | 0.722193i | \(0.743134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.78556 | + | 15.7176i | −0.411682 | + | 0.661243i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.69553i | 0.113202i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.05998 | −0.170203 | −0.0851015 | − | 0.996372i | \(-0.527121\pi\) | ||||
−0.0851015 | + | 0.996372i | \(0.527121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7533 | −0.910347 | −0.455174 | − | 0.890403i | \(-0.650423\pi\) | ||||
−0.455174 | + | 0.890403i | \(0.650423\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.3951i | 0.601362i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.48675 | − | 2.20661i | 0.187110 | − | 0.0920219i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23.6094i | − | 0.982872i | −0.870914 | − | 0.491436i | \(-0.836472\pi\) | ||
0.870914 | − | 0.491436i | \(-0.163528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.02259 | −0.167173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0681 | 0.708105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.7991i | − | 0.530083i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.68939 | − | 13.9569i | 0.359262 | − | 0.577046i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2321i | 0.546146i | 0.961993 | + | 0.273073i | \(0.0880400\pi\) | ||||
−0.961993 | + | 0.273073i | \(0.911960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.77824 | −0.0732713 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.137294 | −0.00564750 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.85971i | 0.363825i | 0.983315 | + | 0.181912i | \(0.0582287\pi\) | ||||
−0.983315 | + | 0.181912i | \(0.941771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.5032 | + | 7.78432i | 0.512580 | + | 0.319126i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.69670i | 0.0694412i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.01552 | −0.327505 | −0.163753 | − | 0.986501i | \(-0.552360\pi\) | ||||
−0.163753 | + | 0.986501i | \(0.552360\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.3621 | 0.993752 | 0.496876 | − | 0.867821i | \(-0.334480\pi\) | ||||
0.496876 | + | 0.867821i | \(0.334480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.90940i | − | 0.0777568i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.5072 | + | 9.03199i | 0.589801 | + | 0.367203i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.5642i | − | 1.48409i | −0.670348 | − | 0.742047i | \(-0.733855\pi\) | ||
0.670348 | − | 0.742047i | \(-0.266145\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.74768 | 0.0708197 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00665 | 0.0407249 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.21498i | − | 0.372190i | −0.982532 | − | 0.186095i | \(-0.940417\pi\) | ||
0.982532 | − | 0.186095i | \(-0.0595832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.39318 | + | 2.23773i | −0.0561784 | + | 0.0902338i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.4154i | − | 1.46603i | −0.680213 | − | 0.733015i | \(-0.738113\pi\) | ||
0.680213 | − | 0.733015i | \(-0.261887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.3781 | −1.38177 | −0.690886 | − | 0.722963i | \(-0.742780\pi\) | ||||
−0.690886 | + | 0.722963i | \(0.742780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.57433 | 0.183561 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.96324i | 0.278976i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.2618 | + | 19.8010i | −0.610471 | + | 0.792039i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.03272i | 0.360732i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4047 | −0.813588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.3309 | 1.68517 | 0.842584 | − | 0.538565i | \(-0.181033\pi\) | ||||
0.842584 | + | 0.538565i | \(0.181033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.5786i | 0.817928i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.4719 | − | 20.0323i | 0.494931 | − | 0.794958i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7689i | 0.783272i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.78390 | 0.0705699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.2608 | 1.70870 | 0.854349 | − | 0.519699i | \(-0.173956\pi\) | ||||
0.854349 | + | 0.519699i | \(0.173956\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.36283i | 0.0931809i | 0.998914 | + | 0.0465905i | \(0.0148356\pi\) | ||||
−0.998914 | + | 0.0465905i | \(0.985164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.91335 | − | 6.17193i | −0.390338 | − | 0.243019i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.9473i | 0.862837i | 0.902152 | + | 0.431418i | \(0.141987\pi\) | ||||
−0.902152 | + | 0.431418i | \(0.858013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.3989 | −0.682966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.273151 | 0.0107056 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.7170i | 1.35858i | 0.733869 | + | 0.679291i | \(0.237713\pi\) | ||||
−0.733869 | + | 0.679291i | \(0.762287\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9005 | − | 9.27687i | −0.582211 | − | 0.362477i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.1627i | 0.669580i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.1858 | 0.903192 | 0.451596 | − | 0.892223i | \(-0.350855\pi\) | ||||
0.451596 | + | 0.892223i | \(0.350855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.6148 | −1.54084 | −0.770418 | − | 0.637539i | \(-0.779953\pi\) | ||||
−0.770418 | + | 0.637539i | \(0.779953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 19.0511i | − | 0.739882i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.62010 | − | 10.6332i | 0.256716 | − | 0.412338i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.01596i | 0.0780583i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.37949 | 0.323970 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1909 | 0.393414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3084i | 1.16830i | 0.811645 | + | 0.584152i | \(0.198573\pi\) | ||||
−0.811645 | + | 0.584152i | \(0.801427\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.5238 | + | 10.0937i | −0.789963 | + | 0.388508i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.26419i | 0.356052i | 0.984026 | + | 0.178026i | \(0.0569711\pi\) | ||||
−0.984026 | + | 0.178026i | \(0.943029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.4419 | −0.707736 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.65382 | −0.331615 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.9835i | − | 0.879439i | −0.898135 | − | 0.439720i | \(-0.855078\pi\) | ||
0.898135 | − | 0.439720i | \(-0.144922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9585 | + | 17.6016i | −0.418705 | + | 0.672523i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.28126i | 0.163340i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.9574 | 0.874606 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2916 | −1.03822 | −0.519111 | − | 0.854707i | \(-0.673737\pi\) | ||||
−0.519111 | + | 0.854707i | \(0.673737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.06853i | 0.154551i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.1729 | + | 21.8982i | 1.33419 | + | 0.830648i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.95664i | − | 0.339257i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.3745 | −0.505871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.1308 | 0.911407 | 0.455704 | − | 0.890132i | \(-0.349388\pi\) | ||||
0.455704 | + | 0.890132i | \(0.349388\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3529i | 0.654479i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.507824 | − | 0.316165i | −0.0191258 | − | 0.0119075i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.90588i | − | 0.297331i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0156 | 0.563922 | 0.281961 | − | 0.959426i | \(-0.409015\pi\) | ||||
0.281961 | + | 0.959426i | \(0.409015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.11802 | 0.304450 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.315080i | 0.0117999i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.11733 | − | 11.4319i | 0.266173 | − | 0.427527i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.38955i | 0.126585i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.4211 | −1.09722 | −0.548611 | − | 0.836078i | \(-0.684843\pi\) | ||||
−0.548611 | + | 0.836078i | \(0.684843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.7011 | 0.621981 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.80475i | 0.215881i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.44843 | − | 9.04510i | −0.165211 | − | 0.335926i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.8025i | 1.77290i | 0.462829 | + | 0.886448i | \(0.346834\pi\) | ||||
−0.462829 | + | 0.886448i | \(0.653166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.91080 | −0.218918 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.6788 | 1.46757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 44.0763i | − | 1.62800i | −0.580867 | − | 0.813998i | \(-0.697286\pi\) | ||
0.580867 | − | 0.813998i | \(-0.302714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.20892 | − | 9.97276i | 0.229019 | − | 0.367851i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.56396i | − | 0.0576091i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.75235 | −0.138032 | −0.0690162 | − | 0.997616i | \(-0.521986\pi\) | ||||
−0.0690162 | + | 0.997616i | \(0.521986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2018 | −0.595187 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.6859i | 0.722205i | 0.932526 | + | 0.361103i | \(0.117600\pi\) | ||||
−0.932526 | + | 0.361103i | \(0.882400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.8415 | + | 27.9178i | 1.64287 | + | 1.02283i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 38.4703i | − | 1.40755i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.6626 | 0.389604 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.3594 | −0.961868 | −0.480934 | − | 0.876757i | \(-0.659702\pi\) | ||||
−0.480934 | + | 0.876757i | \(0.659702\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.08902i | 0.185454i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.5357 | + | 22.7467i | 1.32967 | + | 0.827837i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9270i | 0.433493i | 0.976228 | + | 0.216747i | \(0.0695446\pi\) | ||||
−0.976228 | + | 0.216747i | \(0.930455\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.60047 | 0.0580935 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.03123 | 0.0373821 | 0.0186911 | − | 0.999825i | \(-0.494050\pi\) | ||||
0.0186911 | + | 0.999825i | \(0.494050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.27886i | − | 0.299715i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.5453 | − | 28.1812i | 0.634351 | − | 1.01889i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 31.2080i | − | 1.12685i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.37170 | 0.121587 | 0.0607933 | − | 0.998150i | \(-0.480637\pi\) | ||||
0.0607933 | + | 0.998150i | \(0.480637\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0215 | 0.540986 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.0031i | 1.18704i | 0.804819 | + | 0.593520i | \(0.202262\pi\) | ||||
−0.804819 | + | 0.593520i | \(0.797738\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.695259 | − | 1.41369i | −0.0249744 | − | 0.0507811i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.66553i | − | 0.0956255i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.61708 | −0.272910 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.46116 | 0.0522844 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.22166i | − | 0.329555i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.81395 | + | 12.5508i | −0.278892 | + | 0.447956i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 7.29525i | − | 0.260048i | −0.991511 | − | 0.130024i | \(-0.958495\pi\) | ||
0.991511 | − | 0.130024i | \(-0.0415054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.0631 | 0.607463 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.21823 | 0.292206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.2791i | 0.649110i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.5812 | − | 7.21033i | −0.410744 | − | 0.255724i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.1730i | 1.13963i | 0.821775 | + | 0.569813i | \(0.192984\pi\) | ||||
−0.821775 | + | 0.569813i | \(0.807016\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.03260 | 0.0719082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6946 | 0.554542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.0577i | 0.496084i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.88406 | − | 1.17299i | −0.0664043 | − | 0.0413425i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.5411i | 0.652679i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.6881 | 0.551564 | 0.275782 | − | 0.961220i | \(-0.411063\pi\) | ||||
0.275782 | + | 0.961220i | \(0.411063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.8629 | −1.85627 | −0.928133 | − | 0.372249i | \(-0.878587\pi\) | ||||
−0.928133 | + | 0.372249i | \(0.878587\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.03242i | 0.281709i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.7276 | + | 22.0493i | −0.480857 | + | 0.772353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 33.7444i | − | 1.18057i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.29763 | −0.255000 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.7411 | −0.374866 | −0.187433 | − | 0.982277i | \(-0.560017\pi\) | ||||
−0.187433 | + | 0.982277i | \(0.560017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 50.9828i | − | 1.77715i | −0.458733 | − | 0.888574i | \(-0.651697\pi\) | ||
0.458733 | − | 0.888574i | \(-0.348303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.18092 | + | 3.53162i | −0.250008 | + | 0.122955i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8663i | 1.03855i | 0.854607 | + | 0.519276i | \(0.173798\pi\) | ||||
−0.854607 | + | 0.519276i | \(0.826202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5010 | 0.885685 | 0.442842 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442842 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.42229 | −0.0840283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 39.9166i | 1.38303i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.7786 | − | 34.9808i | 0.753680 | − | 1.21056i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.44128i | − | 0.0498180i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.6417 | 0.367392 | 0.183696 | − | 0.982983i | \(-0.441194\pi\) | ||||
0.183696 | + | 0.982983i | \(0.441194\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9359 | −0.859859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 28.6466i | − | 0.986640i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.17203 | − | 2.59745i | −0.143522 | − | 0.0893552i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.58536i | − | 0.260636i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.6149 | 0.707502 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.07470 | 0.105399 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.9480i | − | 0.374853i | −0.982279 | − | 0.187427i | \(-0.939985\pi\) | ||
0.982279 | − | 0.187427i | \(-0.0600147\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.9664 | − | 14.9212i | −0.819634 | − | 0.510294i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 20.2019i | − | 0.690084i | −0.938587 | − | 0.345042i | \(-0.887865\pi\) | ||
0.938587 | − | 0.345042i | \(-0.112135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8889 | −0.644480 | −0.322240 | − | 0.946658i | \(-0.604436\pi\) | ||||
−0.322240 | + | 0.946658i | \(0.604436\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.17004 | 0.0398748 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.8722i | − | 0.438174i | −0.975705 | − | 0.219087i | \(-0.929692\pi\) | ||
0.975705 | − | 0.219087i | \(-0.0703079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.52311 | − | 10.4774i | 0.221792 | − | 0.356243i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 23.6185i | − | 0.802128i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.64934 | 0.225563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.80523 | 0.0950518 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.5667i | 1.40682i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0416 | + | 1.10554i | 0.373275 | + | 0.0373740i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.27417i | 0.0767933i | 0.999263 | + | 0.0383966i | \(0.0122250\pi\) | ||||
−0.999263 | + | 0.0383966i | \(0.987775\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.60661 | −0.0541897 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.3451 | −1.12343 | −0.561713 | − | 0.827332i | \(-0.689857\pi\) | ||||
−0.561713 | + | 0.827332i | \(0.689857\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.6240i | − | 0.929622i | −0.885410 | − | 0.464811i | \(-0.846122\pi\) | ||
0.885410 | − | 0.464811i | \(-0.153878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.80164 | + | 15.7434i | −0.329478 | + | 0.529208i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.9934i | 1.37643i | 0.725509 | + | 0.688213i | \(0.241604\pi\) | ||||
−0.725509 | + | 0.688213i | \(0.758396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4743 | −0.351296 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.97636 | 0.166714 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.72860i | − | 0.0578455i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.4820 | − | 11.5067i | −0.617785 | − | 0.384625i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.87073i | 0.0958510i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.635189 | 0.0211848 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.3546 | 1.54430 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.18338i | 0.172492i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.4342 | − | 25.7964i | −1.37732 | − | 0.857501i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3313i | 0.409455i | 0.978819 | + | 0.204727i | \(0.0656308\pi\) | ||||
−0.978819 | + | 0.204727i | \(0.934369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.8193 | −0.591027 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2732 | −0.737943 | −0.368972 | − | 0.929441i | \(-0.620290\pi\) | ||||
−0.368972 | + | 0.929441i | \(0.620290\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.5104i | − | 1.04284i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.74101 | − | 9.22121i | 0.189792 | − | 0.304844i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.79102i | 0.257282i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.8277 | 0.522108 | 0.261054 | − | 0.965324i | \(-0.415930\pi\) | ||||
0.261054 | + | 0.965324i | \(0.415930\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.08004 | −0.299198 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.62085i | 0.0862663i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.7954 | + | 6.78466i | −0.453590 | + | 0.223078i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 37.6430i | − | 1.23636i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.6716 | −1.10473 | −0.552365 | − | 0.833602i | \(-0.686275\pi\) | ||||
−0.552365 | + | 0.833602i | \(0.686275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.9467 | 1.11256 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 10.7405i | − | 0.351629i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.3711 | − | 23.0828i | 0.469984 | − | 0.754887i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.9679i | 1.53438i | 0.641422 | + | 0.767188i | \(0.278345\pi\) | ||||
−0.641422 | + | 0.767188i | \(0.721655\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.1066 | −0.492986 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.9027 | 1.33339 | 0.666696 | − | 0.745330i | \(-0.267708\pi\) | ||||
0.666696 | + | 0.745330i | \(0.267708\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.34964i | 0.0439504i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.61829 | + | 5.36564i | 0.280353 | + | 0.174544i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.4956i | 0.893486i | 0.894662 | + | 0.446743i | \(0.147416\pi\) | ||||
−0.894662 | + | 0.446743i | \(0.852584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.2149 | −0.818511 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.3795 | 0.952696 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.30199i | 0.171748i | 0.996306 | + | 0.0858742i | \(0.0273683\pi\) | ||||
−0.996306 | + | 0.0858742i | \(0.972632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.2843 | − | 19.4772i | −1.01234 | − | 0.630268i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.22649i | − | 0.104298i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.20334 | 0.297191 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9007 | −0.996798 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 24.0327i | − | 0.774444i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.44276 | − | 8.74215i | 0.175209 | − | 0.281420i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.8814i | − | 1.25034i | −0.780489 | − | 0.625170i | \(-0.785030\pi\) | ||
0.780489 | − | 0.625170i | \(-0.214970\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.7140 | −1.05093 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.4921 | −1.74873 | −0.874367 | − | 0.485265i | \(-0.838723\pi\) | ||||
−0.874367 | + | 0.485265i | \(0.838723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 18.3908i | − | 0.589583i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.33458 | − | 12.8802i | −0.202869 | − | 0.412498i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.49089i | − | 0.0476979i | −0.999716 | − | 0.0238490i | \(-0.992408\pi\) | ||
0.999716 | − | 0.0238490i | \(-0.00759208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8552 | 0.410854 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6599 | −0.595766 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.0626i | 0.926952i | 0.886110 | + | 0.463476i | \(0.153398\pi\) | ||||
−0.886110 | + | 0.463476i | \(0.846602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.185765 | − | 0.298376i | 0.00591896 | − | 0.00950704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.265525i | 0.00845177i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.97905 | −0.190123 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.9937 | −1.61987 | −0.809933 | − | 0.586522i | \(-0.800497\pi\) | ||||
−0.809933 | + | 0.586522i | \(0.800497\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.57468i | − | 0.272109i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.68738 | − | 2.29572i | −0.116898 | − | 0.0727791i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.4224i | 1.66023i | 0.557590 | + | 0.830116i | \(0.311726\pi\) | ||||
−0.557590 | + | 0.830116i | \(0.688274\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.0647 | −0.444988 |
(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 | 460.2.c.a.369.8 | yes | 12 | |
3.2 | odd | 2 | 4140.2.f.b.829.10 | 12 | |||
4.3 | odd | 2 | 1840.2.e.f.369.5 | 12 | |||
5.2 | odd | 4 | 2300.2.a.n.1.5 | 6 | |||
5.3 | odd | 4 | 2300.2.a.o.1.2 | 6 | |||
5.4 | even | 2 | inner | 460.2.c.a.369.5 | ✓ | 12 | |
15.14 | odd | 2 | 4140.2.f.b.829.9 | 12 | |||
20.3 | even | 4 | 9200.2.a.cx.1.5 | 6 | |||
20.7 | even | 4 | 9200.2.a.cy.1.2 | 6 | |||
20.19 | odd | 2 | 1840.2.e.f.369.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.5 | ✓ | 12 | 5.4 | even | 2 | inner | |
460.2.c.a.369.8 | yes | 12 | 1.1 | even | 1 | trivial | |
1840.2.e.f.369.5 | 12 | 4.3 | odd | 2 | |||
1840.2.e.f.369.8 | 12 | 20.19 | odd | 2 | |||
2300.2.a.n.1.5 | 6 | 5.2 | odd | 4 | |||
2300.2.a.o.1.2 | 6 | 5.3 | odd | 4 | |||
4140.2.f.b.829.9 | 12 | 15.14 | odd | 2 | |||
4140.2.f.b.829.10 | 12 | 3.2 | odd | 2 | |||
9200.2.a.cx.1.5 | 6 | 20.3 | even | 4 | |||
9200.2.a.cy.1.2 | 6 | 20.7 | even | 4 |