Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.9719503790\) |
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: | \( x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.8 | ||
Root | \(0.858825i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.e.1249.5 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.858825i | 0.607281i | 0.952787 | + | 0.303640i | \(0.0982022\pi\) | ||||
−0.952787 | + | 0.303640i | \(0.901798\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.26242 | 0.631210 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.858825 | −0.350614 | ||||||||
\(7\) | 3.88045i | 1.46667i | 0.679865 | + | 0.733337i | \(0.262038\pi\) | ||||
−0.679865 | + | 0.733337i | \(0.737962\pi\) | |||||||
\(8\) | 2.80185i | 0.990603i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.39825 | −0.421589 | −0.210794 | − | 0.977530i | \(-0.567605\pi\) | ||||
−0.210794 | + | 0.977530i | \(0.567605\pi\) | |||||||
\(12\) | 1.26242i | 0.364429i | ||||||||
\(13\) | − 3.36204i | − 0.932461i | −0.884663 | − | 0.466230i | \(-0.845612\pi\) | ||||
0.884663 | − | 0.466230i | \(-0.154388\pi\) | |||||||
\(14\) | −3.33263 | −0.890683 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.118543 | 0.0296359 | ||||||||
\(17\) | 3.11590i | 0.755717i | 0.925863 | + | 0.377859i | \(0.123339\pi\) | ||||
−0.925863 | + | 0.377859i | \(0.876661\pi\) | |||||||
\(18\) | − 0.858825i | − 0.202427i | ||||||||
\(19\) | 2.70595 | 0.620788 | 0.310394 | − | 0.950608i | \(-0.399539\pi\) | ||||
0.310394 | + | 0.950608i | \(0.399539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.88045 | −0.846784 | ||||||||
\(22\) | − 1.20085i | − 0.256023i | ||||||||
\(23\) | 6.43989i | 1.34281i | 0.741091 | + | 0.671405i | \(0.234309\pi\) | ||||
−0.741091 | + | 0.671405i | \(0.765691\pi\) | |||||||
\(24\) | −2.80185 | −0.571925 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.88740 | 0.566266 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 4.89876i | 0.925779i | ||||||||
\(29\) | −8.26242 | −1.53429 | −0.767146 | − | 0.641472i | \(-0.778324\pi\) | ||||
−0.767146 | + | 0.641472i | \(0.778324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.34027 | −1.13875 | −0.569373 | − | 0.822079i | \(-0.692814\pi\) | ||||
−0.569373 | + | 0.822079i | \(0.692814\pi\) | |||||||
\(32\) | 5.70550i | 1.00860i | ||||||||
\(33\) | − 1.39825i | − 0.243404i | ||||||||
\(34\) | −2.67601 | −0.458933 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.26242 | −0.210403 | ||||||||
\(37\) | − 7.49949i | − 1.23291i | −0.787391 | − | 0.616454i | \(-0.788568\pi\) | ||||
0.787391 | − | 0.616454i | \(-0.211432\pi\) | |||||||
\(38\) | 2.32394i | 0.376993i | ||||||||
\(39\) | 3.36204 | 0.538357 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3783 | 1.77700 | 0.888498 | − | 0.458881i | \(-0.151750\pi\) | ||||
0.888498 | + | 0.458881i | \(0.151750\pi\) | |||||||
\(42\) | − 3.33263i | − 0.514236i | ||||||||
\(43\) | 3.39725i | 0.518076i | 0.965867 | + | 0.259038i | \(0.0834054\pi\) | ||||
−0.965867 | + | 0.259038i | \(0.916595\pi\) | |||||||
\(44\) | −1.76518 | −0.266111 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.53074 | −0.815463 | ||||||||
\(47\) | 8.38291i | 1.22277i | 0.791332 | + | 0.611387i | \(0.209388\pi\) | ||||
−0.791332 | + | 0.611387i | \(0.790612\pi\) | |||||||
\(48\) | 0.118543i | 0.0171103i | ||||||||
\(49\) | −8.05792 | −1.15113 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.11590 | −0.436314 | ||||||||
\(52\) | − 4.24430i | − 0.588579i | ||||||||
\(53\) | − 11.4431i | − 1.57184i | −0.618330 | − | 0.785918i | \(-0.712191\pi\) | ||||
0.618330 | − | 0.785918i | \(-0.287809\pi\) | |||||||
\(54\) | 0.858825 | 0.116871 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.8724 | −1.45289 | ||||||||
\(57\) | 2.70595i | 0.358412i | ||||||||
\(58\) | − 7.09597i | − 0.931747i | ||||||||
\(59\) | −7.64074 | −0.994740 | −0.497370 | − | 0.867539i | \(-0.665701\pi\) | ||||
−0.497370 | + | 0.867539i | \(0.665701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8219 | 1.38560 | 0.692798 | − | 0.721132i | \(-0.256378\pi\) | ||||
0.692798 | + | 0.721132i | \(0.256378\pi\) | |||||||
\(62\) | − 5.44518i | − 0.691539i | ||||||||
\(63\) | − 3.88045i | − 0.488891i | ||||||||
\(64\) | −4.66294 | −0.582868 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.20085 | 0.147815 | ||||||||
\(67\) | 3.54377i | 0.432940i | 0.976289 | + | 0.216470i | \(0.0694544\pi\) | ||||
−0.976289 | + | 0.216470i | \(0.930546\pi\) | |||||||
\(68\) | 3.93358i | 0.477016i | ||||||||
\(69\) | −6.43989 | −0.775271 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.18356 | 0.140463 | 0.0702317 | − | 0.997531i | \(-0.477626\pi\) | ||||
0.0702317 | + | 0.997531i | \(0.477626\pi\) | |||||||
\(72\) | − 2.80185i | − 0.330201i | ||||||||
\(73\) | − 2.39461i | − 0.280268i | −0.990133 | − | 0.140134i | \(-0.955247\pi\) | ||||
0.990133 | − | 0.140134i | \(-0.0447533\pi\) | |||||||
\(74\) | 6.44075 | 0.748722 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.41605 | 0.391847 | ||||||||
\(77\) | − 5.42585i | − 0.618333i | ||||||||
\(78\) | 2.88740i | 0.326934i | ||||||||
\(79\) | −10.6245 | −1.19534 | −0.597672 | − | 0.801740i | \(-0.703908\pi\) | ||||
−0.597672 | + | 0.801740i | \(0.703908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.77199i | 1.07914i | ||||||||
\(83\) | − 1.40894i | − 0.154651i | −0.997006 | − | 0.0773255i | \(-0.975362\pi\) | ||||
0.997006 | − | 0.0773255i | \(-0.0246381\pi\) | |||||||
\(84\) | −4.89876 | −0.534499 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.91764 | −0.314617 | ||||||||
\(87\) | − 8.26242i | − 0.885824i | ||||||||
\(88\) | − 3.91769i | − 0.417627i | ||||||||
\(89\) | −4.62972 | −0.490750 | −0.245375 | − | 0.969428i | \(-0.578911\pi\) | ||||
−0.245375 | + | 0.969428i | \(0.578911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.0462 | 1.36762 | ||||||||
\(92\) | 8.12984i | 0.847595i | ||||||||
\(93\) | − 6.34027i | − 0.657456i | ||||||||
\(94\) | −7.19945 | −0.742567 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.70550 | −0.582315 | ||||||||
\(97\) | − 1.51516i | − 0.153841i | −0.997037 | − | 0.0769204i | \(-0.975491\pi\) | ||||
0.997037 | − | 0.0769204i | \(-0.0245087\pi\) | |||||||
\(98\) | − 6.92034i | − 0.699060i | ||||||||
\(99\) | 1.39825 | 0.140530 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2376 | 1.71521 | 0.857604 | − | 0.514310i | \(-0.171952\pi\) | ||||
0.857604 | + | 0.514310i | \(0.171952\pi\) | |||||||
\(102\) | − 2.67601i | − 0.264965i | ||||||||
\(103\) | 10.9905i | 1.08292i | 0.840726 | + | 0.541461i | \(0.182129\pi\) | ||||
−0.840726 | + | 0.541461i | \(0.817871\pi\) | |||||||
\(104\) | 9.41991 | 0.923698 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.82766 | 0.954546 | ||||||||
\(107\) | 6.80699i | 0.658056i | 0.944320 | + | 0.329028i | \(0.106721\pi\) | ||||
−0.944320 | + | 0.329028i | \(0.893279\pi\) | |||||||
\(108\) | − 1.26242i | − 0.121476i | ||||||||
\(109\) | 11.4451 | 1.09624 | 0.548121 | − | 0.836399i | \(-0.315343\pi\) | ||||
0.548121 | + | 0.836399i | \(0.315343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.49949 | 0.711820 | ||||||||
\(112\) | 0.460003i | 0.0434662i | ||||||||
\(113\) | 16.2686i | 1.53042i | 0.643781 | + | 0.765210i | \(0.277365\pi\) | ||||
−0.643781 | + | 0.765210i | \(0.722635\pi\) | |||||||
\(114\) | −2.32394 | −0.217657 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.4306 | −0.968461 | ||||||||
\(117\) | 3.36204i | 0.310820i | ||||||||
\(118\) | − 6.56206i | − 0.604087i | ||||||||
\(119\) | −12.0911 | −1.10839 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.04489 | −0.822263 | ||||||||
\(122\) | 9.29408i | 0.841446i | ||||||||
\(123\) | 11.3783i | 1.02595i | ||||||||
\(124\) | −8.00409 | −0.718788 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.33263 | 0.296894 | ||||||||
\(127\) | − 16.2477i | − 1.44175i | −0.693065 | − | 0.720875i | \(-0.743740\pi\) | ||||
0.693065 | − | 0.720875i | \(-0.256260\pi\) | |||||||
\(128\) | 7.40636i | 0.654636i | ||||||||
\(129\) | −3.39725 | −0.299111 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3119 | −1.33781 | −0.668903 | − | 0.743349i | \(-0.733236\pi\) | ||||
−0.668903 | + | 0.743349i | \(0.733236\pi\) | |||||||
\(132\) | − 1.76518i | − 0.153639i | ||||||||
\(133\) | 10.5003i | 0.910493i | ||||||||
\(134\) | −3.04348 | −0.262916 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.73028 | −0.748615 | ||||||||
\(137\) | 6.86417i | 0.586445i | 0.956044 | + | 0.293223i | \(0.0947277\pi\) | ||||
−0.956044 | + | 0.293223i | \(0.905272\pi\) | |||||||
\(138\) | − 5.53074i | − 0.470808i | ||||||||
\(139\) | −13.8225 | −1.17241 | −0.586203 | − | 0.810164i | \(-0.699378\pi\) | ||||
−0.586203 | + | 0.810164i | \(0.699378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.38291 | −0.705968 | ||||||||
\(142\) | 1.01647i | 0.0853007i | ||||||||
\(143\) | 4.70097i | 0.393115i | ||||||||
\(144\) | −0.118543 | −0.00987862 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.05655 | 0.170201 | ||||||||
\(147\) | − 8.05792i | − 0.664606i | ||||||||
\(148\) | − 9.46751i | − 0.778224i | ||||||||
\(149\) | −7.09597 | −0.581325 | −0.290662 | − | 0.956826i | \(-0.593876\pi\) | ||||
−0.290662 | + | 0.956826i | \(0.593876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.1474 | 1.55819 | 0.779097 | − | 0.626903i | \(-0.215678\pi\) | ||||
0.779097 | + | 0.626903i | \(0.215678\pi\) | |||||||
\(152\) | 7.58166i | 0.614954i | ||||||||
\(153\) | − 3.11590i | − 0.251906i | ||||||||
\(154\) | 4.65986 | 0.375502 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.24430 | 0.339816 | ||||||||
\(157\) | − 11.8114i | − 0.942653i | −0.881959 | − | 0.471326i | \(-0.843775\pi\) | ||||
0.881959 | − | 0.471326i | \(-0.156225\pi\) | |||||||
\(158\) | − 9.12455i | − 0.725910i | ||||||||
\(159\) | 11.4431 | 0.907500 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.9897 | −1.96946 | ||||||||
\(162\) | 0.858825i | 0.0674757i | ||||||||
\(163\) | − 8.92635i | − 0.699165i | −0.936906 | − | 0.349583i | \(-0.886323\pi\) | ||||
0.936906 | − | 0.349583i | \(-0.113677\pi\) | |||||||
\(164\) | 14.3642 | 1.12166 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.21003 | 0.0939166 | ||||||||
\(167\) | 15.8114i | 1.22352i | 0.791042 | + | 0.611762i | \(0.209539\pi\) | ||||
−0.791042 | + | 0.611762i | \(0.790461\pi\) | |||||||
\(168\) | − 10.8724i | − 0.838827i | ||||||||
\(169\) | 1.69672 | 0.130517 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.70595 | −0.206929 | ||||||||
\(172\) | 4.28876i | 0.327015i | ||||||||
\(173\) | − 16.3259i | − 1.24124i | −0.784112 | − | 0.620619i | \(-0.786881\pi\) | ||||
0.784112 | − | 0.620619i | \(-0.213119\pi\) | |||||||
\(174\) | 7.09597 | 0.537944 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.165754 | −0.0124942 | ||||||||
\(177\) | − 7.64074i | − 0.574313i | ||||||||
\(178\) | − 3.97612i | − 0.298023i | ||||||||
\(179\) | 0.852080 | 0.0636875 | 0.0318437 | − | 0.999493i | \(-0.489862\pi\) | ||||
0.0318437 | + | 0.999493i | \(0.489862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.9643 | 1.63260 | 0.816298 | − | 0.577631i | \(-0.196023\pi\) | ||||
0.816298 | + | 0.577631i | \(0.196023\pi\) | |||||||
\(182\) | 11.2044i | 0.830527i | ||||||||
\(183\) | 10.8219i | 0.799974i | ||||||||
\(184\) | −18.0436 | −1.33019 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.44518 | 0.399260 | ||||||||
\(187\) | − 4.35682i | − 0.318602i | ||||||||
\(188\) | 10.5828i | 0.771827i | ||||||||
\(189\) | 3.88045 | 0.282261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.15408 | −0.0835065 | −0.0417532 | − | 0.999128i | \(-0.513294\pi\) | ||||
−0.0417532 | + | 0.999128i | \(0.513294\pi\) | |||||||
\(192\) | − 4.66294i | − 0.336519i | ||||||||
\(193\) | 0.983419i | 0.0707880i | 0.999373 | + | 0.0353940i | \(0.0112686\pi\) | ||||
−0.999373 | + | 0.0353940i | \(0.988731\pi\) | |||||||
\(194\) | 1.30125 | 0.0934246 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.1725 | −0.726606 | ||||||||
\(197\) | − 7.40726i | − 0.527745i | −0.964558 | − | 0.263873i | \(-0.915000\pi\) | ||||
0.964558 | − | 0.263873i | \(-0.0849999\pi\) | |||||||
\(198\) | 1.20085i | 0.0853410i | ||||||||
\(199\) | 13.5887 | 0.963274 | 0.481637 | − | 0.876371i | \(-0.340042\pi\) | ||||
0.481637 | + | 0.876371i | \(0.340042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.54377 | −0.249958 | ||||||||
\(202\) | 14.8041i | 1.04161i | ||||||||
\(203\) | − 32.0619i | − 2.25031i | ||||||||
\(204\) | −3.93358 | −0.275405 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.43888 | −0.657638 | ||||||||
\(207\) | − 6.43989i | − 0.447603i | ||||||||
\(208\) | − 0.398547i | − 0.0276343i | ||||||||
\(209\) | −3.78360 | −0.261717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.2982 | 1.81044 | 0.905221 | − | 0.424941i | \(-0.139705\pi\) | ||||
0.905221 | + | 0.424941i | \(0.139705\pi\) | |||||||
\(212\) | − 14.4461i | − 0.992159i | ||||||||
\(213\) | 1.18356i | 0.0810965i | ||||||||
\(214\) | −5.84601 | −0.399625 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.80185 | 0.190642 | ||||||||
\(217\) | − 24.6031i | − 1.67017i | ||||||||
\(218\) | 9.82934i | 0.665727i | ||||||||
\(219\) | 2.39461 | 0.161813 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4758 | 0.704677 | ||||||||
\(222\) | 6.44075i | 0.432275i | ||||||||
\(223\) | 13.5470i | 0.907176i | 0.891212 | + | 0.453588i | \(0.149856\pi\) | ||||
−0.891212 | + | 0.453588i | \(0.850144\pi\) | |||||||
\(224\) | −22.1399 | −1.47929 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.9719 | −0.929395 | ||||||||
\(227\) | 0.265434i | 0.0176175i | 0.999961 | + | 0.00880874i | \(0.00280395\pi\) | ||||
−0.999961 | + | 0.00880874i | \(0.997196\pi\) | |||||||
\(228\) | 3.41605i | 0.226233i | ||||||||
\(229\) | −4.28115 | −0.282906 | −0.141453 | − | 0.989945i | \(-0.545177\pi\) | ||||
−0.141453 | + | 0.989945i | \(0.545177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.42585 | 0.356995 | ||||||||
\(232\) | − 23.1500i | − 1.51987i | ||||||||
\(233\) | 6.74720i | 0.442024i | 0.975271 | + | 0.221012i | \(0.0709359\pi\) | ||||
−0.975271 | + | 0.221012i | \(0.929064\pi\) | |||||||
\(234\) | −2.88740 | −0.188755 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.64582 | −0.627890 | ||||||||
\(237\) | − 10.6245i | − 0.690133i | ||||||||
\(238\) | − 10.3841i | − 0.673104i | ||||||||
\(239\) | 0.307310 | 0.0198782 | 0.00993912 | − | 0.999951i | \(-0.496836\pi\) | ||||
0.00993912 | + | 0.999951i | \(0.496836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1233 | −0.716513 | −0.358256 | − | 0.933623i | \(-0.616629\pi\) | ||||
−0.358256 | + | 0.933623i | \(0.616629\pi\) | |||||||
\(242\) | − 7.76798i | − 0.499344i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 13.6617 | 0.874602 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.77199 | −0.623039 | ||||||||
\(247\) | − 9.09751i | − 0.578860i | ||||||||
\(248\) | − 17.7645i | − 1.12805i | ||||||||
\(249\) | 1.40894 | 0.0892878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5499 | −1.29710 | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||||
−0.648549 | + | 0.761173i | \(0.724624\pi\) | |||||||
\(252\) | − 4.89876i | − 0.308593i | ||||||||
\(253\) | − 9.00459i | − 0.566114i | ||||||||
\(254\) | 13.9539 | 0.875548 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6866 | −0.980415 | ||||||||
\(257\) | − 2.43352i | − 0.151799i | −0.997115 | − | 0.0758996i | \(-0.975817\pi\) | ||||
0.997115 | − | 0.0758996i | \(-0.0241828\pi\) | |||||||
\(258\) | − 2.91764i | − 0.181644i | ||||||||
\(259\) | 29.1014 | 1.80827 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.26242 | 0.511431 | ||||||||
\(262\) | − 13.1502i | − 0.812425i | ||||||||
\(263\) | 20.1748i | 1.24403i | 0.783004 | + | 0.622017i | \(0.213686\pi\) | ||||
−0.783004 | + | 0.622017i | \(0.786314\pi\) | |||||||
\(264\) | 3.91769 | 0.241117 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.01794 | −0.552925 | ||||||||
\(267\) | − 4.62972i | − 0.283334i | ||||||||
\(268\) | 4.47372i | 0.273276i | ||||||||
\(269\) | 18.6834 | 1.13915 | 0.569574 | − | 0.821940i | \(-0.307108\pi\) | ||||
0.569574 | + | 0.821940i | \(0.307108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.61184 | 0.462387 | 0.231193 | − | 0.972908i | \(-0.425737\pi\) | ||||
0.231193 | + | 0.972908i | \(0.425737\pi\) | |||||||
\(272\) | 0.369370i | 0.0223963i | ||||||||
\(273\) | 13.0462i | 0.789593i | ||||||||
\(274\) | −5.89512 | −0.356137 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.12984 | −0.489359 | ||||||||
\(277\) | − 8.17364i | − 0.491107i | −0.969383 | − | 0.245553i | \(-0.921030\pi\) | ||||
0.969383 | − | 0.245553i | \(-0.0789696\pi\) | |||||||
\(278\) | − 11.8711i | − 0.711980i | ||||||||
\(279\) | 6.34027 | 0.379582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8891 | 0.888211 | 0.444105 | − | 0.895975i | \(-0.353522\pi\) | ||||
0.444105 | + | 0.895975i | \(0.353522\pi\) | |||||||
\(282\) | − 7.19945i | − 0.428721i | ||||||||
\(283\) | 1.35203i | 0.0803698i | 0.999192 | + | 0.0401849i | \(0.0127947\pi\) | ||||
−0.999192 | + | 0.0401849i | \(0.987205\pi\) | |||||||
\(284\) | 1.49416 | 0.0886618 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.03731 | −0.238731 | ||||||||
\(287\) | 44.1531i | 2.60627i | ||||||||
\(288\) | − 5.70550i | − 0.336200i | ||||||||
\(289\) | 7.29115 | 0.428891 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.51516 | 0.0888201 | ||||||||
\(292\) | − 3.02300i | − 0.176908i | ||||||||
\(293\) | 10.4773i | 0.612091i | 0.952017 | + | 0.306045i | \(0.0990059\pi\) | ||||
−0.952017 | + | 0.306045i | \(0.900994\pi\) | |||||||
\(294\) | 6.92034 | 0.403603 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 21.0124 | 1.22132 | ||||||||
\(297\) | 1.39825i | 0.0811348i | ||||||||
\(298\) | − 6.09420i | − 0.353027i | ||||||||
\(299\) | 21.6511 | 1.25212 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.1829 | −0.759848 | ||||||||
\(302\) | 16.4443i | 0.946262i | ||||||||
\(303\) | 17.2376i | 0.990276i | ||||||||
\(304\) | 0.320773 | 0.0183976 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.67601 | 0.152978 | ||||||||
\(307\) | 10.4991i | 0.599216i | 0.954062 | + | 0.299608i | \(0.0968558\pi\) | ||||
−0.954062 | + | 0.299608i | \(0.903144\pi\) | |||||||
\(308\) | − 6.84971i | − 0.390298i | ||||||||
\(309\) | −10.9905 | −0.625225 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68539 | −0.265684 | −0.132842 | − | 0.991137i | \(-0.542410\pi\) | ||||
−0.132842 | + | 0.991137i | \(0.542410\pi\) | |||||||
\(312\) | 9.41991i | 0.533297i | ||||||||
\(313\) | 17.2431i | 0.974635i | 0.873225 | + | 0.487317i | \(0.162025\pi\) | ||||
−0.873225 | + | 0.487317i | \(0.837975\pi\) | |||||||
\(314\) | 10.1439 | 0.572455 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.4125 | −0.754513 | ||||||||
\(317\) | − 8.94648i | − 0.502484i | −0.967924 | − | 0.251242i | \(-0.919161\pi\) | ||||
0.967924 | − | 0.251242i | \(-0.0808390\pi\) | |||||||
\(318\) | 9.82766i | 0.551108i | ||||||||
\(319\) | 11.5529 | 0.646841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.80699 | −0.379929 | ||||||||
\(322\) | − 21.4618i | − 1.19602i | ||||||||
\(323\) | 8.43148i | 0.469140i | ||||||||
\(324\) | 1.26242 | 0.0701344 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.66617 | 0.424590 | ||||||||
\(327\) | 11.4451i | 0.632916i | ||||||||
\(328\) | 31.8803i | 1.76030i | ||||||||
\(329\) | −32.5295 | −1.79341 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0810 | 0.664034 | 0.332017 | − | 0.943273i | \(-0.392271\pi\) | ||||
0.332017 | + | 0.943273i | \(0.392271\pi\) | |||||||
\(332\) | − 1.77867i | − 0.0976172i | ||||||||
\(333\) | 7.49949i | 0.410970i | ||||||||
\(334\) | −13.5792 | −0.743022 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.460003 | −0.0250952 | ||||||||
\(337\) | 15.2014i | 0.828074i | 0.910260 | + | 0.414037i | \(0.135882\pi\) | ||||
−0.910260 | + | 0.414037i | \(0.864118\pi\) | |||||||
\(338\) | 1.45718i | 0.0792603i | ||||||||
\(339\) | −16.2686 | −0.883588 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.86530 | 0.480083 | ||||||||
\(342\) | − 2.32394i | − 0.125664i | ||||||||
\(343\) | − 4.10522i | − 0.221661i | ||||||||
\(344\) | −9.51857 | −0.513207 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0211 | 0.753780 | ||||||||
\(347\) | − 8.51395i | − 0.457053i | −0.973538 | − | 0.228526i | \(-0.926609\pi\) | ||||
0.973538 | − | 0.228526i | \(-0.0733908\pi\) | |||||||
\(348\) | − 10.4306i | − 0.559141i | ||||||||
\(349\) | 6.72703 | 0.360090 | 0.180045 | − | 0.983658i | \(-0.442376\pi\) | ||||
0.180045 | + | 0.983658i | \(0.442376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.36204 | −0.179452 | ||||||||
\(352\) | − 7.97773i | − 0.425215i | ||||||||
\(353\) | − 13.3066i | − 0.708239i | −0.935200 | − | 0.354119i | \(-0.884781\pi\) | ||||
0.935200 | − | 0.354119i | \(-0.115219\pi\) | |||||||
\(354\) | 6.56206 | 0.348770 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.84465 | −0.309766 | ||||||||
\(357\) | − 12.0911i | − 0.639930i | ||||||||
\(358\) | 0.731788i | 0.0386762i | ||||||||
\(359\) | 27.1766 | 1.43433 | 0.717163 | − | 0.696905i | \(-0.245440\pi\) | ||||
0.717163 | + | 0.696905i | \(0.245440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.6778 | −0.614622 | ||||||||
\(362\) | 18.8635i | 0.991445i | ||||||||
\(363\) | − 9.04489i | − 0.474734i | ||||||||
\(364\) | 16.4698 | 0.863253 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.29408 | −0.485809 | ||||||||
\(367\) | 15.9939i | 0.834877i | 0.908705 | + | 0.417439i | \(0.137072\pi\) | ||||
−0.908705 | + | 0.417439i | \(0.862928\pi\) | |||||||
\(368\) | 0.763407i | 0.0397953i | ||||||||
\(369\) | −11.3783 | −0.592332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44.4046 | 2.30537 | ||||||||
\(372\) | − 8.00409i | − 0.414992i | ||||||||
\(373\) | 31.2294i | 1.61700i | 0.588497 | + | 0.808499i | \(0.299720\pi\) | ||||
−0.588497 | + | 0.808499i | \(0.700280\pi\) | |||||||
\(374\) | 3.74174 | 0.193481 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.4876 | −1.21128 | ||||||||
\(377\) | 27.7785i | 1.43067i | ||||||||
\(378\) | 3.33263i | 0.171412i | ||||||||
\(379\) | 32.2022 | 1.65412 | 0.827059 | − | 0.562115i | \(-0.190012\pi\) | ||||
0.827059 | + | 0.562115i | \(0.190012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.2477 | 0.832395 | ||||||||
\(382\) | − 0.991154i | − 0.0507119i | ||||||||
\(383\) | 19.4271i | 0.992678i | 0.868129 | + | 0.496339i | \(0.165323\pi\) | ||||
−0.868129 | + | 0.496339i | \(0.834677\pi\) | |||||||
\(384\) | −7.40636 | −0.377954 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.844584 | −0.0429882 | ||||||||
\(387\) | − 3.39725i | − 0.172692i | ||||||||
\(388\) | − 1.91276i | − 0.0971059i | ||||||||
\(389\) | −7.87404 | −0.399230 | −0.199615 | − | 0.979874i | \(-0.563969\pi\) | ||||
−0.199615 | + | 0.979874i | \(0.563969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0661 | −1.01478 | ||||||||
\(392\) | − 22.5771i | − 1.14031i | ||||||||
\(393\) | − 15.3119i | − 0.772383i | ||||||||
\(394\) | 6.36154 | 0.320490 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.76518 | 0.0887037 | ||||||||
\(397\) | 28.4801i | 1.42938i | 0.699443 | + | 0.714689i | \(0.253432\pi\) | ||||
−0.699443 | + | 0.714689i | \(0.746568\pi\) | |||||||
\(398\) | 11.6703i | 0.584978i | ||||||||
\(399\) | −10.5003 | −0.525674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2147 | 1.15929 | 0.579643 | − | 0.814870i | \(-0.303192\pi\) | ||||
0.579643 | + | 0.814870i | \(0.303192\pi\) | |||||||
\(402\) | − 3.04348i | − 0.151795i | ||||||||
\(403\) | 21.3162i | 1.06184i | ||||||||
\(404\) | 21.7611 | 1.08266 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.5356 | 1.36657 | ||||||||
\(407\) | 10.4862i | 0.519781i | ||||||||
\(408\) | − 8.73028i | − 0.432213i | ||||||||
\(409\) | −4.32217 | −0.213718 | −0.106859 | − | 0.994274i | \(-0.534079\pi\) | ||||
−0.106859 | + | 0.994274i | \(0.534079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.86417 | −0.338584 | ||||||||
\(412\) | 13.8746i | 0.683551i | ||||||||
\(413\) | − 29.6495i | − 1.45896i | ||||||||
\(414\) | 5.53074 | 0.271821 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 19.1821 | 0.940480 | ||||||||
\(417\) | − 13.8225i | − 0.676889i | ||||||||
\(418\) | − 3.24945i | − 0.158936i | ||||||||
\(419\) | 1.96426 | 0.0959604 | 0.0479802 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479802 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.13023 | 0.103821 | 0.0519106 | − | 0.998652i | \(-0.483469\pi\) | ||||
0.0519106 | + | 0.998652i | \(0.483469\pi\) | |||||||
\(422\) | 22.5855i | 1.09945i | ||||||||
\(423\) | − 8.38291i | − 0.407591i | ||||||||
\(424\) | 32.0619 | 1.55707 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.01647 | −0.0492484 | ||||||||
\(427\) | 41.9937i | 2.03222i | ||||||||
\(428\) | 8.59328i | 0.415372i | ||||||||
\(429\) | −4.70097 | −0.226965 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0662228 | 0.00318984 | 0.00159492 | − | 0.999999i | \(-0.499492\pi\) | ||||
0.00159492 | + | 0.999999i | \(0.499492\pi\) | |||||||
\(432\) | − 0.118543i | − 0.00570343i | ||||||||
\(433\) | 1.22844i | 0.0590352i | 0.999564 | + | 0.0295176i | \(0.00939711\pi\) | ||||
−0.999564 | + | 0.0295176i | \(0.990603\pi\) | |||||||
\(434\) | 21.1298 | 1.01426 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4485 | 0.691959 | ||||||||
\(437\) | 17.4260i | 0.833600i | ||||||||
\(438\) | 2.05655i | 0.0982657i | ||||||||
\(439\) | 37.8322 | 1.80563 | 0.902816 | − | 0.430028i | \(-0.141496\pi\) | ||||
0.902816 | + | 0.430028i | \(0.141496\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.05792 | 0.383711 | ||||||||
\(442\) | 8.99686i | 0.427937i | ||||||||
\(443\) | − 26.9171i | − 1.27887i | −0.768845 | − | 0.639435i | \(-0.779168\pi\) | ||||
0.768845 | − | 0.639435i | \(-0.220832\pi\) | |||||||
\(444\) | 9.46751 | 0.449308 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.6345 | −0.550910 | ||||||||
\(447\) | − 7.09597i | − 0.335628i | ||||||||
\(448\) | − 18.0943i | − 0.854877i | ||||||||
\(449\) | 25.3090 | 1.19440 | 0.597202 | − | 0.802091i | \(-0.296279\pi\) | ||||
0.597202 | + | 0.802091i | \(0.296279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.9098 | −0.749162 | ||||||||
\(452\) | 20.5378i | 0.966016i | ||||||||
\(453\) | 19.1474i | 0.899624i | ||||||||
\(454\) | −0.227961 | −0.0106988 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.58166 | −0.355044 | ||||||||
\(457\) | − 38.0944i | − 1.78198i | −0.454023 | − | 0.890990i | \(-0.650012\pi\) | ||||
0.454023 | − | 0.890990i | \(-0.349988\pi\) | |||||||
\(458\) | − 3.67676i | − 0.171804i | ||||||||
\(459\) | 3.11590 | 0.145438 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.53623 | 0.164699 | 0.0823494 | − | 0.996604i | \(-0.473758\pi\) | ||||
0.0823494 | + | 0.996604i | \(0.473758\pi\) | |||||||
\(462\) | 4.65986i | 0.216796i | ||||||||
\(463\) | − 23.7206i | − 1.10239i | −0.834377 | − | 0.551195i | \(-0.814172\pi\) | ||||
0.834377 | − | 0.551195i | \(-0.185828\pi\) | |||||||
\(464\) | −0.979456 | −0.0454701 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.79466 | −0.268433 | ||||||||
\(467\) | 19.0985i | 0.883774i | 0.897071 | + | 0.441887i | \(0.145691\pi\) | ||||
−0.897071 | + | 0.441887i | \(0.854309\pi\) | |||||||
\(468\) | 4.24430i | 0.196193i | ||||||||
\(469\) | −13.7514 | −0.634982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8114 | 0.544241 | ||||||||
\(472\) | − 21.4082i | − 0.985392i | ||||||||
\(473\) | − 4.75021i | − 0.218415i | ||||||||
\(474\) | 9.12455 | 0.419104 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.2641 | −0.699627 | ||||||||
\(477\) | 11.4431i | 0.523946i | ||||||||
\(478\) | 0.263926i | 0.0120717i | ||||||||
\(479\) | −18.3034 | −0.836302 | −0.418151 | − | 0.908378i | \(-0.637322\pi\) | ||||
−0.418151 | + | 0.908378i | \(0.637322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.2136 | −1.14964 | ||||||||
\(482\) | − 9.55294i | − 0.435124i | ||||||||
\(483\) | − 24.9897i | − 1.13707i | ||||||||
\(484\) | −11.4184 | −0.519020 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.858825 | −0.0389571 | ||||||||
\(487\) | − 7.01638i | − 0.317943i | −0.987283 | − | 0.158971i | \(-0.949182\pi\) | ||||
0.987283 | − | 0.158971i | \(-0.0508177\pi\) | |||||||
\(488\) | 30.3212i | 1.37258i | ||||||||
\(489\) | 8.92635 | 0.403663 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.63076 | −0.208983 | −0.104492 | − | 0.994526i | \(-0.533322\pi\) | ||||
−0.104492 | + | 0.994526i | \(0.533322\pi\) | |||||||
\(492\) | 14.3642i | 0.647589i | ||||||||
\(493\) | − 25.7449i | − 1.15949i | ||||||||
\(494\) | 7.81316 | 0.351531 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.751598 | −0.0337477 | ||||||||
\(497\) | 4.59277i | 0.206014i | ||||||||
\(498\) | 1.21003i | 0.0542228i | ||||||||
\(499\) | 5.44561 | 0.243779 | 0.121890 | − | 0.992544i | \(-0.461105\pi\) | ||||
0.121890 | + | 0.992544i | \(0.461105\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.8114 | −0.706401 | ||||||||
\(502\) | − 17.6488i | − 0.787703i | ||||||||
\(503\) | − 17.2645i | − 0.769788i | −0.922961 | − | 0.384894i | \(-0.874238\pi\) | ||||
0.922961 | − | 0.384894i | \(-0.125762\pi\) | |||||||
\(504\) | 10.8724 | 0.484297 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.73336 | 0.343790 | ||||||||
\(507\) | 1.69672i | 0.0753538i | ||||||||
\(508\) | − 20.5114i | − 0.910047i | ||||||||
\(509\) | 10.1973 | 0.451989 | 0.225994 | − | 0.974129i | \(-0.427437\pi\) | ||||
0.225994 | + | 0.974129i | \(0.427437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.29217 | 0.411061 | ||||||||
\(512\) | 1.34063i | 0.0592481i | ||||||||
\(513\) | − 2.70595i | − 0.119471i | ||||||||
\(514\) | 2.08997 | 0.0921847 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.28876 | −0.188802 | ||||||||
\(517\) | − 11.7214i | − 0.515508i | ||||||||
\(518\) | 24.9930i | 1.09813i | ||||||||
\(519\) | 16.3259 | 0.716629 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.5575 | 1.68923 | 0.844617 | − | 0.535371i | \(-0.179828\pi\) | ||||
0.844617 | + | 0.535371i | \(0.179828\pi\) | |||||||
\(522\) | 7.09597i | 0.310582i | ||||||||
\(523\) | 6.40172i | 0.279928i | 0.990157 | + | 0.139964i | \(0.0446987\pi\) | ||||
−0.990157 | + | 0.139964i | \(0.955301\pi\) | |||||||
\(524\) | −19.3300 | −0.844437 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3266 | −0.755478 | ||||||||
\(527\) | − 19.7557i | − 0.860570i | ||||||||
\(528\) | − 0.165754i | − 0.00721350i | ||||||||
\(529\) | −18.4722 | −0.803137 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.64074 | 0.331580 | ||||||||
\(532\) | 13.2558i | 0.574712i | ||||||||
\(533\) | − 38.2543i | − 1.65698i | ||||||||
\(534\) | 3.97612 | 0.172064 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.92910 | −0.428872 | ||||||||
\(537\) | 0.852080i | 0.0367700i | ||||||||
\(538\) | 16.0458i | 0.691783i | ||||||||
\(539\) | 11.2670 | 0.485304 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7378 | 1.23553 | 0.617766 | − | 0.786362i | \(-0.288038\pi\) | ||||
0.617766 | + | 0.786362i | \(0.288038\pi\) | |||||||
\(542\) | 6.53724i | 0.280799i | ||||||||
\(543\) | 21.9643i | 0.942580i | ||||||||
\(544\) | −17.7778 | −0.762216 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.2044 | −0.479505 | ||||||||
\(547\) | 5.20272i | 0.222452i | 0.993795 | + | 0.111226i | \(0.0354778\pi\) | ||||
−0.993795 | + | 0.111226i | \(0.964522\pi\) | |||||||
\(548\) | 8.66546i | 0.370170i | ||||||||
\(549\) | −10.8219 | −0.461865 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.3577 | −0.952470 | ||||||||
\(552\) | − 18.0436i | − 0.767986i | ||||||||
\(553\) | − 41.2277i | − 1.75318i | ||||||||
\(554\) | 7.01973 | 0.298240 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.4498 | −0.740035 | ||||||||
\(557\) | − 33.0079i | − 1.39859i | −0.714833 | − | 0.699296i | \(-0.753497\pi\) | ||||
0.714833 | − | 0.699296i | \(-0.246503\pi\) | |||||||
\(558\) | 5.44518i | 0.230513i | ||||||||
\(559\) | 11.4217 | 0.483085 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.35682 | 0.183945 | ||||||||
\(562\) | 12.7872i | 0.539393i | ||||||||
\(563\) | − 15.1684i | − 0.639270i | −0.947541 | − | 0.319635i | \(-0.896440\pi\) | ||||
0.947541 | − | 0.319635i | \(-0.103560\pi\) | |||||||
\(564\) | −10.5828 | −0.445614 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.16116 | −0.0488070 | ||||||||
\(567\) | 3.88045i | 0.162964i | ||||||||
\(568\) | 3.31617i | 0.139143i | ||||||||
\(569\) | 29.5024 | 1.23681 | 0.618403 | − | 0.785861i | \(-0.287780\pi\) | ||||
0.618403 | + | 0.785861i | \(0.287780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.12393 | 0.130733 | 0.0653663 | − | 0.997861i | \(-0.479178\pi\) | ||||
0.0653663 | + | 0.997861i | \(0.479178\pi\) | |||||||
\(572\) | 5.93460i | 0.248138i | ||||||||
\(573\) | − 1.15408i | − 0.0482125i | ||||||||
\(574\) | −37.9197 | −1.58274 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.66294 | 0.194289 | ||||||||
\(577\) | 28.0748i | 1.16877i | 0.811476 | + | 0.584385i | \(0.198664\pi\) | ||||
−0.811476 | + | 0.584385i | \(0.801336\pi\) | |||||||
\(578\) | 6.26182i | 0.260458i | ||||||||
\(579\) | −0.983419 | −0.0408695 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.46732 | 0.226823 | ||||||||
\(582\) | 1.30125i | 0.0539387i | ||||||||
\(583\) | 16.0004i | 0.662669i | ||||||||
\(584\) | 6.70933 | 0.277634 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.99817 | −0.371711 | ||||||||
\(587\) | − 35.9054i | − 1.48197i | −0.671520 | − | 0.740987i | \(-0.734358\pi\) | ||||
0.671520 | − | 0.740987i | \(-0.265642\pi\) | |||||||
\(588\) | − 10.1725i | − 0.419506i | ||||||||
\(589\) | −17.1565 | −0.706920 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.40726 | 0.304694 | ||||||||
\(592\) | − 0.889016i | − 0.0365383i | ||||||||
\(593\) | 15.3084i | 0.628641i | 0.949317 | + | 0.314321i | \(0.101777\pi\) | ||||
−0.949317 | + | 0.314321i | \(0.898223\pi\) | |||||||
\(594\) | −1.20085 | −0.0492716 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.95810 | −0.366938 | ||||||||
\(597\) | 13.5887i | 0.556147i | ||||||||
\(598\) | 18.5945i | 0.760387i | ||||||||
\(599\) | 16.2538 | 0.664114 | 0.332057 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332057 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.233686 | −0.00953223 | −0.00476612 | − | 0.999989i | \(-0.501517\pi\) | ||||
−0.00476612 | + | 0.999989i | \(0.501517\pi\) | |||||||
\(602\) | − 11.3218i | − 0.461441i | ||||||||
\(603\) | − 3.54377i | − 0.144313i | ||||||||
\(604\) | 24.1721 | 0.983548 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.8041 | −0.601376 | ||||||||
\(607\) | − 10.6590i | − 0.432637i | −0.976323 | − | 0.216318i | \(-0.930595\pi\) | ||||
0.976323 | − | 0.216318i | \(-0.0694049\pi\) | |||||||
\(608\) | 15.4388i | 0.626127i | ||||||||
\(609\) | 32.0619 | 1.29922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.1836 | 1.14019 | ||||||||
\(612\) | − 3.93358i | − 0.159005i | ||||||||
\(613\) | − 17.9094i | − 0.723353i | −0.932304 | − | 0.361677i | \(-0.882204\pi\) | ||||
0.932304 | − | 0.361677i | \(-0.117796\pi\) | |||||||
\(614\) | −9.01689 | −0.363892 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.2024 | 0.612523 | ||||||||
\(617\) | 31.6418i | 1.27385i | 0.770925 | + | 0.636926i | \(0.219794\pi\) | ||||
−0.770925 | + | 0.636926i | \(0.780206\pi\) | |||||||
\(618\) | − 9.43888i | − 0.379687i | ||||||||
\(619\) | −21.8317 | −0.877488 | −0.438744 | − | 0.898612i | \(-0.644577\pi\) | ||||
−0.438744 | + | 0.898612i | \(0.644577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.43989 | 0.258424 | ||||||||
\(622\) | − 4.02393i | − 0.161345i | ||||||||
\(623\) | − 17.9654i | − 0.719769i | ||||||||
\(624\) | 0.398547 | 0.0159547 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.8088 | −0.591877 | ||||||||
\(627\) | − 3.78360i | − 0.151103i | ||||||||
\(628\) | − 14.9110i | − 0.595012i | ||||||||
\(629\) | 23.3677 | 0.931730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.62102 | 0.0645318 | 0.0322659 | − | 0.999479i | \(-0.489728\pi\) | ||||
0.0322659 | + | 0.999479i | \(0.489728\pi\) | |||||||
\(632\) | − 29.7681i | − 1.18411i | ||||||||
\(633\) | 26.2982i | 1.04526i | ||||||||
\(634\) | 7.68346 | 0.305149 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.4461 | 0.572823 | ||||||||
\(637\) | 27.0910i | 1.07339i | ||||||||
\(638\) | 9.92196i | 0.392814i | ||||||||
\(639\) | −1.18356 | −0.0468211 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.53285 | 0.179037 | 0.0895183 | − | 0.995985i | \(-0.471467\pi\) | ||||
0.0895183 | + | 0.995985i | \(0.471467\pi\) | |||||||
\(642\) | − 5.84601i | − 0.230724i | ||||||||
\(643\) | − 12.6562i | − 0.499111i | −0.968360 | − | 0.249556i | \(-0.919715\pi\) | ||||
0.968360 | − | 0.249556i | \(-0.0802846\pi\) | |||||||
\(644\) | −31.5475 | −1.24314 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.24117 | −0.284900 | ||||||||
\(647\) | − 22.3268i | − 0.877757i | −0.898546 | − | 0.438879i | \(-0.855376\pi\) | ||||
0.898546 | − | 0.438879i | \(-0.144624\pi\) | |||||||
\(648\) | 2.80185i | 0.110067i | ||||||||
\(649\) | 10.6837 | 0.419371 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.6031 | 0.964273 | ||||||||
\(652\) | − 11.2688i | − 0.441320i | ||||||||
\(653\) | 29.7988i | 1.16612i | 0.812431 | + | 0.583058i | \(0.198144\pi\) | ||||
−0.812431 | + | 0.583058i | \(0.801856\pi\) | |||||||
\(654\) | −9.82934 | −0.384358 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.34883 | 0.0526628 | ||||||||
\(657\) | 2.39461i | 0.0934226i | ||||||||
\(658\) | − 27.9371i | − 1.08910i | ||||||||
\(659\) | −50.2976 | −1.95932 | −0.979659 | − | 0.200671i | \(-0.935688\pi\) | ||||
−0.979659 | + | 0.200671i | \(0.935688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.8701 | −0.811753 | −0.405877 | − | 0.913928i | \(-0.633034\pi\) | ||||
−0.405877 | + | 0.913928i | \(0.633034\pi\) | |||||||
\(662\) | 10.3755i | 0.403255i | ||||||||
\(663\) | 10.4758i | 0.406845i | ||||||||
\(664\) | 3.94763 | 0.153198 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.44075 | −0.249574 | ||||||||
\(667\) | − 53.2091i | − 2.06026i | ||||||||
\(668\) | 19.9606i | 0.772300i | ||||||||
\(669\) | −13.5470 | −0.523758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.1317 | −0.584152 | ||||||||
\(672\) | − 22.1399i | − 0.854067i | ||||||||
\(673\) | 4.50092i | 0.173498i | 0.996230 | + | 0.0867488i | \(0.0276478\pi\) | ||||
−0.996230 | + | 0.0867488i | \(0.972352\pi\) | |||||||
\(674\) | −13.0554 | −0.502874 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.14197 | 0.0823834 | ||||||||
\(677\) | − 13.5082i | − 0.519161i | −0.965721 | − | 0.259580i | \(-0.916416\pi\) | ||||
0.965721 | − | 0.259580i | \(-0.0835843\pi\) | |||||||
\(678\) | − 13.9719i | − 0.536586i | ||||||||
\(679\) | 5.87950 | 0.225634 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.265434 | −0.0101715 | ||||||||
\(682\) | 7.61374i | 0.291545i | ||||||||
\(683\) | 6.98466i | 0.267261i | 0.991031 | + | 0.133630i | \(0.0426635\pi\) | ||||
−0.991031 | + | 0.133630i | \(0.957337\pi\) | |||||||
\(684\) | −3.41605 | −0.130616 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.52566 | 0.134610 | ||||||||
\(687\) | − 4.28115i | − 0.163336i | ||||||||
\(688\) | 0.402722i | 0.0153536i | ||||||||
\(689\) | −38.4723 | −1.46568 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.6891 | −0.977261 | −0.488630 | − | 0.872491i | \(-0.662503\pi\) | ||||
−0.488630 | + | 0.872491i | \(0.662503\pi\) | |||||||
\(692\) | − 20.6102i | − 0.783482i | ||||||||
\(693\) | 5.42585i | 0.206111i | ||||||||
\(694\) | 7.31200 | 0.277560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 23.1500 | 0.877500 | ||||||||
\(697\) | 35.4537i | 1.34291i | ||||||||
\(698\) | 5.77734i | 0.218676i | ||||||||
\(699\) | −6.74720 | −0.255202 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.35830 | 0.0890717 | 0.0445358 | − | 0.999008i | \(-0.485819\pi\) | ||||
0.0445358 | + | 0.999008i | \(0.485819\pi\) | |||||||
\(702\) | − 2.88740i | − 0.108978i | ||||||||
\(703\) | − 20.2933i | − 0.765375i | ||||||||
\(704\) | 6.51997 | 0.245731 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.4280 | 0.430100 | ||||||||
\(707\) | 66.8898i | 2.51565i | ||||||||
\(708\) | − 9.64582i | − 0.362512i | ||||||||
\(709\) | −13.1277 | −0.493022 | −0.246511 | − | 0.969140i | \(-0.579284\pi\) | ||||
−0.246511 | + | 0.969140i | \(0.579284\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.6245 | 0.398448 | ||||||||
\(712\) | − 12.9718i | − 0.486138i | ||||||||
\(713\) | − 40.8306i | − 1.52912i | ||||||||
\(714\) | 10.3841 | 0.388617 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.07568 | 0.0402002 | ||||||||
\(717\) | 0.307310i | 0.0114767i | ||||||||
\(718\) | 23.3399i | 0.871039i | ||||||||
\(719\) | 29.5306 | 1.10131 | 0.550653 | − | 0.834735i | \(-0.314379\pi\) | ||||
0.550653 | + | 0.834735i | \(0.314379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.6480 | −1.58829 | ||||||||
\(722\) | − 10.0292i | − 0.373248i | ||||||||
\(723\) | − 11.1233i | − 0.413679i | ||||||||
\(724\) | 27.7282 | 1.03051 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.76798 | 0.288297 | ||||||||
\(727\) | − 45.2103i | − 1.67676i | −0.545089 | − | 0.838378i | \(-0.683504\pi\) | ||||
0.545089 | − | 0.838378i | \(-0.316496\pi\) | |||||||
\(728\) | 36.5535i | 1.35476i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5855 | −0.391519 | ||||||||
\(732\) | 13.6617i | 0.504952i | ||||||||
\(733\) | 20.6475i | 0.762633i | 0.924444 | + | 0.381317i | \(0.124529\pi\) | ||||
−0.924444 | + | 0.381317i | \(0.875471\pi\) | |||||||
\(734\) | −13.7360 | −0.507005 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.7428 | −1.35436 | ||||||||
\(737\) | − 4.95508i | − 0.182523i | ||||||||
\(738\) | − 9.77199i | − 0.359712i | ||||||||
\(739\) | −26.6229 | −0.979339 | −0.489670 | − | 0.871908i | \(-0.662883\pi\) | ||||
−0.489670 | + | 0.871908i | \(0.662883\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.09751 | 0.334205 | ||||||||
\(742\) | 38.1358i | 1.40001i | ||||||||
\(743\) | − 34.2594i | − 1.25686i | −0.777868 | − | 0.628428i | \(-0.783699\pi\) | ||||
0.777868 | − | 0.628428i | \(-0.216301\pi\) | |||||||
\(744\) | 17.7645 | 0.651277 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.8206 | −0.981972 | ||||||||
\(747\) | 1.40894i | 0.0515503i | ||||||||
\(748\) | − 5.50013i | − 0.201105i | ||||||||
\(749\) | −26.4142 | −0.965154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.9423 | 1.27506 | 0.637531 | − | 0.770425i | \(-0.279956\pi\) | ||||
0.637531 | + | 0.770425i | \(0.279956\pi\) | |||||||
\(752\) | 0.993739i | 0.0362380i | ||||||||
\(753\) | − 20.5499i | − 0.748880i | ||||||||
\(754\) | −23.8569 | −0.868817 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.89876 | 0.178166 | ||||||||
\(757\) | 25.4445i | 0.924796i | 0.886673 | + | 0.462398i | \(0.153011\pi\) | ||||
−0.886673 | + | 0.462398i | \(0.846989\pi\) | |||||||
\(758\) | 27.6561i | 1.00451i | ||||||||
\(759\) | 9.00459 | 0.326846 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.7352 | −0.534149 | −0.267075 | − | 0.963676i | \(-0.586057\pi\) | ||||
−0.267075 | + | 0.963676i | \(0.586057\pi\) | |||||||
\(762\) | 13.9539i | 0.505498i | ||||||||
\(763\) | 44.4122i | 1.60783i | ||||||||
\(764\) | −1.45694 | −0.0527101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6845 | −0.602834 | ||||||||
\(767\) | 25.6884i | 0.927556i | ||||||||
\(768\) | − 15.6866i | − 0.566043i | ||||||||
\(769\) | −28.9603 | −1.04434 | −0.522168 | − | 0.852843i | \(-0.674877\pi\) | ||||
−0.522168 | + | 0.852843i | \(0.674877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.43352 | 0.0876413 | ||||||||
\(772\) | 1.24149i | 0.0446821i | ||||||||
\(773\) | − 19.7129i | − 0.709022i | −0.935052 | − | 0.354511i | \(-0.884647\pi\) | ||||
0.935052 | − | 0.354511i | \(-0.115353\pi\) | |||||||
\(774\) | 2.91764 | 0.104872 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.24524 | 0.152395 | ||||||||
\(777\) | 29.1014i | 1.04401i | ||||||||
\(778\) | − 6.76242i | − 0.242445i | ||||||||
\(779\) | 30.7892 | 1.10314 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.65492 | −0.0592178 | ||||||||
\(782\) | − 17.2332i | − 0.616259i | ||||||||
\(783\) | 8.26242i | 0.295275i | ||||||||
\(784\) | −0.955214 | −0.0341148 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.1502 | 0.469054 | ||||||||
\(787\) | − 18.0212i | − 0.642385i | −0.947014 | − | 0.321193i | \(-0.895916\pi\) | ||||
0.947014 | − | 0.321193i | \(-0.104084\pi\) | |||||||
\(788\) | − 9.35107i | − 0.333118i | ||||||||
\(789\) | −20.1748 | −0.718243 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −63.1295 | −2.24463 | ||||||||
\(792\) | 3.91769i | 0.139209i | ||||||||
\(793\) | − 36.3835i | − 1.29201i | ||||||||
\(794\) | −24.4595 | −0.868033 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.1546 | 0.608028 | ||||||||
\(797\) | 17.7479i | 0.628663i | 0.949313 | + | 0.314332i | \(0.101780\pi\) | ||||
−0.949313 | + | 0.314332i | \(0.898220\pi\) | |||||||
\(798\) | − 9.01794i | − 0.319232i | ||||||||
\(799\) | −26.1203 | −0.924071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.62972 | 0.163583 | ||||||||
\(802\) | 19.9374i | 0.704012i | ||||||||
\(803\) | 3.34827i | 0.118158i | ||||||||
\(804\) | −4.47372 | −0.157776 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.3069 | −0.644833 | ||||||||
\(807\) | 18.6834i | 0.657687i | ||||||||
\(808\) | 48.2972i | 1.69909i | ||||||||
\(809\) | −24.7020 | −0.868477 | −0.434238 | − | 0.900798i | \(-0.642982\pi\) | ||||
−0.434238 | + | 0.900798i | \(0.642982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6855 | −0.480561 | −0.240281 | − | 0.970703i | \(-0.577239\pi\) | ||||
−0.240281 | + | 0.970703i | \(0.577239\pi\) | |||||||
\(812\) | − 40.4756i | − 1.42042i | ||||||||
\(813\) | 7.61184i | 0.266959i | ||||||||
\(814\) | −9.00579 | −0.315653 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.369370 | −0.0129305 | ||||||||
\(817\) | 9.19279i | 0.321615i | ||||||||
\(818\) | − 3.71199i | − 0.129787i | ||||||||
\(819\) | −13.0462 | −0.455872 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −56.1647 | −1.96016 | −0.980081 | − | 0.198600i | \(-0.936360\pi\) | ||||
−0.980081 | + | 0.198600i | \(0.936360\pi\) | |||||||
\(822\) | − 5.89512i | − 0.205616i | ||||||||
\(823\) | 15.1705i | 0.528810i | 0.964412 | + | 0.264405i | \(0.0851755\pi\) | ||||
−0.964412 | + | 0.264405i | \(0.914825\pi\) | |||||||
\(824\) | −30.7936 | −1.07275 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.4638 | 0.885998 | ||||||||
\(827\) | − 12.2655i | − 0.426515i | −0.976996 | − | 0.213257i | \(-0.931593\pi\) | ||||
0.976996 | − | 0.213257i | \(-0.0684073\pi\) | |||||||
\(828\) | − 8.12984i | − 0.282532i | ||||||||
\(829\) | −29.4191 | −1.02177 | −0.510884 | − | 0.859650i | \(-0.670682\pi\) | ||||
−0.510884 | + | 0.859650i | \(0.670682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.17364 | 0.283540 | ||||||||
\(832\) | 15.6770i | 0.543501i | ||||||||
\(833\) | − 25.1077i | − 0.869930i | ||||||||
\(834\) | 11.8711 | 0.411062 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.77650 | −0.165199 | ||||||||
\(837\) | 6.34027i | 0.219152i | ||||||||
\(838\) | 1.68696i | 0.0582749i | ||||||||
\(839\) | 7.01431 | 0.242161 | 0.121080 | − | 0.992643i | \(-0.461364\pi\) | ||||
0.121080 | + | 0.992643i | \(0.461364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.2676 | 1.35405 | ||||||||
\(842\) | 1.82950i | 0.0630486i | ||||||||
\(843\) | 14.8891i | 0.512809i | ||||||||
\(844\) | 33.1994 | 1.14277 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.19945 | 0.247522 | ||||||||
\(847\) | − 35.0983i | − 1.20599i | ||||||||
\(848\) | − 1.35651i | − 0.0465827i | ||||||||
\(849\) | −1.35203 | −0.0464015 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.2959 | 1.65556 | ||||||||
\(852\) | 1.49416i | 0.0511889i | ||||||||
\(853\) | 27.1094i | 0.928208i | 0.885781 | + | 0.464104i | \(0.153624\pi\) | ||||
−0.885781 | + | 0.464104i | \(0.846376\pi\) | |||||||
\(854\) | −36.0652 | −1.23413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.0721 | −0.651872 | ||||||||
\(857\) | − 5.19405i | − 0.177425i | −0.996057 | − | 0.0887127i | \(-0.971725\pi\) | ||||
0.996057 | − | 0.0887127i | \(-0.0282753\pi\) | |||||||
\(858\) | − 4.03731i | − 0.137832i | ||||||||
\(859\) | 15.2545 | 0.520478 | 0.260239 | − | 0.965544i | \(-0.416199\pi\) | ||||
0.260239 | + | 0.965544i | \(0.416199\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44.1531 | −1.50473 | ||||||||
\(862\) | 0.0568738i | 0.00193713i | ||||||||
\(863\) | 46.8290i | 1.59408i | 0.603929 | + | 0.797038i | \(0.293601\pi\) | ||||
−0.603929 | + | 0.797038i | \(0.706399\pi\) | |||||||
\(864\) | 5.70550 | 0.194105 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.05502 | −0.0358510 | ||||||||
\(867\) | 7.29115i | 0.247621i | ||||||||
\(868\) | − 31.0595i | − 1.05423i | ||||||||
\(869\) | 14.8557 | 0.503944 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9143 | 0.403700 | ||||||||
\(872\) | 32.0674i | 1.08594i | ||||||||
\(873\) | 1.51516i | 0.0512803i | ||||||||
\(874\) | −14.9659 | −0.506229 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.02300 | 0.102138 | ||||||||
\(877\) | − 0.979616i | − 0.0330793i | −0.999863 | − | 0.0165396i | \(-0.994735\pi\) | ||||
0.999863 | − | 0.0165396i | \(-0.00526497\pi\) | |||||||
\(878\) | 32.4912i | 1.09653i | ||||||||
\(879\) | −10.4773 | −0.353391 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.0186 | 1.31457 | 0.657286 | − | 0.753641i | \(-0.271704\pi\) | ||||
0.657286 | + | 0.753641i | \(0.271704\pi\) | |||||||
\(882\) | 6.92034i | 0.233020i | ||||||||
\(883\) | − 8.90989i | − 0.299842i | −0.988698 | − | 0.149921i | \(-0.952098\pi\) | ||||
0.988698 | − | 0.149921i | \(-0.0479019\pi\) | |||||||
\(884\) | 13.2248 | 0.444799 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1171 | 0.776633 | ||||||||
\(887\) | − 51.4215i | − 1.72656i | −0.504721 | − | 0.863282i | \(-0.668405\pi\) | ||||
0.504721 | − | 0.863282i | \(-0.331595\pi\) | |||||||
\(888\) | 21.0124i | 0.705131i | ||||||||
\(889\) | 63.0485 | 2.11458 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.39825 | −0.0468432 | ||||||||
\(892\) | 17.1020i | 0.572618i | ||||||||
\(893\) | 22.6838i | 0.759083i | ||||||||
\(894\) | 6.09420 | 0.203820 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28.7400 | −0.960137 | ||||||||
\(897\) | 21.6511i | 0.722910i | ||||||||
\(898\) | 21.7360i | 0.725339i | ||||||||
\(899\) | 52.3860 | 1.74717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.6557 | 1.18786 | ||||||||
\(902\) | − 13.6637i | − 0.454952i | ||||||||
\(903\) | − 13.1829i | − 0.438698i | ||||||||
\(904\) | −45.5821 | −1.51604 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.4443 | −0.546324 | ||||||||
\(907\) | 18.0057i | 0.597871i | 0.954273 | + | 0.298935i | \(0.0966315\pi\) | ||||
−0.954273 | + | 0.298935i | \(0.903369\pi\) | |||||||
\(908\) | 0.335089i | 0.0111203i | ||||||||
\(909\) | −17.2376 | −0.571736 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.3831 | 1.40421 | 0.702107 | − | 0.712071i | \(-0.252243\pi\) | ||||
0.702107 | + | 0.712071i | \(0.252243\pi\) | |||||||
\(912\) | 0.320773i | 0.0106219i | ||||||||
\(913\) | 1.97005i | 0.0651991i | ||||||||
\(914\) | 32.7164 | 1.08216 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.40460 | −0.178573 | ||||||||
\(917\) | − 59.4171i | − 1.96213i | ||||||||
\(918\) | 2.67601i | 0.0883216i | ||||||||
\(919\) | −15.9252 | −0.525325 | −0.262662 | − | 0.964888i | \(-0.584601\pi\) | ||||
−0.262662 | + | 0.964888i | \(0.584601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.4991 | −0.345957 | ||||||||
\(922\) | 3.03700i | 0.100018i | ||||||||
\(923\) | − 3.97919i | − 0.130977i | ||||||||
\(924\) | 6.84971 | 0.225339 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 20.3718 | 0.669460 | ||||||||
\(927\) | − 10.9905i | − 0.360974i | ||||||||
\(928\) | − 47.1413i | − 1.54749i | ||||||||
\(929\) | −7.47386 | −0.245210 | −0.122605 | − | 0.992456i | \(-0.539125\pi\) | ||||
−0.122605 | + | 0.992456i | \(0.539125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.8043 | −0.714609 | ||||||||
\(932\) | 8.51780i | 0.279010i | ||||||||
\(933\) | − 4.68539i | − 0.153393i | ||||||||
\(934\) | −16.4023 | −0.536699 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.41991 | −0.307899 | ||||||||
\(937\) | − 26.3843i | − 0.861937i | −0.902367 | − | 0.430969i | \(-0.858172\pi\) | ||||
0.902367 | − | 0.430969i | \(-0.141828\pi\) | |||||||
\(938\) | − 11.8101i | − 0.385612i | ||||||||
\(939\) | −17.2431 | −0.562706 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.8626 | 1.33208 | 0.666041 | − | 0.745915i | \(-0.267988\pi\) | ||||
0.666041 | + | 0.745915i | \(0.267988\pi\) | |||||||
\(942\) | 10.1439i | 0.330507i | ||||||||
\(943\) | 73.2751i | 2.38617i | ||||||||
\(944\) | −0.905760 | −0.0294800 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.07960 | 0.132639 | ||||||||
\(947\) | − 44.3060i | − 1.43975i | −0.694103 | − | 0.719876i | \(-0.744199\pi\) | ||||
0.694103 | − | 0.719876i | \(-0.255801\pi\) | |||||||
\(948\) | − 13.4125i | − 0.435619i | ||||||||
\(949\) | −8.05076 | −0.261339 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.94648 | 0.290109 | ||||||||
\(952\) | − 33.8775i | − 1.09797i | ||||||||
\(953\) | 21.0768i | 0.682744i | 0.939928 | + | 0.341372i | \(0.110892\pi\) | ||||
−0.939928 | + | 0.341372i | \(0.889108\pi\) | |||||||
\(954\) | −9.82766 | −0.318182 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.387954 | 0.0125473 | ||||||||
\(957\) | 11.5529i | 0.373454i | ||||||||
\(958\) | − 15.7194i | − 0.507870i | ||||||||
\(959\) | −26.6361 | −0.860124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.19905 | 0.296744 | ||||||||
\(962\) | − 21.6540i | − 0.698154i | ||||||||
\(963\) | − 6.80699i | − 0.219352i | ||||||||
\(964\) | −14.0422 | −0.452270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 21.4618 | 0.690521 | ||||||||
\(967\) | 9.34590i | 0.300544i | 0.988645 | + | 0.150272i | \(0.0480149\pi\) | ||||
−0.988645 | + | 0.150272i | \(0.951985\pi\) | |||||||
\(968\) | − 25.3424i | − 0.814536i | ||||||||
\(969\) | −8.43148 | −0.270858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.2708 | −1.58118 | −0.790588 | − | 0.612348i | \(-0.790225\pi\) | ||||
−0.790588 | + | 0.612348i | \(0.790225\pi\) | |||||||
\(972\) | 1.26242i | 0.0404921i | ||||||||
\(973\) | − 53.6374i | − 1.71954i | ||||||||
\(974\) | 6.02584 | 0.193080 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.28286 | 0.0410634 | ||||||||
\(977\) | − 54.8767i | − 1.75566i | −0.478971 | − | 0.877830i | \(-0.658990\pi\) | ||||
0.478971 | − | 0.877830i | \(-0.341010\pi\) | |||||||
\(978\) | 7.66617i | 0.245137i | ||||||||
\(979\) | 6.47352 | 0.206895 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.4451 | −0.365414 | ||||||||
\(982\) | − 3.97701i | − 0.126912i | ||||||||
\(983\) | 15.9788i | 0.509646i | 0.966988 | + | 0.254823i | \(0.0820172\pi\) | ||||
−0.966988 | + | 0.254823i | \(0.917983\pi\) | |||||||
\(984\) | −31.8803 | −1.01631 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.1104 | 0.704137 | ||||||||
\(987\) | − 32.5295i | − 1.03543i | ||||||||
\(988\) | − 11.4849i | − 0.365382i | ||||||||
\(989\) | −21.8779 | −0.695677 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.2757 | −0.929973 | −0.464986 | − | 0.885318i | \(-0.653941\pi\) | ||||
−0.464986 | + | 0.885318i | \(0.653941\pi\) | |||||||
\(992\) | − 36.1744i | − 1.14854i | ||||||||
\(993\) | 12.0810i | 0.383380i | ||||||||
\(994\) | −3.94438 | −0.125108 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.77867 | 0.0563593 | ||||||||
\(997\) | − 19.6838i | − 0.623392i | −0.950182 | − | 0.311696i | \(-0.899103\pi\) | ||||
0.950182 | − | 0.311696i | \(-0.100897\pi\) | |||||||
\(998\) | 4.67683i | 0.148042i | ||||||||
\(999\) | −7.49949 | −0.237273 |
(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 | 1875.2.b.e.1249.8 | 12 | ||
5.2 | odd | 4 | 1875.2.a.i.1.3 | ✓ | 6 | ||
5.3 | odd | 4 | 1875.2.a.l.1.4 | yes | 6 | ||
5.4 | even | 2 | inner | 1875.2.b.e.1249.5 | 12 | ||
15.2 | even | 4 | 5625.2.a.r.1.4 | 6 | |||
15.8 | even | 4 | 5625.2.a.o.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.i.1.3 | ✓ | 6 | 5.2 | odd | 4 | ||
1875.2.a.l.1.4 | yes | 6 | 5.3 | odd | 4 | ||
1875.2.b.e.1249.5 | 12 | 5.4 | even | 2 | inner | ||
1875.2.b.e.1249.8 | 12 | 1.1 | even | 1 | trivial | ||
5625.2.a.o.1.3 | 6 | 15.8 | even | 4 | |||
5625.2.a.r.1.4 | 6 | 15.2 | even | 4 |