Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.5 | ||
Root | \(1.28913 - 2.23284i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.e.501.5 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.789132 | − | 1.36682i | 0.455606 | − | 0.789132i | −0.543117 | − | 0.839657i | \(-0.682756\pi\) |
0.998723 | + | 0.0505248i | \(0.0160894\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39989 | −0.529110 | −0.264555 | − | 0.964371i | \(-0.585225\pi\) | ||||
−0.264555 | + | 0.964371i | \(0.585225\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.254541 | + | 0.440878i | 0.0848470 | + | 0.146959i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.67848 | −1.41061 | −0.705307 | − | 0.708902i | \(-0.749191\pi\) | ||||
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.696425 | + | 1.20624i | 0.193153 | + | 0.334552i | 0.946294 | − | 0.323308i | \(-0.104795\pi\) |
−0.753140 | + | 0.657860i | \(0.771462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.17388 | + | 3.76528i | −0.527244 | + | 0.913214i | 0.472252 | + | 0.881464i | \(0.343441\pi\) |
−0.999496 | + | 0.0317500i | \(0.989892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.608224 | − | 4.31626i | −0.139536 | − | 0.990217i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.10470 | + | 1.91340i | −0.241066 | + | 0.417538i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.64183 | + | 2.84373i | 0.342345 | + | 0.592960i | 0.984868 | − | 0.173307i | \(-0.0554454\pi\) |
−0.642522 | + | 0.766267i | \(0.722112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.53826 | 1.06584 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.19642 | − | 2.07227i | −0.222170 | − | 0.384811i | 0.733296 | − | 0.679909i | \(-0.237981\pi\) |
−0.955467 | + | 0.295099i | \(0.904647\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.94001 | −0.707647 | −0.353823 | − | 0.935312i | \(-0.615119\pi\) | ||||
−0.353823 | + | 0.935312i | \(0.615119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.69194 | + | 6.39463i | −0.642684 | + | 1.11316i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.3570 | −1.86707 | −0.933536 | − | 0.358483i | \(-0.883294\pi\) | ||||
−0.933536 | + | 0.358483i | \(0.883294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.19828 | 0.352007 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.99312 | + | 10.3804i | −0.935968 | + | 1.62114i | −0.163070 | + | 0.986614i | \(0.552140\pi\) |
−0.772898 | + | 0.634530i | \(0.781194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.68032 | + | 6.37450i | −0.561243 | + | 0.972102i | 0.436145 | + | 0.899876i | \(0.356343\pi\) |
−0.997388 | + | 0.0722255i | \(0.976990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.48093 | + | 2.56504i | 0.216015 | + | 0.374149i | 0.953586 | − | 0.301120i | \(-0.0973606\pi\) |
−0.737571 | + | 0.675270i | \(0.764027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.04030 | −0.720042 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.43096 | + | 5.94260i | 0.480431 | + | 0.832131i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.81219 | + | 6.60291i | 0.523645 | + | 0.906979i | 0.999621 | + | 0.0275214i | \(0.00876144\pi\) |
−0.475976 | + | 0.879458i | \(0.657905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.37950 | − | 2.57476i | −0.844985 | − | 0.341036i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.34285 | − | 9.25409i | 0.695580 | − | 1.20478i | −0.274405 | − | 0.961614i | \(-0.588481\pi\) |
0.969985 | − | 0.243166i | \(-0.0781859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.146691 | + | 0.254076i | 0.0187818 | + | 0.0325311i | 0.875264 | − | 0.483646i | \(-0.160688\pi\) |
−0.856482 | + | 0.516177i | \(0.827355\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.356331 | − | 0.617183i | −0.0448934 | − | 0.0777577i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.77020 | + | 6.53018i | 0.460604 | + | 0.797789i | 0.998991 | − | 0.0449086i | \(-0.0142997\pi\) |
−0.538388 | + | 0.842697i | \(0.680966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.18249 | 0.623898 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0920970 | + | 0.159517i | −0.0109299 | + | 0.0189311i | −0.871439 | − | 0.490505i | \(-0.836812\pi\) |
0.860509 | + | 0.509436i | \(0.170146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.919287 | + | 1.59225i | −0.107594 | + | 0.186359i | −0.914795 | − | 0.403918i | \(-0.867648\pi\) |
0.807201 | + | 0.590277i | \(0.200981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.54938 | 0.746371 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.875405 | + | 1.51625i | −0.0984907 | + | 0.170591i | −0.911060 | − | 0.412273i | \(-0.864735\pi\) |
0.812569 | + | 0.582864i | \(0.198068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.60679 | − | 6.24715i | 0.400755 | − | 0.694128i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.49503 | −0.273866 | −0.136933 | − | 0.990580i | \(-0.543724\pi\) | ||||
−0.136933 | + | 0.990580i | \(0.543724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.77655 | −0.404888 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.02719 | + | 1.77915i | 0.108882 | + | 0.188590i | 0.915318 | − | 0.402733i | \(-0.131940\pi\) |
−0.806435 | + | 0.591322i | \(0.798606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.974921 | − | 1.68861i | −0.102199 | − | 0.177015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.10919 | + | 5.38527i | −0.322408 | + | 0.558427i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.261586 | − | 0.453081i | 0.0265601 | − | 0.0460034i | −0.852440 | − | 0.522825i | \(-0.824878\pi\) |
0.879000 | + | 0.476822i | \(0.158211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.19087 | − | 2.06264i | −0.119686 | − | 0.207303i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61367 | + | 2.79497i | 0.160567 | + | 0.278110i | 0.935072 | − | 0.354458i | \(-0.115335\pi\) |
−0.774505 | + | 0.632567i | \(0.782001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4295 | −1.32325 | −0.661624 | − | 0.749835i | \(-0.730133\pi\) | ||||
−0.661624 | + | 0.749835i | \(0.730133\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.8197 | 1.43268 | 0.716339 | − | 0.697752i | \(-0.245816\pi\) | ||||
0.716339 | + | 0.697752i | \(0.245816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.591723 | + | 1.02489i | −0.0566768 | + | 0.0981671i | −0.892972 | − | 0.450113i | \(-0.851384\pi\) |
0.836295 | + | 0.548280i | \(0.184717\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.96214 | + | 15.5229i | −0.850649 | + | 1.47337i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.57115 | −0.524090 | −0.262045 | − | 0.965056i | \(-0.584397\pi\) | ||||
−0.262045 | + | 0.965056i | \(0.584397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.354537 | + | 0.614077i | −0.0327770 | + | 0.0567714i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.04321 | − | 5.27099i | 0.278970 | − | 0.483191i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8882 | 0.989834 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.45873 | + | 16.3830i | 0.852865 | + | 1.47721i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.68102 | + | 2.91161i | 0.149166 | + | 0.258363i | 0.930920 | − | 0.365224i | \(-0.119008\pi\) |
−0.781753 | + | 0.623588i | \(0.785674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.80851 | + | 10.0606i | 0.511411 | + | 0.885790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.73438 | − | 6.46814i | 0.326275 | − | 0.565124i | −0.655495 | − | 0.755200i | \(-0.727540\pi\) |
0.981769 | + | 0.190075i | \(0.0608733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.851450 | + | 6.04230i | 0.0738300 | + | 0.523934i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.40898 | − | 4.17247i | −0.205813 | − | 0.356478i | 0.744579 | − | 0.667535i | \(-0.232650\pi\) |
−0.950391 | + | 0.311057i | \(0.899317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7854 | − | 18.6809i | −0.914807 | − | 1.58449i | −0.807183 | − | 0.590301i | \(-0.799009\pi\) |
−0.107624 | − | 0.994192i | \(-0.534324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.67458 | 0.393671 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.25821 | − | 5.64338i | −0.272465 | − | 0.471923i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.97746 | + | 6.88916i | −0.328055 | + | 0.568208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6341 | − | 20.1508i | 0.953102 | − | 1.65082i | 0.214450 | − | 0.976735i | \(-0.431204\pi\) |
0.738652 | − | 0.674087i | \(-0.235463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2567 | 0.834682 | 0.417341 | − | 0.908750i | \(-0.362962\pi\) | ||||
0.417341 | + | 0.908750i | \(0.362962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.21337 | −0.178940 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2392 | + | 19.4669i | −0.896988 | + | 1.55363i | −0.0656625 | + | 0.997842i | \(0.520916\pi\) |
−0.831325 | + | 0.555786i | \(0.812417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0333 | 0.954302 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.29839 | − | 3.98093i | −0.181138 | − | 0.313741i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.27491 | −0.569815 | −0.284907 | − | 0.958555i | \(-0.591963\pi\) | ||||
−0.284907 | + | 0.958555i | \(0.591963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.41834 | + | 5.92075i | 0.264519 | + | 0.458161i | 0.967438 | − | 0.253110i | \(-0.0814533\pi\) |
−0.702918 | + | 0.711271i | \(0.748120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.52999 | − | 9.57822i | 0.425383 | − | 0.736786i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.74812 | − | 1.36682i | 0.133682 | − | 0.104523i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.58985 | + | 6.21780i | −0.272931 | + | 0.472731i | −0.969611 | − | 0.244651i | \(-0.921326\pi\) |
0.696680 | + | 0.717382i | \(0.254660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.43243 | − | 14.6054i | −0.633820 | − | 1.09781i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.47867 | −0.260008 | −0.130004 | − | 0.991513i | \(-0.541499\pi\) | ||||
−0.130004 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.22373 | + | 15.9760i | 0.685594 | + | 1.18748i | 0.973250 | + | 0.229750i | \(0.0737909\pi\) |
−0.287655 | + | 0.957734i | \(0.592876\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.463034 | 0.0342284 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1705 | − | 17.6158i | 0.743739 | − | 1.28819i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.75298 | −0.563946 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.1007 | −1.81622 | −0.908112 | − | 0.418727i | \(-0.862477\pi\) | ||||
−0.908112 | + | 0.418727i | \(0.862477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.65851 | + | 9.80083i | −0.407309 | + | 0.705479i | −0.994587 | − | 0.103906i | \(-0.966866\pi\) |
0.587279 | + | 0.809385i | \(0.300199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1926 | 0.726195 | 0.363098 | − | 0.931751i | \(-0.381719\pi\) | ||||
0.363098 | + | 0.931751i | \(0.381719\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2142 | + | 17.6916i | 0.724068 | + | 1.25412i | 0.959357 | + | 0.282197i | \(0.0910632\pi\) |
−0.235289 | + | 0.971926i | \(0.575604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.9008 | 0.839414 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.67487 | + | 2.90096i | 0.117553 | + | 0.203607i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.835827 | + | 1.44769i | −0.0580940 | + | 0.100622i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.84556 | + | 20.1935i | 0.196832 | + | 1.39681i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0585254 | + | 0.101369i | −0.00402905 | + | 0.00697853i | −0.868033 | − | 0.496507i | \(-0.834616\pi\) |
0.864004 | + | 0.503485i | \(0.167949\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.145353 | + | 0.251759i | 0.00995945 | + | 0.0172503i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.51560 | 0.374423 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.45088 | + | 2.51299i | 0.0980412 | + | 0.169812i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.05578 | −0.407356 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.80869 | − | 11.7930i | 0.455944 | − | 0.789718i | −0.542798 | − | 0.839863i | \(-0.682635\pi\) |
0.998742 | + | 0.0501456i | \(0.0159685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.84713 | −0.388088 | −0.194044 | − | 0.980993i | \(-0.562160\pi\) | ||||
−0.194044 | + | 0.980993i | \(0.562160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.9558 | −1.58305 | −0.791523 | − | 0.611140i | \(-0.790711\pi\) | ||||
−0.791523 | + | 0.611140i | \(0.790711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.16832 | − | 8.95180i | 0.340051 | − | 0.588985i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.84858 | − | 17.0582i | 0.645202 | − | 1.11752i | −0.339053 | − | 0.940767i | \(-0.610107\pi\) |
0.984255 | − | 0.176755i | \(-0.0565600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.38162 | + | 2.39304i | 0.0897459 | + | 0.155444i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6424 | −1.20587 | −0.602937 | − | 0.797789i | \(-0.706003\pi\) | ||||
−0.602937 | + | 0.797789i | \(0.706003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.57780 | − | 6.19693i | −0.230466 | − | 0.399179i | 0.727479 | − | 0.686130i | \(-0.240692\pi\) |
−0.957945 | + | 0.286951i | \(0.907358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.61491 | + | 4.52916i | 0.167747 | + | 0.290546i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.78287 | − | 3.73961i | 0.304327 | − | 0.237946i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.96891 | + | 3.41025i | −0.124775 | + | 0.216116i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.67103 | − | 6.35840i | −0.231713 | − | 0.401339i | 0.726599 | − | 0.687062i | \(-0.241100\pi\) |
−0.958312 | + | 0.285723i | \(0.907766\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.68127 | − | 13.3044i | −0.482917 | − | 0.836438i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.57010 | + | 7.91565i | 0.285075 | + | 0.493764i | 0.972627 | − | 0.232370i | \(-0.0746481\pi\) |
−0.687552 | + | 0.726135i | \(0.741315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8985 | 0.987887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.609078 | − | 1.05495i | 0.0377010 | − | 0.0653001i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.9226 | − | 20.6505i | 0.735177 | − | 1.27336i | −0.219469 | − | 0.975619i | \(-0.570432\pi\) |
0.954646 | − | 0.297744i | \(-0.0962342\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.24236 | 0.198429 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.56760 | + | 13.1075i | −0.461405 | + | 0.799176i | −0.999031 | − | 0.0440068i | \(-0.985988\pi\) |
0.537627 | + | 0.843183i | \(0.319321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.744750 | + | 1.28994i | −0.0452403 | + | 0.0783586i | −0.887759 | − | 0.460309i | \(-0.847739\pi\) |
0.842519 | + | 0.538667i | \(0.181072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.07737 | −0.186251 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8346 | −0.831241 | −0.415621 | − | 0.909538i | \(-0.636436\pi\) | ||||
−0.415621 | + | 0.909538i | \(0.636436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00289 | − | 1.73706i | −0.0600417 | − | 0.103995i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.437342 | − | 0.757498i | −0.0260896 | − | 0.0451885i | 0.852686 | − | 0.522424i | \(-0.174972\pi\) |
−0.878775 | + | 0.477236i | \(0.841639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.52975 | − | 11.3099i | 0.388153 | − | 0.672301i | −0.604048 | − | 0.796948i | \(-0.706446\pi\) |
0.992201 | + | 0.124647i | \(0.0397798\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.38974 | − | 14.5314i | 0.495230 | − | 0.857764i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.951541 | − | 1.64812i | −0.0559730 | − | 0.0969481i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.412852 | − | 0.715081i | −0.0242018 | − | 0.0419188i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4807 | 0.787548 | 0.393774 | − | 0.919207i | \(-0.371169\pi\) | ||||
0.393774 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.9106 | −1.50349 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.28682 | + | 3.96089i | −0.132250 | + | 0.229064i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.15206 | − | 8.92362i | 0.296960 | − | 0.514349i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.09361 | 0.292620 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.9744 | − | 20.7403i | 0.683418 | − | 1.18371i | −0.290514 | − | 0.956871i | \(-0.593826\pi\) |
0.973931 | − | 0.226843i | \(-0.0728405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.5977 | + | 18.3557i | −0.602880 | + | 1.04422i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8129 | −1.18019 | −0.590095 | − | 0.807334i | \(-0.700910\pi\) | ||||
−0.590095 | + | 0.807334i | \(0.700910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.34701 | − | 9.26130i | −0.302231 | − | 0.523479i | 0.674410 | − | 0.738357i | \(-0.264398\pi\) |
−0.976641 | + | 0.214878i | \(0.931065\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6592 | − | 25.3905i | −0.823343 | − | 1.42607i | −0.903179 | − | 0.429264i | \(-0.858773\pi\) |
0.0798355 | − | 0.996808i | \(-0.474561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.59745 | + | 9.69507i | 0.313397 | + | 0.542819i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6947 | − | 20.2559i | 0.652736 | − | 1.13057i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.5741 | + | 7.09291i | 0.977849 | + | 0.394660i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.933895 | + | 1.61755i | 0.0516445 | + | 0.0894509i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.07314 | − | 3.59078i | −0.114296 | − | 0.197966i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8654 | −1.64155 | −0.820777 | − | 0.571249i | \(-0.806459\pi\) | ||||
−0.820777 | + | 0.571249i | \(0.806459\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.89081 | − | 5.00703i | −0.158416 | − | 0.274384i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.86326 | + | 17.0837i | −0.537286 | + | 0.930607i | 0.461763 | + | 0.887003i | \(0.347217\pi\) |
−0.999049 | + | 0.0436035i | \(0.986116\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.39637 | + | 7.61474i | −0.238778 | + | 0.413576i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.4333 | 0.998217 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8551 | 0.910092 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.92364 | + | 15.4562i | −0.479046 | + | 0.829732i | −0.999711 | − | 0.0240287i | \(-0.992351\pi\) |
0.520665 | + | 0.853761i | \(0.325684\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4218 | −0.879040 | −0.439520 | − | 0.898233i | \(-0.644851\pi\) | ||||
−0.439520 | + | 0.898233i | \(0.644851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.85698 | + | 6.68049i | 0.205870 | + | 0.356578i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.9506 | −1.00864 | −0.504319 | − | 0.863517i | \(-0.668257\pi\) | ||||
−0.504319 | + | 0.863517i | \(0.668257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.80299 | − | 8.31902i | −0.254201 | − | 0.440289i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.9335 | − | 24.1335i | 0.735380 | − | 1.27371i | −0.219177 | − | 0.975685i | \(-0.570337\pi\) |
0.954557 | − | 0.298030i | \(-0.0963295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2601 | + | 5.25050i | −0.961059 | + | 0.276342i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.59221 | − | 14.8821i | 0.450974 | − | 0.781110i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.2265 | + | 22.9090i | 0.690418 | + | 1.19584i | 0.971701 | + | 0.236214i | \(0.0759067\pi\) |
−0.281283 | + | 0.959625i | \(0.590760\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.10198 | −0.317656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.33667 | − | 9.24338i | −0.277066 | − | 0.479892i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3566 | 1.52003 | 0.760013 | − | 0.649908i | \(-0.225193\pi\) | ||||
0.760013 | + | 0.649908i | \(0.225193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.66644 | − | 2.88636i | 0.0858260 | − | 0.148655i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.49172 | 0.384824 | 0.192412 | − | 0.981314i | \(-0.438369\pi\) | ||||
0.192412 | + | 0.981314i | \(0.438369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.30618 | 0.271844 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.44220 | − | 5.96207i | 0.175888 | − | 0.304648i | −0.764580 | − | 0.644529i | \(-0.777054\pi\) |
0.940468 | + | 0.339881i | \(0.110387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.74717 | −0.190479 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.1533 | + | 17.5861i | 0.514794 | + | 0.891650i | 0.999853 | + | 0.0171681i | \(0.00546505\pi\) |
−0.485058 | + | 0.874482i | \(0.661202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.2766 | −0.721999 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.89384 | − | 10.2084i | −0.297305 | − | 0.514948i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.89768 | + | 8.48303i | −0.245808 | + | 0.425751i | −0.962358 | − | 0.271784i | \(-0.912386\pi\) |
0.716551 | + | 0.697535i | \(0.245720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.93063 | + | 3.60440i | 0.447091 | + | 0.180446i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.78057 | − | 3.08404i | 0.0889174 | − | 0.154009i | −0.818136 | − | 0.575024i | \(-0.804993\pi\) |
0.907054 | + | 0.421015i | \(0.138326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.74392 | − | 4.75261i | −0.136684 | − | 0.236744i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 53.1333 | 2.63372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9468 | − | 18.9604i | −0.541285 | − | 0.937533i | −0.998831 | − | 0.0483469i | \(-0.984605\pi\) |
0.457546 | − | 0.889186i | \(-0.348729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.60400 | −0.375078 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.47943 | + | 12.9547i | −0.368039 | + | 0.637462i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.0445 | −1.66717 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.6000 | 1.25064 | 0.625322 | − | 0.780367i | \(-0.284968\pi\) | ||||
0.625322 | + | 0.780367i | \(0.284968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.61245 | − | 9.72105i | 0.273534 | − | 0.473775i | −0.696230 | − | 0.717819i | \(-0.745141\pi\) |
0.969764 | + | 0.244044i | \(0.0784740\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.753913 | + | 1.30582i | −0.0366565 | + | 0.0634909i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.205352 | − | 0.355680i | −0.00993766 | − | 0.0172125i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.2846 | −0.496547 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4540 | + | 23.3030i | 0.648057 | + | 1.12247i | 0.983586 | + | 0.180438i | \(0.0577515\pi\) |
−0.335529 | + | 0.942030i | \(0.608915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5168 | − | 26.8758i | −0.745688 | − | 1.29157i | −0.949873 | − | 0.312637i | \(-0.898788\pi\) |
0.204185 | − | 0.978932i | \(-0.434546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.2757 | − | 8.81619i | 0.539389 | − | 0.421736i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.4195 | + | 19.7791i | −0.545022 | + | 0.944005i | 0.453584 | + | 0.891214i | \(0.350145\pi\) |
−0.998606 | + | 0.0527915i | \(0.983188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.28296 | − | 2.22216i | −0.0610934 | − | 0.105817i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.7905 | − | 22.1538i | −0.607696 | − | 1.05256i | −0.991619 | − | 0.129196i | \(-0.958760\pi\) |
0.383923 | − | 0.923365i | \(-0.374573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.3617 | − | 31.8034i | −0.868478 | − | 1.50425i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.7102 | −1.40211 | −0.701055 | − | 0.713107i | \(-0.747287\pi\) | ||||
−0.701055 | + | 0.713107i | \(0.747287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0387 | − | 48.5644i | 1.32029 | − | 2.28681i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.09393 | − | 14.0191i | 0.380286 | − | 0.658674i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.9693 | 0.653458 | 0.326729 | − | 0.945118i | \(-0.394054\pi\) | ||||
0.326729 | + | 0.945118i | \(0.394054\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.0395 | + | 20.8531i | −0.561957 | + | 0.973338i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7999 | − | 18.7060i | 0.503001 | − | 0.871224i | −0.496993 | − | 0.867755i | \(-0.665562\pi\) |
0.999994 | − | 0.00346920i | \(-0.00110428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4002 | 0.669233 | 0.334617 | − | 0.942354i | \(-0.391393\pi\) | ||||
0.334617 | + | 0.942354i | \(0.391393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.9770 | 1.61854 | 0.809271 | − | 0.587435i | \(-0.199862\pi\) | ||||
0.809271 | + | 0.587435i | \(0.199862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.27789 | − | 9.14157i | −0.243710 | − | 0.422118i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7385 | + | 30.7239i | 0.817345 | + | 1.41568i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.2183 | − | 29.8230i | 0.791698 | − | 1.37126i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.94072 | + | 3.36142i | −0.0888594 | + | 0.153909i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.14007 | + | 15.8311i | 0.417620 | + | 0.723340i | 0.995700 | − | 0.0926410i | \(-0.0295309\pi\) |
−0.578079 | + | 0.815981i | \(0.696198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.90927 | − | 13.6993i | −0.360632 | − | 0.624632i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.25493 | −0.330111 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.3488 | −0.876780 | −0.438390 | − | 0.898785i | \(-0.644451\pi\) | ||||
−0.438390 | + | 0.898785i | \(0.644451\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.74086 | + | 9.94347i | −0.259611 | + | 0.449659i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.23725 | − | 10.8032i | 0.281483 | − | 0.487543i | −0.690267 | − | 0.723554i | \(-0.742507\pi\) |
0.971750 | + | 0.236012i | \(0.0758404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.4036 | 0.468552 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.128926 | − | 0.223306i | 0.00578312 | − | 0.0100167i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.58105 | + | 11.3987i | −0.294608 | + | 0.510276i | −0.974894 | − | 0.222671i | \(-0.928522\pi\) |
0.680286 | + | 0.732947i | \(0.261856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7901 | 0.482066 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.87656 | + | 17.1067i | 0.440374 | + | 0.762750i | 0.997717 | − | 0.0675323i | \(-0.0215126\pi\) |
−0.557343 | + | 0.830282i | \(0.688179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.72778 | − | 15.1170i | −0.387614 | − | 0.671368i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.63237 | − | 9.75556i | −0.249651 | − | 0.432407i | 0.713778 | − | 0.700372i | \(-0.246982\pi\) |
−0.963429 | + | 0.267964i | \(0.913649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.28690 | − | 2.22898i | 0.0569293 | − | 0.0986044i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.36850 | − | 23.9045i | −0.148723 | − | 1.05541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.92848 | − | 12.0005i | −0.304714 | − | 0.527781i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.66573 | + | 9.81333i | 0.248698 | + | 0.430758i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.2410 | −0.580098 | −0.290049 | − | 0.957012i | \(-0.593672\pi\) | ||||
−0.290049 | + | 0.957012i | \(0.593672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.74503 | − | 4.75453i | −0.120032 | − | 0.207901i | 0.799748 | − | 0.600336i | \(-0.204966\pi\) |
−0.919780 | + | 0.392434i | \(0.871633\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.56512 | − | 14.8352i | 0.373103 | − | 0.646233i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.10878 | − | 10.5807i | 0.265599 | − | 0.460031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.43990 | 0.236072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6950 | −0.723142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.74513 | + | 4.75470i | −0.118461 | + | 0.205181i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.5809 | 1.01570 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.888663 | − | 1.53921i | −0.0382066 | − | 0.0661758i | 0.846290 | − | 0.532723i | \(-0.178831\pi\) |
−0.884496 | + | 0.466547i | \(0.845498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.1150 | 1.24944 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5968 | − | 33.9427i | −0.837899 | − | 1.45128i | −0.891648 | − | 0.452730i | \(-0.850450\pi\) |
0.0537486 | − | 0.998554i | \(-0.482883\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0746777 | + | 0.129346i | −0.00318717 | + | 0.00552033i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.21675 | + | 6.42448i | −0.350045 | + | 0.273692i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.22547 | − | 2.12258i | 0.0521125 | − | 0.0902615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3691 | + | 38.7443i | 0.947807 | + | 1.64165i | 0.750031 | + | 0.661403i | \(0.230039\pi\) |
0.197777 | + | 0.980247i | \(0.436628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.2523 | −0.433624 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0517 | − | 27.8023i | −0.677703 | − | 1.17382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.3322 | −0.688318 | −0.344159 | − | 0.938911i | \(-0.611836\pi\) | ||||
−0.344159 | + | 0.938911i | \(0.611836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.04913 | + | 8.74535i | −0.212044 | + | 0.367270i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.0171 | 1.13261 | 0.566307 | − | 0.824194i | \(-0.308372\pi\) | ||||
0.566307 | + | 0.824194i | \(0.308372\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0260 | 1.42395 | 0.711973 | − | 0.702207i | \(-0.247802\pi\) | ||||
0.711973 | + | 0.702207i | \(0.247802\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.8078 | + | 34.3081i | −0.827482 | + | 1.43324i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.96551 | 0.331608 | 0.165804 | − | 0.986159i | \(-0.446978\pi\) | ||||
0.165804 | + | 0.986159i | \(0.446978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.93063 | + | 15.4683i | 0.371144 | + | 0.642841i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.49278 | 0.144905 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.8353 | − | 30.8916i | −0.738661 | − | 1.27940i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.4543 | − | 19.8395i | 0.472771 | − | 0.818864i | −0.526743 | − | 0.850025i | \(-0.676587\pi\) |
0.999514 | + | 0.0311607i | \(0.00992035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39641 | + | 17.0061i | 0.0987423 | + | 0.700724i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.04334 | − | 13.9315i | 0.330859 | − | 0.573064i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.51758 | + | 2.62852i | 0.0623194 | + | 0.107940i | 0.895502 | − | 0.445058i | \(-0.146817\pi\) |
−0.833182 | + | 0.552998i | \(0.813484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.2415 | 1.31956 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.0457108 | + | 0.0791734i | 0.00186769 | + | 0.00323494i | 0.866958 | − | 0.498382i | \(-0.166072\pi\) |
−0.865090 | + | 0.501617i | \(0.832739\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.2190 | 1.11029 | 0.555144 | − | 0.831754i | \(-0.312663\pi\) | ||||
0.555144 | + | 0.831754i | \(0.312663\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.91934 | + | 3.32440i | −0.0781617 | + | 0.135380i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.9612 | −0.931965 | −0.465983 | − | 0.884794i | \(-0.654299\pi\) | ||||
−0.465983 | + | 0.884794i | \(0.654299\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.28677 | 0.214231 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.06271 | + | 3.57271i | −0.0834482 | + | 0.144536i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7101 | + | 20.2825i | −0.472967 | + | 0.819202i | −0.999521 | − | 0.0309391i | \(-0.990150\pi\) |
0.526555 | + | 0.850141i | \(0.323484\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.4969 | + | 23.3773i | 0.543365 | + | 0.941136i | 0.998708 | + | 0.0508196i | \(0.0161833\pi\) |
−0.455343 | + | 0.890316i | \(0.650483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.52401 | −0.342609 | −0.171304 | − | 0.985218i | \(-0.554798\pi\) | ||||
−0.171304 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.09288 | + | 15.7493i | 0.364885 | + | 0.631999i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.43796 | − | 2.49062i | −0.0576107 | − | 0.0997847i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 29.8464 | + | 12.0460i | 1.19195 | + | 0.481070i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.6887 | − | 42.7621i | 0.984403 | − | 1.70504i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.243045 | − | 0.420966i | −0.00967547 | − | 0.0167584i | 0.861147 | − | 0.508356i | \(-0.169747\pi\) |
−0.870823 | + | 0.491597i | \(0.836413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0923685 | + | 0.159987i | 0.00367132 | + | 0.00635891i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.51019 | − | 6.07982i | −0.139079 | − | 0.240891i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0937698 | −0.00370948 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.40147 | + | 7.62356i | −0.173847 | + | 0.301113i | −0.939762 | − | 0.341830i | \(-0.888953\pi\) |
0.765914 | + | 0.642943i | \(0.222287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0490 | + | 24.3336i | −0.554039 | + | 0.959623i | 0.443939 | + | 0.896057i | \(0.353581\pi\) |
−0.997978 | + | 0.0635663i | \(0.979753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.9675 | 0.902946 | 0.451473 | − | 0.892285i | \(-0.350899\pi\) | ||||
0.451473 | + | 0.892285i | \(0.350899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.9964 | + | 43.2951i | −0.981195 | + | 1.69948i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.35254 | − | 7.53881i | 0.170589 | − | 0.295469i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.8297 | 1.87172 | 0.935860 | − | 0.352372i | \(-0.114625\pi\) | ||||
0.935860 | + | 0.352372i | \(0.114625\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.935985 | −0.0365162 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.61520 | + | 4.52966i | 0.101874 | + | 0.176451i | 0.912457 | − | 0.409173i | \(-0.134183\pi\) |
−0.810583 | + | 0.585624i | \(0.800850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6767 | + | 27.1529i | 0.609754 | + | 1.05613i | 0.991281 | + | 0.131767i | \(0.0420652\pi\) |
−0.381527 | + | 0.924358i | \(0.624602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.77881 | + | 8.27715i | −0.185594 | + | 0.321458i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.92865 | − | 6.80463i | 0.152118 | − | 0.263476i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.7459 | − | 18.6125i | −0.415461 | − | 0.719600i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.686290 | − | 1.18869i | −0.0264939 | − | 0.0458888i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.6781 | −1.10546 | −0.552729 | − | 0.833361i | \(-0.686414\pi\) | ||||
−0.552729 | + | 0.833361i | \(0.686414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.1600 | 0.659513 | 0.329757 | − | 0.944066i | \(-0.393033\pi\) | ||||
0.329757 | + | 0.944066i | \(0.393033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.366193 | + | 0.634265i | −0.0140532 | + | 0.0243409i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.61416 | + | 7.99195i | −0.176815 | + | 0.306252i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.150796 | −0.00577004 | −0.00288502 | − | 0.999996i | \(-0.500918\pi\) | ||||
−0.00288502 | + | 0.999996i | \(0.500918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.9043 | + | 32.7432i | −0.721244 | + | 1.24923i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.30981 | + | 9.19686i | −0.202288 | + | 0.350372i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.0669 | −1.25792 | −0.628962 | − | 0.777436i | \(-0.716520\pi\) | ||||
−0.628962 | + | 0.777436i | \(0.716520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.66709 | + | 2.88748i | 0.0633273 | + | 0.109686i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.0567 | − | 45.1315i | −0.986968 | − | 1.70948i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.5437 | − | 26.9224i | −0.587915 | − | 1.01830i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7648 | + | 34.2336i | −0.746505 | + | 1.29298i | 0.202984 | + | 0.979182i | \(0.434936\pi\) |
−0.949488 | + | 0.313802i | \(0.898397\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.90758 | + | 49.0195i | 0.260524 | + | 1.84881i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.25897 | − | 3.91266i | −0.0849575 | − | 0.147151i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2276 | − | 33.3032i | −0.722108 | − | 1.25073i | −0.960153 | − | 0.279474i | \(-0.909840\pi\) |
0.238045 | − | 0.971254i | \(-0.423493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.891306 | −0.0334266 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.46883 | − | 11.2043i | −0.242260 | − | 0.419606i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.7113 | + | 25.4807i | −0.549403 | + | 0.951593i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.7416 | − | 23.8011i | 0.512475 | − | 0.887633i | −0.487420 | − | 0.873167i | \(-0.662062\pi\) |
0.999895 | − | 0.0144653i | \(-0.00460462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.7999 | 0.700145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2934 | −0.420007 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6371 | + | 42.6727i | −0.913739 | + | 1.58264i | −0.105003 | + | 0.994472i | \(0.533485\pi\) |
−0.808737 | + | 0.588171i | \(0.799848\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8948 | 1.10722 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0012 | − | 27.7148i | −0.591825 | − | 1.02507i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.6606 | −1.46490 | −0.732449 | − | 0.680821i | \(-0.761623\pi\) | ||||
−0.732449 | + | 0.680821i | \(0.761623\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.6388 | − | 30.5513i | −0.649734 | − | 1.12537i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9817 | − | 29.4131i | 0.624680 | − | 1.08198i | −0.363922 | − | 0.931429i | \(-0.618563\pi\) |
0.988603 | − | 0.150549i | \(-0.0481040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.33705 | − | 9.48836i | −0.0491177 | − | 0.348563i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.41651 | + | 2.45347i | −0.0519668 | + | 0.0900091i | −0.890839 | − | 0.454320i | \(-0.849882\pi\) |
0.838872 | + | 0.544329i | \(0.183216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.635088 | − | 1.10001i | −0.0232367 | − | 0.0402471i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.7461 | −0.758045 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9289 | + | 29.3217i | 0.617743 | + | 1.06996i | 0.989897 | + | 0.141792i | \(0.0452863\pi\) |
−0.372153 | + | 0.928171i | \(0.621380\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.5877 | −0.422279 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.2423 | + | 19.4722i | −0.408608 | + | 0.707729i | −0.994734 | − | 0.102490i | \(-0.967319\pi\) |
0.586126 | + | 0.810220i | \(0.300652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.2462 | −0.880080 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.7383 | −1.00551 | −0.502755 | − | 0.864429i | \(-0.667680\pi\) | ||||
−0.502755 | + | 0.864429i | \(0.667680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.828350 | − | 1.43474i | 0.0299883 | − | 0.0519412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8836 | 0.537415 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.2036 | + | 43.6539i | 0.908865 | + | 1.57420i | 0.815643 | + | 0.578556i | \(0.196383\pi\) |
0.0932225 | + | 0.995645i | \(0.470283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.4257 | 0.519527 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.5558 | + | 33.8717i | 0.703374 | + | 1.21828i | 0.967275 | + | 0.253730i | \(0.0816574\pi\) |
−0.263901 | + | 0.964550i | \(0.585009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5461 | − | 21.7304i | 0.450087 | − | 0.779574i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 48.4496 | + | 19.5542i | 1.73589 | + | 0.700603i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.430874 | − | 0.746295i | 0.0154179 | − | 0.0267046i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.62611 | − | 11.4768i | −0.236798 | − | 0.410146i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.6415 | −0.379328 | −0.189664 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189664 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.8170 | − | 32.5919i | −0.669901 | − | 1.16030i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.79902 | 0.277301 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.204318 | + | 0.353890i | −0.00725555 | + | 0.0125670i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.1004 | 0.570304 | 0.285152 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285152 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8774 | −0.455571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.522926 | + | 0.905734i | −0.0184767 | + | 0.0320025i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.30086 | − | 7.44932i | 0.151774 | − | 0.262881i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.9437 | + | 20.6870i | 0.420437 | + | 0.728218i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1658 | 0.744151 | 0.372075 | − | 0.928202i | \(-0.378646\pi\) | ||||
0.372075 | + | 0.928202i | \(0.378646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6707 | + | 35.8028i | 0.725848 | + | 1.25721i | 0.958624 | + | 0.284675i | \(0.0918857\pi\) |
−0.232776 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.17541 | + | 2.03587i | 0.0412235 | + | 0.0714012i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.7524 | + | 12.0081i | 1.04091 | + | 0.420109i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.496315 | − | 0.859642i | 0.0173426 | − | 0.0300383i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.98387 | + | 5.16822i | 0.104138 | + | 0.180372i | 0.913386 | − | 0.407095i | \(-0.133458\pi\) |
−0.809248 | + | 0.587467i | \(0.800125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4868 | + | 26.8239i | 0.539835 | + | 0.935022i | 0.998912 | + | 0.0466254i | \(0.0148467\pi\) |
−0.459077 | + | 0.888396i | \(0.651820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0562 | − | 22.6140i | −0.454009 | − | 0.786367i | 0.544622 | − | 0.838682i | \(-0.316673\pi\) |
−0.998631 | + | 0.0523152i | \(0.983340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.68227 | 0.0931591 | 0.0465795 | − | 0.998915i | \(-0.485168\pi\) | ||||
0.0465795 | + | 0.998915i | \(0.485168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.9173 | + | 18.9094i | −0.378718 | + | 0.655959i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9570 | − | 18.9781i | 0.379638 | − | 0.657553i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.8208 | −0.754237 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.25063 | + | 9.09436i | −0.181272 | + | 0.313972i | −0.942314 | − | 0.334730i | \(-0.891355\pi\) |
0.761042 | + | 0.648703i | \(0.224688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.6371 | − | 20.1561i | 0.401281 | − | 0.695038i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.38048 | −0.0475463 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.2423 | −0.523731 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.3057 | − | 17.8499i | −0.353690 | − | 0.612608i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.6462 | − | 32.2962i | −0.639184 | − | 1.10710i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.8508 | − | 34.3826i | 0.679678 | − | 1.17724i | −0.295400 | − | 0.955374i | \(-0.595453\pi\) |
0.975078 | − | 0.221863i | \(-0.0712138\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.03975 | + | 15.6573i | −0.308792 | + | 0.534843i | −0.978098 | − | 0.208143i | \(-0.933258\pi\) |
0.669306 | + | 0.742986i | \(0.266591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4851 | − | 23.3569i | −0.460105 | − | 0.796926i | 0.538860 | − | 0.842395i | \(-0.318855\pi\) |
−0.998966 | + | 0.0454693i | \(0.985522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2412 | − | 22.9345i | −0.451260 | − | 0.781605i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.3734 | 0.625438 | 0.312719 | − | 0.949846i | \(-0.398760\pi\) | ||||
0.312719 | + | 0.949846i | \(0.398760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.00357 | −0.102006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.09556 | − | 7.09373i | 0.138933 | − | 0.240638i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.25132 | + | 9.09556i | −0.177934 | + | 0.308191i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.266338 | 0.00901416 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.6617 | + | 40.9832i | −0.798998 | + | 1.38391i | 0.121271 | + | 0.992619i | \(0.461303\pi\) |
−0.920269 | + | 0.391286i | \(0.872030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.6380 | − | 18.4256i | 0.358811 | − | 0.621480i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8395 | −0.533646 | −0.266823 | − | 0.963745i | \(-0.585974\pi\) | ||||
−0.266823 | + | 0.963745i | \(0.585974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3443 | + | 36.9695i | 0.718294 | + | 1.24412i | 0.961675 | + | 0.274191i | \(0.0884101\pi\) |
−0.243381 | + | 0.969931i | \(0.578257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.9515 | − | 20.7006i | −0.401293 | − | 0.695059i | 0.592589 | − | 0.805505i | \(-0.298106\pi\) |
−0.993882 | + | 0.110445i | \(0.964772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.35325 | − | 4.07594i | −0.0789254 | − | 0.136703i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.8743 | + | 29.2272i | −0.565311 | + | 0.979147i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1706 | − | 7.95217i | 0.340347 | − | 0.266109i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.60921 | + | 6.25134i | 0.120508 | + | 0.208726i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.71393 | + | 8.16476i | 0.157218 | + | 0.272310i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.1490 | −1.10435 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.13131 | − | 14.0838i | −0.270593 | − | 0.468681i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2637 | + | 31.6336i | −0.606435 | + | 1.05038i | 0.385387 | + | 0.922755i | \(0.374068\pi\) |
−0.991823 | + | 0.127622i | \(0.959266\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.821493 | + | 1.42287i | −0.0272472 | + | 0.0471935i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1950 | −0.834749 | −0.417374 | − | 0.908735i | \(-0.637050\pi\) | ||||
−0.417374 | + | 0.908735i | \(0.637050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.6730 | 0.386319 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.22774 | + | 9.05472i | −0.172635 | + | 0.299013i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.16199 | 0.269239 | 0.134620 | − | 0.990897i | \(-0.457019\pi\) | ||||
0.134620 | + | 0.990897i | \(0.457019\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.8988 | − | 32.7338i | −0.622738 | − | 1.07861i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.256554 | −0.00844459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.41836 | − | 5.92078i | −0.112274 | − | 0.194464i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.01835 | − | 10.4241i | 0.197456 | − | 0.342003i | −0.750247 | − | 0.661158i | \(-0.770065\pi\) |
0.947703 | + | 0.319154i | \(0.103399\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.06563 | + | 21.7552i | 0.100472 | + | 0.712998i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.4241 | + | 28.4474i | −0.537701 | + | 0.931326i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.5593 | − | 30.4135i | −0.573636 | − | 0.993567i | −0.996188 | − | 0.0872286i | \(-0.972199\pi\) |
0.422552 | − | 0.906339i | \(-0.361134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8780 | −0.550793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8189 | + | 51.6478i | 0.972067 | + | 1.68367i | 0.689292 | + | 0.724483i | \(0.257922\pi\) |
0.282775 | + | 0.959186i | \(0.408745\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.3588 | −1.28170 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.07831 | − | 8.79590i | 0.165023 | − | 0.285828i | −0.771640 | − | 0.636059i | \(-0.780563\pi\) |
0.936663 | + | 0.350231i | \(0.113897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.56086 | −0.0831289 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −46.2722 | −1.50048 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.8376 | + | 43.0199i | −0.804568 | + | 1.39355i | 0.112015 | + | 0.993707i | \(0.464270\pi\) |
−0.916583 | + | 0.399846i | \(0.869064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.6685 | 0.571142 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.37231 | + | 5.84102i | 0.108898 | + | 0.188616i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4763 | −0.499236 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.77223 | + | 6.53370i | 0.121558 | + | 0.210545i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.9740 | + | 31.1319i | −0.578005 | + | 1.00113i | 0.417703 | + | 0.908584i | \(0.362835\pi\) |
−0.995708 | + | 0.0925508i | \(0.970498\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.5630 | − | 18.4233i | 0.756952 | − | 0.591843i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.8394 | + | 34.3628i | −0.636676 | + | 1.10276i | 0.349481 | + | 0.936943i | \(0.386358\pi\) |
−0.986157 | + | 0.165812i | \(0.946975\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.0984 | + | 26.1513i | 0.484034 | + | 0.838372i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.3337 | 1.09843 | 0.549216 | − | 0.835681i | \(-0.314926\pi\) | ||||
0.549216 | + | 0.835681i | \(0.314926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.80570 | − | 8.32372i | −0.153591 | − | 0.266027i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.602471 | −0.0192354 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.03255 | + | 5.25253i | −0.0967234 | + | 0.167530i | −0.910327 | − | 0.413891i | \(-0.864170\pi\) |
0.813603 | + | 0.581421i | \(0.197503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.54392 | −0.208295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.1698 | −0.768556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7694 | − | 23.8493i | 0.437400 | − | 0.757599i | −0.560088 | − | 0.828433i | \(-0.689233\pi\) |
0.997488 | + | 0.0708340i | \(0.0225661\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.5678 | + | 40.8206i | −0.747901 | + | 1.29540i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.15784 | + | 3.73748i | 0.0683394 | + | 0.118367i | 0.898170 | − | 0.439647i | \(-0.144897\pi\) |
−0.829831 | + | 0.558015i | \(0.811563\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −62.8978 | −1.99000 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1900.2.i.e.201.5 | ✓ | 12 | |
5.2 | odd | 4 | 1900.2.s.e.49.4 | 24 | |||
5.3 | odd | 4 | 1900.2.s.e.49.9 | 24 | |||
5.4 | even | 2 | 1900.2.i.f.201.2 | yes | 12 | ||
19.7 | even | 3 | inner | 1900.2.i.e.501.5 | yes | 12 | |
95.7 | odd | 12 | 1900.2.s.e.349.9 | 24 | |||
95.64 | even | 6 | 1900.2.i.f.501.2 | yes | 12 | ||
95.83 | odd | 12 | 1900.2.s.e.349.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.i.e.201.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1900.2.i.e.501.5 | yes | 12 | 19.7 | even | 3 | inner | |
1900.2.i.f.201.2 | yes | 12 | 5.4 | even | 2 | ||
1900.2.i.f.501.2 | yes | 12 | 95.64 | even | 6 | ||
1900.2.s.e.49.4 | 24 | 5.2 | odd | 4 | |||
1900.2.s.e.49.9 | 24 | 5.3 | odd | 4 | |||
1900.2.s.e.349.4 | 24 | 95.83 | odd | 12 | |||
1900.2.s.e.349.9 | 24 | 95.7 | odd | 12 |