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 | 201.2 | ||
Root | \(1.28913 - 2.23284i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.f.501.2 |
$q$-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 | −0.998723 | − | 0.0505248i | \(-0.983911\pi\) |
0.543117 | + | 0.839657i | \(0.317244\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.39989 | 0.529110 | 0.264555 | − | 0.964371i | \(-0.414775\pi\) | ||||
0.264555 | + | 0.964371i | \(0.414775\pi\) | |||||||
\(8\) | 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 | 0.753140 | − | 0.657860i | \(-0.228538\pi\) |
−0.946294 | + | 0.323308i | \(0.895205\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.17388 | − | 3.76528i | 0.527244 | − | 0.913214i | −0.472252 | − | 0.881464i | \(-0.656559\pi\) |
0.999496 | − | 0.0317500i | \(-0.0101080\pi\) | |||||||
\(18\) | 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 | 0.642522 | − | 0.766267i | \(-0.277888\pi\) |
−0.984868 | + | 0.173307i | \(0.944555\pi\) | |||||||
\(24\) | 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 | \(-0.116706\pi\) | ||||
0.933536 | + | 0.358483i | \(0.116706\pi\) | |||||||
\(38\) | 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 | \(-0.643657\pi\) |
0.997388 | − | 0.0722255i | \(-0.0230101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.48093 | − | 2.56504i | −0.216015 | − | 0.374149i | 0.737571 | − | 0.675270i | \(-0.235973\pi\) |
−0.953586 | + | 0.301120i | \(0.902639\pi\) | |||||||
\(48\) | 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 | \(-0.991239\pi\) |
0.475976 | − | 0.879458i | \(-0.342095\pi\) | |||||||
\(54\) | 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 | 0.538388 | − | 0.842697i | \(-0.319034\pi\) |
−0.998991 | + | 0.0449086i | \(0.985700\pi\) | |||||||
\(68\) | 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 | −0.807201 | − | 0.590277i | \(-0.799019\pi\) |
0.914795 | + | 0.403918i | \(0.132352\pi\) | |||||||
\(74\) | 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 | \(-0.456276\pi\) | ||||
0.136933 | + | 0.990580i | \(0.456276\pi\) | |||||||
\(84\) | 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 | −0.879000 | − | 0.476822i | \(-0.841789\pi\) |
0.852440 | + | 0.522825i | \(0.175122\pi\) | |||||||
\(98\) | 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 | \(-0.269867\pi\) | ||||
0.661624 | + | 0.749835i | \(0.269867\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.8197 | −1.43268 | −0.716339 | − | 0.697752i | \(-0.754184\pi\) | ||||
−0.716339 | + | 0.697752i | \(0.754184\pi\) | |||||||
\(108\) | 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 | \(-0.415603\pi\) | ||||
0.262045 | + | 0.965056i | \(0.415603\pi\) | |||||||
\(114\) | 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 | 0.781753 | − | 0.623588i | \(-0.214326\pi\) |
−0.930920 | + | 0.365224i | \(0.880992\pi\) | |||||||
\(128\) | 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 | 0.950391 | − | 0.311057i | \(-0.100683\pi\) |
−0.744579 | + | 0.667535i | \(0.767350\pi\) | |||||||
\(138\) | 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 | \(-0.479084\pi\) |
0.831325 | − | 0.555786i | \(-0.187583\pi\) | |||||||
\(158\) | 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 | \(-0.408037\pi\) | ||||
0.284907 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.41834 | − | 5.92075i | −0.264519 | − | 0.458161i | 0.702918 | − | 0.711271i | \(-0.251880\pi\) |
−0.967438 | + | 0.253110i | \(0.918547\pi\) | |||||||
\(168\) | 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 | −0.696680 | − | 0.717382i | \(-0.745340\pi\) |
0.969611 | + | 0.244651i | \(0.0786735\pi\) | |||||||
\(174\) | 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 | −0.587279 | − | 0.809385i | \(-0.699801\pi\) |
0.994587 | + | 0.103906i | \(0.0331340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1926 | −0.726195 | −0.363098 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363098 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(198\) | 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 | −0.998742 | − | 0.0501456i | \(-0.984031\pi\) |
0.542798 | + | 0.839863i | \(0.317365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.84713 | 0.388088 | 0.194044 | − | 0.980993i | \(-0.437840\pi\) | ||||
0.194044 | + | 0.980993i | \(0.437840\pi\) | |||||||
\(228\) | 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 | \(0.389893\pi\) |
−0.984255 | + | 0.176755i | \(0.943440\pi\) | |||||||
\(234\) | 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 | 0.687552 | − | 0.726135i | \(-0.258685\pi\) |
−0.972627 | + | 0.232370i | \(0.925352\pi\) | |||||||
\(258\) | 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 | \(0.429568\pi\) |
−0.954646 | + | 0.297744i | \(0.903766\pi\) | |||||||
\(264\) | 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 | \(-0.363564\pi\) | ||||
0.415621 | + | 0.909538i | \(0.363564\pi\) | |||||||
\(278\) | 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 | −0.992201 | − | 0.124647i | \(-0.960220\pi\) |
0.604048 | + | 0.796948i | \(0.293554\pi\) | |||||||
\(284\) | 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 | \(-0.628831\pi\) | ||||
−0.393774 | + | 0.919207i | \(0.628831\pi\) | |||||||
\(294\) | 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 | \(0.406174\pi\) |
−0.973931 | + | 0.226843i | \(0.927159\pi\) | |||||||
\(308\) | 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 | 0.976641 | − | 0.214878i | \(-0.0689353\pi\) |
−0.674410 | + | 0.738357i | \(0.735602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6592 | + | 25.3905i | 0.823343 | + | 1.42607i | 0.903179 | + | 0.429264i | \(0.141227\pi\) |
−0.0798355 | + | 0.996808i | \(0.525439\pi\) | |||||||
\(318\) | 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 | \(-0.652783\pi\) |
0.999049 | − | 0.0436035i | \(-0.0138838\pi\) | |||||||
\(338\) | 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 | −0.520665 | − | 0.853761i | \(-0.674316\pi\) |
0.999711 | + | 0.0240287i | \(0.00764932\pi\) | |||||||
\(348\) | 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 | \(-0.331743\pi\) | ||||
0.504319 | + | 0.863517i | \(0.331743\pi\) | |||||||
\(354\) | 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 | \(-0.924093\pi\) |
0.281283 | − | 0.959625i | \(-0.409240\pi\) | |||||||
\(368\) | 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 | \(-0.774807\pi\) | ||||
−0.760013 | + | 0.649908i | \(0.774807\pi\) | |||||||
\(374\) | 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 | −0.940468 | − | 0.339881i | \(-0.889613\pi\) |
0.764580 | + | 0.644529i | \(0.222946\pi\) | |||||||
\(384\) | 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 | −0.716551 | − | 0.697535i | \(-0.754280\pi\) |
0.962358 | + | 0.271784i | \(0.0876135\pi\) | |||||||
\(398\) | 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 | \(0.101212\pi\) |
−0.204185 | + | 0.978932i | \(0.565454\pi\) | |||||||
\(434\) | 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 | \(0.0412396\pi\) |
−0.383923 | + | 0.923365i | \(0.625427\pi\) | |||||||
\(444\) | 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 | \(-0.605946\pi\) | ||||
−0.326729 | + | 0.945118i | \(0.605946\pi\) | |||||||
\(458\) | 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 | \(-0.608607\pi\) | ||||
−0.334617 | + | 0.942354i | \(0.608607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.9770 | −1.61854 | −0.809271 | − | 0.587435i | \(-0.800138\pi\) | ||||
−0.809271 | + | 0.587435i | \(0.800138\pi\) | |||||||
\(468\) | 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 | \(-0.355549\pi\) | ||||
0.438390 | + | 0.898785i | \(0.355549\pi\) | |||||||
\(488\) | 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 | 0.557343 | − | 0.830282i | \(-0.311821\pi\) |
−0.997717 | + | 0.0675323i | \(0.978487\pi\) | |||||||
\(504\) | 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 | 0.919780 | − | 0.392434i | \(-0.128367\pi\) |
−0.799748 | + | 0.600336i | \(0.795034\pi\) | |||||||
\(524\) | 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 | \(0.149550\pi\) |
−0.0537486 | + | 0.998554i | \(0.517117\pi\) | |||||||
\(548\) | 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 | \(-0.769961\pi\) |
−0.197777 | − | 0.980247i | \(-0.563372\pi\) | |||||||
\(558\) | 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 | \(-0.388164\pi\) | ||||
0.344159 | + | 0.938911i | \(0.388164\pi\) | |||||||
\(564\) | 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 | \(-0.553022\pi\) | ||||
−0.165804 | + | 0.986159i | \(0.553022\pi\) | |||||||
\(578\) | 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 | −0.999514 | − | 0.0311607i | \(-0.990080\pi\) |
0.526743 | + | 0.850025i | \(0.323413\pi\) | |||||||
\(588\) | 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 | 0.833182 | − | 0.552998i | \(-0.186516\pi\) |
−0.895502 | + | 0.445058i | \(0.853183\pi\) | |||||||
\(594\) | 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 | \(-0.345701\pi\) | ||||
0.465983 | + | 0.884794i | \(0.345701\pi\) | |||||||
\(608\) | 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 | −0.526555 | − | 0.850141i | \(-0.676516\pi\) |
0.999521 | + | 0.0309391i | \(0.00984979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4969 | − | 23.3773i | −0.543365 | − | 0.941136i | −0.998708 | − | 0.0508196i | \(-0.983817\pi\) |
0.455343 | − | 0.890316i | \(-0.349517\pi\) | |||||||
\(618\) | 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 | \(-0.646419\pi\) |
0.997978 | − | 0.0635663i | \(-0.0202474\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.9675 | −0.902946 | −0.451473 | − | 0.892285i | \(-0.649101\pi\) | ||||
−0.451473 | + | 0.892285i | \(0.649101\pi\) | |||||||
\(648\) | 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 | \(-0.885375\pi\) | ||||
−0.935860 | + | 0.352372i | \(0.885375\pi\) | |||||||
\(654\) | 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 | \(-0.313586\pi\) | ||||
0.552729 | + | 0.833361i | \(0.313586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1600 | −0.659513 | −0.329757 | − | 0.944066i | \(-0.606967\pi\) | ||||
−0.329757 | + | 0.944066i | \(0.606967\pi\) | |||||||
\(678\) | 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 | \(-0.499082\pi\) | ||||
0.00288502 | + | 0.999996i | \(0.499082\pi\) | |||||||
\(684\) | 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 | \(-0.466515\pi\) |
0.808737 | − | 0.588171i | \(-0.200152\pi\) | |||||||
\(728\) | 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 | \(-0.238377\pi\) | ||||
0.732449 | + | 0.680821i | \(0.238377\pi\) | |||||||
\(734\) | 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 | −0.838872 | − | 0.544329i | \(-0.816784\pi\) |
0.890839 | + | 0.454320i | \(0.150118\pi\) | |||||||
\(744\) | 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 | −0.586126 | − | 0.810220i | \(-0.699348\pi\) |
0.994734 | + | 0.102490i | \(0.0326811\pi\) | |||||||
\(758\) | 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 | \(-0.918343\pi\) |
0.263901 | − | 0.964550i | \(-0.414991\pi\) | |||||||
\(774\) | 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 | \(-0.439260\pi\) | ||||
0.189664 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(788\) | 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 | \(-0.592044\pi\) | ||||
−0.285152 | + | 0.958482i | \(0.592044\pi\) | |||||||
\(798\) | 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 | \(-0.985153\pi\) |
0.459077 | − | 0.888396i | \(-0.348180\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.0562 | + | 22.6140i | 0.454009 | + | 0.786367i | 0.998631 | − | 0.0523152i | \(-0.0166601\pi\) |
−0.544622 | + | 0.838682i | \(0.683327\pi\) | |||||||
\(828\) | 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 | \(0.404547\pi\) |
−0.975078 | + | 0.221863i | \(0.928786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.03975 | − | 15.6573i | 0.308792 | − | 0.534843i | −0.669306 | − | 0.742986i | \(-0.733409\pi\) |
0.978098 | + | 0.208143i | \(0.0667420\pi\) | |||||||
\(858\) | 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 | \(-0.601240\pi\) | ||||
−0.312719 | + | 0.949846i | \(0.601240\pi\) | |||||||
\(864\) | 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 | \(-0.538697\pi\) |
0.920269 | − | 0.391286i | \(-0.127970\pi\) | |||||||
\(878\) | 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 | \(-0.911590\pi\) |
0.243381 | − | 0.969931i | \(-0.421743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9515 | + | 20.7006i | 0.401293 | + | 0.695059i | 0.993882 | − | 0.110445i | \(-0.0352277\pi\) |
−0.592589 | + | 0.805505i | \(0.701894\pi\) | |||||||
\(888\) | 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 | \(-0.625932\pi\) |
0.991823 | − | 0.127622i | \(-0.0407345\pi\) | |||||||
\(908\) | 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 | \(0.0278011\pi\) |
−0.422552 | + | 0.906339i | \(0.638866\pi\) | |||||||
\(938\) | 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 | −0.936663 | − | 0.350231i | \(-0.886103\pi\) |
0.771640 | + | 0.636059i | \(0.219437\pi\) | |||||||
\(948\) | 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 | \(-0.535730\pi\) |
0.916583 | − | 0.399846i | \(-0.130936\pi\) | |||||||
\(954\) | 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 | \(-0.637165\pi\) |
0.995708 | − | 0.0925508i | \(-0.0295021\pi\) | |||||||
\(968\) | 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 | \(-0.685074\pi\) | ||||
−0.549216 | + | 0.835681i | \(0.685074\pi\) | |||||||
\(978\) | 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 | −0.813603 | − | 0.581421i | \(-0.802497\pi\) |
0.910327 | + | 0.413891i | \(0.135830\pi\) | |||||||
\(984\) | 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 | 0.829831 | − | 0.558015i | \(-0.188437\pi\) |
−0.898170 | + | 0.439647i | \(0.855103\pi\) | |||||||
\(998\) | 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.f.201.2 | yes | 12 | |
5.2 | odd | 4 | 1900.2.s.e.49.9 | 24 | |||
5.3 | odd | 4 | 1900.2.s.e.49.4 | 24 | |||
5.4 | even | 2 | 1900.2.i.e.201.5 | ✓ | 12 | ||
19.7 | even | 3 | inner | 1900.2.i.f.501.2 | yes | 12 | |
95.7 | odd | 12 | 1900.2.s.e.349.4 | 24 | |||
95.64 | even | 6 | 1900.2.i.e.501.5 | yes | 12 | ||
95.83 | odd | 12 | 1900.2.s.e.349.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.i.e.201.5 | ✓ | 12 | 5.4 | even | 2 | ||
1900.2.i.e.501.5 | yes | 12 | 95.64 | even | 6 | ||
1900.2.i.f.201.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1900.2.i.f.501.2 | yes | 12 | 19.7 | even | 3 | inner | |
1900.2.s.e.49.4 | 24 | 5.3 | odd | 4 | |||
1900.2.s.e.49.9 | 24 | 5.2 | odd | 4 | |||
1900.2.s.e.349.4 | 24 | 95.7 | odd | 12 | |||
1900.2.s.e.349.9 | 24 | 95.83 | odd | 12 |