Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.1 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.20 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23543 | + | 0.0533841i | −0.999715 | + | 0.0238741i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.50874i | − | 1.70414i | −0.523424 | − | 0.852072i | \(-0.675346\pi\) | ||
0.523424 | − | 0.852072i | \(-0.324654\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.971195 | 0.292826 | 0.146413 | − | 0.989224i | \(-0.453227\pi\) | ||||
0.146413 | + | 0.989224i | \(0.453227\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.87337i | 0.519580i | 0.965665 | + | 0.259790i | \(0.0836533\pi\) | ||||
−0.965665 | + | 0.259790i | \(0.916347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0533841 | + | 2.23543i | 0.0137837 | + | 0.577186i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.03013i | − | 1.21999i | −0.792407 | − | 0.609993i | \(-0.791172\pi\) | ||
0.792407 | − | 0.609993i | \(-0.208828\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.77783 | 0.407863 | 0.203932 | − | 0.978985i | \(-0.434628\pi\) | ||||
0.203932 | + | 0.978985i | \(0.434628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.50874 | −0.983888 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.44812i | − | 1.13601i | −0.823024 | − | 0.568006i | \(-0.807715\pi\) | ||
0.823024 | − | 0.568006i | \(-0.192285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99430 | − | 0.238673i | 0.998860 | − | 0.0477345i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.85056 | 0.715031 | 0.357515 | − | 0.933907i | \(-0.383624\pi\) | ||||
0.357515 | + | 0.933907i | \(0.383624\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.05491 | 0.907889 | 0.453945 | − | 0.891030i | \(-0.350016\pi\) | ||||
0.453945 | + | 0.891030i | \(0.350016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.971195i | − | 0.169063i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.240695 | + | 10.0790i | 0.0406849 | + | 1.70366i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.1759i | − | 1.67291i | −0.548036 | − | 0.836455i | \(-0.684624\pi\) | ||
0.548036 | − | 0.836455i | \(-0.315376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.87337 | 0.299980 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.79630 | 0.905230 | 0.452615 | − | 0.891706i | \(-0.350491\pi\) | ||||
0.452615 | + | 0.891706i | \(0.350491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.65164i | − | 1.31936i | −0.751546 | − | 0.659681i | \(-0.770691\pi\) | ||
0.751546 | − | 0.659681i | \(-0.229309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23543 | − | 0.0533841i | 0.333238 | − | 0.00795803i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.27397i | 0.185827i | 0.995674 | + | 0.0929137i | \(0.0296181\pi\) | ||||
−0.995674 | + | 0.0929137i | \(0.970382\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.3288 | −1.90411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.03013 | −0.704359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.85441i | 0.666805i | 0.942785 | + | 0.333402i | \(0.108197\pi\) | ||||
−0.942785 | + | 0.333402i | \(0.891803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.17104 | + | 0.0518463i | −0.292743 | + | 0.00699096i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.77783i | − | 0.235480i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.801017 | 0.104283 | 0.0521417 | − | 0.998640i | \(-0.483395\pi\) | ||||
0.0521417 | + | 0.998640i | \(0.483395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.97361 | −1.27699 | −0.638495 | − | 0.769626i | \(-0.720443\pi\) | ||||
−0.638495 | + | 0.769626i | \(0.720443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.50874i | 0.568048i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.100008 | − | 4.18779i | −0.0124045 | − | 0.519432i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.44812 | −0.655877 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3349 | −1.46388 | −0.731941 | − | 0.681368i | \(-0.761385\pi\) | ||||
−0.731941 | + | 0.681368i | \(0.761385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.73950i | − | 1.13992i | −0.821672 | − | 0.569961i | \(-0.806958\pi\) | ||
0.821672 | − | 0.569961i | \(-0.193042\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.238673 | − | 4.99430i | −0.0275596 | − | 0.576692i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.37887i | − | 0.499018i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.68322 | 0.639413 | 0.319706 | − | 0.947517i | \(-0.396416\pi\) | ||||
0.319706 | + | 0.947517i | \(0.396416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.8058i | 1.84467i | 0.386388 | + | 0.922336i | \(0.373723\pi\) | ||||
−0.386388 | + | 0.922336i | \(0.626277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.268529 | + | 11.2445i | 0.0291260 | + | 1.21964i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.85056i | − | 0.412823i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.4007 | −1.73847 | −0.869235 | − | 0.494399i | \(-0.835388\pi\) | ||||
−0.869235 | + | 0.494399i | \(0.835388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.44655 | 0.885439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.05491i | − | 0.524170i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.97422 | + | 0.0949080i | −0.407747 | + | 0.00973736i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.3278i | − | 1.15017i | −0.818095 | − | 0.575083i | \(-0.804970\pi\) | ||
0.818095 | − | 0.575083i | \(-0.195030\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.971195 | −0.0976087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.75522 | 0.871177 | 0.435589 | − | 0.900146i | \(-0.356540\pi\) | ||||
0.435589 | + | 0.900146i | \(0.356540\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.99346i | 0.294954i | 0.989065 | + | 0.147477i | \(0.0471153\pi\) | ||||
−0.989065 | + | 0.147477i | \(0.952885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0790 | − | 0.240695i | 0.983608 | − | 0.0234894i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.83928i | − | 0.177810i | −0.996040 | − | 0.0889052i | \(-0.971663\pi\) | ||
0.996040 | − | 0.0889052i | \(-0.0283368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2793 | 1.08036 | 0.540179 | − | 0.841550i | \(-0.318356\pi\) | ||||
0.540179 | + | 0.841550i | \(0.318356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1759 | −0.965855 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1469i | 1.14269i | 0.820711 | + | 0.571344i | \(0.193578\pi\) | ||||
−0.820711 | + | 0.571344i | \(0.806422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.290843 | + | 12.1789i | 0.0271212 | + | 1.13569i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.87337i | − | 0.173193i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.6796 | −2.07903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0568 | −0.914253 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.79630i | − | 0.522635i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1517 | + | 0.800152i | −0.997436 | + | 0.0715678i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.5167i | 1.90930i | 0.297730 | + | 0.954650i | \(0.403771\pi\) | ||||
−0.297730 | + | 0.954650i | \(0.596229\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.65164 | −0.761734 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7230 | 1.72321 | 0.861603 | − | 0.507582i | \(-0.169461\pi\) | ||||
0.861603 | + | 0.507582i | \(0.169461\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.01580i | − | 0.695058i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0533841 | − | 2.23543i | −0.00459457 | − | 0.192395i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.0580i | − | 1.45737i | −0.684851 | − | 0.728683i | \(-0.740133\pi\) | ||
0.684851 | − | 0.728683i | \(-0.259867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.94806 | 0.589327 | 0.294663 | − | 0.955601i | \(-0.404792\pi\) | ||||
0.294663 | + | 0.955601i | \(0.404792\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.27397 | 0.107287 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.81941i | 0.152147i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.60766 | + | 0.205558i | −0.714827 | + | 0.0170707i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.3288i | 1.09934i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.4588 | −1.43028 | −0.715142 | − | 0.698979i | \(-0.753638\pi\) | ||||
−0.715142 | + | 0.698979i | \(0.753638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.90694 | −0.562079 | −0.281040 | − | 0.959696i | \(-0.590679\pi\) | ||||
−0.281040 | + | 0.959696i | \(0.590679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.03013i | 0.406662i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2999 | + | 0.269852i | −0.907630 | + | 0.0216750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.22557i | − | 0.736281i | −0.929770 | − | 0.368141i | \(-0.879995\pi\) | ||
0.929770 | − | 0.368141i | \(-0.120005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.85441 | 0.384980 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.5642 | −1.93593 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25.2659i | 1.97897i | 0.144620 | + | 0.989487i | \(0.453804\pi\) | ||||
−0.144620 | + | 0.989487i | \(0.546196\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0518463 | + | 2.17104i | 0.00403623 | + | 0.169015i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.666796i | 0.0515982i | 0.999667 | + | 0.0257991i | \(0.00821302\pi\) | ||||
−0.999667 | + | 0.0257991i | \(0.991787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.49048 | 0.730037 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.77783 | −0.135954 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8775i | 1.28317i | 0.767052 | + | 0.641585i | \(0.221723\pi\) | ||||
−0.767052 | + | 0.641585i | \(0.778277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.07611 | − | 22.5180i | −0.0813466 | − | 1.70220i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.801017i | − | 0.0602081i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.1781 | −1.88190 | −0.940949 | − | 0.338549i | \(-0.890064\pi\) | ||||
−0.940949 | + | 0.338549i | \(0.890064\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.21845 | 0.313555 | 0.156777 | − | 0.987634i | \(-0.449890\pi\) | ||||
0.156777 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.97361i | 0.737271i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.543232 | + | 22.7475i | 0.0399392 | + | 1.67243i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.88524i | − | 0.357244i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50874 | 0.327963 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3167 | −1.39771 | −0.698854 | − | 0.715264i | \(-0.746306\pi\) | ||||
−0.698854 | + | 0.715264i | \(0.746306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 22.0344i | − | 1.58607i | −0.609174 | − | 0.793036i | \(-0.708499\pi\) | ||
0.609174 | − | 0.793036i | \(-0.291501\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.18779 | + | 0.100008i | −0.299894 | + | 0.00716174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8537i | 1.69951i | 0.527179 | + | 0.849754i | \(0.323250\pi\) | ||||
−0.527179 | + | 0.849754i | \(0.676750\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.29391 | −0.375276 | −0.187638 | − | 0.982238i | \(-0.560083\pi\) | ||||
−0.187638 | + | 0.982238i | \(0.560083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 17.3612i | − | 1.21852i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.9572 | + | 0.309430i | −0.904972 | + | 0.0216115i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.44812i | 0.378671i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.72662 | 0.119433 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.36599 | 0.300567 | 0.150283 | − | 0.988643i | \(-0.451981\pi\) | ||||
0.150283 | + | 0.988643i | \(0.451981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3349i | 0.845172i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.461859 | + | 19.3401i | 0.0314986 | + | 1.31899i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 22.7913i | − | 1.54717i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.73950 | −0.658134 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.42330 | 0.633880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.00754i | − | 0.335329i | −0.985844 | − | 0.167665i | \(-0.946377\pi\) | ||
0.985844 | − | 0.167665i | \(-0.0536226\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99430 | + | 0.238673i | −0.332953 | + | 0.0159115i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3845i | 1.22022i | 0.792316 | + | 0.610111i | \(0.208875\pi\) | ||||
−0.792316 | + | 0.610111i | \(0.791125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.6317 | −1.62771 | −0.813855 | − | 0.581068i | \(-0.802635\pi\) | ||||
−0.813855 | + | 0.581068i | \(0.802635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.37887 | −0.288108 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 8.36272i | − | 0.547860i | −0.961750 | − | 0.273930i | \(-0.911676\pi\) | ||
0.961750 | − | 0.273930i | \(-0.0883237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0680096 | − | 2.84787i | −0.00443646 | − | 0.185774i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.68322i | − | 0.369165i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6245 | −1.46346 | −0.731730 | − | 0.681595i | \(-0.761287\pi\) | ||||
−0.731730 | + | 0.681595i | \(0.761287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5883 | 1.06854 | 0.534272 | − | 0.845313i | \(-0.320586\pi\) | ||||
0.534272 | + | 0.845313i | \(0.320586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.7955 | − | 0.711543i | 1.90357 | − | 0.0454588i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.33054i | 0.211917i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.8058 | 1.06502 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.0957 | 1.89963 | 0.949813 | − | 0.312819i | \(-0.101273\pi\) | ||||
0.949813 | + | 0.312819i | \(0.101273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.29119i | − | 0.332654i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.2445 | − | 0.268529i | 0.704158 | − | 0.0168159i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4033i | 0.711319i | 0.934616 | + | 0.355659i | \(0.115744\pi\) | ||||
−0.934616 | + | 0.355659i | \(0.884256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −45.8806 | −2.85088 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.85056 | −0.238344 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.9006i | − | 1.28879i | −0.764695 | − | 0.644393i | \(-0.777110\pi\) | ||
0.764695 | − | 0.644393i | \(-0.222890\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.259148 | − | 10.8517i | −0.0159194 | − | 0.666615i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.4007i | 1.00371i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.93394 | −0.422770 | −0.211385 | − | 0.977403i | \(-0.567797\pi\) | ||||
−0.211385 | + | 0.977403i | \(0.567797\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.74661 | −0.166845 | −0.0834223 | − | 0.996514i | \(-0.526585\pi\) | ||||
−0.0834223 | + | 0.996514i | \(0.526585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 8.44655i | − | 0.511209i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.85044 | − | 0.231798i | 0.292492 | − | 0.0139779i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.9747i | − | 1.56067i | −0.625362 | − | 0.780334i | \(-0.715049\pi\) | ||
0.625362 | − | 0.780334i | \(-0.284951\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.05491 | −0.302630 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.2101 | 1.56356 | 0.781782 | − | 0.623552i | \(-0.214311\pi\) | ||||
0.781782 | + | 0.623552i | \(0.214311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 23.3253i | − | 1.38654i | −0.720677 | − | 0.693271i | \(-0.756169\pi\) | ||
0.720677 | − | 0.693271i | \(-0.243831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0949080 | + | 3.97422i | 0.00562186 | + | 0.235413i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 26.1340i | − | 1.54264i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.30221 | −0.488365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.3278 | −0.664049 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17.1915i | − | 1.00434i | −0.864770 | − | 0.502168i | \(-0.832536\pi\) | ||
0.864770 | − | 0.502168i | \(-0.167464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.79062 | + | 0.0427615i | −0.104254 | + | 0.00248967i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.971195i | 0.0563544i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2064 | 0.590249 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.0080 | −2.24838 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 8.75522i | − | 0.502974i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.2953 | − | 0.532432i | 1.27663 | − | 0.0304870i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2599i | − | 1.15629i | −0.815934 | − | 0.578145i | \(-0.803777\pi\) | ||
0.815934 | − | 0.578145i | \(-0.196223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.99346 | 0.170292 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1037 | −0.629632 | −0.314816 | − | 0.949153i | \(-0.601943\pi\) | ||||
−0.314816 | + | 0.949153i | \(0.601943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.11630i | 0.0630967i | 0.999502 | + | 0.0315484i | \(0.0100438\pi\) | ||||
−0.999502 | + | 0.0315484i | \(0.989956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.240695 | − | 10.0790i | −0.0135616 | − | 0.567886i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.89619i | 0.162666i | 0.996687 | + | 0.0813331i | \(0.0259178\pi\) | ||||
−0.996687 | + | 0.0813331i | \(0.974082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.73964 | 0.209380 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.83928 | −0.102659 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.94274i | − | 0.497587i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.447123 | + | 9.35618i | 0.0248019 | + | 0.518988i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 11.2793i | − | 0.623745i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.74399 | 0.316677 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0647 | 0.828028 | 0.414014 | − | 0.910270i | \(-0.364126\pi\) | ||||
0.414014 | + | 0.910270i | \(0.364126\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1759i | 0.557637i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0533841 | + | 2.23543i | 0.00291668 | + | 0.122135i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1955i | 0.936697i | 0.883544 | + | 0.468348i | \(0.155151\pi\) | ||||
−0.883544 | + | 0.468348i | \(0.844849\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1469 | 0.659731 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.90930 | 0.265854 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 28.5348i | 1.54073i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.1789 | − | 0.290843i | 0.655690 | − | 0.0156585i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.96587i | 0.266582i | 0.991077 | + | 0.133291i | \(0.0425544\pi\) | ||||
−0.991077 | + | 0.133291i | \(0.957446\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5284 | −0.777689 | −0.388844 | − | 0.921304i | \(-0.627126\pi\) | ||||
−0.388844 | + | 0.921304i | \(0.627126\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.87337 | −0.0999932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2401i | 0.598251i | 0.954214 | + | 0.299125i | \(0.0966948\pi\) | ||||
−0.954214 | + | 0.299125i | \(0.903305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.5738 | − | 0.658486i | 1.46346 | − | 0.0349488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.6796i | 1.20033i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.47309 | 0.341636 | 0.170818 | − | 0.985303i | \(-0.445359\pi\) | ||||
0.170818 | + | 0.985303i | \(0.445359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8393 | −0.833648 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.0568i | 0.527844i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.519934 | + | 21.7720i | 0.0272146 | + | 1.13960i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.66944i | − | 0.243743i | −0.992546 | − | 0.121871i | \(-0.961110\pi\) | ||
0.992546 | − | 0.121871i | \(-0.0388896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.79630 | −0.301743 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.8873 | 1.13633 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 33.8473i | − | 1.75255i | −0.481815 | − | 0.876273i | \(-0.660022\pi\) | ||
0.481815 | − | 0.876273i | \(-0.339978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.800152 | + | 11.1517i | 0.0413197 | + | 0.575870i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.21353i | 0.371516i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.6749 | −1.37020 | −0.685098 | − | 0.728450i | \(-0.740241\pi\) | ||||
−0.685098 | + | 0.728450i | \(0.740241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.5167 | 1.10234 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.72526i | 0.241449i | 0.992686 | + | 0.120725i | \(0.0385218\pi\) | ||||
−0.992686 | + | 0.120725i | \(0.961478\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.233762 | + | 9.78865i | 0.0119136 | + | 0.498876i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.65164i | 0.439787i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8613 | 0.804198 | 0.402099 | − | 0.915596i | \(-0.368281\pi\) | ||||
0.402099 | + | 0.915596i | \(0.368281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.4048 | −1.38592 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.7230i | − | 0.994894i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.7044 | + | 0.303393i | −0.639230 | + | 0.0152654i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.9367i | 0.900218i | 0.892974 | + | 0.450109i | \(0.148615\pi\) | ||||
−0.892974 | + | 0.450109i | \(0.851385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.01580 | −0.401292 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.83427 | 0.391225 | 0.195612 | − | 0.980681i | \(-0.437331\pi\) | ||||
0.195612 | + | 0.980681i | \(0.437331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.46973i | 0.471721i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.23543 | + | 0.0533841i | −0.111079 | + | 0.00265268i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.88279i | − | 0.489872i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7241 | 1.22253 | 0.611265 | − | 0.791426i | \(-0.290661\pi\) | ||||
0.611265 | + | 0.791426i | \(0.290661\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0580 | −0.841411 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.61158i | − | 0.177714i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.897160 | − | 37.5681i | −0.0440399 | − | 1.84415i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.94806i | − | 0.340248i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.4506 | −0.657105 | −0.328553 | − | 0.944486i | \(-0.606561\pi\) | ||||
−0.328553 | + | 0.944486i | \(0.606561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7666 | −0.524732 | −0.262366 | − | 0.964968i | \(-0.584503\pi\) | ||||
−0.262366 | + | 0.964968i | \(0.584503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.27397i | − | 0.0619424i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20055 | − | 25.1220i | −0.0582355 | − | 1.21859i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.9685i | 2.17618i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.81941 | 0.0878419 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6621 | −0.561746 | −0.280873 | − | 0.959745i | \(-0.590624\pi\) | ||||
−0.280873 | + | 0.959745i | \(0.590624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.61780i | − | 0.269974i | −0.990847 | − | 0.134987i | \(-0.956901\pi\) | ||
0.990847 | − | 0.134987i | \(-0.0430993\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.205558 | + | 8.60766i | 0.00985578 | + | 0.412706i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.68586i | − | 0.463338i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.31288 | 0.205842 | 0.102921 | − | 0.994690i | \(-0.467181\pi\) | ||||
0.102921 | + | 0.994690i | \(0.467181\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.3288 | 0.634703 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.40726i | 0.256907i | 0.991716 | + | 0.128453i | \(0.0410012\pi\) | ||||
−0.991716 | + | 0.128453i | \(0.958999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.6626 | − | 0.875535i | 1.73797 | − | 0.0415044i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.4588i | 0.825775i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.546480 | −0.0257900 | −0.0128950 | − | 0.999917i | \(-0.504105\pi\) | ||||
−0.0128950 | + | 0.999917i | \(0.504105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.62933 | 0.265075 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.90694i | 0.324517i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.8817 | + | 0.450911i | −0.885187 | + | 0.0211390i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7141i | 0.781852i | 0.920422 | + | 0.390926i | \(0.127845\pi\) | ||||
−0.920422 | + | 0.390926i | \(0.872155\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.03013 | 0.234786 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0447 | 0.980151 | 0.490075 | − | 0.871680i | \(-0.336969\pi\) | ||||
0.490075 | + | 0.871680i | \(0.336969\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.1870i | − | 1.40291i | −0.712714 | − | 0.701455i | \(-0.752534\pi\) | ||
0.712714 | − | 0.701455i | \(-0.247466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.269852 | + | 11.2999i | 0.0125141 | + | 0.524021i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.97008i | 0.415086i | 0.978226 | + | 0.207543i | \(0.0665467\pi\) | ||||
−0.978226 | + | 0.207543i | \(0.933453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.50874 | −0.208194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.22557 | −0.425092 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.40242i | − | 0.386344i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.87904 | − | 0.424321i | 0.407398 | − | 0.0194692i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4.85441i | − | 0.222268i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.7966 | 0.995910 | 0.497955 | − | 0.867203i | \(-0.334084\pi\) | ||||
0.497955 | + | 0.867203i | \(0.334084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0633 | 0.869210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.5642i | 1.11771i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.604725 | + | 25.3226i | 0.0274591 | + | 1.14984i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5188i | 0.703222i | 0.936146 | + | 0.351611i | \(0.114366\pi\) | ||||
−0.936146 | + | 0.351611i | \(0.885634\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.2659 | 1.14256 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.9191 | −0.628160 | −0.314080 | − | 0.949397i | \(-0.601696\pi\) | ||||
−0.314080 | + | 0.949397i | \(0.601696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 19.3688i | − | 0.872327i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.17104 | − | 0.0518463i | 0.0975809 | − | 0.00233032i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 55.6148i | 2.49467i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0156 | 0.448359 | 0.224179 | − | 0.974548i | \(-0.428030\pi\) | ||||
0.224179 | + | 0.974548i | \(0.428030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.666796 | 0.0297902 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.95986i | − | 0.0873860i | −0.999045 | − | 0.0436930i | \(-0.986088\pi\) | ||
0.999045 | − | 0.0436930i | \(-0.0139123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.5717 | + | 0.467389i | −0.870929 | + | 0.0207986i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.49048i | − | 0.421487i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.3393 | −0.635579 | −0.317790 | − | 0.948161i | \(-0.602941\pi\) | ||||
−0.317790 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.9129 | −1.94259 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.77783i | 0.0784933i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.159803 | − | 6.69167i | −0.00704176 | − | 0.294870i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.23727i | 0.0544151i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.8775 | 0.740839 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8190 | −0.999717 | −0.499858 | − | 0.866107i | \(-0.666615\pi\) | ||||
−0.499858 | + | 0.866107i | \(0.666615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.43411i | − | 0.106436i | −0.998583 | − | 0.0532182i | \(-0.983052\pi\) | ||
0.998583 | − | 0.0532182i | \(-0.0169479\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.5180 | + | 1.07611i | −0.982767 | + | 0.0469655i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 25.4269i | − | 1.10761i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.68206 | −0.290524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.801017 | −0.0347612 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.8586i | 0.470339i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0981885 | + | 4.11159i | 0.00424506 | + | 0.177760i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.1781i | 1.08651i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.9448 | −0.557573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0605 | 0.475528 | 0.237764 | − | 0.971323i | \(-0.423585\pi\) | ||||
0.237764 | + | 0.971323i | \(0.423585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 4.21845i | − | 0.181031i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.2140 | + | 0.602133i | −1.08005 | + | 0.0257926i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.45735i | − | 0.276096i | −0.990426 | − | 0.138048i | \(-0.955917\pi\) | ||
0.990426 | − | 0.138048i | \(-0.0440829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.97361 | 0.425663 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.84566 | 0.291635 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 25.6242i | − | 1.08965i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.7475 | − | 0.543232i | 0.965580 | − | 0.0230589i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.22074i | 0.263581i | 0.991278 | + | 0.131791i | \(0.0420727\pi\) | ||||
−0.991278 | + | 0.131791i | \(0.957927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2077 | 0.685514 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.88524 | −0.206255 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 0.338641i | − | 0.0142720i | −0.999975 | − | 0.00713601i | \(-0.997729\pi\) | ||
0.999975 | − | 0.00713601i | \(-0.00227148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.648453 | − | 27.1536i | −0.0272806 | − | 1.14236i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.50874i | − | 0.189349i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.4703 | 0.816238 | 0.408119 | − | 0.912929i | \(-0.366185\pi\) | ||||
0.408119 | + | 0.912929i | \(0.366185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.0804 | 1.76101 | 0.880506 | − | 0.474036i | \(-0.157203\pi\) | ||||
0.880506 | + | 0.474036i | \(0.157203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.3167i | 0.806967i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.30032 | − | 27.2096i | −0.0542270 | − | 1.13472i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.7519i | 1.65489i | 0.561545 | + | 0.827446i | \(0.310207\pi\) | ||||
−0.561545 | + | 0.827446i | \(0.689793\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0344 | −0.915720 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 75.7729 | 3.14359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.71458i | 0.195258i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.100008 | + | 4.18779i | 0.00413483 | + | 0.173144i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 35.0378i | − | 1.44616i | −0.690762 | − | 0.723082i | \(-0.742725\pi\) | ||
0.690762 | − | 0.723082i | \(-0.257275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.98680 | 0.370295 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.8537 | 0.981212 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.07946i | − | 0.249653i | −0.992179 | − | 0.124827i | \(-0.960163\pi\) | ||
0.992179 | − | 0.124827i | \(-0.0398375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.6986 | − | 1.21073i | 2.07844 | − | 0.0496350i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.29391i | 0.216665i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.3951 | 1.20105 | 0.600526 | − | 0.799605i | \(-0.294958\pi\) | ||||
0.600526 | + | 0.799605i | \(0.294958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.7322 | 1.49834 | 0.749168 | − | 0.662380i | \(-0.230453\pi\) | ||||
0.749168 | + | 0.662380i | \(0.230453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.4812 | − | 0.536872i | 0.913992 | − | 0.0218269i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.9776i | − | 0.810868i | −0.914124 | − | 0.405434i | \(-0.867120\pi\) | ||
0.914124 | − | 0.405434i | \(-0.132880\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.3612 | −0.703511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.38662 | −0.0965521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8707i | 1.73153i | 0.500449 | + | 0.865766i | \(0.333168\pi\) | ||||
−0.500449 | + | 0.865766i | \(0.666832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.309430 | + | 12.9572i | 0.0124774 | + | 0.522486i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0503i | 0.887713i | 0.896098 | + | 0.443856i | \(0.146390\pi\) | ||||
−0.896098 | + | 0.443856i | \(0.853610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2362 | −1.01433 | −0.507164 | − | 0.861850i | \(-0.669306\pi\) | ||||
−0.507164 | + | 0.861850i | \(0.669306\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.44812 | 0.218626 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 73.9465i | 2.96260i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8861 | − | 2.38401i | 0.995443 | − | 0.0953603i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.72662i | − | 0.0689547i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.1862 | −2.04093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3673 | −1.80604 | −0.903021 | − | 0.429596i | \(-0.858656\pi\) | ||||
−0.903021 | + | 0.429596i | \(0.858656\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 4.36599i | − | 0.173532i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.14865 | − | 48.0991i | −0.0455828 | − | 1.90876i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 24.9697i | − | 0.989337i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.3349 | 0.487960 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.22317 | 0.0878099 | 0.0439050 | − | 0.999036i | \(-0.486020\pi\) | ||||
0.0439050 | + | 0.999036i | \(0.486020\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.2031i | − | 0.441806i | −0.975296 | − | 0.220903i | \(-0.929100\pi\) | ||
0.975296 | − | 0.220903i | \(-0.0709005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.3401 | − | 0.461859i | 0.761517 | − | 0.0181857i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 10.0190i | − | 0.393889i | −0.980415 | − | 0.196944i | \(-0.936898\pi\) | ||
0.980415 | − | 0.196944i | \(-0.0631019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.777943 | 0.0305369 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.7913 | −0.893262 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 36.4424i | − | 1.42610i | −0.701112 | − | 0.713051i | \(-0.747313\pi\) | ||
0.701112 | − | 0.713051i | \(-0.252687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.0894 | + | 1.05289i | −1.72272 | + | 0.0411400i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.73950i | 0.379974i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.19584 | 0.319264 | 0.159632 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159632 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5546 | 0.799480 | 0.399740 | − | 0.916629i | \(-0.369100\pi\) | ||||
0.399740 | + | 0.916629i | \(0.369100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 9.42330i | − | 0.365971i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.427916 | + | 17.9188i | 0.0165939 | + | 0.694860i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.9783i | − | 0.812284i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.00754 | −0.193603 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.68632 | −0.373936 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.667917i | 0.0257463i | 0.999917 | + | 0.0128731i | \(0.00409776\pi\) | ||||
−0.999917 | + | 0.0128731i | \(0.995902\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.238673 | + | 4.99430i | 0.00918652 | + | 0.192231i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.6730i | 0.448628i | 0.974517 | + | 0.224314i | \(0.0720141\pi\) | ||||
−0.974517 | + | 0.224314i | \(0.927986\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −51.0742 | −1.96005 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.3845 | 0.704496 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4.30766i | − | 0.164828i | −0.996598 | − | 0.0824141i | \(-0.973737\pi\) | ||
0.996598 | − | 0.0824141i | \(-0.0262630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.910627 | + | 38.1321i | 0.0347933 | + | 1.45695i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.6317i | 0.939759i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.09412 | −0.346458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.59363 | 0.136708 | 0.0683541 | − | 0.997661i | \(-0.478225\pi\) | ||||
0.0683541 | + | 0.997661i | \(0.478225\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.37887i | 0.166339i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.5319 | + | 0.370916i | −0.589159 | + | 0.0140696i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 29.1561i | − | 1.10437i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.36272 | −0.316307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.93948 | 0.148792 | 0.0743961 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743961 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 18.0911i | − | 0.682318i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.84787 | + | 0.0680096i | −0.107257 | + | 0.00256139i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 39.4750i | − | 1.48461i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.7293 | 0.478057 | 0.239029 | − | 0.971013i | \(-0.423171\pi\) | ||||
0.239029 | + | 0.971013i | \(0.423171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.68322 | −0.213138 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.5398i | − | 1.03137i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0971274 | − | 4.06716i | −0.00363236 | − | 0.152103i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.6245i | 0.844929i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.9125 | −1.60037 | −0.800184 | − | 0.599755i | \(-0.795265\pi\) | ||||
−0.800184 | + | 0.599755i | \(0.795265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4967 | 0.502645 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.5883i | − | 0.616924i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.2308 | − | 0.919023i | 0.714216 | − | 0.0341317i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.4563i | − | 0.795769i | −0.917435 | − | 0.397885i | \(-0.869744\pi\) | ||
0.917435 | − | 0.397885i | \(-0.130256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.5189 | −1.60960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 28.7221i | − | 1.06087i | −0.847724 | − | 0.530437i | \(-0.822028\pi\) | ||
0.847724 | − | 0.530437i | \(-0.177972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.711543 | − | 29.7955i | −0.0262457 | − | 1.09902i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.971195i | − | 0.0357744i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.08106 | −0.334052 | −0.167026 | − | 0.985952i | \(-0.553416\pi\) | ||||
−0.167026 | + | 0.985952i | \(0.553416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.33054 | 0.122351 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.5678i | 1.15811i | 0.815288 | + | 0.579055i | \(0.196579\pi\) | ||||
−0.815288 | + | 0.579055i | \(0.803421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.0280 | − | 0.932024i | 1.42988 | − | 0.0341467i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.8058i | − | 0.614891i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.29286 | −0.303014 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.509836 | 0.0186042 | 0.00930208 | − | 0.999957i | \(-0.497039\pi\) | ||||
0.00930208 | + | 0.999957i | \(0.497039\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 30.0957i | − | 1.09675i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4400 | − | 0.368721i | 0.561919 | − | 0.0134191i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28.3209i | − | 1.02934i | −0.857388 | − | 0.514671i | \(-0.827914\pi\) | ||
0.857388 | − | 0.514671i | \(-0.172086\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.29119 | −0.192058 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.7335 | 1.80284 | 0.901419 | − | 0.432947i | \(-0.142526\pi\) | ||||
0.901419 | + | 0.432947i | \(0.142526\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 50.8553i | − | 1.84109i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.268529 | − | 11.2445i | −0.00970868 | − | 0.406546i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.50060i | 0.0541836i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.9613 | −1.29680 | −0.648398 | − | 0.761301i | \(-0.724561\pi\) | ||||
−0.648398 | + | 0.761301i | \(0.724561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4033 | 0.410680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 17.5692i | − | 0.631919i | −0.948773 | − | 0.315960i | \(-0.897674\pi\) | ||
0.948773 | − | 0.315960i | \(-0.102326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2458 | − | 1.20647i | 0.906854 | − | 0.0433377i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.8806i | 1.64596i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3049 | 0.369210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.9796 | −0.428663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.85056i | 0.137608i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.492499 | + | 20.6231i | 0.0175780 | + | 0.736071i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.129874i | − | 0.00462949i | −0.999997 | − | 0.00231475i | \(-0.999263\pi\) | ||
0.999997 | − | 0.00231475i | \(-0.000736808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9006 | −0.744080 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.7674 | 1.94731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.6843i | − | 0.663498i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.8517 | + | 0.259148i | −0.384870 | + | 0.00919104i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.40948i | 0.120770i | 0.998175 | + | 0.0603850i | \(0.0192328\pi\) | ||||
−0.998175 | + | 0.0603850i | \(0.980767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.40822 | 0.226707 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.4007 | 0.579490 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.45895i | − | 0.333799i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.9115 | − | 1.31134i | 1.93538 | − | 0.0462185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.93394i | 0.244086i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.2513 | −1.34484 | −0.672422 | − | 0.740168i | \(-0.734746\pi\) | ||||
−0.672422 | + | 0.740168i | \(0.734746\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2871 | 1.34444 | 0.672221 | − | 0.740351i | \(-0.265341\pi\) | ||||
0.672221 | + | 0.740351i | \(0.265341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.74661i | 0.0963278i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.34879 | − | 56.4801i | −0.0472462 | − | 1.97841i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.3812i | − | 0.538119i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.44655 | −0.295146 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.6119 | 1.06836 | 0.534182 | − | 0.845370i | \(-0.320620\pi\) | ||||
0.534182 | + | 0.845370i | \(0.320620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.0704i | 1.32705i | 0.748153 | + | 0.663526i | \(0.230941\pi\) | ||||
−0.748153 | + | 0.663526i | \(0.769059\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.231798 | − | 4.85044i | −0.00807016 | − | 0.168871i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.4687i | 0.364033i | 0.983295 | + | 0.182017i | \(0.0582625\pi\) | ||||
−0.983295 | + | 0.182017i | \(0.941738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.1155 | 0.698641 | 0.349321 | − | 0.937003i | \(-0.386412\pi\) | ||||
0.349321 | + | 0.937003i | \(0.386412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.9747 | −0.901053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 67.0454i | 2.32299i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.0355963 | − | 1.49058i | −0.00123186 | − | 0.0515835i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.05491i | 0.174723i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.6037 | 1.29822 | 0.649111 | − | 0.760694i | \(-0.275141\pi\) | ||||
0.649111 | + | 0.760694i | \(0.275141\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1732 | −0.488731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 26.2101i | − | 0.902724i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.2153 | + | 0.506640i | −0.729829 | + | 0.0174290i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45.3434i | 1.55802i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3253 | −0.800521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.4396 | −1.90045 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.2936i | 0.729080i | 0.931188 | + | 0.364540i | \(0.118774\pi\) | ||||
−0.931188 | + | 0.364540i | \(0.881226\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.97422 | − | 0.0949080i | 0.135916 | − | 0.00324579i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 39.2788i | − | 1.34174i | −0.741575 | − | 0.670870i | \(-0.765921\pi\) | ||
0.741575 | − | 0.670870i | \(-0.234079\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4314 | 1.00419 | 0.502094 | − | 0.864813i | \(-0.332563\pi\) | ||||
0.502094 | + | 0.864813i | \(0.332563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.1340 | −0.890645 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1452i | 0.787870i | 0.919138 | + | 0.393935i | \(0.128887\pi\) | ||||
−0.919138 | + | 0.393935i | \(0.871113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.900988 | − | 37.7284i | −0.0306345 | − | 1.28280i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.30221i | 0.281958i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.51952 | 0.187237 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.87337 | 0.0634768 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.3278i | 0.383389i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.60768 | + | 50.2800i | 0.121962 | + | 1.69977i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 35.5897i | − | 1.20178i | −0.799332 | − | 0.600889i | \(-0.794813\pi\) | ||
0.799332 | − | 0.600889i | \(-0.205187\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1915 | −0.579854 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.5078 | 1.39843 | 0.699216 | − | 0.714911i | \(-0.253533\pi\) | ||||
0.699216 | + | 0.714911i | \(0.253533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.7409i | 0.395113i | 0.980291 | + | 0.197557i | \(0.0633006\pi\) | ||||
−0.980291 | + | 0.197557i | \(0.936699\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0427615 | + | 1.79062i | 0.00143741 | + | 0.0601909i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.61930i | 0.222254i | 0.993806 | + | 0.111127i | \(0.0354461\pi\) | ||||
−0.993806 | + | 0.111127i | \(0.964554\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 97.0134 | 3.25372 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.971195 | 0.0325362 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.26490i | 0.0757921i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.2838 | − | 1.34411i | 1.88136 | − | 0.0449286i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 10.2064i | − | 0.340781i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.4642 | 0.649169 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.4183 | 0.813492 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 39.0080i | 1.29810i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.43004 | + | 0.225198i | −0.313465 | + | 0.00748583i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.2030i | 1.60055i | 0.599631 | + | 0.800276i | \(0.295314\pi\) | ||||
−0.599631 | + | 0.800276i | \(0.704686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.75522 | −0.290392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0787 | 0.499580 | 0.249790 | − | 0.968300i | \(-0.419638\pi\) | ||||
0.249790 | + | 0.968300i | \(0.419638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3217i | 0.540169i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.532432 | − | 22.2953i | −0.0176017 | − | 0.737060i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 88.9260i | − | 2.93659i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4880 | −0.906747 | −0.453374 | − | 0.891321i | \(-0.649780\pi\) | ||||
−0.453374 | + | 0.891321i | \(0.649780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2599 | −0.667585 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 23.1078i | − | 0.760603i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.42871 | − | 50.8216i | −0.0798556 | − | 1.67100i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.99346i | − | 0.0983181i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.8975 | 0.587200 | 0.293600 | − | 0.955928i | \(-0.405147\pi\) | ||||
0.293600 | + | 0.955928i | \(0.405147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.6963 | −0.776616 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1037i | 0.363518i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.260794 | + | 10.9206i | 0.00852887 | + | 0.357142i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33.2302i | − | 1.08558i | −0.839868 | − | 0.542791i | \(-0.817368\pi\) | ||
0.839868 | − | 0.542791i | \(-0.182632\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.11630 | 0.0364289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.94439 | 0.0959843 | 0.0479921 | − | 0.998848i | \(-0.484718\pi\) | ||||
0.0479921 | + | 0.998848i | \(0.484718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31.5789i | − | 1.02835i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.0790 | + | 0.240695i | −0.327869 | + | 0.00782981i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.65790i | − | 0.151362i | −0.997132 | − | 0.0756808i | \(-0.975887\pi\) | ||
0.997132 | − | 0.0756808i | \(-0.0241130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.2457 | 0.592280 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.89619 | 0.0939154 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.5089i | 1.50657i | 0.657694 | + | 0.753285i | \(0.271532\pi\) | ||||
−0.657694 | + | 0.753285i | \(0.728468\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.1812 | − | 1.03120i | 1.39731 | − | 0.0333690i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.73964i | − | 0.120885i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −76.9103 | −2.48356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.44785 | −0.175737 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.83928i | 0.0592701i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.17629 | + | 49.2564i | 0.0378660 | + | 1.58562i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.2301i | 1.45450i | 0.686371 | + | 0.727251i | \(0.259203\pi\) | ||||
−0.686371 | + | 0.727251i | \(0.740797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.94274 | −0.287282 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.66050 | 0.0853796 | 0.0426898 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426898 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 31.3270i | − | 1.00430i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.35618 | − | 0.447123i | 0.299638 | − | 0.0143194i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 18.8779i | − | 0.603959i | −0.953314 | − | 0.301980i | \(-0.902353\pi\) | ||
0.953314 | − | 0.301980i | \(-0.0976474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9283 | −0.509070 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.2793 | −0.360120 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 22.8392i | − | 0.728458i | −0.931309 | − | 0.364229i | \(-0.881333\pi\) | ||
0.931309 | − | 0.364229i | \(-0.118667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.27341 | − | 53.3234i | −0.0405742 | − | 1.69902i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 5.74399i | − | 0.182833i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.1352 | −1.49881 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.1334 | −0.385431 | −0.192716 | − | 0.981255i | \(-0.561729\pi\) | ||||
−0.192716 | + | 0.981255i | \(0.561729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15.0647i | − | 0.478062i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8342 | − | 0.282611i | 0.375169 | − | 0.00895936i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 24.9901i | − | 0.791443i | −0.918371 | − | 0.395722i | \(-0.870495\pi\) | ||
0.918371 | − | 0.395722i | \(-0.129505\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.1759 | 0.321952 |
(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 | 4020.2.g.c.1609.1 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.20 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.1 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.20 | yes | 38 | 5.4 | even | 2 | inner |