Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(49,1900)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 17x^{14} + 215x^{12} - 1176x^{10} + 4775x^{8} - 2898x^{6} + 1385x^{4} - 164x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.7 | ||
Root | \(2.18309 - 1.26041i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.49 |
Dual form | 1900.2.s.d.349.7 |
$q$-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 | ||||||||
\(3\) | 2.18309 | + | 1.26041i | 1.26041 | + | 0.727698i | 0.973154 | − | 0.230156i | \(-0.0739236\pi\) |
0.287256 | + | 0.957854i | \(0.407257\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.72743i | − | 1.03087i | −0.856928 | − | 0.515435i | \(-0.827630\pi\) | ||
0.856928 | − | 0.515435i | \(-0.172370\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.67727 | + | 2.90511i | 0.559089 | + | 0.968370i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31421 | 0.999273 | 0.499636 | − | 0.866235i | \(-0.333467\pi\) | ||||
0.499636 | + | 0.866235i | \(0.333467\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81306 | − | 1.62412i | 0.780204 | − | 0.450451i | −0.0562987 | − | 0.998414i | \(-0.517930\pi\) |
0.836502 | + | 0.547963i | \(0.184597\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.03909 | − | 1.17727i | −0.494551 | − | 0.285529i | 0.231910 | − | 0.972737i | \(-0.425503\pi\) |
−0.726460 | + | 0.687208i | \(0.758836\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11494 | − | 3.04912i | 0.714617 | − | 0.699516i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.43768 | − | 5.95423i | 0.750163 | − | 1.29932i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.86016 | − | 1.07396i | 0.387870 | − | 0.223937i | −0.293367 | − | 0.956000i | \(-0.594776\pi\) |
0.681237 | + | 0.732063i | \(0.261442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.893714i | 0.171995i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.96702 | − | 3.40697i | −0.365266 | − | 0.632659i | 0.623553 | − | 0.781781i | \(-0.285689\pi\) |
−0.988819 | + | 0.149122i | \(0.952355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1896 | −1.83010 | −0.915050 | − | 0.403340i | \(-0.867849\pi\) | ||||
−0.915050 | + | 0.403340i | \(0.867849\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.23524 | + | 4.17727i | 1.25949 | + | 0.727169i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.68579i | 0.605940i | 0.953000 | + | 0.302970i | \(0.0979782\pi\) | ||||
−0.953000 | + | 0.302970i | \(0.902022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.18825 | 1.31117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.363714 | − | 0.629971i | 0.0568025 | − | 0.0983849i | −0.836226 | − | 0.548385i | \(-0.815243\pi\) |
0.893028 | + | 0.450000i | \(0.148576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.05499 | + | 1.18645i | 0.313383 | + | 0.180931i | 0.648439 | − | 0.761267i | \(-0.275422\pi\) |
−0.335057 | + | 0.942198i | \(0.608755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.54644 | − | 5.51164i | 1.39249 | − | 0.803955i | 0.398901 | − | 0.916994i | \(-0.369392\pi\) |
0.993591 | + | 0.113039i | \(0.0360585\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438860 | −0.0626942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.96768 | − | 5.14017i | −0.415558 | − | 0.719767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.77947 | + | 4.49148i | −1.06859 | + | 0.616952i | −0.927797 | − | 0.373087i | \(-0.878299\pi\) |
−0.140796 | + | 0.990039i | \(0.544966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.6434 | − | 2.73041i | 1.40975 | − | 0.361652i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.48784 | + | 9.50521i | −0.714456 | + | 1.23747i | 0.248714 | + | 0.968577i | \(0.419992\pi\) |
−0.963169 | + | 0.268896i | \(0.913341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.22743 | + | 7.32212i | 0.541267 | + | 0.937501i | 0.998832 | + | 0.0483251i | \(0.0153884\pi\) |
−0.457565 | + | 0.889176i | \(0.651278\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.92348 | − | 4.57462i | 0.998264 | − | 0.576348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.44436 | − | 4.87535i | 1.03164 | − | 0.595619i | 0.114188 | − | 0.993459i | \(-0.463573\pi\) |
0.917455 | + | 0.397840i | \(0.130240\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.41453 | 0.651833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.45850 | + | 5.99029i | −0.410448 | + | 0.710917i | −0.994939 | − | 0.100484i | \(-0.967961\pi\) |
0.584491 | + | 0.811400i | \(0.301294\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.14818 | + | 1.24025i | 0.251425 | + | 0.145160i | 0.620417 | − | 0.784272i | \(-0.286964\pi\) |
−0.368992 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9.03927i | − | 1.03012i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.99948 | − | 10.3914i | 0.674994 | − | 1.16912i | −0.301477 | − | 0.953474i | \(-0.597480\pi\) |
0.976471 | − | 0.215650i | \(-0.0691871\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.90535 | − | 6.76427i | 0.433928 | − | 0.751586i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.68711i | 0.514477i | 0.966348 | + | 0.257238i | \(0.0828126\pi\) | ||||
−0.966348 | + | 0.257238i | \(0.917187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 9.91699i | − | 1.06321i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.27205 | + | 7.39941i | 0.452836 | + | 0.784336i | 0.998561 | − | 0.0536291i | \(-0.0170789\pi\) |
−0.545725 | + | 0.837965i | \(0.683746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.42968 | − | 7.67243i | −0.464357 | − | 0.804289i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.2448 | − | 12.8430i | −2.30668 | − | 1.33176i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.26127 | + | 3.61494i | 0.635735 | + | 0.367042i | 0.782970 | − | 0.622060i | \(-0.213704\pi\) |
−0.147235 | + | 0.989102i | \(0.547037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.55882 | + | 9.62816i | 0.558682 | + | 0.967666i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.88818 | + | 5.00247i | 0.287384 | + | 0.497764i | 0.973185 | − | 0.230026i | \(-0.0738810\pi\) |
−0.685800 | + | 0.727790i | \(0.740548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.0576i | − | 1.48367i | −0.670581 | − | 0.741836i | \(-0.733955\pi\) | ||
0.670581 | − | 0.741836i | \(-0.266045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1896i | 1.46843i | 0.678917 | + | 0.734215i | \(0.262450\pi\) | ||||
−0.678917 | + | 0.734215i | \(0.737550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31057 | + | 10.9302i | −0.604443 | + | 1.04693i | 0.387696 | + | 0.921787i | \(0.373271\pi\) |
−0.992139 | + | 0.125139i | \(0.960062\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.64560 | + | 8.04642i | −0.440941 | + | 0.763732i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.10761i | − | 0.574555i | −0.957847 | − | 0.287278i | \(-0.907250\pi\) | ||
0.957847 | − | 0.287278i | \(-0.0927502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.43652 | + | 5.44818i | 0.872406 | + | 0.503684i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.21091 | + | 5.56146i | −0.294344 | + | 0.509818i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0159950 | −0.00145409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.58804 | − | 0.916857i | 0.143189 | − | 0.0826702i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.90013 | − | 4.56114i | 0.701023 | − | 0.404736i | −0.106705 | − | 0.994291i | \(-0.534030\pi\) |
0.807728 | + | 0.589555i | \(0.200697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.99082 | + | 5.18025i | 0.263327 | + | 0.456096i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1328 | + | 19.2825i | −0.972676 | + | 1.68472i | −0.285274 | + | 0.958446i | \(0.592085\pi\) |
−0.687402 | + | 0.726277i | \(0.741249\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.31625 | − | 8.49578i | −0.721110 | − | 0.736678i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.60527 | − | 3.81355i | 0.564326 | − | 0.325814i | −0.190554 | − | 0.981677i | \(-0.561028\pi\) |
0.754880 | + | 0.655863i | \(0.227695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.45916 | + | 14.6517i | 0.717496 | + | 1.24274i | 0.961989 | + | 0.273089i | \(0.0880453\pi\) |
−0.244493 | + | 0.969651i | \(0.578621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.7877 | 2.34015 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.32309 | − | 5.38269i | 0.779636 | − | 0.450123i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.958072 | − | 0.553143i | −0.0790204 | − | 0.0456225i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.19809 | + | 10.7354i | −0.507767 | + | 0.879478i | 0.492193 | + | 0.870486i | \(0.336196\pi\) |
−0.999960 | + | 0.00899193i | \(0.997138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4549 | −1.17632 | −0.588160 | − | 0.808745i | \(-0.700147\pi\) | ||||
−0.588160 | + | 0.808745i | \(0.700147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 7.89836i | − | 0.638544i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.7728 | − | 9.10642i | −1.25881 | − | 0.726772i | −0.285963 | − | 0.958241i | \(-0.592313\pi\) |
−0.972842 | + | 0.231469i | \(0.925647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.6444 | −1.79582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.92916 | − | 5.07345i | −0.230850 | − | 0.399844i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2642i | 1.50889i | 0.656362 | + | 0.754446i | \(0.272094\pi\) | ||||
−0.656362 | + | 0.754446i | \(0.727906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.92404 | + | 2.84289i | −0.381033 | + | 0.219990i | −0.678268 | − | 0.734815i | \(-0.737269\pi\) |
0.297234 | + | 0.954805i | \(0.403936\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.22445 | + | 2.12080i | −0.0941881 | + | 0.163139i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.0826 | + | 3.93507i | 1.07692 | + | 0.300922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.92864 | + | 4.57760i | 0.602804 | + | 0.348029i | 0.770144 | − | 0.637870i | \(-0.220184\pi\) |
−0.167340 | + | 0.985899i | \(0.553518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.9609 | + | 13.8338i | −1.80101 | + | 1.03982i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1810 | −0.910448 | −0.455224 | − | 0.890377i | \(-0.650441\pi\) | ||||
−0.455224 | + | 0.890377i | \(0.650441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.70608 | − | 13.3473i | −0.572789 | − | 0.992099i | −0.996278 | − | 0.0861980i | \(-0.972528\pi\) |
0.423489 | − | 0.905901i | \(-0.360805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3132i | 1.57551i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.75796 | − | 3.90171i | −0.494191 | − | 0.285321i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43754 | 0.177305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2482 | −1.17568 | −0.587841 | − | 0.808977i | \(-0.700022\pi\) | ||||
−0.587841 | + | 0.808977i | \(0.700022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.737011 | − | 0.425514i | −0.0530512 | − | 0.0306292i | 0.473240 | − | 0.880934i | \(-0.343084\pi\) |
−0.526291 | + | 0.850305i | \(0.676418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.9843i | − | 1.42382i | −0.702270 | − | 0.711910i | \(-0.747830\pi\) | ||
0.702270 | − | 0.711910i | \(-0.252170\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.22861 | − | 5.59212i | −0.228870 | − | 0.396415i | 0.728603 | − | 0.684936i | \(-0.240170\pi\) |
−0.957474 | + | 0.288521i | \(0.906836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5798 | 1.73372 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.29227 | + | 5.36490i | −0.652190 | + | 0.376542i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.23996 | + | 3.60264i | 0.433707 | + | 0.250401i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3236 | − | 10.1054i | 0.714097 | − | 0.699007i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.27205 | + | 9.13146i | −0.362943 | + | 0.628635i | −0.988444 | − | 0.151588i | \(-0.951561\pi\) |
0.625501 | + | 0.780223i | \(0.284895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.1004 | + | 8.71825i | −1.03467 | + | 0.597364i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.7913i | 1.88660i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.12645 | + | 5.41516i | 0.211266 | + | 0.365923i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.64811 | −0.514467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.42329 | − | 4.86319i | −0.564065 | − | 0.325663i | 0.190710 | − | 0.981646i | \(-0.438921\pi\) |
−0.754776 | + | 0.655983i | \(0.772254\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 22.5798i | − | 1.49867i | −0.662190 | − | 0.749336i | \(-0.730373\pi\) | ||
0.662190 | − | 0.749336i | \(-0.269627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2239 | 1.07211 | 0.536053 | − | 0.844184i | \(-0.319915\pi\) | ||||
0.536053 | + | 0.844184i | \(0.319915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3932 | − | 19.7336i | 0.749617 | − | 1.29837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1624 | + | 9.33139i | 1.05884 | + | 0.611320i | 0.925110 | − | 0.379699i | \(-0.123972\pi\) |
0.133727 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.1948 | − | 15.1236i | 1.70154 | − | 0.982383i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.602780 | −0.0389906 | −0.0194953 | − | 0.999810i | \(-0.506206\pi\) | ||||
−0.0194953 | + | 0.999810i | \(0.506206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.9408 | − | 18.9500i | −0.704759 | − | 1.22068i | −0.966779 | − | 0.255615i | \(-0.917722\pi\) |
0.262020 | − | 0.965062i | \(-0.415611\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.3734 | − | 11.1853i | 1.24281 | − | 0.717535i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.81039 | − | 13.6364i | 0.242449 | − | 0.867665i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.90768 | + | 10.2324i | −0.374384 | + | 0.648452i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.13629 | − | 7.16426i | −0.261080 | − | 0.452204i | 0.705449 | − | 0.708761i | \(-0.250745\pi\) |
−0.966529 | + | 0.256557i | \(0.917412\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.16496 | − | 3.55934i | 0.387588 | − | 0.223774i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.2897 | + | 7.09544i | −0.766608 | + | 0.442602i | −0.831663 | − | 0.555280i | \(-0.812611\pi\) |
0.0650550 | + | 0.997882i | \(0.479278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0527 | 0.624645 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.59842 | − | 11.4288i | 0.408432 | − | 0.707425i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0588 | + | 9.27153i | 0.990225 | + | 0.571707i | 0.905342 | − | 0.424684i | \(-0.139615\pi\) |
0.0848836 | + | 0.996391i | \(0.472948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.5381i | 1.31811i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.33371 | − | 5.77416i | 0.203260 | − | 0.352057i | −0.746317 | − | 0.665591i | \(-0.768180\pi\) |
0.949577 | + | 0.313534i | \(0.101513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0331 | + | 19.1099i | −0.670214 | + | 1.16085i | 0.307629 | + | 0.951506i | \(0.400464\pi\) |
−0.977843 | + | 0.209339i | \(0.932869\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 22.3328i | − | 1.35165i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4624i | 1.46980i | 0.678173 | + | 0.734902i | \(0.262772\pi\) | ||||
−0.678173 | + | 0.734902i | \(0.737228\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.0906 | − | 29.6018i | −1.02319 | − | 1.77221i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.33139 | − | 16.1624i | −0.556664 | − | 0.964170i | −0.997772 | − | 0.0667164i | \(-0.978748\pi\) |
0.441108 | − | 0.897454i | \(-0.354586\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.89384 | − | 2.24811i | −0.231465 | − | 0.133636i | 0.379783 | − | 0.925076i | \(-0.375999\pi\) |
−0.611248 | + | 0.791439i | \(0.709332\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.71820 | − | 0.992002i | −0.101422 | − | 0.0585561i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.72809 | − | 9.92134i | −0.336946 | − | 0.583608i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.11262 | + | 15.7835i | 0.534191 | + | 0.925246i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.27021i | 0.0742063i | 0.999311 | + | 0.0371031i | \(0.0118130\pi\) | ||||
−0.999311 | + | 0.0371031i | \(0.988187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.96196i | 0.171870i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.48850 | − | 6.04225i | 0.201745 | − | 0.349433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.23595 | − | 5.60483i | 0.186517 | − | 0.323057i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.5611i | 0.836516i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.49350 | − | 4.32638i | −0.427677 | − | 0.246919i | 0.270680 | − | 0.962669i | \(-0.412752\pi\) |
−0.698356 | + | 0.715750i | \(0.746085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9788 | − | 32.8722i | 1.07967 | − | 1.87004i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8497 | 1.35239 | 0.676196 | − | 0.736721i | \(-0.263627\pi\) | ||||
0.676196 | + | 0.736721i | \(0.263627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.672340 | + | 0.388175i | −0.0380029 | + | 0.0219410i | −0.518881 | − | 0.854846i | \(-0.673651\pi\) |
0.480878 | + | 0.876787i | \(0.340318\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9878 | − | 6.92116i | 0.673302 | − | 0.388731i | −0.124025 | − | 0.992279i | \(-0.539580\pi\) |
0.797327 | + | 0.603548i | \(0.206247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.51911 | − | 11.2914i | −0.365000 | − | 0.632199i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.1451 | + | 33.1603i | −1.06857 | + | 1.85082i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.94126 | + | 2.55030i | −0.553147 | + | 0.141902i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.5531 | + | 15.9078i | −1.52369 | + | 0.879704i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0326 | − | 26.0372i | −0.828774 | − | 1.43548i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6993 | 1.57746 | 0.788728 | − | 0.614742i | \(-0.210740\pi\) | ||||
0.788728 | + | 0.614742i | \(0.210740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.7076 | + | 6.18205i | −0.586774 | + | 0.338774i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.5928 | − | 17.6628i | −1.66650 | − | 0.962153i | −0.969504 | − | 0.245076i | \(-0.921187\pi\) |
−0.696994 | − | 0.717077i | \(-0.745480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.69809 | − | 13.3335i | 0.418103 | − | 0.724175i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.7704 | −1.82877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.8950i | − | 0.966241i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.5221 | + | 13.0031i | 1.20905 | + | 0.698044i | 0.962551 | − | 0.271100i | \(-0.0873873\pi\) |
0.246496 | + | 0.969144i | \(0.420721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.44757 | −0.131015 | −0.0655077 | − | 0.997852i | \(-0.520867\pi\) | ||||
−0.0655077 | + | 0.997852i | \(0.520867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45150 | + | 2.51408i | 0.0774755 | + | 0.134191i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.85103i | − | 0.258194i | −0.991632 | − | 0.129097i | \(-0.958792\pi\) | ||
0.991632 | − | 0.129097i | \(-0.0412079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.0194 | + | 8.09412i | −0.741987 | + | 0.428386i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.67376 | + | 6.36314i | −0.193894 | + | 0.335834i | −0.946537 | − | 0.322594i | \(-0.895445\pi\) |
0.752644 | + | 0.658428i | \(0.228778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.405741 | − | 18.9957i | 0.0213548 | − | 0.999772i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0349186 | − | 0.0201603i | −0.00183275 | − | 0.00105814i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.2892 | + | 6.51784i | −0.589293 | + | 0.340228i | −0.764818 | − | 0.644247i | \(-0.777171\pi\) |
0.175525 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.44018 | 0.127031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2502 | + | 21.2179i | 0.635998 | + | 1.10158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 28.5514i | − | 1.47833i | −0.673522 | − | 0.739167i | \(-0.735219\pi\) | ||
0.673522 | − | 0.739167i | \(-0.264781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.0667 | − | 6.38936i | −0.569964 | − | 0.329069i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2128 | −0.678698 | −0.339349 | − | 0.940661i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940661i | \(0.610207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.9956 | 1.17810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.6160 | + | 18.8309i | 1.66660 | + | 0.962212i | 0.969450 | + | 0.245287i | \(0.0788823\pi\) |
0.697150 | + | 0.716925i | \(0.254451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.95995i | 0.404627i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8223 | − | 22.2090i | −0.650119 | − | 1.12604i | −0.983094 | − | 0.183103i | \(-0.941386\pi\) |
0.332975 | − | 0.942936i | \(-0.391948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.05736 | −0.255762 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48.6078 | + | 28.0637i | −2.45194 | + | 1.41563i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8154 | − | 16.6366i | −1.44620 | − | 0.834965i | −0.447949 | − | 0.894059i | \(-0.647845\pi\) |
−0.998252 | + | 0.0590940i | \(0.981179\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.44699 | − | 29.0290i | −0.372816 | − | 1.45327i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.70674 | + | 8.15232i | −0.235044 | + | 0.407107i | −0.959285 | − | 0.282439i | \(-0.908857\pi\) |
0.724242 | + | 0.689546i | \(0.242190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.6639 | + | 16.5491i | −1.42785 | + | 0.824370i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2155i | 0.605499i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.25545 | − | 2.17450i | −0.0620779 | − | 0.107522i | 0.833316 | − | 0.552797i | \(-0.186439\pi\) |
−0.895394 | + | 0.445275i | \(0.853106\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.2266 | 0.948376 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.9248 | + | 14.9677i | 1.27567 | + | 0.736511i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.6480i | 2.08848i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.5638 | 1.93282 | 0.966409 | − | 0.257011i | \(-0.0827376\pi\) | ||||
0.966409 | + | 0.257011i | \(0.0827376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.07892 | − | 12.2611i | 0.345006 | − | 0.597567i | −0.640349 | − | 0.768084i | \(-0.721210\pi\) |
0.985355 | + | 0.170517i | \(0.0545437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 32.0238 | + | 18.4890i | 1.55705 | + | 0.898965i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.9705 | − | 11.5300i | 0.966442 | − | 0.557976i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.1376 | 1.31022 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.26287 | + | 5.65145i | 0.157167 | + | 0.272221i | 0.933846 | − | 0.357676i | \(-0.116431\pi\) |
−0.776679 | + | 0.629897i | \(0.783097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.44908 | + | 4.30073i | −0.357980 | + | 0.206680i | −0.668194 | − | 0.743987i | \(-0.732933\pi\) |
0.310214 | + | 0.950667i | \(0.399599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.51965 | − | 9.01718i | 0.120531 | − | 0.431350i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.77939 | + | 10.0102i | −0.275835 | + | 0.477760i | −0.970345 | − | 0.241722i | \(-0.922288\pi\) |
0.694510 | + | 0.719483i | \(0.255621\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.736084 | − | 1.27494i | −0.0350516 | − | 0.0607112i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.86626 | + | 5.69629i | −0.468760 | + | 0.270639i | −0.715721 | − | 0.698387i | \(-0.753902\pi\) |
0.246960 | + | 0.969026i | \(0.420568\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.0620 | + | 15.6243i | −1.27999 | + | 0.739002i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2252 | −0.812909 | −0.406455 | − | 0.913671i | \(-0.633235\pi\) | ||||
−0.406455 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20542 | − | 2.08786i | 0.0567612 | − | 0.0983133i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.5563 | − | 18.2190i | −1.48264 | − | 0.856005i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1885i | 1.22505i | 0.790452 | + | 0.612524i | \(0.209846\pi\) | ||||
−0.790452 | + | 0.612524i | \(0.790154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.05214 | − | 1.82236i | 0.0491097 | − | 0.0850605i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2166 | + | 35.0162i | −0.941580 | + | 1.63086i | −0.179122 | + | 0.983827i | \(0.557326\pi\) |
−0.762458 | + | 0.647038i | \(0.776008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.48542i | 0.440825i | 0.975407 | + | 0.220412i | \(0.0707403\pi\) | ||||
−0.975407 | + | 0.220412i | \(0.929260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.2462i | 1.81610i | 0.418867 | + | 0.908048i | \(0.362427\pi\) | ||||
−0.418867 | + | 0.908048i | \(0.637573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2972 | − | 23.0314i | −0.614006 | − | 1.06349i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.9557 | − | 39.7604i | −1.05774 | − | 1.83206i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.81066 | + | 3.93214i | 0.313155 | + | 0.180800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.0965 | − | 15.0668i | −1.19488 | − | 0.689862i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.72677 | + | 4.72290i | 0.124589 | + | 0.215795i | 0.921572 | − | 0.388207i | \(-0.126905\pi\) |
−0.796983 | + | 0.604002i | \(0.793572\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.98617 | + | 10.3684i | 0.272946 | + | 0.472756i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 14.7677i | − | 0.671956i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.0662i | − | 1.13586i | −0.823077 | − | 0.567930i | \(-0.807744\pi\) | ||
0.823077 | − | 0.567930i | \(-0.192256\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.2808 | + | 42.0557i | −1.09802 | + | 1.90182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8412 | + | 25.7057i | −0.669773 | + | 1.16008i | 0.308194 | + | 0.951324i | \(0.400275\pi\) |
−0.977967 | + | 0.208758i | \(0.933058\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.26281i | 0.417176i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.3381 | + | 9.43280i | 0.732863 | + | 0.423119i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.85519 | + | 11.8735i | −0.306881 | + | 0.531533i | −0.977678 | − | 0.210108i | \(-0.932619\pi\) |
0.670798 | + | 0.741640i | \(0.265952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3328 | −0.640344 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7404 | − | 18.3253i | 1.41523 | − | 0.817086i | 0.419359 | − | 0.907820i | \(-0.362255\pi\) |
0.995875 | + | 0.0907343i | \(0.0289214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.34616 | + | 3.08661i | −0.237431 | + | 0.137081i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.32519 | − | 10.9556i | −0.280359 | − | 0.485596i | 0.691114 | − | 0.722746i | \(-0.257120\pi\) |
−0.971473 | + | 0.237149i | \(0.923787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.38269 | − | 5.85899i | 0.149641 | − | 0.259187i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.72504 | + | 2.78387i | 0.120314 | + | 0.122911i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.6389 | − | 18.2667i | 1.39148 | − | 0.803371i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.5393 | + | 19.9867i | 0.506520 | + | 0.877318i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3339 | 0.715601 | 0.357800 | − | 0.933798i | \(-0.383527\pi\) | ||||
0.357800 | + | 0.933798i | \(0.383527\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.91086 | + | 4.56734i | −0.345918 | + | 0.199716i | −0.662886 | − | 0.748720i | \(-0.730669\pi\) |
0.316968 | + | 0.948436i | \(0.397335\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7774 | + | 11.9958i | 0.905078 | + | 0.522547i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.19321 | + | 15.9231i | −0.399705 | + | 0.692309i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.8183 | −1.59778 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.36286i | − | 0.102347i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.5922 | − | 15.3530i | −1.14754 | − | 0.662531i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.45447 | −0.0626486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.45954 | + | 2.52800i | 0.0627507 | + | 0.108687i | 0.895694 | − | 0.444671i | \(-0.146679\pi\) |
−0.832943 | + | 0.553358i | \(0.813346\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 38.8513i | − | 1.66727i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.01329 | − | 1.73973i | 0.128839 | − | 0.0743853i | −0.434195 | − | 0.900819i | \(-0.642967\pi\) |
0.563034 | + | 0.826433i | \(0.309634\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.1810 | + | 24.5623i | −0.605232 | + | 1.04829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5154 | − | 4.61486i | −0.703580 | − | 0.196600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.3418 | − | 16.3631i | −1.20522 | − | 0.695831i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7920 | + | 7.96280i | −0.584385 | + | 0.337395i | −0.762874 | − | 0.646547i | \(-0.776212\pi\) |
0.178489 | + | 0.983942i | \(0.442879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.70775 | 0.326003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.83551 | − | 17.0356i | −0.415256 | − | 0.719244i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.6274i | 0.827195i | 0.910460 | + | 0.413598i | \(0.135728\pi\) | ||||
−0.910460 | + | 0.413598i | \(0.864272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.4491 | − | 10.6516i | −0.774788 | − | 0.447324i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7544 | 0.492770 | 0.246385 | − | 0.969172i | \(-0.420757\pi\) | ||||
0.246385 | + | 0.969172i | \(0.420757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4868 | 1.35953 | 0.679766 | − | 0.733429i | \(-0.262081\pi\) | ||||
0.679766 | + | 0.733429i | \(0.262081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.4715 | − | 20.4795i | −1.48184 | − | 0.855541i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.7287i | − | 1.07110i | −0.844503 | − | 0.535551i | \(-0.820104\pi\) | ||
0.844503 | − | 0.535551i | \(-0.179896\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.07264 | − | 1.85787i | −0.0445775 | − | 0.0772106i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7837 | 0.530359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.7828 | + | 14.8857i | −1.06782 | + | 0.616503i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.0750 | − | 20.8279i | −1.48897 | − | 0.859659i | −0.489052 | − | 0.872255i | \(-0.662657\pi\) |
−0.999921 | + | 0.0125958i | \(0.995991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.7399 | + | 31.0692i | −1.30782 | + | 1.28018i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.1884 | − | 43.6276i | 1.03611 | − | 1.79460i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.2986 | − | 8.83267i | 0.628239 | − | 0.362714i | −0.151831 | − | 0.988407i | \(-0.548517\pi\) |
0.780070 | + | 0.625692i | \(0.215183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 16.2775i | − | 0.666193i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.1925 | − | 22.8502i | −0.539033 | − | 0.933632i | −0.998956 | − | 0.0456738i | \(-0.985457\pi\) |
0.459924 | − | 0.887959i | \(-0.347877\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.46838 | 0.386223 | 0.193112 | − | 0.981177i | \(-0.438142\pi\) | ||||
0.193112 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.3269 | + | 16.3545i | 1.15356 | + | 0.666008i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.26529i | 0.335478i | 0.985831 | + | 0.167739i | \(0.0536465\pi\) | ||||
−0.985831 | + | 0.167739i | \(0.946353\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.0479 | −1.09604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.9032 | − | 31.0092i | 0.724285 | − | 1.25450i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.89620 | − | 3.40417i | −0.238145 | − | 0.137493i | 0.376179 | − | 0.926547i | \(-0.377238\pi\) |
−0.614324 | + | 0.789054i | \(0.710571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.20772 | + | 3.00668i | −0.209655 | + | 0.121044i | −0.601151 | − | 0.799135i | \(-0.705291\pi\) |
0.391496 | + | 0.920180i | \(0.371958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.2299 | −0.531754 | −0.265877 | − | 0.964007i | \(-0.585662\pi\) | ||||
−0.265877 | + | 0.964007i | \(0.585662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.959816 | + | 1.66245i | 0.0385161 | + | 0.0667118i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.1813 | − | 11.6517i | 0.808548 | − | 0.466816i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.2743 | − | 9.04916i | 1.40872 | − | 0.361389i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.33915 | − | 7.51564i | 0.173013 | − | 0.299668i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8932 | + | 20.5996i | 0.473460 | + | 0.820058i | 0.999538 | − | 0.0303788i | \(-0.00967135\pi\) |
−0.526078 | + | 0.850436i | \(0.676338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.0188 | + | 13.2899i | −0.914914 | + | 0.528226i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23454 | + | 0.712762i | −0.0489143 | + | 0.0282407i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.2033 | −0.917908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.14239 | + | 10.6389i | −0.242610 | + | 0.420212i | −0.961457 | − | 0.274956i | \(-0.911337\pi\) |
0.718847 | + | 0.695168i | \(0.244670\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2492 | − | 14.5776i | −0.995729 | − | 0.574885i | −0.0887474 | − | 0.996054i | \(-0.528286\pi\) |
−0.906982 | + | 0.421170i | \(0.861620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.7499i | 1.44479i | 0.691481 | + | 0.722394i | \(0.256958\pi\) | ||||
−0.691481 | + | 0.722394i | \(0.743042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.1879 | + | 31.5023i | −0.713936 | + | 1.23657i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.0284 | + | 60.6710i | −1.37287 | + | 2.37788i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7707i | 0.969351i | 0.874694 | + | 0.484675i | \(0.161062\pi\) | ||||
−0.874694 | + | 0.484675i | \(0.838938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.32092i | 0.324630i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1156 | + | 19.2528i | 0.433002 | + | 0.749982i | 0.997130 | − | 0.0757053i | \(-0.0241208\pi\) |
−0.564128 | + | 0.825687i | \(0.690787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4684 | − | 35.4524i | −0.796130 | − | 1.37894i | −0.922119 | − | 0.386905i | \(-0.873544\pi\) |
0.125990 | − | 0.992032i | \(-0.459789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.6965 | − | 9.63975i | −0.648440 | − | 0.374377i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.31793 | − | 4.22501i | −0.283351 | − | 0.163593i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2592 | − | 21.2336i | −0.473969 | − | 0.820939i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0106 | + | 24.2671i | 0.540873 | + | 0.936819i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 33.5992i | − | 1.29515i | −0.762000 | − | 0.647577i | \(-0.775783\pi\) | ||
0.762000 | − | 0.647577i | \(-0.224217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 29.5883i | − | 1.13717i | −0.822624 | − | 0.568585i | \(-0.807491\pi\) | ||
0.822624 | − | 0.568585i | \(-0.192509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.85949 | − | 17.0771i | 0.378373 | − | 0.655361i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4598 | − | 49.2938i | 1.09058 | − | 1.88894i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.0567i | 1.57099i | 0.618868 | + | 0.785495i | \(0.287592\pi\) | ||||
−0.618868 | + | 0.785495i | \(0.712408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 35.4183 | + | 20.4488i | 1.35129 | + | 0.780170i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.5894 | + | 25.2696i | −0.555813 | + | 0.962697i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.22497 | 0.0466000 | 0.0233000 | − | 0.999729i | \(-0.492583\pi\) | ||||
0.0233000 | + | 0.999729i | \(0.492583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.2601 | − | 15.1613i | 0.997538 | − | 0.575929i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48329 | + | 0.856376i | −0.0561835 | + | 0.0324375i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.5228 | + | 40.7426i | 0.889712 | + | 1.54103i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0101 | + | 38.1226i | −0.831309 | + | 1.43987i | 0.0656918 | + | 0.997840i | \(0.479075\pi\) |
−0.897001 | + | 0.442029i | \(0.854259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2384 | + | 11.4810i | 0.423865 | + | 0.433015i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.6439 | − | 7.87729i | 0.513130 | − | 0.296256i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.16255 | + | 14.1379i | 0.306551 | + | 0.530962i | 0.977605 | − | 0.210446i | \(-0.0674917\pi\) |
−0.671055 | + | 0.741408i | \(0.734158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.2509 | 1.50953 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.9542 | + | 10.9432i | −0.709841 | + | 0.409827i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.31593 | − | 0.759750i | −0.0491442 | − | 0.0283734i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.08574 | − | 8.80876i | 0.189666 | − | 0.328511i | −0.755473 | − | 0.655180i | \(-0.772593\pi\) |
0.945139 | + | 0.326669i | \(0.105926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.0686 | −1.52947 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 55.1595i | − | 2.05141i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.96541 | + | 4.02148i | 0.258333 | + | 0.149148i | 0.623574 | − | 0.781765i | \(-0.285680\pi\) |
−0.365241 | + | 0.930913i | \(0.619013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.9600 | 1.22074 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.79353 | − | 4.83853i | −0.103322 | − | 0.178960i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2325i | 1.52296i | 0.648190 | + | 0.761479i | \(0.275526\pi\) | ||||
−0.648190 | + | 0.761479i | \(0.724474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.9864 | − | 16.1580i | 1.03089 | − | 0.595186i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5253 | − | 28.6227i | 0.607893 | − | 1.05290i | −0.383694 | − | 0.923460i | \(-0.625348\pi\) |
0.991587 | − | 0.129442i | \(-0.0413186\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.5059 | − | 24.9669i | 0.936983 | − | 0.917184i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.1261 | − | 17.3933i | −1.10522 | − | 0.638099i | −0.167633 | − | 0.985849i | \(-0.553612\pi\) |
−0.937587 | + | 0.347750i | \(0.886946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.6166 | + | 7.86153i | −0.498204 | + | 0.287638i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.4284 | 1.51376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.7350 | + | 37.6462i | 0.793123 | + | 1.37373i | 0.924024 | + | 0.382334i | \(0.124879\pi\) |
−0.130902 | + | 0.991395i | \(0.541787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 20.8537i | − | 0.759950i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.34328 | − | 3.08494i | −0.194205 | − | 0.112124i | 0.399745 | − | 0.916626i | \(-0.369099\pi\) |
−0.593949 | + | 0.804502i | \(0.702432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.9449 | 0.651359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.81318 | −0.355728 | −0.177864 | − | 0.984055i | \(-0.556919\pi\) | ||||
−0.177864 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.8114 | + | 17.2116i | 1.07925 | + | 0.623103i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.6517i | 1.28731i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.7452 | − | 35.9317i | −0.748090 | − | 1.29573i | −0.948737 | − | 0.316066i | \(-0.897638\pi\) |
0.200647 | − | 0.979664i | \(-0.435695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.7727 | −1.28832 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.1279 | − | 20.8584i | 1.29943 | − | 0.750226i | 0.319124 | − | 0.947713i | \(-0.396611\pi\) |
0.980306 | + | 0.197487i | \(0.0632779\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.9460 | + | 12.6705i | 0.787309 | + | 0.454553i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.787908 | − | 3.07133i | −0.0282297 | − | 0.110042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4622 | + | 19.8531i | −0.410149 | + | 0.710400i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.04486 | − | 1.75795i | 0.108814 | − | 0.0628240i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0342i | 0.464621i | 0.972642 | + | 0.232310i | \(0.0746285\pi\) | ||||
−0.972642 | + | 0.232310i | \(0.925371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.3718 | + | 40.4812i | 0.832060 | + | 1.44117i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6580 | −0.592292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.7841 | + | 13.7317i | 0.844596 | + | 0.487628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 33.1911i | − | 1.17569i | −0.808974 | − | 0.587844i | \(-0.799977\pi\) | ||
0.808974 | − | 0.587844i | \(-0.200023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.9547 | −0.918210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.3307 | + | 24.8216i | −0.506351 | + | 0.877026i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.11951 | + | 4.11045i | 0.251242 | + | 0.145055i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5556 | − | 8.40369i | 0.512382 | − | 0.295824i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.5271 | 1.03812 | 0.519058 | − | 0.854739i | \(-0.326283\pi\) | ||||
0.519058 | + | 0.854739i | \(0.326283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4097 | − | 24.9583i | −0.505993 | − | 0.876406i | −0.999976 | − | 0.00693438i | \(-0.997793\pi\) |
0.493983 | − | 0.869472i | \(-0.335541\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −48.1727 | + | 27.8125i | −1.68949 | + | 0.975427i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0188 | − | 2.57018i | 0.350513 | − | 0.0899194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.8595 | − | 25.7374i | 0.519233 | − | 0.899338i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.40280 | + | 16.2861i | 0.328160 | + | 0.568390i | 0.982147 | − | 0.188116i | \(-0.0602382\pi\) |
−0.653987 | + | 0.756506i | \(0.726905\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.55545 | − | 3.78479i | 0.228509 | − | 0.131929i | −0.381375 | − | 0.924420i | \(-0.624549\pi\) |
0.609884 | + | 0.792491i | \(0.291216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.2560 | + | 17.4683i | −1.05211 | + | 0.607434i | −0.923238 | − | 0.384228i | \(-0.874468\pi\) |
−0.128868 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.8376 | 1.59201 | 0.796003 | − | 0.605293i | \(-0.206944\pi\) | ||||
0.796003 | + | 0.605293i | \(0.206944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.8327 | + | 53.4037i | −1.06957 | + | 1.85256i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.894872 | + | 0.516655i | 0.0310055 | + | 0.0179010i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.10656i | − | 0.314769i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.00502 | − | 12.1330i | 0.241840 | − | 0.418879i | −0.719398 | − | 0.694598i | \(-0.755582\pi\) |
0.961238 | + | 0.275719i | \(0.0889158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.76169 | − | 11.7116i | 0.233162 | − | 0.403848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 47.0455i | − | 1.62033i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0436252i | 0.00149898i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.66708 | − | 9.81568i | −0.194494 | − | 0.336873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.95840 | + | 6.85615i | 0.135692 | + | 0.235026i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.5205 | + | 18.7757i | 1.11348 | + | 0.642869i | 0.939729 | − | 0.341920i | \(-0.111077\pi\) |
0.173753 | + | 0.984789i | \(0.444411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.52261 | + | 2.03378i | 0.120330 | + | 0.0694726i | 0.558957 | − | 0.829197i | \(-0.311202\pi\) |
−0.438627 | + | 0.898669i | \(0.644535\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.31785 | + | 10.9428i | 0.215562 | + | 0.373365i | 0.953446 | − | 0.301563i | \(-0.0975082\pi\) |
−0.737884 | + | 0.674928i | \(0.764175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.50066 | − | 4.33127i | −0.0852223 | − | 0.147609i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 14.5147i | − | 0.494085i | −0.969005 | − | 0.247042i | \(-0.920541\pi\) | ||
0.969005 | − | 0.247042i | \(-0.0794587\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 28.8790i | − | 0.980781i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.8835 | − | 34.4393i | 0.674503 | − | 1.16827i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8364 | − | 27.4294i | 0.536594 | − | 0.929409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.2529i | 0.820836i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.67583 | + | 0.967541i | 0.0565887 | + | 0.0326715i | 0.528027 | − | 0.849227i | \(-0.322932\pi\) |
−0.471439 | + | 0.881899i | \(0.656265\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.60098 | + | 2.77298i | −0.0539998 | + | 0.0935303i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9037 | 0.535811 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.3483 | + | 17.5216i | −1.02130 | + | 0.589648i | −0.914480 | − | 0.404631i | \(-0.867400\pi\) |
−0.106820 | + | 0.994278i | \(0.534067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0089 | − | 8.08806i | 0.470374 | − | 0.271571i | −0.246022 | − | 0.969264i | \(-0.579124\pi\) |
0.716396 | + | 0.697694i | \(0.245790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4402 | − | 21.5470i | −0.417230 | − | 0.722664i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.9432 | − | 22.4182i | 0.433613 | − | 0.751039i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.9310 | − | 46.2767i | 0.432718 | − | 1.54859i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.2314 | − | 8.79387i | 0.508563 | − | 0.293619i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.0431 | + | 34.7156i | 0.668473 | + | 1.15783i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.1507 | 0.704631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.1288 | − | 8.15724i | 0.470176 | − | 0.271456i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.9143 | + | 11.4975i | 0.661244 | + | 0.381770i | 0.792751 | − | 0.609546i | \(-0.208648\pi\) |
−0.131507 | + | 0.991315i | \(0.541981\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.68848 | + | 16.7809i | −0.321347 | + | 0.556589i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0833 | −0.764783 | −0.382392 | − | 0.924000i | \(-0.624899\pi\) | ||||
−0.382392 | + | 0.924000i | \(0.624899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5341i | 0.514103i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.5917 | + | 30.3638i | 1.73673 | + | 1.00270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5454 | −0.413835 | −0.206918 | − | 0.978358i | \(-0.566343\pi\) | ||||
−0.206918 | + | 0.978358i | \(0.566343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.9060 | − | 18.8898i | −0.359365 | − | 0.622439i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4681i | 0.739547i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.7441 | − | 25.2557i | 1.43674 | − | 0.829505i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6494 | + | 46.1581i | −0.874338 | + | 1.51440i | −0.0168714 | + | 0.999858i | \(0.505371\pi\) |
−0.857466 | + | 0.514540i | \(0.827963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.36702 | + | 1.33814i | −0.0448024 | + | 0.0438556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.0662 | + | 30.0604i | 1.70457 | + | 0.984134i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4152 | − | 17.5602i | 0.993622 | − | 0.573668i | 0.0872667 | − | 0.996185i | \(-0.472187\pi\) |
0.906355 | + | 0.422517i | \(0.138853\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.95704 | −0.0638656 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.57898 | − | 11.3951i | −0.214469 | − | 0.371470i | 0.738639 | − | 0.674101i | \(-0.235469\pi\) |
−0.953108 | + | 0.302630i | \(0.902135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.56246i | − | 0.0508807i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.05015 | − | 5.22510i | −0.294090 | − | 0.169793i | 0.345695 | − | 0.938347i | \(-0.387643\pi\) |
−0.639785 | + | 0.768554i | \(0.720977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.05728 | 0.261550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.8940 | 1.13152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.76057 | − | 2.17117i | −0.121817 | − | 0.0703310i | 0.437853 | − | 0.899046i | \(-0.355739\pi\) |
−0.559670 | + | 0.828715i | \(0.689072\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 32.8670i | − | 1.06244i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.4012 | − | 18.0154i | −0.335872 | − | 0.581747i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.8272 | 2.34927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.1274 | + | 25.4770i | −1.42198 | + | 0.820983i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5810 | − | 7.84100i | −0.436736 | − | 0.252149i | 0.265476 | − | 0.964117i | \(-0.414471\pi\) |
−0.702212 | + | 0.711968i | \(0.747804\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.9171 | − | 6.96253i | −0.800454 | − | 0.223669i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.33867 | + | 2.31865i | −0.0429601 | + | 0.0744091i | −0.886706 | − | 0.462334i | \(-0.847012\pi\) |
0.843746 | + | 0.536743i | \(0.180346\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.9614 | − | 23.0717i | 1.28110 | − | 0.739646i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.87156i | − | 0.0918693i | −0.998944 | − | 0.0459347i | \(-0.985373\pi\) | ||
0.998944 | − | 0.0459347i | \(-0.0146266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1585 | + | 24.5232i | 0.452507 | + | 0.783765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.3380 | −1.35175 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.3660 | + | 16.9545i | 0.936630 | + | 0.540764i | 0.888902 | − | 0.458097i | \(-0.151469\pi\) |
0.0477276 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 75.7889i | − | 2.41239i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.09680 | 0.162069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0649 | − | 34.7535i | 0.637383 | − | 1.10398i | −0.348622 | − | 0.937264i | \(-0.613350\pi\) |
0.986005 | − | 0.166716i | \(-0.0533165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 62.6533 | + | 36.1729i | 1.98824 | + | 1.14791i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.03748 | + | 1.75369i | −0.0961979 | + | 0.0555399i | −0.547327 | − | 0.836919i | \(-0.684355\pi\) |
0.451129 | + | 0.892459i | \(0.351021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.29404 | −0.104219 |
(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.s.d.49.7 | 16 | ||
5.2 | odd | 4 | 380.2.i.c.201.4 | yes | 8 | ||
5.3 | odd | 4 | 1900.2.i.d.201.1 | 8 | |||
5.4 | even | 2 | inner | 1900.2.s.d.49.2 | 16 | ||
15.2 | even | 4 | 3420.2.t.w.3241.3 | 8 | |||
19.7 | even | 3 | inner | 1900.2.s.d.349.2 | 16 | ||
20.7 | even | 4 | 1520.2.q.m.961.1 | 8 | |||
95.7 | odd | 12 | 380.2.i.c.121.4 | ✓ | 8 | ||
95.27 | even | 12 | 7220.2.a.p.1.4 | 4 | |||
95.64 | even | 6 | inner | 1900.2.s.d.349.7 | 16 | ||
95.83 | odd | 12 | 1900.2.i.d.501.1 | 8 | |||
95.87 | odd | 12 | 7220.2.a.r.1.1 | 4 | |||
285.197 | even | 12 | 3420.2.t.w.1261.3 | 8 | |||
380.7 | even | 12 | 1520.2.q.m.881.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.c.121.4 | ✓ | 8 | 95.7 | odd | 12 | ||
380.2.i.c.201.4 | yes | 8 | 5.2 | odd | 4 | ||
1520.2.q.m.881.1 | 8 | 380.7 | even | 12 | |||
1520.2.q.m.961.1 | 8 | 20.7 | even | 4 | |||
1900.2.i.d.201.1 | 8 | 5.3 | odd | 4 | |||
1900.2.i.d.501.1 | 8 | 95.83 | odd | 12 | |||
1900.2.s.d.49.2 | 16 | 5.4 | even | 2 | inner | ||
1900.2.s.d.49.7 | 16 | 1.1 | even | 1 | trivial | ||
1900.2.s.d.349.2 | 16 | 19.7 | even | 3 | inner | ||
1900.2.s.d.349.7 | 16 | 95.64 | even | 6 | inner | ||
3420.2.t.w.1261.3 | 8 | 285.197 | even | 12 | |||
3420.2.t.w.3241.3 | 8 | 15.2 | even | 4 | |||
7220.2.a.p.1.4 | 4 | 95.27 | even | 12 | |||
7220.2.a.r.1.1 | 4 | 95.87 | odd | 12 |