Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(111,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.11 | ||
Root | \(-1.38133 + 0.303194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1120.111 |
Dual form | 1120.2.h.a.111.6 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.34113i | 0.774303i | 0.922016 | + | 0.387152i | \(0.126541\pi\) | ||||
−0.922016 | + | 0.387152i | \(0.873459\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.28003 | − | 2.31550i | −0.483806 | − | 0.875175i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.20136 | 0.400454 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44809 | −0.738125 | −0.369063 | − | 0.929404i | \(-0.620321\pi\) | ||||
−0.369063 | + | 0.929404i | \(0.620321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57090 | 0.435690 | 0.217845 | − | 0.975983i | \(-0.430097\pi\) | ||||
0.217845 | + | 0.975983i | \(0.430097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.34113i | − | 0.346279i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11987i | 0.271609i | 0.990736 | + | 0.135804i | \(0.0433619\pi\) | ||||
−0.990736 | + | 0.135804i | \(0.956638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.44773i | 1.93804i | 0.246978 | + | 0.969021i | \(0.420563\pi\) | ||||
−0.246978 | + | 0.969021i | \(0.579437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.10539 | − | 1.71669i | 0.677651 | − | 0.374613i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.62959i | 0.548307i | 0.961686 | + | 0.274154i | \(0.0883977\pi\) | ||||
−0.961686 | + | 0.274154i | \(0.911602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63459i | 1.08438i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43282i | 0.637458i | 0.947846 | + | 0.318729i | \(0.103256\pi\) | ||||
−0.947846 | + | 0.318729i | \(0.896744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.70304 | −1.74272 | −0.871359 | − | 0.490647i | \(-0.836761\pi\) | ||||
−0.871359 | + | 0.490647i | \(0.836761\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.28321i | − | 0.571533i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.28003 | + | 2.31550i | 0.216365 | + | 0.391390i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.22712i | 1.02373i | 0.859065 | + | 0.511866i | \(0.171046\pi\) | ||||
−0.859065 | + | 0.511866i | \(0.828954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.10679i | 0.337357i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.13128i | 0.489024i | 0.969646 | + | 0.244512i | \(0.0786277\pi\) | ||||
−0.969646 | + | 0.244512i | \(0.921372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.45492 | −1.13687 | −0.568433 | − | 0.822730i | \(-0.692450\pi\) | ||||
−0.568433 | + | 0.822730i | \(0.692450\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.20136 | −0.179089 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.40956 | 1.37253 | 0.686263 | − | 0.727354i | \(-0.259250\pi\) | ||||
0.686263 | + | 0.727354i | \(0.259250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.72304 | + | 5.92781i | −0.531863 | + | 0.846830i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50190 | −0.210308 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.6067i | − | 1.59430i | −0.603778 | − | 0.797152i | \(-0.706339\pi\) | ||
0.603778 | − | 0.797152i | \(-0.293661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.44809 | 0.330100 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.3295 | −1.50063 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6.16041i | − | 0.802017i | −0.916074 | − | 0.401009i | \(-0.868660\pi\) | ||
0.916074 | − | 0.401009i | \(-0.131340\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.44231 | −1.20896 | −0.604482 | − | 0.796619i | \(-0.706620\pi\) | ||||
−0.604482 | + | 0.796619i | \(0.706620\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.53778 | − | 2.78175i | −0.193742 | − | 0.350468i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.57090 | −0.194847 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15461 | 0.263228 | 0.131614 | − | 0.991301i | \(-0.457984\pi\) | ||||
0.131614 | + | 0.991301i | \(0.457984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.52663 | −0.424556 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.87185i | 0.934217i | 0.884200 | + | 0.467108i | \(0.154704\pi\) | ||||
−0.884200 | + | 0.467108i | \(0.845296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6145i | 1.47642i | 0.674571 | + | 0.738210i | \(0.264329\pi\) | ||||
−0.674571 | + | 0.738210i | \(0.735671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.34113i | 0.154861i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.13362 | + | 5.66853i | 0.357110 | + | 0.645989i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.70558i | − | 0.866946i | −0.901167 | − | 0.433473i | \(-0.857288\pi\) | ||
0.901167 | − | 0.433473i | \(-0.142712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.95264 | −0.439182 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.813234i | − | 0.0892640i | −0.999003 | − | 0.0446320i | \(-0.985788\pi\) | ||
0.999003 | − | 0.0446320i | \(-0.0142115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.11987i | − | 0.121467i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.60387 | −0.493586 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.12287i | 0.543023i | 0.962435 | + | 0.271512i | \(0.0875235\pi\) | ||||
−0.962435 | + | 0.271512i | \(0.912476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.01081 | − | 3.63742i | −0.210790 | − | 0.381305i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 13.0131i | − | 1.34939i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 8.44773i | − | 0.866719i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.833955i | − | 0.0846753i | −0.999103 | − | 0.0423377i | \(-0.986519\pi\) | ||
0.999103 | − | 0.0423377i | \(-0.0134805\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.94104 | −0.295585 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.52401 | −0.549660 | −0.274830 | − | 0.961493i | \(-0.588622\pi\) | ||||
−0.274830 | + | 0.961493i | \(0.588622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7675 | 1.15949 | 0.579745 | − | 0.814798i | \(-0.303152\pi\) | ||||
0.579745 | + | 0.814798i | \(0.303152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.10539 | + | 1.71669i | −0.303055 | + | 0.167532i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.38992 | 0.134369 | 0.0671844 | − | 0.997741i | \(-0.478598\pi\) | ||||
0.0671844 | + | 0.997741i | \(0.478598\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.07524i | 0.102990i | 0.998673 | + | 0.0514949i | \(0.0163986\pi\) | ||||
−0.998673 | + | 0.0514949i | \(0.983601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.35140 | −0.792680 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1967 | 1.05329 | 0.526647 | − | 0.850084i | \(-0.323449\pi\) | ||||
0.526647 | + | 0.850084i | \(0.323449\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.62959i | − | 0.245210i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.88722 | 0.174474 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.59306 | − | 1.43347i | 0.237705 | − | 0.131406i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00688 | −0.455171 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.19946 | −0.378653 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4186i | 1.45692i | 0.685089 | + | 0.728459i | \(0.259763\pi\) | ||||
−0.685089 | + | 0.728459i | \(0.740237\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 9.99804i | − | 0.880279i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.00348i | − | 0.175045i | −0.996163 | − | 0.0875223i | \(-0.972105\pi\) | ||
0.996163 | − | 0.0875223i | \(-0.0278949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.5607 | − | 10.8134i | 1.69613 | − | 0.937637i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.63459i | − | 0.484948i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.20941 | 0.359634 | 0.179817 | − | 0.983700i | \(-0.442449\pi\) | ||||
0.179817 | + | 0.983700i | \(0.442449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.20658i | − | 0.356798i | −0.983958 | − | 0.178399i | \(-0.942908\pi\) | ||
0.983958 | − | 0.178399i | \(-0.0570917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6195i | 1.06275i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.84571 | −0.321594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.43282i | − | 0.285080i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.94998 | − | 4.99310i | −0.655704 | − | 0.411824i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1438i | 1.56832i | 0.620560 | + | 0.784159i | \(0.286906\pi\) | ||||
−0.620560 | + | 0.784159i | \(0.713094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.73232i | 0.222353i | 0.993801 | + | 0.111177i | \(0.0354619\pi\) | ||||
−0.993801 | + | 0.111177i | \(0.964538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.34537i | 0.108767i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.70304 | 0.779367 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5441 | −1.08094 | −0.540468 | − | 0.841365i | \(-0.681753\pi\) | ||||
−0.540468 | + | 0.841365i | \(0.681753\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.5661 | 1.23448 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.08880 | − | 3.36595i | 0.479865 | − | 0.265274i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5317 | 1.45151 | 0.725756 | − | 0.687953i | \(-0.241490\pi\) | ||||
0.725756 | + | 0.687953i | \(0.241490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.28321i | 0.255597i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.74592 | −0.599397 | −0.299699 | − | 0.954034i | \(-0.596886\pi\) | ||||
−0.299699 | + | 0.954034i | \(0.596886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5323 | −0.810174 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.1488i | 0.776097i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6112 | 1.03484 | 0.517421 | − | 0.855731i | \(-0.326892\pi\) | ||||
0.517421 | + | 0.855731i | \(0.326892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.28003 | − | 2.31550i | −0.0967612 | − | 0.175035i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.26193 | 0.621005 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3370 | 1.29583 | 0.647914 | − | 0.761714i | \(-0.275642\pi\) | ||||
0.647914 | + | 0.761714i | \(0.275642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8268 | −0.879076 | −0.439538 | − | 0.898224i | \(-0.644858\pi\) | ||||
−0.439538 | + | 0.898224i | \(0.644858\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.6634i | − | 0.936105i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.22712i | − | 0.457827i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.74154i | − | 0.200481i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.0469 | − | 7.21244i | 0.949019 | − | 0.524628i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.5823i | 1.48929i | 0.667463 | + | 0.744643i | \(0.267380\pi\) | ||||
−0.667463 | + | 0.744643i | \(0.732620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0690 | 0.724781 | 0.362391 | − | 0.932026i | \(-0.381961\pi\) | ||||
0.362391 | + | 0.932026i | \(0.381961\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.10679i | − | 0.150870i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.59538i | − | 0.327407i | −0.986510 | − | 0.163704i | \(-0.947656\pi\) | ||
0.986510 | − | 0.163704i | \(-0.0523441\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.15447 | −0.152727 | −0.0763633 | − | 0.997080i | \(-0.524331\pi\) | ||||
−0.0763633 | + | 0.997080i | \(0.524331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.88962i | 0.203818i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.94868 | − | 4.39411i | 0.557888 | − | 0.308406i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.13128i | − | 0.218698i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.15909i | 0.219572i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 20.6808i | − | 1.43052i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7444 | 0.808515 | 0.404258 | − | 0.914645i | \(-0.367530\pi\) | ||||
0.404258 | + | 0.914645i | \(0.367530\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.5572 | −0.723367 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.45492 | 0.508422 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.4202 | + | 22.4673i | 0.843137 | + | 1.52518i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.9178 | −1.14320 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75921i | 0.118337i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92127 | −0.463482 | −0.231741 | − | 0.972777i | \(-0.574442\pi\) | ||||
−0.231741 | + | 0.972777i | \(0.574442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.20136 | 0.0800908 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.2022i | − | 0.809890i | −0.914341 | − | 0.404945i | \(-0.867291\pi\) | ||
0.914341 | − | 0.404945i | \(-0.132709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.2581 | −0.810041 | −0.405021 | − | 0.914308i | \(-0.632736\pi\) | ||||
−0.405021 | + | 0.914308i | \(0.632736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.60226 | + | 4.20261i | −0.500192 | + | 0.276511i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1521 | −0.665083 | −0.332542 | − | 0.943089i | \(-0.607906\pi\) | ||||
−0.332542 | + | 0.943089i | \(0.607906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.40956 | −0.613812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3342 | 0.671279 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.57510i | − | 0.360624i | −0.983610 | − | 0.180312i | \(-0.942289\pi\) | ||
0.983610 | − | 0.180312i | \(-0.0577107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.9813i | − | 1.35152i | −0.737120 | − | 0.675762i | \(-0.763815\pi\) | ||
0.737120 | − | 0.675762i | \(-0.236185\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.6027i | 0.744316i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.72304 | − | 5.92781i | 0.237857 | − | 0.378714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2706i | 0.844386i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.09065 | 0.0691174 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.8742i | − | 1.44381i | −0.691995 | − | 0.721903i | \(-0.743268\pi\) | ||
0.691995 | − | 0.721903i | \(-0.256732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.43746i | − | 0.404720i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.50190 | 0.0940525 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 28.8767i | − | 1.80128i | −0.434566 | − | 0.900640i | \(-0.643098\pi\) | ||
0.434566 | − | 0.900640i | \(-0.356902\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4189 | − | 7.97091i | 0.895946 | − | 0.495288i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.12406i | 0.255273i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 19.6017i | − | 1.20869i | −0.796722 | − | 0.604347i | \(-0.793434\pi\) | ||
0.796722 | − | 0.604347i | \(-0.206566\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6067i | 0.712995i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.87045 | −0.420465 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.2431 | −1.66104 | −0.830520 | − | 0.556988i | \(-0.811957\pi\) | ||||
−0.830520 | + | 0.556988i | \(0.811957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0339 | 1.58144 | 0.790722 | − | 0.612175i | \(-0.209705\pi\) | ||||
0.790722 | + | 0.612175i | \(0.209705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.87827 | − | 2.69676i | 0.295246 | − | 0.163215i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.44809 | −0.147625 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.64829i | 0.339373i | 0.985498 | + | 0.169687i | \(0.0542755\pi\) | ||||
−0.985498 | + | 0.169687i | \(0.945724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.6569 | −0.697878 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.9379 | 1.54733 | 0.773663 | − | 0.633598i | \(-0.218422\pi\) | ||||
0.773663 | + | 0.633598i | \(0.218422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.6062i | − | 0.749358i | −0.927155 | − | 0.374679i | \(-0.877753\pi\) | ||
0.927155 | − | 0.374679i | \(-0.122247\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.3295 | 0.671103 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.25047 | − | 4.00813i | 0.427982 | − | 0.236593i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7459 | 0.926229 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.11844 | 0.0655644 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.7982 | 0.981362 | 0.490681 | − | 0.871339i | \(-0.336748\pi\) | ||||
0.490681 | + | 0.871339i | \(0.336748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16041i | 0.358673i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 13.7939i | − | 0.800406i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.13083i | 0.238892i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.54253 | + | 17.2618i | 0.550022 | + | 0.994956i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 7.40844i | − | 0.425604i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.44231 | 0.540665 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.08609i | 0.290279i | 0.989411 | + | 0.145139i | \(0.0463630\pi\) | ||||
−0.989411 | + | 0.145139i | \(0.953637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.7818i | 0.897797i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.9297 | −0.959994 | −0.479997 | − | 0.877270i | \(-0.659362\pi\) | ||||
−0.479997 | + | 0.877270i | \(0.659362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.30791i | 0.469591i | 0.972045 | + | 0.234795i | \(0.0754420\pi\) | ||||
−0.972045 | + | 0.234795i | \(0.924558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.53778 | + | 2.78175i | 0.0866441 | + | 0.156734i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.7428i | − | 0.603376i | −0.953407 | − | 0.301688i | \(-0.902450\pi\) | ||
0.953407 | − | 0.301688i | \(-0.0975501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.40383i | − | 0.470524i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.86407i | 0.104042i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.46038 | −0.526390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.57090 | 0.0871381 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.44205 | −0.0797453 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0445 | − | 21.7878i | −0.664036 | − | 1.20120i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1739 | −0.669140 | −0.334570 | − | 0.942371i | \(-0.608591\pi\) | ||||
−0.334570 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.48103i | 0.409958i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.15461 | −0.117719 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5686 | −0.630179 | −0.315090 | − | 0.949062i | \(-0.602035\pi\) | ||||
−0.315090 | + | 0.949062i | \(0.602035\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0162i | 0.815569i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.7539 | 1.28634 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4914 | + | 1.03291i | 0.998444 | + | 0.0557721i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.52663 | 0.189867 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6711 | 0.572854 | 0.286427 | − | 0.958102i | \(-0.407532\pi\) | ||||
0.286427 | + | 0.958102i | \(0.407532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5060 | 0.776486 | 0.388243 | − | 0.921557i | \(-0.373082\pi\) | ||||
0.388243 | + | 0.921557i | \(0.373082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.85139i | 0.472452i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 33.2031i | − | 1.76722i | −0.468221 | − | 0.883611i | \(-0.655105\pi\) | ||
0.468221 | − | 0.883611i | \(-0.344895\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.87185i | − | 0.417794i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.92247 | + | 3.47764i | 0.101748 | + | 0.184056i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 13.3218i | − | 0.703097i | −0.936170 | − | 0.351549i | \(-0.885655\pi\) | ||
0.936170 | − | 0.351549i | \(-0.114345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −52.3642 | −2.75601 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.71489i | − | 0.352440i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.6145i | − | 0.660275i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.9412 | −1.35412 | −0.677059 | − | 0.735929i | \(-0.736746\pi\) | ||||
−0.677059 | + | 0.735929i | \(0.736746\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.76180i | 0.195832i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.8753 | + | 14.8569i | −1.39530 | + | 0.771334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 30.5923i | − | 1.58401i | −0.610515 | − | 0.792005i | \(-0.709037\pi\) | ||
0.610515 | − | 0.792005i | \(-0.290963\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.34113i | − | 0.0692558i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.39263i | 0.277734i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6930 | 0.549262 | 0.274631 | − | 0.961550i | \(-0.411444\pi\) | ||||
0.274631 | + | 0.961550i | \(0.411444\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.0196 | −1.12810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.36792 | 0.478679 | 0.239339 | − | 0.970936i | \(-0.423069\pi\) | ||||
0.239339 | + | 0.970936i | \(0.423069\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.13362 | − | 5.66853i | −0.159704 | − | 0.288895i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.95606 | −0.455262 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.30373i | 0.116804i | 0.998293 | + | 0.0584019i | \(0.0186005\pi\) | ||||
−0.998293 | + | 0.0584019i | \(0.981399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.94480 | −0.148925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.68693 | 0.135538 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.70558i | 0.387710i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.77718 | −0.0891942 | −0.0445971 | − | 0.999005i | \(-0.514200\pi\) | ||||
−0.0445971 | + | 0.999005i | \(0.514200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.5021 | + | 26.2335i | 0.726015 | + | 1.31332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8159 | 0.889682 | 0.444841 | − | 0.895609i | \(-0.353260\pi\) | ||||
0.444841 | + | 0.895609i | \(0.353260\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.2425 | −0.759285 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.95264 | 0.196408 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.2445i | − | 0.755643i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.8691i | 1.87250i | 0.351329 | + | 0.936252i | \(0.385730\pi\) | ||||
−0.351329 | + | 0.936252i | \(0.614270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.64538i | 0.278466i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.2644 | + | 7.88551i | −0.701906 | + | 0.388021i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.813234i | 0.0399201i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.64159 | 0.276270 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 3.11076i | − | 0.151971i | −0.997109 | − | 0.0759854i | \(-0.975790\pi\) | ||
0.997109 | − | 0.0759854i | \(-0.0242102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8952i | 0.920893i | 0.887687 | + | 0.460447i | \(0.152311\pi\) | ||||
−0.887687 | + | 0.460447i | \(0.847689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3043 | 0.549634 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.11987i | 0.0543218i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0864 | + | 21.8636i | 0.584904 | + | 1.05805i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 5.15760i | − | 0.249011i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.2730i | 1.84355i | 0.387730 | + | 0.921773i | \(0.373259\pi\) | ||||
−0.387730 | + | 0.921773i | \(0.626741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.50589i | − | 0.0723684i | −0.999345 | − | 0.0361842i | \(-0.988480\pi\) | ||
0.999345 | − | 0.0361842i | \(-0.0115203\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.60387 | 0.220738 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.2141 | −1.06264 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00779 | −0.239009 | −0.119504 | − | 0.992834i | \(-0.538131\pi\) | ||||
−0.119504 | + | 0.992834i | \(0.538131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.47272 | + | 7.12145i | −0.212987 | + | 0.339117i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.9714 | 1.18643 | 0.593213 | − | 0.805046i | \(-0.297859\pi\) | ||||
0.593213 | + | 0.805046i | \(0.297859\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.12287i | − | 0.242847i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.6743 | −1.21435 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.85721 | −0.229226 | −0.114613 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114613 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.66564i | − | 0.360961i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.66441 | −0.172169 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.01081 | + | 3.63742i | 0.0942680 | + | 0.170525i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1002 | −0.987025 | −0.493513 | − | 0.869739i | \(-0.664287\pi\) | ||||
−0.493513 | + | 0.869739i | \(0.664287\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.31002 | −0.294526 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2426 | 0.523620 | 0.261810 | − | 0.965119i | \(-0.415681\pi\) | ||||
0.261810 | + | 0.965119i | \(0.415681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.4199i | − | 1.83200i | −0.401179 | − | 0.916000i | \(-0.631399\pi\) | ||
0.401179 | − | 0.916000i | \(-0.368601\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.0131i | 0.603466i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.4941i | − | 1.22600i | −0.790083 | − | 0.613000i | \(-0.789963\pi\) | ||
0.790083 | − | 0.613000i | \(-0.210037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.75797 | − | 4.98899i | −0.127351 | − | 0.230370i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 18.1644i | − | 0.836973i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.2503 | 0.839149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.44773i | 0.387608i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 13.9439i | − | 0.638446i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.7827 | −1.63495 | −0.817477 | − | 0.575961i | \(-0.804628\pi\) | ||||
−0.817477 | + | 0.575961i | \(0.804628\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.78221i | 0.446031i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.51419 | + | 8.16590i | 0.205403 | + | 0.371561i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.833955i | 0.0378680i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4491i | 0.564125i | 0.959396 | + | 0.282062i | \(0.0910185\pi\) | ||||
−0.959396 | + | 0.282062i | \(0.908982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.8534i | 1.12391i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4396 | 0.651649 | 0.325824 | − | 0.945430i | \(-0.394358\pi\) | ||||
0.325824 | + | 0.945430i | \(0.394358\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.84432 | −0.173139 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.94104 | 0.132190 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.2272 | − | 10.0762i | 0.817603 | − | 0.451980i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0969 | −0.989195 | −0.494597 | − | 0.869122i | \(-0.664685\pi\) | ||||
−0.494597 | + | 0.869122i | \(0.664685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.3883i | − | 0.464116i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.8311 | 0.973401 | 0.486701 | − | 0.873569i | \(-0.338200\pi\) | ||||
0.486701 | + | 0.873569i | \(0.338200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.52401 | 0.245815 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 14.1252i | − | 0.627320i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.6514 | 1.35860 | 0.679300 | − | 0.733861i | \(-0.262284\pi\) | ||||
0.679300 | + | 0.733861i | \(0.262284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.2089 | − | 16.1470i | 1.29213 | − | 0.714301i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −47.5995 | −2.10157 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.7675 | −0.518539 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.0354 | −1.01310 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.2545i | 0.801282i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.13741i | 0.312696i | 0.987702 | + | 0.156348i | \(0.0499721\pi\) | ||||
−0.987702 | + | 0.156348i | \(0.950028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.6160i | 1.38247i | 0.722630 | + | 0.691235i | \(0.242933\pi\) | ||||
−0.722630 | + | 0.691235i | \(0.757067\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.10539 | − | 1.71669i | 0.135530 | − | 0.0749225i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.8662i | − | 0.473338i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0853 | 0.699359 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7.40088i | − | 0.321171i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.91894i | 0.213063i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.38992 | −0.0600916 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.2512i | 1.00336i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.11433 | − | 14.5118i | 0.392582 | − | 0.625067i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.5347i | 1.69973i | 0.526999 | + | 0.849866i | \(0.323317\pi\) | ||||
−0.526999 | + | 0.849866i | \(0.676683\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 15.8613i | − | 0.680672i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.07524i | − | 0.0460584i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.6549 | −1.18244 | −0.591218 | − | 0.806512i | \(-0.701353\pi\) | ||||
−0.591218 | + | 0.806512i | \(0.701353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.3436 | −0.484134 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.9995 | −1.23542 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.8422 | + | 9.86338i | −0.758730 | + | 0.419434i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.35140 | 0.354497 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.2830i | 1.24076i | 0.784301 | + | 0.620380i | \(0.213022\pi\) | ||||
−0.784301 | + | 0.620380i | \(0.786978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7110 | −0.495321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.67677 | 0.155234 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.22412i | 0.220170i | 0.993922 | + | 0.110085i | \(0.0351124\pi\) | ||||
−0.993922 | + | 0.110085i | \(0.964888\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1967 | −0.471047 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.05950 | + | 9.15233i | 0.212479 | + | 0.384362i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.8297 | 0.495925 | 0.247963 | − | 0.968770i | \(-0.420239\pi\) | ||||
0.247963 | + | 0.968770i | \(0.420239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.3223 | 0.934158 | 0.467079 | − | 0.884216i | \(-0.345306\pi\) | ||||
0.467079 | + | 0.884216i | \(0.345306\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.6037 | −1.15316 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.62959i | 0.109661i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.4830i | 1.06087i | 0.847725 | + | 0.530436i | \(0.177972\pi\) | ||||
−0.847725 | + | 0.530436i | \(0.822028\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.5038i | 0.561201i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.88304 | + | 1.04096i | −0.0781216 | + | 0.0431865i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4142i | 1.17680i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.88722 | −0.0780271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.1365i | 1.12004i | 0.828478 | + | 0.560021i | \(0.189207\pi\) | ||||
−0.828478 | + | 0.560021i | \(0.810793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 81.9687i | − | 3.37746i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.16301 | 0.253512 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.7929i | 1.38771i | 0.720116 | + | 0.693853i | \(0.244088\pi\) | ||||
−0.720116 | + | 0.693853i | \(0.755912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.59306 | + | 1.43347i | −0.106305 | + | 0.0587666i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.88943i | − | 0.118257i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.0094i | 1.06271i | 0.847148 | + | 0.531357i | \(0.178318\pi\) | ||||
−0.847148 | + | 0.531357i | \(0.821682\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5296i | 1.04137i | 0.853747 | + | 0.520687i | \(0.174324\pi\) | ||||
−0.853747 | + | 0.520687i | \(0.825676\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.58847 | 0.105411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00688 | 0.203559 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2033 | 0.860615 | 0.430307 | − | 0.902682i | \(-0.358405\pi\) | ||||
0.430307 | + | 0.902682i | \(0.358405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.89309 | + | 10.6602i | 0.238800 | + | 0.431974i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.7815 | 0.597996 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.381509i | 0.0154090i | 0.999970 | + | 0.00770450i | \(0.00245244\pi\) | ||||
−0.999970 | + | 0.00770450i | \(0.997548\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.19946 | 0.169339 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.7394 | −0.955714 | −0.477857 | − | 0.878438i | \(-0.658586\pi\) | ||||
−0.477857 | + | 0.878438i | \(0.658586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.66231i | 0.147201i | 0.997288 | + | 0.0736004i | \(0.0234489\pi\) | ||||
−0.997288 | + | 0.0736004i | \(0.976551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.8166 | −0.594571 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8620 | − | 6.55743i | 0.475240 | − | 0.262718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.7357 | 1.10766 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.97358 | −0.278055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.6277i | − | 0.423080i | −0.977369 | − | 0.211540i | \(-0.932152\pi\) | ||
0.977369 | − | 0.211540i | \(-0.0678479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.7508i | 0.626036i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 16.4186i | − | 0.651554i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.84854 | + | 9.31202i | −0.231728 | + | 0.368956i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.45694i | 0.374111i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4300 | −1.24141 | −0.620705 | − | 0.784044i | \(-0.713154\pi\) | ||||
−0.620705 | + | 0.784044i | \(0.713154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.82074i | − | 0.308420i | −0.988038 | − | 0.154210i | \(-0.950717\pi\) | ||
0.988038 | − | 0.154210i | \(-0.0492832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.99804i | 0.393673i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.3346 | 1.07463 | 0.537317 | − | 0.843381i | \(-0.319438\pi\) | ||||
0.537317 | + | 0.843381i | \(0.319438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0812i | 0.591989i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.1317 | + | 16.6571i | −1.18095 | + | 0.652844i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.6566i | 0.769221i | 0.923079 | + | 0.384611i | \(0.125664\pi\) | ||||
−0.923079 | + | 0.384611i | \(0.874336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00348i | 0.0782823i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.1546i | 0.591239i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1522 | −0.551293 | −0.275647 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275647 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.32100 | 0.284754 | 0.142377 | − | 0.989812i | \(-0.454525\pi\) | ||||
0.142377 | + | 0.989812i | \(0.454525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.35934 | −0.0916291 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.5607 | + | 10.8134i | −0.758531 | + | 0.419324i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.02690 | −0.349523 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 9.28234i | − | 0.358876i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.1156 | 0.892367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.5006 | 0.828786 | 0.414393 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414393 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.63459i | 0.216875i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.7438 | 1.60434 | 0.802172 | − | 0.597093i | \(-0.203678\pi\) | ||||
0.802172 | + | 0.597093i | \(0.203678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.93102 | + | 1.06749i | −0.0741057 | + | 0.0409664i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3648 | 0.627101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.9066 | −1.02955 | −0.514777 | − | 0.857324i | \(-0.672125\pi\) | ||||
−0.514777 | + | 0.857324i | \(0.672125\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.20941 | −0.160833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16.4398i | − | 0.627218i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18.2330i | − | 0.694623i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.3610i | 0.660443i | 0.943904 | + | 0.330221i | \(0.107123\pi\) | ||||
−0.943904 | + | 0.330221i | \(0.892877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.76462 | + | 6.80996i | 0.143006 | + | 0.258689i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20658i | 0.159565i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.50663 | −0.132823 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 13.6153i | − | 0.514976i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.9368i | − | 1.20624i | −0.797651 | − | 0.603119i | \(-0.793924\pi\) | ||
0.797651 | − | 0.603119i | \(-0.206076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.6051 | −1.98404 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 12.6195i | − | 0.475277i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.07091 | + | 12.7908i | 0.265929 | + | 0.481049i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.65295i | − | 0.0620777i | −0.999518 | − | 0.0310389i | \(-0.990118\pi\) | ||
0.999518 | − | 0.0310389i | \(-0.00988157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.25720i | − | 0.347172i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.5150i | − | 0.955544i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.84571 | 0.143821 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.47696 | 0.279232 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0007 | −0.596725 | −0.298363 | − | 0.954453i | \(-0.596440\pi\) | ||||
−0.298363 | + | 0.954453i | \(0.596440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.0628 | − | 27.2477i | −0.560968 | − | 1.01476i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.1387 | 1.04649 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.43282i | 0.127492i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.28793 | −0.270294 | −0.135147 | − | 0.990826i | \(-0.543151\pi\) | ||||
−0.135147 | + | 0.990826i | \(0.543151\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.4187 | −1.01551 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.34856i | − | 0.308783i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.79246 | 0.177013 | 0.0885067 | − | 0.996076i | \(-0.471791\pi\) | ||||
0.0885067 | + | 0.996076i | \(0.471791\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.94998 | + | 4.99310i | 0.293240 | + | 0.184173i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.27467 | −0.194295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.3432 | −1.37369 | −0.686845 | − | 0.726804i | \(-0.741005\pi\) | ||||
−0.686845 | + | 0.726804i | \(0.741005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −17.7976 | −0.653811 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9317i | 0.547789i | 0.961760 | + | 0.273895i | \(0.0883119\pi\) | ||||
−0.961760 | + | 0.273895i | \(0.911688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 19.1438i | − | 0.701373i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.976988i | − | 0.0357461i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.77914 | − | 3.21836i | −0.0650085 | − | 0.117596i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 32.2962i | − | 1.17851i | −0.807948 | − | 0.589253i | \(-0.799422\pi\) | ||
0.807948 | − | 0.589253i | \(-0.200578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.6773 | 1.11794 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.73232i | − | 0.0994394i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.1662i | 0.769299i | 0.923063 | + | 0.384650i | \(0.125678\pi\) | ||||
−0.923063 | + | 0.384650i | \(0.874322\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.63349 | 0.313376 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.98517i | − | 0.325712i | −0.986650 | − | 0.162856i | \(-0.947929\pi\) | ||
0.986650 | − | 0.162856i | \(-0.0520706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.48972 | − | 1.37635i | 0.0901341 | − | 0.0498271i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 1.34537i | − | 0.0486420i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.67741i | − | 0.349431i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 38.3718i | − | 1.38372i | −0.722031 | − | 0.691861i | \(-0.756791\pi\) | ||
0.722031 | − | 0.691861i | \(-0.243209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.7275 | 1.39474 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.61383 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.70304 | −0.348543 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.6900 | + | 19.3376i | 0.383503 | + | 0.693734i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.4522 | −0.947749 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 19.2710i | − | 0.689569i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.3425 | −0.691245 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.5441 | 0.483409 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1424i | 0.468474i | 0.972180 | + | 0.234237i | \(0.0752592\pi\) | ||||
−0.972180 | + | 0.234237i | \(0.924741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.2885 | 0.935895 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.3321 | − | 25.9258i | −0.509590 | − | 0.921817i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8330 | −0.526734 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.5661 | −0.552074 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.8837 | −0.952269 | −0.476134 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476134 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5375i | 0.372790i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.15442i | 0.217456i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 30.8815i | − | 1.08978i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.08880 | + | 3.36595i | −0.214602 | + | 0.118634i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 36.5366i | − | 1.28615i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.28389 | 0.326404 | 0.163202 | − | 0.986593i | \(-0.447818\pi\) | ||||
0.163202 | + | 0.986593i | \(0.447818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.2011i | 1.65745i | 0.559653 | + | 0.828727i | \(0.310935\pi\) | ||||
−0.559653 | + | 0.828727i | \(0.689065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.9149i | 1.22452i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.5317 | −0.649136 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 62.9772i | − | 2.20329i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.41571 | − | 4.36986i | −0.0844116 | − | 0.152695i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 28.6713i | − | 1.00063i | −0.865842 | − | 0.500317i | \(-0.833217\pi\) | ||
0.865842 | − | 0.500317i | \(-0.166783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8578i | 0.552769i | 0.961047 | + | 0.276385i | \(0.0891364\pi\) | ||||
−0.961047 | + | 0.276385i | \(0.910864\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.28321i | − | 0.114307i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.33173 | −0.324496 | −0.162248 | − | 0.986750i | \(-0.551874\pi\) | ||||
−0.162248 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2966 | 1.74687 | 0.873436 | − | 0.486939i | \(-0.161887\pi\) | ||||
0.873436 | + | 0.486939i | \(0.161887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.57511 | −0.262778 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.63839 | − | 4.16933i | −0.230007 | − | 0.144459i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.74592 | 0.268059 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 54.6726i | − | 1.88976i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.0155 | 1.34697 | 0.673483 | − | 0.739203i | \(-0.264797\pi\) | ||||
0.673483 | + | 0.739203i | \(0.264797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.2158 | 0.593647 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.7862i | 1.19810i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.5323 | 0.362321 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.40896 | + | 11.5934i | 0.220214 | + | 0.398354i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9065 | 0.580231 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.3748 | −0.561320 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.1812 | 0.382836 | 0.191418 | − | 0.981509i | \(-0.438691\pi\) | ||||
0.191418 | + | 0.981509i | \(0.438691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.1488i | − | 0.347081i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 36.5484i | − | 1.24847i | −0.781236 | − | 0.624235i | \(-0.785411\pi\) | ||
0.781236 | − | 0.624235i | \(-0.214589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.59801i | 0.225121i | 0.993645 | + | 0.112561i | \(0.0359052\pi\) | ||||
−0.993645 | + | 0.112561i | \(0.964095\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.37544 | + | 9.72384i | 0.183195 | + | 0.331388i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.48314i | 0.220689i | 0.993893 | + | 0.110344i | \(0.0351954\pi\) | ||||
−0.993893 | + | 0.110344i | \(0.964805\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.6112 | −0.462795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.1173i | 0.717182i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.8639i | 0.639915i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.38469 | 0.114686 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1.00188i | − | 0.0339086i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.28003 | + | 2.31550i | 0.0432729 | + | 0.0782781i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0472i | 0.778248i | 0.921185 | + | 0.389124i | \(0.127222\pi\) | ||||
−0.921185 | + | 0.389124i | \(0.872778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5286i | 0.759872i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.8703i | − | 1.20850i | −0.796794 | − | 0.604251i | \(-0.793472\pi\) | ||
0.796794 | − | 0.604251i | \(-0.206528\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.9029 | −1.71302 | −0.856509 | − | 0.516131i | \(-0.827372\pi\) | ||||
−0.856509 | + | 0.516131i | \(0.827372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.26193 | −0.277722 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.6009 | −0.893172 | −0.446586 | − | 0.894741i | \(-0.647360\pi\) | ||||
−0.446586 | + | 0.894741i | \(0.647360\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.0173 | − | 21.0164i | 1.27506 | − | 0.704866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.67640 | 0.324172 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 79.4895i | 2.66001i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.3370 | −0.579511 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.54000 | −0.184975 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 33.3088i | − | 1.11091i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9980 | 0.433027 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.1504 | + | 12.7978i | −0.770398 | + | 0.425884i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.8268 | 0.393135 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7572 | 0.921662 | 0.460831 | − | 0.887488i | \(-0.347551\pi\) | ||||
0.460831 | + | 0.887488i | \(0.347551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.63634 | −0.220114 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.35676i | 0.0780829i | 0.999238 | + | 0.0390414i | \(0.0124304\pi\) | ||||
−0.999238 | + | 0.0390414i | \(0.987570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.99087i | 0.0658880i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.6634i | 0.418639i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.63904 | + | 2.56451i | −0.153195 | + | 0.0846876i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.11186i | − | 0.168625i | −0.996439 | − | 0.0843124i | \(-0.973131\pi\) | ||
0.996439 | − | 0.0843124i | \(-0.0268694\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.82113 | −0.224764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.3659i | 0.407029i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.22712i | 0.204747i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1371 | 0.464322 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.8134i | 1.63432i | 0.576408 | + | 0.817162i | \(0.304454\pi\) | ||||
−0.576408 | + | 0.817162i | \(0.695546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.0766 | − | 31.4513i | −1.64119 | − | 1.03077i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 22.7049i | − | 0.743326i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.74154i | 0.0896580i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.7887i | − | 0.515794i | −0.966172 | − | 0.257897i | \(-0.916970\pi\) | ||
0.966172 | − | 0.257897i | \(-0.0830296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1420 | −0.363606 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.58455 | −0.0842538 | −0.0421269 | − | 0.999112i | \(-0.513413\pi\) | ||||
−0.0421269 | + | 0.999112i | \(0.513413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.23398 | −0.268135 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0469 | + | 7.21244i | −0.424414 | + | 0.234621i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.5390 | −0.569940 | −0.284970 | − | 0.958536i | \(-0.591984\pi\) | ||||
−0.284970 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.8162i | 0.643262i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.4075 | 0.467196 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.0362 | −0.811001 | −0.405501 | − | 0.914095i | \(-0.632903\pi\) | ||||
−0.405501 | + | 0.914095i | \(0.632903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.5823i | − | 0.666029i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.2707 | 0.364329 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.38817 | − | 9.74687i | −0.173993 | − | 0.314743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.1490 | 2.03706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.66980 | 0.0538086 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0690 | −0.324132 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 18.7066i | − | 0.601564i | −0.953693 | − | 0.300782i | \(-0.902752\pi\) | ||
0.953693 | − | 0.300782i | \(-0.0972477\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 12.6876i | − | 0.407585i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 32.0975i | − | 1.03006i | −0.857173 | − | 0.515029i | \(-0.827781\pi\) | ||
0.857173 | − | 0.515029i | \(-0.172219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.74033 | + | 5.38455i | −0.312261 | + | 0.172621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.10679i | 0.0674713i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.17448 | 0.165546 | 0.0827731 | − | 0.996568i | \(-0.473622\pi\) | ||||
0.0827731 | + | 0.996568i | \(0.473622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.5412i | − | 0.400819i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.29176i | 0.0412427i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.3909 | 0.809843 | 0.404921 | − | 0.914352i | \(-0.367299\pi\) | ||||
0.404921 | + | 0.914352i | \(0.367299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.59538i | 0.146421i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.2203 | − | 16.1533i | 0.930094 | − | 0.514166i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 19.6034i | − | 0.623351i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 37.1976i | − | 1.18162i | −0.806810 | − | 0.590810i | \(-0.798808\pi\) | ||
0.806810 | − | 0.590810i | \(-0.201192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16.3269i | − | 0.518117i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.15447 | 0.0683014 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.0979 | 1.42827 | 0.714133 | − | 0.700011i | \(-0.246821\pi\) | ||||
0.714133 | + | 0.700011i | \(0.246821\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.0873 | −1.11011 |
(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 | 1120.2.h.a.111.11 | 16 | ||
4.3 | odd | 2 | 280.2.h.a.251.2 | yes | 16 | ||
7.6 | odd | 2 | 1120.2.h.b.111.6 | 16 | |||
8.3 | odd | 2 | 1120.2.h.b.111.11 | 16 | |||
8.5 | even | 2 | 280.2.h.b.251.1 | yes | 16 | ||
28.27 | even | 2 | 280.2.h.b.251.2 | yes | 16 | ||
56.13 | odd | 2 | 280.2.h.a.251.1 | ✓ | 16 | ||
56.27 | even | 2 | inner | 1120.2.h.a.111.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.1 | ✓ | 16 | 56.13 | odd | 2 | ||
280.2.h.a.251.2 | yes | 16 | 4.3 | odd | 2 | ||
280.2.h.b.251.1 | yes | 16 | 8.5 | even | 2 | ||
280.2.h.b.251.2 | yes | 16 | 28.27 | even | 2 | ||
1120.2.h.a.111.6 | 16 | 56.27 | even | 2 | inner | ||
1120.2.h.a.111.11 | 16 | 1.1 | even | 1 | trivial | ||
1120.2.h.b.111.6 | 16 | 7.6 | odd | 2 | |||
1120.2.h.b.111.11 | 16 | 8.3 | odd | 2 |