Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.3 | ||
Root | \(-1.27121 - 1.27121i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.g.369.12 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.78665i | − | 1.03152i | −0.856732 | − | 0.515761i | \(-0.827509\pi\) | ||
0.856732 | − | 0.515761i | \(-0.172491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.46089 | + | 1.69287i | 0.653331 | + | 0.757072i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.75578i | 0.663622i | 0.943346 | + | 0.331811i | \(0.107660\pi\) | ||||
−0.943346 | + | 0.331811i | \(0.892340\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.192116 | −0.0640385 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77574 | 1.43994 | 0.719970 | − | 0.694005i | \(-0.244155\pi\) | ||||
0.719970 | + | 0.694005i | \(0.244155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.72967i | 0.479724i | 0.970807 | + | 0.239862i | \(0.0771022\pi\) | ||||
−0.970807 | + | 0.239862i | \(0.922898\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.02456 | − | 2.61010i | 0.780937 | − | 0.673926i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.81453i | 1.89530i | 0.319309 | + | 0.947651i | \(0.396549\pi\) | ||||
−0.319309 | + | 0.947651i | \(0.603451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.43970 | −0.559706 | −0.279853 | − | 0.960043i | \(-0.590286\pi\) | ||||
−0.279853 | + | 0.960043i | \(0.590286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.13696 | 0.684541 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.731587 | + | 4.94619i | −0.146317 | + | 0.989238i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.01670i | − | 0.965465i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.86235 | −1.46000 | −0.730001 | − | 0.683446i | \(-0.760480\pi\) | ||||
−0.730001 | + | 0.683446i | \(0.760480\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.14217 | −1.10317 | −0.551583 | − | 0.834120i | \(-0.685976\pi\) | ||||
−0.551583 | + | 0.834120i | \(0.685976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 8.53258i | − | 1.48533i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.97230 | + | 2.56501i | −0.502410 | + | 0.433565i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.83324i | 1.12338i | 0.827349 | + | 0.561689i | \(0.189848\pi\) | ||||
−0.827349 | + | 0.561689i | \(0.810152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.09031 | 0.494846 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50416 | −0.391084 | −0.195542 | − | 0.980695i | \(-0.562647\pi\) | ||||
−0.195542 | + | 0.980695i | \(0.562647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.26755i | 0.498297i | 0.968465 | + | 0.249148i | \(0.0801507\pi\) | ||||
−0.968465 | + | 0.249148i | \(0.919849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.280660 | − | 0.325226i | −0.0418383 | − | 0.0484818i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.46487i | 1.23473i | 0.786678 | + | 0.617364i | \(0.211799\pi\) | ||||
−0.786678 | + | 0.617364i | \(0.788201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.91724 | 0.559605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.9618 | 1.95505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.76559i | − | 0.379883i | −0.981795 | − | 0.189942i | \(-0.939170\pi\) | ||
0.981795 | − | 0.189942i | \(-0.0608299\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.97685 | + | 8.08469i | 0.940758 | + | 1.09014i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.35889i | 0.577349i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.91706 | 0.249580 | 0.124790 | − | 0.992183i | \(-0.460174\pi\) | ||||
0.124790 | + | 0.992183i | \(0.460174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50364 | −0.448595 | −0.224297 | − | 0.974521i | \(-0.572009\pi\) | ||||
−0.224297 | + | 0.974521i | \(0.572009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.337313i | − | 0.0424974i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.92810 | + | 2.52686i | −0.363186 | + | 0.313418i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.7649i | − | 1.55948i | −0.626102 | − | 0.779741i | \(-0.715351\pi\) | ||
0.626102 | − | 0.779741i | \(-0.284649\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.78665 | 0.215087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3973 | 1.58997 | 0.794984 | − | 0.606630i | \(-0.207479\pi\) | ||||
0.794984 | + | 0.606630i | \(0.207479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0111737i | 0.00130778i | 1.00000 | 0.000653890i | \(0.000208140\pi\) | |||||
−1.00000 | 0.000653890i | \(0.999792\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.83710 | + | 1.30709i | 1.02042 | + | 0.150930i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.38515i | 0.955577i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6960 | −1.87844 | −0.939222 | − | 0.343310i | \(-0.888452\pi\) | ||||
−0.939222 | + | 0.343310i | \(0.888452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.53944 | −1.05994 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.64145i | 0.289937i | 0.989436 | + | 0.144969i | \(0.0463081\pi\) | ||||
−0.989436 | + | 0.144969i | \(0.953692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.2289 | + | 11.4162i | −1.43488 | + | 1.23826i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0473i | 1.50602i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.1729 | 1.39632 | 0.698160 | − | 0.715942i | \(-0.254002\pi\) | ||||
0.698160 | + | 0.715942i | \(0.254002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.03692 | −0.318356 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9739i | 1.13794i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.56414 | − | 4.13009i | −0.365673 | − | 0.423738i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.8568i | − | 1.61001i | −0.593268 | − | 0.805005i | \(-0.702162\pi\) | ||
0.593268 | − | 0.805005i | \(-0.297838\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.917494 | −0.0922117 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6987 | 1.56208 | 0.781040 | − | 0.624481i | \(-0.214689\pi\) | ||||
0.781040 | + | 0.624481i | \(0.214689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.37467i | − | 0.825180i | −0.910917 | − | 0.412590i | \(-0.864624\pi\) | ||
0.910917 | − | 0.412590i | \(-0.135376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.58277 | + | 5.31046i | 0.447232 | + | 0.518247i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.52262i | − | 0.630565i | −0.948998 | − | 0.315283i | \(-0.897901\pi\) | ||
0.948998 | − | 0.315283i | \(-0.102099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.11474 | 0.777251 | 0.388626 | − | 0.921396i | \(-0.372950\pi\) | ||||
0.388626 | + | 0.921396i | \(0.372950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2086 | 1.15879 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.9224i | − | 1.21563i | −0.794077 | − | 0.607817i | \(-0.792045\pi\) | ||
0.794077 | − | 0.607817i | \(-0.207955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.69287 | + | 1.46089i | −0.157861 | + | 0.136229i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.332296i | − | 0.0307208i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.7206 | −1.25776 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8077 | 1.07343 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.47406i | 0.403412i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.44200 | + | 5.98737i | −0.844518 | + | 0.535527i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.05406i | 0.625947i | 0.949762 | + | 0.312973i | \(0.101325\pi\) | ||||
−0.949762 | + | 0.312973i | \(0.898675\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.83797 | 0.514004 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1585 | 0.974923 | 0.487461 | − | 0.873145i | \(-0.337923\pi\) | ||||
0.487461 | + | 0.873145i | \(0.337923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.28358i | − | 0.371434i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.49261 | − | 7.32887i | 0.730927 | − | 0.630768i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.71462i | − | 0.231926i | −0.993254 | − | 0.115963i | \(-0.963005\pi\) | ||
0.993254 | − | 0.115963i | \(-0.0369953\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0913 | 1.11039 | 0.555197 | − | 0.831719i | \(-0.312643\pi\) | ||||
0.555197 | + | 0.831719i | \(0.312643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.1238 | 1.27365 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.26046i | 0.690774i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.4861 | − | 13.3099i | −0.953865 | − | 1.10533i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 6.99873i | − | 0.577245i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0898 | 0.990435 | 0.495217 | − | 0.868769i | \(-0.335088\pi\) | ||||
0.495217 | + | 0.868769i | \(0.335088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.9430 | −1.21604 | −0.608021 | − | 0.793921i | \(-0.708036\pi\) | ||||
−0.608021 | + | 0.793921i | \(0.708036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.50129i | − | 0.121372i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.97305 | − | 10.3979i | −0.720732 | − | 0.835177i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.78395i | − | 0.381800i | −0.981609 | − | 0.190900i | \(-0.938859\pi\) | ||
0.981609 | − | 0.190900i | \(-0.0611407\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.94114 | −0.391858 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.75578 | −0.138375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.49063i | − | 0.430059i | −0.976608 | − | 0.215030i | \(-0.931015\pi\) | ||
0.976608 | − | 0.215030i | \(-0.0689848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.4445 | − | 12.4652i | 1.12450 | − | 0.970413i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.26932i | − | 0.562517i | −0.959632 | − | 0.281258i | \(-0.909248\pi\) | ||
0.959632 | − | 0.281258i | \(-0.0907518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0082 | 0.769865 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.468705 | 0.0358427 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.50892i | − | 0.570893i | −0.958395 | − | 0.285446i | \(-0.907858\pi\) | ||
0.958395 | − | 0.285446i | \(-0.0921418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.68442 | − | 1.28451i | −0.656480 | − | 0.0970995i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.42511i | − | 0.257447i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.73414 | −0.428590 | −0.214295 | − | 0.976769i | \(-0.568745\pi\) | ||||
−0.214295 | + | 0.976769i | \(0.568745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.2262 | 1.87505 | 0.937523 | − | 0.347923i | \(-0.113113\pi\) | ||||
0.937523 | + | 0.347923i | \(0.113113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.25977i | 0.462736i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.5678 | + | 9.98263i | −0.850478 | + | 0.733937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.3202i | 2.72912i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.80823 | 0.640704 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.63151 | −0.262767 | −0.131383 | − | 0.991332i | \(-0.541942\pi\) | ||||
−0.131383 | + | 0.991332i | \(0.541942\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7050i | 1.56236i | 0.624307 | + | 0.781179i | \(0.285381\pi\) | ||||
−0.624307 | + | 0.781179i | \(0.714619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.51461 | + | 5.23148i | 0.323298 | + | 0.374634i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 7.26526i | − | 0.517628i | −0.965927 | − | 0.258814i | \(-0.916668\pi\) | ||
0.965927 | − | 0.258814i | \(-0.0833317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52705 | 0.462690 | 0.231345 | − | 0.972872i | \(-0.425687\pi\) | ||||
0.231345 | + | 0.972872i | \(0.425687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.8064 | −1.60864 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 13.8046i | − | 0.968890i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.65831 | − | 4.23921i | −0.255508 | − | 0.296079i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.192116i | − | 0.0133530i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6514 | −0.805944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.7856 | 1.56863 | 0.784313 | − | 0.620365i | \(-0.213016\pi\) | ||||
0.784313 | + | 0.620365i | \(0.213016\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 23.9363i | − | 1.64009i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.53152 | + | 4.77354i | −0.377247 | + | 0.325553i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.7843i | − | 0.732086i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0199634 | 0.00134900 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5165 | −0.909221 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.86315i | − | 0.459591i | −0.973239 | − | 0.229795i | \(-0.926194\pi\) | ||
0.973239 | − | 0.229795i | \(-0.0738057\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.140549 | − | 0.950240i | 0.00936995 | − | 0.0633493i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.5001i | 1.16152i | 0.814074 | + | 0.580761i | \(0.197245\pi\) | ||||
−0.814074 | + | 0.580761i | \(0.802755\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8643 | 1.57700 | 0.788498 | − | 0.615038i | \(-0.210859\pi\) | ||||
0.788498 | + | 0.615038i | \(0.210859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9813 | 0.985699 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.8957i | − | 1.43444i | −0.696849 | − | 0.717218i | \(-0.745415\pi\) | ||
0.696849 | − | 0.717218i | \(-0.254585\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.3299 | + | 12.3663i | −0.934779 | + | 0.806686i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.8299i | 1.93766i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3443 | −1.25128 | −0.625639 | − | 0.780113i | \(-0.715162\pi\) | ||||
−0.625639 | + | 0.780113i | \(0.715162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4761 | 0.739240 | 0.369620 | − | 0.929183i | \(-0.379488\pi\) | ||||
0.369620 | + | 0.929183i | \(0.379488\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.99352i | 0.127884i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.72266 | + | 6.63135i | 0.365607 | + | 0.423662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.21988i | − | 0.268504i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.71935 | 0.299077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0040 | −1.07328 | −0.536641 | − | 0.843811i | \(-0.680307\pi\) | ||||
−0.536641 | + | 0.843811i | \(0.680307\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.77574i | 0.300248i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.3967 | + | 23.6355i | 1.27729 | + | 1.48011i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6462i | 0.913607i | 0.889568 | + | 0.456803i | \(0.151006\pi\) | ||||
−0.889568 | + | 0.456803i | \(0.848994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9977 | −0.745499 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.51048 | 0.0934964 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.2641i | − | 0.632912i | −0.948607 | − | 0.316456i | \(-0.897507\pi\) | ||
0.948607 | − | 0.316456i | \(-0.102493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.68178 | − | 4.04023i | 0.287599 | − | 0.248190i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 23.5353i | − | 1.44034i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.61485 | 0.159430 | 0.0797150 | − | 0.996818i | \(-0.474599\pi\) | ||||
0.0797150 | + | 0.996818i | \(0.474599\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.87492 | −0.599859 | −0.299929 | − | 0.953961i | \(-0.596963\pi\) | ||||
−0.299929 | + | 0.953961i | \(0.596963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.42591i | 0.328391i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.49387 | + | 23.6217i | −0.210688 | + | 1.42444i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.21949i | 0.253525i | 0.991933 | + | 0.126762i | \(0.0404585\pi\) | ||||
−0.991933 | + | 0.126762i | \(0.959541\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.18001 | 0.0706451 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4058 | −0.799724 | −0.399862 | − | 0.916575i | \(-0.630942\pi\) | ||||
−0.399862 | + | 0.916575i | \(0.630942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.66084i | 0.336502i | 0.985744 | + | 0.168251i | \(0.0538119\pi\) | ||||
−0.985744 | + | 0.168251i | \(0.946188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.37902 | + | 6.36787i | −0.437095 | + | 0.377200i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.39676i | − | 0.259532i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −44.0668 | −2.59217 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.3305 | −1.66076 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.70404i | 0.333233i | 0.986022 | + | 0.166617i | \(0.0532842\pi\) | ||||
−0.986022 | + | 0.166617i | \(0.946716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.80062 | + | 3.24532i | 0.163058 | + | 0.188950i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 23.9585i | − | 1.39021i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.72967 | −0.100029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.73710 | −0.330681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 28.0481i | − | 1.61132i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.11844 | − | 5.93119i | −0.293081 | − | 0.339619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8943i | 0.850065i | 0.905178 | + | 0.425033i | \(0.139737\pi\) | ||||
−0.905178 | + | 0.425033i | \(0.860263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9626 | −0.851192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0355 | 0.569059 | 0.284530 | − | 0.958667i | \(-0.408163\pi\) | ||||
0.284530 | + | 0.958667i | \(0.408163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.5043i | − | 1.32854i | −0.747491 | − | 0.664272i | \(-0.768742\pi\) | ||
0.747491 | − | 0.664272i | \(-0.231258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.571025 | − | 0.492777i | 0.0321736 | − | 0.0277649i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.94093i | 0.446007i | 0.974818 | + | 0.223004i | \(0.0715862\pi\) | ||||
−0.974818 | + | 0.223004i | \(0.928414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.5486 | −2.10232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.6536 | −0.650442 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.0651i | − | 1.06081i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.55527 | − | 1.26540i | −0.474561 | − | 0.0701919i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 14.4982i | − | 0.801752i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.8625 | −0.819393 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.31442 | −0.347072 | −0.173536 | − | 0.984828i | \(-0.555519\pi\) | ||||
−0.173536 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.31277i | − | 0.0719394i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.6093 | − | 18.6482i | 1.18064 | − | 1.01886i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 23.4516i | − | 1.27749i | −0.769418 | − | 0.638746i | \(-0.779453\pi\) | ||
0.769418 | − | 0.638746i | \(-0.220547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.0877 | −1.25395 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.3334 | −1.58849 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1683i | 1.03499i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.61010 | + | 3.02456i | 0.140523 | + | 0.162837i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 15.4757i | − | 0.830780i | −0.909643 | − | 0.415390i | \(-0.863645\pi\) | ||
0.909643 | − | 0.415390i | \(-0.136355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.5514 | 1.36773 | 0.683867 | − | 0.729607i | \(-0.260297\pi\) | ||||
0.683867 | + | 0.729607i | \(0.260297\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.67724 | 0.463157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.5917i | 1.25566i | 0.778352 | + | 0.627829i | \(0.216056\pi\) | ||||
−0.778352 | + | 0.627829i | \(0.783944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.5720 | + | 22.6798i | 1.03878 | + | 1.20372i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.5139i | 1.29741i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.14840 | 0.166166 | 0.0830832 | − | 0.996543i | \(-0.473523\pi\) | ||||
0.0830832 | + | 0.996543i | \(0.473523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0479 | −0.686729 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.0963i | − | 1.10727i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0189155 | + | 0.0163235i | −0.000990084 | + | 0.000854413i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4297i | 1.69282i | 0.532534 | + | 0.846408i | \(0.321240\pi\) | ||||
−0.532534 | + | 0.846408i | \(0.678760\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.481088 | 0.0250445 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85577 | 0.252099 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.99302i | − | 0.413863i | −0.978355 | − | 0.206931i | \(-0.933652\pi\) | ||
0.978355 | − | 0.206931i | \(-0.0663477\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.6973 | + | 16.8695i | 0.552408 | + | 0.871140i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.5993i | − | 0.700398i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.96061 | 0.460275 | 0.230138 | − | 0.973158i | \(-0.426082\pi\) | ||||
0.230138 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6031 | 0.645678 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 36.7195i | − | 1.87628i | −0.346255 | − | 0.938141i | \(-0.612547\pi\) | ||
0.346255 | − | 0.938141i | \(-0.387453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.1949 | + | 12.2498i | −0.723441 | + | 0.624308i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 0.627747i | − | 0.0319102i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0627294 | −0.00318051 | −0.00159025 | − | 0.999999i | \(-0.500506\pi\) | ||||
−0.00159025 | + | 0.999999i | \(0.500506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.81453 | −0.395198 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 19.9363i | − | 1.00565i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.3910 | − | 28.2640i | −1.22725 | − | 1.42212i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.9714i | 1.05252i | 0.850323 | + | 0.526262i | \(0.176407\pi\) | ||||
−0.850323 | + | 0.526262i | \(0.823593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.65326 | −0.383142 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.8567 | −0.691972 | −0.345986 | − | 0.938240i | \(-0.612456\pi\) | ||||
−0.345986 | + | 0.938240i | \(0.612456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.6239i | − | 0.529215i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.9361 | − | 16.1490i | −0.692490 | − | 0.802450i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.6338i | 1.61760i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5868 | −0.622378 | −0.311189 | − | 0.950348i | \(-0.600727\pi\) | ||||
−0.311189 | + | 0.950348i | \(0.600727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.85007 | −0.239236 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.36593i | 0.165627i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.47162 | + | 3.85888i | −0.219503 | + | 0.189425i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 23.3896i | − | 1.14540i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.4927 | −1.58737 | −0.793685 | − | 0.608328i | \(-0.791840\pi\) | ||||
−0.793685 | + | 0.608328i | \(0.791840\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.8356 | 0.917992 | 0.458996 | − | 0.888438i | \(-0.348209\pi\) | ||||
0.458996 | + | 0.888438i | \(0.348209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.62623i | − | 0.0790702i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38.6521 | − | 5.71701i | −1.87490 | − | 0.277316i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.15162i | − | 0.297698i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.7585 | 0.712549 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.66739 | −0.0803155 | −0.0401577 | − | 0.999193i | \(-0.512786\pi\) | ||||
−0.0401577 | + | 0.999193i | \(0.512786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.83595i | − | 0.280458i | −0.990119 | − | 0.140229i | \(-0.955216\pi\) | ||
0.990119 | − | 0.140229i | \(-0.0447839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.7801 | + | 20.5215i | −1.14017 | + | 0.983933i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.43970i | − | 0.116707i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5742 | 1.45923 | 0.729614 | − | 0.683860i | \(-0.239700\pi\) | ||||
0.729614 | + | 0.683860i | \(0.239700\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.752562 | −0.0358363 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 34.9173i | − | 1.65897i | −0.558530 | − | 0.829485i | \(-0.688634\pi\) | ||
0.558530 | − | 0.829485i | \(-0.311366\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2441 | + | 22.2999i | 0.912259 | + | 1.05712i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 21.6002i | − | 1.02166i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.1265 | 1.56334 | 0.781668 | − | 0.623694i | \(-0.214369\pi\) | ||||
0.781668 | + | 0.623694i | \(0.214369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9592 | −0.563138 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.6978i | 1.25437i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.43661 | − | 5.14109i | −0.207992 | − | 0.241018i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.27252i | − | 0.199860i | −0.994994 | − | 0.0999299i | \(-0.968138\pi\) | ||
0.994994 | − | 0.0999299i | \(-0.0318619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.2032 | 1.82985 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.4702 | −1.79173 | −0.895867 | − | 0.444322i | \(-0.853444\pi\) | ||||
−0.895867 | + | 0.444322i | \(0.853444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.94727i | 0.415815i | 0.978148 | + | 0.207908i | \(0.0666653\pi\) | ||||
−0.978148 | + | 0.207908i | \(0.933335\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.5773 | + | 16.0317i | −0.861503 | + | 0.743452i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 16.3171i | − | 0.755064i | −0.925996 | − | 0.377532i | \(-0.876773\pi\) | ||
0.925996 | − | 0.377532i | \(-0.123227\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.4124 | 1.03491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.54723 | −0.393836 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.6050i | 0.717518i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.78485 | − | 12.0672i | 0.0818947 | − | 0.553682i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.531313i | 0.0243272i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.9574 | 0.546349 | 0.273174 | − | 0.961965i | \(-0.411926\pi\) | ||||
0.273174 | + | 0.961965i | \(0.411926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8192 | −0.538911 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.13696i | 0.142737i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.8434 | − | 23.1650i | 1.21889 | − | 1.05187i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.19495i | 0.0541484i | 0.999633 | + | 0.0270742i | \(0.00861904\pi\) | ||||
−0.999633 | + | 0.0270742i | \(0.991381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.80982 | −0.443616 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6912 | 0.617874 | 0.308937 | − | 0.951083i | \(-0.400027\pi\) | ||||
0.308937 | + | 0.951083i | \(0.400027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 61.4406i | − | 2.76714i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34036 | − | 1.55319i | −0.0602447 | − | 0.0698109i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.5227i | 1.05514i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.9774 | 0.536184 | 0.268092 | − | 0.963393i | \(-0.413607\pi\) | ||||
0.268092 | + | 0.963393i | \(0.413607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.9877 | −0.580249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 32.3666i | − | 1.44316i | −0.692333 | − | 0.721578i | \(-0.743417\pi\) | ||
0.692333 | − | 0.721578i | \(-0.256583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.9341 | + | 26.5758i | 1.02056 | + | 1.18261i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 17.8812i | − | 0.794133i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.6507 | −0.693706 | −0.346853 | − | 0.937919i | \(-0.612750\pi\) | ||||
−0.346853 | + | 0.937919i | \(0.612750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0196185 | −0.000867872 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.2393i | 0.540377i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.1772 | − | 12.2345i | 0.624721 | − | 0.539116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.4261i | 1.77794i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.4158 | −0.588889 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7184 | 0.951499 | 0.475749 | − | 0.879581i | \(-0.342177\pi\) | ||||
0.475749 | + | 0.879581i | \(0.342177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.89014i | − | 0.388739i | −0.980928 | − | 0.194369i | \(-0.937734\pi\) | ||
0.980928 | − | 0.194369i | \(-0.0622660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.29496 | + | 15.5160i | −0.100160 | + | 0.677174i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 47.9981i | − | 2.09083i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.368297 | −0.0159827 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.33137i | − | 0.187613i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0419 | − | 9.52884i | 0.477384 | − | 0.411968i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.2449i | 0.442100i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.7077 | 0.805798 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0112 | −1.24729 | −0.623645 | − | 0.781708i | \(-0.714349\pi\) | ||||
−0.623645 | + | 0.781708i | \(0.714349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 45.0703i | − | 1.93415i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.8548 | + | 13.7372i | 0.507802 | + | 0.588436i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.9089i | 1.06503i | 0.846421 | + | 0.532514i | \(0.178753\pi\) | ||||
−0.846421 | + | 0.532514i | \(0.821247\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.673103 | 0.0287273 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.1818 | 0.817172 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 29.3145i | − | 1.24658i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.8355 | + | 20.6675i | 0.757073 | + | 0.877287i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.3536i | − | 0.650552i | −0.945619 | − | 0.325276i | \(-0.894543\pi\) | ||
0.945619 | − | 0.325276i | \(-0.105457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65178 | −0.239045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 66.6781 | 2.81515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.8264i | 0.709146i | 0.935028 | + | 0.354573i | \(0.115374\pi\) | ||||
−0.935028 | + | 0.354573i | \(0.884626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.8758 | − | 18.8782i | 0.920323 | − | 0.794212i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 16.7492i | − | 0.703398i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.75646 | −0.0736344 | −0.0368172 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368172 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.4273 | −0.561913 | −0.280956 | − | 0.959721i | \(-0.590652\pi\) | ||||
−0.280956 | + | 0.959721i | \(0.590652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.48823i | 0.271050i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.94619 | − | 0.731587i | −0.206270 | − | 0.0305093i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.4806i | 0.852620i | 0.904577 | + | 0.426310i | \(0.140187\pi\) | ||||
−0.904577 | + | 0.426310i | \(0.859813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.7792 | 1.61161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.63781 | −0.192409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13.2078i | − | 0.547010i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.562533 | − | 0.485449i | 0.0232579 | − | 0.0200709i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.3569i | 1.87208i | 0.351893 | + | 0.936040i | \(0.385538\pi\) | ||||
−0.351893 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.9851 | 0.617449 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9805 | −0.533945 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.8520i | − | 1.18481i | −0.805641 | − | 0.592404i | \(-0.798179\pi\) | ||
0.805641 | − | 0.592404i | \(-0.201821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0443 | − | 23.2271i | −0.821736 | − | 0.952219i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 11.6615i | − | 0.477275i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.78767 | 0.359054 | 0.179527 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179527 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.7810 | −1.82665 | −0.913327 | − | 0.407227i | \(-0.866496\pi\) | ||||
−0.913327 | + | 0.407227i | \(0.866496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.45234i | 0.0998669i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.2498 | + | 19.9889i | 0.701305 | + | 0.812664i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.96387i | 0.282655i | 0.989963 | + | 0.141327i | \(0.0451370\pi\) | ||||
−0.989963 | + | 0.141327i | \(0.954863\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.6639 | −0.999432 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.6414 | −0.592329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.6214i | 1.23679i | 0.785869 | + | 0.618393i | \(0.212216\pi\) | ||||
−0.785869 | + | 0.618393i | \(0.787784\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.57398 | + | 6.53612i | −0.305412 | + | 0.263562i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.6041i | − | 0.426905i | −0.976953 | − | 0.213452i | \(-0.931529\pi\) | ||
0.976953 | − | 0.213452i | \(-0.0684709\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.0095 | 0.844445 | 0.422223 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422223 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.01670 | 0.201313 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.1286i | 0.926629i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9296 | − | 7.23713i | −0.957182 | − | 0.289485i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.8170i | 0.831349i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −53.3985 | −2.12914 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.45489 | −0.217156 | −0.108578 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108578 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 40.7099i | − | 1.61807i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.9416 | + | 10.3052i | −0.473887 | + | 0.408950i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.77552i | 0.268456i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.57383 | −0.101819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.7734 | −1.13648 | −0.568241 | − | 0.822862i | \(-0.692376\pi\) | ||||
−0.568241 | + | 0.822862i | \(0.692376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5319i | 0.454775i | 0.973804 | + | 0.227388i | \(0.0730185\pi\) | ||||
−0.973804 | + | 0.227388i | \(0.926982\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.52864 | + | 9.88289i | 0.335815 | + | 0.389138i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.18564i | − | 0.125240i | −0.998037 | − | 0.0626202i | \(-0.980054\pi\) | ||
0.998037 | − | 0.0626202i | \(-0.0199457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.15538 | 0.359380 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.2678 | −0.755163 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 28.6814i | − | 1.12239i | −0.827684 | − | 0.561194i | \(-0.810342\pi\) | ||
0.827684 | − | 0.561194i | \(-0.189658\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.3014 | + | 18.8898i | 0.636947 | + | 0.738087i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.00214664i | − | 8.37483e-5i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0012 | 0.934954 | 0.467477 | − | 0.884005i | \(-0.345163\pi\) | ||||
0.467477 | + | 0.884005i | \(0.345163\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.9043 | 1.24093 | 0.620467 | − | 0.784232i | \(-0.286943\pi\) | ||||
0.620467 | + | 0.784232i | \(0.286943\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.1493i | 0.937882i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.25153 | − | 6.25785i | 0.281202 | − | 0.242669i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.86235i | − | 0.304431i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2620 | −0.474078 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.7325 | −0.645950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.87848i | − | 0.0724101i | −0.999344 | − | 0.0362051i | \(-0.988473\pi\) | ||
0.999344 | − | 0.0362051i | \(-0.0115269\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.8136 | + | 3.67016i | 0.955075 | + | 0.141264i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 34.6119i | − | 1.33024i | −0.746736 | − | 0.665121i | \(-0.768380\pi\) | ||
0.746736 | − | 0.665121i | \(-0.231620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.8410 | 1.06844 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.2665 | 1.19814 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0493i | 0.614110i | 0.951692 | + | 0.307055i | \(0.0993436\pi\) | ||||
−0.951692 | + | 0.307055i | \(0.900656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.59549 | − | 3.96577i | 0.175584 | − | 0.151524i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 42.6371i | − | 1.62671i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.78356 | 0.182239 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5985 | 0.745564 | 0.372782 | − | 0.927919i | \(-0.378404\pi\) | ||||
0.372782 | + | 0.927919i | \(0.378404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.61092i | − | 0.0611937i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.1250 | + | 22.1619i | 0.725454 | + | 0.840648i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 19.5688i | − | 0.741223i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.1199 | −1.47965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.5536 | −1.94715 | −0.973575 | − | 0.228366i | \(-0.926662\pi\) | ||||
−0.973575 | + | 0.228366i | \(0.926662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.6711i | − | 0.628761i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 22.0942 | + | 25.6025i | 0.832115 | + | 0.964245i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.5635i | 1.03663i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.64772 | −0.324772 | −0.162386 | − | 0.986727i | \(-0.551919\pi\) | ||||
−0.162386 | + | 0.986727i | \(0.551919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.20756 | 0.120293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6.14217i | − | 0.230026i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.9838 | + | 12.0676i | −0.522966 | + | 0.451304i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.5615i | 1.29072i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.50754 | −0.279984 | −0.139992 | − | 0.990153i | \(-0.544708\pi\) | ||||
−0.139992 | + | 0.990153i | \(0.544708\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7041 | 0.547608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.5037i | − | 0.762543i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.75199 | − | 38.8887i | 0.213624 | − | 1.44429i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.79852i | 0.103791i | 0.998653 | + | 0.0518956i | \(0.0165263\pi\) | ||||
−0.998653 | + | 0.0518956i | \(0.983474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0566 | −0.928022 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.5344 | −0.944423 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.38900i | − | 0.0513038i | −0.999671 | − | 0.0256519i | \(-0.991834\pi\) | ||
0.999671 | − | 0.0256519i | \(-0.00816615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8479 | − | 10.2244i | 0.437017 | − | 0.377132i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 60.9619i | − | 2.24556i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.31935 | 0.232461 | 0.116230 | − | 0.993222i | \(-0.462919\pi\) | ||||
0.116230 | + | 0.993222i | \(0.462919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.53944 | −0.276968 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.7611i | 1.45869i | 0.684144 | + | 0.729347i | \(0.260176\pi\) | ||||
−0.684144 | + | 0.729347i | \(0.739824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6619 | + | 20.4664i | 0.647082 | + | 0.749831i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 0.507464i | − | 0.0185671i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.4523 | 0.418457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.27267 | −0.265384 | −0.132692 | − | 0.991157i | \(-0.542362\pi\) | ||||
−0.132692 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.3801i | 1.10711i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8301 | − | 25.2964i | −0.794478 | − | 0.920632i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.8682i | − | 0.576739i | −0.957519 | − | 0.288369i | \(-0.906887\pi\) | ||
0.957519 | − | 0.288369i | \(-0.0931131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.53258 | 0.309713 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.80457 | −0.174166 | −0.0870828 | − | 0.996201i | \(-0.527754\pi\) | ||||
−0.0870828 | + | 0.996201i | \(0.527754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2477i | 0.515801i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.54149 | − | 2.19323i | 0.0918876 | − | 0.0792963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.31588i | 0.119729i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.1358 | −1.08673 | −0.543363 | − | 0.839498i | \(-0.682849\pi\) | ||||
−0.543363 | + | 0.839498i | \(0.682849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.1677 | 0.942406 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.35253i | 0.120582i | 0.998181 | + | 0.0602910i | \(0.0192029\pi\) | ||||
−0.998181 | + | 0.0602910i | \(0.980797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.49353 | − | 30.3803i | 0.161412 | − | 1.09129i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.4356i | 0.768999i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.10941 | 0.218892 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 63.9821 | 2.28946 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.4431i | 1.40958i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.09858 | − | 6.98883i | 0.289051 | − | 0.249442i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.36807i | 0.0844126i | 0.999109 | + | 0.0422063i | \(0.0134387\pi\) | ||||
−0.999109 | + | 0.0422063i | \(0.986561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.3384 | −0.652863 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.6888 | 0.806722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.06013i | − | 0.215202i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.21848 | − | 8.36469i | −0.256013 | − | 0.296665i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0367i | 1.17022i | 0.810954 | + | 0.585110i | \(0.198949\pi\) | ||||
−0.810954 | + | 0.585110i | \(0.801051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −66.1490 | −2.34018 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.53071 | −0.0894183 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0533626i | 0.00188313i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56501 | − | 2.97230i | −0.0904046 | − | 0.104760i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.67181i | − | 0.164456i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.7157 | 0.587692 | 0.293846 | − | 0.955853i | \(-0.405065\pi\) | ||||
0.293846 | + | 0.955853i | \(0.405065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.85752 | 0.205685 | 0.102843 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102843 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.6430i | 0.618768i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.29489 | − | 8.02121i | 0.325586 | − | 0.280971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.97185i | − | 0.278900i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.583439 | 0.0203870 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.3966 | 0.921249 | 0.460625 | − | 0.887595i | \(-0.347625\pi\) | ||||
0.460625 | + | 0.887595i | \(0.347625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5803i | 0.891672i | 0.895115 | + | 0.445836i | \(0.147094\pi\) | ||||
−0.895115 | + | 0.445836i | \(0.852906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.2037 | + | 6.24232i | 1.46935 | + | 0.217330i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.74132i | 0.338739i | 0.985553 | + | 0.169369i | \(0.0541731\pi\) | ||||
−0.985553 | + | 0.169369i | \(0.945827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.7679 | 1.90217 | 0.951085 | − | 0.308931i | \(-0.0999711\pi\) | ||||
0.951085 | + | 0.308931i | \(0.0999711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.53875 | 0.261516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.6114i | 1.06062i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.3060 | − | 10.6197i | 0.425866 | − | 0.367510i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.8134i | 1.06507i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.2171 | −1.76821 | −0.884106 | − | 0.467286i | \(-0.845232\pi\) | ||||
−0.884106 | + | 0.467286i | \(0.845232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8166 | 1.13161 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.9515i | 0.824933i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.6210 | + | 16.9426i | 0.502977 | + | 0.582844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.7318i | 0.712352i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.1139 | 0.347109 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.83324 | −0.234240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.2520i | − | 0.796135i | −0.917356 | − | 0.398067i | \(-0.869681\pi\) | ||
0.917356 | − | 0.398067i | \(-0.130319\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.684727 | + | 0.793454i | 0.0234172 | + | 0.0271356i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 48.8722i | − | 1.66944i | −0.550674 | − | 0.834721i | \(-0.685629\pi\) | ||
0.550674 | − | 0.834721i | \(-0.314371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7171 | −0.433903 | −0.216952 | − | 0.976182i | \(-0.569611\pi\) | ||||
−0.216952 | + | 0.976182i | \(0.569611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.85546 | −0.267713 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.5511i | 0.461285i | 0.973039 | + | 0.230642i | \(0.0740827\pi\) | ||||
−0.973039 | + | 0.230642i | \(0.925917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7116 | − | 10.9697i | 0.432207 | − | 0.372982i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 78.7320i | 2.67388i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −79.7357 | −2.70485 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.0791 | 0.748121 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.04633i | 0.103103i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5125 | − | 16.5781i | −0.355388 | − | 0.560441i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.88341i | 0.164901i | 0.996595 | + | 0.0824505i | \(0.0262746\pi\) | ||||
−0.996595 | + | 0.0824505i | \(0.973725\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1911 | 0.343738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5717 | −0.760461 | −0.380230 | − | 0.924892i | \(-0.624155\pi\) | ||||
−0.380230 | + | 0.924892i | \(0.624155\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 0.202906i | − | 0.00682834i | −0.999994 | − | 0.00341417i | \(-0.998913\pi\) | ||
0.999994 | − | 0.00341417i | \(-0.00108677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.79825 | − | 5.00372i | 0.194906 | − | 0.168198i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1859i | 0.644201i | 0.946705 | + | 0.322100i | \(0.104389\pi\) | ||||
−0.946705 | + | 0.322100i | \(0.895611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.3854 | −0.415392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.5579 | −1.52625 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20.6518i | − | 0.691085i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.37696 | − | 9.70713i | −0.280011 | − | 0.324473i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.09031i | 0.103183i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.2919 | 1.61062 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.6118 | 0.719993 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.2502i | 0.341105i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.8527 | + | 42.7045i | 1.22503 | + | 1.41955i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 12.9713i | − | 0.430704i | −0.976536 | − | 0.215352i | \(-0.930910\pi\) | ||
0.976536 | − | 0.215352i | \(-0.0690899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.01597 | −0.100033 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3377 | −1.03826 | −0.519132 | − | 0.854694i | \(-0.673745\pi\) | ||||
−0.519132 | + | 0.854694i | \(0.673745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.6149i | 0.417492i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.5970 | + | 9.14485i | −0.350324 | + | 0.302320i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.5919i | 0.646980i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.4577 | 1.26860 | 0.634302 | − | 0.773085i | \(-0.281288\pi\) | ||||
0.634302 | + | 0.773085i | \(0.281288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.6110 | 0.876861 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.1729i | 0.762746i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.7985 | − | 4.99911i | −1.11129 | − | 0.164370i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.60890i | 0.0528433i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.3396 | 1.78282 | 0.891412 | − | 0.453193i | \(-0.149715\pi\) | ||||
0.891412 | + | 0.453193i | \(0.149715\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.55689 | −0.313215 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 17.9299i | − | 0.586998i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −63.1780 | + | 54.5208i | −2.06614 | + | 1.78302i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.1182i | 1.40861i | 0.709898 | + | 0.704304i | \(0.248741\pi\) | ||||
−0.709898 | + | 0.704304i | \(0.751259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.9940 | −1.37042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.22344 | 0.300676 | 0.150338 | − | 0.988635i | \(-0.451964\pi\) | ||||
0.150338 | + | 0.988635i | \(0.451964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.50416i | − | 0.0815467i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.8679 | + | 14.9111i | 0.418592 | + | 0.485060i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 45.8127i | − | 1.48871i | −0.667782 | − | 0.744357i | \(-0.732756\pi\) | ||
0.667782 | − | 0.744357i | \(-0.267244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0193268 | −0.000627374 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1877 | 0.460066 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2363i | 0.687913i | 0.938986 | + | 0.343956i | \(0.111767\pi\) | ||||
−0.938986 | + | 0.343956i | \(0.888233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.30524 | − | 6.14765i | −0.171674 | − | 0.198933i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 67.0861i | 2.16859i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.76627 | 0.153911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.72623 | 0.216975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25310i | 0.0403805i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.7436 | + | 31.7086i | −1.18282 | + | 1.02074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.88651i | 0.189297i | 0.995511 | + | 0.0946486i | \(0.0301728\pi\) | ||||
−0.995511 | + | 0.0946486i | \(0.969827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.0627 | −1.09425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.1841 | −0.872378 | −0.436189 | − | 0.899855i | \(-0.643672\pi\) | ||||
−0.436189 | + | 0.899855i | \(0.643672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.9855i | 0.736882i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.26083 | + | 15.2853i | −0.0724046 | + | 0.489520i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.5280i | 1.55255i | 0.630395 | + | 0.776274i | \(0.282893\pi\) | ||||
−0.630395 | + | 0.776274i | \(0.717107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.9102 | 2.01062 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.55897 | −0.0497740 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 50.7935i | − | 1.62006i | −0.586388 | − | 0.810030i | \(-0.699451\pi\) | ||
0.586388 | − | 0.810030i | \(-0.300549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.2991 | − | 10.6138i | 0.391882 | − | 0.338182i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.5540i | 0.845223i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.26755 | −0.103902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.42740 | 0.299471 | 0.149736 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149736 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.2816i | 0.358012i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.53531 | + | 11.0494i | 0.302290 | + | 0.350290i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 6.78817i | − | 0.214984i | −0.994206 | − | 0.107492i | \(-0.965718\pi\) | ||
0.994206 | − | 0.107492i | \(-0.0342819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.2803 | 1.08458 |
(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 | 1840.2.e.g.369.3 | 14 | ||
4.3 | odd | 2 | 920.2.e.b.369.12 | yes | 14 | ||
5.2 | odd | 4 | 9200.2.a.cz.1.2 | 7 | |||
5.3 | odd | 4 | 9200.2.a.dc.1.6 | 7 | |||
5.4 | even | 2 | inner | 1840.2.e.g.369.12 | 14 | ||
20.3 | even | 4 | 4600.2.a.bh.1.2 | 7 | |||
20.7 | even | 4 | 4600.2.a.bi.1.6 | 7 | |||
20.19 | odd | 2 | 920.2.e.b.369.3 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.3 | ✓ | 14 | 20.19 | odd | 2 | ||
920.2.e.b.369.12 | yes | 14 | 4.3 | odd | 2 | ||
1840.2.e.g.369.3 | 14 | 1.1 | even | 1 | trivial | ||
1840.2.e.g.369.12 | 14 | 5.4 | even | 2 | inner | ||
4600.2.a.bh.1.2 | 7 | 20.3 | even | 4 | |||
4600.2.a.bi.1.6 | 7 | 20.7 | even | 4 | |||
9200.2.a.cz.1.2 | 7 | 5.2 | odd | 4 | |||
9200.2.a.dc.1.6 | 7 | 5.3 | odd | 4 |