Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 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("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 8 x^{10} + 4 x^{9} + 36 x^{8} - 128 x^{7} + 232 x^{6} + 104 x^{5} + 324 x^{4} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.6 | ||
Root | \(0.531065 - 0.531065i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.k.2431.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.549104i | − | 0.207542i | −0.994601 | − | 0.103771i | \(-0.966909\pi\) | ||
0.994601 | − | 0.103771i | \(-0.0330909\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.98504i | 0.598513i | 0.954173 | + | 0.299257i | \(0.0967387\pi\) | ||||
−0.954173 | + | 0.299257i | \(0.903261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38877i | 0.662525i | 0.943539 | + | 0.331262i | \(0.107474\pi\) | ||||
−0.943539 | + | 0.331262i | \(0.892526\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.49807 | −1.09094 | −0.545471 | − | 0.838130i | \(-0.683649\pi\) | ||||
−0.545471 | + | 0.838130i | \(0.683649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.14448 | − | 1.35030i | −0.950808 | − | 0.309780i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.549104i | − | 0.119824i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.88909i | 0.602418i | 0.953558 | + | 0.301209i | \(0.0973901\pi\) | ||||
−0.953558 | + | 0.301209i | \(0.902610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.54699i | − | 0.658660i | −0.944215 | − | 0.329330i | \(-0.893177\pi\) | ||
0.944215 | − | 0.329330i | \(-0.106823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0281611 | 0.00505789 | 0.00252895 | − | 0.999997i | \(-0.499195\pi\) | ||||
0.00252895 | + | 0.999997i | \(0.499195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.98504i | 0.345552i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.549104i | 0.0928155i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.37396i | 0.554675i | 0.960773 | + | 0.277338i | \(0.0894521\pi\) | ||||
−0.960773 | + | 0.277338i | \(0.910548\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.38877i | 0.382509i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.40793i | − | 0.688402i | −0.938896 | − | 0.344201i | \(-0.888150\pi\) | ||
0.938896 | − | 0.344201i | \(-0.111850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.83806i | − | 1.04279i | −0.853314 | − | 0.521397i | \(-0.825411\pi\) | ||
0.853314 | − | 0.521397i | \(-0.174589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.4981i | − | 1.53130i | −0.643257 | − | 0.765650i | \(-0.722417\pi\) | ||
0.643257 | − | 0.765650i | \(-0.277583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.69848 | 0.956926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.49807 | −0.629856 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.4775i | − | 1.71391i | −0.515391 | − | 0.856955i | \(-0.672353\pi\) | ||
0.515391 | − | 0.856955i | \(-0.327647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.98504i | − | 0.267663i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.14448 | − | 1.35030i | −0.548949 | − | 0.178851i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.79880 | 0.494562 | 0.247281 | − | 0.968944i | \(-0.420463\pi\) | ||||
0.247281 | + | 0.968944i | \(0.420463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8231 | −1.38576 | −0.692878 | − | 0.721055i | \(-0.743658\pi\) | ||||
−0.692878 | + | 0.721055i | \(0.743658\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 0.549104i | − | 0.0691806i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.38877i | − | 0.296290i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.92887 | −0.602157 | −0.301079 | − | 0.953599i | \(-0.597347\pi\) | ||||
−0.301079 | + | 0.953599i | \(0.597347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.88909i | 0.347806i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.1763 | −1.80110 | −0.900548 | − | 0.434757i | \(-0.856834\pi\) | ||||
−0.900548 | + | 0.434757i | \(0.856834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.76272 | −0.908558 | −0.454279 | − | 0.890859i | \(-0.650103\pi\) | ||||
−0.454279 | + | 0.890859i | \(0.650103\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.09000 | 0.124217 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.04703 | 0.230309 | 0.115154 | − | 0.993348i | \(-0.463264\pi\) | ||||
0.115154 | + | 0.993348i | \(0.463264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.95317i | − | 0.872974i | −0.899711 | − | 0.436487i | \(-0.856223\pi\) | ||
0.899711 | − | 0.436487i | \(-0.143777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.49807 | 0.487884 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.54699i | − | 0.380278i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0323659i | 0.00343078i | 0.999999 | + | 0.00171539i | \(0.000546026\pi\) | ||||
−0.999999 | + | 0.00171539i | \(0.999454\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.31168 | 0.137502 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0281611 | 0.00292017 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.14448 | + | 1.35030i | 0.425214 | + | 0.138538i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.596131i | − | 0.0605279i | −0.999542 | − | 0.0302640i | \(-0.990365\pi\) | ||
0.999542 | − | 0.0302640i | \(-0.00963479\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.98504i | 0.199504i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8004 | −1.37319 | −0.686594 | − | 0.727041i | \(-0.740895\pi\) | ||||
−0.686594 | + | 0.727041i | \(0.740895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5966 | 1.04411 | 0.522056 | − | 0.852911i | \(-0.325165\pi\) | ||||
0.522056 | + | 0.852911i | \(0.325165\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.549104i | 0.0535871i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.48472 | 0.143533 | 0.0717665 | − | 0.997421i | \(-0.477136\pi\) | ||||
0.0717665 | + | 0.997421i | \(0.477136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.973949i | 0.0932874i | 0.998912 | + | 0.0466437i | \(0.0148525\pi\) | ||||
−0.998912 | + | 0.0466437i | \(0.985147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.37396i | 0.320242i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.25885i | 0.776927i | 0.921464 | + | 0.388464i | \(0.126994\pi\) | ||||
−0.921464 | + | 0.388464i | \(0.873006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.88909i | − | 0.269409i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.38877i | 0.220842i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.46991i | 0.226416i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.05960 | 0.641782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.40793i | − | 0.397449i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2186 | −1.08423 | −0.542113 | − | 0.840306i | \(-0.682376\pi\) | ||||
−0.542113 | + | 0.840306i | \(0.682376\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.83806i | − | 0.602058i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.4849i | − | 1.09081i | −0.838173 | − | 0.545404i | \(-0.816376\pi\) | ||
0.838173 | − | 0.545404i | \(-0.183624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.741454 | + | 2.27575i | −0.0642922 | + | 0.197333i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.63266 | 0.566666 | 0.283333 | − | 0.959022i | \(-0.408560\pi\) | ||||
0.283333 | + | 0.959022i | \(0.408560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.43383i | − | 0.376073i | −0.982162 | − | 0.188036i | \(-0.939788\pi\) | ||
0.982162 | − | 0.188036i | \(-0.0602123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 10.4981i | − | 0.884097i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.74181 | −0.396530 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.54699i | 0.294562i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.69848 | 0.552482 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.58255 | −0.375417 | −0.187709 | − | 0.982225i | \(-0.560106\pi\) | ||||
−0.187709 | + | 0.982225i | \(0.560106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.32098 | 0.595773 | 0.297886 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297886 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.49807 | −0.363647 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0281611 | −0.00226196 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4479 | −0.833830 | −0.416915 | − | 0.908946i | \(-0.636889\pi\) | ||||
−0.416915 | + | 0.908946i | \(0.636889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 12.4775i | − | 0.989527i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.58641 | 0.125027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6983i | − | 0.994611i | −0.867576 | − | 0.497305i | \(-0.834323\pi\) | ||
0.867576 | − | 0.497305i | \(-0.165677\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.98504i | − | 0.154536i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.2673 | −1.25880 | −0.629399 | − | 0.777082i | \(-0.716699\pi\) | ||||
−0.629399 | + | 0.777082i | \(0.716699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.29380 | 0.561061 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.14448 | − | 1.35030i | −0.316936 | − | 0.103260i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.4612i | 1.32755i | 0.747932 | + | 0.663776i | \(0.231047\pi\) | ||||
−0.747932 | + | 0.663776i | \(0.768953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.549104i | − | 0.0415084i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79880 | 0.285536 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.91855 | −0.442373 | −0.221186 | − | 0.975232i | \(-0.570993\pi\) | ||||
−0.221186 | + | 0.975232i | \(0.570993\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.8524i | 1.77294i | 0.462789 | + | 0.886469i | \(0.346849\pi\) | ||||
−0.462789 | + | 0.886469i | \(0.653151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8231 | −0.800067 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.37396i | − | 0.248058i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.92887i | − | 0.652944i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.549104i | − | 0.0399414i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.779128i | − | 0.0563757i | −0.999603 | − | 0.0281879i | \(-0.991026\pi\) | ||
0.999603 | − | 0.0281879i | \(-0.00897367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1438i | 1.01809i | 0.860740 | + | 0.509045i | \(0.170001\pi\) | ||||
−0.860740 | + | 0.509045i | \(0.829999\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.38877i | − | 0.171063i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.5679 | −1.82164 | −0.910820 | − | 0.412803i | \(-0.864550\pi\) | ||||
−0.910820 | + | 0.412803i | \(0.864550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.29620i | 0.517214i | 0.965983 | + | 0.258607i | \(0.0832634\pi\) | ||||
−0.965983 | + | 0.258607i | \(0.916737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.92887 | −0.347656 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.94767 | −0.136700 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.40793i | 0.307863i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.88909i | 0.200806i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.68040 | − | 8.22697i | 0.185407 | − | 0.569072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7321 | 0.807674 | 0.403837 | − | 0.914831i | \(-0.367676\pi\) | ||||
0.403837 | + | 0.914831i | \(0.367676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.1763 | −1.03986 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.83806i | 0.466352i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.0154634i | − | 0.00104972i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.76272 | −0.524556 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.7448i | − | 0.722776i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.27596 | −0.353304 | −0.176652 | − | 0.984273i | \(-0.556527\pi\) | ||||
−0.176652 | + | 0.984273i | \(0.556527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.83586 | −0.320967 | −0.160484 | − | 0.987038i | \(-0.551305\pi\) | ||||
−0.160484 | + | 0.987038i | \(0.551305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.1941 | −1.20230 | −0.601151 | − | 0.799135i | \(-0.705291\pi\) | ||||
−0.601151 | + | 0.799135i | \(0.705291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.09000 | 0.0717165 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.14794 | −0.337253 | −0.168626 | − | 0.985680i | \(-0.553933\pi\) | ||||
−0.168626 | + | 0.985680i | \(0.553933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4981i | 0.684819i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.04703 | 0.132969 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.9516i | − | 0.837767i | −0.908040 | − | 0.418884i | \(-0.862422\pi\) | ||
0.908040 | − | 0.418884i | \(-0.137578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.60963i | − | 0.554595i | −0.960784 | − | 0.277298i | \(-0.910561\pi\) | ||
0.960784 | − | 0.277298i | \(-0.0894388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.69848 | −0.427950 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.22555 | − | 9.90019i | 0.205237 | − | 0.629934i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 7.95317i | − | 0.504012i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 27.3239i | − | 1.72467i | −0.506338 | − | 0.862335i | \(-0.669001\pi\) | ||
0.506338 | − | 0.862335i | \(-0.330999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.73498 | −0.360555 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.49807 | 0.281680 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 15.0604i | − | 0.939441i | −0.882815 | − | 0.469720i | \(-0.844355\pi\) | ||
0.882815 | − | 0.469720i | \(-0.155645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85265 | 0.115118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 3.54699i | − | 0.219553i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.5652i | − | 1.76141i | −0.473668 | − | 0.880703i | \(-0.657070\pi\) | ||
0.473668 | − | 0.880703i | \(-0.342930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.4775i | 0.766484i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.0323659i | 0.00198076i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.4252i | 1.67214i | 0.548621 | + | 0.836071i | \(0.315153\pi\) | ||||
−0.548621 | + | 0.836071i | \(0.684847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.5383i | − | 1.67284i | −0.548093 | − | 0.836418i | \(-0.684646\pi\) | ||
0.548093 | − | 0.836418i | \(-0.315354\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.31168 | 0.0793866 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.98504i | 0.119703i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2412 | −0.855672 | −0.427836 | − | 0.903856i | \(-0.640724\pi\) | ||||
−0.427836 | + | 0.903856i | \(0.640724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0281611 | 0.00168596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.13443i | 0.246640i | 0.992367 | + | 0.123320i | \(0.0393541\pi\) | ||||
−0.992367 | + | 0.123320i | \(0.960646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.4044i | − | 1.33180i | −0.746040 | − | 0.665901i | \(-0.768047\pi\) | ||
0.746040 | − | 0.665901i | \(-0.231953\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.14448 | + | 1.35030i | 0.245498 | + | 0.0799847i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.42041 | −0.142872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.23263 | 0.190155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 0.596131i | − | 0.0349458i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.64601i | 0.563526i | 0.959484 | + | 0.281763i | \(0.0909192\pi\) | ||||
−0.959484 | + | 0.281763i | \(0.909081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79880 | −0.221175 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.98504i | 0.115184i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.90137 | −0.399117 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.75481 | −0.216423 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.8004 | −0.792811 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.8231 | 0.619729 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.6037 | 1.57542 | 0.787712 | − | 0.616043i | \(-0.211265\pi\) | ||||
0.787712 | + | 0.616043i | \(0.211265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5966 | 0.602818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.71077i | 0.380533i | 0.981732 | + | 0.190266i | \(0.0609352\pi\) | ||||
−0.981732 | + | 0.190266i | \(0.939065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.30165 | 0.0735734 | 0.0367867 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367867 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.549104i | 0.0309385i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 21.4736i | − | 1.20608i | −0.797712 | − | 0.603039i | \(-0.793956\pi\) | ||
0.797712 | − | 0.603039i | \(-0.206044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.04094 | 0.394217 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.48472 | 0.0828688 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6422 | + | 6.07373i | 1.03728 | + | 0.337952i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.38877i | 0.132505i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.973949i | 0.0538595i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.76453 | −0.317809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.9657 | −1.64706 | −0.823532 | − | 0.567270i | \(-0.808000\pi\) | ||||
−0.823532 | + | 0.567270i | \(0.808000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.37396i | 0.184892i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.92887 | 0.269293 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.3254i | 1.59746i | 0.601693 | + | 0.798728i | \(0.294493\pi\) | ||||
−0.601693 | + | 0.798728i | \(0.705507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.25885i | 0.448559i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0559011i | 0.00302722i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.52189i | − | 0.406144i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2.88909i | − | 0.155544i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.22343i | 0.334091i | 0.985949 | + | 0.167046i | \(0.0534228\pi\) | ||||
−0.985949 | + | 0.167046i | \(0.946577\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.83180 | 0.419227 | 0.209613 | − | 0.977784i | \(-0.432779\pi\) | ||||
0.209613 | + | 0.977784i | \(0.432779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.38877i | 0.127503i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.10154 | −0.218303 | −0.109151 | − | 0.994025i | \(-0.534813\pi\) | ||||
−0.109151 | + | 0.994025i | \(0.534813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1763 | 0.805474 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.46991i | 0.130721i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.67706i | 0.457958i | 0.973431 | + | 0.228979i | \(0.0735387\pi\) | ||||
−0.973431 | + | 0.228979i | \(0.926461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3534 | + | 11.1926i | 0.808073 | + | 0.589082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.05960 | 0.370533 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.76272 | 0.406320 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.58967i | 0.343978i | 0.985099 | + | 0.171989i | \(0.0550193\pi\) | ||||
−0.985099 | + | 0.171989i | \(0.944981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.40793i | − | 0.229467i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.85142 | −0.355708 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1789i | 1.09660i | 0.836281 | + | 0.548302i | \(0.184725\pi\) | ||||
−0.836281 | + | 0.548302i | \(0.815275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.47294 | 0.436379 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3582 | 1.19983 | 0.599914 | − | 0.800064i | \(-0.295201\pi\) | ||||
0.599914 | + | 0.800064i | \(0.295201\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2186 | −0.625978 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.77542 | −0.448403 | −0.224201 | − | 0.974543i | \(-0.571977\pi\) | ||||
−0.224201 | + | 0.974543i | \(0.571977\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.09000 | −0.0555514 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.83806i | − | 0.347598i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.15133 | 0.463991 | 0.231995 | − | 0.972717i | \(-0.425475\pi\) | ||||
0.231995 | + | 0.972717i | \(0.425475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.9953i | − | 0.657203i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.4849i | − | 0.629778i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.04703 | −0.102997 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7505 | 0.890873 | 0.445436 | − | 0.895314i | \(-0.353049\pi\) | ||||
0.445436 | + | 0.895314i | \(0.353049\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.741454 | + | 2.27575i | −0.0371191 | + | 0.113930i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.1362i | − | 1.65474i | −0.561655 | − | 0.827372i | \(-0.689835\pi\) | ||
0.561655 | − | 0.827372i | \(-0.310165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0672704i | 0.00335098i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.69746 | −0.331981 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.8447i | − | 0.536235i | −0.963386 | − | 0.268117i | \(-0.913599\pi\) | ||
0.963386 | − | 0.268117i | \(-0.0864015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.63266 | 0.327165 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.08594i | − | 0.102642i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.95317i | 0.390406i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.43383i | − | 0.217126i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.6151i | 1.78876i | 0.447305 | + | 0.894381i | \(0.352384\pi\) | ||||
−0.447305 | + | 0.894381i | \(0.647616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2843i | 1.52470i | 0.647163 | + | 0.762352i | \(0.275955\pi\) | ||||
−0.647163 | + | 0.762352i | \(0.724045\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 10.4981i | − | 0.510434i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.49807 | −0.218188 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.94301i | 0.287602i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.74181 | −0.228937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.11974 | −0.102104 | −0.0510522 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510522 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.68020i | 0.224916i | 0.993656 | + | 0.112458i | \(0.0358724\pi\) | ||||
−0.993656 | + | 0.112458i | \(0.964128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.54699i | 0.170065i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.90114 | − | 11.9738i | 0.186617 | − | 0.572784i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9361 | 0.521952 | 0.260976 | − | 0.965345i | \(-0.415956\pi\) | ||||
0.260976 | + | 0.965345i | \(0.415956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.69848 | 0.318975 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.6930i | − | 0.793107i | −0.918012 | − | 0.396554i | \(-0.870206\pi\) | ||
0.918012 | − | 0.396554i | \(-0.129794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 0.0323659i | − | 0.00153429i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.58255 | −0.216747 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.4864i | 1.06120i | 0.847622 | + | 0.530600i | \(0.178033\pi\) | ||||
−0.847622 | + | 0.530600i | \(0.821967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.74993 | 0.412018 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.32098 | 0.343969 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.31168 | −0.0614926 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.8834 | 1.35111 | 0.675555 | − | 0.737310i | \(-0.263904\pi\) | ||||
0.675555 | + | 0.737310i | \(0.263904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.49807 | −0.209952 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.2365 | −0.756208 | −0.378104 | − | 0.925763i | \(-0.623424\pi\) | ||||
−0.378104 | + | 0.925763i | \(0.623424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.2699i | − | 0.988498i | −0.869320 | − | 0.494249i | \(-0.835443\pi\) | ||
0.869320 | − | 0.494249i | \(-0.164557\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.0281611 | −0.00130594 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.74688i | 0.127111i | 0.997978 | + | 0.0635553i | \(0.0202439\pi\) | ||||
−0.997978 | + | 0.0635553i | \(0.979756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.70646i | 0.124973i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4479 | −0.481412 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.5739 | 0.624126 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.14448 | − | 1.35030i | −0.190162 | − | 0.0619559i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.4775i | − | 0.571303i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.8836i | 1.04558i | 0.852462 | + | 0.522790i | \(0.175109\pi\) | ||||
−0.852462 | + | 0.522790i | \(0.824891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.05960 | −0.367486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.58641 | 0.0721843 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.596131i | 0.0270689i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.9321 | 1.22041 | 0.610205 | − | 0.792244i | \(-0.291087\pi\) | ||||
0.610205 | + | 0.792244i | \(0.291087\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.6983i | − | 0.574239i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.99912i | − | 0.270737i | −0.990795 | − | 0.135368i | \(-0.956778\pi\) | ||
0.990795 | − | 0.135368i | \(-0.0432217\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.9546i | 0.718560i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 1.98504i | − | 0.0892211i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.33337i | 0.373803i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8066i | 0.483768i | 0.970305 | + | 0.241884i | \(0.0777653\pi\) | ||||
−0.970305 | + | 0.241884i | \(0.922235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.2673 | −0.726767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 21.9373i | − | 0.978135i | −0.872246 | − | 0.489068i | \(-0.837337\pi\) | ||
0.872246 | − | 0.489068i | \(-0.162663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.8004 | 0.614109 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.29380 | 0.323929 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 17.1858i | − | 0.761748i | −0.924627 | − | 0.380874i | \(-0.875623\pi\) | ||
0.924627 | − | 0.380874i | \(-0.124377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.26254i | 0.188564i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.14448 | − | 1.35030i | −0.182983 | − | 0.0596171i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5966 | −0.466941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.8391 | 0.916504 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.4612i | 0.766462i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4.41552i | − | 0.193447i | −0.995311 | − | 0.0967237i | \(-0.969164\pi\) | ||
0.995311 | − | 0.0967237i | \(-0.0308363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.4144 | −0.542842 | −0.271421 | − | 0.962461i | \(-0.587494\pi\) | ||||
−0.271421 | + | 0.962461i | \(0.587494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 0.549104i | − | 0.0239649i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.126671 | −0.00551787 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.6531 | 0.637093 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.79880 | 0.164854 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5295 | 0.456084 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.48472 | −0.0641899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.91855 | −0.255404 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.2968i | 0.572733i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.9115 | −0.899057 | −0.449528 | − | 0.893266i | \(-0.648408\pi\) | ||||
−0.449528 | + | 0.893266i | \(0.648408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.8524i | 1.02361i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.973949i | − | 0.0417194i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.4357 | −1.68615 | −0.843075 | − | 0.537796i | \(-0.819257\pi\) | ||||
−0.843075 | + | 0.537796i | \(0.819257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.8231 | −0.461919 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.78950 | + | 14.7004i | −0.204039 | + | 0.626260i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.12403i | − | 0.0477987i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3.37396i | − | 0.143217i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.9645 | −1.10015 | −0.550075 | − | 0.835115i | \(-0.685401\pi\) | ||||
−0.550075 | + | 0.835115i | \(0.685401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3345 | 0.690877 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 8.92887i | − | 0.376977i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.9955 | −1.39060 | −0.695298 | − | 0.718721i | \(-0.744728\pi\) | ||||
−0.695298 | + | 0.718721i | \(0.744728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.25885i | − | 0.347452i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.549104i | − | 0.0230602i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.61692i | − | 0.0677849i | −0.999425 | − | 0.0338924i | \(-0.989210\pi\) | ||
0.999425 | − | 0.0338924i | \(-0.0107904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.46476i | 0.186844i | 0.995627 | + | 0.0934221i | \(0.0297806\pi\) | ||||
−0.995627 | + | 0.0934221i | \(0.970219\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 0.779128i | − | 0.0325485i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.88909i | 0.120484i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5216 | −1.39552 | −0.697761 | − | 0.716331i | \(-0.745820\pi\) | ||||
−0.697761 | + | 0.716331i | \(0.745820\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1438i | 0.587795i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.36712 | −0.181179 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.7683 | 1.02580 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.38877i | − | 0.0987633i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.24563i | − | 0.340333i | −0.985415 | − | 0.170167i | \(-0.945569\pi\) | ||
0.985415 | − | 0.170167i | \(-0.0544306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.116713 | − | 0.0380259i | −0.00480908 | − | 0.00156683i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5679 | −1.05172 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.4320 | −0.428392 | −0.214196 | − | 0.976791i | \(-0.568713\pi\) | ||||
−0.214196 | + | 0.976791i | \(0.568713\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.46991i | − | 0.101256i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.29620i | 0.298614i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7797 | 1.09419 | 0.547094 | − | 0.837071i | \(-0.315734\pi\) | ||||
0.547094 | + | 0.837071i | \(0.315734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.8979i | − | 0.811652i | −0.913950 | − | 0.405826i | \(-0.866984\pi\) | ||
0.913950 | − | 0.405826i | \(-0.133016\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.92887 | −0.200719 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.05960 | −0.287013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.1488 | −0.411928 | −0.205964 | − | 0.978560i | \(-0.566033\pi\) | ||||
−0.205964 | + | 0.978560i | \(0.566033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.94767 | −0.0789235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.0774 | 1.01452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9759 | 0.483701 | 0.241851 | − | 0.970313i | \(-0.422246\pi\) | ||||
0.241851 | + | 0.970313i | \(0.422246\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.40793i | 0.177745i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.74054 | 0.110330 | 0.0551650 | − | 0.998477i | \(-0.482432\pi\) | ||||
0.0551650 | + | 0.998477i | \(0.482432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1098i | 1.00925i | 0.863339 | + | 0.504625i | \(0.168369\pi\) | ||||
−0.863339 | + | 0.504625i | \(0.831631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.88909i | 0.115935i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.0177723 | 0.000712031 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.68040 | − | 8.22697i | 0.107045 | − | 0.328554i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 15.1763i | − | 0.605119i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.7053i | 0.983501i | 0.870736 | + | 0.491750i | \(0.163643\pi\) | ||||
−0.870736 | + | 0.491750i | \(0.836357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.7321 | 0.466311 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.2186 | 0.484881 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0011i | 0.633987i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.1763 | −0.600365 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.8782i | 0.864137i | 0.901841 | + | 0.432068i | \(0.142216\pi\) | ||||
−0.901841 | + | 0.432068i | \(0.857784\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.1896i | 1.26943i | 0.772745 | + | 0.634717i | \(0.218883\pi\) | ||||
−0.772745 | + | 0.634717i | \(0.781117\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.83806i | 0.269248i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 5.96906i | − | 0.234668i | −0.993093 | − | 0.117334i | \(-0.962565\pi\) | ||
0.993093 | − | 0.117334i | \(-0.0374348\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.54079i | 0.296002i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 0.0154634i | − | 0.000606058i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.1388 | −0.592429 | −0.296214 | − | 0.955121i | \(-0.595724\pi\) | ||||
−0.296214 | + | 0.955121i | \(0.595724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.4849i | 0.487824i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.76272 | −0.302853 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.6974 | 1.00103 | 0.500515 | − | 0.865728i | \(-0.333144\pi\) | ||||
0.500515 | + | 0.865728i | \(0.333144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 40.2383i | − | 1.56509i | −0.622595 | − | 0.782545i | \(-0.713921\pi\) | ||
0.622595 | − | 0.782545i | \(-0.286079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 10.7448i | − | 0.417295i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.741454 | − | 2.27575i | 0.0287524 | − | 0.0882498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.2476 | 0.396789 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.27596 | −0.203980 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.4843i | − | 0.829394i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.5749i | 1.48695i | 0.668763 | + | 0.743476i | \(0.266824\pi\) | ||||
−0.668763 | + | 0.743476i | \(0.733176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.86548i | 0.110129i | 0.998483 | + | 0.0550646i | \(0.0175365\pi\) | ||||
−0.998483 | + | 0.0550646i | \(0.982464\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.327338 | −0.0125621 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.83586 | −0.185311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.62407 | −0.138671 | −0.0693355 | − | 0.997593i | \(-0.522088\pi\) | ||||
−0.0693355 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.63266 | −0.253421 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.1941 | −0.694150 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.8057 | 1.13551 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.2507i | − | 1.11275i | −0.830932 | − | 0.556375i | \(-0.812192\pi\) | ||
0.830932 | − | 0.556375i | \(-0.187808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.09000 | 0.0414055 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.43383i | 0.168185i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.8272i | 0.751007i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.14794 | −0.194713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.9657 | −0.829635 | −0.414817 | − | 0.909905i | \(-0.636155\pi\) | ||||
−0.414817 | + | 0.909905i | \(0.636155\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.55585 | − | 13.9833i | 0.171827 | − | 0.527390i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.4981i | 0.395380i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.57784i | 0.284994i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.9631 | 1.95151 | 0.975757 | − | 0.218855i | \(-0.0702321\pi\) | ||||
0.975757 | + | 0.218855i | \(0.0702321\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.04703 | 0.0767695 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0813602i | 0.00304696i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.74181 | 0.177334 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 12.9516i | − | 0.483685i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.1730i | 1.05068i | 0.850894 | + | 0.525338i | \(0.176061\pi\) | ||||
−0.850894 | + | 0.525338i | \(0.823939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5.81863i | − | 0.216697i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8.60963i | − | 0.320196i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3.54699i | − | 0.131732i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.6145i | − | 0.875814i | −0.899020 | − | 0.437907i | \(-0.855720\pi\) | ||
0.899020 | − | 0.437907i | \(-0.144280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.7581i | 1.13763i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7108 | −0.654164 | −0.327082 | − | 0.944996i | \(-0.606065\pi\) | ||||
−0.327082 | + | 0.944996i | \(0.606065\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.69848 | −0.247077 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9.78403i | − | 0.360399i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.44899i | − | 0.200444i | −0.994965 | − | 0.100222i | \(-0.968045\pi\) | ||
0.994965 | − | 0.100222i | \(-0.0319553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.22555 | − | 9.90019i | 0.118493 | − | 0.363693i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.92965 | −0.144165 | −0.0720825 | − | 0.997399i | \(-0.522964\pi\) | ||||
−0.0720825 | + | 0.997399i | \(0.522964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.58255 | 0.167892 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 7.95317i | − | 0.290991i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 0.815264i | − | 0.0297891i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.9639 | 0.473061 | 0.236530 | − | 0.971624i | \(-0.423990\pi\) | ||||
0.236530 | + | 0.971624i | \(0.423990\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 27.3239i | − | 0.995739i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.32098 | −0.266438 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1638 | 1.05998 | 0.529989 | − | 0.848004i | \(-0.322196\pi\) | ||||
0.529989 | + | 0.848004i | \(0.322196\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.73498 | −0.208167 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.6750 | 0.966970 | 0.483485 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483485 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.534800 | 0.0193610 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.49807 | 0.162628 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.07445i | 0.327660i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0447 | 1.04738 | 0.523690 | − | 0.851909i | \(-0.324555\pi\) | ||||
0.523690 | + | 0.851909i | \(0.324555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.0604i | − | 0.542386i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 11.6718i | − | 0.419806i | −0.977722 | − | 0.209903i | \(-0.932685\pi\) | ||
0.977722 | − | 0.209903i | \(-0.0673149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0281611 | 0.00101158 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.85265 | 0.0664636 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.95201 | + | 18.2686i | −0.213253 | + | 0.654539i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 30.1256i | − | 1.07798i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 3.54699i | − | 0.126759i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.4479 | 0.372900 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.9721 | 1.67438 | 0.837188 | − | 0.546916i | \(-0.184198\pi\) | ||||
0.837188 | + | 0.546916i | \(0.184198\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 28.5652i | − | 1.01695i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.53497 | 0.161245 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.8539i | − | 0.918098i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.4775i | 0.442530i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 22.4468i | − | 0.795107i | −0.917579 | − | 0.397554i | \(-0.869859\pi\) | ||
0.917579 | − | 0.397554i | \(-0.130141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.2211i | 1.67056i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0323659i | 0.00114359i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 15.4094i | − | 0.543784i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.58641 | −0.0559137 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.4252i | 0.965412i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.7277 | 1.29128 | 0.645639 | − | 0.763643i | \(-0.276591\pi\) | ||||
0.645639 | + | 0.763643i | \(0.276591\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.26926 | −0.325488 | −0.162744 | − | 0.986668i | \(-0.552034\pi\) | ||||
−0.162744 | + | 0.986668i | \(0.552034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 27.5383i | − | 0.965812i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.6983i | 0.444803i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.23342 | + | 28.3402i | −0.323036 | + | 0.991498i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.31168 | 0.0458339 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.20869 | 0.251585 | 0.125792 | − | 0.992057i | \(-0.459853\pi\) | ||||
0.125792 | + | 0.992057i | \(0.459853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7708i | 0.445163i | 0.974914 | + | 0.222582i | \(0.0714484\pi\) | ||||
−0.974914 | + | 0.222582i | \(0.928552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.98504i | 0.0691104i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.41946 | −0.118906 | −0.0594532 | − | 0.998231i | \(-0.518936\pi\) | ||||
−0.0594532 | + | 0.998231i | \(0.518936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.4787i | 0.641791i | 0.947115 | + | 0.320895i | \(0.103984\pi\) | ||||
−0.947115 | + | 0.320895i | \(0.896016\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2412 | −0.494022 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.1303 | −1.04395 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2673 | 0.562952 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.0281611 | 0.000973391 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.4966 | 0.707622 | 0.353811 | − | 0.935317i | \(-0.384886\pi\) | ||||
0.353811 | + | 0.935317i | \(0.384886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4188 | 0.566167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.13443i | 0.142397i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.29380 | −0.250914 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.87645i | − | 0.133197i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 22.4044i | − | 0.768916i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.74768 | −0.334146 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.2946 | −1.72206 | −0.861028 | − | 0.508558i | \(-0.830179\pi\) | ||||
−0.861028 | + | 0.508558i | \(0.830179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.14448 | + | 1.35030i | 0.141738 | + | 0.0461792i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41.0677i | − | 1.40285i | −0.712745 | − | 0.701423i | \(-0.752548\pi\) | ||
0.712745 | − | 0.701423i | \(-0.247452\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.8104i | 1.83599i | 0.396596 | + | 0.917993i | \(0.370191\pi\) | ||||
−0.396596 | + | 0.917993i | \(0.629809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.42041 | −0.0824874 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.7392 | 1.11445 | 0.557227 | − | 0.830360i | \(-0.311865\pi\) | ||||
0.557227 | + | 0.830360i | \(0.311865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 17.4612i | − | 0.593699i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.23263 | 0.109786 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.06344i | 0.137843i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 11.7739i | − | 0.398944i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.596131i | − | 0.0201760i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.549104i | 0.0185631i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.2494i | 0.751309i | 0.926760 | + | 0.375655i | \(0.122582\pi\) | ||||
−0.926760 | + | 0.375655i | \(0.877418\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.64601i | 0.325352i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4761 | 0.824622 | 0.412311 | − | 0.911043i | \(-0.364722\pi\) | ||||
0.412311 | + | 0.911043i | \(0.364722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 23.6715i | − | 0.796611i | −0.917253 | − | 0.398305i | \(-0.869598\pi\) | ||
0.917253 | − | 0.398305i | \(-0.130402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.79880 | −0.127695 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.2726 | −1.55368 | −0.776840 | − | 0.629697i | \(-0.783179\pi\) | ||||
−0.776840 | + | 0.629697i | \(0.783179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.70929i | 0.225022i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.98504i | 0.0665015i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.1755 | + | 43.5090i | −0.474366 | + | 1.45597i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.91855 | 0.197835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.90137 | −0.230430 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.0998874i | − | 0.00333143i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.1245i | 1.86978i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.75481 | −0.124952 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 23.8524i | − | 0.792882i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.9697 | −0.430651 | −0.215325 | − | 0.976542i | \(-0.569081\pi\) | ||||
−0.215325 | + | 0.976542i | \(0.569081\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.8004 | −0.457730 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.6057 | 0.815222 | 0.407611 | − | 0.913156i | \(-0.366362\pi\) | ||||
0.407611 | + | 0.913156i | \(0.366362\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.7874 | 0.522487 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.8231 | 0.357801 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.85549 | −0.226388 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.4360i | 1.03698i | 0.855084 | + | 0.518490i | \(0.173506\pi\) | ||||
−0.855084 | + | 0.518490i | \(0.826494\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.6037 | 0.909572 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 36.2526i | − | 1.19327i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.37396i | 0.110935i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5966 | 0.348037 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.57967 | 0.0846361 | 0.0423180 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423180 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.7617 | − | 9.04495i | −0.909854 | − | 0.296436i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.71077i | 0.219701i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.92887i | 0.292005i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.9943 | 0.816527 | 0.408264 | − | 0.912864i | \(-0.366134\pi\) | ||||
0.408264 | + | 0.912864i | \(0.366134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30165 | 0.0424776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8521i | 0.484164i | 0.970256 | + | 0.242082i | \(0.0778303\pi\) | ||||
−0.970256 | + | 0.242082i | \(0.922170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.7349 | 0.414706 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.549104i | 0.0178624i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.00685i | 0.0327183i | 0.999866 | + | 0.0163592i | \(0.00520752\pi\) | ||||
−0.999866 | + | 0.0163592i | \(0.994792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 18.5433i | − | 0.601942i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.4736i | − | 0.696329i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 8.23298i | − | 0.266692i | −0.991070 | − | 0.133346i | \(-0.957428\pi\) | ||
0.991070 | − | 0.133346i | \(-0.0425722\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.779128i | 0.0252120i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.04094 | 0.227601 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 3.64202i | − | 0.117607i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9992 | −0.999974 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.48472 | 0.0478443 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 14.1438i | − | 0.455304i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.69905i | 0.279743i | 0.990170 | + | 0.139871i | \(0.0446689\pi\) | ||||
−0.990170 | + | 0.139871i | \(0.955331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.6422 | + | 6.07373i | 0.598872 | + | 0.195116i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.1366 | −1.92988 | −0.964938 | − | 0.262479i | \(-0.915460\pi\) | ||||
−0.964938 | + | 0.262479i | \(0.915460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.43463 | −0.0780508 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.38877i | 0.0765017i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 35.3094i | − | 1.12965i | −0.825211 | − | 0.564824i | \(-0.808944\pi\) | ||
0.825211 | − | 0.564824i | \(-0.191056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0642478 | −0.00205337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.973949i | 0.0310958i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.04148 | −0.128903 | −0.0644516 | − | 0.997921i | \(-0.520530\pi\) | ||||
−0.0644516 | + | 0.997921i | \(0.520530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.5679 | 0.814662 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.76453 | −0.183487 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7558 | 0.628198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.28257 | −0.0725082 | −0.0362541 | − | 0.999343i | \(-0.511543\pi\) | ||||
−0.0362541 | + | 0.999343i | \(0.511543\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.9657 | −0.950933 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.29620i | − | 0.231305i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.58884 | −0.240341 | −0.120170 | − | 0.992753i | \(-0.538344\pi\) | ||||
−0.120170 | + | 0.992753i | \(0.538344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.37396i | 0.106747i |
(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 | 4560.2.d.k.2431.6 | yes | 12 | |
4.3 | odd | 2 | 4560.2.d.i.2431.7 | yes | 12 | ||
19.18 | odd | 2 | 4560.2.d.i.2431.6 | ✓ | 12 | ||
76.75 | even | 2 | inner | 4560.2.d.k.2431.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.i.2431.6 | ✓ | 12 | 19.18 | odd | 2 | ||
4560.2.d.i.2431.7 | yes | 12 | 4.3 | odd | 2 | ||
4560.2.d.k.2431.6 | yes | 12 | 1.1 | even | 1 | trivial | |
4560.2.d.k.2431.7 | yes | 12 | 76.75 | even | 2 | inner |