Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, 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("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.26 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.25 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.01811 | −1.89667 | −0.948335 | − | 0.317272i | \(-0.897233\pi\) | ||||
−0.948335 | + | 0.317272i | \(0.897233\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.36711 | −0.713710 | −0.356855 | − | 0.934160i | \(-0.616151\pi\) | ||||
−0.356855 | + | 0.934160i | \(0.616151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.01660 | 1.39135 | 0.695677 | − | 0.718354i | \(-0.255104\pi\) | ||||
0.695677 | + | 0.718354i | \(0.255104\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.91641i | 0.464797i | 0.972621 | + | 0.232398i | \(0.0746573\pi\) | ||||
−0.972621 | + | 0.232398i | \(0.925343\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.78232 | 1.09714 | 0.548569 | − | 0.836105i | \(-0.315173\pi\) | ||||
0.548569 | + | 0.836105i | \(0.315173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.01811i | − | 1.09504i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.28367 | − | 3.49535i | 0.684693 | − | 0.728831i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.75850 | 1.06933 | 0.534663 | − | 0.845065i | \(-0.320439\pi\) | ||||
0.534663 | + | 0.845065i | \(0.320439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.94661i | 0.708833i | 0.935088 | + | 0.354416i | \(0.115320\pi\) | ||||
−0.935088 | + | 0.354416i | \(0.884680\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.36711i | − | 0.412061i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 5.01811i | − | 0.848216i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.21675i | − | 1.35082i | −0.737440 | − | 0.675412i | \(-0.763966\pi\) | ||
0.737440 | − | 0.675412i | \(-0.236034\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.01660i | 0.803299i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.26306 | 0.978125 | 0.489063 | − | 0.872249i | \(-0.337339\pi\) | ||||
0.489063 | + | 0.872249i | \(0.337339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.50959 | −1.29770 | −0.648850 | − | 0.760916i | \(-0.724750\pi\) | ||||
−0.648850 | + | 0.760916i | \(0.724750\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.32504i | 1.21433i | 0.794575 | + | 0.607166i | \(0.207694\pi\) | ||||
−0.794575 | + | 0.607166i | \(0.792306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.1815 | 2.59735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.91641 | −0.268351 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.72989i | − | 0.237619i | −0.992917 | − | 0.118809i | \(-0.962092\pi\) | ||
0.992917 | − | 0.118809i | \(-0.0379078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.36711i | − | 0.319181i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.78232i | 0.633433i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4.37464i | − | 0.569530i | −0.958597 | − | 0.284765i | \(-0.908084\pi\) | ||
0.958597 | − | 0.284765i | \(-0.0919156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.56392i | 0.328276i | 0.986437 | + | 0.164138i | \(0.0524843\pi\) | ||||
−0.986437 | + | 0.164138i | \(0.947516\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.01811 | 0.632223 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.01660i | 0.622233i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.18000 | 0.632838 | 0.316419 | − | 0.948620i | \(-0.397519\pi\) | ||||
0.316419 | + | 0.948620i | \(0.397519\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.49535 | + | 3.28367i | 0.420791 | + | 0.395308i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.36201i | − | 1.11107i | −0.831494 | − | 0.555533i | \(-0.812514\pi\) | ||
0.831494 | − | 0.555533i | \(-0.187486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.89991 | −0.807574 | −0.403787 | − | 0.914853i | \(-0.632306\pi\) | ||||
−0.403787 | + | 0.914853i | \(0.632306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8784 | 1.35367 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.143570 | 0.0161529 | 0.00807644 | − | 0.999967i | \(-0.497429\pi\) | ||||
0.00807644 | + | 0.999967i | \(0.497429\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.9654 | −1.31337 | −0.656684 | − | 0.754166i | \(-0.728041\pi\) | ||||
−0.656684 | + | 0.754166i | \(0.728041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.91641 | −0.207864 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.75850i | 0.617376i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4681i | 1.21561i | 0.794085 | + | 0.607807i | \(0.207951\pi\) | ||||
−0.794085 | + | 0.607807i | \(0.792049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.1739 | −2.63894 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.94661 | −0.409245 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.78232i | 0.490655i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.2966i | − | 1.45160i | −0.687908 | − | 0.725798i | \(-0.741471\pi\) | ||
0.687908 | − | 0.725798i | \(-0.258529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.36711 | 0.237903 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.9368 | −1.38676 | −0.693379 | − | 0.720573i | \(-0.743879\pi\) | ||||
−0.693379 | + | 0.720573i | \(0.743879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.5326 | 1.82608 | 0.913038 | − | 0.407875i | \(-0.133730\pi\) | ||||
0.913038 | + | 0.407875i | \(0.133730\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.01811 | 0.489718 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.84039 | 0.661286 | 0.330643 | − | 0.943756i | \(-0.392734\pi\) | ||||
0.330643 | + | 0.943756i | \(0.392734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8804i | 1.61685i | 0.588598 | + | 0.808426i | \(0.299680\pi\) | ||||
−0.588598 | + | 0.808426i | \(0.700320\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.21675 | 0.779899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.3526i | 1.16203i | 0.813892 | + | 0.581016i | \(0.197345\pi\) | ||||
−0.813892 | + | 0.581016i | \(0.802655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.49535 | + | 3.28367i | 0.325943 | + | 0.306204i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.01660 | −0.463785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.61675i | − | 0.881566i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.39679 | −0.490617 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.26306i | 0.564721i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.03827i | 0.624545i | 0.949992 | + | 0.312273i | \(0.101090\pi\) | ||||
−0.949992 | + | 0.312273i | \(0.898910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 8.50959i | − | 0.749227i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8340i | 1.38342i | 0.722174 | + | 0.691712i | \(0.243143\pi\) | ||||
−0.722174 | + | 0.691712i | \(0.756857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.9982 | −2.08091 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.41398i | 0.804291i | 0.915576 | + | 0.402145i | \(0.131735\pi\) | ||||
−0.915576 | + | 0.402145i | \(0.868265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.23682i | 0.444181i | 0.975026 | + | 0.222090i | \(0.0712880\pi\) | ||||
−0.975026 | + | 0.222090i | \(0.928712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.32504 | −0.701095 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.8748 | −0.993024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.75850i | 0.478217i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.1815i | 1.49958i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.1290i | 1.73096i | 0.500947 | + | 0.865478i | \(0.332985\pi\) | ||||
−0.500947 | + | 0.865478i | \(0.667015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8189i | 1.77559i | 0.460235 | + | 0.887797i | \(0.347765\pi\) | ||||
−0.460235 | + | 0.887797i | \(0.652235\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.91641i | − | 0.154932i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.94661 | −0.317000 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.15443i | 0.411368i | 0.978618 | + | 0.205684i | \(0.0659419\pi\) | ||||
−0.978618 | + | 0.205684i | \(0.934058\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.72989 | 0.137189 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.4779 | + | 17.5401i | −1.29864 | + | 1.38235i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.43764i | − | 0.504235i | −0.967697 | − | 0.252117i | \(-0.918873\pi\) | ||
0.967697 | − | 0.252117i | \(-0.0811269\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.36711 | 0.184279 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.86457i | 0.376432i | 0.982128 | + | 0.188216i | \(0.0602705\pi\) | ||||
−0.982128 | + | 0.188216i | \(0.939729\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1663 | 0.935868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.78232 | −0.365713 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.1408 | 1.53128 | 0.765638 | − | 0.643272i | \(-0.222424\pi\) | ||||
0.765638 | + | 0.643272i | \(0.222424\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.01811 | 0.379334 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.37464 | 0.328818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.1505i | − | 0.908175i | −0.890957 | − | 0.454087i | \(-0.849965\pi\) | ||
0.890957 | − | 0.454087i | \(-0.150035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.58656i | − | 0.192258i | −0.995369 | − | 0.0961288i | \(-0.969354\pi\) | ||
0.995369 | − | 0.0961288i | \(-0.0306461\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.56392 | −0.189530 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.21675 | 0.604107 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.53635i | − | 0.331730i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.01811i | 0.365014i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.97384 | 0.287537 | 0.143768 | − | 0.989611i | \(-0.454078\pi\) | ||||
0.143768 | + | 0.989611i | \(0.454078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8995 | 1.00051 | 0.500254 | − | 0.865879i | \(-0.333240\pi\) | ||||
0.500254 | + | 0.865879i | \(0.333240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.01660 | −0.359246 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.0037 | 1.49646 | 0.748228 | − | 0.663442i | \(-0.230905\pi\) | ||||
0.748228 | + | 0.663442i | \(0.230905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.1044 | −1.70872 | −0.854358 | − | 0.519686i | \(-0.826049\pi\) | ||||
−0.854358 | + | 0.519686i | \(0.826049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.18000i | 0.365369i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.8968 | −2.02816 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.26306i | 0.437431i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.28367 | + | 3.49535i | −0.228231 | + | 0.242944i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.3203 | −0.783039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.03788i | 0.140294i | 0.997537 | + | 0.0701469i | \(0.0223468\pi\) | ||||
−0.997537 | + | 0.0701469i | \(0.977653\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.36201 | 0.641475 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.50959i | − | 0.580349i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.8046i | − | 1.34442i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 6.89991i | − | 0.466253i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.61385i | 0.646698i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5574i | 1.17573i | 0.808959 | + | 0.587865i | \(0.200031\pi\) | ||||
−0.808959 | + | 0.587865i | \(0.799969\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9674 | −0.794307 | −0.397154 | − | 0.917752i | \(-0.630002\pi\) | ||||
−0.397154 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.7251i | 1.10523i | 0.833438 | + | 0.552613i | \(0.186369\pi\) | ||||
−0.833438 | + | 0.552613i | \(0.813631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.8784i | 0.781543i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.6780 | −1.94427 | −0.972134 | − | 0.234425i | \(-0.924679\pi\) | ||||
−0.972134 | + | 0.234425i | \(0.924679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.32504 | −0.543066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.143570i | 0.00932587i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.9888i | 1.03423i | 0.855917 | + | 0.517113i | \(0.172993\pi\) | ||||
−0.855917 | + | 0.517113i | \(0.827007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 9.18015i | − | 0.591345i | −0.955289 | − | 0.295673i | \(-0.904456\pi\) | ||
0.955289 | − | 0.295673i | \(-0.0955438\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.1815i | 1.16157i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.9910 | 1.52651 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 11.9654i | − | 0.758273i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2154 | 1.21286 | 0.606432 | − | 0.795135i | \(-0.292600\pi\) | ||||
0.606432 | + | 0.795135i | \(0.292600\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.77282 | + | 8.27388i | −0.488673 | + | 0.520174i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 1.91641i | − | 0.120010i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.57519 | −0.597284 | −0.298642 | − | 0.954365i | \(-0.596534\pi\) | ||||
−0.298642 | + | 0.954365i | \(0.596534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41.2326i | 2.56207i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.75850 | −0.356442 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.3872 | −0.702168 | −0.351084 | − | 0.936344i | \(-0.614187\pi\) | ||||
−0.351084 | + | 0.936344i | \(0.614187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.72989 | 0.106266 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4681 | −0.701835 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8812 | 1.27315 | 0.636575 | − | 0.771215i | \(-0.280351\pi\) | ||||
0.636575 | + | 0.771215i | \(0.280351\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 23.1526i | − | 1.40642i | −0.710983 | − | 0.703209i | \(-0.751750\pi\) | ||
0.710983 | − | 0.703209i | \(-0.248250\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.1739i | − | 1.52359i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.36711 | 0.142742 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.52150 | 0.331755 | 0.165877 | − | 0.986146i | \(-0.446954\pi\) | ||||
0.165877 | + | 0.986146i | \(0.446954\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 3.94661i | − | 0.236278i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.0586i | − | 0.838665i | −0.907833 | − | 0.419333i | \(-0.862264\pi\) | ||
0.907833 | − | 0.419333i | \(-0.137736\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.4300 | −1.63054 | −0.815272 | − | 0.579078i | \(-0.803413\pi\) | ||||
−0.815272 | + | 0.579078i | \(0.803413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.78232 | −0.283280 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.4287 | −1.85518 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.3274 | 0.783964 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2966 | 0.838079 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.25711i | − | 0.365545i | −0.983155 | − | 0.182772i | \(-0.941493\pi\) | ||
0.983155 | − | 0.182772i | \(-0.0585071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.37464 | 0.254702 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.36711i | 0.137354i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.4729 | − | 17.5348i | 0.952651 | − | 1.01406i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.7021 | 2.46131 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 13.9368i | − | 0.800645i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.56392 | −0.146810 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 33.1297i | − | 1.89081i | −0.325899 | − | 0.945405i | \(-0.605667\pi\) | ||
0.325899 | − | 0.945405i | \(-0.394333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.5326i | 1.05429i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.1899i | 1.37168i | 0.727752 | + | 0.685841i | \(0.240565\pi\) | ||||
−0.727752 | + | 0.685841i | \(0.759435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.05898i | − | 0.229427i | −0.993399 | − | 0.114714i | \(-0.963405\pi\) | ||
0.993399 | − | 0.114714i | \(-0.0365950\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.01811i | 0.282739i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.25580 | −0.126698 | −0.0633491 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633491 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6310 | −0.763189 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.84039i | 0.381794i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.16486i | 0.509947i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.01660 | −0.278271 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8804 | −0.933490 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 41.7760i | − | 2.30319i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.5510i | 1.45938i | 0.683781 | + | 0.729688i | \(0.260334\pi\) | ||||
−0.683781 | + | 0.729688i | \(0.739666\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.21675i | 0.450275i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.18000i | 0.283014i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.0158041i | − | 0.000860902i | −1.00000 | 0.000430451i | \(-0.999863\pi\) | |||
1.00000 | 0.000430451i | \(-0.000137017\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3526 | −0.670899 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9.34207i | − | 0.505901i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −56.1099 | −3.02965 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.28367 | + | 3.49535i | −0.176787 | + | 0.188183i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 10.4024i | − | 0.558431i | −0.960229 | − | 0.279215i | \(-0.909926\pi\) | ||
0.960229 | − | 0.279215i | \(-0.0900743\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0381635 | 0.00204285 | 0.00102142 | − | 0.999999i | \(-0.499675\pi\) | ||||
0.00102142 | + | 0.999999i | \(0.499675\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.01660i | − | 0.267766i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.08032 | −0.163949 | −0.0819743 | − | 0.996634i | \(-0.526123\pi\) | ||||
−0.0819743 | + | 0.996634i | \(0.526123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.36201 | 0.496884 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.61675 | 0.508972 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2252 | 1.06744 | 0.533722 | − | 0.845660i | \(-0.320793\pi\) | ||||
0.533722 | + | 0.845660i | \(0.320793\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.87054 | 0.203713 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.39679i | − | 0.283258i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.89991i | − | 0.361158i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.4553 | 0.545765 | 0.272882 | − | 0.962047i | \(-0.412023\pi\) | ||||
0.272882 | + | 0.962047i | \(0.412023\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.26306 | −0.326042 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.68080i | 0.450684i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.09776i | 0.315730i | 0.987461 | + | 0.157865i | \(0.0504611\pi\) | ||||
−0.987461 | + | 0.157865i | \(0.949539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.8881 | 1.48781 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48922 | 0.127863 | 0.0639313 | − | 0.997954i | \(-0.479636\pi\) | ||||
0.0639313 | + | 0.997954i | \(0.479636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.03827 | −0.360582 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.24159 | 0.114540 | 0.0572699 | − | 0.998359i | \(-0.481760\pi\) | ||||
0.0572699 | + | 0.998359i | \(0.481760\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.8784i | 0.605381i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.50959 | 0.432567 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 30.0070i | − | 1.52142i | −0.649095 | − | 0.760708i | \(-0.724852\pi\) | ||
0.649095 | − | 0.760708i | \(-0.275148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.69852 | + | 6.29286i | 0.338759 | + | 0.318243i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.8340 | −0.798720 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.143570i | 0.00722379i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.7912 | −1.39480 | −0.697400 | − | 0.716682i | \(-0.745660\pi\) | ||||
−0.697400 | + | 0.716682i | \(0.745660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 23.9982i | − | 1.20141i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8010i | 0.888939i | 0.895794 | + | 0.444469i | \(0.146608\pi\) | ||||
−0.895794 | + | 0.444469i | \(0.853392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.7986i | 0.986238i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4499i | 0.964098i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.0839 | −1.58644 | −0.793222 | − | 0.608932i | \(-0.791598\pi\) | ||||
−0.793222 | + | 0.608932i | \(0.791598\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.41398 | −0.464358 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.9525i | 1.08021i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.9654i | − | 0.587356i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.23682 | −0.256448 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.157810 | −0.00770954 | −0.00385477 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385477 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.3945i | − | 0.799019i | −0.916729 | − | 0.399509i | \(-0.869181\pi\) | ||
0.916729 | − | 0.399509i | \(-0.130819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.32504i | − | 0.404777i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.91641i | − | 0.0929594i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 12.8660i | − | 0.622632i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 11.8748i | − | 0.573323i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3831 | 1.36717 | 0.683583 | − | 0.729873i | \(-0.260421\pi\) | ||||
0.683583 | + | 0.729873i | \(0.260421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.68466i | − | 0.369301i | −0.982804 | − | 0.184651i | \(-0.940885\pi\) | ||
0.982804 | − | 0.184651i | \(-0.0591153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.75850 | −0.276099 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7036 | − | 16.7159i | 0.751203 | − | 0.799629i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.5914i | − | 1.60323i | −0.597839 | − | 0.801616i | \(-0.703974\pi\) | ||
0.597839 | − | 0.801616i | \(-0.296026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.1815 | −0.865785 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.9677i | − | 0.806158i | −0.915165 | − | 0.403079i | \(-0.867940\pi\) | ||
0.915165 | − | 0.403079i | \(-0.132060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4681 | −0.543639 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.1290 | −0.999368 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1197 | 1.27986 | 0.639928 | − | 0.768435i | \(-0.278964\pi\) | ||||
0.639928 | + | 0.768435i | \(0.278964\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8253 | −0.698098 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.8189 | −1.02514 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 25.1739i | − | 1.18017i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 13.9545i | − | 0.652762i | −0.945238 | − | 0.326381i | \(-0.894171\pi\) | ||
0.945238 | − | 0.326381i | \(-0.105829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.91641 | 0.0894502 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.7791 | 1.52668 | 0.763338 | − | 0.646000i | \(-0.223559\pi\) | ||||
0.763338 | + | 0.646000i | \(0.223559\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9485i | 0.555295i | 0.960683 | + | 0.277647i | \(0.0895547\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3.94661i | − | 0.183020i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.87190 | 0.225445 | 0.112722 | − | 0.993627i | \(-0.464043\pi\) | ||||
0.112722 | + | 0.993627i | \(0.464043\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.9938 | −1.20028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.15443 | −0.237504 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.1431 | 0.926182 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.78232 | −0.219428 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.72989i | 0.0792063i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.6174 | 1.07911 | 0.539553 | − | 0.841952i | \(-0.318593\pi\) | ||||
0.539553 | + | 0.841952i | \(0.318593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 41.2201i | − | 1.87948i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.5401 | − | 16.4779i | −0.798101 | − | 0.749768i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.2966 | 0.649174 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.2403i | 1.41564i | 0.706395 | + | 0.707818i | \(0.250320\pi\) | ||||
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.43764 | 0.291120 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.7693i | 1.61425i | 0.590382 | + | 0.807124i | \(0.298977\pi\) | ||||
−0.590382 | + | 0.807124i | \(0.701023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.0356i | 0.497020i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.36711i | 0.106394i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.9797i | 2.10733i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.3511i | 0.866273i | 0.901328 | + | 0.433137i | \(0.142593\pi\) | ||||
−0.901328 | + | 0.433137i | \(0.857407\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.86457 | −0.217333 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9151 | 1.02174 | 0.510868 | − | 0.859659i | \(-0.329324\pi\) | ||||
0.510868 | + | 0.859659i | \(0.329324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 13.9368i | − | 0.620177i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1663i | 0.540324i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5920 | 0.824075 | 0.412038 | − | 0.911167i | \(-0.364817\pi\) | ||||
0.412038 | + | 0.911167i | \(0.364817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.6245 | 1.53170 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.78232i | − | 0.211144i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.5326i | 0.816646i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.7063i | − | 0.866681i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.1408i | 0.884082i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.9529i | 1.04940i | 0.851288 | + | 0.524699i | \(0.175822\pi\) | ||||
−0.851288 | + | 0.524699i | \(0.824178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.4800 | −1.24534 | −0.622671 | − | 0.782484i | \(-0.713953\pi\) | ||||
−0.622671 | + | 0.782484i | \(0.713953\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.01811i | 0.219008i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.56332 | −0.329463 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.43497 | − | 22.9552i | −0.0623900 | − | 0.998052i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.37464i | 0.189843i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.4193 | 1.36092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.84039i | 0.295736i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.1505 | 0.524335 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −43.0375 | −1.85376 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.40647 | 0.146455 | 0.0732277 | − | 0.997315i | \(-0.476670\pi\) | ||||
0.0732277 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.58656 | 0.111000 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.8804 | −0.723078 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.0754i | − | 1.07215i | −0.844171 | − | 0.536074i | \(-0.819907\pi\) | ||
0.844171 | − | 0.536074i | \(-0.180093\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2.56392i | − | 0.109425i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.5390 | 1.17320 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.720451 | −0.0306367 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.21675i | 0.348781i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.8190i | 1.77193i | 0.463754 | + | 0.885964i | \(0.346502\pi\) | ||||
−0.463754 | + | 0.885964i | \(0.653498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.6892 | −1.80556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.53635 | 0.191525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.1917 | 1.56744 | 0.783721 | − | 0.621113i | \(-0.213319\pi\) | ||||
0.783721 | + | 0.621113i | \(0.213319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.3526 | −0.519676 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.01811 | −0.210741 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.5972i | 1.57616i | 0.615575 | + | 0.788078i | \(0.288924\pi\) | ||||
−0.615575 | + | 0.788078i | \(0.711076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.91777 | −0.247651 | −0.123826 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123826 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.97384i | 0.166009i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.28367 | + | 3.49535i | −0.136939 | + | 0.145766i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.8360 | −1.74166 | −0.870828 | − | 0.491588i | \(-0.836416\pi\) | ||||
−0.870828 | + | 0.491588i | \(0.836416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8995i | 0.577643i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 60.0435 | 2.49102 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.09484i | 0.169591i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.01660i | − | 0.207411i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.8621i | 1.19127i | 0.803256 | + | 0.595634i | \(0.203099\pi\) | ||||
−0.803256 | + | 0.595634i | \(0.796901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8740i | 0.777688i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.0037i | 0.863979i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.0315 | −1.02792 | −0.513960 | − | 0.857814i | \(-0.671822\pi\) | ||||
−0.513960 | + | 0.857814i | \(0.671822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.61675 | 0.394248 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 24.1044i | − | 0.986527i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.7838i | − | 0.604049i | −0.953300 | − | 0.302025i | \(-0.902338\pi\) | ||
0.953300 | − | 0.302025i | \(-0.0976625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5582 | 0.675424 | 0.337712 | − | 0.941249i | \(-0.390347\pi\) | ||||
0.337712 | + | 0.941249i | \(0.390347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.18000 | −0.210946 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 5.39679i | − | 0.219411i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 28.2229i | − | 1.14553i | −0.819719 | − | 0.572766i | \(-0.805870\pi\) | ||
0.819719 | − | 0.572766i | \(-0.194130\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 28.8968i | − | 1.17096i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.7634i | 1.68957i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.7909i | 1.24363i | 0.783164 | + | 0.621816i | \(0.213605\pi\) | ||||
−0.783164 | + | 0.621816i | \(0.786395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.26306 | −0.252551 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.4530i | − | 0.903924i | −0.892037 | − | 0.451962i | \(-0.850724\pi\) | ||
0.892037 | − | 0.451962i | \(-0.149276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.43745 | −0.258743 | −0.129371 | − | 0.991596i | \(-0.541296\pi\) | ||||
−0.129371 | + | 0.991596i | \(0.541296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.49535 | − | 3.28367i | −0.140264 | − | 0.131769i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 57.5482i | − | 2.30562i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 11.3203i | − | 0.452088i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.7466 | 0.627859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.8844 | 0.871205 | 0.435602 | − | 0.900139i | \(-0.356535\pi\) | ||||
0.435602 | + | 0.900139i | \(0.356535\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.03788 | −0.0809986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.03827 | −0.279305 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 91.2092 | 3.61384 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.36201i | 0.370355i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 23.5428i | − | 0.929886i | −0.885341 | − | 0.464943i | \(-0.846075\pi\) | ||
0.885341 | − | 0.464943i | \(-0.153925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.72929 | 0.304814 | 0.152407 | − | 0.988318i | \(-0.451298\pi\) | ||||
0.152407 | + | 0.988318i | \(0.451298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.50959 | 0.335065 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0794i | 0.396260i | 0.980176 | + | 0.198130i | \(0.0634869\pi\) | ||||
−0.980176 | + | 0.198130i | \(0.936513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3553i | 0.406480i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8046 | 0.776202 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2513 | −0.870760 | −0.435380 | − | 0.900247i | \(-0.643386\pi\) | ||||
−0.435380 | + | 0.900247i | \(0.643386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.8340 | −0.618686 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.89991 | 0.269191 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4657 | 0.641412 | 0.320706 | − | 0.947179i | \(-0.396080\pi\) | ||||
0.320706 | + | 0.947179i | \(0.396080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9479i | 0.853673i | 0.904329 | + | 0.426837i | \(0.140372\pi\) | ||||
−0.904329 | + | 0.426837i | \(0.859628\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.61385 | −0.373371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 23.9982i | − | 0.930611i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9090 | − | 20.1280i | 0.732161 | − | 0.779358i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.5574 | −0.678808 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.06908i | − | 0.234294i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.4405 | −1.32759 | −0.663793 | − | 0.747917i | \(-0.731054\pi\) | ||||
−0.663793 | + | 0.747917i | \(0.731054\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.97780i | 0.152879i | 0.997074 | + | 0.0764396i | \(0.0243552\pi\) | ||||
−0.997074 | + | 0.0764396i | \(0.975645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 71.7418i | 2.75320i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 11.9674i | − | 0.458594i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.5259i | 1.39762i | 0.715305 | + | 0.698812i | \(0.246288\pi\) | ||||
−0.715305 | + | 0.698812i | \(0.753712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.41398 | −0.359690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.7251 | −0.638103 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 8.67818i | − | 0.330612i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0940i | 0.726368i | 0.931717 | + | 0.363184i | \(0.118310\pi\) | ||||
−0.931717 | + | 0.363184i | \(0.881690\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.8784 | −0.451224 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.23682 | −0.198644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0026i | 0.454630i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 29.6780i | − | 1.12252i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0819i | 1.17395i | 0.809606 | + | 0.586974i | \(0.199681\pi\) | ||||
−0.809606 | + | 0.586974i | \(0.800319\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 39.2951i | − | 1.48204i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 8.32504i | − | 0.313539i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69.9362 | 2.63022 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.4053i | 0.503445i | 0.967799 | + | 0.251722i | \(0.0809970\pi\) | ||||
−0.967799 | + | 0.251722i | \(0.919003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.143570 | −0.00538429 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.7948 | + | 12.9594i | 0.516620 | + | 0.485333i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 11.8748i | − | 0.444094i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.9888 | −0.597111 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.98233i | − | 0.0739283i | −0.999317 | − | 0.0369642i | \(-0.988231\pi\) | ||
0.999317 | − | 0.0369642i | \(-0.0117687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −92.9989 | −3.46346 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.18015 | 0.341413 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.75850 | −0.213865 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7228 | −1.21362 | −0.606810 | − | 0.794847i | \(-0.707551\pi\) | ||||
−0.606810 | + | 0.794847i | \(0.707551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.3078i | − | 0.603167i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.1233i | − | 1.55586i | −0.628351 | − | 0.777930i | \(-0.716270\pi\) | ||
0.628351 | − | 0.777930i | \(-0.283730\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.1815 | −0.670634 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2616 | −0.451663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.8040i | 1.72171i | 0.508847 | + | 0.860857i | \(0.330072\pi\) | ||||
−0.508847 | + | 0.860857i | \(0.669928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.9910i | 0.881330i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.1188 | 1.03158 | 0.515789 | − | 0.856716i | \(-0.327499\pi\) | ||||
0.515789 | + | 0.856716i | \(0.327499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1290 | −0.774107 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9654 | 0.437789 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.3259 | −1.25424 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.6426 | −0.570808 | −0.285404 | − | 0.958407i | \(-0.592128\pi\) | ||||
−0.285404 | + | 0.958407i | \(0.592128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.2154i | 0.700247i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8189 | −0.794070 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.79486i | 0.0652352i | 0.999468 | + | 0.0326176i | \(0.0103843\pi\) | ||||
−0.999468 | + | 0.0326176i | \(0.989616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.27388 | − | 7.77282i | −0.300323 | − | 0.282135i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.48747 | 0.343921 | 0.171960 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171960 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 84.7080i | − | 3.06663i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.91641 | 0.0692878 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 21.9458i | − | 0.792419i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.9546i | 0.431092i | 0.976494 | + | 0.215546i | \(0.0691532\pi\) | ||||
−0.976494 | + | 0.215546i | \(0.930847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.57519i | − | 0.344842i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5282i | 0.522544i | 0.965265 | + | 0.261272i | \(0.0841420\pi\) | ||||
−0.965265 | + | 0.261272i | \(0.915858\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.94661i | − | 0.141767i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −41.2326 | −1.47921 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.9519 | 1.07314 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.1609i | 0.792980i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.75850i | − | 0.205792i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.15443 | −0.183969 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.31988 | −0.153987 | −0.0769936 | − | 0.997032i | \(-0.524532\pi\) | ||||
−0.0769936 | + | 0.997032i | \(0.524532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 11.3872i | − | 0.405397i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 61.9866i | − | 2.20399i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8622i | 0.456749i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.72989i | 0.0613529i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.6869i | 0.768190i | 0.923294 | + | 0.384095i | \(0.125486\pi\) | ||||
−0.923294 | + | 0.384095i | \(0.874514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9542 | −0.564418 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 11.4681i | − | 0.405205i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.3328 | 0.576374 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.5401 | − | 16.4779i | −0.618206 | − | 0.580768i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.8812i | 0.735053i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.66984 | −0.0587084 | −0.0293542 | − | 0.999569i | \(-0.509345\pi\) | ||||
−0.0293542 | + | 0.999569i | \(0.509345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.4099i | 1.84036i | 0.391494 | + | 0.920181i | \(0.371958\pi\) | ||||
−0.391494 | + | 0.920181i | \(0.628042\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.1526 | 0.811996 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.43764 | 0.225501 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.6955 | −1.42376 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.1739 | 0.879647 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.02238 | 0.210183 | 0.105091 | − | 0.994463i | \(-0.466487\pi\) | ||||
0.105091 | + | 0.994463i | \(0.466487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.44724i | − | 0.120163i | −0.998193 | − | 0.0600816i | \(-0.980864\pi\) | ||
0.998193 | − | 0.0600816i | \(-0.0191361\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.36711i | 0.0824122i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8981 | −0.448511 | −0.224256 | − | 0.974530i | \(-0.571995\pi\) | ||||
−0.224256 | + | 0.974530i | \(0.571995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.6205 | −0.542522 | −0.271261 | − | 0.962506i | \(-0.587441\pi\) | ||||
−0.271261 | + | 0.962506i | \(0.587441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.52150i | 0.191539i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.8431i | 1.20724i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.86457 | −0.168346 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.94661 | 0.136415 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.9432 | 1.48256 | 0.741282 | − | 0.671194i | \(-0.234218\pi\) | ||||
0.741282 | + | 0.671194i | \(0.234218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.16030 | 0.143458 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.0586 | 0.484204 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1663i | 0.418533i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.0817 | 0.930539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 27.4300i | − | 0.941395i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7204 | − | 26.9811i | −0.984523 | − | 0.924901i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.2298 | 1.00081 | 0.500405 | − | 0.865792i | \(-0.333185\pi\) | ||||
0.500405 | + | 0.865792i | \(0.333185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 4.78232i | − | 0.163552i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.3368 | 0.899646 | 0.449823 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449823 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.244563i | 0.00834439i | 0.999991 | + | 0.00417219i | \(0.00132805\pi\) | ||||
−0.999991 | + | 0.00417219i | \(0.998672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 31.4287i | − | 1.07109i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36.3987i | − | 1.23903i | −0.784986 | − | 0.619513i | \(-0.787330\pi\) | ||
0.784986 | − | 0.619513i | \(-0.212670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.1408i | 0.684807i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.3274i | 0.452622i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.339846 | −0.0115285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.9860 | 0.880502 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2966i | 0.483865i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.01811i | 0.169643i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.20892 | 0.0745900 | 0.0372950 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372950 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.25711 | 0.211047 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.96526i | 0.0999022i | 0.998752 | + | 0.0499511i | \(0.0159065\pi\) | ||||
−0.998752 | + | 0.0499511i | \(0.984093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.2315i | − | 0.983717i | −0.870675 | − | 0.491859i | \(-0.836318\pi\) | ||
0.870675 | − | 0.491859i | \(-0.163682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.37464i | 0.147052i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.89988i | 0.0973684i | 0.998814 | + | 0.0486842i | \(0.0155028\pi\) | ||||
−0.998814 | + | 0.0486842i | \(0.984497\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 35.3188i | − | 1.18456i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.36711 | −0.0793012 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.8130i | 1.33229i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.1505 | 0.406148 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.5348 | + | 16.4729i | 0.585469 | + | 0.550014i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7266i | 0.757974i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.31518 | 0.110445 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.7021i | 1.42104i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.58656 | 0.0859802 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.2617 | 1.00482 | 0.502412 | − | 0.864628i | \(-0.332446\pi\) | ||||
0.502412 | + | 0.864628i | \(0.332446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.9368 | 0.462253 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.7435 | 0.952315 | 0.476157 | − | 0.879360i | \(-0.342029\pi\) | ||||
0.476157 | + | 0.879360i | \(0.342029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.3233 | 0.937364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 2.56392i | − | 0.0847606i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 79.4568i | − | 2.62390i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.8503 | 0.456880 | 0.228440 | − | 0.973558i | \(-0.426638\pi\) | ||||
0.228440 | + | 0.973558i | \(0.426638\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.1297 | 1.09166 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 46.9655i | − | 1.54589i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.21675i | 0.270165i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.5326 | −0.608692 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.51430 | −0.180918 | −0.0904591 | − | 0.995900i | \(-0.528833\pi\) | ||||
−0.0904591 | + | 0.995900i | \(0.528833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 86.9496 | 2.84966 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.1899 | −0.791941 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.53635 | 0.148354 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.62485i | − | 0.183756i | −0.995770 | − | 0.0918780i | \(-0.970713\pi\) | ||
0.995770 | − | 0.0918780i | \(-0.0292870\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.05898 | 0.132460 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6793i | 0.511132i | 0.966792 | + | 0.255566i | \(0.0822618\pi\) | ||||
−0.966792 | + | 0.255566i | \(0.917738\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.5658 | − | 21.8916i | 0.669716 | − | 0.712888i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.01811 | −0.163239 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.95458i | 0.161002i | 0.996755 | + | 0.0805012i | \(0.0256521\pi\) | ||||
−0.996755 | + | 0.0805012i | \(0.974348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.6141 | −1.12362 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.25580i | − | 0.0731492i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0234i | 0.875374i | 0.899127 | + | 0.437687i | \(0.144202\pi\) | ||||
−0.899127 | + | 0.437687i | \(0.855798\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.97384i | 0.128590i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 13.6310i | − | 0.440628i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 47.2404i | − | 1.52547i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4242 | 0.497556 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.84039 | −0.220429 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.8995i | 0.447440i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.1961i | 1.35694i | 0.734630 | + | 0.678468i | \(0.237356\pi\) | ||||
−0.734630 | + | 0.678468i | \(0.762644\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.16486 | −0.294418 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.32455 | 0.170873 | 0.0854365 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854365 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 26.2789i | − | 0.842464i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 5.01660i | − | 0.160660i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.22163i | 0.0710761i | 0.999368 | + | 0.0355381i | \(0.0113145\pi\) | ||||
−0.999368 | + | 0.0355381i | \(0.988686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.1462i | − | 0.867597i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 16.8804i | − | 0.538951i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.0536 | −1.78783 | −0.893916 | − | 0.448235i | \(-0.852053\pi\) | ||||
−0.893916 | + | 0.448235i | \(0.852053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.0037i | 0.669235i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 41.7760 | 1.32974 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.9427 | + | 29.7440i | −0.888527 | + | 0.945804i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.3205i | − | 1.12199i | −0.827818 | − | 0.560997i | \(-0.810418\pi\) | ||
0.827818 | − | 0.560997i | \(-0.189582\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.5510 | −0.842571 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 24.1044i | − | 0.764161i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.5485 | −1.31585 | −0.657927 | − | 0.753082i | \(-0.728566\pi\) | ||||
−0.657927 | + | 0.753082i | \(0.728566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.21675 | −0.259966 |
(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 | 5520.2.be.c.1471.26 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.25 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.26 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.25 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.25 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.26 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.25 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.26 | yes | 32 | 23.22 | odd | 2 |