Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(449,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2800.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.g (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.449 |
Dual form | 2800.2.g.t.449.1 |
$q$-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 \(\left(\mathbb{Z}/2800\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(801\) | \(2101\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.56155i | 1.47891i | 0.673204 | + | 0.739457i | \(0.264917\pi\) | ||||
−0.673204 | + | 0.739457i | \(0.735083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56155i | 1.26515i | 0.774500 | + | 0.632574i | \(0.218001\pi\) | ||||
−0.774500 | + | 0.632574i | \(0.781999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.56155i | 1.10634i | 0.833069 | + | 0.553170i | \(0.186582\pi\) | ||||
−0.833069 | + | 0.553170i | \(0.813418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.12311i | 1.06824i | 0.845408 | + | 0.534121i | \(0.179357\pi\) | ||||
−0.845408 | + | 0.534121i | \(0.820643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.43845i | − 0.276829i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68466 | 1.05561 | 0.527807 | − | 0.849364i | \(-0.323014\pi\) | ||||
0.527807 | + | 0.849364i | \(0.323014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 6.56155i | − 1.14222i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.00000i | − 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.6847 | −1.87104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12311 | −0.487747 | −0.243874 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243874 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.12311i | − 1.39126i | −0.718400 | − | 0.695630i | \(-0.755125\pi\) | ||||
0.718400 | − | 0.695630i | \(-0.244875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.68466i | 0.537463i | 0.963215 | + | 0.268731i | \(0.0866044\pi\) | ||||
−0.963215 | + | 0.268731i | \(0.913396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.6847 | −1.63618 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.12311i | 0.428992i | 0.976725 | + | 0.214496i | \(0.0688108\pi\) | ||||
−0.976725 | + | 0.214496i | \(0.931189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.87689i | 0.381054i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.36932 | −1.19962 | −0.599809 | − | 0.800143i | \(-0.704757\pi\) | ||||
−0.599809 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56155i | 0.448713i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.24621i | − 0.763096i | −0.924349 | − | 0.381548i | \(-0.875391\pi\) | ||||
0.924349 | − | 0.381548i | \(-0.124609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.1231 | −1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.24621i | 0.496981i | 0.968634 | + | 0.248491i | \(0.0799345\pi\) | ||||
−0.968634 | + | 0.248491i | \(0.920065\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.56155i | 0.291916i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.56155 | −0.738232 | −0.369116 | − | 0.929383i | \(-0.620340\pi\) | ||||
−0.369116 | + | 0.929383i | \(0.620340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.00000i | − 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.5616i | 1.56116i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.12311 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.56155 | 0.478181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8078i | 1.50350i | 0.659448 | + | 0.751750i | \(0.270790\pi\) | ||||
−0.659448 | + | 0.751750i | \(0.729210\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.12311 | 0.916907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.43845i | − 0.141734i | −0.997486 | − | 0.0708672i | \(-0.977423\pi\) | ||||
0.997486 | − | 0.0708672i | \(-0.0225767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.3693i | − 1.09911i | −0.835456 | − | 0.549557i | \(-0.814797\pi\) | ||||
0.835456 | − | 0.549557i | \(-0.185203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6847 | −1.69388 | −0.846942 | − | 0.531686i | \(-0.821559\pi\) | ||||
−0.846942 | + | 0.531686i | \(0.821559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.3693 | 1.45879 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.0000i | − 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 16.2462i | − 1.50196i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.56155 | 0.418157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 8.00000i | − 0.721336i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2462i | 0.909204i | 0.890695 | + | 0.454602i | \(0.150219\pi\) | ||||
−0.890695 | + | 0.454602i | \(0.849781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.3693 | 2.05755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.12311 | 0.797089 | 0.398545 | − | 0.917149i | \(-0.369515\pi\) | ||||
0.398545 | + | 0.917149i | \(0.369515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.12311i | − 0.0973856i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.87689i | 0.758404i | 0.925314 | + | 0.379202i | \(0.123801\pi\) | ||||
−0.925314 | + | 0.379202i | \(0.876199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.87689 | −0.583291 | −0.291645 | − | 0.956527i | \(-0.594203\pi\) | ||||
−0.291645 | + | 0.956527i | \(0.594203\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.43845 | −0.794861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 11.6847i | − 0.977120i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.56155i | − 0.211273i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.9309 | −1.78471 | −0.892354 | − | 0.451335i | \(-0.850948\pi\) | ||||
−0.892354 | + | 0.451335i | \(0.850948\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 16.2462i | − 1.31343i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.75379i | − 0.299585i | −0.988717 | − | 0.149792i | \(-0.952139\pi\) | ||||
0.988717 | − | 0.149792i | \(-0.0478606\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.12311i | − 0.0879684i | −0.999032 | − | 0.0439842i | \(-0.985995\pi\) | ||||
0.999032 | − | 0.0439842i | \(-0.0140051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.9309i | 1.69706i | 0.529146 | + | 0.848531i | \(0.322512\pi\) | ||||
−0.529146 | + | 0.848531i | \(0.677488\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.80776 | −0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.56155i | − 0.650923i | −0.945555 | − | 0.325461i | \(-0.894480\pi\) | ||||
0.945555 | − | 0.325461i | \(-0.105520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 10.2462i | − 0.770152i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0000 | 1.49487 | 0.747435 | − | 0.664335i | \(-0.231285\pi\) | ||||
0.747435 | + | 0.664335i | \(0.231285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6155 | 1.75533 | 0.877664 | − | 0.479276i | \(-0.159101\pi\) | ||||
0.877664 | + | 0.479276i | \(0.159101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 24.0000i | − 1.77413i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.6847i | − 0.854467i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.43845 | −0.104632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.43845 | 0.682942 | 0.341471 | − | 0.939892i | \(-0.389075\pi\) | ||||
0.341471 | + | 0.939892i | \(0.389075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 5.36932i | − 0.386492i | −0.981150 | − | 0.193246i | \(-0.938098\pi\) | ||||
0.981150 | − | 0.193246i | \(-0.0619015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.12311i | 0.507500i | 0.967270 | + | 0.253750i | \(0.0816641\pi\) | ||||
−0.967270 | + | 0.253750i | \(0.918336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 5.68466i | − 0.398985i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.2462i | − 1.26820i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.87689 | −0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0540 | 1.58710 | 0.793551 | − | 0.608504i | \(-0.208230\pi\) | ||||
0.793551 | + | 0.608504i | \(0.208230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 20.4924i | − 1.40412i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.8769 | −0.734992 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8078 | −1.39968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.56155i | 0.439394i | 0.975568 | + | 0.219697i | \(0.0705069\pi\) | ||||
−0.975568 | + | 0.219697i | \(0.929493\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.6847i | 1.57201i | 0.618223 | + | 0.786003i | \(0.287853\pi\) | ||||
−0.618223 | + | 0.786003i | \(0.712147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.1231 | −1.26369 | −0.631845 | − | 0.775095i | \(-0.717702\pi\) | ||||
−0.631845 | + | 0.775095i | \(0.717702\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3.12311i | − 0.204601i | −0.994754 | − | 0.102301i | \(-0.967380\pi\) | ||||
0.994754 | − | 0.102301i | \(-0.0326204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.8078i | − 1.09178i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.807764 | −0.0522499 | −0.0261250 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261250 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 22.2462i | − 1.42710i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.12311i | 0.325975i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2462 | 0.649327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.1231 | 1.08080 | 0.540400 | − | 0.841408i | \(-0.318273\pi\) | ||||
0.540400 | + | 0.841408i | \(0.318273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 13.1231i | − 0.825043i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 22.4924i | − 1.40304i | −0.712650 | − | 0.701519i | \(-0.752505\pi\) | ||||
0.712650 | − | 0.701519i | \(-0.247495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.2462 | −1.25321 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.1231i | 1.30251i | 0.758860 | + | 0.651253i | \(0.225756\pi\) | ||||
−0.758860 | + | 0.651253i | \(0.774244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 18.2462i | − 1.11665i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.7386 | −1.75223 | −0.876113 | − | 0.482106i | \(-0.839872\pi\) | ||||
−0.876113 | + | 0.482106i | \(0.839872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6847i | 0.707188i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 16.2462i | − 0.976140i | −0.872804 | − | 0.488070i | \(-0.837701\pi\) | ||||
0.872804 | − | 0.488070i | \(-0.162299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5616 | 0.987979 | 0.493990 | − | 0.869468i | \(-0.335538\pi\) | ||||
0.493990 | + | 0.869468i | \(0.335538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6847i | 1.40791i | 0.710246 | + | 0.703953i | \(0.248584\pi\) | ||||
−0.710246 | + | 0.703953i | \(0.751416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.12311i | 0.184351i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.80776 | −0.223986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.9309 | −2.22355 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.68466i | 0.565784i | 0.959152 | + | 0.282892i | \(0.0912938\pi\) | ||||
−0.959152 | + | 0.282892i | \(0.908706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.68466i | 0.213806i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.3693 | −1.35148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.12311 | −0.525847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.630683i | 0.0362318i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 31.6847i | − 1.80834i | −0.427174 | − | 0.904169i | \(-0.640491\pi\) | ||||
0.427174 | − | 0.904169i | \(-0.359509\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.68466 | 0.209613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.61553 | 0.545247 | 0.272623 | − | 0.962121i | \(-0.412109\pi\) | ||||
0.272623 | + | 0.962121i | \(0.412109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3002i | 1.76919i | 0.466359 | + | 0.884596i | \(0.345566\pi\) | ||||
−0.466359 | + | 0.884596i | \(0.654434\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4924i | 1.26330i | 0.775254 | + | 0.631650i | \(0.217622\pi\) | ||||
−0.775254 | + | 0.631650i | \(0.782378\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.5616 | −0.815290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.1231 | 1.62549 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.12311i | 0.285057i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 45.3002i | − 2.50511i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.68466 | 0.203142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.3693i | 1.17103i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.4924i | 1.87892i | 0.342656 | + | 0.939461i | \(0.388674\pi\) | ||||
−0.342656 | + | 0.939461i | \(0.611326\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 35.8617 | 1.94774 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.12311i | − 0.0602915i | −0.999546 | − | 0.0301457i | \(-0.990403\pi\) | ||||
0.999546 | − | 0.0301457i | \(-0.00959714\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4924 | 1.20399 | 0.601996 | − | 0.798499i | \(-0.294372\pi\) | ||||
0.601996 | + | 0.798499i | \(0.294372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.56155 | 0.350230 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 14.8078i | − 0.788138i | −0.919081 | − | 0.394069i | \(-0.871067\pi\) | ||||
0.919081 | − | 0.394069i | \(-0.128933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.6847i | 0.618418i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 11.3693i | − 0.596734i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.68466i | 0.192338i | 0.995365 | + | 0.0961688i | \(0.0306589\pi\) | ||||
−0.995365 | + | 0.0961688i | \(0.969341\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1231 | 0.579046 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.12311 | 0.162144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3693i | 1.52069i | 0.649522 | + | 0.760343i | \(0.274969\pi\) | ||||
−0.649522 | + | 0.760343i | \(0.725031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.9309i | 1.33551i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4924 | 0.847159 | 0.423579 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.2462 | −1.34463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2462i | 0.523557i | 0.965128 | + | 0.261778i | \(0.0843090\pi\) | ||||
−0.965128 | + | 0.261778i | \(0.915691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.4924i | 1.65168i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.93087 | −0.199303 | −0.0996515 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996515 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.3693 | −1.18184 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.3693i | 1.17883i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 23.4384i | − 1.17634i | −0.808737 | − | 0.588171i | \(-0.799848\pi\) | ||||
0.808737 | − | 0.588171i | \(-0.200152\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.87689 | 0.144025 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.4384 | 1.37021 | 0.685105 | − | 0.728444i | \(-0.259756\pi\) | ||||
0.685105 | + | 0.728444i | \(0.259756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.3693i | 0.761829i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4924 | 1.30997 | 0.654983 | − | 0.755644i | \(-0.272676\pi\) | ||||
0.654983 | + | 0.755644i | \(0.272676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.7386 | −1.12161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 17.6155i | − 0.862636i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.75379 | 0.476504 | 0.238252 | − | 0.971203i | \(-0.423426\pi\) | ||||
0.238252 | + | 0.971203i | \(0.423426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.68466 | 0.472001 | 0.236001 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236001 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 13.1231i | − 0.638067i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.36932i | 0.453413i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.9309 | 1.44508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.807764 | −0.0389086 | −0.0194543 | − | 0.999811i | \(-0.506193\pi\) | ||||
−0.0194543 | + | 0.999811i | \(0.506193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 8.24621i | − 0.396288i | −0.980173 | − | 0.198144i | \(-0.936509\pi\) | ||||
0.980173 | − | 0.198144i | \(-0.0634913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.75379i | 0.275241i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3693 | −0.733537 | −0.366769 | − | 0.930312i | \(-0.619536\pi\) | ||||
−0.366769 | + | 0.930312i | \(0.619536\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.3693i | 1.30036i | 0.759782 | + | 0.650178i | \(0.225306\pi\) | ||||
−0.759782 | + | 0.650178i | \(0.774694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.8769i | 0.514459i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.8078 | −0.887593 | −0.443797 | − | 0.896128i | \(-0.646369\pi\) | ||||
−0.443797 | + | 0.896128i | \(0.646369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 56.1771i | − 2.63943i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.87689i | 0.415244i | 0.978209 | + | 0.207622i | \(0.0665723\pi\) | ||||
−0.978209 | + | 0.207622i | \(0.933428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.56155 | 0.306267 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.87689 | −0.227140 | −0.113570 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113570 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924i | 0.952364i | 0.879347 | + | 0.476182i | \(0.157980\pi\) | ||||
−0.879347 | + | 0.476182i | \(0.842020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.5616i | 1.22912i | 0.788869 | + | 0.614561i | \(0.210667\pi\) | ||||
−0.788869 | + | 0.614561i | \(0.789333\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.24621 | −0.288423 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.61553 | 0.443060 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.3693i | 1.07452i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 11.1231i | − 0.509292i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.1231 | 0.599610 | 0.299805 | − | 0.954001i | \(-0.403078\pi\) | ||||
0.299805 | + | 0.954001i | \(0.403078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3693 | 1.24793 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.1231i | 0.597122i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.12311i | 0.232150i | 0.993240 | + | 0.116075i | \(0.0370313\pi\) | ||||
−0.993240 | + | 0.116075i | \(0.962969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.87689 | 0.130098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.17708 | −0.188509 | −0.0942545 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942545 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.9309i | 1.16787i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.17708 | −0.186992 | −0.0934959 | − | 0.995620i | \(-0.529804\pi\) | ||||
−0.0934959 | + | 0.995620i | \(0.529804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.1771 | −2.50981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 10.0691i | − 0.448960i | −0.974479 | − | 0.224480i | \(-0.927932\pi\) | ||||
0.974479 | − | 0.224480i | \(-0.0720684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 20.0000i | − 0.888231i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.2462 | 1.25199 | 0.625996 | − | 0.779827i | \(-0.284693\pi\) | ||||
0.625996 | + | 0.779827i | \(0.284693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.24621 | 0.187841 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.61553i | − 0.0713273i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.43845i | − 0.415102i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.9309 | 0.962658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.50758i | − 0.328283i | −0.986437 | − | 0.164142i | \(-0.947515\pi\) | ||||
0.986437 | − | 0.164142i | \(-0.0524854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2462 | 0.618233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 14.2462i | − 0.617072i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51.2311i | 2.21078i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.56155 | 0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1922 | −0.739152 | −0.369576 | − | 0.929201i | \(-0.620497\pi\) | ||||
−0.369576 | + | 0.929201i | \(0.620497\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.4924i | 2.59598i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2462i | 0.609124i | 0.952493 | + | 0.304562i | \(0.0985101\pi\) | ||||
−0.952493 | + | 0.304562i | \(0.901490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.3693 | 1.42417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.38447 | 0.271988 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.56155i | 0.279026i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.87689i | 0.206641i | 0.994648 | + | 0.103320i | \(0.0329467\pi\) | ||||
−0.994648 | + | 0.103320i | \(0.967053\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.6155 | 1.76015 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.9309 | 1.26368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.0000i | 1.18006i | 0.807382 | + | 0.590030i | \(0.200884\pi\) | ||||
−0.807382 | + | 0.590030i | \(0.799116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.00000i | 0.293972i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.9848 | −1.46664 | −0.733320 | − | 0.679883i | \(-0.762031\pi\) | ||||
−0.733320 | + | 0.679883i | \(0.762031\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.50758 | −0.314182 | −0.157091 | − | 0.987584i | \(-0.550212\pi\) | ||||
−0.157091 | + | 0.987584i | \(0.550212\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.1771i | 1.01001i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 13.0540i | − 0.543444i | −0.962376 | − | 0.271722i | \(-0.912407\pi\) | ||||
0.962376 | − | 0.271722i | \(-0.0875931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.7538 | 0.571588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 8.00000i | − 0.331326i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9.75379i | − 0.402582i | −0.979531 | − | 0.201291i | \(-0.935486\pi\) | ||||
0.979531 | − | 0.201291i | \(-0.0645137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2462 | −0.750549 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 23.4384i | − 0.962502i | −0.876583 | − | 0.481251i | \(-0.840183\pi\) | ||||
0.876583 | − | 0.481251i | \(-0.159817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 46.7386i | − 1.91288i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.80776 | 0.359875 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4924 | −1.08065 | −0.540324 | − | 0.841457i | \(-0.681698\pi\) | ||||
−0.540324 | + | 0.841457i | \(0.681698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.2462i | 0.905936i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.94602i | − 0.200753i | −0.994950 | − | 0.100376i | \(-0.967995\pi\) | ||||
0.994950 | − | 0.100376i | \(-0.0320047\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.5616 | 0.590064 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8078 | −0.679969 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 8.73863i | − 0.352950i | −0.984305 | − | 0.176475i | \(-0.943531\pi\) | ||||
0.984305 | − | 0.176475i | \(-0.0564695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 15.7538i | − 0.634224i | −0.948388 | − | 0.317112i | \(-0.897287\pi\) | ||||
0.948388 | − | 0.317112i | \(-0.102713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.1080 | −1.69246 | −0.846231 | − | 0.532817i | \(-0.821134\pi\) | ||||
−0.846231 | + | 0.532817i | \(0.821134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.36932 | 0.295720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.12311i | 0.285381i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.36932i | − 0.294302i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3693 | 1.09129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.80776 | −0.350632 | −0.175316 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175316 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.0540i | 2.34718i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.56155i | − 0.180735i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.4924 | 1.12714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.56155i | 0.101018i | 0.998724 | + | 0.0505089i | \(0.0160843\pi\) | ||||
−0.998724 | + | 0.0505089i | \(0.983916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.50758i | 0.137897i | 0.997620 | + | 0.0689486i | \(0.0219644\pi\) | ||||
−0.997620 | + | 0.0689486i | \(0.978036\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2462 | 0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 49.2311i | 1.92656i | 0.268499 | + | 0.963280i | \(0.413473\pi\) | ||||
−0.268499 | + | 0.963280i | \(0.586527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 15.1231i | − 0.590009i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1771 | −1.40926 | −0.704629 | − | 0.709575i | \(-0.748887\pi\) | ||||
−0.704629 | + | 0.709575i | \(0.748887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.12311 | 0.121475 | 0.0607374 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607374 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 53.3002i | − 2.07001i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.1231i | 1.12765i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.8078 | −0.649826 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 25.8617i | − 0.996897i | −0.866919 | − | 0.498448i | \(-0.833903\pi\) | ||||
0.866919 | − | 0.498448i | \(-0.166097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.9309i | 0.919738i | 0.887987 | + | 0.459869i | \(0.152104\pi\) | ||||
−0.887987 | + | 0.459869i | \(0.847896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.8078 | 0.568270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.6695 | −2.32486 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 42.7386i | − 1.63535i | −0.575681 | − | 0.817674i | \(-0.695263\pi\) | ||||
0.575681 | − | 0.817674i | \(-0.304737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 48.9848i | − 1.86889i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.2462 | −0.542737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.49242 | −0.323067 | −0.161533 | − | 0.986867i | \(-0.551644\pi\) | ||||
−0.161533 | + | 0.986867i | \(0.551644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.12311i | − 0.346558i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 14.2462i | − 0.539614i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.00000 | 0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0691303 | 0.00261102 | 0.00130551 | − | 0.999999i | \(-0.499584\pi\) | ||||
0.00130551 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.73863i | − 0.254152i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.246211i | − 0.00925973i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1771 | 0.682655 | 0.341327 | − | 0.939945i | \(-0.389124\pi\) | ||||
0.341327 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.3693 | 0.876418 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.06913i | − 0.0772731i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 49.6155 | 1.85035 | 0.925173 | − | 0.379544i | \(-0.123919\pi\) | ||||
0.925173 | + | 0.379544i | \(0.123919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43845 | −0.0535706 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.3693i | 1.16664i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5076i | 0.723496i | 0.932276 | + | 0.361748i | \(0.117820\pi\) | ||||
−0.932276 | + | 0.361748i | \(0.882180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.6155 | 1.53921 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5.68466i | − 0.209968i | −0.994474 | − | 0.104984i | \(-0.966521\pi\) | ||||
0.994474 | − | 0.104984i | \(-0.0334791\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000i | 0.589368i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.06913 | 0.223257 | 0.111628 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111628 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1231 | −0.482089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32.9848i | − 1.21010i | −0.796189 | − | 0.605048i | \(-0.793154\pi\) | ||||
0.796189 | − | 0.605048i | \(-0.206846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.2462i | 0.521242i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3693 | −0.415426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.9309 | −1.67604 | −0.838021 | − | 0.545639i | \(-0.816287\pi\) | ||||
−0.838021 | + | 0.545639i | \(0.816287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 43.8617i | 1.59841i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 14.6307i | − 0.531761i | −0.964006 | − | 0.265881i | \(-0.914337\pi\) | ||||
0.964006 | − | 0.265881i | \(-0.0856627\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.6155 | 1.22017 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.7538 | 1.15107 | 0.575537 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575537 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6847i | 0.640228i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 18.2462i | − 0.658833i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.50758 | 0.342852 | 0.171426 | − | 0.985197i | \(-0.445163\pi\) | ||||
0.171426 | + | 0.985197i | \(0.445163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.6155 | 2.07497 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.06913i | 0.290226i | 0.989415 | + | 0.145113i | \(0.0463546\pi\) | ||||
−0.989415 | + | 0.145113i | \(0.953645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 15.3693i | − 0.551371i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.50758 | −0.125672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.4924 | 0.733277 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 8.17708i | − 0.292225i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.82292i | − 0.136272i | −0.997676 | − | 0.0681362i | \(-0.978295\pi\) | ||||
0.997676 | − | 0.0681362i | \(-0.0217052\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.1080 | −1.92629 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 42.7386i | − 1.51769i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.0540i | 0.462396i | 0.972907 | + | 0.231198i | \(0.0742644\pi\) | ||||
−0.972907 | + | 0.231198i | \(0.925736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8078 | −0.594616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.3693 | 0.896381 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10.8769i | − 0.383837i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 73.6155i | − 2.59139i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.5464 | 1.88259 | 0.941296 | − | 0.337584i | \(-0.109610\pi\) | ||||
0.941296 | + | 0.337584i | \(0.109610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.6155 | 0.759024 | 0.379512 | − | 0.925187i | \(-0.376092\pi\) | ||||
0.379512 | + | 0.925187i | \(0.376092\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.9848i | 1.43740i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 10.2462i | − 0.358470i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.2462 | −0.567689 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4233 | 1.41078 | 0.705391 | − | 0.708818i | \(-0.250771\pi\) | ||||
0.705391 | + | 0.708818i | \(0.250771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.50758i | 0.122266i | 0.998130 | + | 0.0611332i | \(0.0194715\pi\) | ||||
−0.998130 | + | 0.0611332i | \(0.980529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.3693i | 0.673537i | 0.941587 | + | 0.336769i | \(0.109334\pi\) | ||||
−0.941587 | + | 0.336769i | \(0.890666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.1231 | −1.49773 | −0.748864 | − | 0.662724i | \(-0.769400\pi\) | ||||
−0.748864 | + | 0.662724i | \(0.769400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.6155 | 1.44363 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.56155i | − 0.158048i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.1231 | −1.28163 | −0.640816 | − | 0.767695i | \(-0.721404\pi\) | ||||
−0.640816 | + | 0.767695i | \(0.721404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.4233i | 1.46114i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.43845i | 0.152507i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.6695 | −2.08217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.7386 | 1.05371 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 56.7386i | − 1.94269i | −0.237666 | − | 0.971347i | \(-0.576382\pi\) | ||||
0.237666 | − | 0.971347i | \(-0.423618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2462i | 1.10151i | 0.834667 | + | 0.550755i | \(0.185660\pi\) | ||||
−0.834667 | + | 0.550755i | \(0.814340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4924 | 0.562714 | 0.281357 | − | 0.959603i | \(-0.409215\pi\) | ||||
0.281357 | + | 0.959603i | \(0.409215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.2462i | 1.43808i | 0.694970 | + | 0.719039i | \(0.255418\pi\) | ||||
−0.694970 | + | 0.719039i | \(0.744582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 9.75379i | − 0.331256i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8078 | 0.570164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4924 | 0.965429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 52.7386i | − 1.78493i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7538i | 0.802108i | 0.916054 | + | 0.401054i | \(0.131356\pi\) | ||||
−0.916054 | + | 0.401054i | \(0.868644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.8078 | −0.836745 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8617 | 1.54512 | 0.772561 | − | 0.634941i | \(-0.218976\pi\) | ||||
0.772561 | + | 0.634941i | \(0.218976\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.4924i | − 0.824236i | −0.911131 | − | 0.412118i | \(-0.864789\pi\) | ||||
0.911131 | − | 0.412118i | \(-0.135211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 12.4924i | − 0.419454i | −0.977760 | − | 0.209727i | \(-0.932742\pi\) | ||||
0.977760 | − | 0.209727i | \(-0.0672576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2462 | 0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.9309 | 0.600707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.13826i | 0.138482i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 59.8617i | − 1.99873i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2462 | −0.474610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 23.3693i | − 0.777682i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.1080i | 1.66381i | 0.554920 | + | 0.831904i | \(0.312749\pi\) | ||||
−0.554920 | + | 0.831904i | \(0.687251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.876894 | −0.0290848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.49242 | −0.148841 | −0.0744203 | − | 0.997227i | \(-0.523711\pi\) | ||||
−0.0744203 | + | 0.997227i | \(0.523711\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.2462i | 0.339100i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 9.12311i | − 0.301271i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.3002 | −0.438733 | −0.219366 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219366 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 81.1619 | 2.67438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 36.4924i | − 1.20116i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.12311i | 0.168265i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.1080 | 1.70961 | 0.854803 | − | 0.518952i | \(-0.173678\pi\) | ||||
0.854803 | + | 0.518952i | \(0.173678\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12311 | −0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.6307i | 0.806372i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 22.6695i | − 0.740580i | −0.928916 | − | 0.370290i | \(-0.879258\pi\) | ||||
0.928916 | − | 0.370290i | \(-0.120742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.1771 | −2.61648 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8617 | −0.451880 | −0.225940 | − | 0.974141i | \(-0.572545\pi\) | ||||
−0.225940 | + | 0.974141i | \(0.572545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 16.0000i | − 0.521032i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000i | 0.129983i | 0.997886 | + | 0.0649913i | \(0.0207020\pi\) | ||||
−0.997886 | + | 0.0649913i | \(0.979298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3693 | −0.628755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.6155 | −1.86831 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 24.8769i | − 0.805842i | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
0.915235 | − | 0.402921i | \(-0.132005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 37.3002i | − 1.20574i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.87689 | 0.286650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.4924i | 1.30485i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 26.8769i | − 0.864303i | −0.901801 | − | 0.432151i | \(-0.857755\pi\) | ||||
0.901801 | − | 0.432151i | \(-0.142245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.1231 | −0.421575 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.4773 | 1.58780 | 0.793901 | − | 0.608048i | \(-0.208047\pi\) | ||||
0.793901 | + | 0.608048i | \(0.208047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.87689i | 0.220463i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.2311i | 1.57504i | 0.616288 | + | 0.787521i | \(0.288636\pi\) | ||||
−0.616288 | + | 0.787521i | \(0.711364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2462 | 0.583151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 62.9848 | 2.01095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.4233i | 0.332451i | 0.986088 | + | 0.166226i | \(0.0531580\pi\) | ||||
−0.986088 | + | 0.166226i | \(0.946842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.43845i | 0.300429i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46.7386 | 1.48620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4924 | 0.650963 | 0.325482 | − | 0.945548i | \(-0.394474\pi\) | ||||
0.325482 | + | 0.945548i | \(0.394474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 30.7386i | − 0.975461i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 9.68466i | − 0.306716i | −0.988171 | − | 0.153358i | \(-0.950991\pi\) | ||||
0.988171 | − | 0.153358i | \(-0.0490088\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.63068 | −0.273063 |
(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 | 2800.2.g.t.449.4 | 4 | ||
4.3 | odd | 2 | 175.2.b.b.99.2 | 4 | |||
5.2 | odd | 4 | 560.2.a.i.1.2 | 2 | |||
5.3 | odd | 4 | 2800.2.a.bi.1.1 | 2 | |||
5.4 | even | 2 | inner | 2800.2.g.t.449.1 | 4 | ||
12.11 | even | 2 | 1575.2.d.e.1324.3 | 4 | |||
15.2 | even | 4 | 5040.2.a.bt.1.2 | 2 | |||
20.3 | even | 4 | 175.2.a.f.1.1 | 2 | |||
20.7 | even | 4 | 35.2.a.b.1.2 | ✓ | 2 | ||
20.19 | odd | 2 | 175.2.b.b.99.3 | 4 | |||
28.27 | even | 2 | 1225.2.b.f.99.2 | 4 | |||
35.27 | even | 4 | 3920.2.a.bs.1.1 | 2 | |||
40.27 | even | 4 | 2240.2.a.bh.1.2 | 2 | |||
40.37 | odd | 4 | 2240.2.a.bd.1.1 | 2 | |||
60.23 | odd | 4 | 1575.2.a.p.1.2 | 2 | |||
60.47 | odd | 4 | 315.2.a.e.1.1 | 2 | |||
60.59 | even | 2 | 1575.2.d.e.1324.2 | 4 | |||
140.27 | odd | 4 | 245.2.a.d.1.2 | 2 | |||
140.47 | odd | 12 | 245.2.e.h.116.1 | 4 | |||
140.67 | even | 12 | 245.2.e.i.226.1 | 4 | |||
140.83 | odd | 4 | 1225.2.a.s.1.1 | 2 | |||
140.87 | odd | 12 | 245.2.e.h.226.1 | 4 | |||
140.107 | even | 12 | 245.2.e.i.116.1 | 4 | |||
140.139 | even | 2 | 1225.2.b.f.99.3 | 4 | |||
220.87 | odd | 4 | 4235.2.a.m.1.1 | 2 | |||
260.207 | even | 4 | 5915.2.a.l.1.1 | 2 | |||
420.167 | even | 4 | 2205.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.2 | ✓ | 2 | 20.7 | even | 4 | ||
175.2.a.f.1.1 | 2 | 20.3 | even | 4 | |||
175.2.b.b.99.2 | 4 | 4.3 | odd | 2 | |||
175.2.b.b.99.3 | 4 | 20.19 | odd | 2 | |||
245.2.a.d.1.2 | 2 | 140.27 | odd | 4 | |||
245.2.e.h.116.1 | 4 | 140.47 | odd | 12 | |||
245.2.e.h.226.1 | 4 | 140.87 | odd | 12 | |||
245.2.e.i.116.1 | 4 | 140.107 | even | 12 | |||
245.2.e.i.226.1 | 4 | 140.67 | even | 12 | |||
315.2.a.e.1.1 | 2 | 60.47 | odd | 4 | |||
560.2.a.i.1.2 | 2 | 5.2 | odd | 4 | |||
1225.2.a.s.1.1 | 2 | 140.83 | odd | 4 | |||
1225.2.b.f.99.2 | 4 | 28.27 | even | 2 | |||
1225.2.b.f.99.3 | 4 | 140.139 | even | 2 | |||
1575.2.a.p.1.2 | 2 | 60.23 | odd | 4 | |||
1575.2.d.e.1324.2 | 4 | 60.59 | even | 2 | |||
1575.2.d.e.1324.3 | 4 | 12.11 | even | 2 | |||
2205.2.a.x.1.1 | 2 | 420.167 | even | 4 | |||
2240.2.a.bd.1.1 | 2 | 40.37 | odd | 4 | |||
2240.2.a.bh.1.2 | 2 | 40.27 | even | 4 | |||
2800.2.a.bi.1.1 | 2 | 5.3 | odd | 4 | |||
2800.2.g.t.449.1 | 4 | 5.4 | even | 2 | inner | ||
2800.2.g.t.449.4 | 4 | 1.1 | even | 1 | trivial | ||
3920.2.a.bs.1.1 | 2 | 35.27 | even | 4 | |||
4235.2.a.m.1.1 | 2 | 220.87 | odd | 4 | |||
5040.2.a.bt.1.2 | 2 | 15.2 | even | 4 | |||
5915.2.a.l.1.1 | 2 | 260.207 | even | 4 |