Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,2,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("175.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (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: | \(1.39738203537\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.2.b.b.99.3 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.56155i | − 1.10418i | −0.833783 | − | 0.552092i | \(-0.813830\pi\) | ||||
0.833783 | − | 0.552092i | \(-0.186170\pi\) | |||||||
\(3\) | − 2.56155i | − 1.47891i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
0.673204 | − | 0.739457i | \(-0.264917\pi\) | |||||||
\(4\) | −0.438447 | −0.219224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.00000 | −1.63299 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − 2.43845i | − 0.862121i | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | 1.12311i | 0.324213i | ||||||||
\(13\) | 4.56155i | 1.26515i | 0.774500 | + | 0.632574i | \(0.218001\pi\) | ||||
−0.774500 | + | 0.632574i | \(0.781999\pi\) | |||||||
\(14\) | 1.56155 | 0.417343 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 4.56155i | 1.10634i | 0.833069 | + | 0.553170i | \(0.186582\pi\) | ||||
−0.833069 | + | 0.553170i | \(0.813418\pi\) | |||||||
\(18\) | 5.56155i | 1.31087i | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | − 4.00000i | − 0.852803i | ||||||||
\(23\) | − 5.12311i | − 1.06824i | −0.845408 | − | 0.534121i | \(-0.820643\pi\) | ||||
0.845408 | − | 0.534121i | \(-0.179357\pi\) | |||||||
\(24\) | −6.24621 | −1.27500 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.12311 | 1.39696 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | − 0.438447i | − 0.0828587i | ||||||||
\(29\) | 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 | \(0.5\pi\) | |||||||||
\(32\) | 2.43845i | 0.431061i | ||||||||
\(33\) | − 6.56155i | − 1.14222i | ||||||||
\(34\) | 7.12311 | 1.22160 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.56155 | 0.260259 | ||||||||
\(37\) | − 6.00000i | − 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | 1.75379i | 0.284502i | ||||||||
\(39\) | 11.6847 | 1.87104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12311 | −0.487747 | −0.243874 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243874 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(42\) | − 4.00000i | − 0.617213i | ||||||||
\(43\) | 9.12311i | 1.39126i | 0.718400 | + | 0.695630i | \(0.244875\pi\) | ||||
−0.718400 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(44\) | −1.12311 | −0.169315 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | − 3.68466i | − 0.537463i | −0.963215 | − | 0.268731i | \(-0.913396\pi\) | ||||
0.963215 | − | 0.268731i | \(-0.0866044\pi\) | |||||||
\(48\) | 12.0000i | 1.73205i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.6847 | 1.63618 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | 3.12311i | 0.428992i | 0.976725 | + | 0.214496i | \(0.0688108\pi\) | ||||
−0.976725 | + | 0.214496i | \(0.931189\pi\) | |||||||
\(54\) | 2.24621 | 0.305671 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 2.87689i | 0.381054i | ||||||||
\(58\) | − 8.87689i | − 1.16559i | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 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 | ||||||||
\(64\) | −5.56155 | −0.695194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.2462 | −1.26122 | ||||||||
\(67\) | 6.24621i | 0.763096i | 0.924349 | + | 0.381548i | \(0.124609\pi\) | ||||
−0.924349 | + | 0.381548i | \(0.875391\pi\) | |||||||
\(68\) | − 2.00000i | − 0.242536i | ||||||||
\(69\) | −13.1231 | −1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 8.68466i | 1.02350i | ||||||||
\(73\) | 4.24621i | 0.496981i | 0.968634 | + | 0.248491i | \(0.0799345\pi\) | ||||
−0.968634 | + | 0.248491i | \(0.920065\pi\) | |||||||
\(74\) | −9.36932 | −1.08916 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.492423 | 0.0564847 | ||||||||
\(77\) | 2.56155i | 0.291916i | ||||||||
\(78\) | − 18.2462i | − 2.06598i | ||||||||
\(79\) | 6.56155 | 0.738232 | 0.369116 | − | 0.929383i | \(-0.379660\pi\) | ||||
0.369116 | + | 0.929383i | \(0.379660\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 4.87689i | 0.538563i | ||||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | −1.12311 | −0.122541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.2462 | 1.53621 | ||||||||
\(87\) | − 14.5616i | − 1.56116i | ||||||||
\(88\) | − 6.24621i | − 0.665848i | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 2.24621i | 0.234184i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.75379 | −0.593458 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.24621 | 0.637501 | ||||||||
\(97\) | 14.8078i | 1.50350i | 0.659448 | + | 0.751750i | \(0.270790\pi\) | ||||
−0.659448 | + | 0.751750i | \(0.729210\pi\) | |||||||
\(98\) | 1.56155i | 0.157741i | ||||||||
\(99\) | −9.12311 | −0.916907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | − 18.2462i | − 1.80664i | ||||||||
\(103\) | 1.43845i | 0.141734i | 0.997486 | + | 0.0708672i | \(0.0225767\pi\) | ||||
−0.997486 | + | 0.0708672i | \(0.977423\pi\) | |||||||
\(104\) | 11.1231 | 1.09071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.87689 | 0.473686 | ||||||||
\(107\) | 11.3693i | 1.09911i | 0.835456 | + | 0.549557i | \(0.185203\pi\) | ||||
−0.835456 | + | 0.549557i | \(0.814797\pi\) | |||||||
\(108\) | − 0.630683i | − 0.0606875i | ||||||||
\(109\) | −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 | ||||||||
\(112\) | − 4.68466i | − 0.442659i | ||||||||
\(113\) | − 14.0000i | − 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 4.49242 | 0.420754 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.49242 | −0.231416 | ||||||||
\(117\) | − 16.2462i | − 1.50196i | ||||||||
\(118\) | − 6.24621i | − 0.575010i | ||||||||
\(119\) | −4.56155 | −0.418157 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 14.6307i | 1.32460i | ||||||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.56155 | −0.495463 | ||||||||
\(127\) | − 10.2462i | − 0.909204i | −0.890695 | − | 0.454602i | \(-0.849781\pi\) | ||||
0.890695 | − | 0.454602i | \(-0.150219\pi\) | |||||||
\(128\) | 13.5616i | 1.19868i | ||||||||
\(129\) | 23.3693 | 2.05755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.12311 | −0.797089 | −0.398545 | − | 0.917149i | \(-0.630485\pi\) | ||||
−0.398545 | + | 0.917149i | \(0.630485\pi\) | |||||||
\(132\) | 2.87689i | 0.250402i | ||||||||
\(133\) | − 1.12311i | − 0.0973856i | ||||||||
\(134\) | 9.75379 | 0.842599 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.1231 | 0.953798 | ||||||||
\(137\) | 8.87689i | 0.758404i | 0.925314 | + | 0.379202i | \(0.123801\pi\) | ||||
−0.925314 | + | 0.379202i | \(0.876199\pi\) | |||||||
\(138\) | 20.4924i | 1.74443i | ||||||||
\(139\) | 6.87689 | 0.583291 | 0.291645 | − | 0.956527i | \(-0.405797\pi\) | ||||
0.291645 | + | 0.956527i | \(0.405797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.43845 | −0.794861 | ||||||||
\(142\) | − 12.4924i | − 1.04834i | ||||||||
\(143\) | 11.6847i | 0.977120i | ||||||||
\(144\) | 16.6847 | 1.39039 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.63068 | 0.548759 | ||||||||
\(147\) | 2.56155i | 0.211273i | ||||||||
\(148\) | 2.63068i | 0.216241i | ||||||||
\(149\) | 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 | \(-0.149052\pi\) | ||||
0.892354 | + | 0.451335i | \(0.149052\pi\) | |||||||
\(152\) | 2.73863i | 0.222133i | ||||||||
\(153\) | − 16.2462i | − 1.31343i | ||||||||
\(154\) | 4.00000 | 0.322329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.12311 | −0.410177 | ||||||||
\(157\) | − 3.75379i | − 0.299585i | −0.988717 | − | 0.149792i | \(-0.952139\pi\) | ||||
0.988717 | − | 0.149792i | \(-0.0478606\pi\) | |||||||
\(158\) | − 10.2462i | − 0.815145i | ||||||||
\(159\) | 8.00000 | 0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 10.9309i | 0.858810i | ||||||||
\(163\) | 1.12311i | 0.0879684i | 0.999032 | + | 0.0439842i | \(0.0140051\pi\) | ||||
−0.999032 | + | 0.0439842i | \(0.985995\pi\) | |||||||
\(164\) | 1.36932 | 0.106926 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.24621 | 0.484800 | ||||||||
\(167\) | − 21.9309i | − 1.69706i | −0.529146 | − | 0.848531i | \(-0.677488\pi\) | ||||
0.529146 | − | 0.848531i | \(-0.322512\pi\) | |||||||
\(168\) | − 6.24621i | − 0.481906i | ||||||||
\(169\) | −7.80776 | −0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | − 4.00000i | − 0.304997i | ||||||||
\(173\) | − 8.56155i | − 0.650923i | −0.945555 | − | 0.325461i | \(-0.894480\pi\) | ||||
0.945555 | − | 0.325461i | \(-0.105520\pi\) | |||||||
\(174\) | −22.7386 | −1.72381 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | − 10.2462i | − 0.770152i | ||||||||
\(178\) | 11.1231i | 0.833712i | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6155 | 1.75533 | 0.877664 | − | 0.479276i | \(-0.159101\pi\) | ||||
0.877664 | + | 0.479276i | \(0.159101\pi\) | |||||||
\(182\) | 7.12311i | 0.528000i | ||||||||
\(183\) | 24.0000i | 1.77413i | ||||||||
\(184\) | −12.4924 | −0.920954 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6847i | 0.854467i | ||||||||
\(188\) | 1.61553i | 0.117824i | ||||||||
\(189\) | −1.43845 | −0.104632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.43845 | −0.682942 | −0.341471 | − | 0.939892i | \(-0.610925\pi\) | ||||
−0.341471 | + | 0.939892i | \(0.610925\pi\) | |||||||
\(192\) | 14.2462i | 1.02813i | ||||||||
\(193\) | − 5.36932i | − 0.386492i | −0.981150 | − | 0.193246i | \(-0.938098\pi\) | ||||
0.981150 | − | 0.193246i | \(-0.0619015\pi\) | |||||||
\(194\) | 23.1231 | 1.66014 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | 7.12311i | 0.507500i | 0.967270 | + | 0.253750i | \(0.0816641\pi\) | ||||
−0.967270 | + | 0.253750i | \(0.918336\pi\) | |||||||
\(198\) | 14.2462i | 1.01243i | ||||||||
\(199\) | 18.2462 | 1.29344 | 0.646720 | − | 0.762728i | \(-0.276140\pi\) | ||||
0.646720 | + | 0.762728i | \(0.276140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | − 0.384472i | − 0.0270513i | ||||||||
\(203\) | 5.68466i | 0.398985i | ||||||||
\(204\) | −5.12311 | −0.358689 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.24621 | 0.156501 | ||||||||
\(207\) | 18.2462i | 1.26820i | ||||||||
\(208\) | − 21.3693i | − 1.48170i | ||||||||
\(209\) | −2.87689 | −0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0540 | −1.58710 | −0.793551 | − | 0.608504i | \(-0.791770\pi\) | ||||
−0.793551 | + | 0.608504i | \(0.791770\pi\) | |||||||
\(212\) | − 1.36932i | − 0.0940451i | ||||||||
\(213\) | − 20.4924i | − 1.40412i | ||||||||
\(214\) | 17.7538 | 1.21362 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.50758 | 0.238660 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.6155i | 1.87036i | ||||||||
\(219\) | 10.8769 | 0.734992 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.8078 | −1.39968 | ||||||||
\(222\) | 24.0000i | 1.61077i | ||||||||
\(223\) | − 6.56155i | − 0.439394i | −0.975568 | − | 0.219697i | \(-0.929493\pi\) | ||||
0.975568 | − | 0.219697i | \(-0.0705069\pi\) | |||||||
\(224\) | −2.43845 | −0.162926 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.8617 | −1.45422 | ||||||||
\(227\) | − 23.6847i | − 1.57201i | −0.618223 | − | 0.786003i | \(-0.712147\pi\) | ||||
0.618223 | − | 0.786003i | \(-0.287853\pi\) | |||||||
\(228\) | − 1.26137i | − 0.0835360i | ||||||||
\(229\) | −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 | ||||||||
\(232\) | − 13.8617i | − 0.910068i | ||||||||
\(233\) | − 3.12311i | − 0.204601i | −0.994754 | − | 0.102301i | \(-0.967380\pi\) | ||||
0.994754 | − | 0.102301i | \(-0.0326204\pi\) | |||||||
\(234\) | −25.3693 | −1.65844 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.75379 | −0.114162 | ||||||||
\(237\) | − 16.8078i | − 1.09178i | ||||||||
\(238\) | 7.12311i | 0.461722i | ||||||||
\(239\) | 0.807764 | 0.0522499 | 0.0261250 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261250 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | 6.93087i | 0.445533i | ||||||||
\(243\) | 22.2462i | 1.42710i | ||||||||
\(244\) | 4.10795 | 0.262985 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.4924 | 0.796488 | ||||||||
\(247\) | − 5.12311i | − 0.325975i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2462 | 0.649327 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1231 | −1.08080 | −0.540400 | − | 0.841408i | \(-0.681727\pi\) | ||||
−0.540400 | + | 0.841408i | \(0.681727\pi\) | |||||||
\(252\) | 1.56155i | 0.0983686i | ||||||||
\(253\) | − 13.1231i | − 0.825043i | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | − 22.4924i | − 1.40304i | −0.712650 | − | 0.701519i | \(-0.752505\pi\) | ||||
0.712650 | − | 0.701519i | \(-0.247495\pi\) | |||||||
\(258\) | − 36.4924i | − 2.27192i | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.2462 | −1.25321 | ||||||||
\(262\) | 14.2462i | 0.880134i | ||||||||
\(263\) | − 21.1231i | − 1.30251i | −0.758860 | − | 0.651253i | \(-0.774244\pi\) | ||||
0.758860 | − | 0.651253i | \(-0.225756\pi\) | |||||||
\(264\) | −16.0000 | −0.984732 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.75379 | −0.107532 | ||||||||
\(267\) | 18.2462i | 1.11665i | ||||||||
\(268\) | − 2.73863i | − 0.167289i | ||||||||
\(269\) | −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 | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | − 21.3693i | − 1.29571i | ||||||||
\(273\) | 11.6847i | 0.707188i | ||||||||
\(274\) | 13.8617 | 0.837418 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.75379 | 0.346337 | ||||||||
\(277\) | − 16.2462i | − 0.976140i | −0.872804 | − | 0.488070i | \(-0.837701\pi\) | ||||
0.872804 | − | 0.488070i | \(-0.162299\pi\) | |||||||
\(278\) | − 10.7386i | − 0.644060i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5616 | 0.987979 | 0.493990 | − | 0.869468i | \(-0.335538\pi\) | ||||
0.493990 | + | 0.869468i | \(0.335538\pi\) | |||||||
\(282\) | 14.7386i | 0.877673i | ||||||||
\(283\) | − 23.6847i | − 1.40791i | −0.710246 | − | 0.703953i | \(-0.751416\pi\) | ||||
0.710246 | − | 0.703953i | \(-0.248584\pi\) | |||||||
\(284\) | −3.50758 | −0.208136 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.2462 | 1.07892 | ||||||||
\(287\) | − 3.12311i | − 0.184351i | ||||||||
\(288\) | − 8.68466i | − 0.511748i | ||||||||
\(289\) | −3.80776 | −0.223986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.9309 | 2.22355 | ||||||||
\(292\) | − 1.86174i | − 0.108950i | ||||||||
\(293\) | 9.68466i | 0.565784i | 0.959152 | + | 0.282892i | \(0.0912938\pi\) | ||||
−0.959152 | + | 0.282892i | \(0.908706\pi\) | |||||||
\(294\) | 4.00000 | 0.233285 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.6307 | −0.850391 | ||||||||
\(297\) | 3.68466i | 0.213806i | ||||||||
\(298\) | − 6.63068i | − 0.384105i | ||||||||
\(299\) | 23.3693 | 1.35148 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.12311 | −0.525847 | ||||||||
\(302\) | − 34.2462i | − 1.97065i | ||||||||
\(303\) | − 0.630683i | − 0.0362318i | ||||||||
\(304\) | 5.26137 | 0.301760 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −25.3693 | −1.45027 | ||||||||
\(307\) | 31.6847i | 1.80834i | 0.427174 | + | 0.904169i | \(0.359509\pi\) | ||||
−0.427174 | + | 0.904169i | \(0.640491\pi\) | |||||||
\(308\) | − 1.12311i | − 0.0639949i | ||||||||
\(309\) | 3.68466 | 0.209613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.61553 | −0.545247 | −0.272623 | − | 0.962121i | \(-0.587891\pi\) | ||||
−0.272623 | + | 0.962121i | \(0.587891\pi\) | |||||||
\(312\) | − 28.4924i | − 1.61307i | ||||||||
\(313\) | 31.3002i | 1.76919i | 0.466359 | + | 0.884596i | \(0.345566\pi\) | ||||
−0.466359 | + | 0.884596i | \(0.654434\pi\) | |||||||
\(314\) | −5.86174 | −0.330797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.87689 | −0.161838 | ||||||||
\(317\) | 22.4924i | 1.26330i | 0.775254 | + | 0.631650i | \(0.217622\pi\) | ||||
−0.775254 | + | 0.631650i | \(0.782378\pi\) | |||||||
\(318\) | − 12.4924i | − 0.700540i | ||||||||
\(319\) | 14.5616 | 0.815290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.1231 | 1.62549 | ||||||||
\(322\) | − 8.00000i | − 0.445823i | ||||||||
\(323\) | − 5.12311i | − 0.285057i | ||||||||
\(324\) | 3.06913 | 0.170507 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.75379 | 0.0971334 | ||||||||
\(327\) | 45.3002i | 2.50511i | ||||||||
\(328\) | 7.61553i | 0.420497i | ||||||||
\(329\) | 3.68466 | 0.203142 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | − 1.75379i | − 0.0962517i | ||||||||
\(333\) | 21.3693i | 1.17103i | ||||||||
\(334\) | −34.2462 | −1.87387 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −12.0000 | −0.654654 | ||||||||
\(337\) | 34.4924i | 1.87892i | 0.342656 | + | 0.939461i | \(0.388674\pi\) | ||||
−0.342656 | + | 0.939461i | \(0.611326\pi\) | |||||||
\(338\) | 12.1922i | 0.663170i | ||||||||
\(339\) | −35.8617 | −1.94774 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 6.24621i | − 0.337756i | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 22.2462 | 1.19944 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.3693 | −0.718739 | ||||||||
\(347\) | 1.12311i | 0.0602915i | 0.999546 | + | 0.0301457i | \(0.00959714\pi\) | ||||
−0.999546 | + | 0.0301457i | \(0.990403\pi\) | |||||||
\(348\) | 6.38447i | 0.342244i | ||||||||
\(349\) | 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 | ||||||||
\(352\) | 6.24621i | 0.332924i | ||||||||
\(353\) | − 14.8078i | − 0.788138i | −0.919081 | − | 0.394069i | \(-0.871067\pi\) | ||||
0.919081 | − | 0.394069i | \(-0.128933\pi\) | |||||||
\(354\) | −16.0000 | −0.850390 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.12311 | 0.165524 | ||||||||
\(357\) | 11.6847i | 0.618418i | ||||||||
\(358\) | 31.2311i | 1.65061i | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | − 36.8769i | − 1.93821i | ||||||||
\(363\) | 11.3693i | 0.596734i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 37.4773 | 1.95897 | ||||||||
\(367\) | − 3.68466i | − 0.192338i | −0.995365 | − | 0.0961688i | \(-0.969341\pi\) | ||||
0.995365 | − | 0.0961688i | \(-0.0306589\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | 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 | \(0.725031\pi\) | |||||||
\(374\) | 18.2462 | 0.943489 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.98485 | −0.463358 | ||||||||
\(377\) | 25.9309i | 1.33551i | ||||||||
\(378\) | 2.24621i | 0.115533i | ||||||||
\(379\) | −16.4924 | −0.847159 | −0.423579 | − | 0.905859i | \(-0.639227\pi\) | ||||
−0.423579 | + | 0.905859i | \(0.639227\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.2462 | −1.34463 | ||||||||
\(382\) | 14.7386i | 0.754094i | ||||||||
\(383\) | − 10.2462i | − 0.523557i | −0.965128 | − | 0.261778i | \(-0.915691\pi\) | ||||
0.965128 | − | 0.261778i | \(-0.0843090\pi\) | |||||||
\(384\) | 34.7386 | 1.77275 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.38447 | −0.426758 | ||||||||
\(387\) | − 32.4924i | − 1.65168i | ||||||||
\(388\) | − 6.49242i | − 0.329603i | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 2.43845i | 0.123160i | ||||||||
\(393\) | 23.3693i | 1.17883i | ||||||||
\(394\) | 11.1231 | 0.560374 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | − 23.4384i | − 1.17634i | −0.808737 | − | 0.588171i | \(-0.799848\pi\) | ||||
0.808737 | − | 0.588171i | \(-0.200152\pi\) | |||||||
\(398\) | − 28.4924i | − 1.42820i | ||||||||
\(399\) | −2.87689 | −0.144025 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.4384 | 1.37021 | 0.685105 | − | 0.728444i | \(-0.259756\pi\) | ||||
0.685105 | + | 0.728444i | \(0.259756\pi\) | |||||||
\(402\) | − 24.9848i | − 1.24613i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.107951 | −0.00537074 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.87689 | 0.440553 | ||||||||
\(407\) | − 15.3693i | − 0.761829i | ||||||||
\(408\) | − 28.4924i | − 1.41059i | ||||||||
\(409\) | 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 | ||||||||
\(412\) | − 0.630683i | − 0.0310715i | ||||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | 28.4924 | 1.40033 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.1231 | −0.545355 | ||||||||
\(417\) | − 17.6155i | − 0.862636i | ||||||||
\(418\) | 4.49242i | 0.219732i | ||||||||
\(419\) | −9.75379 | −0.476504 | −0.238252 | − | 0.971203i | \(-0.576574\pi\) | ||||
−0.238252 | + | 0.971203i | \(0.576574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.68466 | 0.472001 | 0.236001 | − | 0.971753i | \(-0.424163\pi\) | ||||
0.236001 | + | 0.971753i | \(0.424163\pi\) | |||||||
\(422\) | 36.0000i | 1.75245i | ||||||||
\(423\) | 13.1231i | 0.638067i | ||||||||
\(424\) | 7.61553 | 0.369843 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −32.0000 | −1.55041 | ||||||||
\(427\) | − 9.36932i | − 0.453413i | ||||||||
\(428\) | − 4.98485i | − 0.240952i | ||||||||
\(429\) | 29.9309 | 1.44508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.807764 | 0.0389086 | 0.0194543 | − | 0.999811i | \(-0.493807\pi\) | ||||
0.0194543 | + | 0.999811i | \(0.493807\pi\) | |||||||
\(432\) | − 6.73863i | − 0.324213i | ||||||||
\(433\) | − 8.24621i | − 0.396288i | −0.980173 | − | 0.198144i | \(-0.936509\pi\) | ||||
0.980173 | − | 0.198144i | \(-0.0634913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.75379 | 0.371339 | ||||||||
\(437\) | 5.75379i | 0.275241i | ||||||||
\(438\) | − 16.9848i | − 0.811567i | ||||||||
\(439\) | 15.3693 | 0.733537 | 0.366769 | − | 0.930312i | \(-0.380464\pi\) | ||||
0.366769 | + | 0.930312i | \(0.380464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 32.4924i | 1.54551i | ||||||||
\(443\) | − 27.3693i | − 1.30036i | −0.759782 | − | 0.650178i | \(-0.774694\pi\) | ||||
0.759782 | − | 0.650178i | \(-0.225306\pi\) | |||||||
\(444\) | 6.73863 | 0.319801 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.2462 | −0.485172 | ||||||||
\(447\) | − 10.8769i | − 0.514459i | ||||||||
\(448\) | − 5.56155i | − 0.262759i | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 6.13826i | 0.288719i | ||||||||
\(453\) | − 56.1771i | − 2.63943i | ||||||||
\(454\) | −36.9848 | −1.73578 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.01515 | 0.328515 | ||||||||
\(457\) | 8.87689i | 0.415244i | 0.978209 | + | 0.207622i | \(0.0665723\pi\) | ||||
−0.978209 | + | 0.207622i | \(0.933428\pi\) | |||||||
\(458\) | 29.8617i | 1.39535i | ||||||||
\(459\) | −6.56155 | −0.306267 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.87689 | −0.227140 | −0.113570 | − | 0.993530i | \(-0.536229\pi\) | ||||
−0.113570 | + | 0.993530i | \(0.536229\pi\) | |||||||
\(462\) | − 10.2462i | − 0.476697i | ||||||||
\(463\) | − 20.4924i | − 0.952364i | −0.879347 | − | 0.476182i | \(-0.842020\pi\) | ||||
0.879347 | − | 0.476182i | \(-0.157980\pi\) | |||||||
\(464\) | −26.6307 | −1.23630 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.87689 | −0.225918 | ||||||||
\(467\) | − 26.5616i | − 1.22912i | −0.788869 | − | 0.614561i | \(-0.789333\pi\) | ||||
0.788869 | − | 0.614561i | \(-0.210667\pi\) | |||||||
\(468\) | 7.12311i | 0.329266i | ||||||||
\(469\) | −6.24621 | −0.288423 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.61553 | −0.443060 | ||||||||
\(472\) | − 9.75379i | − 0.448955i | ||||||||
\(473\) | 23.3693i | 1.07452i | ||||||||
\(474\) | −26.2462 | −1.20553 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | − 11.1231i | − 0.509292i | ||||||||
\(478\) | − 1.26137i | − 0.0576935i | ||||||||
\(479\) | −13.1231 | −0.599610 | −0.299805 | − | 0.954001i | \(-0.596922\pi\) | ||||
−0.299805 | + | 0.954001i | \(0.596922\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3693 | 1.24793 | ||||||||
\(482\) | − 19.1231i | − 0.871034i | ||||||||
\(483\) | − 13.1231i | − 0.597122i | ||||||||
\(484\) | 1.94602 | 0.0884557 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 34.7386 | 1.57578 | ||||||||
\(487\) | − 5.12311i | − 0.232150i | −0.993240 | − | 0.116075i | \(-0.962969\pi\) | ||||
0.993240 | − | 0.116075i | \(-0.0370313\pi\) | |||||||
\(488\) | 22.8466i | 1.03422i | ||||||||
\(489\) | 2.87689 | 0.130098 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.17708 | 0.188509 | 0.0942545 | − | 0.995548i | \(-0.469953\pi\) | ||||
0.0942545 | + | 0.995548i | \(0.469953\pi\) | |||||||
\(492\) | − 3.50758i | − 0.158134i | ||||||||
\(493\) | 25.9309i | 1.16787i | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | − 16.0000i | − 0.716977i | ||||||||
\(499\) | 4.17708 | 0.186992 | 0.0934959 | − | 0.995620i | \(-0.470196\pi\) | ||||
0.0934959 | + | 0.995620i | \(0.470196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.1771 | −2.50981 | ||||||||
\(502\) | 26.7386i | 1.19340i | ||||||||
\(503\) | 10.0691i | 0.448960i | 0.974479 | + | 0.224480i | \(0.0720684\pi\) | ||||
−0.974479 | + | 0.224480i | \(0.927932\pi\) | |||||||
\(504\) | −8.68466 | −0.386845 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.4924 | −0.910999 | ||||||||
\(507\) | 20.0000i | 0.888231i | ||||||||
\(508\) | 4.49242i | 0.199319i | ||||||||
\(509\) | 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 | ||||||||
\(512\) | 11.4233i | 0.504843i | ||||||||
\(513\) | − 1.61553i | − 0.0713273i | ||||||||
\(514\) | −35.1231 | −1.54921 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.2462 | −0.451064 | ||||||||
\(517\) | − 9.43845i | − 0.415102i | ||||||||
\(518\) | − 9.36932i | − 0.411664i | ||||||||
\(519\) | −21.9309 | −0.962658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 31.6155i | 1.38377i | ||||||||
\(523\) | 7.50758i | 0.328283i | 0.986437 | + | 0.164142i | \(0.0524854\pi\) | ||||
−0.986437 | + | 0.164142i | \(0.947515\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.9848 | −1.43821 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 30.7386i | 1.33773i | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2462 | −0.618233 | ||||||||
\(532\) | 0.492423i | 0.0213492i | ||||||||
\(533\) | − 14.2462i | − 0.617072i | ||||||||
\(534\) | 28.4924 | 1.23299 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.2311 | 0.657881 | ||||||||
\(537\) | 51.2311i | 2.21078i | ||||||||
\(538\) | 44.8769i | 1.93478i | ||||||||
\(539\) | −2.56155 | −0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.1922 | −0.739152 | −0.369576 | − | 0.929201i | \(-0.620497\pi\) | ||||
−0.369576 | + | 0.929201i | \(0.620497\pi\) | |||||||
\(542\) | 24.9848i | 1.07319i | ||||||||
\(543\) | − 60.4924i | − 2.59598i | ||||||||
\(544\) | −11.1231 | −0.476899 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.2462 | 0.780866 | ||||||||
\(547\) | − 14.2462i | − 0.609124i | −0.952493 | − | 0.304562i | \(-0.901490\pi\) | ||||
0.952493 | − | 0.304562i | \(-0.0985101\pi\) | |||||||
\(548\) | − 3.89205i | − 0.166260i | ||||||||
\(549\) | 33.3693 | 1.42417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.38447 | −0.271988 | ||||||||
\(552\) | 32.0000i | 1.36201i | ||||||||
\(553\) | 6.56155i | 0.279026i | ||||||||
\(554\) | −25.3693 | −1.07784 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.01515 | −0.127871 | ||||||||
\(557\) | 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 | ||||||||
\(562\) | − 25.8617i | − 1.09091i | ||||||||
\(563\) | − 28.0000i | − 1.18006i | −0.807382 | − | 0.590030i | \(-0.799116\pi\) | ||||
0.807382 | − | 0.590030i | \(-0.200884\pi\) | |||||||
\(564\) | 4.13826 | 0.174252 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −36.9848 | −1.55459 | ||||||||
\(567\) | − 7.00000i | − 0.293972i | ||||||||
\(568\) | − 19.5076i | − 0.818520i | ||||||||
\(569\) | −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 | \(-0.449788\pi\) | ||||
0.157091 | + | 0.987584i | \(0.449788\pi\) | |||||||
\(572\) | − 5.12311i | − 0.214208i | ||||||||
\(573\) | 24.1771i | 1.01001i | ||||||||
\(574\) | −4.87689 | −0.203558 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.8078 | 0.825324 | ||||||||
\(577\) | − 13.0540i | − 0.543444i | −0.962376 | − | 0.271722i | \(-0.912407\pi\) | ||||
0.962376 | − | 0.271722i | \(-0.0875931\pi\) | |||||||
\(578\) | 5.94602i | 0.247322i | ||||||||
\(579\) | −13.7538 | −0.571588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | − 59.2311i | − 2.45521i | ||||||||
\(583\) | 8.00000i | 0.331326i | ||||||||
\(584\) | 10.3542 | 0.428458 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.1231 | 0.624730 | ||||||||
\(587\) | 9.75379i | 0.402582i | 0.979531 | + | 0.201291i | \(0.0645137\pi\) | ||||
−0.979531 | + | 0.201291i | \(0.935486\pi\) | |||||||
\(588\) | − 1.12311i | − 0.0463161i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.2462 | 0.750549 | ||||||||
\(592\) | 28.1080i | 1.15523i | ||||||||
\(593\) | − 23.4384i | − 0.962502i | −0.876583 | − | 0.481251i | \(-0.840183\pi\) | ||||
0.876583 | − | 0.481251i | \(-0.159817\pi\) | |||||||
\(594\) | 5.75379 | 0.236081 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.86174 | −0.0762598 | ||||||||
\(597\) | − 46.7386i | − 1.91288i | ||||||||
\(598\) | − 36.4924i | − 1.49229i | ||||||||
\(599\) | −8.80776 | −0.359875 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4924 | −1.08065 | −0.540324 | − | 0.841457i | \(-0.681698\pi\) | ||||
−0.540324 | + | 0.841457i | \(0.681698\pi\) | |||||||
\(602\) | 14.2462i | 0.580632i | ||||||||
\(603\) | − 22.2462i | − 0.905936i | ||||||||
\(604\) | −9.61553 | −0.391250 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.984845 | −0.0400066 | ||||||||
\(607\) | 4.94602i | 0.200753i | 0.994950 | + | 0.100376i | \(0.0320047\pi\) | ||||
−0.994950 | + | 0.100376i | \(0.967995\pi\) | |||||||
\(608\) | − 2.73863i | − 0.111066i | ||||||||
\(609\) | 14.5616 | 0.590064 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.8078 | 0.679969 | ||||||||
\(612\) | 7.12311i | 0.287934i | ||||||||
\(613\) | − 8.73863i | − 0.352950i | −0.984305 | − | 0.176475i | \(-0.943531\pi\) | ||||
0.984305 | − | 0.176475i | \(-0.0564695\pi\) | |||||||
\(614\) | 49.4773 | 1.99674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.24621 | 0.251667 | ||||||||
\(617\) | − 15.7538i | − 0.634224i | −0.948388 | − | 0.317112i | \(-0.897287\pi\) | ||||
0.948388 | − | 0.317112i | \(-0.102713\pi\) | |||||||
\(618\) | − 5.75379i | − 0.231451i | ||||||||
\(619\) | 42.1080 | 1.69246 | 0.846231 | − | 0.532817i | \(-0.178866\pi\) | ||||
0.846231 | + | 0.532817i | \(0.178866\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.36932 | 0.295720 | ||||||||
\(622\) | 15.0152i | 0.602053i | ||||||||
\(623\) | − 7.12311i | − 0.285381i | ||||||||
\(624\) | −54.7386 | −2.19130 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 48.8769 | 1.95351 | ||||||||
\(627\) | 7.36932i | 0.294302i | ||||||||
\(628\) | 1.64584i | 0.0656761i | ||||||||
\(629\) | 27.3693 | 1.09129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.80776 | 0.350632 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(632\) | − 16.0000i | − 0.636446i | ||||||||
\(633\) | 59.0540i | 2.34718i | ||||||||
\(634\) | 35.1231 | 1.39492 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.50758 | −0.139084 | ||||||||
\(637\) | − 4.56155i | − 0.180735i | ||||||||
\(638\) | − 22.7386i | − 0.900231i | ||||||||
\(639\) | −28.4924 | −1.12714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | − 45.4773i | − 1.79484i | ||||||||
\(643\) | − 2.56155i | − 0.101018i | −0.998724 | − | 0.0505089i | \(-0.983916\pi\) | ||||
0.998724 | − | 0.0505089i | \(-0.0160843\pi\) | |||||||
\(644\) | −2.24621 | −0.0885131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | − 3.50758i | − 0.137897i | −0.997620 | − | 0.0689486i | \(-0.978036\pi\) | ||||
0.997620 | − | 0.0689486i | \(-0.0219644\pi\) | |||||||
\(648\) | 17.0691i | 0.670539i | ||||||||
\(649\) | 10.2462 | 0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 0.492423i | − 0.0192848i | ||||||||
\(653\) | 49.2311i | 1.92656i | 0.268499 | + | 0.963280i | \(0.413473\pi\) | ||||
−0.268499 | + | 0.963280i | \(0.586527\pi\) | |||||||
\(654\) | 70.7386 | 2.76610 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.6307 | 0.571232 | ||||||||
\(657\) | − 15.1231i | − 0.590009i | ||||||||
\(658\) | − 5.75379i | − 0.224306i | ||||||||
\(659\) | 36.1771 | 1.40926 | 0.704629 | − | 0.709575i | \(-0.251113\pi\) | ||||
0.704629 | + | 0.709575i | \(0.251113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.12311 | 0.121475 | 0.0607374 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607374 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(662\) | − 18.7386i | − 0.728298i | ||||||||
\(663\) | 53.3002i | 2.07001i | ||||||||
\(664\) | 9.75379 | 0.378520 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 33.3693 | 1.29303 | ||||||||
\(667\) | − 29.1231i | − 1.12765i | ||||||||
\(668\) | 9.61553i | 0.372036i | ||||||||
\(669\) | −16.8078 | −0.649826 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 6.24621i | 0.240953i | ||||||||
\(673\) | − 25.8617i | − 0.996897i | −0.866919 | − | 0.498448i | \(-0.833903\pi\) | ||||
0.866919 | − | 0.498448i | \(-0.166097\pi\) | |||||||
\(674\) | 53.8617 | 2.07468 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | 23.9309i | 0.919738i | 0.887987 | + | 0.459869i | \(0.152104\pi\) | ||||
−0.887987 | + | 0.459869i | \(0.847896\pi\) | |||||||
\(678\) | 56.0000i | 2.15067i | ||||||||
\(679\) | −14.8078 | −0.568270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.6695 | −2.32486 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.7386i | 1.63535i | 0.575681 | + | 0.817674i | \(0.304737\pi\) | ||||
−0.575681 | + | 0.817674i | \(0.695263\pi\) | |||||||
\(684\) | −1.75379 | −0.0670578 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.56155 | −0.0596204 | ||||||||
\(687\) | 48.9848i | 1.86889i | ||||||||
\(688\) | − 42.7386i | − 1.62940i | ||||||||
\(689\) | −14.2462 | −0.542737 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.49242 | 0.323067 | 0.161533 | − | 0.986867i | \(-0.448356\pi\) | ||||
0.161533 | + | 0.986867i | \(0.448356\pi\) | |||||||
\(692\) | 3.75379i | 0.142698i | ||||||||
\(693\) | − 9.12311i | − 0.346558i | ||||||||
\(694\) | 1.75379 | 0.0665729 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −35.5076 | −1.34591 | ||||||||
\(697\) | − 14.2462i | − 0.539614i | ||||||||
\(698\) | − 35.1231i | − 1.32943i | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.0691303 | 0.00261102 | 0.00130551 | − | 0.999999i | \(-0.499584\pi\) | ||||
0.00130551 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(702\) | 10.2462i | 0.386718i | ||||||||
\(703\) | 6.73863i | 0.254152i | ||||||||
\(704\) | −14.2462 | −0.536924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1231 | −0.870250 | ||||||||
\(707\) | 0.246211i | 0.00925973i | ||||||||
\(708\) | 4.49242i | 0.168836i | ||||||||
\(709\) | 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 | ||||||||
\(712\) | 17.3693i | 0.650943i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 18.2462 | 0.682847 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.76894 | 0.327711 | ||||||||
\(717\) | − 2.06913i | − 0.0772731i | ||||||||
\(718\) | 12.4924i | 0.466213i | ||||||||
\(719\) | −49.6155 | −1.85035 | −0.925173 | − | 0.379544i | \(-0.876081\pi\) | ||||
−0.925173 | + | 0.379544i | \(0.876081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43845 | −0.0535706 | ||||||||
\(722\) | 27.6998i | 1.03088i | ||||||||
\(723\) | − 31.3693i | − 1.16664i | ||||||||
\(724\) | −10.3542 | −0.384809 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.7538 | 0.658905 | ||||||||
\(727\) | − 19.5076i | − 0.723496i | −0.932276 | − | 0.361748i | \(-0.882180\pi\) | ||||
0.932276 | − | 0.361748i | \(-0.117820\pi\) | |||||||
\(728\) | 11.1231i | 0.412250i | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.6155 | −1.53921 | ||||||||
\(732\) | − 10.5227i | − 0.388931i | ||||||||
\(733\) | − 5.68466i | − 0.209968i | −0.994474 | − | 0.104984i | \(-0.966521\pi\) | ||||
0.994474 | − | 0.104984i | \(-0.0334791\pi\) | |||||||
\(734\) | −5.75379 | −0.212376 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.4924 | 0.460477 | ||||||||
\(737\) | 16.0000i | 0.589368i | ||||||||
\(738\) | − 17.3693i | − 0.639373i | ||||||||
\(739\) | −6.06913 | −0.223257 | −0.111628 | − | 0.993750i | \(-0.535607\pi\) | ||||
−0.111628 | + | 0.993750i | \(0.535607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1231 | −0.482089 | ||||||||
\(742\) | 4.87689i | 0.179036i | ||||||||
\(743\) | 32.9848i | 1.21010i | 0.796189 | + | 0.605048i | \(0.206846\pi\) | ||||
−0.796189 | + | 0.605048i | \(0.793154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.8617 | 1.67912 | ||||||||
\(747\) | − 14.2462i | − 0.521242i | ||||||||
\(748\) | − 5.12311i | − 0.187319i | ||||||||
\(749\) | −11.3693 | −0.415426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.9309 | 1.67604 | 0.838021 | − | 0.545639i | \(-0.183713\pi\) | ||||
0.838021 | + | 0.545639i | \(0.183713\pi\) | |||||||
\(752\) | 17.2614i | 0.629457i | ||||||||
\(753\) | 43.8617i | 1.59841i | ||||||||
\(754\) | 40.4924 | 1.47465 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.630683 | 0.0229377 | ||||||||
\(757\) | − 14.6307i | − 0.531761i | −0.964006 | − | 0.265881i | \(-0.914337\pi\) | ||||
0.964006 | − | 0.265881i | \(-0.0856627\pi\) | |||||||
\(758\) | 25.7538i | 0.935420i | ||||||||
\(759\) | −33.6155 | −1.22017 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.7538 | 1.15107 | 0.575537 | − | 0.817776i | \(-0.304793\pi\) | ||||
0.575537 | + | 0.817776i | \(0.304793\pi\) | |||||||
\(762\) | 40.9848i | 1.48472i | ||||||||
\(763\) | − 17.6847i | − 0.640228i | ||||||||
\(764\) | 4.13826 | 0.149717 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 18.2462i | 0.658833i | ||||||||
\(768\) | − 25.7538i | − 0.929310i | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 2.35416i | 0.0847281i | ||||||||
\(773\) | 8.06913i | 0.290226i | 0.989415 | + | 0.145113i | \(0.0463546\pi\) | ||||
−0.989415 | + | 0.145113i | \(0.953645\pi\) | |||||||
\(774\) | −50.7386 | −1.82376 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36.1080 | 1.29620 | ||||||||
\(777\) | − 15.3693i | − 0.551371i | ||||||||
\(778\) | 6.13826i | 0.220067i | ||||||||
\(779\) | 3.50758 | 0.125672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.4924 | 0.733277 | ||||||||
\(782\) | − 36.4924i | − 1.30497i | ||||||||
\(783\) | 8.17708i | 0.292225i | ||||||||
\(784\) | 4.68466 | 0.167309 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 36.4924 | 1.30164 | ||||||||
\(787\) | 3.82292i | 0.136272i | 0.997676 | + | 0.0681362i | \(0.0217052\pi\) | ||||
−0.997676 | + | 0.0681362i | \(0.978295\pi\) | |||||||
\(788\) | − 3.12311i | − 0.111256i | ||||||||
\(789\) | −54.1080 | −1.92629 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0000 | 0.497783 | ||||||||
\(792\) | 22.2462i | 0.790485i | ||||||||
\(793\) | − 42.7386i | − 1.51769i | ||||||||
\(794\) | −36.6004 | −1.29890 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 13.0540i | 0.462396i | 0.972907 | + | 0.231198i | \(0.0742644\pi\) | ||||
−0.972907 | + | 0.231198i | \(0.925736\pi\) | |||||||
\(798\) | 4.49242i | 0.159030i | ||||||||
\(799\) | 16.8078 | 0.594616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.3693 | 0.896381 | ||||||||
\(802\) | − 42.8466i | − 1.51297i | ||||||||
\(803\) | 10.8769i | 0.383837i | ||||||||
\(804\) | −7.01515 | −0.247405 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 73.6155i | 2.59139i | ||||||||
\(808\) | − 0.600373i | − 0.0211211i | ||||||||
\(809\) | 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 | \(-0.623908\pi\) | ||||
−0.379512 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(812\) | − 2.49242i | − 0.0874669i | ||||||||
\(813\) | 40.9848i | 1.43740i | ||||||||
\(814\) | −24.0000 | −0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −54.7386 | −1.91624 | ||||||||
\(817\) | − 10.2462i | − 0.358470i | ||||||||
\(818\) | − 41.3693i | − 1.44644i | ||||||||
\(819\) | 16.2462 | 0.567689 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4233 | 1.41078 | 0.705391 | − | 0.708818i | \(-0.250771\pi\) | ||||
0.705391 | + | 0.708818i | \(0.250771\pi\) | |||||||
\(822\) | − 35.5076i | − 1.23847i | ||||||||
\(823\) | − 3.50758i | − 0.122266i | −0.998130 | − | 0.0611332i | \(-0.980529\pi\) | ||||
0.998130 | − | 0.0611332i | \(-0.0194715\pi\) | |||||||
\(824\) | 3.50758 | 0.122192 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.24621 | 0.217333 | ||||||||
\(827\) | − 19.3693i | − 0.673537i | −0.941587 | − | 0.336769i | \(-0.890666\pi\) | ||||
0.941587 | − | 0.336769i | \(-0.109334\pi\) | |||||||
\(828\) | − 8.00000i | − 0.278019i | ||||||||
\(829\) | −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 | ||||||||
\(832\) | − 25.3693i | − 0.879523i | ||||||||
\(833\) | − 4.56155i | − 0.158048i | ||||||||
\(834\) | −27.5076 | −0.952510 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.26137 | 0.0436253 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.2311i | 0.526148i | ||||||||
\(839\) | 37.1231 | 1.28163 | 0.640816 | − | 0.767695i | \(-0.278596\pi\) | ||||
0.640816 | + | 0.767695i | \(0.278596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | − 15.1231i | − 0.521177i | ||||||||
\(843\) | − 42.4233i | − 1.46114i | ||||||||
\(844\) | 10.1080 | 0.347930 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 20.4924 | 0.704544 | ||||||||
\(847\) | − 4.43845i | − 0.152507i | ||||||||
\(848\) | − 14.6307i | − 0.502420i | ||||||||
\(849\) | −60.6695 | −2.08217 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.7386 | −1.05371 | ||||||||
\(852\) | 8.98485i | 0.307816i | ||||||||
\(853\) | − 56.7386i | − 1.94269i | −0.237666 | − | 0.971347i | \(-0.576382\pi\) | ||||
0.237666 | − | 0.971347i | \(-0.423618\pi\) | |||||||
\(854\) | −14.6307 | −0.500652 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.7235 | 0.947569 | ||||||||
\(857\) | 32.2462i | 1.10151i | 0.834667 | + | 0.550755i | \(0.185660\pi\) | ||||
−0.834667 | + | 0.550755i | \(0.814340\pi\) | |||||||
\(858\) | − 46.7386i | − 1.59563i | ||||||||
\(859\) | −16.4924 | −0.562714 | −0.281357 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281357 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | − 1.26137i | − 0.0429623i | ||||||||
\(863\) | − 42.2462i | − 1.43808i | −0.694970 | − | 0.719039i | \(-0.744582\pi\) | ||||
0.694970 | − | 0.719039i | \(-0.255418\pi\) | |||||||
\(864\) | −3.50758 | −0.119330 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.8769 | −0.437575 | ||||||||
\(867\) | 9.75379i | 0.331256i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8078 | 0.570164 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.4924 | −0.965429 | ||||||||
\(872\) | 43.1231i | 1.46033i | ||||||||
\(873\) | − 52.7386i | − 1.78493i | ||||||||
\(874\) | 8.98485 | 0.303917 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.76894 | −0.161128 | ||||||||
\(877\) | 23.7538i | 0.802108i | 0.916054 | + | 0.401054i | \(0.131356\pi\) | ||||
−0.916054 | + | 0.401054i | \(0.868644\pi\) | |||||||
\(878\) | − 24.0000i | − 0.809961i | ||||||||
\(879\) | 24.8078 | 0.836745 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.8617 | 1.54512 | 0.772561 | − | 0.634941i | \(-0.218976\pi\) | ||||
0.772561 | + | 0.634941i | \(0.218976\pi\) | |||||||
\(882\) | − 5.56155i | − 0.187267i | ||||||||
\(883\) | 24.4924i | 0.824236i | 0.911131 | + | 0.412118i | \(0.135211\pi\) | ||||
−0.911131 | + | 0.412118i | \(0.864789\pi\) | |||||||
\(884\) | 9.12311 | 0.306843 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −42.7386 | −1.43583 | ||||||||
\(887\) | 12.4924i | 0.419454i | 0.977760 | + | 0.209727i | \(0.0672576\pi\) | ||||
−0.977760 | + | 0.209727i | \(0.932742\pi\) | |||||||
\(888\) | 37.4773i | 1.25765i | ||||||||
\(889\) | 10.2462 | 0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.9309 | −0.600707 | ||||||||
\(892\) | 2.87689i | 0.0963255i | ||||||||
\(893\) | 4.13826i | 0.138482i | ||||||||
\(894\) | −16.9848 | −0.568058 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | − 59.8617i | − 1.99873i | ||||||||
\(898\) | 29.3693i | 0.980067i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2462 | −0.474610 | ||||||||
\(902\) | 12.4924i | 0.415952i | ||||||||
\(903\) | 23.3693i | 0.777682i | ||||||||
\(904\) | −34.1383 | −1.13542 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −87.7235 | −2.91442 | ||||||||
\(907\) | − 50.1080i | − 1.66381i | −0.554920 | − | 0.831904i | \(-0.687251\pi\) | ||||
0.554920 | − | 0.831904i | \(-0.312749\pi\) | |||||||
\(908\) | 10.3845i | 0.344621i | ||||||||
\(909\) | −0.876894 | −0.0290848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.49242 | 0.148841 | 0.0744203 | − | 0.997227i | \(-0.476289\pi\) | ||||
0.0744203 | + | 0.997227i | \(0.476289\pi\) | |||||||
\(912\) | − 13.4773i | − 0.446277i | ||||||||
\(913\) | 10.2462i | 0.339100i | ||||||||
\(914\) | 13.8617 | 0.458506 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.38447 | 0.277031 | ||||||||
\(917\) | − 9.12311i | − 0.301271i | ||||||||
\(918\) | 10.2462i | 0.338175i | ||||||||
\(919\) | 13.3002 | 0.438733 | 0.219366 | − | 0.975643i | \(-0.429601\pi\) | ||||
0.219366 | + | 0.975643i | \(0.429601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 81.1619 | 2.67438 | ||||||||
\(922\) | 7.61553i | 0.250804i | ||||||||
\(923\) | 36.4924i | 1.20116i | ||||||||
\(924\) | −2.87689 | −0.0946429 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | − 5.12311i | − 0.168265i | ||||||||
\(928\) | 13.8617i | 0.455034i | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 1.36932i | 0.0448535i | ||||||||
\(933\) | 24.6307i | 0.806372i | ||||||||
\(934\) | −41.4773 | −1.35718 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.6155 | −1.29487 | ||||||||
\(937\) | − 22.6695i | − 0.740580i | −0.928916 | − | 0.370290i | \(-0.879258\pi\) | ||||
0.928916 | − | 0.370290i | \(-0.120742\pi\) | |||||||
\(938\) | 9.75379i | 0.318472i | ||||||||
\(939\) | 80.1771 | 2.61648 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.8617 | −0.451880 | −0.225940 | − | 0.974141i | \(-0.572545\pi\) | ||||
−0.225940 | + | 0.974141i | \(0.572545\pi\) | |||||||
\(942\) | 15.0152i | 0.489220i | ||||||||
\(943\) | 16.0000i | 0.521032i | ||||||||
\(944\) | −18.7386 | −0.609891 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.4924 | 1.18647 | ||||||||
\(947\) | − 4.00000i | − 0.129983i | −0.997886 | − | 0.0649913i | \(-0.979298\pi\) | ||||
0.997886 | − | 0.0649913i | \(-0.0207020\pi\) | |||||||
\(948\) | 7.36932i | 0.239344i | ||||||||
\(949\) | −19.3693 | −0.628755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.6155 | 1.86831 | ||||||||
\(952\) | 11.1231i | 0.360502i | ||||||||
\(953\) | − 24.8769i | − 0.805842i | −0.915235 | − | 0.402921i | \(-0.867995\pi\) | ||||
0.915235 | − | 0.402921i | \(-0.132005\pi\) | |||||||
\(954\) | −17.3693 | −0.562352 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.354162 | −0.0114544 | ||||||||
\(957\) | − 37.3002i | − 1.20574i | ||||||||
\(958\) | 20.4924i | 0.662080i | ||||||||
\(959\) | −8.87689 | −0.286650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | − 42.7386i | − 1.37795i | ||||||||
\(963\) | − 40.4924i | − 1.30485i | ||||||||
\(964\) | −5.36932 | −0.172934 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.4924 | −0.659333 | ||||||||
\(967\) | 26.8769i | 0.864303i | 0.901801 | + | 0.432151i | \(0.142245\pi\) | ||||
−0.901801 | + | 0.432151i | \(0.857755\pi\) | |||||||
\(968\) | 10.8229i | 0.347862i | ||||||||
\(969\) | −13.1231 | −0.421575 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4773 | −1.58780 | −0.793901 | − | 0.608048i | \(-0.791953\pi\) | ||||
−0.793901 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(972\) | − 9.75379i | − 0.312853i | ||||||||
\(973\) | 6.87689i | 0.220463i | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.8920 | 1.40495 | ||||||||
\(977\) | 49.2311i | 1.57504i | 0.616288 | + | 0.787521i | \(0.288636\pi\) | ||||
−0.616288 | + | 0.787521i | \(0.711364\pi\) | |||||||
\(978\) | − 4.49242i | − 0.143652i | ||||||||
\(979\) | −18.2462 | −0.583151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 62.9848 | 2.01095 | ||||||||
\(982\) | − 6.52273i | − 0.208149i | ||||||||
\(983\) | − 10.4233i | − 0.332451i | −0.986088 | − | 0.166226i | \(-0.946842\pi\) | ||||
0.986088 | − | 0.166226i | \(-0.0531580\pi\) | |||||||
\(984\) | 19.5076 | 0.621879 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40.4924 | 1.28954 | ||||||||
\(987\) | − 9.43845i | − 0.300429i | ||||||||
\(988\) | 2.24621i | 0.0714615i | ||||||||
\(989\) | 46.7386 | 1.48620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4924 | −0.650963 | −0.325482 | − | 0.945548i | \(-0.605526\pi\) | ||||
−0.325482 | + | 0.945548i | \(0.605526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 30.7386i | − 0.975461i | ||||||||
\(994\) | 12.4924 | 0.396236 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.49242 | −0.142348 | ||||||||
\(997\) | − 9.68466i | − 0.306716i | −0.988171 | − | 0.153358i | \(-0.950991\pi\) | ||||
0.988171 | − | 0.153358i | \(-0.0490088\pi\) | |||||||
\(998\) | − 6.52273i | − 0.206473i | ||||||||
\(999\) | 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 | 175.2.b.b.99.2 | 4 | ||
3.2 | odd | 2 | 1575.2.d.e.1324.3 | 4 | |||
4.3 | odd | 2 | 2800.2.g.t.449.4 | 4 | |||
5.2 | odd | 4 | 35.2.a.b.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 175.2.a.f.1.1 | 2 | |||
5.4 | even | 2 | inner | 175.2.b.b.99.3 | 4 | ||
7.6 | odd | 2 | 1225.2.b.f.99.2 | 4 | |||
15.2 | even | 4 | 315.2.a.e.1.1 | 2 | |||
15.8 | even | 4 | 1575.2.a.p.1.2 | 2 | |||
15.14 | odd | 2 | 1575.2.d.e.1324.2 | 4 | |||
20.3 | even | 4 | 2800.2.a.bi.1.1 | 2 | |||
20.7 | even | 4 | 560.2.a.i.1.2 | 2 | |||
20.19 | odd | 2 | 2800.2.g.t.449.1 | 4 | |||
35.2 | odd | 12 | 245.2.e.i.116.1 | 4 | |||
35.12 | even | 12 | 245.2.e.h.116.1 | 4 | |||
35.13 | even | 4 | 1225.2.a.s.1.1 | 2 | |||
35.17 | even | 12 | 245.2.e.h.226.1 | 4 | |||
35.27 | even | 4 | 245.2.a.d.1.2 | 2 | |||
35.32 | odd | 12 | 245.2.e.i.226.1 | 4 | |||
35.34 | odd | 2 | 1225.2.b.f.99.3 | 4 | |||
40.27 | even | 4 | 2240.2.a.bd.1.1 | 2 | |||
40.37 | odd | 4 | 2240.2.a.bh.1.2 | 2 | |||
55.32 | even | 4 | 4235.2.a.m.1.1 | 2 | |||
60.47 | odd | 4 | 5040.2.a.bt.1.2 | 2 | |||
65.12 | odd | 4 | 5915.2.a.l.1.1 | 2 | |||
105.62 | odd | 4 | 2205.2.a.x.1.1 | 2 | |||
140.27 | odd | 4 | 3920.2.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
175.2.a.f.1.1 | 2 | 5.3 | odd | 4 | |||
175.2.b.b.99.2 | 4 | 1.1 | even | 1 | trivial | ||
175.2.b.b.99.3 | 4 | 5.4 | even | 2 | inner | ||
245.2.a.d.1.2 | 2 | 35.27 | even | 4 | |||
245.2.e.h.116.1 | 4 | 35.12 | even | 12 | |||
245.2.e.h.226.1 | 4 | 35.17 | even | 12 | |||
245.2.e.i.116.1 | 4 | 35.2 | odd | 12 | |||
245.2.e.i.226.1 | 4 | 35.32 | odd | 12 | |||
315.2.a.e.1.1 | 2 | 15.2 | even | 4 | |||
560.2.a.i.1.2 | 2 | 20.7 | even | 4 | |||
1225.2.a.s.1.1 | 2 | 35.13 | even | 4 | |||
1225.2.b.f.99.2 | 4 | 7.6 | odd | 2 | |||
1225.2.b.f.99.3 | 4 | 35.34 | odd | 2 | |||
1575.2.a.p.1.2 | 2 | 15.8 | even | 4 | |||
1575.2.d.e.1324.2 | 4 | 15.14 | odd | 2 | |||
1575.2.d.e.1324.3 | 4 | 3.2 | odd | 2 | |||
2205.2.a.x.1.1 | 2 | 105.62 | odd | 4 | |||
2240.2.a.bd.1.1 | 2 | 40.27 | even | 4 | |||
2240.2.a.bh.1.2 | 2 | 40.37 | odd | 4 | |||
2800.2.a.bi.1.1 | 2 | 20.3 | even | 4 | |||
2800.2.g.t.449.1 | 4 | 20.19 | odd | 2 | |||
2800.2.g.t.449.4 | 4 | 4.3 | odd | 2 | |||
3920.2.a.bs.1.1 | 2 | 140.27 | odd | 4 | |||
4235.2.a.m.1.1 | 2 | 55.32 | even | 4 | |||
5040.2.a.bt.1.2 | 2 | 60.47 | odd | 4 | |||
5915.2.a.l.1.1 | 2 | 65.12 | odd | 4 |