Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.4 | ||
Root | \(1.84258 - 0.777752i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.3.l.b.223.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.78830 | + | 4.78830i | 0.957661 | + | 0.957661i | 0.999139 | − | 0.0414785i | \(-0.0132068\pi\) |
−0.0414785 | + | 0.999139i | \(0.513207\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.3302 | 1.47575 | 0.737875 | − | 0.674937i | \(-0.235829\pi\) | ||||
0.737875 | + | 0.674937i | \(0.235829\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.526169 | + | 0.526169i | −0.0478335 | + | 0.0478335i | −0.730619 | − | 0.682785i | \(-0.760768\pi\) |
0.682785 | + | 0.730619i | \(0.260768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.2840 | + | 17.2840i | −1.32953 | + | 1.32953i | −0.423761 | + | 0.905774i | \(0.639290\pi\) |
−0.905774 | + | 0.423761i | \(0.860710\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11.7289i | − | 0.781927i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.71650 | 0.277441 | 0.138721 | − | 0.990332i | \(-0.455701\pi\) | ||||
0.138721 | + | 0.990332i | \(0.455701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.53604 | − | 2.53604i | −0.133476 | − | 0.133476i | 0.637213 | − | 0.770688i | \(-0.280087\pi\) |
−0.770688 | + | 0.637213i | \(0.780087\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.6519 | − | 12.6519i | −0.602472 | − | 0.602472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.5864 | 0.547236 | 0.273618 | − | 0.961838i | \(-0.411780\pi\) | ||||
0.273618 | + | 0.961838i | \(0.411780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.8557i | 0.834229i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.19683 | − | 2.19683i | 0.0757526 | − | 0.0757526i | −0.668215 | − | 0.743968i | \(-0.732942\pi\) |
0.743968 | + | 0.668215i | \(0.232942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.0521i | 0.904908i | 0.891788 | + | 0.452454i | \(0.149451\pi\) | ||||
−0.891788 | + | 0.452454i | \(0.850549\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.28884 | 0.0390559 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 49.4644 | + | 49.4644i | 1.41327 | + | 1.41327i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.1128 | + | 32.1128i | 0.867914 | + | 0.867914i | 0.992241 | − | 0.124327i | \(-0.0396773\pi\) |
−0.124327 | + | 0.992241i | \(0.539677\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 42.3369 | 1.08556 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.1145i | 0.563768i | 0.959449 | + | 0.281884i | \(0.0909593\pi\) | ||||
−0.959449 | + | 0.281884i | \(0.909041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79441 | − | 4.79441i | 0.111498 | − | 0.111498i | −0.649157 | − | 0.760655i | \(-0.724878\pi\) |
0.760655 | + | 0.649157i | \(0.224878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.3649 | + | 14.3649i | −0.319220 | + | 0.319220i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 39.0095i | − | 0.829989i | −0.909824 | − | 0.414994i | \(-0.863784\pi\) | ||
0.909824 | − | 0.414994i | \(-0.136216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.7141 | 1.17784 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.77651 | − | 5.77651i | −0.113265 | − | 0.113265i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27.9768 | + | 27.9768i | 0.527864 | + | 0.527864i | 0.919935 | − | 0.392071i | \(-0.128241\pi\) |
−0.392071 | + | 0.919935i | \(0.628241\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.03891 | −0.0916166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.21200i | 0.108982i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 79.8538 | − | 79.8538i | 1.35345 | − | 1.35345i | 0.471691 | − | 0.881764i | \(-0.343644\pi\) |
0.881764 | − | 0.471691i | \(-0.156356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.7762 | − | 36.7762i | 0.602888 | − | 0.602888i | −0.338190 | − | 0.941078i | \(-0.609815\pi\) |
0.941078 | + | 0.338190i | \(0.109815\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 30.9907i | 0.491917i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −165.522 | −2.54649 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9869 | − | 10.9869i | −0.163984 | − | 0.163984i | 0.620345 | − | 0.784329i | \(-0.286992\pi\) |
−0.784329 | + | 0.620345i | \(0.786992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.4152 | − | 15.4152i | −0.223408 | − | 0.223408i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −52.6605 | −0.741697 | −0.370849 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370849 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 67.8061i | 0.928850i | 0.885612 | + | 0.464425i | \(0.153739\pi\) | ||||
−0.885612 | + | 0.464425i | \(0.846261\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.5429 | − | 25.5429i | 0.340573 | − | 0.340573i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.43545 | + | 5.43545i | −0.0705903 | + | 0.0705903i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56.4602i | 0.714686i | 0.933973 | + | 0.357343i | \(0.116317\pi\) | ||||
−0.933973 | + | 0.357343i | \(0.883683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −58.3697 | − | 58.3697i | −0.703249 | − | 0.703249i | 0.261857 | − | 0.965107i | \(-0.415665\pi\) |
−0.965107 | + | 0.261857i | \(0.915665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.5840 | + | 22.5840i | 0.265694 | + | 0.265694i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.38110 | −0.0618518 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 131.566i | − | 1.47827i | −0.673558 | − | 0.739135i | \(-0.735235\pi\) | ||
0.673558 | − | 0.739135i | \(-0.264765\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −178.548 | + | 178.548i | −1.96206 | + | 1.96206i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34.3567 | − | 34.3567i | 0.369427 | − | 0.369427i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 24.2866i | − | 0.255649i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 60.9413 | 0.628261 | 0.314131 | − | 0.949380i | \(-0.398287\pi\) | ||||
0.314131 | + | 0.949380i | \(0.398287\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.57851 | − | 1.57851i | −0.0159445 | − | 0.0159445i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109.986 | − | 109.986i | −1.08897 | − | 1.08897i | −0.995635 | − | 0.0933326i | \(-0.970248\pi\) |
−0.0933326 | − | 0.995635i | \(-0.529752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −173.295 | −1.68248 | −0.841239 | − | 0.540663i | \(-0.818174\pi\) | ||||
−0.841239 | + | 0.540663i | \(0.818174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 121.162i | − | 1.15393i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −25.4747 | + | 25.4747i | −0.238081 | + | 0.238081i | −0.816055 | − | 0.577974i | \(-0.803844\pi\) |
0.577974 | + | 0.816055i | \(0.303844\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.0605 | + | 33.0605i | −0.303307 | + | 0.303307i | −0.842306 | − | 0.538999i | \(-0.818803\pi\) |
0.538999 | + | 0.842306i | \(0.318803\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 78.6600i | − | 0.708649i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 140.159 | 1.24034 | 0.620171 | − | 0.784466i | \(-0.287063\pi\) | ||||
0.620171 | + | 0.784466i | \(0.287063\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 60.2677 | + | 60.2677i | 0.524067 | + | 0.524067i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −51.8519 | − | 51.8519i | −0.443178 | − | 0.443178i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 48.7226 | 0.409434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.446i | 0.995424i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.3093 | − | 28.3093i | 0.230157 | − | 0.230157i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 19.8441 | − | 19.8441i | 0.158752 | − | 0.158752i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 40.8458i | − | 0.321620i | −0.986985 | − | 0.160810i | \(-0.948589\pi\) | ||
0.986985 | − | 0.160810i | \(-0.0514107\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7439 | −0.0910377 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −75.0168 | − | 75.0168i | −0.572647 | − | 0.572647i | 0.360220 | − | 0.932867i | \(-0.382702\pi\) |
−0.932867 | + | 0.360220i | \(0.882702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.1979 | − | 26.1979i | −0.196977 | − | 0.196977i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 35.1867 | 0.260642 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 134.028i | − | 0.978308i | −0.872197 | − | 0.489154i | \(-0.837306\pi\) | ||
0.872197 | − | 0.489154i | \(-0.162694\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.8798 | − | 22.8798i | 0.164603 | − | 0.164603i | −0.619999 | − | 0.784602i | \(-0.712867\pi\) |
0.784602 | + | 0.619999i | \(0.212867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −47.7767 | + | 47.7767i | −0.338842 | + | 0.338842i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 18.1885i | − | 0.127193i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0381 | 0.145091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −70.6850 | − | 70.6850i | −0.480850 | − | 0.480850i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.32124 | + | 9.32124i | 0.0625587 | + | 0.0625587i | 0.737694 | − | 0.675135i | \(-0.235915\pi\) |
−0.675135 | + | 0.737694i | \(0.735915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 50.5403 | 0.334704 | 0.167352 | − | 0.985897i | \(-0.446478\pi\) | ||||
0.167352 | + | 0.985897i | \(0.446478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.1495i | 0.0924803i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −134.322 | + | 134.322i | −0.866595 | + | 0.866595i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 95.8844 | − | 95.8844i | 0.610729 | − | 0.610729i | −0.332407 | − | 0.943136i | \(-0.607861\pi\) |
0.943136 | + | 0.332407i | \(0.107861\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 68.5288i | − | 0.430999i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 130.021 | 0.807584 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −140.885 | − | 140.885i | −0.864324 | − | 0.864324i | 0.127513 | − | 0.991837i | \(-0.459301\pi\) |
−0.991837 | + | 0.127513i | \(0.959301\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.17138 | + | 6.17138i | 0.0374023 | + | 0.0374023i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 107.849 | 0.645800 | 0.322900 | − | 0.946433i | \(-0.395342\pi\) | ||||
0.322900 | + | 0.946433i | \(0.395342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 428.470i | − | 2.53533i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.60811 | − | 7.60811i | 0.0444919 | − | 0.0444919i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 53.8845 | − | 53.8845i | 0.311471 | − | 0.311471i | −0.534008 | − | 0.845479i | \(-0.679315\pi\) |
0.845479 | + | 0.534008i | \(0.179315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 215.445i | 1.23111i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −195.601 | −1.10509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 104.178 | + | 104.178i | 0.582002 | + | 0.582002i | 0.935453 | − | 0.353451i | \(-0.114992\pi\) |
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 205.498 | + | 205.498i | 1.13535 | + | 1.13535i | 0.989274 | + | 0.146073i | \(0.0466635\pi\) |
0.146073 | + | 0.989274i | \(0.453336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −90.0828 | −0.492256 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 307.532i | 1.66233i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.48167 | + | 2.48167i | −0.0132710 | + | 0.0132710i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 37.9558 | − | 37.9558i | 0.200824 | − | 0.200824i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 248.255i | 1.29977i | 0.760034 | + | 0.649883i | \(0.225182\pi\) | ||||
−0.760034 | + | 0.649883i | \(0.774818\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −129.921 | −0.673166 | −0.336583 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336583 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 202.722 | + | 202.722i | 1.03960 | + | 1.03960i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −237.001 | − | 237.001i | −1.20305 | − | 1.20305i | −0.973234 | − | 0.229816i | \(-0.926188\pi\) |
−0.229816 | − | 0.973234i | \(-0.573812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −246.508 | −1.23873 | −0.619366 | − | 0.785102i | \(-0.712610\pi\) | ||||
−0.619366 | + | 0.785102i | \(0.712610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.9123i | 0.133892i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.6938 | − | 22.6938i | 0.111792 | − | 0.111792i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −110.679 | + | 110.679i | −0.539898 | + | 0.539898i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 37.7593i | 0.182412i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.66877 | 0.0127692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4139 | − | 13.4139i | −0.0635728 | − | 0.0635728i | 0.674606 | − | 0.738178i | \(-0.264314\pi\) |
−0.738178 | + | 0.674606i | \(0.764314\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 64.4957 | + | 64.4957i | 0.302797 | + | 0.302797i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45.9142 | 0.213554 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 289.786i | 1.33542i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 83.0451 | − | 83.0451i | 0.379201 | − | 0.379201i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −81.5197 | + | 81.5197i | −0.368867 | + | 0.368867i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 295.580i | − | 1.32547i | −0.748854 | − | 0.662735i | \(-0.769396\pi\) | ||
0.748854 | − | 0.662735i | \(-0.230604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −62.5672 | −0.278076 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −97.0742 | − | 97.0742i | −0.427640 | − | 0.427640i | 0.460184 | − | 0.887824i | \(-0.347783\pi\) |
−0.887824 | + | 0.460184i | \(0.847783\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −34.2565 | − | 34.2565i | −0.149592 | − | 0.149592i | 0.628344 | − | 0.777936i | \(-0.283733\pi\) |
−0.777936 | + | 0.628344i | \(0.783733\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.3141 | 0.0576367 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 62.8176i | 0.269604i | 0.990873 | + | 0.134802i | \(0.0430398\pi\) | ||||
−0.990873 | + | 0.134802i | \(0.956960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 186.789 | − | 186.789i | 0.794848 | − | 0.794848i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 69.1493 | − | 69.1493i | 0.291769 | − | 0.291769i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 355.910i | − | 1.48916i | −0.667532 | − | 0.744581i | \(-0.732649\pi\) | ||
0.667532 | − | 0.744581i | \(-0.267351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 66.2545 | 0.274915 | 0.137458 | − | 0.990508i | \(-0.456107\pi\) | ||||
0.137458 | + | 0.990508i | \(0.456107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 276.352 | + | 276.352i | 1.12797 | + | 1.12797i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 87.6655 | 0.354921 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 142.976i | 0.574201i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 325.395 | − | 325.395i | 1.29640 | − | 1.29640i | 0.365638 | − | 0.930757i | \(-0.380851\pi\) |
0.930757 | − | 0.365638i | \(-0.119149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.62259 | + | 6.62259i | −0.0261762 | + | 0.0261762i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 55.3193i | − | 0.216939i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −312.011 | −1.21405 | −0.607026 | − | 0.794682i | \(-0.707638\pi\) | ||||
−0.607026 | + | 0.794682i | \(0.707638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 331.733 | + | 331.733i | 1.28082 | + | 1.28082i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.59048 | + | 6.59048i | 0.0252509 | + | 0.0252509i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 168.163 | 0.639403 | 0.319702 | − | 0.947518i | \(-0.396417\pi\) | ||||
0.319702 | + | 0.947518i | \(0.396417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 267.923i | 1.01103i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −161.135 | + | 161.135i | −0.603501 | + | 0.603501i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −212.116 | + | 212.116i | −0.788535 | + | 0.788535i | −0.981254 | − | 0.192719i | \(-0.938269\pi\) |
0.192719 | + | 0.981254i | \(0.438269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 173.450i | 0.640037i | 0.947411 | + | 0.320019i | \(0.103689\pi\) | ||||
−0.947411 | + | 0.320019i | \(0.896311\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 437.350 | 1.60202 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.9736 | − | 10.9736i | −0.0399041 | − | 0.0399041i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 38.4049 | + | 38.4049i | 0.138646 | + | 0.138646i | 0.773023 | − | 0.634377i | \(-0.218743\pi\) |
−0.634377 | + | 0.773023i | \(0.718743\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −84.1564 | −0.301636 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 223.573i | 0.795632i | 0.917465 | + | 0.397816i | \(0.130232\pi\) | ||||
−0.917465 | + | 0.397816i | \(0.869768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 247.755 | − | 247.755i | 0.875459 | − | 0.875459i | −0.117602 | − | 0.993061i | \(-0.537521\pi\) |
0.993061 | + | 0.117602i | \(0.0375206\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.7449 | + | 29.7449i | −0.104368 | + | 0.104368i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 238.778i | 0.831980i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −266.755 | −0.923026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −74.6376 | − | 74.6376i | −0.256487 | − | 0.256487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 102.262 | + | 102.262i | 0.349016 | + | 0.349016i | 0.859743 | − | 0.510727i | \(-0.170624\pi\) |
−0.510727 | + | 0.859743i | \(0.670624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 764.729 | 2.59230 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.86653i | 0.0130186i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −217.543 | + | 217.543i | −0.727570 | + | 0.727570i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 49.5275 | − | 49.5275i | 0.164543 | − | 0.164543i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 269.409i | 0.889138i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 352.191 | 1.15472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 138.292 | + | 138.292i | 0.450463 | + | 0.450463i | 0.895508 | − | 0.445045i | \(-0.146812\pi\) |
−0.445045 | + | 0.895508i | \(0.646812\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 212.243 | + | 212.243i | 0.686869 | + | 0.686869i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −205.789 | −0.661702 | −0.330851 | − | 0.943683i | \(-0.607336\pi\) | ||||
−0.330851 | + | 0.943683i | \(0.607336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 223.861i | − | 0.715209i | −0.933873 | − | 0.357605i | \(-0.883594\pi\) | ||
0.933873 | − | 0.357605i | \(-0.116406\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −148.393 | + | 148.393i | −0.471089 | + | 0.471089i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 176.488 | − | 176.488i | 0.556744 | − | 0.556744i | −0.371635 | − | 0.928379i | \(-0.621203\pi\) |
0.928379 | + | 0.371635i | \(0.121203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.31180i | 0.00724703i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 62.4000 | 0.194393 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.9612 | − | 11.9612i | −0.0370316 | − | 0.0370316i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −360.469 | − | 360.469i | −1.10914 | − | 1.10914i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 80.9813 | 0.247649 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 402.978i | − | 1.22486i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −183.939 | + | 183.939i | −0.555706 | + | 0.555706i | −0.928082 | − | 0.372376i | \(-0.878543\pi\) |
0.372376 | + | 0.928082i | \(0.378543\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −96.3384 | + | 96.3384i | −0.289305 | + | 0.289305i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 105.217i | − | 0.314081i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7162 | 0.0377336 | 0.0188668 | − | 0.999822i | \(-0.493994\pi\) | ||||
0.0188668 | + | 0.999822i | \(0.493994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −171.659 | − | 171.659i | −0.506368 | − | 0.506368i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.7602 | − | 14.7602i | −0.0432849 | − | 0.0432849i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 90.0184 | 0.262444 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 147.625i | − | 0.427899i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −113.546 | + | 113.546i | −0.327221 | + | 0.327221i | −0.851529 | − | 0.524308i | \(-0.824324\pi\) |
0.524308 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −90.9653 | + | 90.9653i | −0.260645 | + | 0.260645i | −0.825316 | − | 0.564671i | \(-0.809003\pi\) |
0.564671 | + | 0.825316i | \(0.309003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 127.011i | 0.361854i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.2208 | 0.102609 | 0.0513043 | − | 0.998683i | \(-0.483662\pi\) | ||||
0.0513043 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −252.155 | − | 252.155i | −0.710294 | − | 0.710294i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −59.6727 | − | 59.6727i | −0.167151 | − | 0.167151i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −142.121 | −0.395880 | −0.197940 | − | 0.980214i | \(-0.563425\pi\) | ||||
−0.197940 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 348.137i | − | 0.964369i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 147.516 | − | 147.516i | 0.406380 | − | 0.406380i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −324.676 | + | 324.676i | −0.889523 | + | 0.889523i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 654.218i | − | 1.78261i | −0.453404 | − | 0.891305i | \(-0.649791\pi\) | ||
0.453404 | − | 0.891305i | \(-0.350209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −69.3434 | −0.187923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 289.007 | + | 289.007i | 0.778995 | + | 0.778995i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −335.277 | − | 335.277i | −0.898867 | − | 0.898867i | 0.0964690 | − | 0.995336i | \(-0.469245\pi\) |
−0.995336 | + | 0.0964690i | \(0.969245\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −48.6078 | −0.129621 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 75.9397i | 0.201432i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −98.7497 | + | 98.7497i | −0.260553 | + | 0.260553i | −0.825279 | − | 0.564725i | \(-0.808982\pi\) |
0.564725 | + | 0.825279i | \(0.308982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −50.0257 | + | 50.0257i | −0.131301 | + | 0.131301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 156.144i | 0.407687i | 0.979003 | + | 0.203844i | \(0.0653434\pi\) | ||||
−0.979003 | + | 0.203844i | \(0.934657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −52.0532 | −0.135203 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.3832 | + | 14.3832i | 0.0371660 | + | 0.0371660i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 391.047 | + | 391.047i | 1.00526 | + | 1.00526i | 0.999986 | + | 0.00527486i | \(0.00167905\pi\) |
0.00527486 | + | 0.999986i | \(0.498321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.3639 | 0.151826 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 183.753i | 0.467565i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −270.349 | + | 270.349i | −0.684427 | + | 0.684427i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −243.862 | + | 243.862i | −0.614262 | + | 0.614262i | −0.944054 | − | 0.329791i | \(-0.893022\pi\) |
0.329791 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 64.1715i | 0.160831i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −175.261 | −0.437059 | −0.218529 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218529 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −484.852 | − | 484.852i | −1.20311 | − | 1.20311i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −43.0947 | − | 43.0947i | −0.106407 | − | 0.106407i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.7935 | −0.0830307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 44.4504i | 0.108681i | 0.998522 | + | 0.0543404i | \(0.0173056\pi\) | ||||
−0.998522 | + | 0.0543404i | \(0.982694\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −164.150 | + | 164.150i | −0.399393 | + | 0.399393i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 824.910 | − | 824.910i | 1.99736 | − | 1.99736i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 558.984i | − | 1.34695i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −56.0438 | −0.134398 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.9985 | + | 14.9985i | 0.0357959 | + | 0.0357959i | 0.724778 | − | 0.688982i | \(-0.241942\pi\) |
−0.688982 | + | 0.724778i | \(0.741942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −312.907 | − | 312.907i | −0.743247 | − | 0.743247i | 0.229954 | − | 0.973201i | \(-0.426142\pi\) |
−0.973201 | + | 0.229954i | \(0.926142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 117.028 | 0.276663 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 98.3660i | 0.231449i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 379.907 | − | 379.907i | 0.889712 | − | 0.889712i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.2763 | + | 22.2763i | −0.0519262 | + | 0.0519262i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 532.400i | 1.23527i | 0.786466 | + | 0.617633i | \(0.211908\pi\) | ||||
−0.786466 | + | 0.617633i | \(0.788092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 553.451 | 1.27818 | 0.639089 | − | 0.769133i | \(-0.279312\pi\) | ||||
0.639089 | + | 0.769133i | \(0.279312\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.7664 | − | 25.7664i | −0.0592330 | − | 0.0592330i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.9197 | − | 31.9197i | −0.0730427 | − | 0.0730427i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −645.291 | −1.46991 | −0.734956 | − | 0.678115i | \(-0.762797\pi\) | ||||
−0.734956 | + | 0.678115i | \(0.762797\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 173.142i | 0.392613i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 315.833 | − | 315.833i | 0.712941 | − | 0.712941i | −0.254208 | − | 0.967149i | \(-0.581815\pi\) |
0.967149 | + | 0.254208i | \(0.0818149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 629.978 | − | 629.978i | 1.41568 | − | 1.41568i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 22.8323i | − | 0.0510789i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 218.589 | 0.486835 | 0.243417 | − | 0.969922i | \(-0.421732\pi\) | ||||
0.243417 | + | 0.969922i | \(0.421732\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1621 | − | 12.1621i | −0.0269670 | − | 0.0269670i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −61.8990 | − | 61.8990i | −0.136642 | − | 0.136642i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1709.88 | −3.75798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 296.561i | − | 0.648930i | −0.945898 | − | 0.324465i | \(-0.894816\pi\) | ||
0.945898 | − | 0.324465i | \(-0.105184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.3295 | − | 17.3295i | 0.0377549 | − | 0.0377549i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −118.061 | + | 118.061i | −0.256097 | + | 0.256097i | −0.823465 | − | 0.567368i | \(-0.807962\pi\) |
0.567368 | + | 0.823465i | \(0.307962\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 409.453i | 0.884348i | 0.896929 | + | 0.442174i | \(0.145793\pi\) | ||||
−0.896929 | + | 0.442174i | \(0.854207\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 329.021 | 0.707572 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 494.764 | + | 494.764i | 1.05945 | + | 1.05945i | 0.998117 | + | 0.0613343i | \(0.0195356\pi\) |
0.0613343 | + | 0.998117i | \(0.480464\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −113.497 | − | 113.497i | −0.241999 | − | 0.241999i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −234.868 | −0.498658 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.04534i | 0.0106667i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 52.8909 | − | 52.8909i | 0.111349 | − | 0.111349i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −83.9303 | + | 83.9303i | −0.175955 | + | 0.175955i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 558.806i | − | 1.16661i | −0.812254 | − | 0.583305i | \(-0.801759\pi\) | ||
0.812254 | − | 0.583305i | \(-0.198241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1110.07 | −2.30784 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −159.243 | − | 159.243i | −0.329695 | − | 0.329695i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 291.806 | + | 291.806i | 0.601661 | + | 0.601661i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 361.328 | 0.741946 | 0.370973 | − | 0.928644i | \(-0.379024\pi\) | ||||
0.370973 | + | 0.928644i | \(0.379024\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 345.096i | 0.705718i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −488.975 | + | 488.975i | −0.995876 | + | 0.995876i | −0.999992 | − | 0.00411514i | \(-0.998690\pi\) |
0.00411514 | + | 0.999992i | \(0.498690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3613 | − | 10.3613i | 0.0210169 | − | 0.0210169i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 15.1167i | − | 0.0305389i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −543.996 | −1.09456 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −102.895 | − | 102.895i | −0.206203 | − | 0.206203i | 0.596448 | − | 0.802652i | \(-0.296578\pi\) |
−0.802652 | + | 0.596448i | \(0.796578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −132.087 | − | 132.087i | −0.263647 | − | 0.263647i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 881.975 | 1.75343 | 0.876715 | − | 0.481011i | \(-0.159730\pi\) | ||||
0.876715 | + | 0.481011i | \(0.159730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1053.29i | − | 2.08572i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −524.767 | + | 524.767i | −1.03504 | + | 1.03504i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −161.639 | + | 161.639i | −0.317563 | + | 0.317563i | −0.847830 | − | 0.530268i | \(-0.822091\pi\) |
0.530268 | + | 0.847830i | \(0.322091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 700.454i | 1.37075i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.6360 | −0.0363275 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −829.791 | − | 829.791i | −1.61124 | − | 1.61124i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.5256 | + | 20.5256i | 0.0397013 | + | 0.0397013i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −131.989 | −0.254315 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 763.931i | − | 1.46628i | −0.680078 | − | 0.733140i | \(-0.738054\pi\) | ||
0.680078 | − | 0.733140i | \(-0.261946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 295.573 | − | 295.573i | 0.565150 | − | 0.565150i | −0.365616 | − | 0.930766i | \(-0.619142\pi\) |
0.930766 | + | 0.365616i | \(0.119142\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 263.865 | − | 263.865i | 0.502600 | − | 0.502600i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 132.308i | 0.251059i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −370.582 | −0.700532 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 239.561 | + | 239.561i | 0.451152 | + | 0.451152i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −399.509 | − | 399.509i | −0.749549 | − | 0.749549i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −243.961 | −0.456002 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 255.184i | − | 0.475203i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.3673 | + | 30.3673i | −0.0563401 | + | 0.0563401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −243.037 | + | 243.037i | −0.449236 | + | 0.449236i | −0.895100 | − | 0.445865i | \(-0.852896\pi\) |
0.445865 | + | 0.895100i | \(0.352896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 503.365i | − | 0.927007i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −316.607 | −0.580931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 424.574 | + | 424.574i | 0.776187 | + | 0.776187i | 0.979180 | − | 0.202993i | \(-0.0650669\pi\) |
−0.202993 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 110.328 | + | 110.328i | 0.200963 | + | 0.200963i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.1425 | −0.0202223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 583.248i | 1.05470i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 376.648 | − | 376.648i | 0.678645 | − | 0.678645i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 445.773 | − | 445.773i | 0.800311 | − | 0.800311i | −0.182833 | − | 0.983144i | \(-0.558527\pi\) |
0.983144 | + | 0.182833i | \(0.0585268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 165.733i | 0.296481i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.07883 | 0.0108357 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −529.295 | − | 529.295i | −0.940133 | − | 0.940133i | 0.0581732 | − | 0.998307i | \(-0.481472\pi\) |
−0.998307 | + | 0.0581732i | \(0.981472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 671.123 | + | 671.123i | 1.18783 | + | 1.18783i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −92.9722 | −0.163972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 346.814i | 0.609516i | 0.952430 | + | 0.304758i | \(0.0985755\pi\) | ||||
−0.952430 | + | 0.304758i | \(0.901424\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −155.711 | + | 155.711i | −0.272699 | + | 0.272699i | −0.830186 | − | 0.557487i | \(-0.811766\pi\) |
0.557487 | + | 0.830186i | \(0.311766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 304.049 | − | 304.049i | 0.530627 | − | 0.530627i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 262.499i | 0.456520i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 620.510 | 1.07541 | 0.537704 | − | 0.843134i | \(-0.319292\pi\) | ||||
0.537704 | + | 0.843134i | \(0.319292\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 159.120 | + | 159.120i | 0.274819 | + | 0.274819i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −602.974 | − | 602.974i | −1.03782 | − | 1.03782i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.4410 | −0.0504992 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 496.565i | − | 0.848829i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 561.656 | − | 561.656i | 0.956825 | − | 0.956825i | −0.0422810 | − | 0.999106i | \(-0.513462\pi\) |
0.999106 | + | 0.0422810i | \(0.0134625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.1413 | − | 71.1413i | 0.120783 | − | 0.120783i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 580.531i | 0.982286i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 851.739 | 1.43632 | 0.718161 | − | 0.695877i | \(-0.244984\pi\) | ||||
0.718161 | + | 0.695877i | \(0.244984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 233.299 | + | 233.299i | 0.392099 | + | 0.392099i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 301.909 | + | 301.909i | 0.505710 | + | 0.505710i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1001.69 | 1.67228 | 0.836138 | − | 0.548519i | \(-0.184808\pi\) | ||||
0.836138 | + | 0.548519i | \(0.184808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 955.182i | 1.58932i | 0.607054 | + | 0.794661i | \(0.292351\pi\) | ||||
−0.607054 | + | 0.794661i | \(0.707649\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.9607 | − | 32.9607i | 0.0546612 | − | 0.0546612i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −576.734 | + | 576.734i | −0.953279 | + | 0.953279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 291.885i | 0.480865i | 0.970666 | + | 0.240432i | \(0.0772892\pi\) | ||||
−0.970666 | + | 0.240432i | \(0.922711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −55.5881 | −0.0912777 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 674.238 | + | 674.238i | 1.10350 | + | 1.10350i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 332.933 | + | 332.933i | 0.543121 | + | 0.543121i | 0.924442 | − | 0.381322i | \(-0.124531\pi\) |
−0.381322 | + | 0.924442i | \(0.624531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 271.107 | 0.440825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 970.864i | 1.57352i | 0.617257 | + | 0.786762i | \(0.288244\pi\) | ||||
−0.617257 | + | 0.786762i | \(0.711756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −696.761 | + | 696.761i | −1.12562 | + | 1.12562i | −0.134744 | + | 0.990881i | \(0.543021\pi\) |
−0.990881 | + | 0.134744i | \(0.956979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 46.2455 | − | 46.2455i | 0.0744694 | − | 0.0744694i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1359.11i | − | 2.18156i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 711.432 | 1.13829 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.26856 | − | 3.26856i | −0.00521301 | − | 0.00521301i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 151.460 | + | 151.460i | 0.240795 | + | 0.240795i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 377.591 | 0.598401 | 0.299200 | − | 0.954190i | \(-0.403280\pi\) | ||||
0.299200 | + | 0.954190i | \(0.403280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.8571i | 0.0519069i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 195.582 | − | 195.582i | 0.308003 | − | 0.308003i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −997.527 | + | 997.527i | −1.56598 | + | 1.56598i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 157.981i | − | 0.247232i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 729.200 | 1.13760 | 0.568799 | − | 0.822477i | \(-0.307408\pi\) | ||||
0.568799 | + | 0.822477i | \(0.307408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 243.958 | + | 243.958i | 0.379406 | + | 0.379406i | 0.870888 | − | 0.491482i | \(-0.163545\pi\) |
−0.491482 | + | 0.870888i | \(0.663545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −56.2332 | − | 56.2332i | −0.0871832 | − | 0.0871832i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 281.594 | 0.435230 | 0.217615 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217615 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 84.0331i | 0.129481i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 354.913 | − | 354.913i | 0.545182 | − | 0.545182i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −323.704 | + | 323.704i | −0.495718 | + | 0.495718i | −0.910102 | − | 0.414384i | \(-0.863997\pi\) |
0.414384 | + | 0.910102i | \(0.363997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 718.407i | − | 1.09680i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −203.418 | −0.309617 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 507.811 | + | 507.811i | 0.770578 | + | 0.770578i | 0.978208 | − | 0.207629i | \(-0.0665748\pi\) |
−0.207629 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −57.1593 | − | 57.1593i | −0.0864741 | − | 0.0864741i | 0.662547 | − | 0.749021i | \(-0.269476\pi\) |
−0.749021 | + | 0.662547i | \(0.769476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 199.682 | 0.301179 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 250.887i | − | 0.377274i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.6502 | − | 27.6502i | 0.0414546 | − | 0.0414546i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −362.010 | + | 362.010i | −0.541121 | + | 0.541121i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.7009i | 0.0576765i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1110.84 | 1.65059 | 0.825293 | − | 0.564705i | \(-0.191010\pi\) | ||||
0.825293 | + | 0.564705i | \(0.191010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 76.6288 | + | 76.6288i | 0.113524 | + | 0.113524i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −397.465 | − | 397.465i | −0.587097 | − | 0.587097i | 0.349747 | − | 0.936844i | \(-0.386268\pi\) |
−0.936844 | + | 0.349747i | \(0.886268\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 629.539 | 0.927156 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 237.782i | 0.349166i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −238.015 | + | 238.015i | −0.348485 | + | 0.348485i | −0.859545 | − | 0.511060i | \(-0.829253\pi\) |
0.511060 | + | 0.859545i | \(0.329253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 641.768 | − | 641.768i | 0.936887 | − | 0.936887i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 83.9109i | 0.122141i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −967.099 | −1.40363 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −685.172 | − | 685.172i | −0.991565 | − | 0.991565i | 0.00839951 | − | 0.999965i | \(-0.497326\pi\) |
−0.999965 | + | 0.00839951i | \(0.997326\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.3064 | − | 16.3064i | −0.0235301 | − | 0.0235301i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 219.111 | 0.315267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 109.019i | 0.156412i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 76.9356 | − | 76.9356i | 0.110065 | − | 0.110065i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −543.074 | + | 543.074i | −0.774713 | + | 0.774713i | −0.978926 | − | 0.204214i | \(-0.934536\pi\) |
0.204214 | + | 0.978926i | \(0.434536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 162.879i | − | 0.231691i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −457.538 | −0.648991 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1136.18 | − | 1136.18i | −1.60704 | − | 1.60704i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 488.019 | + | 488.019i | 0.688320 | + | 0.688320i | 0.961860 | − | 0.273541i | \(-0.0881948\pi\) |
−0.273541 | + | 0.961860i | \(0.588195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −169.381 | −0.238229 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 353.076i | 0.495198i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 87.0923 | − | 87.0923i | 0.121807 | − | 0.121807i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −435.899 | + | 435.899i | −0.607948 | + | 0.607948i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 297.369i | 0.413587i | 0.978385 | + | 0.206793i | \(0.0663028\pi\) | ||||
−0.978385 | + | 0.206793i | \(0.933697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1790.18 | −2.48292 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −81.1449 | − | 81.1449i | −0.112234 | − | 0.112234i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 45.8164 | + | 45.8164i | 0.0631950 | + | 0.0631950i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1158.85 | −1.59402 | −0.797009 | − | 0.603967i | \(-0.793586\pi\) | ||||
−0.797009 | + | 0.603967i | \(0.793586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.6128 | − | 22.6128i | 0.0309341 | − | 0.0309341i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 348.835 | − | 348.835i | 0.475901 | − | 0.475901i | −0.427917 | − | 0.903818i | \(-0.640752\pi\) |
0.903818 | + | 0.427917i | \(0.140752\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 676.923i | − | 0.920983i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.5619 | 0.0156878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 825.489 | + | 825.489i | 1.11703 | + | 1.11703i | 0.992174 | + | 0.124860i | \(0.0398482\pi\) |
0.124860 | + | 0.992174i | \(0.460152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −107.368 | − | 107.368i | −0.144896 | − | 0.144896i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 899.725 | 1.21094 | 0.605468 | − | 0.795870i | \(-0.292986\pi\) | ||||
0.605468 | + | 0.795870i | \(0.292986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 89.2659i | 0.119820i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 175.109 | − | 175.109i | 0.234416 | − | 0.234416i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −263.160 | + | 263.160i | −0.351348 | + | 0.351348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 80.4386i | − | 0.107109i | −0.998565 | − | 0.0535543i | \(-0.982945\pi\) | ||
0.998565 | − | 0.0535543i | \(-0.0170550\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −797.052 | −1.05850 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 242.003 | + | 242.003i | 0.320533 | + | 0.320533i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −233.298 | − | 233.298i | −0.308187 | − | 0.308187i | 0.536019 | − | 0.844206i | \(-0.319928\pi\) |
−0.844206 | + | 0.536019i | \(0.819928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.2220 | 0.0213728 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 56.1906i | 0.0738378i | 0.999318 | + | 0.0369189i | \(0.0117543\pi\) | ||||
−0.999318 | + | 0.0369189i | \(0.988246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −341.523 | + | 341.523i | −0.447606 | + | 0.447606i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −67.7521 | + | 67.7521i | −0.0885648 | + | 0.0885648i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2760.38i | 3.59893i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 517.343 | 0.672748 | 0.336374 | − | 0.941728i | \(-0.390799\pi\) | ||||
0.336374 | + | 0.941728i | \(0.390799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 382.134 | + | 382.134i | 0.495635 | + | 0.495635i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 523.925 | + | 523.925i | 0.677781 | + | 0.677781i | 0.959498 | − | 0.281716i | \(-0.0909037\pi\) |
−0.281716 | + | 0.959498i | \(0.590904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −585.048 | −0.754900 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 812.578i | − | 1.04579i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.6192 | − | 58.6192i | 0.0752492 | − | 0.0752492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.7083 | − | 27.7083i | 0.0354780 | − | 0.0354780i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 16.1433i | − | 0.0206173i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 918.248 | 1.16974 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.6965 | − | 46.6965i | −0.0593348 | − | 0.0593348i | 0.676817 | − | 0.736152i | \(-0.263359\pi\) |
−0.736152 | + | 0.676817i | \(0.763359\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −205.957 | − | 205.957i | −0.261035 | − | 0.261035i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1447.87 | 1.83044 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1271.27i | 1.60312i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 328.137 | − | 328.137i | 0.412751 | − | 0.412751i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −127.126 | + | 127.126i | −0.159505 | + | 0.159505i | −0.782348 | − | 0.622842i | \(-0.785978\pi\) |
0.622842 | + | 0.782348i | \(0.285978\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 183.988i | − | 0.230273i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 394.698 | 0.492756 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.6774 | − | 35.6774i | −0.0444302 | − | 0.0444302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 622.580 | + | 622.580i | 0.773392 | + | 0.773392i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 519.576 | 0.643836 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1047.16i | − | 1.29439i | −0.762325 | − | 0.647194i | \(-0.775942\pi\) | ||
0.762325 | − | 0.647194i | \(-0.224058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −112.206 | + | 112.206i | −0.138356 | + | 0.138356i | −0.772893 | − | 0.634537i | \(-0.781191\pi\) |
0.634537 | + | 0.772893i | \(0.281191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 212.432 | − | 212.432i | 0.261294 | − | 0.261294i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1349.20i | − | 1.65546i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.3176 | −0.0297645 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −535.643 | − | 535.643i | −0.654020 | − | 0.654020i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.63080 | + | 7.63080i | 0.00929452 | + | 0.00929452i | 0.711739 | − | 0.702444i | \(-0.247908\pi\) |
−0.702444 | + | 0.711739i | \(0.747908\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1316.28 | −1.59937 | −0.799687 | − | 0.600417i | \(-0.795001\pi\) | ||||
−0.799687 | + | 0.600417i | \(0.795001\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.8798i | 0.0325816i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 341.515 | − | 341.515i | 0.412957 | − | 0.412957i | −0.469810 | − | 0.882767i | \(-0.655678\pi\) |
0.882767 | + | 0.469810i | \(0.155678\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 621.672 | − | 621.672i | 0.749905 | − | 0.749905i | −0.224556 | − | 0.974461i | \(-0.572093\pi\) |
0.974461 | + | 0.224556i | \(0.0720931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 94.0725i | − | 0.113204i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 272.208 | 0.326781 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 516.412 | + | 516.412i | 0.618457 | + | 0.618457i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 103.070 | + | 103.070i | 0.123142 | + | 0.123142i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1440.49 | −1.71692 | −0.858459 | − | 0.512883i | \(-0.828578\pi\) | ||||
−0.858459 | + | 0.512883i | \(0.828578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 831.348i | 0.988523i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 273.820 | − | 273.820i | 0.324816 | − | 0.324816i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2051.65 | − | 2051.65i | 2.42798 | − | 2.42798i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1244.24i | 1.46900i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −606.873 | −0.714809 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 404.186 | + | 404.186i | 0.474954 | + | 0.474954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 625.193 | + | 625.193i | 0.732934 | + | 0.732934i | 0.971200 | − | 0.238266i | \(-0.0765789\pi\) |
−0.238266 | + | 0.971200i | \(0.576579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72.8599 | 0.0852163 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1105.18i | − | 1.28959i | −0.764356 | − | 0.644794i | \(-0.776943\pi\) | ||
0.764356 | − | 0.644794i | \(-0.223057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 379.841 | − | 379.841i | 0.442190 | − | 0.442190i | −0.450558 | − | 0.892747i | \(-0.648775\pi\) |
0.892747 | + | 0.450558i | \(0.148775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 292.442 | − | 292.442i | 0.339654 | − | 0.339654i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 381.969i | − | 0.442606i | −0.975205 | − | 0.221303i | \(-0.928969\pi\) | ||
0.975205 | − | 0.221303i | \(-0.0710311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 516.031 | 0.596567 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 326.706 | + | 326.706i | 0.376824 | + | 0.376824i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.7076 | − | 29.7076i | −0.0341859 | − | 0.0341859i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 379.794 | 0.436044 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 182.824i | 0.209420i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 204.994 | − | 204.994i | 0.234279 | − | 0.234279i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −638.602 | + | 638.602i | −0.728166 | + | 0.728166i | −0.970254 | − | 0.242088i | \(-0.922168\pi\) |
0.242088 | + | 0.970254i | \(0.422168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 250.489i | − | 0.284971i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1362.97 | −1.54707 | −0.773533 | − | 0.633756i | \(-0.781512\pi\) | ||||
−0.773533 | + | 0.633756i | \(0.781512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −897.988 | − | 897.988i | −1.01697 | − | 1.01697i | −0.999853 | − | 0.0171209i | \(-0.994550\pi\) |
−0.0171209 | − | 0.999853i | \(-0.505450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −936.598 | − | 936.598i | −1.05830 | − | 1.05830i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1343.56 | −1.51472 | −0.757359 | − | 0.652998i | \(-0.773511\pi\) | ||||
−0.757359 | + | 0.652998i | \(0.773511\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 421.947i | − | 0.474631i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.73552 | − | 4.73552i | 0.00531483 | − | 0.00531483i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −98.9295 | + | 98.9295i | −0.110783 | + | 0.110783i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 997.676i | 1.11472i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 532.870 | 0.594058 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.6257 | + | 61.6257i | 0.0685491 | + | 0.0685491i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 131.952 | + | 131.952i | 0.146451 | + | 0.146451i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −121.317 | −0.134349 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1967.97i | 2.17456i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −671.651 | + | 671.651i | −0.740519 | + | 0.740519i | −0.972678 | − | 0.232159i | \(-0.925421\pi\) |
0.232159 | + | 0.972678i | \(0.425421\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 329.957 | − | 329.957i | 0.362989 | − | 0.362989i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 770.729i | − | 0.846025i | −0.906124 | − | 0.423012i | \(-0.860973\pi\) | ||
0.906124 | − | 0.423012i | \(-0.139027\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61.4246 | 0.0672778 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −431.344 | − | 431.344i | −0.471414 | − | 0.471414i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −774.942 | − | 774.942i | −0.845084 | − | 0.845084i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1153.98 | 1.25569 | 0.627843 | − | 0.778340i | \(-0.283938\pi\) | ||||
0.627843 | + | 0.778340i | \(0.283938\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 338.745i | − | 0.367801i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 910.182 | − | 910.182i | 0.986112 | − | 0.986112i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −669.736 | + | 669.736i | −0.724039 | + | 0.724039i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 519.886i | − | 0.560826i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −652.736 | −0.702622 | −0.351311 | − | 0.936259i | \(-0.614264\pi\) | ||||
−0.351311 | + | 0.936259i | \(0.614264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −146.365 | − | 146.365i | −0.157213 | − | 0.157213i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 252.039 | + | 252.039i | 0.270139 | + | 0.270139i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.7660 | −0.0254182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 644.074i | − | 0.687378i | −0.939083 | − | 0.343689i | \(-0.888323\pi\) | ||
0.939083 | − | 0.343689i | \(-0.111677\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −274.172 | + | 274.172i | −0.291983 | + | 0.291983i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −171.348 | + | 171.348i | −0.182092 | + | 0.182092i | −0.792267 | − | 0.610175i | \(-0.791099\pi\) |
0.610175 | + | 0.792267i | \(0.291099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 290.929i | 0.308514i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 363.487 | 0.384643 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 731.249 | + | 731.249i | 0.772174 | + | 0.772174i | 0.978486 | − | 0.206312i | \(-0.0661461\pi\) |
−0.206312 | + | 0.978486i | \(0.566146\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1171.96 | − | 1171.96i | −1.23494 | − | 1.23494i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −432.305 | −0.454580 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1745.08i | − | 1.83115i | −0.402152 | − | 0.915573i | \(-0.631738\pi\) | ||
0.402152 | − | 0.915573i | \(-0.368262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1188.72 | + | 1188.72i | −1.24473 | + | 1.24473i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.83137 | − | 2.83137i | 0.00295859 | − | 0.00295859i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1384.54i | − | 1.44374i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 174.077 | 0.181142 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −76.4241 | − | 76.4241i | −0.0793604 | − | 0.0793604i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −622.102 | − | 622.102i | −0.644665 | − | 0.644665i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −904.237 | −0.935095 | −0.467548 | − | 0.883968i | \(-0.654862\pi\) | ||||
−0.467548 | + | 0.883968i | \(0.654862\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.2989i | 0.0302362i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1010.37 | + | 1010.37i | −1.04055 | + | 1.04055i | −0.0414029 | + | 0.999143i | \(0.513183\pi\) |
−0.999143 | + | 0.0414029i | \(0.986817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 236.354 | − | 236.354i | 0.242913 | − | 0.242913i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 882.966i | 0.905606i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −396.922 | −0.406266 | −0.203133 | − | 0.979151i | \(-0.565112\pi\) | ||||
−0.203133 | + | 0.979151i | \(0.565112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 69.2259 | + | 69.2259i | 0.0707108 | + | 0.0707108i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −99.1815 | − | 99.1815i | −0.101102 | − | 0.101102i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1672.52 | −1.70145 | −0.850724 | − | 0.525612i | \(-0.823836\pi\) | ||||
−0.850724 | + | 0.525612i | \(0.823836\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2269.66i | − | 2.30423i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −493.545 | + | 493.545i | −0.500045 | + | 0.500045i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.3446 | − | 60.3446i | 0.0610157 | − | 0.0610157i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 775.801i | − | 0.782847i | −0.920211 | − | 0.391423i | \(-0.871983\pi\) | ||
0.920211 | − | 0.391423i | \(-0.128017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 450.556 | 0.453732 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1180.35 | − | 1180.35i | −1.18629 | − | 1.18629i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −201.495 | − | 201.495i | −0.202101 | − | 0.202101i | 0.598799 | − | 0.800900i | \(-0.295645\pi\) |
−0.800900 | + | 0.598799i | \(0.795645\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 235.980 | 0.236216 |
(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 | 384.3.l.b.31.4 | 16 | ||
3.2 | odd | 2 | 1152.3.m.c.415.2 | 16 | |||
4.3 | odd | 2 | 384.3.l.a.31.8 | 16 | |||
8.3 | odd | 2 | 48.3.l.a.43.1 | yes | 16 | ||
8.5 | even | 2 | 192.3.l.a.79.5 | 16 | |||
12.11 | even | 2 | 1152.3.m.f.415.2 | 16 | |||
16.3 | odd | 4 | inner | 384.3.l.b.223.4 | 16 | ||
16.5 | even | 4 | 48.3.l.a.19.1 | ✓ | 16 | ||
16.11 | odd | 4 | 192.3.l.a.175.5 | 16 | |||
16.13 | even | 4 | 384.3.l.a.223.8 | 16 | |||
24.5 | odd | 2 | 576.3.m.c.271.7 | 16 | |||
24.11 | even | 2 | 144.3.m.c.91.8 | 16 | |||
48.5 | odd | 4 | 144.3.m.c.19.8 | 16 | |||
48.11 | even | 4 | 576.3.m.c.559.7 | 16 | |||
48.29 | odd | 4 | 1152.3.m.f.991.2 | 16 | |||
48.35 | even | 4 | 1152.3.m.c.991.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.1 | ✓ | 16 | 16.5 | even | 4 | ||
48.3.l.a.43.1 | yes | 16 | 8.3 | odd | 2 | ||
144.3.m.c.19.8 | 16 | 48.5 | odd | 4 | |||
144.3.m.c.91.8 | 16 | 24.11 | even | 2 | |||
192.3.l.a.79.5 | 16 | 8.5 | even | 2 | |||
192.3.l.a.175.5 | 16 | 16.11 | odd | 4 | |||
384.3.l.a.31.8 | 16 | 4.3 | odd | 2 | |||
384.3.l.a.223.8 | 16 | 16.13 | even | 4 | |||
384.3.l.b.31.4 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.b.223.4 | 16 | 16.3 | odd | 4 | inner | ||
576.3.m.c.271.7 | 16 | 24.5 | odd | 2 | |||
576.3.m.c.559.7 | 16 | 48.11 | even | 4 | |||
1152.3.m.c.415.2 | 16 | 3.2 | odd | 2 | |||
1152.3.m.c.991.2 | 16 | 48.35 | even | 4 | |||
1152.3.m.f.415.2 | 16 | 12.11 | even | 2 | |||
1152.3.m.f.991.2 | 16 | 48.29 | odd | 4 |