Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(55,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.60771337450861625344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 11x^{8} - 26x^{6} + 44x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.8 | ||
Root | \(-0.840028 - 1.13770i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.55 |
Dual form | 756.2.b.d.55.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.840028 | + | 1.13770i | 0.593990 | + | 0.804473i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.588705 | + | 1.91139i | −0.294352 | + | 0.955697i | ||||
\(5\) | − | 2.67907i | − | 1.19812i | −0.800706 | − | 0.599058i | \(-0.795542\pi\) | ||
0.800706 | − | 0.599058i | \(-0.204458\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.370556 | − | 2.61967i | 0.140057 | − | 0.990143i | ||||
\(8\) | −2.66911 | + | 0.935858i | −0.943674 | + | 0.330876i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.04797 | − | 2.25049i | 0.963852 | − | 0.711669i | ||||
\(11\) | 1.39642i | 0.421037i | 0.977590 | + | 0.210519i | \(0.0675153\pi\) | ||||
−0.977590 | + | 0.210519i | \(0.932485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.08443i | − | 0.855467i | −0.903905 | − | 0.427733i | \(-0.859312\pi\) | ||
0.903905 | − | 0.427733i | \(-0.140688\pi\) | |||||||
\(14\) | 3.29167 | − | 1.77902i | 0.879736 | − | 0.475463i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.30685 | − | 2.25049i | −0.826713 | − | 0.562623i | ||||
\(17\) | − | 5.83343i | − | 1.41481i | −0.706806 | − | 0.707407i | \(-0.749865\pi\) | ||
0.706806 | − | 0.707407i | \(-0.250135\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.91852 | 0.440139 | 0.220070 | − | 0.975484i | \(-0.429372\pi\) | ||||
0.220070 | + | 0.975484i | \(0.429372\pi\) | |||||||
\(20\) | 5.12076 | + | 1.57718i | 1.14504 | + | 0.352668i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.58870 | + | 1.17303i | −0.338713 | + | 0.250092i | ||||
\(23\) | − | 1.39642i | − | 0.291174i | −0.989345 | − | 0.145587i | \(-0.953493\pi\) | ||
0.989345 | − | 0.145587i | \(-0.0465071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.17741 | −0.435482 | ||||||||
\(26\) | 3.50914 | − | 2.59101i | 0.688199 | − | 0.508138i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.78908 | + | 2.25049i | 0.905051 | + | 0.425303i | ||||
\(29\) | −4.90328 | −0.910517 | −0.455258 | − | 0.890359i | \(-0.650453\pi\) | ||||
−0.455258 | + | 0.890359i | \(0.650453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.53223 | 1.71204 | 0.856019 | − | 0.516944i | \(-0.172930\pi\) | ||||
0.856019 | + | 0.516944i | \(0.172930\pi\) | |||||||
\(32\) | −0.217472 | − | 5.65267i | −0.0384441 | − | 0.999261i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.63667 | − | 4.90025i | 1.13818 | − | 0.840385i | ||||
\(35\) | −7.01828 | − | 0.992746i | −1.18631 | − | 0.167805i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.83705 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(38\) | 1.61161 | + | 2.18270i | 0.261438 | + | 0.354080i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.50723 | + | 7.15074i | 0.396427 | + | 1.13063i | ||||
\(41\) | − | 0.693576i | − | 0.108318i | −0.998532 | − | 0.0541592i | \(-0.982752\pi\) | ||
0.998532 | − | 0.0541592i | \(-0.0172479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.678200i | − | 0.103424i | −0.998662 | − | 0.0517122i | \(-0.983532\pi\) | ||
0.998662 | − | 0.0517122i | \(-0.0164679\pi\) | |||||||
\(44\) | −2.66911 | − | 0.822081i | −0.402384 | − | 0.123933i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.58870 | − | 1.17303i | 0.234242 | − | 0.172955i | ||||
\(47\) | −8.26340 | −1.20534 | −0.602670 | − | 0.797990i | \(-0.705897\pi\) | ||||
−0.602670 | + | 0.797990i | \(0.705897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.72538 | − | 1.94147i | −0.960768 | − | 0.277353i | ||||
\(50\) | −1.82909 | − | 2.47723i | −0.258672 | − | 0.350333i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.89556 | + | 1.81582i | 0.817567 | + | 0.251809i | ||||
\(53\) | 10.6765 | 1.46652 | 0.733262 | − | 0.679946i | \(-0.237997\pi\) | ||||
0.733262 | + | 0.679946i | \(0.237997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.74111 | 0.504452 | ||||||||
\(56\) | 1.46258 | + | 7.33899i | 0.195446 | + | 0.980714i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.11890 | − | 5.57845i | −0.540838 | − | 0.732486i | ||||
\(59\) | −12.2196 | −1.59086 | −0.795430 | − | 0.606046i | \(-0.792755\pi\) | ||||
−0.795430 | + | 0.606046i | \(0.792755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8849i | 1.64975i | 0.565319 | + | 0.824873i | \(0.308753\pi\) | ||||
−0.565319 | + | 0.824873i | \(0.691247\pi\) | |||||||
\(62\) | 8.00734 | + | 10.8448i | 1.01693 | + | 1.37729i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.24834 | − | 4.99582i | 0.781043 | − | 0.624478i | ||||
\(65\) | −8.26340 | −1.02495 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.08443i | 0.376823i | 0.982090 | + | 0.188411i | \(0.0603339\pi\) | ||||
−0.982090 | + | 0.188411i | \(0.939666\pi\) | |||||||
\(68\) | 11.1500 | + | 3.43417i | 1.35213 | + | 0.416454i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.76611 | − | 8.81861i | −0.569660 | − | 1.05403i | ||||
\(71\) | 9.79515i | 1.16247i | 0.813736 | + | 0.581235i | \(0.197430\pi\) | ||||
−0.813736 | + | 0.581235i | \(0.802570\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.91755i | − | 0.692596i | −0.938124 | − | 0.346298i | \(-0.887439\pi\) | ||
0.938124 | − | 0.346298i | \(-0.112561\pi\) | |||||||
\(74\) | 5.74331 | + | 7.77848i | 0.667646 | + | 0.904230i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.12944 | + | 3.66705i | −0.129556 | + | 0.420640i | ||||
\(77\) | 3.65817 | + | 0.517454i | 0.416887 | + | 0.0589693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0864i | 1.35983i | 0.733293 | + | 0.679913i | \(0.237983\pi\) | ||||
−0.733293 | + | 0.679913i | \(0.762017\pi\) | |||||||
\(80\) | −6.02923 | + | 8.85929i | −0.674088 | + | 0.990498i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.789079 | − | 0.582624i | 0.0871392 | − | 0.0643400i | ||||
\(83\) | 5.77317 | 0.633688 | 0.316844 | − | 0.948478i | \(-0.397377\pi\) | ||||
0.316844 | + | 0.948478i | \(0.397377\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.6282 | −1.69511 | ||||||||
\(86\) | 0.771585 | − | 0.569707i | 0.0832021 | − | 0.0614331i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.30685 | − | 3.72721i | −0.139311 | − | 0.397322i | ||||
\(89\) | 6.65005i | 0.704904i | 0.935830 | + | 0.352452i | \(0.114652\pi\) | ||||
−0.935830 | + | 0.352452i | \(0.885348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.08020 | − | 1.14295i | −0.847035 | − | 0.119814i | ||||
\(92\) | 2.66911 | + | 0.822081i | 0.278274 | + | 0.0857079i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.94149 | − | 9.40123i | −0.715960 | − | 0.969663i | ||||
\(95\) | − | 5.13985i | − | 0.527338i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.8849i | − | 1.30827i | −0.756380 | − | 0.654133i | \(-0.773034\pi\) | ||
0.756380 | − | 0.654133i | \(-0.226966\pi\) | |||||||
\(98\) | −3.44070 | − | 9.28233i | −0.347563 | − | 0.937657i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.28185 | − | 4.16189i | 0.128185 | − | 0.416189i | ||||
\(101\) | − | 14.1276i | − | 1.40575i | −0.711312 | − | 0.702877i | \(-0.751899\pi\) | ||
0.711312 | − | 0.702877i | \(-0.248101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.56370 | −0.548208 | −0.274104 | − | 0.961700i | \(-0.588381\pi\) | ||||
−0.274104 | + | 0.961700i | \(0.588381\pi\) | |||||||
\(104\) | 2.88659 | + | 8.23269i | 0.283053 | + | 0.807282i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.96853 | + | 12.1466i | 0.871100 | + | 1.17978i | ||||
\(107\) | 7.44814i | 0.720039i | 0.932945 | + | 0.360019i | \(0.117230\pi\) | ||||
−0.932945 | + | 0.360019i | \(0.882770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.3693 | 1.28054 | 0.640272 | − | 0.768148i | \(-0.278822\pi\) | ||||
0.640272 | + | 0.768148i | \(0.278822\pi\) | |||||||
\(110\) | 3.14264 | + | 4.25625i | 0.299639 | + | 0.405817i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.12093 | + | 7.82894i | −0.672865 | + | 0.739765i | ||||
\(113\) | −3.36011 | −0.316093 | −0.158046 | − | 0.987432i | \(-0.550520\pi\) | ||||
−0.158046 | + | 0.987432i | \(0.550520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.74111 | −0.348861 | ||||||||
\(116\) | 2.88659 | − | 9.37211i | 0.268013 | − | 0.870178i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.2648 | − | 13.9022i | −0.944954 | − | 1.27980i | ||||
\(119\) | −15.2817 | − | 2.16162i | −1.40087 | − | 0.198155i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05000 | 0.822728 | ||||||||
\(122\) | −14.6591 | + | 10.8237i | −1.32717 | + | 0.979932i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.61167 | + | 18.2198i | −0.503943 | + | 1.63619i | ||||
\(125\) | − | 7.56191i | − | 0.676358i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.9694i | − | 1.41705i | −0.705685 | − | 0.708525i | \(-0.749361\pi\) | ||
0.705685 | − | 0.708525i | \(-0.250639\pi\) | |||||||
\(128\) | 10.9325 | + | 2.91208i | 0.966307 | + | 0.257394i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.94149 | − | 9.40123i | −0.608809 | − | 0.824543i | ||||
\(131\) | −1.81694 | −0.158747 | −0.0793735 | − | 0.996845i | \(-0.525292\pi\) | ||||
−0.0793735 | + | 0.996845i | \(0.525292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.710921 | − | 5.02590i | 0.0616447 | − | 0.435801i | ||||
\(134\) | −3.50914 | + | 2.59101i | −0.303144 | + | 0.223829i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.45926 | + | 15.5701i | 0.468128 | + | 1.33512i | ||||
\(137\) | −18.9399 | −1.61814 | −0.809070 | − | 0.587712i | \(-0.800029\pi\) | ||||
−0.809070 | + | 0.587712i | \(0.800029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2878 | −1.29669 | −0.648347 | − | 0.761345i | \(-0.724539\pi\) | ||||
−0.648347 | + | 0.761345i | \(0.724539\pi\) | |||||||
\(140\) | 6.02923 | − | 12.8303i | 0.509563 | − | 1.08436i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.1439 | + | 8.22820i | −0.935175 | + | 0.690495i | ||||
\(143\) | 4.30717 | 0.360183 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.1362i | 1.09090i | ||||||||
\(146\) | 6.73237 | − | 4.97091i | 0.557175 | − | 0.411395i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.02500 | + | 13.0683i | −0.330853 | + | 1.07421i | ||||
\(149\) | 17.3967 | 1.42519 | 0.712596 | − | 0.701575i | \(-0.247519\pi\) | ||||
0.712596 | + | 0.701575i | \(0.247519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.57509i | − | 0.697831i | −0.937154 | − | 0.348915i | \(-0.886550\pi\) | ||
0.937154 | − | 0.348915i | \(-0.113450\pi\) | |||||||
\(152\) | −5.12076 | + | 1.79546i | −0.415348 | + | 0.145631i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.48426 | + | 4.59656i | 0.200188 | + | 0.370402i | ||||
\(155\) | − | 25.5375i | − | 2.05122i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8025i | 1.50060i | 0.661097 | + | 0.750300i | \(0.270091\pi\) | ||||
−0.661097 | + | 0.750300i | \(0.729909\pi\) | |||||||
\(158\) | −13.7507 | + | 10.1529i | −1.09394 | + | 0.807723i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.1439 | + | 0.582624i | −1.19723 | + | 0.0460605i | ||||
\(161\) | −3.65817 | − | 0.517454i | −0.288304 | − | 0.0407810i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.251311i | − | 0.0196842i | −0.999952 | − | 0.00984211i | \(-0.996867\pi\) | ||
0.999952 | − | 0.00984211i | \(-0.00313289\pi\) | |||||||
\(164\) | 1.32570 | + | 0.408312i | 0.103520 | + | 0.0318838i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.84963 | + | 6.56812i | 0.376404 | + | 0.509785i | ||||
\(167\) | 14.0366 | 1.08618 | 0.543091 | − | 0.839674i | \(-0.317254\pi\) | ||||
0.543091 | + | 0.839674i | \(0.317254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.48630 | 0.268177 | ||||||||
\(170\) | −13.1281 | − | 17.7801i | −1.00688 | − | 1.36367i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.29631 | + | 0.399259i | 0.0988424 | + | 0.0304432i | ||||
\(173\) | 14.8212i | 1.12684i | 0.826172 | + | 0.563418i | \(0.190514\pi\) | ||||
−0.826172 | + | 0.563418i | \(0.809486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.806853 | + | 5.70410i | −0.0609924 | + | 0.431190i | ||||
\(176\) | 3.14264 | − | 4.61777i | 0.236885 | − | 0.348077i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.56574 | + | 5.58623i | −0.567076 | + | 0.418706i | ||||
\(179\) | 13.9001i | 1.03894i | 0.854488 | + | 0.519471i | \(0.173871\pi\) | ||||
−0.854488 | + | 0.519471i | \(0.826129\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.11903i | 0.380494i | 0.981736 | + | 0.190247i | \(0.0609289\pi\) | ||||
−0.981736 | + | 0.190247i | \(0.939071\pi\) | |||||||
\(182\) | −5.48726 | − | 10.1529i | −0.406743 | − | 0.752585i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.30685 | + | 3.72721i | 0.0963425 | + | 0.274774i | ||||
\(185\) | − | 18.3169i | − | 1.34669i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.14594 | 0.595690 | ||||||||
\(188\) | 4.86470 | − | 15.7946i | 0.354795 | − | 1.15194i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.84759 | − | 4.31762i | 0.424229 | − | 0.313233i | ||||
\(191\) | − | 5.34887i | − | 0.387030i | −0.981097 | − | 0.193515i | \(-0.938011\pi\) | ||
0.981097 | − | 0.193515i | \(-0.0619889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.22334 | −0.160039 | −0.0800197 | − | 0.996793i | \(-0.525498\pi\) | ||||
−0.0800197 | + | 0.996793i | \(0.525498\pi\) | |||||||
\(194\) | 14.6591 | − | 10.8237i | 1.05246 | − | 0.777096i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.67018 | − | 11.7119i | 0.547870 | − | 0.836563i | ||||
\(197\) | 23.8431 | 1.69875 | 0.849377 | − | 0.527787i | \(-0.176978\pi\) | ||||
0.849377 | + | 0.527787i | \(0.176978\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5467 | −1.24385 | −0.621926 | − | 0.783076i | \(-0.713649\pi\) | ||||
−0.621926 | + | 0.783076i | \(0.713649\pi\) | |||||||
\(200\) | 5.81175 | − | 2.03775i | 0.410953 | − | 0.144090i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.0730 | − | 11.8676i | 1.13089 | − | 0.835003i | ||||
\(203\) | −1.81694 | + | 12.8450i | −0.127524 | + | 0.901542i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.85814 | −0.129778 | ||||||||
\(206\) | −4.67367 | − | 6.32980i | −0.325630 | − | 0.441018i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.94149 | + | 10.1998i | −0.481306 | + | 0.707226i | ||||
\(209\) | 2.67907i | 0.185315i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.76263i | 0.259030i | 0.991577 | + | 0.129515i | \(0.0413420\pi\) | ||||
−0.991577 | + | 0.129515i | \(0.958658\pi\) | |||||||
\(212\) | −6.28528 | + | 20.4069i | −0.431675 | + | 1.40155i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.47372 | + | 6.25665i | −0.579251 | + | 0.427696i | ||||
\(215\) | −1.81694 | −0.123915 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.53223 | − | 24.9713i | 0.239783 | − | 1.69516i | ||||
\(218\) | 11.2306 | + | 15.2102i | 0.760630 | + | 1.03016i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.20241 | + | 7.15074i | −0.148487 | + | 0.482103i | ||||
\(221\) | −17.9928 | −1.21033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8056 | −0.723595 | −0.361797 | − | 0.932257i | \(-0.617837\pi\) | ||||
−0.361797 | + | 0.932257i | \(0.617837\pi\) | |||||||
\(224\) | −14.8887 | − | 1.52493i | −0.994796 | − | 0.101889i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.82259 | − | 3.82279i | −0.187756 | − | 0.254288i | ||||
\(227\) | 24.1169 | 1.60070 | 0.800348 | − | 0.599536i | \(-0.204648\pi\) | ||||
0.800348 | + | 0.599536i | \(0.204648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.9367i | 1.51570i | 0.652428 | + | 0.757851i | \(0.273751\pi\) | ||||
−0.652428 | + | 0.757851i | \(0.726249\pi\) | |||||||
\(230\) | −3.14264 | − | 4.25625i | −0.207220 | − | 0.280649i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.0874 | − | 4.58878i | 0.859231 | − | 0.301268i | ||||
\(233\) | −0.869890 | −0.0569884 | −0.0284942 | − | 0.999594i | \(-0.509071\pi\) | ||||
−0.0284942 | + | 0.999594i | \(0.509071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.1382i | 1.44414i | ||||||||
\(236\) | 7.19375 | − | 23.3565i | 0.468273 | − | 1.52038i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.3778 | − | 19.2017i | −0.672692 | − | 1.24466i | ||||
\(239\) | 21.1005i | 1.36488i | 0.730943 | + | 0.682439i | \(0.239081\pi\) | ||||
−0.730943 | + | 0.682439i | \(0.760919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.08443i | 0.198686i | 0.995053 | + | 0.0993428i | \(0.0316740\pi\) | ||||
−0.995053 | + | 0.0993428i | \(0.968326\pi\) | |||||||
\(242\) | 7.60226 | + | 10.2962i | 0.488692 | + | 0.661862i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.6282 | − | 7.58542i | −1.57666 | − | 0.485606i | ||||
\(245\) | −5.20134 | + | 18.0177i | −0.332302 | + | 1.15111i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.91755i | − | 0.376524i | ||||||
\(248\) | −25.4426 | + | 8.92081i | −1.61561 | + | 0.566472i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.60316 | − | 6.35222i | 0.544112 | − | 0.401750i | ||||
\(251\) | 16.5268 | 1.04316 | 0.521581 | − | 0.853202i | \(-0.325342\pi\) | ||||
0.521581 | + | 0.853202i | \(0.325342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.95000 | 0.122595 | ||||||||
\(254\) | 18.1683 | − | 13.4147i | 1.13998 | − | 0.841714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.87056 | + | 14.8841i | 0.366910 | + | 0.930257i | ||||
\(257\) | 20.1794i | 1.25875i | 0.777100 | + | 0.629377i | \(0.216690\pi\) | ||||
−0.777100 | + | 0.629377i | \(0.783310\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.53351 | − | 17.9108i | 0.157425 | − | 1.11292i | ||||
\(260\) | 4.86470 | − | 15.7946i | 0.301696 | − | 0.979540i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.52628 | − | 2.06713i | −0.0942941 | − | 0.127708i | ||||
\(263\) | − | 21.7941i | − | 1.34388i | −0.740606 | − | 0.671940i | \(-0.765461\pi\) | ||
0.740606 | − | 0.671940i | \(-0.234539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 28.6030i | − | 1.75707i | ||||||
\(266\) | 6.31514 | − | 3.41309i | 0.387206 | − | 0.209270i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.89556 | − | 1.81582i | −0.360129 | − | 0.110919i | ||||
\(269\) | − | 11.4486i | − | 0.698032i | −0.937117 | − | 0.349016i | \(-0.886516\pi\) | ||
0.937117 | − | 0.349016i | \(-0.113484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6782 | 0.891635 | 0.445817 | − | 0.895124i | \(-0.352913\pi\) | ||||
0.445817 | + | 0.895124i | \(0.352913\pi\) | |||||||
\(272\) | −13.1281 | + | 19.2903i | −0.796008 | + | 1.16965i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.9100 | − | 21.5478i | −0.961159 | − | 1.30175i | ||||
\(275\) | − | 3.04058i | − | 0.183354i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.6782 | −0.942010 | −0.471005 | − | 0.882131i | \(-0.656109\pi\) | ||||
−0.471005 | + | 0.882131i | \(0.656109\pi\) | |||||||
\(278\) | −12.8422 | − | 17.3929i | −0.770223 | − | 1.04315i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.6617 | − | 3.91836i | 1.17501 | − | 0.234167i | ||||
\(281\) | 0.947053 | 0.0564965 | 0.0282482 | − | 0.999601i | \(-0.491007\pi\) | ||||
0.0282482 | + | 0.999601i | \(0.491007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.03555 | −0.537108 | −0.268554 | − | 0.963265i | \(-0.586546\pi\) | ||||
−0.268554 | + | 0.963265i | \(0.586546\pi\) | |||||||
\(284\) | −18.7224 | − | 5.76645i | −1.11097 | − | 0.342176i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.61814 | + | 4.90025i | 0.213945 | + | 0.289758i | ||||
\(287\) | −1.81694 | − | 0.257009i | −0.107251 | − | 0.0151708i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0289 | −1.00170 | ||||||||
\(290\) | −14.9450 | + | 11.0348i | −0.877603 | + | 0.647986i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.3108 | + | 3.48369i | 0.661912 | + | 0.203867i | ||||
\(293\) | 7.22058i | 0.421831i | 0.977504 | + | 0.210915i | \(0.0676445\pi\) | ||||
−0.977504 | + | 0.210915i | \(0.932356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.7372i | 1.90603i | ||||||||
\(296\) | −18.2489 | + | 6.39850i | −1.06069 | + | 0.371905i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.6137 | + | 19.7921i | 0.846549 | + | 1.14653i | ||||
\(299\) | −4.30717 | −0.249090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77666 | − | 0.251311i | −0.102405 | − | 0.0144853i | ||||
\(302\) | 9.75584 | − | 7.20332i | 0.561386 | − | 0.414504i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.34427 | − | 4.31762i | −0.363869 | − | 0.247633i | ||||
\(305\) | 34.5196 | 1.97659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.6885 | 1.40905 | 0.704525 | − | 0.709679i | \(-0.251160\pi\) | ||||
0.704525 | + | 0.709679i | \(0.251160\pi\) | |||||||
\(308\) | −3.14264 | + | 6.68758i | −0.179069 | + | 0.381060i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.0539 | − | 21.4522i | 1.65015 | − | 1.21840i | ||||
\(311\) | 32.3803 | 1.83612 | 0.918059 | − | 0.396443i | \(-0.129756\pi\) | ||||
0.918059 | + | 0.396443i | \(0.129756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.75066i | − | 0.494617i | −0.968937 | − | 0.247308i | \(-0.920454\pi\) | ||
0.968937 | − | 0.247308i | \(-0.0795461\pi\) | |||||||
\(314\) | −21.3915 | + | 15.7946i | −1.20719 | + | 0.891341i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.1019 | − | 7.11532i | −1.29958 | − | 0.400268i | ||||
\(317\) | −19.2136 | −1.07914 | −0.539572 | − | 0.841939i | \(-0.681414\pi\) | ||||
−0.539572 | + | 0.841939i | \(0.681414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.84706i | − | 0.383362i | ||||||
\(320\) | −13.3842 | − | 16.7397i | −0.748197 | − | 0.935780i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.48426 | − | 4.59656i | −0.138443 | − | 0.256156i | ||||
\(323\) | − | 11.1916i | − | 0.622715i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.71606i | 0.372540i | ||||||||
\(326\) | 0.285916 | − | 0.211109i | 0.0158354 | − | 0.0116922i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.649089 | + | 1.85123i | 0.0358399 | + | 0.102217i | ||||
\(329\) | −3.06205 | + | 21.6474i | −0.168817 | + | 1.19346i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6.59575i | − | 0.362535i | −0.983434 | − | 0.181267i | \(-0.941980\pi\) | ||
0.983434 | − | 0.181267i | \(-0.0580200\pi\) | |||||||
\(332\) | −3.39870 | + | 11.0348i | −0.186528 | + | 0.605614i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.7911 | + | 15.9694i | 0.645181 | + | 0.873804i | ||||
\(335\) | 8.26340 | 0.451478 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.6741 | 0.908296 | 0.454148 | − | 0.890926i | \(-0.349944\pi\) | ||||
0.454148 | + | 0.890926i | \(0.349944\pi\) | |||||||
\(338\) | 2.92859 | + | 3.96635i | 0.159294 | + | 0.215741i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.20037 | − | 29.8716i | 0.498960 | − | 1.62001i | ||||
\(341\) | 13.3110i | 0.720832i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.57816 | + | 16.8989i | −0.409182 | + | 0.912453i | ||||
\(344\) | 0.634698 | + | 1.81019i | 0.0342206 | + | 0.0975990i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.8620 | + | 12.4502i | −0.906509 | + | 0.669329i | ||||
\(347\) | 2.53584i | 0.136131i | 0.997681 | + | 0.0680654i | \(0.0216827\pi\) | ||||
−0.997681 | + | 0.0680654i | \(0.978317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.54918i | 0.511156i | 0.966788 | + | 0.255578i | \(0.0822658\pi\) | ||||
−0.966788 | + | 0.255578i | \(0.917734\pi\) | |||||||
\(350\) | −7.16731 | + | 3.87365i | −0.383109 | + | 0.207055i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.89352 | − | 0.303684i | 0.420726 | − | 0.0161864i | ||||
\(353\) | − | 3.27741i | − | 0.174439i | −0.996189 | − | 0.0872194i | \(-0.972202\pi\) | ||
0.996189 | − | 0.0872194i | \(-0.0277981\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.2419 | 1.39277 | ||||||||
\(356\) | −12.7109 | − | 3.91492i | −0.673675 | − | 0.207490i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.8141 | + | 11.6765i | −0.835800 | + | 0.617121i | ||||
\(359\) | − | 11.6467i | − | 0.614688i | −0.951598 | − | 0.307344i | \(-0.900560\pi\) | ||
0.951598 | − | 0.307344i | \(-0.0994402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3193 | −0.806277 | ||||||||
\(362\) | −5.82390 | + | 4.30013i | −0.306097 | + | 0.226010i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.94149 | − | 14.7716i | 0.363833 | − | 0.774241i | ||||
\(365\) | −15.8535 | −0.829811 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.5111 | 1.38387 | 0.691935 | − | 0.721960i | \(-0.256758\pi\) | ||||
0.691935 | + | 0.721960i | \(0.256758\pi\) | |||||||
\(368\) | −3.14264 | + | 4.61777i | −0.163821 | + | 0.240718i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.8391 | − | 15.3867i | 1.08337 | − | 0.799918i | ||||
\(371\) | 3.95623 | − | 27.9688i | 0.205397 | − | 1.45207i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.56370 | 0.184522 | 0.0922608 | − | 0.995735i | \(-0.470591\pi\) | ||||
0.0922608 | + | 0.995735i | \(0.470591\pi\) | |||||||
\(374\) | 6.84282 | + | 9.26760i | 0.353834 | + | 0.479216i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.0559 | − | 7.73336i | 1.13745 | − | 0.398818i | ||||
\(377\) | 15.1238i | 0.778917i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.37361i | − | 0.481490i | −0.970588 | − | 0.240745i | \(-0.922608\pi\) | ||
0.970588 | − | 0.240745i | \(-0.0773917\pi\) | |||||||
\(380\) | 9.82429 | + | 3.02586i | 0.503975 | + | 0.155223i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.08539 | − | 4.49320i | 0.311355 | − | 0.229892i | ||||
\(383\) | 3.95623 | 0.202154 | 0.101077 | − | 0.994879i | \(-0.467771\pi\) | ||||
0.101077 | + | 0.994879i | \(0.467771\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.38629 | − | 9.80049i | 0.0706521 | − | 0.499479i | ||||
\(386\) | −1.86767 | − | 2.52948i | −0.0950618 | − | 0.128747i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.6282 | + | 7.58542i | 1.25031 | + | 0.385091i | ||||
\(389\) | −3.36011 | −0.170365 | −0.0851823 | − | 0.996365i | \(-0.527147\pi\) | ||||
−0.0851823 | + | 0.996365i | \(0.527147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.14594 | −0.411958 | ||||||||
\(392\) | 19.7677 | − | 1.11198i | 0.998422 | − | 0.0561635i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.0289 | + | 27.1262i | 1.00904 | + | 1.36660i | ||||
\(395\) | 32.3803 | 1.62923 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.2672i | 1.26813i | 0.773282 | + | 0.634063i | \(0.218614\pi\) | ||||
−0.773282 | + | 0.634063i | \(0.781386\pi\) | |||||||
\(398\) | −14.7397 | − | 19.9628i | −0.738835 | − | 1.00064i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.20037 | + | 4.90025i | 0.360019 | + | 0.245012i | ||||
\(401\) | 35.7404 | 1.78479 | 0.892396 | − | 0.451254i | \(-0.149023\pi\) | ||||
0.892396 | + | 0.451254i | \(0.149023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.4015i | − | 1.46459i | ||||||
\(404\) | 27.0035 | + | 8.31701i | 1.34347 | + | 0.413787i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.1400 | + | 8.72303i | −0.801014 | + | 0.432917i | ||||
\(407\) | 9.54741i | 0.473247i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.5166i | − | 0.816691i | −0.912827 | − | 0.408346i | \(-0.866106\pi\) | ||
0.912827 | − | 0.408346i | \(-0.133894\pi\) | |||||||
\(410\) | −1.56089 | − | 2.11400i | −0.0770868 | − | 0.104403i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.27538 | − | 10.6344i | 0.161366 | − | 0.523921i | ||||
\(413\) | −4.52806 | + | 32.0114i | −0.222811 | + | 1.57518i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.4667i | − | 0.759232i | ||||||
\(416\) | −17.4353 | + | 0.670778i | −0.854834 | + | 0.0328876i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.04797 | + | 2.25049i | −0.149081 | + | 0.110075i | ||||
\(419\) | −17.9928 | −0.879006 | −0.439503 | − | 0.898241i | \(-0.644845\pi\) | ||||
−0.439503 | + | 0.898241i | \(0.644845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.9304 | 1.65367 | 0.826834 | − | 0.562447i | \(-0.190140\pi\) | ||||
0.826834 | + | 0.562447i | \(0.190140\pi\) | |||||||
\(422\) | −4.28073 | + | 3.16071i | −0.208383 | + | 0.153861i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −28.4967 | + | 9.99165i | −1.38392 | + | 0.485237i | ||||
\(425\) | 12.7018i | 0.616126i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.7543 | + | 4.77459i | 1.63348 | + | 0.231059i | ||||
\(428\) | −14.2363 | − | 4.38475i | −0.688139 | − | 0.211945i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.52628 | − | 2.06713i | −0.0736039 | − | 0.0996858i | ||||
\(431\) | 21.0053i | 1.01179i | 0.862596 | + | 0.505894i | \(0.168837\pi\) | ||||
−0.862596 | + | 0.505894i | \(0.831163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.1362i | − | 0.631287i | −0.948878 | − | 0.315644i | \(-0.897780\pi\) | ||
0.948878 | − | 0.315644i | \(-0.102220\pi\) | |||||||
\(434\) | 31.3770 | − | 16.9580i | 1.50614 | − | 0.814011i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.87056 | + | 25.5539i | −0.376931 | + | 1.22381i | ||||
\(437\) | − | 2.67907i | − | 0.128157i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.68073 | −0.318854 | −0.159427 | − | 0.987210i | \(-0.550965\pi\) | ||||
−0.159427 | + | 0.987210i | \(0.550965\pi\) | |||||||
\(440\) | −9.98546 | + | 3.50115i | −0.476038 | + | 0.166911i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.1145 | − | 20.4703i | −0.718922 | − | 0.973675i | ||||
\(443\) | 34.6391i | 1.64575i | 0.568221 | + | 0.822876i | \(0.307632\pi\) | ||||
−0.568221 | + | 0.822876i | \(0.692368\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.8160 | 0.844557 | ||||||||
\(446\) | −9.07699 | − | 12.2935i | −0.429808 | − | 0.582112i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.7721 | − | 18.2198i | −0.508932 | − | 0.860807i | ||||
\(449\) | 4.23000 | 0.199626 | 0.0998131 | − | 0.995006i | \(-0.468176\pi\) | ||||
0.0998131 | + | 0.995006i | \(0.468176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.968526 | 0.0456061 | ||||||||
\(452\) | 1.97811 | − | 6.42250i | 0.0930427 | − | 0.302089i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.2589 | + | 27.4377i | 0.950797 | + | 1.28772i | ||||
\(455\) | −3.06205 | + | 21.6474i | −0.143551 | + | 1.01485i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2522 | −0.713470 | −0.356735 | − | 0.934206i | \(-0.616110\pi\) | ||||
−0.356735 | + | 0.934206i | \(0.616110\pi\) | |||||||
\(458\) | −26.0950 | + | 19.2675i | −1.21934 | + | 0.900311i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.20241 | − | 7.15074i | 0.102688 | − | 0.333405i | ||||
\(461\) | − | 14.4690i | − | 0.673887i | −0.941525 | − | 0.336944i | \(-0.890607\pi\) | ||
0.941525 | − | 0.336944i | \(-0.109393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.0518i | − | 0.467147i | −0.972339 | − | 0.233573i | \(-0.924958\pi\) | ||
0.972339 | − | 0.233573i | \(-0.0750419\pi\) | |||||||
\(464\) | 16.2144 | + | 11.0348i | 0.752736 | + | 0.512278i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.730732 | − | 0.989670i | −0.0338505 | − | 0.0458456i | ||||
\(467\) | −15.8535 | −0.733613 | −0.366807 | − | 0.930297i | \(-0.619549\pi\) | ||||
−0.366807 | + | 0.930297i | \(0.619549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.08020 | + | 1.14295i | 0.373109 | + | 0.0527768i | ||||
\(470\) | −25.1866 | + | 18.5967i | −1.16177 | + | 0.857803i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.6156 | − | 11.4358i | 1.50125 | − | 0.526377i | ||||
\(473\) | 0.947053 | 0.0435456 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.17741 | −0.191673 | ||||||||
\(476\) | 13.1281 | − | 27.9368i | 0.601725 | − | 1.28048i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.0059 | + | 17.7250i | −1.09801 | + | 0.810723i | ||||
\(479\) | 3.63389 | 0.166037 | 0.0830183 | − | 0.996548i | \(-0.473544\pi\) | ||||
0.0830183 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 21.0884i | − | 0.961547i | ||||||
\(482\) | −3.50914 | + | 2.59101i | −0.159837 | + | 0.118017i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.32778 | + | 17.2981i | −0.242172 | + | 0.786278i | ||||
\(485\) | −34.5196 | −1.56745 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.79723i | − | 0.262697i | −0.991336 | − | 0.131349i | \(-0.958069\pi\) | ||
0.991336 | − | 0.131349i | \(-0.0419308\pi\) | |||||||
\(488\) | −12.0585 | − | 34.3913i | −0.545861 | − | 1.55682i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −24.8680 | + | 9.21787i | −1.12342 | + | 0.416421i | ||||
\(491\) | − | 11.2666i | − | 0.508455i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.6030i | 1.28821i | ||||||||
\(494\) | 6.73237 | − | 4.97091i | 0.302904 | − | 0.223652i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.5217 | − | 21.4522i | −1.41537 | − | 0.963233i | ||||
\(497\) | 25.6601 | + | 3.62965i | 1.15101 | + | 0.162812i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.6615i | − | 0.924935i | −0.886636 | − | 0.462468i | \(-0.846964\pi\) | ||
0.886636 | − | 0.462468i | \(-0.153036\pi\) | |||||||
\(500\) | 14.4538 | + | 4.45174i | 0.646393 | + | 0.199088i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.8830 | + | 18.8025i | 0.619627 | + | 0.839195i | ||||
\(503\) | −12.2196 | −0.544846 | −0.272423 | − | 0.962178i | \(-0.587825\pi\) | ||||
−0.272423 | + | 0.962178i | \(0.587825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.8489 | −1.68426 | ||||||||
\(506\) | 1.63805 | + | 2.21850i | 0.0728203 | + | 0.0986245i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.5237 | + | 9.40123i | 1.35427 | + | 0.417112i | ||||
\(509\) | 12.8248i | 0.568450i | 0.958758 | + | 0.284225i | \(0.0917363\pi\) | ||||
−0.958758 | + | 0.284225i | \(0.908264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.5020 | − | 2.19278i | −0.685770 | − | 0.0970031i | ||||
\(512\) | −12.0022 | + | 19.1820i | −0.530425 | + | 0.847732i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.9580 | + | 16.9512i | −1.01263 | + | 0.747687i | ||||
\(515\) | 14.9055i | 0.656817i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.5392i | − | 0.507493i | ||||||
\(518\) | 22.5053 | − | 12.1632i | 0.988826 | − | 0.534422i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22.0559 | − | 7.73336i | 0.967217 | − | 0.339130i | ||||
\(521\) | − | 34.9509i | − | 1.53123i | −0.643300 | − | 0.765614i | \(-0.722435\pi\) | ||
0.643300 | − | 0.765614i | \(-0.277565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.70964 | −0.337119 | −0.168559 | − | 0.985691i | \(-0.553912\pi\) | ||||
−0.168559 | + | 0.985691i | \(0.553912\pi\) | |||||||
\(524\) | 1.06964 | − | 3.47289i | 0.0467276 | − | 0.151714i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7950 | − | 18.3076i | 1.08111 | − | 0.798251i | ||||
\(527\) | − | 55.6056i | − | 2.42222i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0500 | 0.915218 | ||||||||
\(530\) | 32.5415 | − | 24.0273i | 1.41351 | − | 1.04368i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.18796 | + | 4.31762i | 0.398348 | + | 0.187193i | ||||
\(533\) | −2.13929 | −0.0926628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.9541 | 0.862690 | ||||||||
\(536\) | −2.88659 | − | 8.23269i | −0.124682 | − | 0.355598i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.0250 | − | 9.61713i | 0.561548 | − | 0.414624i | ||||
\(539\) | 2.71112 | − | 9.39147i | 0.116776 | − | 0.404519i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7741 | −1.06512 | −0.532561 | − | 0.846392i | \(-0.678770\pi\) | ||||
−0.532561 | + | 0.846392i | \(0.678770\pi\) | |||||||
\(542\) | 12.3301 | + | 16.6993i | 0.529622 | + | 0.717296i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.9745 | + | 1.26861i | −1.41377 | + | 0.0543912i | ||||
\(545\) | − | 35.8172i | − | 1.53424i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.5584i | 1.22107i | 0.791990 | + | 0.610534i | \(0.209045\pi\) | ||||
−0.791990 | + | 0.610534i | \(0.790955\pi\) | |||||||
\(548\) | 11.1500 | − | 36.2015i | 0.476304 | − | 1.54645i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.45926 | − | 2.55418i | 0.147503 | − | 0.108910i | ||||
\(551\) | −9.40706 | −0.400754 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.6624 | + | 4.47869i | 1.34642 | + | 0.190453i | ||||
\(554\) | −13.1701 | − | 17.8370i | −0.559544 | − | 0.757821i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.00000 | − | 29.2210i | 0.381685 | − | 1.23925i | ||||
\(557\) | 7.31634 | 0.310003 | 0.155002 | − | 0.987914i | \(-0.450462\pi\) | ||||
0.155002 | + | 0.987914i | \(0.450462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.09186 | −0.0884762 | ||||||||
\(560\) | 20.9743 | + | 19.0775i | 0.886325 | + | 0.806170i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.795552 | + | 1.07746i | 0.0335583 | + | 0.0454499i | ||||
\(563\) | 38.8268 | 1.63635 | 0.818176 | − | 0.574967i | \(-0.194985\pi\) | ||||
0.818176 | + | 0.574967i | \(0.194985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.00197i | 0.378716i | ||||||||
\(566\) | −7.59012 | − | 10.2797i | −0.319036 | − | 0.432088i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.16686 | − | 26.1444i | −0.384633 | − | 1.09699i | ||||
\(569\) | −15.9307 | −0.667849 | −0.333924 | − | 0.942600i | \(-0.608373\pi\) | ||||
−0.333924 | + | 0.942600i | \(0.608373\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8849i | 0.539217i | 0.962970 | + | 0.269609i | \(0.0868943\pi\) | ||||
−0.962970 | + | 0.269609i | \(0.913106\pi\) | |||||||
\(572\) | −2.53565 | + | 8.23269i | −0.106021 | + | 0.344226i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.23389 | − | 2.28302i | −0.0515014 | − | 0.0952916i | ||||
\(575\) | 3.04058i | 0.126801i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15.7180i | − | 0.654351i | −0.944964 | − | 0.327175i | \(-0.893903\pi\) | ||
0.944964 | − | 0.327175i | \(-0.106097\pi\) | |||||||
\(578\) | −14.3048 | − | 19.3737i | −0.595000 | − | 0.805841i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.1085 | − | 7.73336i | −1.04257 | − | 0.321110i | ||||
\(581\) | 2.13929 | − | 15.1238i | 0.0887526 | − | 0.627442i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.9088i | 0.617461i | ||||||||
\(584\) | 5.53798 | + | 15.7946i | 0.229163 | + | 0.653585i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.21483 | + | 6.06549i | −0.339351 | + | 0.250563i | ||||
\(587\) | −17.9928 | −0.742642 | −0.371321 | − | 0.928504i | \(-0.621095\pi\) | ||||
−0.371321 | + | 0.928504i | \(0.621095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.2878 | 0.753536 | ||||||||
\(590\) | −37.2450 | + | 27.5002i | −1.53335 | + | 1.13216i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.6091 | − | 15.3867i | −0.929228 | − | 0.632391i | ||||
\(593\) | 5.49210i | 0.225534i | 0.993621 | + | 0.112767i | \(0.0359713\pi\) | ||||
−0.993621 | + | 0.112767i | \(0.964029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.79112 | + | 40.9407i | −0.237413 | + | 1.67840i | ||||
\(596\) | −10.2415 | + | 33.2519i | −0.419509 | + | 1.36205i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.61814 | − | 4.90025i | −0.147957 | − | 0.200386i | ||||
\(599\) | − | 38.6101i | − | 1.57756i | −0.614673 | − | 0.788782i | \(-0.710712\pi\) | ||
0.614673 | − | 0.788782i | \(-0.289288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.4667i | − | 0.630901i | −0.948942 | − | 0.315451i | \(-0.897844\pi\) | ||
0.948942 | − | 0.315451i | \(-0.102156\pi\) | |||||||
\(602\) | −1.20653 | − | 2.23241i | −0.0491745 | − | 0.0909862i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.3904 | + | 5.04819i | 0.666915 | + | 0.205408i | ||||
\(605\) | − | 24.2456i | − | 0.985723i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.1959 | −1.02267 | −0.511336 | − | 0.859381i | \(-0.670849\pi\) | ||||
−0.511336 | + | 0.859381i | \(0.670849\pi\) | |||||||
\(608\) | −0.417226 | − | 10.8448i | −0.0169207 | − | 0.439814i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.9974 | + | 39.2728i | 1.17407 | + | 1.59011i | ||||
\(611\) | 25.4879i | 1.03113i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7556 | −0.878699 | −0.439350 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439350 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(614\) | 20.7391 | + | 28.0881i | 0.836961 | + | 1.13354i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.2483 | + | 2.04239i | −0.412917 | + | 0.0822901i | ||||
\(617\) | −21.7038 | −0.873764 | −0.436882 | − | 0.899519i | \(-0.643917\pi\) | ||||
−0.436882 | + | 0.899519i | \(0.643917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.6385 | −1.03050 | −0.515250 | − | 0.857040i | \(-0.672301\pi\) | ||||
−0.515250 | + | 0.857040i | \(0.672301\pi\) | |||||||
\(620\) | 48.8122 | + | 15.0340i | 1.96035 | + | 0.603782i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.2004 | + | 36.8389i | 1.09064 | + | 1.47711i | ||||
\(623\) | 17.4210 | + | 2.46422i | 0.697956 | + | 0.0987269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1459 | −1.24584 | ||||||||
\(626\) | 9.95560 | − | 7.35081i | 0.397906 | − | 0.293797i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −35.9389 | − | 11.0691i | −1.43412 | − | 0.441705i | ||||
\(629\) | − | 39.8834i | − | 1.59026i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.4513i | − | 1.21225i | −0.795370 | − | 0.606124i | \(-0.792724\pi\) | ||
0.795370 | − | 0.606124i | \(-0.207276\pi\) | |||||||
\(632\) | −11.3112 | − | 32.2600i | −0.449934 | − | 1.28323i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.1400 | − | 21.8593i | −0.641001 | − | 0.868142i | ||||
\(635\) | −42.7830 | −1.69779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.98834 | + | 20.7439i | −0.237267 | + | 0.821905i | ||||
\(638\) | 7.78987 | − | 5.75172i | 0.308404 | − | 0.227713i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.80166 | − | 29.2889i | 0.308388 | − | 1.15775i | ||||
\(641\) | 10.6765 | 0.421695 | 0.210847 | − | 0.977519i | \(-0.432378\pi\) | ||||
0.210847 | + | 0.977519i | \(0.432378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.3693 | −0.763850 | −0.381925 | − | 0.924193i | \(-0.624739\pi\) | ||||
−0.381925 | + | 0.924193i | \(0.624739\pi\) | |||||||
\(644\) | 3.14264 | − | 6.68758i | 0.123837 | − | 0.263528i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.7326 | − | 9.40123i | 0.500958 | − | 0.369887i | ||||
\(647\) | 13.3633 | 0.525365 | 0.262683 | − | 0.964882i | \(-0.415393\pi\) | ||||
0.262683 | + | 0.964882i | \(0.415393\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17.0638i | − | 0.669811i | ||||||
\(650\) | −7.64084 | + | 5.64168i | −0.299698 | + | 0.221285i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.480355 | + | 0.147948i | 0.0188121 | + | 0.00579410i | ||||
\(653\) | 15.2574 | 0.597068 | 0.298534 | − | 0.954399i | \(-0.403502\pi\) | ||||
0.298534 | + | 0.954399i | \(0.403502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.86772i | 0.190197i | ||||||||
\(656\) | −1.56089 | + | 2.29356i | −0.0609425 | + | 0.0895483i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.2004 | + | 14.7007i | −1.06038 | + | 0.573095i | ||||
\(659\) | 3.36337i | 0.131018i | 0.997852 | + | 0.0655092i | \(0.0208672\pi\) | ||||
−0.997852 | + | 0.0655092i | \(0.979133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.251311i | 0.00977487i | 0.999988 | + | 0.00488744i | \(0.00155573\pi\) | ||||
−0.999988 | + | 0.00488744i | \(0.998444\pi\) | |||||||
\(662\) | 7.50395 | − | 5.54061i | 0.291649 | − | 0.215342i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.4093 | + | 5.40287i | −0.597995 | + | 0.209672i | ||||
\(665\) | −13.4647 | − | 1.90461i | −0.522140 | − | 0.0738575i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.84706i | 0.265119i | ||||||||
\(668\) | −8.26340 | + | 26.8294i | −0.319720 | + | 1.03806i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.94149 | + | 9.40123i | 0.268173 | + | 0.363201i | ||||
\(671\) | −17.9928 | −0.694604 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6767 | −0.450102 | −0.225051 | − | 0.974347i | \(-0.572255\pi\) | ||||
−0.225051 | + | 0.974347i | \(0.572255\pi\) | |||||||
\(674\) | 14.0067 | + | 18.9700i | 0.539518 | + | 0.730699i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.05240 | + | 6.66369i | −0.0789385 | + | 0.256296i | ||||
\(677\) | 12.0082i | 0.461512i | 0.973012 | + | 0.230756i | \(0.0741200\pi\) | ||||
−0.973012 | + | 0.230756i | \(0.925880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.7543 | − | 4.77459i | −1.29537 | − | 0.183232i | ||||
\(680\) | 41.7133 | − | 14.6257i | 1.59963 | − | 0.560871i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.1439 | + | 11.1816i | −0.579890 | + | 0.428167i | ||||
\(683\) | − | 20.6345i | − | 0.789556i | −0.918777 | − | 0.394778i | \(-0.870822\pi\) | ||
0.918777 | − | 0.394778i | \(-0.129178\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.7412i | 1.93872i | ||||||||
\(686\) | −25.5916 | + | 5.57388i | −0.977093 | + | 0.212812i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.52628 | + | 2.24271i | −0.0581890 | + | 0.0855024i | ||||
\(689\) | − | 32.9308i | − | 1.25456i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5756 | −0.478398 | −0.239199 | − | 0.970971i | \(-0.576885\pi\) | ||||
−0.239199 | + | 0.970971i | \(0.576885\pi\) | |||||||
\(692\) | −28.3292 | − | 8.72533i | −1.07691 | − | 0.331687i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.88501 | + | 2.13017i | −0.109514 | + | 0.0808603i | ||||
\(695\) | 40.9571i | 1.55359i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.04593 | −0.153250 | ||||||||
\(698\) | −10.8641 | + | 8.02158i | −0.411211 | + | 0.303621i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.4278 | − | 4.90025i | −0.394133 | − | 0.185212i | ||||
\(701\) | −39.4229 | −1.48898 | −0.744491 | − | 0.667633i | \(-0.767308\pi\) | ||||
−0.744491 | + | 0.667633i | \(0.767308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1170 | 0.494718 | ||||||||
\(704\) | 6.97628 | + | 8.72533i | 0.262928 | + | 0.328848i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.72870 | − | 2.75312i | 0.140331 | − | 0.103615i | ||||
\(707\) | −37.0098 | − | 5.23509i | −1.39190 | − | 0.196886i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3733 | 0.539802 | 0.269901 | − | 0.962888i | \(-0.413009\pi\) | ||||
0.269901 | + | 0.962888i | \(0.413009\pi\) | |||||||
\(710\) | 22.0439 | + | 29.8553i | 0.827293 | + | 1.12045i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.22350 | − | 17.7498i | −0.233236 | − | 0.665200i | ||||
\(713\) | − | 13.3110i | − | 0.498502i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 11.5392i | − | 0.431541i | ||||||
\(716\) | −26.5686 | − | 8.18305i | −0.992913 | − | 0.305815i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.2504 | − | 9.78354i | 0.494500 | − | 0.365118i | ||||
\(719\) | −38.8268 | −1.44799 | −0.723997 | − | 0.689803i | \(-0.757697\pi\) | ||||
−0.723997 | + | 0.689803i | \(0.757697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.06167 | + | 14.5751i | −0.0767805 | + | 0.542805i | ||||
\(722\) | −12.8686 | − | 17.4287i | −0.478921 | − | 0.648628i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.78448 | − | 3.01360i | −0.363637 | − | 0.111999i | ||||
\(725\) | 10.6765 | 0.396514 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.9015 | 1.07190 | 0.535949 | − | 0.844251i | \(-0.319954\pi\) | ||||
0.535949 | + | 0.844251i | \(0.319954\pi\) | |||||||
\(728\) | 22.6366 | − | 4.51124i | 0.838968 | − | 0.167198i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.3174 | − | 18.0365i | −0.492899 | − | 0.667560i | ||||
\(731\) | −3.95623 | −0.146326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.2074i | 0.967993i | 0.875070 | + | 0.483996i | \(0.160815\pi\) | ||||
−0.875070 | + | 0.483996i | \(0.839185\pi\) | |||||||
\(734\) | 22.2701 | + | 30.1616i | 0.822005 | + | 1.11329i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.89352 | + | 0.303684i | −0.290959 | + | 0.0111939i | ||||
\(737\) | −4.30717 | −0.158657 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.0351i | 1.54629i | 0.634232 | + | 0.773143i | \(0.281316\pi\) | ||||
−0.634232 | + | 0.773143i | \(0.718684\pi\) | |||||||
\(740\) | 35.0108 | + | 10.7833i | 1.28702 | + | 0.396400i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.1434 | − | 18.9936i | 1.29015 | − | 0.697278i | ||||
\(743\) | 41.3642i | 1.51750i | 0.651379 | + | 0.758752i | \(0.274191\pi\) | ||||
−0.651379 | + | 0.758752i | \(0.725809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 46.6069i | − | 1.70755i | ||||||
\(746\) | 2.99361 | + | 4.05441i | 0.109604 | + | 0.148443i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.79555 | + | 15.5701i | −0.175343 | + | 0.569299i | ||||
\(749\) | 19.5117 | + | 2.75996i | 0.712941 | + | 0.100847i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.6117i | 0.715640i | 0.933791 | + | 0.357820i | \(0.116480\pi\) | ||||
−0.933791 | + | 0.357820i | \(0.883520\pi\) | |||||||
\(752\) | 27.3258 | + | 18.5967i | 0.996471 | + | 0.678153i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.2063 | + | 12.7044i | −0.626617 | + | 0.462669i | ||||
\(755\) | −22.9732 | −0.836082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.86852 | 0.213295 | 0.106647 | − | 0.994297i | \(-0.465988\pi\) | ||||
0.106647 | + | 0.994297i | \(0.465988\pi\) | |||||||
\(758\) | 10.6643 | − | 7.87409i | 0.387345 | − | 0.286000i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.81017 | + | 13.7189i | 0.174483 | + | 0.497635i | ||||
\(761\) | 16.1131i | 0.584101i | 0.956403 | + | 0.292050i | \(0.0943375\pi\) | ||||
−0.956403 | + | 0.292050i | \(0.905662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.95407 | − | 35.0231i | 0.179349 | − | 1.26792i | ||||
\(764\) | 10.2238 | + | 3.14890i | 0.369884 | + | 0.113923i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.32335 | + | 4.50099i | 0.120077 | + | 0.162627i | ||||
\(767\) | 37.6906i | 1.36093i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.3589i | 1.38326i | 0.722254 | + | 0.691628i | \(0.243106\pi\) | ||||
−0.722254 | + | 0.691628i | \(0.756894\pi\) | |||||||
\(770\) | 12.3145 | − | 6.65551i | 0.443784 | − | 0.239848i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.30889 | − | 4.24968i | 0.0471080 | − | 0.152949i | ||||
\(773\) | 8.12153i | 0.292111i | 0.989276 | + | 0.146056i | \(0.0466578\pi\) | ||||
−0.989276 | + | 0.146056i | \(0.953342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.7556 | −0.745562 | ||||||||
\(776\) | 12.0585 | + | 34.3913i | 0.432873 | + | 1.23458i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.82259 | − | 3.82279i | −0.101195 | − | 0.137054i | ||||
\(779\) | − | 1.33064i | − | 0.0476752i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6782 | −0.489443 | ||||||||
\(782\) | −6.84282 | − | 9.26760i | −0.244699 | − | 0.331409i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17.8706 | + | 21.5556i | 0.638234 | + | 0.769842i | ||||
\(785\) | 50.3731 | 1.79789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.54925 | −0.233455 | −0.116728 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116728 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(788\) | −14.0366 | + | 45.5736i | −0.500032 | + | 1.62349i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.2004 | + | 36.8389i | 0.967746 | + | 1.31067i | ||||
\(791\) | −1.24511 | + | 8.80240i | −0.0442711 | + | 0.312977i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.7426 | 1.41130 | ||||||||
\(794\) | −28.7464 | + | 21.2252i | −1.02017 | + | 0.753254i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.3298 | − | 33.5386i | 0.366131 | − | 1.18875i | ||||
\(797\) | 10.0227i | 0.355022i | 0.984119 | + | 0.177511i | \(0.0568046\pi\) | ||||
−0.984119 | + | 0.177511i | \(0.943195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.2039i | 1.70533i | ||||||||
\(800\) | 0.473527 | + | 12.3082i | 0.0167417 | + | 0.435160i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.0230 | + | 40.6617i | 1.06015 | + | 1.43582i | ||||
\(803\) | 8.26340 | 0.291609 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.38629 | + | 9.80049i | −0.0488604 | + | 0.345422i | ||||
\(806\) | 33.4499 | − | 24.6981i | 1.17822 | − | 0.869953i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.2215 | + | 37.7083i | 0.465130 | + | 1.32657i | ||||
\(809\) | −37.9569 | −1.33449 | −0.667246 | − | 0.744837i | \(-0.732527\pi\) | ||||
−0.667246 | + | 0.744837i | \(0.732527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.8056 | −0.800812 | −0.400406 | − | 0.916338i | \(-0.631131\pi\) | ||||
−0.400406 | + | 0.916338i | \(0.631131\pi\) | |||||||
\(812\) | −23.4822 | − | 11.0348i | −0.824064 | − | 0.387246i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.8620 | + | 8.02009i | −0.380715 | + | 0.281104i | ||||
\(815\) | −0.673280 | −0.0235840 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.30114i | − | 0.0455212i | ||||||
\(818\) | 18.7908 | − | 13.8744i | 0.657006 | − | 0.485106i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.09390 | − | 3.55163i | 0.0382005 | − | 0.124028i | ||||
\(821\) | 29.9387 | 1.04487 | 0.522433 | − | 0.852680i | \(-0.325024\pi\) | ||||
0.522433 | + | 0.852680i | \(0.325024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.28591i | 0.0796818i | 0.999206 | + | 0.0398409i | \(0.0126851\pi\) | ||||
−0.999206 | + | 0.0398409i | \(0.987315\pi\) | |||||||
\(824\) | 14.8502 | − | 5.20684i | 0.517330 | − | 0.181389i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.2230 | + | 21.7389i | −1.39954 | + | 0.756395i | ||||
\(827\) | − | 21.3188i | − | 0.741326i | −0.928767 | − | 0.370663i | \(-0.879130\pi\) | ||
0.928767 | − | 0.370663i | \(-0.120870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.58181i | 0.0896698i | 0.998994 | + | 0.0448349i | \(0.0142762\pi\) | ||||
−0.998994 | + | 0.0448349i | \(0.985724\pi\) | |||||||
\(830\) | 17.5964 | − | 12.9925i | 0.610781 | − | 0.450976i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.4093 | − | 19.2726i | −0.534220 | − | 0.668156i | ||||
\(833\) | −11.3255 | + | 39.2320i | −0.392404 | + | 1.35931i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 37.6049i | − | 1.30137i | ||||||
\(836\) | −5.12076 | − | 1.57718i | −0.177105 | − | 0.0545479i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.1145 | − | 20.4703i | −0.522120 | − | 0.707136i | ||||
\(839\) | −46.7392 | −1.61362 | −0.806809 | − | 0.590813i | \(-0.798807\pi\) | ||||
−0.806809 | + | 0.590813i | \(0.798807\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.95781 | −0.170959 | ||||||||
\(842\) | 28.5025 | + | 38.6025i | 0.982261 | + | 1.33033i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.19186 | − | 2.21508i | −0.247554 | − | 0.0762461i | ||||
\(845\) | − | 9.34004i | − | 0.321307i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.35354 | − | 23.7081i | 0.115229 | − | 0.814618i | ||||
\(848\) | −35.3055 | − | 24.0273i | −1.21239 | − | 0.825101i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.4508 | + | 10.6698i | −0.495657 | + | 0.365973i | ||||
\(851\) | − | 9.54741i | − | 0.327281i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.547208i | − | 0.0187360i | −0.999956 | − | 0.00936801i | \(-0.997018\pi\) | ||
0.999956 | − | 0.00936801i | \(-0.00298198\pi\) | |||||||
\(854\) | 22.9225 | + | 42.4129i | 0.784393 | + | 1.45134i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.97040 | − | 19.8799i | −0.238243 | − | 0.679482i | ||||
\(857\) | 1.20759i | 0.0412506i | 0.999787 | + | 0.0206253i | \(0.00656571\pi\) | ||||
−0.999787 | + | 0.0206253i | \(0.993434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0474 | −0.956966 | −0.478483 | − | 0.878097i | \(-0.658813\pi\) | ||||
−0.478483 | + | 0.878097i | \(0.658813\pi\) | |||||||
\(860\) | 1.06964 | − | 3.47289i | 0.0364745 | − | 0.118425i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.8976 | + | 17.6450i | −0.813955 | + | 0.600991i | ||||
\(863\) | − | 42.8853i | − | 1.45983i | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||
0.683537 | − | 0.729916i | \(-0.260441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.7071 | 1.35008 | ||||||||
\(866\) | 14.9450 | − | 11.0348i | 0.507853 | − | 0.374978i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 45.6506 | + | 21.4522i | 1.54948 | + | 0.728136i | ||||
\(869\) | −16.8777 | −0.572538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.51370 | 0.322359 | ||||||||
\(872\) | −35.6841 | + | 12.5117i | −1.20842 | + | 0.423701i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.04797 | − | 2.25049i | 0.103099 | − | 0.0761241i | ||||
\(875\) | −19.8097 | − | 2.80212i | −0.669692 | − | 0.0947288i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.8330 | 0.635944 | 0.317972 | − | 0.948100i | \(-0.396998\pi\) | ||||
0.317972 | + | 0.948100i | \(0.396998\pi\) | |||||||
\(878\) | −5.61200 | − | 7.60064i | −0.189396 | − | 0.256509i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.3713 | − | 8.41935i | −0.417037 | − | 0.283816i | ||||
\(881\) | 24.1116i | 0.812341i | 0.913797 | + | 0.406171i | \(0.133136\pi\) | ||||
−0.913797 | + | 0.406171i | \(0.866864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.26525i | − | 0.143537i | −0.997421 | − | 0.0717686i | \(-0.977136\pi\) | ||
0.997421 | − | 0.0717686i | \(-0.0228643\pi\) | |||||||
\(884\) | 10.5924 | − | 34.3913i | 0.356263 | − | 1.15671i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.4087 | + | 29.0978i | −1.32396 | + | 0.977560i | ||||
\(887\) | −22.3000 | −0.748760 | −0.374380 | − | 0.927275i | \(-0.622144\pi\) | ||||
−0.374380 | + | 0.927275i | \(0.622144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.8345 | − | 5.91755i | −1.40308 | − | 0.198468i | ||||
\(890\) | 14.9659 | + | 20.2691i | 0.501658 | + | 0.679423i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.36129 | − | 20.6537i | 0.212992 | − | 0.691537i | ||||
\(893\) | −15.8535 | −0.530518 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.2393 | 1.24477 | ||||||||
\(896\) | 11.6798 | − | 27.5605i | 0.390195 | − | 0.920732i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.55332 | + | 4.81246i | 0.118576 | + | 0.160594i | ||||
\(899\) | −46.7392 | −1.55884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 62.2804i | − | 2.07486i | ||||||
\(902\) | 0.813589 | + | 1.10189i | 0.0270896 | + | 0.0366889i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.96853 | − | 3.14459i | 0.298289 | − | 0.104587i | ||||
\(905\) | 13.7142 | 0.455876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 58.1354i | − | 1.93036i | −0.261595 | − | 0.965178i | \(-0.584249\pi\) | ||
0.261595 | − | 0.965178i | \(-0.415751\pi\) | |||||||
\(908\) | −14.1977 | + | 46.0969i | −0.471169 | + | 1.52978i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.2004 | + | 14.7007i | −0.901684 | + | 0.487325i | ||||
\(911\) | − | 50.9890i | − | 1.68934i | −0.535286 | − | 0.844671i | \(-0.679796\pi\) | ||
0.535286 | − | 0.844671i | \(-0.320204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.06179i | 0.266806i | ||||||||
\(914\) | −12.8123 | − | 17.3524i | −0.423794 | − | 0.573967i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −43.8411 | − | 13.5030i | −1.44855 | − | 0.446150i | ||||
\(917\) | −0.673280 | + | 4.75980i | −0.0222337 | + | 0.157182i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.7492i | − | 0.915361i | −0.889117 | − | 0.457681i | \(-0.848680\pi\) | ||
0.889117 | − | 0.457681i | \(-0.151320\pi\) | |||||||
\(920\) | 9.98546 | − | 3.50115i | 0.329211 | − | 0.115429i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.4613 | − | 12.1544i | 0.542124 | − | 0.400282i | ||||
\(923\) | 30.2124 | 0.994454 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.8870 | −0.489483 | ||||||||
\(926\) | 11.4359 | − | 8.44380i | 0.375807 | − | 0.277481i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.06633 | + | 27.7167i | 0.0350040 | + | 0.909844i | ||||
\(929\) | − | 47.6636i | − | 1.56379i | −0.623408 | − | 0.781896i | \(-0.714253\pi\) | ||
0.623408 | − | 0.781896i | \(-0.285747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9028 | − | 3.72476i | −0.422872 | − | 0.122074i | ||||
\(932\) | 0.512108 | − | 1.66270i | 0.0167747 | − | 0.0544636i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.3174 | − | 18.0365i | −0.435759 | − | 0.590172i | ||||
\(935\) | − | 21.8235i | − | 0.713705i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42.7240i | − | 1.39573i | −0.716229 | − | 0.697866i | \(-0.754133\pi\) | ||
0.716229 | − | 0.697866i | \(-0.245867\pi\) | |||||||
\(938\) | 5.48726 | + | 10.1529i | 0.179165 | + | 0.331505i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −42.3148 | − | 13.0329i | −1.38016 | − | 0.425085i | ||||
\(941\) | − | 25.7449i | − | 0.839259i | −0.907696 | − | 0.419629i | \(-0.862160\pi\) | ||
0.907696 | − | 0.419629i | \(-0.137840\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.968526 | −0.0315395 | ||||||||
\(944\) | 40.4085 | + | 27.5002i | 1.31519 | + | 0.895055i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.795552 | + | 1.07746i | 0.0258656 | + | 0.0350312i | ||||
\(947\) | 36.2740i | 1.17875i | 0.807861 | + | 0.589373i | \(0.200625\pi\) | ||||
−0.807861 | + | 0.589373i | \(0.799375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2522 | −0.592493 | ||||||||
\(950\) | −3.50914 | − | 4.75262i | −0.113852 | − | 0.154195i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 42.8115 | − | 8.53188i | 1.38753 | − | 0.276520i | ||||
\(953\) | 18.0700 | 0.585344 | 0.292672 | − | 0.956213i | \(-0.405456\pi\) | ||||
0.292672 | + | 0.956213i | \(0.405456\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.3300 | −0.463707 | ||||||||
\(956\) | −40.3313 | − | 12.4220i | −1.30441 | − | 0.401755i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.05257 | + | 4.13426i | 0.0986240 | + | 0.133572i | ||||
\(959\) | −7.01828 | + | 49.6162i | −0.226632 | + | 1.60219i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.8634 | 1.93108 | ||||||||
\(962\) | 23.9922 | − | 17.7148i | 0.773538 | − | 0.571149i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.89556 | − | 1.81582i | −0.189883 | − | 0.0584836i | ||||
\(965\) | 5.95648i | 0.191746i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.3843i | − | 0.687672i | −0.939030 | − | 0.343836i | \(-0.888274\pi\) | ||
0.939030 | − | 0.343836i | \(-0.111726\pi\) | |||||||
\(968\) | −24.1555 | + | 8.46952i | −0.776387 | + | 0.272221i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.9974 | − | 39.2728i | −0.931052 | − | 1.26097i | ||||
\(971\) | 7.23918 | 0.232316 | 0.116158 | − | 0.993231i | \(-0.462942\pi\) | ||||
0.116158 | + | 0.993231i | \(0.462942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.66499 | + | 40.0490i | −0.181611 | + | 1.28391i | ||||
\(974\) | 6.59548 | − | 4.86983i | 0.211333 | − | 0.156040i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.9974 | − | 42.6085i | 0.928185 | − | 1.36387i | ||||
\(977\) | −34.2458 | −1.09562 | −0.547810 | − | 0.836603i | \(-0.684538\pi\) | ||||
−0.547810 | + | 0.836603i | \(0.684538\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.28629 | −0.296791 | ||||||||
\(980\) | −31.3770 | − | 20.5489i | −1.00230 | − | 0.656412i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.8180 | − | 9.46428i | 0.409038 | − | 0.302017i | ||||
\(983\) | −7.23918 | −0.230894 | −0.115447 | − | 0.993314i | \(-0.536830\pi\) | ||||
−0.115447 | + | 0.993314i | \(0.536830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 63.8774i | − | 2.03530i | ||||||
\(986\) | −32.5415 | + | 24.0273i | −1.03633 | + | 0.765185i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.3108 | + | 3.48369i | 0.359843 | + | 0.110831i | ||||
\(989\) | −0.947053 | −0.0301145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.633615i | 0.0201274i | 0.999949 | + | 0.0100637i | \(0.00320343\pi\) | ||||
−0.999949 | + | 0.0100637i | \(0.996797\pi\) | |||||||
\(992\) | −2.07300 | − | 53.8826i | −0.0658177 | − | 1.71077i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17.4258 | + | 32.2424i | 0.552711 | + | 1.02267i | ||||
\(995\) | 47.0088i | 1.49028i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.9348i | − | 0.441318i | −0.975351 | − | 0.220659i | \(-0.929179\pi\) | ||
0.975351 | − | 0.220659i | \(-0.0708208\pi\) | |||||||
\(998\) | 23.5065 | − | 17.3562i | 0.744085 | − | 0.549402i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.b.d.55.8 | yes | 12 | |
3.2 | odd | 2 | inner | 756.2.b.d.55.5 | yes | 12 | |
4.3 | odd | 2 | 756.2.b.c.55.7 | yes | 12 | ||
7.6 | odd | 2 | 756.2.b.c.55.8 | yes | 12 | ||
12.11 | even | 2 | 756.2.b.c.55.6 | yes | 12 | ||
21.20 | even | 2 | 756.2.b.c.55.5 | ✓ | 12 | ||
28.27 | even | 2 | inner | 756.2.b.d.55.7 | yes | 12 | |
84.83 | odd | 2 | inner | 756.2.b.d.55.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.b.c.55.5 | ✓ | 12 | 21.20 | even | 2 | ||
756.2.b.c.55.6 | yes | 12 | 12.11 | even | 2 | ||
756.2.b.c.55.7 | yes | 12 | 4.3 | odd | 2 | ||
756.2.b.c.55.8 | yes | 12 | 7.6 | odd | 2 | ||
756.2.b.d.55.5 | yes | 12 | 3.2 | odd | 2 | inner | |
756.2.b.d.55.6 | yes | 12 | 84.83 | odd | 2 | inner | |
756.2.b.d.55.7 | yes | 12 | 28.27 | even | 2 | inner | |
756.2.b.d.55.8 | yes | 12 | 1.1 | even | 1 | trivial |