Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(181,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.t (of order \(4\), degree \(2\), 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.541 |
Dual form | 720.2.t.b.181.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.874559 | + | 1.11137i | −0.618406 | + | 0.785858i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.470294 | − | 1.94392i | −0.235147 | − | 0.971960i | ||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 2.57172 | + | 1.17740i | 0.909239 | + | 0.416274i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.167452 | − | 1.40426i | −0.0529530 | − | 0.444068i | ||||
\(11\) | 0.808530 | − | 0.808530i | 0.243781 | − | 0.243781i | −0.574631 | − | 0.818412i | \(-0.694855\pi\) |
0.818412 | + | 0.574631i | \(0.194855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.749118 | − | 0.749118i | −0.207768 | − | 0.207768i | 0.595550 | − | 0.803318i | \(-0.296934\pi\) |
−0.803318 | + | 0.595550i | \(0.796934\pi\) | |||||||
\(14\) | 1.57172 | + | 1.23681i | 0.420059 | + | 0.330552i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.55765 | + | 1.82843i | −0.889412 | + | 0.457107i | ||||
\(17\) | −5.97186 | −1.44839 | −0.724195 | − | 0.689596i | \(-0.757788\pi\) | ||||
−0.724195 | + | 0.689596i | \(0.757788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.88784 | − | 1.88784i | −0.433100 | − | 0.433100i | 0.456582 | − | 0.889682i | \(-0.349074\pi\) |
−0.889682 | + | 0.456582i | \(0.849074\pi\) | |||||||
\(20\) | 1.70711 | + | 1.04201i | 0.381721 | + | 0.233001i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.191470 | + | 1.60568i | 0.0408216 | + | 0.342333i | ||||
\(23\) | 1.88118i | 0.392252i | 0.980579 | + | 0.196126i | \(0.0628362\pi\) | ||||
−0.980579 | + | 0.196126i | \(0.937164\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 1.48770 | − | 0.177401i | 0.291761 | − | 0.0347911i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.74912 | + | 0.665096i | −0.519534 | + | 0.125691i | ||||
\(29\) | −5.88784 | − | 5.88784i | −1.09334 | − | 1.09334i | −0.995169 | − | 0.0981752i | \(-0.968699\pi\) |
−0.0981752 | − | 0.995169i | \(-0.531301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61040 | 0.289236 | 0.144618 | − | 0.989488i | \(-0.453805\pi\) | ||||
0.144618 | + | 0.989488i | \(0.453805\pi\) | |||||||
\(32\) | 1.07931 | − | 5.55294i | 0.190797 | − | 0.981630i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.22274 | − | 6.63696i | 0.895693 | − | 1.13823i | ||||
\(35\) | 1.00000 | + | 1.00000i | 0.169031 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.69637 | − | 3.69637i | 0.607679 | − | 0.607679i | −0.334660 | − | 0.942339i | \(-0.608621\pi\) |
0.942339 | + | 0.334660i | \(0.108621\pi\) | |||||||
\(38\) | 3.74912 | − | 0.447065i | 0.608187 | − | 0.0725235i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.65103 | + | 0.985930i | −0.419164 | + | 0.155889i | ||||
\(41\) | − | 8.77215i | − | 1.36998i | −0.728553 | − | 0.684990i | \(-0.759807\pi\) | ||
0.728553 | − | 0.684990i | \(-0.240193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.744406 | + | 0.744406i | −0.113521 | + | 0.113521i | −0.761585 | − | 0.648065i | \(-0.775579\pi\) |
0.648065 | + | 0.761585i | \(0.275579\pi\) | |||||||
\(44\) | −1.95196 | − | 1.19147i | −0.294270 | − | 0.179621i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.09069 | − | 1.64520i | −0.308255 | − | 0.242571i | ||||
\(47\) | −13.5608 | −1.97804 | −0.989022 | − | 0.147771i | \(-0.952790\pi\) | ||||
−0.989022 | + | 0.147771i | \(0.952790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 1.11137 | + | 0.874559i | 0.157172 | + | 0.123681i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.10392 | + | 1.80853i | −0.153086 | + | 0.250798i | ||||
\(53\) | −0.863230 | + | 0.863230i | −0.118574 | + | 0.118574i | −0.763904 | − | 0.645330i | \(-0.776720\pi\) |
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14343i | 0.154181i | ||||||||
\(56\) | 1.66510 | − | 3.63696i | 0.222508 | − | 0.486009i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.6928 | − | 1.39432i | 1.53535 | − | 0.183083i | ||||
\(59\) | 10.7523 | − | 10.7523i | 1.39982 | − | 1.39982i | 0.599298 | − | 0.800526i | \(-0.295447\pi\) |
0.800526 | − | 0.599298i | \(-0.204553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.05588 | − | 9.05588i | −1.15949 | − | 1.15949i | −0.984586 | − | 0.174901i | \(-0.944040\pi\) |
−0.174901 | − | 0.984586i | \(-0.555960\pi\) | |||||||
\(62\) | −1.40839 | + | 1.78975i | −0.178865 | + | 0.227298i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.22746 | + | 6.05588i | 0.653432 | + | 0.756985i | ||||
\(65\) | 1.05941 | 0.131404 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.94725 | − | 2.94725i | −0.360064 | − | 0.360064i | 0.503772 | − | 0.863836i | \(-0.331945\pi\) |
−0.863836 | + | 0.503772i | \(0.831945\pi\) | |||||||
\(68\) | 2.80853 | + | 11.6088i | 0.340584 | + | 1.40778i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.98593 | + | 0.236813i | −0.237364 | + | 0.0283046i | ||||
\(71\) | 6.78863i | 0.805662i | 0.915274 | + | 0.402831i | \(0.131974\pi\) | ||||
−0.915274 | + | 0.402831i | \(0.868026\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.32666i | 0.272315i | 0.990687 | + | 0.136158i | \(0.0434754\pi\) | ||||
−0.990687 | + | 0.136158i | \(0.956525\pi\) | |||||||
\(74\) | 0.875348 | + | 7.34073i | 0.101757 | + | 0.853343i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.78197 | + | 4.55765i | −0.319114 | + | 0.522798i | ||||
\(77\) | −1.14343 | − | 1.14343i | −0.130306 | − | 0.130306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.27078 | −0.480500 | −0.240250 | − | 0.970711i | \(-0.577229\pi\) | ||||
−0.240250 | + | 0.970711i | \(0.577229\pi\) | |||||||
\(80\) | 1.22274 | − | 3.80853i | 0.136707 | − | 0.425807i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.74912 | + | 7.67176i | 1.07661 | + | 0.847204i | ||||
\(83\) | 3.11529 | + | 3.11529i | 0.341948 | + | 0.341948i | 0.857099 | − | 0.515151i | \(-0.172264\pi\) |
−0.515151 | + | 0.857099i | \(0.672264\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.22274 | − | 4.22274i | 0.458021 | − | 0.458021i | ||||
\(86\) | −0.176285 | − | 1.47834i | −0.0190093 | − | 0.159413i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.03127 | − | 1.12735i | 0.323135 | − | 0.120175i | ||||
\(89\) | − | 10.3172i | − | 1.09363i | −0.837255 | − | 0.546813i | \(-0.815841\pi\) | ||
0.837255 | − | 0.546813i | \(-0.184159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.05941 | + | 1.05941i | −0.111057 | + | 0.111057i | ||||
\(92\) | 3.65685 | − | 0.884705i | 0.381253 | − | 0.0922369i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.8597 | − | 15.0711i | 1.22323 | − | 1.55446i | ||||
\(95\) | 2.66981 | 0.273917 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.72256 | −0.377968 | −0.188984 | − | 0.981980i | \(-0.560519\pi\) | ||||
−0.188984 | + | 0.981980i | \(0.560519\pi\) | |||||||
\(98\) | −4.37279 | + | 5.55686i | −0.441719 | + | 0.561327i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.94392 | + | 0.470294i | −0.194392 | + | 0.0470294i | ||||
\(101\) | 5.29539 | − | 5.29539i | 0.526911 | − | 0.526911i | −0.392739 | − | 0.919650i | \(-0.628472\pi\) |
0.919650 | + | 0.392739i | \(0.128472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8503i | 1.56177i | 0.624672 | + | 0.780887i | \(0.285233\pi\) | ||||
−0.624672 | + | 0.780887i | \(0.714767\pi\) | |||||||
\(104\) | −1.04451 | − | 2.80853i | −0.102422 | − | 0.275399i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.204424 | − | 1.71431i | −0.0198554 | − | 0.166509i | ||||
\(107\) | 1.33962 | − | 1.33962i | 0.129506 | − | 0.129506i | −0.639383 | − | 0.768888i | \(-0.720810\pi\) |
0.768888 | + | 0.639383i | \(0.220810\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.67294 | − | 8.67294i | −0.830717 | − | 0.830717i | 0.156898 | − | 0.987615i | \(-0.449851\pi\) |
−0.987615 | + | 0.156898i | \(0.949851\pi\) | |||||||
\(110\) | −1.27078 | − | 1.00000i | −0.121164 | − | 0.0953463i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.58579 | + | 5.03127i | 0.244334 | + | 0.475411i | ||||
\(113\) | 15.3248 | 1.44164 | 0.720818 | − | 0.693124i | \(-0.243766\pi\) | ||||
0.720818 | + | 0.693124i | \(0.243766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.33019 | − | 1.33019i | −0.124041 | − | 0.124041i | ||||
\(116\) | −8.67647 | + | 14.2145i | −0.805590 | + | 1.31978i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.54627 | + | 21.3532i | 0.234403 | + | 1.96572i | ||||
\(119\) | 8.44549i | 0.774196i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.69256i | 0.881142i | ||||||||
\(122\) | 17.9844 | − | 2.14455i | 1.62823 | − | 0.194158i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.757359 | − | 3.13048i | −0.0680129 | − | 0.281125i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.18636 | 0.371480 | 0.185740 | − | 0.982599i | \(-0.440532\pi\) | ||||
0.185740 | + | 0.982599i | \(0.440532\pi\) | |||||||
\(128\) | −11.3021 | + | 0.513421i | −0.998970 | + | 0.0453804i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.926518 | + | 1.17740i | −0.0812610 | + | 0.103265i | ||||
\(131\) | −4.29734 | − | 4.29734i | −0.375460 | − | 0.375460i | 0.494001 | − | 0.869461i | \(-0.335534\pi\) |
−0.869461 | + | 0.494001i | \(0.835534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.66981 | + | 2.66981i | −0.231502 | + | 0.231502i | ||||
\(134\) | 5.85304 | − | 0.697947i | 0.505625 | − | 0.0602934i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.3579 | − | 7.03127i | −1.31693 | − | 0.602927i | ||||
\(137\) | 7.68499i | 0.656573i | 0.944578 | + | 0.328287i | \(0.106471\pi\) | ||||
−0.944578 | + | 0.328287i | \(0.893529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8776 | + | 10.8776i | −0.922630 | + | 0.922630i | −0.997215 | − | 0.0745848i | \(-0.976237\pi\) |
0.0745848 | + | 0.997215i | \(0.476237\pi\) | |||||||
\(140\) | 1.47363 | − | 2.41421i | 0.124544 | − | 0.204038i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.54469 | − | 5.93706i | −0.633137 | − | 0.498227i | ||||
\(143\) | −1.21137 | −0.101300 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.32666 | 0.691492 | ||||||||
\(146\) | −2.58579 | − | 2.03480i | −0.214001 | − | 0.168401i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.92382 | − | 5.44706i | −0.733534 | − | 0.447746i | ||||
\(149\) | −12.0559 | + | 12.0559i | −0.987656 | + | 0.987656i | −0.999925 | − | 0.0122684i | \(-0.996095\pi\) |
0.0122684 | + | 0.999925i | \(0.496095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.21450i | − | 0.342971i | −0.985187 | − | 0.171486i | \(-0.945143\pi\) | ||
0.985187 | − | 0.171486i | \(-0.0548567\pi\) | |||||||
\(152\) | −2.63224 | − | 7.07773i | −0.213503 | − | 0.574080i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.27078 | − | 0.270780i | 0.182985 | − | 0.0218201i | ||||
\(155\) | −1.13872 | + | 1.13872i | −0.0914643 | + | 0.0914643i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.53775 | − | 9.53775i | −0.761195 | − | 0.761195i | 0.215343 | − | 0.976538i | \(-0.430913\pi\) |
−0.976538 | + | 0.215343i | \(0.930913\pi\) | |||||||
\(158\) | 3.73505 | − | 4.74642i | 0.297144 | − | 0.377605i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.16333 | + | 4.68971i | 0.250083 | + | 0.370754i | ||||
\(161\) | 2.66038 | 0.209668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0805 | + | 11.0805i | 0.867891 | + | 0.867891i | 0.992239 | − | 0.124348i | \(-0.0396838\pi\) |
−0.124348 | + | 0.992239i | \(0.539684\pi\) | |||||||
\(164\) | −17.0524 | + | 4.12549i | −1.33157 | + | 0.322146i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.18676 | + | 0.737742i | −0.480186 | + | 0.0572599i | ||||
\(167\) | 11.7359i | 0.908150i | 0.890963 | + | 0.454075i | \(0.150030\pi\) | ||||
−0.890963 | + | 0.454075i | \(0.849970\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.8776i | − | 0.913665i | ||||||
\(170\) | 1.00000 | + | 8.38607i | 0.0766965 | + | 0.643183i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.79715 | + | 1.09698i | 0.137032 | + | 0.0836436i | ||||
\(173\) | −7.18766 | − | 7.18766i | −0.546468 | − | 0.546468i | 0.378950 | − | 0.925417i | \(-0.376285\pi\) |
−0.925417 | + | 0.378950i | \(0.876285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41421 | −0.106904 | ||||||||
\(176\) | −1.39813 | + | 4.35480i | −0.105388 | + | 0.328256i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.4663 | + | 9.02303i | 0.859434 | + | 0.676305i | ||||
\(179\) | 6.84832 | + | 6.84832i | 0.511868 | + | 0.511868i | 0.915098 | − | 0.403231i | \(-0.132113\pi\) |
−0.403231 | + | 0.915098i | \(0.632113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.26725 | − | 8.26725i | 0.614500 | − | 0.614500i | −0.329615 | − | 0.944115i | \(-0.606919\pi\) |
0.944115 | + | 0.329615i | \(0.106919\pi\) | |||||||
\(182\) | −0.250882 | − | 2.10392i | −0.0185966 | − | 0.155953i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.21490 | + | 4.83785i | −0.163284 | + | 0.356651i | ||||
\(185\) | 5.22746i | 0.384330i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.82843 | + | 4.82843i | −0.353090 | + | 0.353090i | ||||
\(188\) | 6.37755 | + | 26.3611i | 0.465131 | + | 1.92258i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.33490 | + | 2.96715i | −0.169392 | + | 0.215260i | ||||
\(191\) | −17.2435 | −1.24770 | −0.623849 | − | 0.781545i | \(-0.714432\pi\) | ||||
−0.623849 | + | 0.781545i | \(0.714432\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.8347 | −1.93160 | −0.965802 | − | 0.259281i | \(-0.916514\pi\) | ||||
−0.965802 | + | 0.259281i | \(0.916514\pi\) | |||||||
\(194\) | 3.25559 | − | 4.13714i | 0.233738 | − | 0.297030i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.35147 | − | 9.71960i | −0.167962 | − | 0.694257i | ||||
\(197\) | −0.821763 | + | 0.821763i | −0.0585482 | + | 0.0585482i | −0.735775 | − | 0.677226i | \(-0.763182\pi\) |
0.677226 | + | 0.735775i | \(0.263182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3263i | 1.44089i | 0.693512 | + | 0.720445i | \(0.256063\pi\) | ||||
−0.693512 | + | 0.720445i | \(0.743937\pi\) | |||||||
\(200\) | 1.17740 | − | 2.57172i | 0.0832548 | − | 0.181848i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.25402 | + | 10.5163i | 0.0882323 | + | 0.739922i | ||||
\(203\) | −8.32666 | + | 8.32666i | −0.584417 | + | 0.584417i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.20285 | + | 6.20285i | 0.433226 | + | 0.433226i | ||||
\(206\) | −17.6155 | − | 13.8620i | −1.22733 | − | 0.965811i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.03480 | + | 1.29539i | 0.279763 | + | 0.0898191i | ||||
\(209\) | −3.05275 | −0.211163 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0625 | + | 20.0625i | 1.38116 | + | 1.38116i | 0.842560 | + | 0.538603i | \(0.181048\pi\) |
0.538603 | + | 0.842560i | \(0.318952\pi\) | |||||||
\(212\) | 2.08402 | + | 1.27208i | 0.143131 | + | 0.0873667i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.317238 | + | 2.66038i | 0.0216860 | + | 0.181860i | ||||
\(215\) | − | 1.05275i | − | 0.0717969i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.27744i | − | 0.154603i | ||||||
\(218\) | 17.2239 | − | 2.05386i | 1.16655 | − | 0.139105i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.22274 | − | 0.537750i | 0.149857 | − | 0.0362551i | ||||
\(221\) | 4.47363 | + | 4.47363i | 0.300929 | + | 0.300929i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.6787 | 0.715099 | 0.357549 | − | 0.933894i | \(-0.383612\pi\) | ||||
0.357549 | + | 0.933894i | \(0.383612\pi\) | |||||||
\(224\) | −7.85304 | − | 1.52637i | −0.524703 | − | 0.101985i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.4024 | + | 17.0316i | −0.891517 | + | 1.13292i | ||||
\(227\) | −17.5514 | − | 17.5514i | −1.16492 | − | 1.16492i | −0.983383 | − | 0.181541i | \(-0.941891\pi\) |
−0.181541 | − | 0.983383i | \(-0.558109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.61077 | + | 9.61077i | −0.635098 | + | 0.635098i | −0.949342 | − | 0.314245i | \(-0.898249\pi\) |
0.314245 | + | 0.949342i | \(0.398249\pi\) | |||||||
\(230\) | 2.64167 | − | 0.315007i | 0.174186 | − | 0.0207709i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.20951 | − | 22.0742i | −0.538981 | − | 1.44924i | ||||
\(233\) | 16.4268i | 1.07615i | 0.842896 | + | 0.538077i | \(0.180849\pi\) | ||||
−0.842896 | + | 0.538077i | \(0.819151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.58892 | − | 9.58892i | 0.625512 | − | 0.625512i | ||||
\(236\) | −25.9582 | − | 15.8448i | −1.68974 | − | 1.03141i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.38607 | − | 7.38607i | −0.608409 | − | 0.478768i | ||||
\(239\) | 14.6439 | 0.947235 | 0.473618 | − | 0.880731i | \(-0.342948\pi\) | ||||
0.473618 | + | 0.880731i | \(0.342948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.3529 | 1.50430 | 0.752148 | − | 0.658995i | \(-0.229018\pi\) | ||||
0.752148 | + | 0.658995i | \(0.229018\pi\) | |||||||
\(242\) | −10.7720 | − | 8.47671i | −0.692453 | − | 0.544904i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.3450 | + | 21.8628i | −0.854325 | + | 1.39962i | ||||
\(245\) | −3.53553 | + | 3.53553i | −0.225877 | + | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.82843i | 0.179969i | ||||||||
\(248\) | 4.14148 | + | 1.89608i | 0.262984 | + | 0.120401i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.40426 | + | 0.167452i | −0.0888135 | + | 0.0105906i | ||||
\(251\) | 12.8085 | − | 12.8085i | 0.808467 | − | 0.808467i | −0.175935 | − | 0.984402i | \(-0.556295\pi\) |
0.984402 | + | 0.175935i | \(0.0562947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.52099 | + | 1.52099i | 0.0956236 | + | 0.0956236i | ||||
\(254\) | −3.66122 | + | 4.65260i | −0.229725 | + | 0.291930i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.31371 | − | 13.0098i | 0.582107 | − | 0.813112i | ||||
\(257\) | 22.3024 | 1.39119 | 0.695594 | − | 0.718436i | \(-0.255141\pi\) | ||||
0.695594 | + | 0.718436i | \(0.255141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.22746 | − | 5.22746i | −0.324818 | − | 0.324818i | ||||
\(260\) | −0.498235 | − | 2.05941i | −0.0308992 | − | 0.127719i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.53422 | − | 1.01767i | 0.527246 | − | 0.0628716i | ||||
\(263\) | 2.49471i | 0.153830i | 0.997038 | + | 0.0769151i | \(0.0245070\pi\) | ||||
−0.997038 | + | 0.0769151i | \(0.975493\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.22079i | − | 0.0749926i | ||||||
\(266\) | −0.632245 | − | 5.30205i | −0.0387654 | − | 0.325090i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.34315 | + | 7.11529i | −0.265300 | + | 0.434636i | ||||
\(269\) | −19.0031 | − | 19.0031i | −1.15864 | − | 1.15864i | −0.984768 | − | 0.173874i | \(-0.944372\pi\) |
−0.173874 | − | 0.984768i | \(-0.555628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.7918 | 1.32376 | 0.661878 | − | 0.749612i | \(-0.269760\pi\) | ||||
0.661878 | + | 0.749612i | \(0.269760\pi\) | |||||||
\(272\) | 21.2458 | − | 10.9191i | 1.28821 | − | 0.662068i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.54088 | − | 6.72098i | −0.515974 | − | 0.406029i | ||||
\(275\) | −0.808530 | − | 0.808530i | −0.0487562 | − | 0.0487562i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6401 | + | 11.6401i | −0.699385 | + | 0.699385i | −0.964278 | − | 0.264893i | \(-0.914663\pi\) |
0.264893 | + | 0.964278i | \(0.414663\pi\) | |||||||
\(278\) | −2.57597 | − | 21.6022i | −0.154496 | − | 1.29562i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.39432 | + | 3.74912i | 0.0833263 | + | 0.224053i | ||||
\(281\) | 1.55136i | 0.0925462i | 0.998929 | + | 0.0462731i | \(0.0147344\pi\) | ||||
−0.998929 | + | 0.0462731i | \(0.985266\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.5737 | − | 18.5737i | 1.10409 | − | 1.10409i | 0.110183 | − | 0.993911i | \(-0.464856\pi\) |
0.993911 | − | 0.110183i | \(-0.0351436\pi\) | |||||||
\(284\) | 13.1966 | − | 3.19265i | 0.783072 | − | 0.189449i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05941 | − | 1.34628i | 0.0626444 | − | 0.0796072i | ||||
\(287\) | −12.4057 | −0.732285 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.6631 | 1.09783 | ||||||||
\(290\) | −7.28216 | + | 9.25402i | −0.427623 | + | 0.543415i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.52284 | − | 1.09422i | 0.264679 | − | 0.0640341i | ||||
\(293\) | 10.5671 | − | 10.5671i | 0.617335 | − | 0.617335i | −0.327512 | − | 0.944847i | \(-0.606210\pi\) |
0.944847 | + | 0.327512i | \(0.106210\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.2060i | 0.885326i | ||||||||
\(296\) | 13.8581 | − | 5.15391i | 0.805487 | − | 0.299565i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.85499 | − | 23.9421i | −0.165385 | − | 1.38693i | ||||
\(299\) | 1.40922 | − | 1.40922i | 0.0814974 | − | 0.0814974i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.05275 | + | 1.05275i | 0.0606794 | + | 0.0606794i | ||||
\(302\) | 4.68388 | + | 3.68583i | 0.269527 | + | 0.212096i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.1680 | + | 3.26449i | 0.583177 | + | 0.187231i | ||||
\(305\) | 12.8070 | 0.733324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4584 | − | 11.4584i | −0.653968 | − | 0.653968i | 0.299978 | − | 0.953946i | \(-0.403021\pi\) |
−0.953946 | + | 0.299978i | \(0.903021\pi\) | |||||||
\(308\) | −1.68499 | + | 2.76049i | −0.0960114 | + | 0.157294i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.269664 | − | 2.26142i | −0.0153159 | − | 0.128440i | ||||
\(311\) | 6.80196i | 0.385704i | 0.981228 | + | 0.192852i | \(0.0617737\pi\) | ||||
−0.981228 | + | 0.192852i | \(0.938226\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.8382i | − | 0.895229i | −0.894227 | − | 0.447615i | \(-0.852274\pi\) | ||
0.894227 | − | 0.447615i | \(-0.147726\pi\) | |||||||
\(314\) | 18.9413 | − | 2.25866i | 1.06892 | − | 0.127464i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00852 | + | 8.30205i | 0.112988 | + | 0.467027i | ||||
\(317\) | 9.37665 | + | 9.37665i | 0.526645 | + | 0.526645i | 0.919570 | − | 0.392925i | \(-0.128537\pi\) |
−0.392925 | + | 0.919570i | \(0.628537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.52099 | −0.533073 | ||||||||
\(320\) | −7.97852 | − | 0.585786i | −0.446013 | − | 0.0327465i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.32666 | + | 2.95668i | −0.129660 | + | 0.164769i | ||||
\(323\) | 11.2739 | + | 11.2739i | 0.627297 | + | 0.627297i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.749118 | + | 0.749118i | −0.0415536 | + | 0.0415536i | ||||
\(326\) | −22.0051 | + | 2.62400i | −1.21875 | + | 0.145330i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.3283 | − | 22.5595i | 0.570287 | − | 1.24564i | ||||
\(329\) | 19.1778i | 1.05731i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.26059 | − | 9.26059i | 0.509008 | − | 0.509008i | −0.405214 | − | 0.914222i | \(-0.632803\pi\) |
0.914222 | + | 0.405214i | \(0.132803\pi\) | |||||||
\(332\) | 4.59078 | − | 7.52099i | 0.251952 | − | 0.412768i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.0429 | − | 10.2637i | −0.713677 | − | 0.561606i | ||||
\(335\) | 4.16804 | 0.227725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.99411 | 0.163099 | 0.0815497 | − | 0.996669i | \(-0.474013\pi\) | ||||
0.0815497 | + | 0.996669i | \(0.474013\pi\) | |||||||
\(338\) | 13.2005 | + | 10.3877i | 0.718011 | + | 0.565016i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.1946 | − | 6.22274i | −0.552880 | − | 0.337476i | ||||
\(341\) | 1.30205 | − | 1.30205i | 0.0705101 | − | 0.0705101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | −2.79086 | + | 1.03794i | −0.150473 | + | 0.0559618i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.2742 | − | 1.70213i | 0.767385 | − | 0.0915071i | ||||
\(347\) | 14.4455 | − | 14.4455i | 0.775474 | − | 0.775474i | −0.203583 | − | 0.979058i | \(-0.565259\pi\) |
0.979058 | + | 0.203583i | \(0.0652588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.63668 | − | 5.63668i | −0.301724 | − | 0.301724i | 0.539964 | − | 0.841688i | \(-0.318438\pi\) |
−0.841688 | + | 0.539964i | \(0.818438\pi\) | |||||||
\(350\) | 1.23681 | − | 1.57172i | 0.0661104 | − | 0.0840118i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.61706 | − | 5.36237i | −0.192790 | − | 0.285815i | ||||
\(353\) | 26.9058 | 1.43205 | 0.716025 | − | 0.698074i | \(-0.245960\pi\) | ||||
0.716025 | + | 0.698074i | \(0.245960\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.80029 | − | 4.80029i | −0.254773 | − | 0.254773i | ||||
\(356\) | −20.0559 | + | 4.85213i | −1.06296 | + | 0.257163i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.6003 | + | 1.62177i | −0.718798 | + | 0.0857133i | ||||
\(359\) | 14.7533i | 0.778649i | 0.921101 | + | 0.389325i | \(0.127292\pi\) | ||||
−0.921101 | + | 0.389325i | \(0.872708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.8721i | − | 0.624849i | ||||||
\(362\) | 1.95779 | + | 16.4182i | 0.102899 | + | 0.862921i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.55765 | + | 1.56118i | 0.134057 | + | 0.0818279i | ||||
\(365\) | −1.64520 | − | 1.64520i | −0.0861136 | − | 0.0861136i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.6779 | −1.81017 | −0.905086 | − | 0.425228i | \(-0.860194\pi\) | ||||
−0.905086 | + | 0.425228i | \(0.860194\pi\) | |||||||
\(368\) | −3.43959 | − | 6.69256i | −0.179301 | − | 0.348874i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.80965 | − | 4.57172i | −0.302029 | − | 0.237672i | ||||
\(371\) | 1.22079 | + | 1.22079i | 0.0633803 | + | 0.0633803i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8679 | − | 10.8679i | 0.562721 | − | 0.562721i | −0.367359 | − | 0.930079i | \(-0.619738\pi\) |
0.930079 | + | 0.367359i | \(0.119738\pi\) | |||||||
\(374\) | −1.14343 | − | 9.58892i | −0.0591256 | − | 0.495831i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −34.8745 | − | 15.9665i | −1.79851 | − | 0.823408i | ||||
\(377\) | 8.82137i | 0.454324i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9374 | − | 12.9374i | 0.664551 | − | 0.664551i | −0.291898 | − | 0.956449i | \(-0.594287\pi\) |
0.956449 | + | 0.291898i | \(0.0942868\pi\) | |||||||
\(380\) | −1.25559 | − | 5.18989i | −0.0644106 | − | 0.266236i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0805 | − | 19.1640i | 0.771585 | − | 0.980515i | ||||
\(383\) | 12.1814 | 0.622439 | 0.311219 | − | 0.950338i | \(-0.399263\pi\) | ||||
0.311219 | + | 0.950338i | \(0.399263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.61706 | 0.0824130 | ||||||||
\(386\) | 23.4685 | − | 29.8233i | 1.19452 | − | 1.51797i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.75070 | + | 7.23635i | 0.0888781 | + | 0.367370i | ||||
\(389\) | 2.57246 | − | 2.57246i | 0.130429 | − | 0.130429i | −0.638879 | − | 0.769308i | \(-0.720601\pi\) |
0.769308 | + | 0.638879i | \(0.220601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.2341i | − | 0.568134i | ||||||
\(392\) | 12.8586 | + | 5.88700i | 0.649457 | + | 0.297339i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.194604 | − | 1.63196i | −0.00980402 | − | 0.0822172i | ||||
\(395\) | 3.01990 | − | 3.01990i | 0.151948 | − | 0.151948i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.94753 | + | 8.94753i | 0.449064 | + | 0.449064i | 0.895043 | − | 0.445979i | \(-0.147145\pi\) |
−0.445979 | + | 0.895043i | \(0.647145\pi\) | |||||||
\(398\) | −22.5900 | − | 17.7765i | −1.13234 | − | 0.891056i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.82843 | + | 3.55765i | 0.0914214 | + | 0.177882i | ||||
\(401\) | −14.3306 | −0.715634 | −0.357817 | − | 0.933792i | \(-0.616479\pi\) | ||||
−0.357817 | + | 0.933792i | \(0.616479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20638 | − | 1.20638i | −0.0600939 | − | 0.0600939i | ||||
\(404\) | −12.7842 | − | 7.80342i | −0.636038 | − | 0.388235i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.97186 | − | 16.5362i | −0.0978618 | − | 0.820676i | ||||
\(407\) | − | 5.97725i | − | 0.296281i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.2019i | 0.553900i | 0.960884 | + | 0.276950i | \(0.0893237\pi\) | ||||
−0.960884 | + | 0.276950i | \(0.910676\pi\) | |||||||
\(410\) | −12.3184 | + | 1.46891i | −0.608363 | + | 0.0725445i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.8117 | − | 7.45429i | 1.51798 | − | 0.367246i | ||||
\(413\) | −15.2060 | − | 15.2060i | −0.748237 | − | 0.748237i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.40569 | −0.216267 | ||||||||
\(416\) | −4.96833 | + | 3.35127i | −0.243592 | + | 0.164310i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.66981 | − | 3.39274i | 0.130585 | − | 0.165944i | ||||
\(419\) | 12.6405 | + | 12.6405i | 0.617528 | + | 0.617528i | 0.944897 | − | 0.327369i | \(-0.106162\pi\) |
−0.327369 | + | 0.944897i | \(0.606162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.83862 | + | 2.83862i | −0.138346 | + | 0.138346i | −0.772888 | − | 0.634542i | \(-0.781189\pi\) |
0.634542 | + | 0.772888i | \(0.281189\pi\) | |||||||
\(422\) | −39.8428 | + | 4.75107i | −1.93952 | + | 0.231278i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.23635 | + | 1.20362i | −0.157171 | + | 0.0584527i | ||||
\(425\) | 5.97186i | 0.289678i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8070 | + | 12.8070i | −0.619772 | + | 0.619772i | ||||
\(428\) | −3.23412 | − | 1.97409i | −0.156327 | − | 0.0954214i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.16999 | + | 0.920690i | 0.0564222 | + | 0.0443996i | ||||
\(431\) | 29.9874 | 1.44444 | 0.722222 | − | 0.691662i | \(-0.243121\pi\) | ||||
0.722222 | + | 0.691662i | \(0.243121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.2176 | −1.11577 | −0.557884 | − | 0.829919i | \(-0.688387\pi\) | ||||
−0.557884 | + | 0.829919i | \(0.688387\pi\) | |||||||
\(434\) | 2.53109 | + | 1.99176i | 0.121496 | + | 0.0956075i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.7807 | + | 20.9383i | −0.612083 | + | 1.00276i | ||||
\(437\) | 3.55136 | − | 3.55136i | 0.169884 | − | 0.169884i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2110i | 0.535070i | 0.963548 | + | 0.267535i | \(0.0862092\pi\) | ||||
−0.963548 | + | 0.267535i | \(0.913791\pi\) | |||||||
\(440\) | −1.34628 | + | 2.94059i | −0.0641814 | + | 0.140187i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.88431 | + | 1.05941i | −0.422584 | + | 0.0503911i | ||||
\(443\) | −21.0684 | + | 21.0684i | −1.00099 | + | 1.00099i | −0.000992295 | 1.00000i | \(0.500316\pi\) | |
−1.00000 | 0.000992295i | \(0.999684\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.29539 | + | 7.29539i | 0.345835 | + | 0.345835i | ||||
\(446\) | −9.33915 | + | 11.8680i | −0.442222 | + | 0.561966i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.56431 | − | 7.39274i | 0.404626 | − | 0.349274i | ||||
\(449\) | −20.6970 | −0.976753 | −0.488376 | − | 0.872633i | \(-0.662411\pi\) | ||||
−0.488376 | + | 0.872633i | \(0.662411\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.09254 | − | 7.09254i | −0.333975 | − | 0.333975i | ||||
\(452\) | −7.20716 | − | 29.7902i | −0.338996 | − | 1.40121i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 34.8558 | − | 4.15639i | 1.63586 | − | 0.195069i | ||||
\(455\) | − | 1.49824i | − | 0.0702383i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7986i | 0.879362i | 0.898154 | + | 0.439681i | \(0.144909\pi\) | ||||
−0.898154 | + | 0.439681i | \(0.855091\pi\) | |||||||
\(458\) | −2.27595 | − | 19.0863i | −0.106348 | − | 0.891845i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.96021 | + | 3.21137i | −0.0913950 | + | 0.149731i | ||||
\(461\) | 1.68943 | + | 1.68943i | 0.0786844 | + | 0.0786844i | 0.745354 | − | 0.666669i | \(-0.232281\pi\) |
−0.666669 | + | 0.745354i | \(0.732281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.0434 | −1.76803 | −0.884014 | − | 0.467460i | \(-0.845169\pi\) | ||||
−0.884014 | + | 0.467460i | \(0.845169\pi\) | |||||||
\(464\) | 31.7123 | + | 10.1814i | 1.47221 | + | 0.472658i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.2562 | − | 14.3662i | −0.845704 | − | 0.665500i | ||||
\(467\) | −15.2247 | − | 15.2247i | −0.704515 | − | 0.704515i | 0.260861 | − | 0.965376i | \(-0.415993\pi\) |
−0.965376 | + | 0.260861i | \(0.915993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.16804 | + | 4.16804i | −0.192462 | + | 0.192462i | ||||
\(470\) | 2.27078 | + | 19.0429i | 0.104743 | + | 0.878385i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 40.3115 | − | 14.9920i | 1.85549 | − | 0.690064i | ||||
\(473\) | 1.20375i | 0.0553484i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.88784 | + | 1.88784i | −0.0866200 | + | 0.0866200i | ||||
\(476\) | 16.4173 | − | 3.97186i | 0.752488 | − | 0.182050i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8070 | + | 16.2748i | −0.585776 | + | 0.744393i | ||||
\(479\) | 13.0004 | 0.594002 | 0.297001 | − | 0.954877i | \(-0.404013\pi\) | ||||
0.297001 | + | 0.954877i | \(0.404013\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.53803 | −0.252512 | ||||||||
\(482\) | −20.4235 | + | 25.9538i | −0.930266 | + | 1.18216i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.8416 | − | 4.55835i | 0.856434 | − | 0.207198i | ||||
\(485\) | 2.63224 | − | 2.63224i | 0.119524 | − | 0.119524i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.1068i | − | 0.729868i | −0.931033 | − | 0.364934i | \(-0.881092\pi\) | ||
0.931033 | − | 0.364934i | \(-0.118908\pi\) | |||||||
\(488\) | −12.6268 | − | 33.9516i | −0.571587 | − | 1.53692i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.837260 | − | 7.02132i | −0.0378235 | − | 0.317191i | ||||
\(491\) | 16.9993 | − | 16.9993i | 0.767169 | − | 0.767169i | −0.210438 | − | 0.977607i | \(-0.567489\pi\) |
0.977607 | + | 0.210438i | \(0.0674891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 35.1614 | + | 35.1614i | 1.58359 | + | 1.58359i | ||||
\(494\) | −3.14343 | − | 2.47363i | −0.141430 | − | 0.111294i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.72922 | + | 2.94449i | −0.257250 | + | 0.132212i | ||||
\(497\) | 9.60058 | 0.430645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.60373 | − | 3.60373i | −0.161325 | − | 0.161325i | 0.621828 | − | 0.783154i | \(-0.286390\pi\) |
−0.783154 | + | 0.621828i | \(0.786390\pi\) | |||||||
\(500\) | 1.04201 | − | 1.70711i | 0.0466001 | − | 0.0763441i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.03322 | + | 25.4368i | 0.135379 | + | 1.13530i | ||||
\(503\) | − | 25.4482i | − | 1.13468i | −0.823484 | − | 0.567340i | \(-0.807972\pi\) | ||
0.823484 | − | 0.567340i | \(-0.192028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.48881i | 0.333248i | ||||||||
\(506\) | −3.02057 | + | 0.360189i | −0.134281 | + | 0.0160124i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.96882 | − | 8.13795i | −0.0873523 | − | 0.361063i | ||||
\(509\) | −8.08087 | − | 8.08087i | −0.358178 | − | 0.358178i | 0.504963 | − | 0.863141i | \(-0.331506\pi\) |
−0.863141 | + | 0.504963i | \(0.831506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.29040 | 0.145559 | ||||||||
\(512\) | 6.31333 | + | 21.7288i | 0.279013 | + | 0.960287i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.5048 | + | 24.7863i | −0.860319 | + | 1.09328i | ||||
\(515\) | −11.2078 | − | 11.2078i | −0.493876 | − | 0.493876i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.9643 | + | 10.9643i | −0.482209 | + | 0.482209i | ||||
\(518\) | 10.3814 | − | 1.23793i | 0.456131 | − | 0.0543915i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.72451 | + | 1.24735i | 0.119478 | + | 0.0547000i | ||||
\(521\) | 10.7981i | 0.473071i | 0.971623 | + | 0.236536i | \(0.0760120\pi\) | ||||
−0.971623 | + | 0.236536i | \(0.923988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.9785 | − | 17.9785i | 0.786146 | − | 0.786146i | −0.194714 | − | 0.980860i | \(-0.562378\pi\) |
0.980860 | + | 0.194714i | \(0.0623779\pi\) | |||||||
\(524\) | −6.33267 | + | 10.3747i | −0.276644 | + | 0.453221i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.77254 | − | 2.18177i | −0.120889 | − | 0.0951295i | ||||
\(527\) | −9.61706 | −0.418926 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4612 | 0.846138 | ||||||||
\(530\) | 1.35675 | + | 1.06765i | 0.0589336 | + | 0.0463759i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.44549 | + | 3.93430i | 0.279447 | + | 0.170573i | ||||
\(533\) | −6.57137 | + | 6.57137i | −0.284638 | + | 0.284638i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.89450i | 0.0819065i | ||||||||
\(536\) | −4.10940 | − | 11.0496i | −0.177499 | − | 0.477270i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.7389 | − | 4.50019i | 1.62704 | − | 0.194017i | ||||
\(539\) | 4.04265 | − | 4.04265i | 0.174129 | − | 0.174129i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.61666 | + | 6.61666i | 0.284473 | + | 0.284473i | 0.834890 | − | 0.550417i | \(-0.185531\pi\) |
−0.550417 | + | 0.834890i | \(0.685531\pi\) | |||||||
\(542\) | −19.0582 | + | 24.2188i | −0.818619 | + | 1.04028i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.44549 | + | 33.1614i | −0.276348 | + | 1.42178i | ||||
\(545\) | 12.2654 | 0.525392 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.62205 | − | 9.62205i | −0.411409 | − | 0.411409i | 0.470820 | − | 0.882229i | \(-0.343958\pi\) |
−0.882229 | + | 0.470820i | \(0.843958\pi\) | |||||||
\(548\) | 14.9390 | − | 3.61421i | 0.638163 | − | 0.154391i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.60568 | − | 0.191470i | 0.0684666 | − | 0.00816432i | ||||
\(551\) | 22.2306i | 0.947055i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.03979i | 0.256838i | ||||||||
\(554\) | −2.75652 | − | 23.1164i | −0.117113 | − | 0.982122i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.2610 | + | 16.0296i | 1.11371 | + | 0.679806i | ||||
\(557\) | 2.50137 | + | 2.50137i | 0.105986 | + | 0.105986i | 0.758111 | − | 0.652125i | \(-0.226122\pi\) |
−0.652125 | + | 0.758111i | \(0.726122\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.11529 | 0.0471719 | ||||||||
\(560\) | −5.38607 | − | 1.72922i | −0.227603 | − | 0.0730729i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.72413 | − | 1.35675i | −0.0727282 | − | 0.0572312i | ||||
\(563\) | 2.20547 | + | 2.20547i | 0.0929496 | + | 0.0929496i | 0.752053 | − | 0.659103i | \(-0.229064\pi\) |
−0.659103 | + | 0.752053i | \(0.729064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8363 | + | 10.8363i | −0.455885 | + | 0.455885i | ||||
\(566\) | 4.39850 | + | 36.8861i | 0.184883 | + | 1.55044i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.99294 | + | 17.4584i | −0.335376 | + | 0.732540i | ||||
\(569\) | − | 17.5569i | − | 0.736023i | −0.929821 | − | 0.368011i | \(-0.880039\pi\) | ||
0.929821 | − | 0.368011i | \(-0.119961\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.36237 | + | 5.36237i | −0.224408 | + | 0.224408i | −0.810352 | − | 0.585944i | \(-0.800724\pi\) |
0.585944 | + | 0.810352i | \(0.300724\pi\) | |||||||
\(572\) | 0.569699 | + | 2.35480i | 0.0238203 | + | 0.0984592i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.8495 | − | 13.7873i | 0.452850 | − | 0.575472i | ||||
\(575\) | 1.88118 | 0.0784504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.7422 | 0.572093 | 0.286047 | − | 0.958216i | \(-0.407659\pi\) | ||||
0.286047 | + | 0.958216i | \(0.407659\pi\) | |||||||
\(578\) | −16.3220 | + | 20.7417i | −0.678906 | + | 0.862740i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.91598 | − | 16.1864i | −0.162602 | − | 0.672102i | ||||
\(581\) | 4.40569 | − | 4.40569i | 0.182779 | − | 0.182779i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.39589i | 0.0578120i | ||||||||
\(584\) | −2.73941 | + | 5.98352i | −0.113358 | + | 0.247600i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.50242 | + | 20.9855i | 0.103374 | + | 0.866902i | ||||
\(587\) | −17.5608 | + | 17.5608i | −0.724811 | + | 0.724811i | −0.969581 | − | 0.244770i | \(-0.921288\pi\) |
0.244770 | + | 0.969581i | \(0.421288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.04017 | − | 3.04017i | −0.125268 | − | 0.125268i | ||||
\(590\) | −16.8995 | − | 13.2985i | −0.695741 | − | 0.547492i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.39184 | + | 19.9089i | −0.262703 | + | 0.818252i | ||||
\(593\) | −41.3973 | −1.69998 | −0.849992 | − | 0.526795i | \(-0.823394\pi\) | ||||
−0.849992 | + | 0.526795i | \(0.823394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.97186 | − | 5.97186i | −0.244822 | − | 0.244822i | ||||
\(596\) | 29.1055 | + | 17.7659i | 1.19221 | + | 0.727718i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.333722 | + | 2.79862i | 0.0136469 | + | 0.114444i | ||||
\(599\) | 36.7651i | 1.50218i | 0.660199 | + | 0.751090i | \(0.270472\pi\) | ||||
−0.660199 | + | 0.751090i | \(0.729528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3396i | 0.544134i | 0.962278 | + | 0.272067i | \(0.0877073\pi\) | ||||
−0.962278 | + | 0.272067i | \(0.912293\pi\) | |||||||
\(602\) | −2.09069 | + | 0.249304i | −0.0852100 | + | 0.0101609i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.19265 | + | 1.98205i | −0.333354 | + | 0.0806486i | ||||
\(605\) | −6.85367 | − | 6.85367i | −0.278641 | − | 0.278641i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.5393 | −0.711898 | −0.355949 | − | 0.934505i | \(-0.615842\pi\) | ||||
−0.355949 | + | 0.934505i | \(0.615842\pi\) | |||||||
\(608\) | −12.5206 | + | 8.44549i | −0.507778 | + | 0.342510i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.2004 | + | 14.2333i | −0.453492 | + | 0.576289i | ||||
\(611\) | 10.1586 | + | 10.1586i | 0.410974 | + | 0.410974i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.9538 | − | 14.9538i | 0.603978 | − | 0.603978i | −0.337388 | − | 0.941366i | \(-0.609543\pi\) |
0.941366 | + | 0.337388i | \(0.109543\pi\) | |||||||
\(614\) | 22.7557 | − | 2.71351i | 0.918344 | − | 0.109508i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.59431 | − | 4.28687i | −0.0642365 | − | 0.172723i | ||||
\(617\) | 7.04165i | 0.283486i | 0.989903 | + | 0.141743i | \(0.0452707\pi\) | ||||
−0.989903 | + | 0.141743i | \(0.954729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2931 | − | 14.2931i | 0.574490 | − | 0.574490i | −0.358890 | − | 0.933380i | \(-0.616845\pi\) |
0.933380 | + | 0.358890i | \(0.116845\pi\) | |||||||
\(620\) | 2.74912 | + | 1.67805i | 0.110407 | + | 0.0673921i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.55951 | − | 5.94871i | −0.303109 | − | 0.238522i | ||||
\(623\) | −14.5908 | −0.584567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 17.6022 | + | 13.8515i | 0.703524 | + | 0.553616i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0551 | + | 23.0262i | −0.560859 | + | 0.918844i | ||||
\(629\) | −22.0742 | + | 22.0742i | −0.880156 | + | 0.880156i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 41.3531i | − | 1.64624i | −0.567867 | − | 0.823121i | \(-0.692231\pi\) | ||
0.567867 | − | 0.823121i | \(-0.307769\pi\) | |||||||
\(632\) | −10.9832 | − | 5.02842i | −0.436890 | − | 0.200020i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.6214 | + | 2.22051i | −0.739549 | + | 0.0881878i | ||||
\(635\) | −2.96021 | + | 2.96021i | −0.117472 | + | 0.117472i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.74559 | − | 3.74559i | −0.148406 | − | 0.148406i | ||||
\(638\) | 8.32666 | − | 10.5814i | 0.329656 | − | 0.418920i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.62872 | − | 8.35480i | 0.301551 | − | 0.330253i | ||||
\(641\) | 14.3228 | 0.565715 | 0.282857 | − | 0.959162i | \(-0.408718\pi\) | ||||
0.282857 | + | 0.959162i | \(0.408718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4370 | + | 13.4370i | 0.529902 | + | 0.529902i | 0.920543 | − | 0.390641i | \(-0.127747\pi\) |
−0.390641 | + | 0.920543i | \(0.627747\pi\) | |||||||
\(644\) | −1.25116 | − | 5.17157i | −0.0493027 | − | 0.203789i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.3892 | + | 2.66981i | −0.880892 | + | 0.105042i | ||||
\(647\) | − | 17.3231i | − | 0.681043i | −0.940237 | − | 0.340521i | \(-0.889396\pi\) | ||
0.940237 | − | 0.340521i | \(-0.110604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17.3870i | − | 0.682501i | ||||||
\(650\) | −0.177401 | − | 1.48770i | −0.00695823 | − | 0.0583522i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.3285 | − | 26.7507i | 0.639473 | − | 1.04764i | ||||
\(653\) | −31.0148 | − | 31.0148i | −1.21370 | − | 1.21370i | −0.969800 | − | 0.243903i | \(-0.921572\pi\) |
−0.243903 | − | 0.969800i | \(-0.578428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.07736 | 0.237462 | ||||||||
\(656\) | 16.0392 | + | 31.2082i | 0.626227 | + | 1.21848i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −21.3137 | − | 16.7721i | −0.830895 | − | 0.653846i | ||||
\(659\) | −29.8050 | − | 29.8050i | −1.16104 | − | 1.16104i | −0.984249 | − | 0.176789i | \(-0.943429\pi\) |
−0.176789 | − | 0.984249i | \(-0.556571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.86546 | + | 3.86546i | −0.150349 | + | 0.150349i | −0.778274 | − | 0.627925i | \(-0.783904\pi\) |
0.627925 | + | 0.778274i | \(0.283904\pi\) | |||||||
\(662\) | 2.19303 | + | 18.3909i | 0.0852344 | + | 0.714782i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.34371 | + | 11.6796i | 0.168568 | + | 0.453257i | ||||
\(665\) | − | 3.77568i | − | 0.146415i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.0761 | − | 11.0761i | 0.428867 | − | 0.428867i | ||||
\(668\) | 22.8136 | − | 5.51931i | 0.882685 | − | 0.213549i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.64520 | + | 4.63224i | −0.140826 | + | 0.178959i | ||||
\(671\) | −14.6439 | −0.565322 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.2478 | −0.934685 | −0.467342 | − | 0.884076i | \(-0.654788\pi\) | ||||
−0.467342 | + | 0.884076i | \(0.654788\pi\) | |||||||
\(674\) | −2.61852 | + | 3.32756i | −0.100862 | + | 0.128173i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.0892 | + | 5.58598i | −0.888046 | + | 0.214846i | ||||
\(677\) | 9.11030 | − | 9.11030i | 0.350137 | − | 0.350137i | −0.510023 | − | 0.860161i | \(-0.670363\pi\) |
0.860161 | + | 0.510023i | \(0.170363\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.26449i | 0.202033i | ||||||||
\(680\) | 15.8316 | − | 5.88784i | 0.607113 | − | 0.225788i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.308343 | + | 2.58579i | 0.0118071 | + | 0.0990149i | ||||
\(683\) | 6.43216 | − | 6.43216i | 0.246120 | − | 0.246120i | −0.573256 | − | 0.819376i | \(-0.694320\pi\) |
0.819376 | + | 0.573256i | \(0.194320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.43411 | − | 5.43411i | −0.207627 | − | 0.207627i | ||||
\(686\) | 18.8606 | + | 14.8418i | 0.720101 | + | 0.566661i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.28724 | − | 4.00942i | 0.0490756 | − | 0.152858i | ||||
\(689\) | 1.29332 | 0.0492716 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.79586 | + | 8.79586i | 0.334610 | + | 0.334610i | 0.854334 | − | 0.519724i | \(-0.173965\pi\) |
−0.519724 | + | 0.854334i | \(0.673965\pi\) | |||||||
\(692\) | −10.5919 | + | 17.3525i | −0.402644 | + | 0.659645i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.42088 | + | 28.6877i | 0.129855 | + | 1.08897i | ||||
\(695\) | − | 15.3833i | − | 0.583522i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.3861i | 1.98426i | ||||||||
\(698\) | 11.1940 | − | 1.33484i | 0.423701 | − | 0.0505244i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.665096 | + | 2.74912i | 0.0251383 | + | 0.103907i | ||||
\(701\) | 27.7073 | + | 27.7073i | 1.04649 | + | 1.04649i | 0.998865 | + | 0.0476269i | \(0.0151659\pi\) |
0.0476269 | + | 0.998865i | \(0.484834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.9563 | −0.526372 | ||||||||
\(704\) | 9.12291 | + | 0.669808i | 0.343833 | + | 0.0252443i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.5307 | + | 29.9023i | −0.885589 | + | 1.12539i | ||||
\(707\) | −7.48881 | − | 7.48881i | −0.281646 | − | 0.281646i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.2865 | + | 25.2865i | −0.949653 | + | 0.949653i | −0.998792 | − | 0.0491386i | \(-0.984352\pi\) |
0.0491386 | + | 0.998792i | \(0.484352\pi\) | |||||||
\(710\) | 9.53304 | − | 1.13677i | 0.357769 | − | 0.0426622i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1475 | − | 26.5330i | 0.455248 | − | 0.994367i | ||||
\(713\) | 3.02944i | 0.113453i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.856566 | − | 0.856566i | 0.0320338 | − | 0.0320338i | ||||
\(716\) | 10.0919 | − | 16.5333i | 0.377151 | − | 0.617879i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.3964 | − | 12.9026i | −0.611908 | − | 0.481522i | ||||
\(719\) | −9.43253 | −0.351774 | −0.175887 | − | 0.984410i | \(-0.556279\pi\) | ||||
−0.175887 | + | 0.984410i | \(0.556279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.4157 | 0.834803 | ||||||||
\(722\) | 13.1943 | + | 10.3829i | 0.491043 | + | 0.386410i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.9589 | − | 12.1828i | −0.741767 | − | 0.452771i | ||||
\(725\) | −5.88784 | + | 5.88784i | −0.218669 | + | 0.218669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.10144i | − | 0.0408501i | −0.999791 | − | 0.0204250i | \(-0.993498\pi\) | ||
0.999791 | − | 0.0204250i | \(-0.00650195\pi\) | |||||||
\(728\) | −3.97186 | + | 1.47716i | −0.147207 | + | 0.0547470i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.26725 | − | 0.389604i | 0.120926 | − | 0.0144199i | ||||
\(731\) | 4.44549 | − | 4.44549i | 0.164422 | − | 0.164422i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2214 | − | 18.2214i | −0.673024 | − | 0.673024i | 0.285388 | − | 0.958412i | \(-0.407878\pi\) |
−0.958412 | + | 0.285388i | \(0.907878\pi\) | |||||||
\(734\) | 30.3279 | − | 38.5400i | 1.11942 | − | 1.42254i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.4460 | + | 2.03037i | 0.385046 | + | 0.0748405i | ||||
\(737\) | −4.76588 | −0.175553 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0953 | − | 22.0953i | −0.812788 | − | 0.812788i | 0.172263 | − | 0.985051i | \(-0.444892\pi\) |
−0.985051 | + | 0.172263i | \(0.944892\pi\) | |||||||
\(740\) | 10.1618 | − | 2.45844i | 0.373553 | − | 0.0903741i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.42441 | + | 0.289099i | −0.0890028 | + | 0.0106132i | ||||
\(743\) | − | 47.3029i | − | 1.73538i | −0.497109 | − | 0.867688i | \(-0.665605\pi\) | ||
0.497109 | − | 0.867688i | \(-0.334395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 17.0496i | − | 0.624649i | ||||||
\(746\) | 2.57367 | + | 21.5830i | 0.0942287 | + | 0.790209i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.6569 | + | 7.11529i | 0.426217 | + | 0.260161i | ||||
\(749\) | −1.89450 | − | 1.89450i | −0.0692236 | − | 0.0692236i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.81234 | −0.175605 | −0.0878024 | − | 0.996138i | \(-0.527984\pi\) | ||||
−0.0878024 | + | 0.996138i | \(0.527984\pi\) | |||||||
\(752\) | 48.2445 | − | 24.7949i | 1.75930 | − | 0.904177i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.80382 | − | 7.71480i | −0.357034 | − | 0.280957i | ||||
\(755\) | 2.98010 | + | 2.98010i | 0.108457 | + | 0.108457i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.5838 | − | 19.5838i | 0.711786 | − | 0.711786i | −0.255123 | − | 0.966909i | \(-0.582116\pi\) |
0.966909 | + | 0.255123i | \(0.0821159\pi\) | |||||||
\(758\) | 3.06375 | + | 25.6928i | 0.111280 | + | 0.933206i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.86599 | + | 3.14343i | 0.249056 | + | 0.114024i | ||||
\(761\) | 0.278003i | 0.0100776i | 0.999987 | + | 0.00503881i | \(0.00160391\pi\) | ||||
−0.999987 | + | 0.00503881i | \(0.998396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.2654 | + | 12.2654i | −0.444037 | + | 0.444037i | ||||
\(764\) | 8.10953 | + | 33.5201i | 0.293393 | + | 1.21271i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6533 | + | 13.5380i | −0.384920 | + | 0.489149i | ||||
\(767\) | −16.1094 | −0.581677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.5808 | −0.742162 | −0.371081 | − | 0.928600i | \(-0.621013\pi\) | ||||
−0.371081 | + | 0.928600i | \(0.621013\pi\) | |||||||
\(770\) | −1.41421 | + | 1.79715i | −0.0509647 | + | 0.0647649i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.6202 | + | 52.1645i | 0.454211 | + | 1.87744i | ||||
\(773\) | −18.3427 | + | 18.3427i | −0.659743 | + | 0.659743i | −0.955319 | − | 0.295576i | \(-0.904488\pi\) |
0.295576 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.61040i | − | 0.0578471i | ||||||
\(776\) | −9.57336 | − | 4.38294i | −0.343664 | − | 0.157338i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.609191 | + | 5.10872i | 0.0218406 | + | 0.183157i | ||||
\(779\) | −16.5604 | + | 16.5604i | −0.593338 | + | 0.593338i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.48881 | + | 5.48881i | 0.196405 | + | 0.196405i | ||||
\(782\) | 12.4853 | + | 9.82490i | 0.446473 | + | 0.351338i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.7882 | + | 9.14214i | −0.635294 | + | 0.326505i | ||||
\(785\) | 13.4884 | 0.481422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.0313 | + | 21.0313i | 0.749684 | + | 0.749684i | 0.974420 | − | 0.224736i | \(-0.0721519\pi\) |
−0.224736 | + | 0.974420i | \(0.572152\pi\) | |||||||
\(788\) | 1.98391 | + | 1.21097i | 0.0706740 | + | 0.0431391i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.715151 | + | 5.99731i | 0.0254439 | + | 0.213375i | ||||
\(791\) | − | 21.6725i | − | 0.770587i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.5678i | 0.481808i | ||||||||
\(794\) | −17.7692 | + | 2.11889i | −0.630604 | + | 0.0751966i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 39.5126 | − | 9.55932i | 1.40049 | − | 0.338821i | ||||
\(797\) | 34.4451 | + | 34.4451i | 1.22011 | + | 1.22011i | 0.967593 | + | 0.252515i | \(0.0812576\pi\) |
0.252515 | + | 0.967593i | \(0.418742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80.9831 | 2.86498 | ||||||||
\(800\) | −5.55294 | − | 1.07931i | −0.196326 | − | 0.0381594i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.5329 | − | 15.9266i | 0.442553 | − | 0.562387i | ||||
\(803\) | 1.88118 | + | 1.88118i | 0.0663852 | + | 0.0663852i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.88118 | + | 1.88118i | −0.0663027 | + | 0.0663027i | ||||
\(806\) | 2.39578 | − | 0.285685i | 0.0843877 | − | 0.0100628i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.8530 | − | 7.38345i | 0.698427 | − | 0.259749i | ||||
\(809\) | − | 4.84727i | − | 0.170421i | −0.996363 | − | 0.0852106i | \(-0.972844\pi\) | ||
0.996363 | − | 0.0852106i | \(-0.0271563\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.5774 | + | 37.5774i | −1.31952 | + | 1.31952i | −0.405369 | + | 0.914153i | \(0.632857\pi\) |
−0.914153 | + | 0.405369i | \(0.867143\pi\) | |||||||
\(812\) | 20.1023 | + | 12.2704i | 0.705454 | + | 0.430606i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.64294 | + | 5.22746i | 0.232835 | + | 0.183222i | ||||
\(815\) | −15.6702 | −0.548903 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.81064 | 0.0983317 | ||||||||
\(818\) | −12.4495 | − | 9.79676i | −0.435287 | − | 0.342536i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.14067 | − | 14.9750i | 0.319206 | − | 0.522950i | ||||
\(821\) | 6.23725 | − | 6.23725i | 0.217682 | − | 0.217682i | −0.589839 | − | 0.807521i | \(-0.700809\pi\) |
0.807521 | + | 0.589839i | \(0.200809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 20.6905i | − | 0.721225i | −0.932716 | − | 0.360613i | \(-0.882568\pi\) | ||
0.932716 | − | 0.360613i | \(-0.117432\pi\) | |||||||
\(824\) | −18.6621 | + | 40.7624i | −0.650126 | + | 1.42003i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.1980 | − | 3.60097i | 1.05072 | − | 0.125294i | ||||
\(827\) | 5.53413 | − | 5.53413i | 0.192440 | − | 0.192440i | −0.604309 | − | 0.796750i | \(-0.706551\pi\) |
0.796750 | + | 0.604309i | \(0.206551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.2582 | − | 21.2582i | −0.738328 | − | 0.738328i | 0.233926 | − | 0.972254i | \(-0.424842\pi\) |
−0.972254 | + | 0.233926i | \(0.924842\pi\) | |||||||
\(830\) | 3.85304 | − | 4.89636i | 0.133741 | − | 0.169955i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.620589 | − | 8.45255i | 0.0215151 | − | 0.293039i | ||||
\(833\) | −29.8593 | −1.03456 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.29852 | − | 8.29852i | −0.287182 | − | 0.287182i | ||||
\(836\) | 1.43569 | + | 5.93430i | 0.0496543 | + | 0.205242i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.1031 | + | 2.99343i | −0.867173 | + | 0.103406i | ||||
\(839\) | 3.55688i | 0.122797i | 0.998113 | + | 0.0613985i | \(0.0195561\pi\) | ||||
−0.998113 | + | 0.0613985i | \(0.980444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40.3333i | 1.39080i | ||||||||
\(842\) | −0.672222 | − | 5.63730i | −0.0231663 | − | 0.194274i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.5647 | − | 48.4353i | 1.01766 | − | 1.66721i | ||||
\(845\) | 8.39876 | + | 8.39876i | 0.288926 | + | 0.288926i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7073 | 0.470990 | ||||||||
\(848\) | 1.49271 | − | 4.64942i | 0.0512600 | − | 0.159662i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.63696 | − | 5.22274i | −0.227646 | − | 0.179139i | ||||
\(851\) | 6.95352 | + | 6.95352i | 0.238364 | + | 0.238364i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.41187 | − | 7.41187i | 0.253777 | − | 0.253777i | −0.568740 | − | 0.822517i | \(-0.692569\pi\) |
0.822517 | + | 0.568740i | \(0.192569\pi\) | |||||||
\(854\) | −3.03285 | − | 25.4337i | −0.103782 | − | 0.870324i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.02238 | − | 1.86785i | 0.171661 | − | 0.0638417i | ||||
\(857\) | − | 31.1426i | − | 1.06381i | −0.846803 | − | 0.531906i | \(-0.821476\pi\) | ||
0.846803 | − | 0.531906i | \(-0.178524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0035 | − | 32.0035i | 1.09195 | − | 1.09195i | 0.0966247 | − | 0.995321i | \(-0.469195\pi\) |
0.995321 | − | 0.0966247i | \(-0.0308047\pi\) | |||||||
\(860\) | −2.04646 | + | 0.495101i | −0.0697837 | + | 0.0168828i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.2258 | + | 33.3272i | −0.893253 | + | 1.13513i | ||||
\(863\) | 29.2347 | 0.995160 | 0.497580 | − | 0.867418i | \(-0.334222\pi\) | ||||
0.497580 | + | 0.867418i | \(0.334222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.1649 | 0.345617 | ||||||||
\(866\) | 20.3052 | − | 25.8034i | 0.689998 | − | 0.876836i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.42717 | + | 1.07107i | −0.150268 | + | 0.0363544i | ||||
\(869\) | −3.45305 | + | 3.45305i | −0.117137 | + | 0.117137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.41568i | 0.149619i | ||||||||
\(872\) | −12.0928 | − | 32.5159i | −0.409515 | − | 1.10113i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.841007 | + | 7.05275i | 0.0284475 | + | 0.238563i | ||||
\(875\) | 1.00000 | − | 1.00000i | 0.0338062 | − | 0.0338062i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9832 | + | 11.9832i | 0.404645 | + | 0.404645i | 0.879866 | − | 0.475221i | \(-0.157632\pi\) |
−0.475221 | + | 0.879866i | \(0.657632\pi\) | |||||||
\(878\) | −12.4596 | − | 9.80465i | −0.420490 | − | 0.330891i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.09069 | − | 4.06793i | −0.0704770 | − | 0.137130i | ||||
\(881\) | −31.6194 | −1.06529 | −0.532643 | − | 0.846340i | \(-0.678801\pi\) | ||||
−0.532643 | + | 0.846340i | \(0.678801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.32520 | − | 9.32520i | −0.313818 | − | 0.313818i | 0.532569 | − | 0.846387i | \(-0.321227\pi\) |
−0.846387 | + | 0.532569i | \(0.821227\pi\) | |||||||
\(884\) | 6.59245 | − | 10.8003i | 0.221728 | − | 0.363253i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.98928 | − | 41.8405i | −0.167618 | − | 1.40566i | ||||
\(887\) | − | 44.8049i | − | 1.50440i | −0.658934 | − | 0.752200i | \(-0.728993\pi\) | ||
0.658934 | − | 0.752200i | \(-0.271007\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.92041i | − | 0.198564i | ||||||
\(890\) | −14.4881 | + | 1.72764i | −0.485643 | + | 0.0579107i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.02213 | − | 20.7585i | −0.168153 | − | 0.695047i | ||||
\(893\) | 25.6006 | + | 25.6006i | 0.856691 | + | 0.856691i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.68499 | −0.323734 | ||||||||
\(896\) | 0.726086 | + | 15.9835i | 0.0242568 | + | 0.533972i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.1008 | − | 23.0021i | 0.604030 | − | 0.767589i | ||||
\(899\) | −9.48175 | − | 9.48175i | −0.316234 | − | 0.316234i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.15509 | − | 5.15509i | 0.171741 | − | 0.171741i | ||||
\(902\) | 14.0853 | − | 1.67961i | 0.468989 | − | 0.0559247i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.4111 | + | 18.0434i | 1.31079 | + | 0.600116i | ||||
\(905\) | 11.6917i | 0.388644i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.4040 | + | 19.4040i | −0.644299 | + | 0.644299i | −0.951609 | − | 0.307310i | \(-0.900571\pi\) |
0.307310 | + | 0.951609i | \(0.400571\pi\) | |||||||
\(908\) | −25.8641 | + | 42.3727i | −0.858331 | + | 1.40619i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.66510 | + | 1.31029i | 0.0551974 | + | 0.0434358i | ||||
\(911\) | −44.4094 | −1.47135 | −0.735674 | − | 0.677336i | \(-0.763134\pi\) | ||||
−0.735674 | + | 0.677336i | \(0.763134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.03762 | 0.166721 | ||||||||
\(914\) | −20.8922 | − | 16.4405i | −0.691054 | − | 0.543803i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.2025 | + | 14.1627i | 0.766631 | + | 0.467948i | ||||
\(917\) | −6.07736 | + | 6.07736i | −0.200692 | + | 0.200692i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.3092i | 0.867861i | 0.900946 | + | 0.433931i | \(0.142874\pi\) | ||||
−0.900946 | + | 0.433931i | \(0.857126\pi\) | |||||||
\(920\) | −1.85471 | − | 4.98705i | −0.0611479 | − | 0.164418i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.35508 | + | 0.400078i | −0.110494 | + | 0.0131759i | ||||
\(923\) | 5.08548 | − | 5.08548i | 0.167391 | − | 0.167391i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.69637 | − | 3.69637i | −0.121536 | − | 0.121536i | ||||
\(926\) | 33.2712 | − | 42.2804i | 1.09336 | − | 1.38942i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −39.0496 | + | 26.3400i | −1.28187 | + | 0.864653i | ||||
\(929\) | 41.9008 | 1.37472 | 0.687360 | − | 0.726317i | \(-0.258770\pi\) | ||||
0.687360 | + | 0.726317i | \(0.258770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.43920 | − | 9.43920i | −0.309357 | − | 0.309357i | ||||
\(932\) | 31.9323 | − | 7.72541i | 1.04598 | − | 0.253054i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.2352 | − | 3.60540i | 0.989325 | − | 0.117972i | ||||
\(935\) | − | 6.82843i | − | 0.223313i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.1251i | − | 1.63752i | −0.574139 | − | 0.818758i | \(-0.694663\pi\) | ||
0.574139 | − | 0.818758i | \(-0.305337\pi\) | |||||||
\(938\) | −0.987046 | − | 8.27744i | −0.0322282 | − | 0.270268i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −23.1497 | − | 14.1305i | −0.755060 | − | 0.460885i | ||||
\(941\) | −17.7315 | − | 17.7315i | −0.578029 | − | 0.578029i | 0.356331 | − | 0.934360i | \(-0.384028\pi\) |
−0.934360 | + | 0.356331i | \(0.884028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5020 | 0.537378 | ||||||||
\(944\) | −18.5930 | + | 57.9124i | −0.605151 | + | 1.88489i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.33781 | − | 1.05275i | −0.0434960 | − | 0.0342278i | ||||
\(947\) | 8.29393 | + | 8.29393i | 0.269516 | + | 0.269516i | 0.828905 | − | 0.559389i | \(-0.188964\pi\) |
−0.559389 | + | 0.828905i | \(0.688964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.74294 | − | 1.74294i | 0.0565783 | − | 0.0565783i | ||||
\(950\) | −0.447065 | − | 3.74912i | −0.0145047 | − | 0.121637i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.94372 | + | 21.7194i | −0.322278 | + | 0.703930i | ||||
\(953\) | − | 22.6285i | − | 0.733010i | −0.930416 | − | 0.366505i | \(-0.880554\pi\) | ||
0.930416 | − | 0.366505i | \(-0.119446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1930 | − | 12.1930i | 0.394557 | − | 0.394557i | ||||
\(956\) | −6.88694 | − | 28.4666i | −0.222739 | − | 0.920675i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.3696 | + | 14.4482i | −0.367335 | + | 0.466802i | ||||
\(959\) | 10.8682 | 0.350953 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4066 | −0.916343 | ||||||||
\(962\) | 4.84333 | − | 6.15481i | 0.156155 | − | 0.198439i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.9827 | − | 45.3962i | −0.353730 | − | 1.46211i | ||||
\(965\) | 18.9750 | − | 18.9750i | 0.610827 | − | 0.610827i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.6144i | − | 1.33823i | −0.743159 | − | 0.669115i | \(-0.766673\pi\) | ||
0.743159 | − | 0.669115i | \(-0.233327\pi\) | |||||||
\(968\) | −11.4120 | + | 24.9265i | −0.366796 | + | 0.801169i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.623349 | + | 5.22746i | 0.0200145 | + | 0.167843i | ||||
\(971\) | −21.7691 | + | 21.7691i | −0.698604 | + | 0.698604i | −0.964109 | − | 0.265505i | \(-0.914461\pi\) |
0.265505 | + | 0.964109i | \(0.414461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3833 | + | 15.3833i | 0.493166 | + | 0.493166i | ||||
\(974\) | 17.9006 | + | 14.0863i | 0.573573 | + | 0.451355i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.7757 | + | 15.6596i | 1.56127 | + | 0.501252i | ||||
\(977\) | −17.3840 | −0.556164 | −0.278082 | − | 0.960557i | \(-0.589699\pi\) | ||||
−0.278082 | + | 0.960557i | \(0.589699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.34179 | − | 8.34179i | −0.266605 | − | 0.266605i | ||||
\(980\) | 8.53553 | + | 5.21005i | 0.272658 | + | 0.166429i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.02566 | + | 33.7595i | 0.128464 | + | 1.07731i | ||||
\(983\) | − | 4.91428i | − | 0.156741i | −0.996924 | − | 0.0783707i | \(-0.975028\pi\) | ||
0.996924 | − | 0.0783707i | \(-0.0249718\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.16215i | − | 0.0370291i | ||||||
\(986\) | −69.8280 | + | 8.32666i | −2.22378 | + | 0.265175i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.49824 | − | 1.33019i | 0.174922 | − | 0.0423190i | ||||
\(989\) | −1.40036 | − | 1.40036i | −0.0445288 | − | 0.0445288i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5415 | 0.747822 | 0.373911 | − | 0.927465i | \(-0.378017\pi\) | ||||
0.373911 | + | 0.927465i | \(0.378017\pi\) | |||||||
\(992\) | 1.73812 | − | 8.94242i | 0.0551852 | − | 0.283922i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.39627 | + | 10.6698i | −0.266313 | + | 0.338426i | ||||
\(995\) | −14.3728 | − | 14.3728i | −0.455650 | − | 0.455650i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.6097 | + | 19.6097i | −0.621046 | + | 0.621046i | −0.945799 | − | 0.324753i | \(-0.894719\pi\) |
0.324753 | + | 0.945799i | \(0.394719\pi\) | |||||||
\(998\) | 7.15676 | − | 0.853410i | 0.226543 | − | 0.0270142i | ||||
\(999\) | 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 | 720.2.t.b.541.1 | 8 | ||
3.2 | odd | 2 | 240.2.s.b.61.4 | ✓ | 8 | ||
4.3 | odd | 2 | 2880.2.t.b.721.1 | 8 | |||
12.11 | even | 2 | 960.2.s.b.721.4 | 8 | |||
16.5 | even | 4 | inner | 720.2.t.b.181.1 | 8 | ||
16.11 | odd | 4 | 2880.2.t.b.2161.1 | 8 | |||
24.5 | odd | 2 | 1920.2.s.c.1441.4 | 8 | |||
24.11 | even | 2 | 1920.2.s.d.1441.1 | 8 | |||
48.5 | odd | 4 | 240.2.s.b.181.4 | yes | 8 | ||
48.11 | even | 4 | 960.2.s.b.241.4 | 8 | |||
48.29 | odd | 4 | 1920.2.s.c.481.4 | 8 | |||
48.35 | even | 4 | 1920.2.s.d.481.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.b.61.4 | ✓ | 8 | 3.2 | odd | 2 | ||
240.2.s.b.181.4 | yes | 8 | 48.5 | odd | 4 | ||
720.2.t.b.181.1 | 8 | 16.5 | even | 4 | inner | ||
720.2.t.b.541.1 | 8 | 1.1 | even | 1 | trivial | ||
960.2.s.b.241.4 | 8 | 48.11 | even | 4 | |||
960.2.s.b.721.4 | 8 | 12.11 | even | 2 | |||
1920.2.s.c.481.4 | 8 | 48.29 | odd | 4 | |||
1920.2.s.c.1441.4 | 8 | 24.5 | odd | 2 | |||
1920.2.s.d.481.1 | 8 | 48.35 | even | 4 | |||
1920.2.s.d.1441.1 | 8 | 24.11 | even | 2 | |||
2880.2.t.b.721.1 | 8 | 4.3 | odd | 2 | |||
2880.2.t.b.2161.1 | 8 | 16.11 | odd | 4 |