Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(321,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.l (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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.349241344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 81x^{4} - 100x^{3} + 96x^{2} - 52x + 17 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 321.2 | ||
Root | \(0.500000 - 1.94924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.321 |
Dual form | 1280.2.l.h.961.2 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.742133 | − | 0.742133i | −0.428470 | − | 0.428470i | 0.459637 | − | 0.888107i | \(-0.347980\pi\) |
−0.888107 | + | 0.459637i | \(0.847980\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.463747i | − | 0.175280i | −0.996152 | − | 0.0876400i | \(-0.972067\pi\) | ||
0.996152 | − | 0.0876400i | \(-0.0279325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.89848i | − | 0.632826i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.04953 | + | 2.04953i | −0.617958 | + | 0.617958i | −0.945007 | − | 0.327049i | \(-0.893946\pi\) |
0.327049 | + | 0.945007i | \(0.393946\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.94801 | − | 3.94801i | −1.09498 | − | 1.09498i | −0.994988 | − | 0.0999936i | \(-0.968118\pi\) |
−0.0999936 | − | 0.994988i | \(-0.531882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04953 | 0.270988 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.34416 | 0.326007 | 0.163004 | − | 0.986625i | \(-0.447882\pi\) | ||||
0.163004 | + | 0.986625i | \(0.447882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.94801 | + | 4.94801i | 1.13515 | + | 1.13515i | 0.989308 | + | 0.145844i | \(0.0465899\pi\) |
0.145844 | + | 0.989308i | \(0.453410\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.344162 | + | 0.344162i | −0.0751023 | + | 0.0751023i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.84894i | 0.802560i | 0.915955 | + | 0.401280i | \(0.131435\pi\) | ||||
−0.915955 | + | 0.401280i | \(0.868565\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.63532 | + | 3.63532i | −0.699618 | + | 0.699618i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.09907 | + | 1.09907i | 0.204092 | + | 0.204092i | 0.801751 | − | 0.597659i | \(-0.203902\pi\) |
−0.597659 | + | 0.801751i | \(0.703902\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.17157 | −0.569631 | −0.284816 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.04205 | 0.529553 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.327919 | + | 0.327919i | 0.0554284 | + | 0.0554284i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.89848 | + | 6.89848i | −1.13410 | + | 1.13410i | −0.144615 | + | 0.989488i | \(0.546194\pi\) |
−0.989488 | + | 0.144615i | \(0.953806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.85990i | 0.938334i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.89848i | − | 0.452666i | −0.974050 | − | 0.226333i | \(-0.927326\pi\) | ||
0.974050 | − | 0.226333i | \(-0.0726738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.62255 | + | 1.62255i | −0.247436 | + | 0.247436i | −0.819918 | − | 0.572482i | \(-0.805981\pi\) |
0.572482 | + | 0.819918i | \(0.305981\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.34243 | + | 1.34243i | 0.200117 | + | 0.200117i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.29217 | −0.480213 | −0.240107 | − | 0.970747i | \(-0.577182\pi\) | ||||
−0.240107 | + | 0.970747i | \(0.577182\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.78494 | 0.969277 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.997546 | − | 0.997546i | −0.139684 | − | 0.139684i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.29217 | + | 3.29217i | −0.452215 | + | 0.452215i | −0.896089 | − | 0.443874i | \(-0.853604\pi\) |
0.443874 | + | 0.896089i | \(0.353604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.89848i | − | 0.390831i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.34416i | − | 0.972758i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.84894 | + | 6.84894i | −0.891657 | + | 0.891657i | −0.994679 | − | 0.103022i | \(-0.967149\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.44323 | − | 3.44323i | −0.440860 | − | 0.440860i | 0.451441 | − | 0.892301i | \(-0.350910\pi\) |
−0.892301 | + | 0.451441i | \(0.850910\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.880415 | −0.110922 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.58333 | 0.692527 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.93524 | − | 5.93524i | −0.725105 | − | 0.725105i | 0.244535 | − | 0.969640i | \(-0.421365\pi\) |
−0.969640 | + | 0.244535i | \(0.921365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.85643 | − | 2.85643i | 0.343873 | − | 0.343873i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.8960i | 1.88651i | 0.332068 | + | 0.943256i | \(0.392254\pi\) | ||||
−0.332068 | + | 0.943256i | \(0.607746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.556770i | 0.0651650i | 0.999469 | + | 0.0325825i | \(0.0103732\pi\) | ||||
−0.999469 | + | 0.0325825i | \(0.989627\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.742133 | + | 0.742133i | −0.0856941 | + | 0.0856941i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.950466 | + | 0.950466i | 0.108316 | + | 0.108316i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.23917 | −0.476944 | −0.238472 | − | 0.971149i | \(-0.576647\pi\) | ||||
−0.238472 | + | 0.971149i | \(0.576647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.299657 | −0.0332952 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.06578 | + | 7.06578i | 0.775570 | + | 0.775570i | 0.979074 | − | 0.203504i | \(-0.0652331\pi\) |
−0.203504 | + | 0.979074i | \(0.565233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.950466 | + | 0.950466i | −0.103093 | + | 0.103093i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.63131i | − | 0.174895i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3068i | 1.83451i | 0.398296 | + | 0.917257i | \(0.369602\pi\) | ||||
−0.398296 | + | 0.917257i | \(0.630398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.83088 | + | 1.83088i | −0.191928 | + | 0.191928i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.35373 | + | 2.35373i | 0.244070 | + | 0.244070i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.99755 | −0.717933 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.04205 | 0.918081 | 0.459041 | − | 0.888415i | \(-0.348193\pi\) | ||||
0.459041 | + | 0.888415i | \(0.348193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.89100 | + | 3.89100i | 0.391060 | + | 0.391060i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.89603 | + | 6.89603i | −0.686180 | + | 0.686180i | −0.961385 | − | 0.275205i | \(-0.911254\pi\) |
0.275205 | + | 0.961385i | \(0.411254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0156i | 1.47953i | 0.672864 | + | 0.739766i | \(0.265064\pi\) | ||||
−0.672864 | + | 0.739766i | \(0.734936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.486719i | − | 0.0474989i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.7687 | − | 11.7687i | 1.13772 | − | 1.13772i | 0.148865 | − | 0.988857i | \(-0.452438\pi\) |
0.988857 | − | 0.148865i | \(-0.0475621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14357 | − | 4.14357i | −0.396882 | − | 0.396882i | 0.480250 | − | 0.877132i | \(-0.340546\pi\) |
−0.877132 | + | 0.480250i | \(0.840546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2392 | 0.971859 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.99509 | −0.752115 | −0.376058 | − | 0.926596i | \(-0.622720\pi\) | ||||
−0.376058 | + | 0.926596i | \(0.622720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.72161 | − | 2.72161i | −0.253792 | − | 0.253792i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.49522 | + | 7.49522i | −0.692933 | + | 0.692933i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.623352i | − | 0.0571426i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.59882i | 0.236257i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.15106 | + | 2.15106i | −0.193954 | + | 0.193954i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9795 | −0.974272 | −0.487136 | − | 0.873326i | \(-0.661958\pi\) | ||||
−0.487136 | + | 0.873326i | \(0.661958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.40829 | 0.212038 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.39124 | + | 4.39124i | 0.383665 | + | 0.383665i | 0.872421 | − | 0.488756i | \(-0.162549\pi\) |
−0.488756 | + | 0.872421i | \(0.662549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29463 | − | 2.29463i | 0.198969 | − | 0.198969i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.14112i | − | 0.442477i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 21.8960i | − | 1.87070i | −0.353719 | − | 0.935352i | \(-0.615083\pi\) | ||
0.353719 | − | 0.935352i | \(-0.384917\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.46129 | + | 4.46129i | −0.378402 | + | 0.378402i | −0.870525 | − | 0.492123i | \(-0.836221\pi\) |
0.492123 | + | 0.870525i | \(0.336221\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.44323 | + | 2.44323i | 0.205757 | + | 0.205757i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.1832 | 1.35330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.55432 | −0.129079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.03532 | − | 5.03532i | −0.415306 | − | 0.415306i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.34416 | − | 7.34416i | 0.601657 | − | 0.601657i | −0.339095 | − | 0.940752i | \(-0.610121\pi\) |
0.940752 | + | 0.339095i | \(0.110121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.0266i | − | 1.38560i | −0.721129 | − | 0.692801i | \(-0.756376\pi\) | ||
0.721129 | − | 0.692801i | \(-0.243624\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.55186i | − | 0.206306i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.24264 | − | 2.24264i | 0.180133 | − | 0.180133i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85643 | + | 3.85643i | 0.307776 | + | 0.307776i | 0.844046 | − | 0.536270i | \(-0.180167\pi\) |
−0.536270 | + | 0.844046i | \(0.680167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.88646 | 0.387521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.78494 | 0.140673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3255 | − | 12.3255i | −0.965405 | − | 0.965405i | 0.0340163 | − | 0.999421i | \(-0.489170\pi\) |
−0.999421 | + | 0.0340163i | \(0.989170\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.15106 | + | 2.15106i | −0.167459 | + | 0.167459i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.6314i | − | 1.44174i | −0.693069 | − | 0.720872i | \(-0.743742\pi\) | ||
0.693069 | − | 0.720872i | \(-0.256258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.1736i | 1.39797i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.39370 | − | 9.39370i | 0.718354 | − | 0.718354i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.51227 | − | 4.51227i | −0.343061 | − | 0.343061i | 0.514456 | − | 0.857517i | \(-0.327994\pi\) |
−0.857517 | + | 0.514456i | \(0.827994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.463747 | −0.0350560 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.1656 | 0.764097 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.1907 | + | 15.1907i | 1.13540 | + | 1.13540i | 0.989264 | + | 0.146139i | \(0.0466845\pi\) |
0.146139 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6834 | − | 11.6834i | 0.868422 | − | 0.868422i | −0.123876 | − | 0.992298i | \(-0.539533\pi\) |
0.992298 | + | 0.123876i | \(0.0395326\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.11067i | 0.377791i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.75592i | − | 0.717270i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75491 | + | 2.75491i | −0.201459 | + | 0.201459i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.68587 | + | 1.68587i | 0.122629 | + | 0.122629i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.89603 | −0.281906 | −0.140953 | − | 0.990016i | \(-0.545017\pi\) | ||||
−0.140953 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0371 | −1.37032 | −0.685162 | − | 0.728391i | \(-0.740269\pi\) | ||||
−0.685162 | + | 0.728391i | \(0.740269\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.14357 | − | 4.14357i | −0.296727 | − | 0.296727i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0470803 | − | 0.0470803i | 0.00335433 | − | 0.00335433i | −0.705428 | − | 0.708782i | \(-0.749245\pi\) |
0.708782 | + | 0.705428i | \(0.249245\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3137i | 0.802008i | 0.916076 | + | 0.401004i | \(0.131339\pi\) | ||||
−0.916076 | + | 0.401004i | \(0.868661\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.80947i | 0.621372i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.509690 | − | 0.509690i | 0.0357732 | − | 0.0357732i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.04953 | + | 2.04953i | 0.143146 | + | 0.143146i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.30714 | 0.507881 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.2822 | −1.40295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.338117 | − | 0.338117i | −0.0232769 | − | 0.0232769i | 0.695373 | − | 0.718649i | \(-0.255239\pi\) |
−0.718649 | + | 0.695373i | \(0.755239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.7970 | − | 11.7970i | 0.808314 | − | 0.808314i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.29463i | − | 0.156492i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.47081i | 0.0998450i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.413197 | − | 0.413197i | 0.0279213 | − | 0.0279213i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.30677 | − | 5.30677i | −0.356972 | − | 0.356972i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.6049 | −1.31284 | −0.656419 | − | 0.754396i | \(-0.727930\pi\) | ||||
−0.656419 | + | 0.754396i | \(0.727930\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.89848 | −0.126565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1549 | − | 16.1549i | −1.07224 | − | 1.07224i | −0.997179 | − | 0.0750599i | \(-0.976085\pi\) |
−0.0750599 | − | 0.997179i | \(-0.523915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.7970 | − | 18.7970i | 1.24214 | − | 1.24214i | 0.283026 | − | 0.959112i | \(-0.408662\pi\) |
0.959112 | − | 0.283026i | \(-0.0913381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.41074i | − | 0.0928201i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.2402i | 1.12944i | 0.825282 | + | 0.564721i | \(0.191016\pi\) | ||||
−0.825282 | + | 0.564721i | \(0.808984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.32792 | − | 2.32792i | 0.151857 | − | 0.151857i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.14603 | + | 3.14603i | 0.204356 | + | 0.204356i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.6930 | 1.79131 | 0.895655 | − | 0.444749i | \(-0.146707\pi\) | ||||
0.895655 | + | 0.444749i | \(0.146707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.09661 | −0.585964 | −0.292982 | − | 0.956118i | \(-0.594648\pi\) | ||||
−0.292982 | + | 0.956118i | \(0.594648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.1283 | + | 11.1283i | 0.713884 | + | 0.713884i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.79768 | + | 4.79768i | −0.306512 | + | 0.306512i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 39.0696i | − | 2.48594i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.4875i | − | 0.664617i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.63388 | + | 8.63388i | −0.544966 | + | 0.544966i | −0.924980 | − | 0.380015i | \(-0.875919\pi\) |
0.380015 | + | 0.924980i | \(0.375919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.88854 | − | 7.88854i | −0.495948 | − | 0.495948i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.41074 | 0.0883442 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0647 | −1.43874 | −0.719369 | − | 0.694628i | \(-0.755569\pi\) | ||||
−0.719369 | + | 0.694628i | \(0.755569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.19915 | + | 3.19915i | 0.198786 | + | 0.198786i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.08656 | − | 2.08656i | 0.129155 | − | 0.129155i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.1833i | − | 1.30622i | −0.757264 | − | 0.653109i | \(-0.773464\pi\) | ||
0.757264 | − | 0.653109i | \(-0.226536\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.65584i | − | 0.286006i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8439 | − | 12.8439i | 0.786035 | − | 0.786035i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.35373 | + | 6.35373i | 0.387394 | + | 0.387394i | 0.873757 | − | 0.486363i | \(-0.161677\pi\) |
−0.486363 | + | 0.873757i | \(0.661677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8235 | −0.657482 | −0.328741 | − | 0.944420i | \(-0.606624\pi\) | ||||
−0.328741 | + | 0.944420i | \(0.606624\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.71751 | 0.164471 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.04953 | + | 2.04953i | 0.123592 | + | 0.123592i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.5074 | + | 16.5074i | −0.991831 | + | 0.991831i | −0.999967 | − | 0.00813590i | \(-0.997410\pi\) |
0.00813590 | + | 0.999967i | \(0.497410\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.02116i | 0.360478i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.6064i | − | 0.632726i | −0.948638 | − | 0.316363i | \(-0.897538\pi\) | ||
0.948638 | − | 0.316363i | \(-0.102462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.80017 | − | 2.80017i | 0.166453 | − | 0.166453i | −0.618966 | − | 0.785418i | \(-0.712448\pi\) |
0.785418 | + | 0.618966i | \(0.212448\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.19311 | + | 5.19311i | 0.307613 | + | 0.307613i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.34416 | −0.0793434 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1932 | −0.893719 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.71040 | − | 6.71040i | −0.393371 | − | 0.393371i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1387 | − | 14.1387i | 0.825990 | − | 0.825990i | −0.160970 | − | 0.986959i | \(-0.551462\pi\) |
0.986959 | + | 0.160970i | \(0.0514621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.68587i | − | 0.563933i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 14.9014i | − | 0.864668i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1957 | − | 15.1957i | 0.878789 | − | 0.878789i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.752452 | + | 0.752452i | 0.0433706 | + | 0.0433706i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2355 | 0.588016 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.86946 | 0.278825 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6912 | − | 21.6912i | −1.23798 | − | 1.23798i | −0.960825 | − | 0.277155i | \(-0.910609\pi\) |
−0.277155 | − | 0.960825i | \(-0.589391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1436 | − | 11.1436i | 0.633936 | − | 0.633936i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.490189i | − | 0.0277960i | −0.999903 | − | 0.0138980i | \(-0.995576\pi\) | ||
0.999903 | − | 0.0138980i | \(-0.00442402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.5794i | 1.27627i | 0.769926 | + | 0.638133i | \(0.220293\pi\) | ||||
−0.769926 | + | 0.638133i | \(0.779707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.622547 | − | 0.622547i | 0.0350766 | − | 0.0350766i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.6314 | + | 18.6314i | 1.04645 | + | 1.04645i | 0.998868 | + | 0.0475778i | \(0.0151502\pi\) |
0.0475778 | + | 0.998868i | \(0.484850\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.50515 | −0.252240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.4679 | −0.974961 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.65093 | + | 6.65093i | 0.370068 | + | 0.370068i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.94801 | + | 3.94801i | −0.218996 | + | 0.218996i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.15016i | 0.340105i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.52674i | 0.0841718i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7460 | − | 17.7460i | 0.975408 | − | 0.975408i | −0.0242972 | − | 0.999705i | \(-0.507735\pi\) |
0.999705 | + | 0.0242972i | \(0.00773479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.0966 | + | 13.0966i | 0.717690 | + | 0.717690i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.39370 | 0.458597 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2972 | 0.669871 | 0.334936 | − | 0.942241i | \(-0.391285\pi\) | ||||
0.334936 | + | 0.942241i | \(0.391285\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.93342 | + | 5.93342i | 0.322259 | + | 0.322259i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.50025 | − | 6.50025i | 0.352008 | − | 0.352008i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.39273i | − | 0.345175i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.03960i | 0.217485i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.37745 | − | 4.37745i | 0.234994 | − | 0.234994i | −0.579779 | − | 0.814773i | \(-0.696861\pi\) |
0.814773 | + | 0.579779i | \(0.196861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.9951 | − | 18.9951i | −1.01678 | − | 1.01678i | −0.999857 | − | 0.0169273i | \(-0.994612\pi\) |
−0.0169273 | − | 0.999857i | \(-0.505388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.7046 | 1.53214 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6785 | 1.31350 | 0.656752 | − | 0.754106i | \(-0.271930\pi\) | ||||
0.656752 | + | 0.754106i | \(0.271930\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.2402 | − | 11.2402i | −0.596567 | − | 0.596567i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.462610 | + | 0.462610i | −0.0244839 | + | 0.0244839i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.5745i | 1.50811i | 0.656813 | + | 0.754053i | \(0.271904\pi\) | ||||
−0.656813 | + | 0.754053i | \(0.728096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.9657i | 1.57714i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.92867 | − | 1.92867i | 0.101229 | − | 0.101229i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.393696 | − | 0.393696i | −0.0206070 | − | 0.0206070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.86594 | −0.514998 | −0.257499 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257499 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.50270 | −0.286459 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52674 | + | 1.52674i | 0.0792643 | + | 0.0792643i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.88891 | − | 7.88891i | 0.408472 | − | 0.408472i | −0.472733 | − | 0.881206i | \(-0.656733\pi\) |
0.881206 | + | 0.472733i | \(0.156733\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.04953i | − | 0.0541977i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.67827i | − | 0.446953i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.39370 | + | 3.39370i | −0.174322 | + | 0.174322i | −0.788875 | − | 0.614553i | \(-0.789336\pi\) |
0.614553 | + | 0.788875i | \(0.289336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.14823 | + | 8.14823i | 0.417447 | + | 0.417447i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.25012 | 0.319366 | 0.159683 | − | 0.987168i | \(-0.448953\pi\) | ||||
0.159683 | + | 0.987168i | \(0.448953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.34416 | −0.0685048 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.08037 | + | 3.08037i | 0.156584 | + | 0.156584i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.04205 | − | 3.04205i | 0.154238 | − | 0.154238i | −0.625770 | − | 0.780008i | \(-0.715215\pi\) |
0.780008 | + | 0.625770i | \(0.215215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.17361i | 0.261640i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.51777i | − | 0.328778i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.99755 | − | 2.99755i | 0.150823 | − | 0.150823i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.93845 | − | 6.93845i | −0.348231 | − | 0.348231i | 0.511220 | − | 0.859450i | \(-0.329194\pi\) |
−0.859450 | + | 0.511220i | \(0.829194\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.40584 | −0.170505 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.1736 | −0.557983 | −0.278992 | − | 0.960294i | \(-0.590000\pi\) | ||||
−0.278992 | + | 0.960294i | \(0.590000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5214 | + | 12.5214i | 0.623736 | + | 0.623736i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.211889 | − | 0.211889i | 0.0105289 | − | 0.0105289i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 28.2773i | − | 1.40166i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.6611i | 1.96111i | 0.196233 | + | 0.980557i | \(0.437129\pi\) | ||||
−0.196233 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2498 | + | 16.2498i | −0.801541 | + | 0.801541i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.17618 | + | 3.17618i | 0.156290 | + | 0.156290i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.99252 | −0.490513 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.62174 | 0.324268 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.81400 | − | 3.81400i | −0.186326 | − | 0.186326i | 0.607780 | − | 0.794106i | \(-0.292060\pi\) |
−0.794106 | + | 0.607780i | \(0.792060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.45280 | − | 8.45280i | 0.411964 | − | 0.411964i | −0.470458 | − | 0.882422i | \(-0.655911\pi\) |
0.882422 | + | 0.470458i | \(0.155911\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.25012i | 0.303891i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.34416i | − | 0.0652014i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.59679 | + | 1.59679i | −0.0772740 | + | 0.0772740i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0101 | − | 12.0101i | −0.579851 | − | 0.579851i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.3909 | −1.12670 | −0.563349 | − | 0.826219i | \(-0.690487\pi\) | ||||
−0.563349 | + | 0.826219i | \(0.690487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.33925 | 0.160474 | 0.0802372 | − | 0.996776i | \(-0.474432\pi\) | ||||
0.0802372 | + | 0.996776i | \(0.474432\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.15351 | + | 1.15351i | 0.0553065 | + | 0.0553065i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.0446 | + | 19.0446i | −0.911028 | + | 0.911028i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.27064i | 0.0606444i | 0.999540 | + | 0.0303222i | \(0.00965333\pi\) | ||||
−0.999540 | + | 0.0303222i | \(0.990347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 12.8811i | − | 0.613384i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.4991 | − | 17.4991i | 0.831406 | − | 0.831406i | −0.156303 | − | 0.987709i | \(-0.549958\pi\) |
0.987709 | + | 0.156303i | \(0.0499577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2377 | − | 12.2377i | −0.580124 | − | 0.580124i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9007 | −0.515585 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.9831 | −0.754288 | −0.377144 | − | 0.926155i | \(-0.623094\pi\) | ||||
−0.377144 | + | 0.926155i | \(0.623094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.94053 | + | 5.94053i | 0.279729 | + | 0.279729i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6360 | + | 12.6360i | −0.593689 | + | 0.593689i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 2.58926i | − | 0.121386i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.78739i | − | 0.317501i | −0.987319 | − | 0.158750i | \(-0.949253\pi\) | ||
0.987319 | − | 0.158750i | \(-0.0507465\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.88646 | + | 4.88646i | −0.228080 | + | 0.228080i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0942 | + | 21.0942i | 0.982453 | + | 0.982453i | 0.999849 | − | 0.0173957i | \(-0.00553750\pi\) |
−0.0173957 | + | 0.999849i | \(0.505537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.3234 | 0.990982 | 0.495491 | − | 0.868613i | \(-0.334988\pi\) | ||||
0.495491 | + | 0.868613i | \(0.334988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.32867 | −0.154364 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.71168 | − | 4.71168i | −0.218031 | − | 0.218031i | 0.589638 | − | 0.807668i | \(-0.299271\pi\) |
−0.807668 | + | 0.589638i | \(0.799271\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.75245 | + | 2.75245i | −0.127096 | + | 0.127096i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.72396i | − | 0.263746i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.65093i | − | 0.305810i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.94801 | − | 4.94801i | 0.227030 | − | 0.227030i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.25012 | + | 6.25012i | 0.286173 | + | 0.286173i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.1932 | −0.465740 | −0.232870 | − | 0.972508i | \(-0.574812\pi\) | ||||
−0.232870 | + | 0.972508i | \(0.574812\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.4706 | 2.48364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.32466 | − | 1.32466i | −0.0602742 | − | 0.0602742i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.39370 | + | 6.39370i | −0.290323 | + | 0.290323i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.87940i | 0.266421i | 0.991088 | + | 0.133210i | \(0.0425286\pi\) | ||||
−0.991088 | + | 0.133210i | \(0.957471\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.2943i | 0.827295i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.01950 | − | 3.01950i | 0.136268 | − | 0.136268i | −0.635682 | − | 0.771951i | \(-0.719281\pi\) |
0.771951 | + | 0.635682i | \(0.219281\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.47733 | + | 1.47733i | 0.0665354 | + | 0.0665354i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.50270 | −0.247328 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.37174 | 0.330668 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1837 | − | 21.1837i | −0.948313 | − | 0.948313i | 0.0504151 | − | 0.998728i | \(-0.483946\pi\) |
−0.998728 | + | 0.0504151i | \(0.983946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8270 | + | 13.8270i | −0.617744 | + | 0.617744i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7450i | 1.41544i | 0.706494 | + | 0.707719i | \(0.250276\pi\) | ||||
−0.706494 | + | 0.707719i | \(0.749724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.75245i | − | 0.433978i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.4872 | − | 13.4872i | 0.598989 | − | 0.598989i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.68342 | − | 1.68342i | −0.0746161 | − | 0.0746161i | 0.668814 | − | 0.743430i | \(-0.266802\pi\) |
−0.743430 | + | 0.668814i | \(0.766802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.258201 | 0.0114221 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.9752 | −1.58834 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.6176 | − | 10.6176i | −0.467869 | − | 0.467869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.74742 | − | 6.74742i | 0.296751 | − | 0.296751i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.69740i | 0.293983i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.1736i | − | 1.01525i | −0.861577 | − | 0.507627i | \(-0.830523\pi\) | ||
0.861577 | − | 0.507627i | \(-0.169477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4991 | + | 29.4991i | −1.28990 | + | 1.28990i | −0.355061 | + | 0.934843i | \(0.615540\pi\) |
−0.934843 | + | 0.355061i | \(0.884460\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.344162 | + | 0.344162i | 0.0150205 | + | 0.0150205i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.26311 | −0.185704 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.18562 | 0.355897 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.0026 | + | 13.0026i | 0.564264 | + | 0.564264i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.4432 | + | 11.4432i | −0.495661 | + | 0.495661i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.6434i | 0.719559i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 22.5470i | − | 0.972973i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.9060 | + | 13.9060i | −0.598972 | + | 0.598972i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3813 | − | 13.3813i | −0.575307 | − | 0.575307i | 0.358299 | − | 0.933607i | \(-0.383357\pi\) |
−0.933607 | + | 0.358299i | \(0.883357\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3413 | −0.744186 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.85990 | 0.251010 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.71168 | + | 4.71168i | 0.201457 | + | 0.201457i | 0.800624 | − | 0.599167i | \(-0.204502\pi\) |
−0.599167 | + | 0.800624i | \(0.704502\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.53690 | + | 6.53690i | −0.278988 | + | 0.278988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8764i | 0.463350i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.96590i | 0.0835988i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.24019 | + | 7.24019i | −0.307329 | + | 0.307329i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.4457 | + | 10.4457i | 0.442598 | + | 0.442598i | 0.892884 | − | 0.450286i | \(-0.148678\pi\) |
−0.450286 | + | 0.892884i | \(0.648678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8117 | 0.541876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.08901 | 0.172638 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.5411 | + | 20.5411i | 0.865705 | + | 0.865705i | 0.991994 | − | 0.126288i | \(-0.0403065\pi\) |
−0.126288 | + | 0.991994i | \(0.540306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.65338 | − | 5.65338i | 0.237840 | − | 0.237840i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.138965i | 0.00583599i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 19.8690i | − | 0.832954i | −0.909146 | − | 0.416477i | \(-0.863265\pi\) | ||
0.909146 | − | 0.416477i | \(-0.136735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7644 | + | 15.7644i | −0.659720 | + | 0.659720i | −0.955314 | − | 0.295593i | \(-0.904483\pi\) |
0.295593 | + | 0.955314i | \(0.404483\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.89137 | + | 2.89137i | 0.120789 | + | 0.120789i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.84894 | 0.160512 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.1927 | 0.632482 | 0.316241 | − | 0.948679i | \(-0.397579\pi\) | ||||
0.316241 | + | 0.948679i | \(0.397579\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1281 | + | 14.1281i | 0.587143 | + | 0.587143i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.27674 | − | 3.27674i | 0.135942 | − | 0.135942i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 13.4948i | − | 0.558899i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 10.5998i | − | 0.438249i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.7118 | + | 21.7118i | −0.896142 | + | 0.896142i | −0.995092 | − | 0.0989505i | \(-0.968451\pi\) |
0.0989505 | + | 0.995092i | \(0.468451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6930 | − | 15.6930i | −0.646618 | − | 0.646618i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0698796 | −0.00287446 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.4757 | 0.881902 | 0.440951 | − | 0.897531i | \(-0.354641\pi\) | ||||
0.440951 | + | 0.897531i | \(0.354641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.440776 | + | 0.440776i | 0.0180701 | + | 0.0180701i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.39627 | − | 8.39627i | 0.343636 | − | 0.343636i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7025i | 1.09104i | 0.838099 | + | 0.545518i | \(0.183667\pi\) | ||||
−0.838099 | + | 0.545518i | \(0.816333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.19053i | 0.293308i | 0.989188 | + | 0.146654i | \(0.0468504\pi\) | ||||
−0.989188 | + | 0.146654i | \(0.953150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2679 | + | 11.2679i | −0.458865 | + | 0.458865i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.83764 | − | 1.83764i | −0.0747109 | − | 0.0747109i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.73930 | −0.232951 | −0.116475 | − | 0.993194i | \(-0.537160\pi\) | ||||
−0.116475 | + | 0.993194i | \(0.537160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.756515 | −0.0306555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9975 | + | 12.9975i | 0.525824 | + | 0.525824i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.61342 | − | 7.61342i | 0.307503 | − | 0.307503i | −0.536437 | − | 0.843940i | \(-0.680230\pi\) |
0.843940 | + | 0.536437i | \(0.180230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 3.04205i | − | 0.122667i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.32012i | 0.214180i | 0.994249 | + | 0.107090i | \(0.0341533\pi\) | ||||
−0.994249 | + | 0.107090i | \(0.965847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6774 | + | 21.6774i | −0.871287 | + | 0.871287i | −0.992613 | − | 0.121326i | \(-0.961285\pi\) |
0.121326 | + | 0.992613i | \(0.461285\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.9921 | − | 13.9921i | −0.561486 | − | 0.561486i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.02597 | 0.321554 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.0521 | + | 15.0521i | 0.601123 | + | 0.601123i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.27267 | + | 9.27267i | −0.369726 | + | 0.369726i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.43468i | − | 0.295970i | −0.988990 | − | 0.147985i | \(-0.952721\pi\) | ||
0.988990 | − | 0.147985i | \(-0.0472787\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.501855i | 0.0199470i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.76367 | − | 7.76367i | 0.308092 | − | 0.308092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.7870 | − | 26.7870i | −1.06134 | − | 1.06134i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.1783 | 1.19383 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9034 | −0.746639 | −0.373319 | − | 0.927703i | \(-0.621780\pi\) | ||||
−0.373319 | + | 0.927703i | \(0.621780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4471 | − | 19.4471i | −0.766918 | − | 0.766918i | 0.210645 | − | 0.977563i | \(-0.432444\pi\) |
−0.977563 | + | 0.210645i | \(0.932444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.70292 | + | 1.70292i | −0.0670523 | + | 0.0670523i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9756i | 1.25709i | 0.777773 | + | 0.628545i | \(0.216349\pi\) | ||||
−0.777773 | + | 0.628545i | \(0.783651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 28.0743i | − | 1.10201i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09154 | − | 1.09154i | 0.0427806 | − | 0.0427806i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.9060 | − | 10.9060i | −0.426783 | − | 0.426783i | 0.460748 | − | 0.887531i | \(-0.347581\pi\) |
−0.887531 | + | 0.460748i | \(0.847581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.21015 | −0.242651 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.05702 | 0.0412381 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.22009 | + | 4.22009i | 0.164391 | + | 0.164391i | 0.784509 | − | 0.620118i | \(-0.212915\pi\) |
−0.620118 | + | 0.784509i | \(0.712915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.8415 | + | 11.8415i | −0.460580 | + | 0.460580i | −0.898845 | − | 0.438266i | \(-0.855593\pi\) |
0.438266 | + | 0.898845i | \(0.355593\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.87665i | 0.305904i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.24509i | 0.125839i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.23025 | + | 4.23025i | −0.163796 | + | 0.163796i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.5494 | + | 14.5494i | 0.562513 | + | 0.562513i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.1140 | 0.544866 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.4089 | 1.17218 | 0.586088 | − | 0.810247i | \(-0.300667\pi\) | ||||
0.586088 | + | 0.810247i | \(0.300667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.63532 | + | 3.63532i | 0.139924 | + | 0.139924i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.6265 | + | 32.6265i | −1.25394 | + | 1.25394i | −0.300000 | + | 0.953939i | \(0.596987\pi\) |
−0.953939 | + | 0.300000i | \(0.903013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.19323i | − | 0.160921i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.9782i | 0.918845i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.7882 | + | 17.7882i | −0.680646 | + | 0.680646i | −0.960146 | − | 0.279499i | \(-0.909831\pi\) |
0.279499 | + | 0.960146i | \(0.409831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4828 | + | 15.4828i | 0.591568 | + | 0.591568i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.8997 | −1.06444 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.9951 | 0.990334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1737 | − | 31.1737i | −1.18590 | − | 1.18590i | −0.978189 | − | 0.207715i | \(-0.933397\pi\) |
−0.207715 | − | 0.978189i | \(-0.566603\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.80444 | − | 1.80444i | 0.0685450 | − | 0.0685450i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.30922i | − | 0.239322i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.89603i | − | 0.147572i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.7945 | − | 12.7945i | 0.483933 | − | 0.483933i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.633761 | + | 0.633761i | 0.0239368 | + | 0.0239368i | 0.718974 | − | 0.695037i | \(-0.244612\pi\) |
−0.695037 | + | 0.718974i | \(0.744612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −68.2675 | −2.57476 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.45525 | −0.130132 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.19801 | + | 3.19801i | 0.120274 | + | 0.120274i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.3021 | + | 11.3021i | −0.424460 | + | 0.424460i | −0.886736 | − | 0.462276i | \(-0.847033\pi\) |
0.462276 | + | 0.886736i | \(0.347033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.04798i | 0.301823i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.2072i | − | 0.457164i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.4432 | + | 11.4432i | −0.427953 | + | 0.427953i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.5519 | − | 20.5519i | −0.767523 | − | 0.767523i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.7820 | −0.737744 | −0.368872 | − | 0.929480i | \(-0.620256\pi\) | ||||
−0.368872 | + | 0.929480i | \(0.620256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.96345 | 0.259332 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.75089 | + | 6.75089i | 0.251068 | + | 0.251068i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.09907 | − | 1.09907i | 0.0408184 | − | 0.0408184i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00706i | 0.185702i | 0.995680 | + | 0.0928508i | \(0.0295980\pi\) | ||||
−0.995680 | + | 0.0928508i | \(0.970402\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 15.6184i | − | 0.578461i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.18097 | + | 2.18097i | −0.0806660 | + | 0.0806660i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.52183 | + | 1.52183i | 0.0562101 | + | 0.0562101i | 0.734653 | − | 0.678443i | \(-0.237345\pi\) |
−0.678443 | + | 0.734653i | \(0.737345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.12102 | 0.262663 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.3289 | 0.896168 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.0436 | + | 15.0436i | 0.553388 | + | 0.553388i | 0.927417 | − | 0.374029i | \(-0.122024\pi\) |
−0.374029 | + | 0.927417i | \(0.622024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.9948 | + | 28.9948i | −1.06515 | + | 1.06515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 40.7480i | − | 1.49490i | −0.664318 | − | 0.747450i | \(-0.731278\pi\) | ||
0.664318 | − | 0.747450i | \(-0.268722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3862i | 0.380521i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4142 | − | 13.4142i | 0.490801 | − | 0.490801i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.45770 | − | 5.45770i | −0.199420 | − | 0.199420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.8596 | −0.761179 | −0.380590 | − | 0.924744i | \(-0.624279\pi\) | ||||
−0.380590 | + | 0.924744i | \(0.624279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.8150 | 0.467004 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0396 | + | 12.0396i | 0.438166 | + | 0.438166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.1062 | − | 14.1062i | 0.512698 | − | 0.512698i | −0.402654 | − | 0.915352i | \(-0.631912\pi\) |
0.915352 | + | 0.402654i | \(0.131912\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.7087i | 0.424998i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.7778i | − | 0.499446i | −0.968317 | − | 0.249723i | \(-0.919660\pi\) | ||
0.968317 | − | 0.249723i | \(-0.0803395\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.92157 | + | 1.92157i | −0.0695656 | + | 0.0695656i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.80444 | + | 1.80444i | 0.0652397 | + | 0.0652397i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.0794 | 1.95270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.89137 | −0.248509 | −0.124255 | − | 0.992250i | \(-0.539654\pi\) | ||||
−0.124255 | + | 0.992250i | \(0.539654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1171 | + | 17.1171i | 0.616457 | + | 0.616457i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.4803 | + | 11.4803i | −0.412916 | + | 0.412916i | −0.882753 | − | 0.469837i | \(-0.844313\pi\) |
0.469837 | + | 0.882753i | \(0.344313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.17157i | 0.113926i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.74839i | − | 0.170348i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3417 | − | 14.3417i | 0.513845 | − | 0.513845i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.5794 | − | 32.5794i | −1.16578 | − | 1.16578i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.99093 | −0.285572 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.45381 | −0.194655 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0609 | − | 15.0609i | −0.536862 | − | 0.536862i | 0.385744 | − | 0.922606i | \(-0.373945\pi\) |
−0.922606 | + | 0.385744i | \(0.873945\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.7208 | + | 15.7208i | −0.559676 | + | 0.559676i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.70770i | 0.131831i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1878i | 0.965468i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.45525 | + | 3.45525i | −0.122545 | + | 0.122545i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4057 | + | 10.4057i | 0.368589 | + | 0.368589i | 0.866963 | − | 0.498373i | \(-0.166069\pi\) |
−0.498373 | + | 0.866963i | \(0.666069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.42522 | −0.156553 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.8565 | 1.16093 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.14112 | − | 1.14112i | −0.0402692 | − | 0.0402692i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.26214 | + | 1.26214i | −0.0444847 | + | 0.0444847i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.43062i | − | 0.331973i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.7970i | − | 0.625708i | −0.949801 | − | 0.312854i | \(-0.898715\pi\) | ||
0.949801 | − | 0.312854i | \(-0.101285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.13364 | − | 2.13364i | 0.0749221 | − | 0.0749221i | −0.668653 | − | 0.743575i | \(-0.733129\pi\) |
0.743575 | + | 0.668653i | \(0.233129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.03249 | + | 8.03249i | 0.281712 | + | 0.281712i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.4308 | 0.610576 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0568 | −0.561755 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.47589 | + | 3.47589i | 0.121457 | + | 0.121457i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.3074 | − | 27.3074i | 0.953034 | − | 0.953034i | −0.0459119 | − | 0.998945i | \(-0.514619\pi\) |
0.998945 | + | 0.0459119i | \(0.0146194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1720i | 1.43516i | 0.696474 | + | 0.717582i | \(0.254751\pi\) | ||||
−0.696474 | + | 0.717582i | \(0.745249\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.04205i | − | 0.105911i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.3202 | + | 36.3202i | −1.26298 | + | 1.26298i | −0.313334 | + | 0.949643i | \(0.601446\pi\) |
−0.949643 | + | 0.313334i | \(0.898554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.8586 | + | 23.8586i | 0.828645 | + | 0.828645i | 0.987329 | − | 0.158685i | \(-0.0507254\pi\) |
−0.158685 | + | 0.987329i | \(0.550725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5013 | 0.849940 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.12006 | 0.315991 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.1744 | + | 13.1744i | 0.455919 | + | 0.455919i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.5297 | − | 11.5297i | 0.398524 | − | 0.398524i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 17.7869i | − | 0.614072i | −0.951698 | − | 0.307036i | \(-0.900663\pi\) | ||
0.951698 | − | 0.307036i | \(-0.0993372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 26.5841i | − | 0.916693i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.87137 | + | 7.87137i | −0.271105 | + | 0.271105i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.8507 | − | 12.8507i | −0.442077 | − | 0.442077i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.20520 | 0.0414111 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.15619 | −0.142640 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.5519 | − | 26.5519i | −0.910186 | − | 0.910186i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.33423 | − | 4.33423i | 0.148401 | − | 0.148401i | −0.629002 | − | 0.777403i | \(-0.716536\pi\) |
0.777403 | + | 0.629002i | \(0.216536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.2847i | 0.454327i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.7072i | 1.35637i | 0.734890 | + | 0.678186i | \(0.237234\pi\) | ||||
−0.734890 | + | 0.678186i | \(0.762766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.45317 | − | 3.45317i | 0.117820 | − | 0.117820i | −0.645738 | − | 0.763559i | \(-0.723450\pi\) |
0.763559 | + | 0.645738i | \(0.223450\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.997546 | + | 0.997546i | 0.0339963 | + | 0.0339963i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.1975 | 1.53854 | 0.769271 | − | 0.638923i | \(-0.220620\pi\) | ||||
0.769271 | + | 0.638923i | \(0.220620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.38131 | 0.216971 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.2754 | + | 11.2754i | 0.382932 | + | 0.382932i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.68832 | − | 8.68832i | 0.294731 | − | 0.294731i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.8648i | 1.58795i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 17.1661i | − | 0.580986i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.327919 | − | 0.327919i | 0.0110857 | − | 0.0110857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3758 | + | 14.3758i | 0.485436 | + | 0.485436i | 0.906863 | − | 0.421426i | \(-0.138470\pi\) |
−0.421426 | + | 0.906863i | \(0.638470\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.9855 | −0.707824 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2102 | −0.411371 | −0.205685 | − | 0.978618i | \(-0.565942\pi\) | ||||
−0.205685 | + | 0.978618i | \(0.565942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.6792 | − | 18.6792i | −0.628605 | − | 0.628605i | 0.319112 | − | 0.947717i | \(-0.396615\pi\) |
−0.947717 | + | 0.319112i | \(0.896615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.18820 | + | 7.18820i | −0.241629 | + | 0.241629i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.4950i | 1.42684i | 0.700736 | + | 0.713421i | \(0.252855\pi\) | ||||
−0.700736 | + | 0.713421i | \(0.747145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.09171i | 0.170770i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.614157 | − | 0.614157i | 0.0205750 | − | 0.0205750i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.2897 | − | 16.2897i | −0.545115 | − | 0.545115i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.4828 | −0.718092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.5544 | −0.753070 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.48577 | − | 3.48577i | −0.116257 | − | 0.116257i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.42522 | + | 4.42522i | −0.147425 | + | 0.147425i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.11684i | − | 0.0371661i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.5228i | 0.549238i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.22149 | − | 4.22149i | 0.140172 | − | 0.140172i | −0.633539 | − | 0.773711i | \(-0.718398\pi\) |
0.773711 | + | 0.633539i | \(0.218398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.0920 | + | 13.0920i | 0.434233 | + | 0.434233i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.0306 | −1.09435 | −0.547177 | − | 0.837017i | \(-0.684297\pi\) | ||||
−0.547177 | + | 0.837017i | \(0.684297\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.9631 | −0.958539 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.61379 | − | 3.61379i | −0.119468 | − | 0.119468i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.03643 | − | 2.03643i | 0.0672488 | − | 0.0672488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.3501i | − | 0.605313i | −0.953100 | − | 0.302657i | \(-0.902126\pi\) | ||
0.953100 | − | 0.302657i | \(-0.0978736\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.1954i | 1.06088i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.7577 | − | 62.7577i | 2.06570 | − | 2.06570i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.89848 | + | 6.89848i | 0.226821 | + | 0.226821i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.5068 | 0.936287 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.7648 | 1.66554 | 0.832770 | − | 0.553619i | \(-0.186754\pi\) | ||||
0.832770 | + | 0.553619i | \(0.186754\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.5720 | + | 33.5720i | 1.10028 | + | 1.10028i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.363785 | + | 0.363785i | −0.0119098 | + | 0.0119098i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.89603i | − | 0.127414i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.2804i | 1.87127i | 0.352971 | + | 0.935634i | \(0.385171\pi\) | ||||
−0.352971 | + | 0.935634i | \(0.614829\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7569 | − | 16.7569i | 0.546842 | − | 0.546842i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.9897 | + | 41.9897i | 1.36882 | + | 1.36882i | 0.862119 | + | 0.506706i | \(0.169137\pi\) |
0.506706 | + | 0.862119i | \(0.330863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.1561 | 0.363292 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.38418 | −0.0775574 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7588 | + | 10.7588i | 0.349613 | + | 0.349613i | 0.859965 | − | 0.510353i | \(-0.170485\pi\) |
−0.510353 | + | 0.859965i | \(0.670485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.19814 | − | 2.19814i | 0.0713545 | − | 0.0713545i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 27.6540i | − | 0.896742i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.6640i | − | 1.09049i | −0.838278 | − | 0.545243i | \(-0.816438\pi\) | ||
0.838278 | − | 0.545243i | \(-0.183562\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.75491 | − | 2.75491i | 0.0891467 | − | 0.0891467i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.34342 | + | 3.34342i | 0.108077 | + | 0.108077i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.1542 | −0.327897 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.9411 | −0.675520 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.3426 | − | 22.3426i | −0.719981 | − | 0.719981i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.4613 | − | 13.4613i | 0.433334 | − | 0.433334i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.6075i | − | 0.405430i | −0.979238 | − | 0.202715i | \(-0.935024\pi\) | ||
0.979238 | − | 0.202715i | \(-0.0649764\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 9.87174i | − | 0.317126i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.401057 | + | 0.401057i | −0.0128705 | + | 0.0128705i | −0.713513 | − | 0.700642i | \(-0.752897\pi\) |
0.700642 | + | 0.713513i | \(0.252897\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.06891 | + | 2.06891i | 0.0663263 | + | 0.0663263i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.85990 | 0.187667 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.1220 | −0.675752 | −0.337876 | − | 0.941191i | \(-0.609708\pi\) | ||||
−0.337876 | + | 0.941191i | \(0.609708\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.4708 | − | 35.4708i | −1.13365 | − | 1.13365i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.86648 | + | 7.86648i | −0.251158 | + | 0.251158i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.2583i | 1.12457i | 0.826945 | + | 0.562283i | \(0.190077\pi\) | ||||
−0.826945 | + | 0.562283i | \(0.809923\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0665816i | 0.00212147i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.13304 | − | 1.13304i | 0.0360651 | − | 0.0360651i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.24509 | − | 6.24509i | −0.198582 | − | 0.198582i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9471 | −0.379513 | −0.189756 | − | 0.981831i | \(-0.560770\pi\) | ||||
−0.189756 | + | 0.981831i | \(0.560770\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.3397 | −0.835867 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | − | 8.00000i | −0.253617 | − | 0.253617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.49031 | − | 7.49031i | 0.237221 | − | 0.237221i | −0.578478 | − | 0.815698i | \(-0.696353\pi\) |
0.815698 | + | 0.578478i | \(0.196353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 50.1564i | − | 1.58688i |
(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 | 1280.2.l.h.321.2 | yes | 8 | |
4.3 | odd | 2 | 1280.2.l.c.321.3 | yes | 8 | ||
8.3 | odd | 2 | 1280.2.l.e.321.2 | yes | 8 | ||
8.5 | even | 2 | 1280.2.l.b.321.3 | ✓ | 8 | ||
16.3 | odd | 4 | 1280.2.l.e.961.2 | yes | 8 | ||
16.5 | even | 4 | inner | 1280.2.l.h.961.2 | yes | 8 | |
16.11 | odd | 4 | 1280.2.l.c.961.3 | yes | 8 | ||
16.13 | even | 4 | 1280.2.l.b.961.3 | yes | 8 | ||
32.5 | even | 8 | 5120.2.a.c.1.3 | 4 | |||
32.11 | odd | 8 | 5120.2.a.p.1.3 | 4 | |||
32.21 | even | 8 | 5120.2.a.j.1.2 | 4 | |||
32.27 | odd | 8 | 5120.2.a.i.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1280.2.l.b.321.3 | ✓ | 8 | 8.5 | even | 2 | ||
1280.2.l.b.961.3 | yes | 8 | 16.13 | even | 4 | ||
1280.2.l.c.321.3 | yes | 8 | 4.3 | odd | 2 | ||
1280.2.l.c.961.3 | yes | 8 | 16.11 | odd | 4 | ||
1280.2.l.e.321.2 | yes | 8 | 8.3 | odd | 2 | ||
1280.2.l.e.961.2 | yes | 8 | 16.3 | odd | 4 | ||
1280.2.l.h.321.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1280.2.l.h.961.2 | yes | 8 | 16.5 | even | 4 | inner | |
5120.2.a.c.1.3 | 4 | 32.5 | even | 8 | |||
5120.2.a.i.1.2 | 4 | 32.27 | odd | 8 | |||
5120.2.a.j.1.2 | 4 | 32.21 | even | 8 | |||
5120.2.a.p.1.3 | 4 | 32.11 | odd | 8 |