Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 493.4 | ||
Character | \(\chi\) | \(=\) | 2100.493 |
Dual form | 2100.2.ce.d.1657.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.258819 | + | 0.965926i | 0.149429 | + | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54352 | − | 0.728357i | 0.961360 | − | 0.275293i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | + | 0.500000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.14536 | − | 3.71588i | 0.646852 | − | 1.12038i | −0.337019 | − | 0.941498i | \(-0.609419\pi\) |
0.983870 | − | 0.178882i | \(-0.0572481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.22938 | − | 3.22938i | 0.895668 | − | 0.895668i | −0.0993812 | − | 0.995049i | \(-0.531686\pi\) |
0.995049 | + | 0.0993812i | \(0.0316863\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.44549 | + | 0.923215i | −0.835653 | + | 0.223913i | −0.651178 | − | 0.758925i | \(-0.725725\pi\) |
−0.184475 | + | 0.982837i | \(0.559058\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.13437 | + | 5.42888i | 0.719073 | + | 1.24547i | 0.961368 | + | 0.275268i | \(0.0887665\pi\) |
−0.242295 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.36185 | + | 2.26834i | 0.297180 | + | 0.494992i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.749302 | − | 2.79643i | 0.156240 | − | 0.583097i | −0.842756 | − | 0.538296i | \(-0.819068\pi\) |
0.998996 | − | 0.0448005i | \(-0.0142652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.84333i | − | 0.527993i | −0.964524 | − | 0.263997i | \(-0.914959\pi\) | ||
0.964524 | − | 0.263997i | \(-0.0850408\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.34333 | − | 0.775572i | −0.241269 | − | 0.139297i | 0.374491 | − | 0.927231i | \(-0.377818\pi\) |
−0.615760 | + | 0.787934i | \(0.711151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.14453 | + | 1.11052i | 0.721469 | + | 0.193317i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.50550 | − | 1.47519i | −0.905098 | − | 0.242520i | −0.223894 | − | 0.974614i | \(-0.571877\pi\) |
−0.681204 | + | 0.732093i | \(0.738544\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.95516 | + | 2.28351i | 0.633333 | + | 0.365655i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.7150i | − | 1.67339i | −0.547665 | − | 0.836697i | \(-0.684483\pi\) | ||
0.547665 | − | 0.836697i | \(-0.315517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.38553 | − | 2.38553i | −0.363790 | − | 0.363790i | 0.501416 | − | 0.865206i | \(-0.332813\pi\) |
−0.865206 | + | 0.501416i | \(0.832813\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.22104 | − | 8.28905i | 0.323973 | − | 1.20908i | −0.591368 | − | 0.806402i | \(-0.701412\pi\) |
0.915341 | − | 0.402681i | \(-0.131921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.93899 | − | 3.70518i | 0.848428 | − | 0.529311i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.78351 | − | 3.08914i | −0.249742 | − | 0.432566i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.76419 | + | 2.34836i | −1.20385 | + | 0.322572i | −0.804348 | − | 0.594159i | \(-0.797485\pi\) |
−0.399506 | + | 0.916730i | \(0.630818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.43266 | + | 4.43266i | −0.587120 | + | 0.587120i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.820799 | − | 1.42166i | 0.106859 | − | 0.185085i | −0.807637 | − | 0.589680i | \(-0.799254\pi\) |
0.914496 | + | 0.404595i | \(0.132587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.94331 | − | 5.16342i | 1.14507 | − | 0.661108i | 0.197391 | − | 0.980325i | \(-0.436753\pi\) |
0.947682 | + | 0.319216i | \(0.103420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.83858 | + | 1.90254i | −0.231639 | + | 0.239697i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.19759 | + | 4.46947i | 0.146309 | + | 0.546032i | 0.999694 | + | 0.0247507i | \(0.00787921\pi\) |
−0.853385 | + | 0.521282i | \(0.825454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.89508 | 0.348527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7381 | 1.39306 | 0.696530 | − | 0.717528i | \(-0.254726\pi\) | ||||
0.696530 | + | 0.717528i | \(0.254726\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.40462 | + | 8.97416i | 0.281439 | + | 1.05035i | 0.951402 | + | 0.307951i | \(0.0996433\pi\) |
−0.669963 | + | 0.742394i | \(0.733690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.75029 | − | 11.0140i | 0.313425 | − | 1.25516i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.68892 | + | 3.86185i | −0.752562 | + | 0.434492i | −0.826619 | − | 0.562762i | \(-0.809739\pi\) |
0.0740567 | + | 0.997254i | \(0.476405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.32417 | + | 3.32417i | −0.364875 | + | 0.364875i | −0.865604 | − | 0.500729i | \(-0.833065\pi\) |
0.500729 | + | 0.865604i | \(0.333065\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.74645 | − | 0.735908i | 0.294450 | − | 0.0788976i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.91203 | + | 15.4361i | 0.944674 | + | 1.63622i | 0.756403 | + | 0.654105i | \(0.226955\pi\) |
0.188270 | + | 0.982117i | \(0.439712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.86185 | − | 10.5661i | 0.614489 | − | 1.10763i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.401465 | − | 1.49829i | 0.0416300 | − | 0.155365i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.100580 | − | 0.100580i | −0.0102123 | − | 0.0102123i | 0.701982 | − | 0.712194i | \(-0.252299\pi\) |
−0.712194 | + | 0.701982i | \(0.752299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.29073i | 0.431235i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.57834 | + | 4.37535i | 0.754073 | + | 0.435364i | 0.827164 | − | 0.561961i | \(-0.189953\pi\) |
−0.0730910 | + | 0.997325i | \(0.523286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.17860 | + | 0.851703i | 0.313197 | + | 0.0839208i | 0.411993 | − | 0.911187i | \(-0.364833\pi\) |
−0.0987966 | + | 0.995108i | \(0.531499\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8346 | + | 3.43903i | 1.24077 | + | 0.332463i | 0.818764 | − | 0.574130i | \(-0.194659\pi\) |
0.422006 | + | 0.906593i | \(0.361326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.3886 | + | 7.15258i | 1.18662 | + | 0.685093i | 0.957536 | − | 0.288315i | \(-0.0930949\pi\) |
0.229080 | + | 0.973408i | \(0.426428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.69971i | − | 0.540993i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.12116 | − | 9.12116i | −0.858047 | − | 0.858047i | 0.133061 | − | 0.991108i | \(-0.457519\pi\) |
−0.991108 | + | 0.133061i | \(0.957519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.18203 | + | 4.41141i | −0.109279 | + | 0.407835i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.09123 | + | 4.85776i | −0.741722 | + | 0.445310i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.70518 | − | 6.41756i | −0.336835 | − | 0.583414i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3499 | − | 2.77323i | 0.933215 | − | 0.250054i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6203 | + | 10.6203i | −0.942403 | + | 0.942403i | −0.998429 | − | 0.0560260i | \(-0.982157\pi\) |
0.0560260 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.68682 | − | 2.92166i | 0.148517 | − | 0.257238i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.84333 | + | 1.64160i | −0.248423 | + | 0.143427i | −0.619042 | − | 0.785358i | \(-0.712479\pi\) |
0.370619 | + | 0.928785i | \(0.379146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.9265 | + | 11.5255i | 1.03416 | + | 0.999390i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.28878 | + | 16.0060i | 0.366415 | + | 1.36748i | 0.865492 | + | 0.500923i | \(0.167006\pi\) |
−0.499077 | + | 0.866558i | \(0.666327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.478566 | 0.0405914 | 0.0202957 | − | 0.999794i | \(-0.493539\pi\) | ||||
0.0202957 | + | 0.999794i | \(0.493539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.58146 | 0.722689 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.07179 | − | 18.9282i | −0.424124 | − | 1.58285i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.11605 | + | 4.77766i | 0.421965 | + | 0.394054i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.41389 | − | 4.85776i | 0.689292 | − | 0.397963i | −0.114055 | − | 0.993474i | \(-0.536384\pi\) |
0.803347 | + | 0.595511i | \(0.203051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2196 | − | 17.7009i | 0.831660 | − | 1.44048i | −0.0650611 | − | 0.997881i | \(-0.520724\pi\) |
0.896721 | − | 0.442596i | \(-0.145942\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.52227 | − | 2.52227i | 0.203914 | − | 0.203914i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.82282 | − | 2.36407i | 0.704138 | − | 0.188673i | 0.111055 | − | 0.993814i | \(-0.464577\pi\) |
0.593083 | + | 0.805141i | \(0.297910\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.53668 | − | 7.85776i | −0.359782 | − | 0.623161i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.130935 | − | 7.65855i | −0.0103192 | − | 0.603578i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.68973 | + | 10.0382i | −0.210676 | + | 0.786252i | 0.776969 | + | 0.629539i | \(0.216756\pi\) |
−0.987644 | + | 0.156713i | \(0.949910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0521 | − | 16.0521i | −1.24215 | − | 1.24215i | −0.959108 | − | 0.283040i | \(-0.908657\pi\) |
−0.283040 | − | 0.959108i | \(-0.591343\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.85776i | − | 0.604443i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.42888 | − | 3.13437i | −0.415157 | − | 0.239691i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3737 | − | 5.99500i | −1.70104 | − | 0.455792i | −0.727837 | − | 0.685750i | \(-0.759474\pi\) |
−0.973201 | + | 0.229958i | \(0.926141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.58566 | + | 0.424877i | 0.119186 | + | 0.0319357i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19615 | − | 3.00000i | −0.388379 | − | 0.224231i | 0.293079 | − | 0.956088i | \(-0.405320\pi\) |
−0.681457 | + | 0.731858i | \(0.738654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.9871i | 1.41130i | 0.708561 | + | 0.705650i | \(0.249345\pi\) | ||||
−0.708561 | + | 0.705650i | \(0.750655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.30218 | + | 7.30218i | 0.539793 | + | 0.539793i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.96127 | + | 14.7836i | −0.289677 | + | 1.08109i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.31357 | − | 1.28351i | −0.168287 | − | 0.0933620i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.56703 | − | 11.3744i | −0.475174 | − | 0.823025i | 0.524422 | − | 0.851458i | \(-0.324281\pi\) |
−0.999596 | + | 0.0284336i | \(0.990948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.67682 | − | 2.32495i | 0.624571 | − | 0.167353i | 0.0673662 | − | 0.997728i | \(-0.478540\pi\) |
0.557205 | + | 0.830375i | \(0.311874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.53033 | − | 7.53033i | 0.536514 | − | 0.536514i | −0.385989 | − | 0.922503i | \(-0.626140\pi\) |
0.922503 | + | 0.385989i | \(0.126140\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0327307 | − | 0.0566912i | 0.00232021 | − | 0.00401873i | −0.864863 | − | 0.502008i | \(-0.832595\pi\) |
0.867183 | + | 0.497989i | \(0.165928\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00721 | + | 2.31357i | −0.282647 | + | 0.163186i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.07096 | − | 7.23207i | −0.145353 | − | 0.507592i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.749302 | + | 2.79643i | 0.0520801 | + | 0.194366i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.8974 | 1.86053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5733 | −1.34748 | −0.673740 | − | 0.738968i | \(-0.735313\pi\) | ||||
−0.673740 | + | 0.738968i | \(0.735313\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.03805 | + | 11.3382i | 0.208164 | + | 0.776878i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.98168 | − | 0.994260i | −0.270294 | − | 0.0674947i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.04601 | + | 4.64536i | −0.543699 | + | 0.313905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.14536 | + | 14.1082i | −0.547917 | + | 0.949019i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.67793 | − | 9.67793i | 0.648082 | − | 0.648082i | −0.304447 | − | 0.952529i | \(-0.598472\pi\) |
0.952529 | + | 0.304447i | \(0.0984717\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9418 | − | 2.93184i | 0.726232 | − | 0.194593i | 0.123281 | − | 0.992372i | \(-0.460658\pi\) |
0.602951 | + | 0.797779i | \(0.293992\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.04693 | + | 1.81334i | 0.0691833 | + | 0.119829i | 0.898542 | − | 0.438888i | \(-0.144627\pi\) |
−0.829359 | + | 0.558716i | \(0.811294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3505 | − | 0.194056i | 0.746811 | − | 0.0127680i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.39622 | + | 23.8710i | −0.419030 | + | 1.56384i | 0.357593 | + | 0.933878i | \(0.383598\pi\) |
−0.776623 | + | 0.629965i | \(0.783069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.46148 | − | 5.46148i | −0.354761 | − | 0.354761i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4022i | 1.38439i | 0.721710 | + | 0.692196i | \(0.243357\pi\) | ||||
−0.721710 | + | 0.692196i | \(0.756643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.4877 | + | 12.9833i | 1.44856 | + | 0.836328i | 0.998396 | − | 0.0566174i | \(-0.0180315\pi\) |
0.450166 | + | 0.892945i | \(0.351365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.965926 | + | 0.258819i | 0.0619642 | + | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.6539 | + | 7.40985i | 1.75958 | + | 0.471478i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.07126 | − | 2.35054i | −0.258006 | − | 0.148960i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.18432i | − | 0.137873i | −0.997621 | − | 0.0689365i | \(-0.978039\pi\) | ||
0.997621 | − | 0.0689365i | \(-0.0219606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.78369 | − | 8.78369i | −0.552226 | − | 0.552226i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.548601 | − | 2.04741i | 0.0342208 | − | 0.127714i | −0.946702 | − | 0.322110i | \(-0.895608\pi\) |
0.980923 | + | 0.194396i | \(0.0622747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0778 | + | 0.257780i | −0.936890 | + | 0.0160177i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.42166 | + | 2.46240i | 0.0879988 | + | 0.152418i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.1450 | + | 6.73759i | −1.55051 | + | 0.415458i | −0.929644 | − | 0.368460i | \(-0.879885\pi\) |
−0.620865 | + | 0.783917i | \(0.713219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6035 | + | 12.6035i | −0.771323 | + | 0.771323i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.89508 | − | 5.01443i | 0.176516 | − | 0.305735i | −0.764169 | − | 0.645016i | \(-0.776851\pi\) |
0.940685 | + | 0.339281i | \(0.110184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.07112 | + | 2.92781i | −0.308049 | + | 0.177852i | −0.646053 | − | 0.763293i | \(-0.723581\pi\) |
0.338004 | + | 0.941145i | \(0.390248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.7233 | + | 2.92740i | 0.709524 | + | 0.177174i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.03040 | − | 7.57756i | −0.121995 | − | 0.455291i | 0.877720 | − | 0.479174i | \(-0.159064\pi\) |
−0.999715 | + | 0.0238829i | \(0.992397\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.55114 | 0.0928645 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.313341 | −0.0186923 | −0.00934617 | − | 0.999956i | \(-0.502975\pi\) | ||||
−0.00934617 | + | 0.999956i | \(0.502975\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.74396 | + | 6.50853i | 0.103667 | + | 0.386892i | 0.998191 | − | 0.0601295i | \(-0.0191514\pi\) |
−0.894523 | + | 0.447022i | \(0.852485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.80431 | − | 27.2537i | −0.460674 | − | 1.60874i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.70338 | + | 2.13815i | −0.217846 | + | 0.125774i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0711205 | − | 0.123184i | 0.00416916 | − | 0.00722119i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.70685 | − | 8.70685i | 0.508659 | − | 0.508659i | −0.405455 | − | 0.914115i | \(-0.632887\pi\) |
0.914115 | + | 0.405455i | \(0.132887\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.14453 | + | 1.11052i | −0.240490 | + | 0.0644391i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.61096 | − | 11.4505i | −0.382322 | − | 0.662201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.80516 | − | 4.33013i | −0.449882 | − | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.26485 | + | 8.45253i | −0.130112 | + | 0.485585i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2469 | − | 22.2469i | −1.26970 | − | 1.26970i | −0.946245 | − | 0.323451i | \(-0.895157\pi\) |
−0.323451 | − | 0.946245i | \(-0.604843\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.29073i | 0.187203i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.56391 | + | 1.48027i | 0.145386 | + | 0.0839385i | 0.570928 | − | 0.821000i | \(-0.306583\pi\) |
−0.425543 | + | 0.904938i | \(0.639917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.11045 | + | 1.36934i | 0.288860 | + | 0.0773998i | 0.400339 | − | 0.916367i | \(-0.368892\pi\) |
−0.111479 | + | 0.993767i | \(0.535559\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.7015 | + | 5.27900i | 1.10655 | + | 0.296498i | 0.765428 | − | 0.643522i | \(-0.222527\pi\) |
0.341119 | + | 0.940020i | \(0.389194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.5655 | − | 6.09998i | −0.591553 | − | 0.341533i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.2874i | 0.741630i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.8114 | − | 15.8114i | −0.879772 | − | 0.879772i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.70245 | + | 13.8177i | −0.204746 | + | 0.764122i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.388112 | − | 22.7011i | −0.0213973 | − | 1.25155i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.91036 | + | 5.04089i | 0.159968 | + | 0.277072i | 0.934857 | − | 0.355025i | \(-0.115528\pi\) |
−0.774889 | + | 0.632097i | \(0.782194\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.50550 | − | 1.47519i | 0.301699 | − | 0.0808401i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2904 | + | 20.2904i | −1.10529 | + | 1.10529i | −0.111526 | + | 0.993761i | \(0.535574\pi\) |
−0.993761 | + | 0.111526i | \(0.964426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.44964 | − | 11.1711i | 0.350296 | − | 0.606731i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.76386 | + | 3.32777i | −0.312131 | + | 0.180209i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4073 | − | 13.7499i | 0.669929 | − | 0.742425i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.54368 | − | 31.8854i | −0.458649 | − | 1.71170i | −0.677134 | − | 0.735860i | \(-0.736778\pi\) |
0.218485 | − | 0.975840i | \(-0.429889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.3566 | −0.661431 | −0.330716 | − | 0.943730i | \(-0.607290\pi\) | ||||
−0.330716 | + | 0.943730i | \(0.607290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.56703 | −0.243770 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.173986 | + | 0.649324i | 0.00926034 | + | 0.0345600i | 0.970401 | − | 0.241498i | \(-0.0776386\pi\) |
−0.961141 | + | 0.276058i | \(0.910972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.78640 | − | 6.55825i | −0.359174 | − | 0.347099i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.7577 | + | 14.2939i | −1.30666 | + | 0.754401i | −0.981537 | − | 0.191271i | \(-0.938739\pi\) |
−0.325123 | + | 0.945672i | \(0.605406\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.1485 | + | 17.5777i | −0.534131 | + | 0.925142i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.23992 | − | 5.23992i | 0.275024 | − | 0.275024i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50744 | + | 0.671865i | −0.130887 | + | 0.0350711i | −0.323668 | − | 0.946171i | \(-0.604916\pi\) |
0.192781 | + | 0.981242i | \(0.438249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.35748 | + | 9.27942i | 0.278899 | + | 0.483068i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.5815 | + | 12.3566i | −1.06854 | + | 0.641520i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.33806 | + | 4.99370i | −0.0692820 | + | 0.258564i | −0.991876 | − | 0.127208i | \(-0.959398\pi\) |
0.922594 | + | 0.385772i | \(0.126065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.18219 | − | 9.18219i | −0.472907 | − | 0.472907i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.44740i | − | 0.433914i | −0.976181 | − | 0.216957i | \(-0.930387\pi\) | ||
0.976181 | − | 0.216957i | \(-0.0696131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.0072 | − | 7.50972i | −0.666380 | − | 0.384735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.28905 | − | 2.22104i | −0.423551 | − | 0.113490i | 0.0407465 | − | 0.999170i | \(-0.487026\pi\) |
−0.464297 | + | 0.885679i | \(0.653693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.25869 | + | 0.873164i | 0.165649 | + | 0.0443854i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0903 | − | 8.71239i | −0.765109 | − | 0.441736i | 0.0660180 | − | 0.997818i | \(-0.478971\pi\) |
−0.831127 | + | 0.556083i | \(0.812304\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3268i | 0.522251i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.32157 | − | 2.32157i | −0.117108 | − | 0.117108i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.46654 | + | 9.20526i | −0.123792 | + | 0.461999i | −0.999794 | − | 0.0203095i | \(-0.993535\pi\) |
0.876002 | + | 0.482308i | \(0.160202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.04601 | + | 14.5031i | −0.402804 | + | 0.726064i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.42479 | + | 9.39601i | 0.270901 | + | 0.469214i | 0.969093 | − | 0.246696i | \(-0.0793451\pi\) |
−0.698192 | + | 0.715911i | \(0.746012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.84273 | + | 1.83350i | −0.340861 | + | 0.0913334i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.2929 | + | 17.2929i | −0.857179 | + | 0.857179i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2986 | − | 28.2299i | 0.805912 | − | 1.39588i | −0.109761 | − | 0.993958i | \(-0.535009\pi\) |
0.915673 | − | 0.401923i | \(-0.131658\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.3505 | + | 8.28529i | −0.707860 | + | 0.408683i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.05224 | − | 4.21387i | 0.0517773 | − | 0.207351i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.123862 | + | 0.462259i | 0.00606555 | + | 0.0226369i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.6179 | −1.10496 | −0.552479 | − | 0.833527i | \(-0.686318\pi\) | ||||
−0.552479 | + | 0.833527i | \(0.686318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0370 | −0.586649 | −0.293325 | − | 0.956013i | \(-0.594762\pi\) | ||||
−0.293325 | + | 0.956013i | \(0.594762\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.22104 | + | 8.28905i | 0.107991 | + | 0.403028i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9867 | − | 19.6472i | 0.918830 | − | 0.950794i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.9705 | − | 9.79794i | 0.819345 | − | 0.473049i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0144 | + | 29.4699i | −0.819556 | + | 1.41951i | 0.0864534 | + | 0.996256i | \(0.472447\pi\) |
−0.906010 | + | 0.423257i | \(0.860887\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.6580 | − | 22.6580i | 1.08888 | − | 1.08888i | 0.0932307 | − | 0.995645i | \(-0.470281\pi\) |
0.995645 | − | 0.0932307i | \(-0.0297194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.5301 | − | 4.69717i | 0.838578 | − | 0.224696i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.99698 | + | 3.45887i | 0.0953106 | + | 0.165083i | 0.909738 | − | 0.415182i | \(-0.136282\pi\) |
−0.814428 | + | 0.580265i | \(0.802949\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.29073 | + | 6.17828i | −0.156701 | + | 0.294204i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50559 | − | 13.0831i | 0.166556 | − | 0.621595i | −0.831281 | − | 0.555853i | \(-0.812392\pi\) |
0.997837 | − | 0.0657421i | \(-0.0209415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.86991 | + | 6.86991i | 0.324936 | + | 0.324936i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 28.8496i | − | 1.36150i | −0.732518 | − | 0.680748i | \(-0.761655\pi\) | ||
0.732518 | − | 0.680748i | \(-0.238345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.8155 | − | 22.9875i | −1.87484 | − | 1.08244i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.7428 | + | 5.29006i | 0.927596 | + | 0.248549i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.1998 | + | 5.68047i | 0.991685 | + | 0.265721i | 0.717958 | − | 0.696086i | \(-0.245077\pi\) |
0.273727 | + | 0.961808i | \(0.411744\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.08914 | + | 1.78351i | 0.144189 | + | 0.0832473i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.11282i | 0.284702i | 0.989816 | + | 0.142351i | \(0.0454662\pi\) | ||||
−0.989816 | + | 0.142351i | \(0.954534\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0346 | + | 27.0346i | 1.25640 | + | 1.25640i | 0.952797 | + | 0.303607i | \(0.0981909\pi\) |
0.303607 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.65012 | + | 9.89037i | −0.122633 | + | 0.457672i | −0.999744 | − | 0.0226152i | \(-0.992801\pi\) |
0.877112 | + | 0.480287i | \(0.159467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.30146 | + | 10.4959i | 0.290974 | + | 0.484656i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.56703 | + | 7.91033i | 0.210438 | + | 0.364489i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.9822 | + | 3.74651i | −0.642901 | + | 0.172265i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.41583 | − | 6.41583i | 0.293761 | − | 0.293761i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3744 | + | 19.7011i | −0.519711 | + | 0.900166i | 0.480027 | + | 0.877254i | \(0.340627\pi\) |
−0.999737 | + | 0.0229118i | \(0.992706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.5433 | + | 13.0154i | −1.02789 | + | 0.593450i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.36370 | − | 2.10865i | 0.335060 | − | 0.0959470i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.94217 | + | 37.1047i | 0.450523 | + | 1.68137i | 0.700927 | + | 0.713233i | \(0.252770\pi\) |
−0.250405 | + | 0.968141i | \(0.580564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3923 | −0.469956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.47626 | −0.247140 | −0.123570 | − | 0.992336i | \(-0.539434\pi\) | ||||
−0.123570 | + | 0.992336i | \(0.539434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.62501 | + | 9.79665i | 0.118224 | + | 0.441219i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.8562 | − | 8.54954i | 1.33923 | − | 0.383499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.2370 | + | 5.91036i | −0.458273 | + | 0.264584i | −0.711318 | − | 0.702871i | \(-0.751901\pi\) |
0.253045 | + | 0.967455i | \(0.418568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3505 | − | 19.6597i | 0.507105 | − | 0.878331i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.7279 | − | 12.7279i | 0.567510 | − | 0.567510i | −0.363920 | − | 0.931430i | \(-0.618562\pi\) |
0.931430 | + | 0.363920i | \(0.118562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.59001 | − | 2.03374i | 0.337084 | − | 0.0903215i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.41389 | − | 14.5733i | −0.372939 | − | 0.645949i | 0.617077 | − | 0.786903i | \(-0.288317\pi\) |
−0.990016 | + | 0.140953i | \(0.954983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.6526 | + | 21.0745i | 0.559717 | + | 0.932282i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.62247 | − | 6.05513i | 0.0716337 | − | 0.267340i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.0362 | − | 26.0362i | −1.14507 | − | 1.14507i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 23.1629i | − | 1.01674i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.5444 | + | 18.2122i | 1.38199 | + | 0.797890i | 0.992395 | − | 0.123098i | \(-0.0392829\pi\) |
0.389592 | + | 0.920988i | \(0.372616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.87764 | + | 1.03901i | 0.169557 | + | 0.0454328i | 0.342599 | − | 0.939482i | \(-0.388693\pi\) |
−0.173042 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.34444 | + | 1.43204i | 0.232808 | + | 0.0623806i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6600 | + | 7.30925i | 0.550434 | + | 0.317793i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.64160i | 0.0712392i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.6026 | − | 34.6026i | −1.49881 | − | 1.49881i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.55291 | − | 5.79555i | 0.0670132 | − | 0.250097i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.02670 | − | 30.0176i | −0.0442230 | − | 1.29295i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.9248 | + | 25.8505i | 0.641667 | + | 1.11140i | 0.985061 | + | 0.172208i | \(0.0550901\pi\) |
−0.343394 | + | 0.939191i | \(0.611577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3401 | + | 4.91422i | −0.787050 | + | 0.210889i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4023 | + | 17.4023i | −0.744067 | + | 0.744067i | −0.973358 | − | 0.229291i | \(-0.926359\pi\) |
0.229291 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.16342 | + | 8.94331i | −0.220369 | + | 0.381691i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.4361 | − | 8.91203i | 0.657600 | − | 0.379665i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.2006 | + | 14.6946i | −0.603871 | + | 0.624879i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.67716 | + | 24.9195i | 0.282920 | + | 1.05587i | 0.950346 | + | 0.311196i | \(0.100730\pi\) |
−0.667426 | + | 0.744677i | \(0.732604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4075 | −0.651670 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3052 | −0.646184 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.88918 | + | 10.7826i | 0.121764 | + | 0.454430i | 0.999704 | − | 0.0243413i | \(-0.00774885\pi\) |
−0.877939 | + | 0.478772i | \(0.841082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.640985 | − | 2.56693i | 0.0269188 | − | 0.107801i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.8189 | + | 8.55572i | −0.621243 | + | 0.358675i | −0.777353 | − | 0.629065i | \(-0.783438\pi\) |
0.156110 | + | 0.987740i | \(0.450105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.56294 | + | 7.90324i | −0.190953 | + | 0.330740i | −0.945566 | − | 0.325429i | \(-0.894491\pi\) |
0.754613 | + | 0.656170i | \(0.227824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.28718 | − | 9.28718i | 0.387978 | − | 0.387978i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5642 | + | 4.43836i | −0.689575 | + | 0.184771i | −0.586557 | − | 0.809908i | \(-0.699517\pi\) |
−0.103019 | + | 0.994679i | \(0.532850\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.49145 | + | 7.77942i | 0.186658 | + | 0.323302i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.03392 | + | 10.8763i | −0.250329 | + | 0.451224i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0762 | + | 37.6048i | −0.417312 | + | 1.55743i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.8269 | − | 30.8269i | −1.27236 | − | 1.27236i | −0.944844 | − | 0.327520i | \(-0.893787\pi\) |
−0.327520 | − | 0.944844i | \(-0.606213\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 9.72370i | − | 0.400658i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.22273 | + | 5.32475i | 0.379373 | + | 0.219031i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.2166 | − | 8.09652i | −1.24085 | − | 0.332484i | −0.422053 | − | 0.906571i | \(-0.638691\pi\) |
−0.818794 | + | 0.574087i | \(0.805357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.0632308 | + | 0.0169426i | 0.00258786 | + | 0.000693416i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.23190 | − | 1.86594i | −0.132052 | − | 0.0762403i | 0.432519 | − | 0.901625i | \(-0.357625\pi\) |
−0.564571 | + | 0.825385i | \(0.690958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0089i | 0.489854i | 0.969542 | + | 0.244927i | \(0.0787639\pi\) | ||||
−0.969542 | + | 0.244927i | \(0.921236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.27188 | − | 3.27188i | −0.133241 | − | 0.133241i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.09786 | − | 11.5614i | 0.125738 | − | 0.469261i | −0.874127 | − | 0.485698i | \(-0.838565\pi\) |
0.999865 | + | 0.0164366i | \(0.00523216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.44964 | − | 3.87219i | 0.261352 | − | 0.156909i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.5959 | − | 33.9411i | −0.792765 | − | 1.37311i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.48478 | − | 0.665794i | 0.100359 | − | 0.0268912i | −0.208290 | − | 0.978067i | \(-0.566790\pi\) |
0.308649 | + | 0.951176i | \(0.400123\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2339 | + | 30.2339i | −1.21717 | + | 1.21717i | −0.248555 | + | 0.968618i | \(0.579956\pi\) |
−0.968618 | + | 0.248555i | \(0.920044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.9215 | + | 18.9166i | −0.438972 | + | 0.760323i | −0.997611 | − | 0.0690889i | \(-0.977991\pi\) |
0.558638 | + | 0.829412i | \(0.311324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.50721 | + | 1.44754i | −0.100611 | + | 0.0580878i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.9109 | + | 32.7709i | 1.35861 | + | 1.31294i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.96157 | + | 25.9809i | 0.278018 | + | 1.03758i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.3310 | 0.810652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.5651 | 1.85373 | 0.926864 | − | 0.375398i | \(-0.122494\pi\) | ||||
0.926864 | + | 0.375398i | \(0.122494\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.06594 | − | 18.9063i | −0.201353 | − | 0.751459i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.21383 | − | 31.1447i | 0.285822 | − | 1.23400i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.1655 | + | 5.86906i | −0.402142 | + | 0.232177i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.7124 | + | 35.8749i | −0.818090 | + | 1.41697i | 0.0889971 | + | 0.996032i | \(0.471634\pi\) |
−0.907087 | + | 0.420942i | \(0.861700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.2798 | + | 27.2798i | −1.07581 | + | 1.07581i | −0.0789320 | + | 0.996880i | \(0.525151\pi\) |
−0.996880 | + | 0.0789320i | \(0.974849\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.2296 | − | 6.76026i | 0.991879 | − | 0.265773i | 0.273839 | − | 0.961775i | \(-0.411706\pi\) |
0.718040 | + | 0.696002i | \(0.245040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.52182 | − | 6.09998i | −0.138244 | − | 0.239445i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0701533 | − | 4.10334i | −0.00274952 | − | 0.160823i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.63993 | + | 13.5844i | −0.142441 | + | 0.531599i | 0.857414 | + | 0.514626i | \(0.172069\pi\) |
−0.999856 | + | 0.0169724i | \(0.994597\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.56954 | − | 6.56954i | −0.256302 | − | 0.256302i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 3.71552i | − | 0.144736i | −0.997378 | − | 0.0723680i | \(-0.976944\pi\) | ||
0.997378 | − | 0.0723680i | \(-0.0230556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1300 | − | 17.9729i | −1.21082 | − | 0.699065i | −0.247878 | − | 0.968791i | \(-0.579733\pi\) |
−0.962937 | + | 0.269727i | \(0.913067\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.7356 | − | 4.21635i | −0.611121 | − | 0.163750i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.95119 | − | 2.13051i | −0.307871 | − | 0.0824938i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.8530 | + | 6.84333i | 0.458263 | + | 0.264578i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 44.3097i | − | 1.71056i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.6052 | − | 31.6052i | −1.21829 | − | 1.21829i | −0.968230 | − | 0.250061i | \(-0.919549\pi\) |
−0.250061 | − | 0.968230i | \(-0.580451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.20311 | − | 19.4183i | 0.199972 | − | 0.746305i | −0.790952 | − | 0.611878i | \(-0.790414\pi\) |
0.990924 | − | 0.134426i | \(-0.0429191\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.329084 | − | 0.182568i | −0.0126291 | − | 0.00700633i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.66389 | + | 9.81014i | 0.217041 | + | 0.375925i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.69375 | − | 1.25769i | 0.179601 | − | 0.0481241i | −0.167897 | − | 0.985804i | \(-0.553698\pi\) |
0.347499 | + | 0.937680i | \(0.387031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.48059 | + | 1.48059i | −0.0564879 | + | 0.0564879i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.7191 | + | 35.8866i | −0.789337 | + | 1.36717i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.9310 | + | 22.4768i | −1.48101 | + | 0.855059i | −0.999768 | − | 0.0215304i | \(-0.993146\pi\) |
−0.481238 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.12518 | + | 10.9136i | 0.118716 | + | 0.414572i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.89221 | + | 36.9182i | 0.374694 | + | 1.39838i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.7131 | −0.934736 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.2455 | −1.14236 | −0.571179 | − | 0.820826i | \(-0.693514\pi\) | ||||
−0.571179 | + | 0.820826i | \(0.693514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.24759 | − | 34.5125i | −0.348779 | − | 1.30166i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.4625 | + | 5.60907i | 0.844788 | + | 0.210951i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0324 | − | 17.3392i | 1.12789 | − | 0.651189i | 0.184488 | − | 0.982835i | \(-0.440937\pi\) |
0.943404 | + | 0.331646i | \(0.107604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.86185 | − | 6.68892i | 0.144831 | − | 0.250854i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.17540 | + | 3.17540i | −0.118920 | + | 0.118920i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.6729 | + | 5.53929i | −0.772044 | + | 0.206869i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.75441 | + | 13.4310i | 0.289191 | + | 0.500893i | 0.973617 | − | 0.228189i | \(-0.0732805\pi\) |
−0.684426 | + | 0.729082i | \(0.739947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.70518 | − | 0.148829i | 0.324198 | − | 0.00554269i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.72065 | + | 25.0818i | −0.249944 | + | 0.932802i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8475 | + | 12.8475i | 0.476489 | + | 0.476489i | 0.904007 | − | 0.427518i | \(-0.140612\pi\) |
−0.427518 | + | 0.904007i | \(0.640612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4217 | + | 6.01695i | 0.385459 | + | 0.222545i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.8913 | + | 3.99011i | 0.550023 | + | 0.147378i | 0.523119 | − | 0.852260i | \(-0.324768\pi\) |
0.0269041 | + | 0.999638i | \(0.491435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.1773 | + | 5.13854i | 0.706404 | + | 0.189280i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.8911 | − | 20.1444i | −1.28349 | − | 0.741024i | −0.306006 | − | 0.952030i | \(-0.598993\pi\) |
−0.977485 | + | 0.211006i | \(0.932326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.6295i | 1.05173i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.23914 | − | 7.23914i | −0.265578 | − | 0.265578i | 0.561737 | − | 0.827316i | \(-0.310133\pi\) |
−0.827316 | + | 0.561737i | \(0.810133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.21673 | − | 4.54090i | 0.0445179 | − | 0.166143i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.1500 | − | 0.600946i | 1.28435 | − | 0.0219581i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.47739 | − | 6.02301i | −0.126892 | − | 0.219783i | 0.795579 | − | 0.605850i | \(-0.207167\pi\) |
−0.922471 | + | 0.386067i | \(0.873833\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.10989 | − | 0.565343i | 0.0768887 | − | 0.0206023i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.5691 | + | 21.5691i | −0.783941 | + | 0.783941i | −0.980493 | − | 0.196552i | \(-0.937025\pi\) |
0.196552 | + | 0.980493i | \(0.437025\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.21101 | − | 10.7578i | 0.225445 | − | 0.390483i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.7783 | − | 16.6152i | 1.04321 | − | 0.602299i | 0.122471 | − | 0.992472i | \(-0.460918\pi\) |
0.920741 | + | 0.390173i | \(0.127585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.7204 | + | 9.16939i | 1.32937 | + | 0.331954i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.94042 | − | 7.24176i | −0.0700647 | − | 0.261485i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2327 | −0.405061 | −0.202530 | − | 0.979276i | \(-0.564917\pi\) | ||||
−0.202530 | + | 0.979276i | \(0.564917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.11963 | 0.0763366 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5342 | + | 39.3142i | 0.378889 | + | 1.41403i | 0.847578 | + | 0.530671i | \(0.178060\pi\) |
−0.468688 | + | 0.883364i | \(0.655273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.15142 | − | 14.4973i | −0.148931 | − | 0.520089i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.1702 | − | 33.5846i | 2.08416 | − | 1.20329i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.1826 | − | 43.6175i | 0.901103 | − | 1.56076i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.01054 | + | 2.01054i | −0.0718508 | + | 0.0718508i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.6110 | − | 13.0253i | 1.73280 | − | 0.464301i | 0.751972 | − | 0.659195i | \(-0.229103\pi\) |
0.980824 | + | 0.194894i | \(0.0624364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.0160 | − | 22.5444i | −0.463383 | − | 0.802603i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.8433 | − | 16.5564i | −1.06111 | − | 0.588678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2067 | − | 45.5560i | 0.433472 | − | 1.61774i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.99837 | + | 7.99837i | 0.283317 | + | 0.283317i | 0.834430 | − | 0.551113i | \(-0.185797\pi\) |
−0.551113 | + | 0.834430i | \(0.685797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.6103i | 1.08292i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4361 | − | 8.91203i | −0.545408 | − | 0.314891i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.5057 | + | 10.3176i | 1.35884 | + | 0.364099i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.59287 | + | 1.49860i | 0.196878 | + | 0.0527534i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.21773 | + | 1.85776i | 0.113129 | + | 0.0653153i | 0.555497 | − | 0.831518i | \(-0.312528\pi\) |
−0.442368 | + | 0.896834i | \(0.645861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.0896i | − | 1.33751i | −0.743484 | − | 0.668754i | \(-0.766828\pi\) | ||
0.743484 | − | 0.668754i | \(-0.233172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.14055 | − | 4.14055i | −0.145216 | − | 0.145216i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.47363 | − | 20.4279i | 0.191498 | − | 0.714681i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.206552 | + | 12.0815i | 0.00721752 | + | 0.422160i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.86906 | + | 4.96937i | 0.100131 | + | 0.173432i | 0.911739 | − | 0.410771i | \(-0.134740\pi\) |
−0.811607 | + | 0.584203i | \(0.801407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.3016 | + | 7.85133i | −1.02139 | + | 0.273680i | −0.730381 | − | 0.683040i | \(-0.760657\pi\) |
−0.291008 | + | 0.956721i | \(0.593991\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4343 | + | 23.4343i | −0.814892 | + | 0.814892i | −0.985363 | − | 0.170471i | \(-0.945471\pi\) |
0.170471 | + | 0.985363i | \(0.445471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.0697 | − | 19.1733i | 0.384466 | − | 0.665915i | −0.607229 | − | 0.794527i | \(-0.707719\pi\) |
0.991695 | + | 0.128612i | \(0.0410522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.79385 | − | 3.92243i | 0.235676 | − | 0.136068i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.0420 | + | 18.2491i | −0.590472 | + | 0.632294i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.401465 | + | 1.49829i | 0.0138767 | + | 0.0517885i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.41782 | 0.0834725 | 0.0417362 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417362 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.9155 | 0.721223 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0810985 | − | 0.302664i | −0.00279318 | − | 0.0104243i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0985 | − | 13.6245i | −0.484429 | − | 0.468143i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.83539 | + | 3.36906i | −0.200270 | + | 0.115626i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.25057 | + | 14.2904i | −0.282826 | + | 0.489869i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6647 | − | 18.6647i | 0.639069 | − | 0.639069i | −0.311257 | − | 0.950326i | \(-0.600750\pi\) |
0.950326 | + | 0.311257i | \(0.100750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.95540 | + | 0.791896i | −0.100954 | + | 0.0270507i | −0.308943 | − | 0.951081i | \(-0.599975\pi\) |
0.207988 | + | 0.978131i | \(0.433308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9260 | − | 29.3166i | −0.577506 | − | 1.00027i | −0.995764 | − | 0.0919421i | \(-0.970693\pi\) |
0.418258 | − | 0.908328i | \(-0.362641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.3052 | − | 14.5922i | 0.828318 | − | 0.497300i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.98044 | + | 7.39110i | −0.0674150 | + | 0.251596i | −0.991407 | − | 0.130817i | \(-0.958240\pi\) |
0.923992 | + | 0.382413i | \(0.124907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.02380 | − | 3.02380i | −0.102694 | − | 0.102694i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.1403i | 1.12421i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3011 | + | 10.5661i | 0.620108 | + | 0.358020i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.137394 | + | 0.0368147i | 0.00465009 | + | 0.00124599i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.5098 | + | 14.6059i | 1.84067 | + | 0.493205i | 0.998911 | − | 0.0466538i | \(-0.0148558\pi\) |
0.841755 | + | 0.539859i | \(0.181522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.6637 | + | 6.15667i | 0.359677 | + | 0.207659i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.5446i | 0.456328i | 0.973623 | + | 0.228164i | \(0.0732723\pi\) | ||||
−0.973623 | + | 0.228164i | \(0.926728\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7205 | − | 34.7205i | −1.16844 | − | 1.16844i | −0.982576 | − | 0.185864i | \(-0.940492\pi\) |
−0.185864 | − | 0.982576i | \(-0.559508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.71328 | + | 21.3222i | −0.191833 | + | 0.715931i | 0.801231 | + | 0.598355i | \(0.204179\pi\) |
−0.993064 | + | 0.117575i | \(0.962488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2777 | + | 34.7485i | −0.646552 | + | 1.16543i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.14536 | − | 3.71588i | −0.0718724 | − | 0.124487i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.9618 | − | 13.9231i | 1.73884 | − | 0.465920i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.34931 | − | 9.34931i | 0.312164 | − | 0.312164i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.20521 | + | 3.81953i | −0.0735477 | + | 0.127388i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.0289 | − | 16.1825i | 0.933777 | − | 0.539116i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.16246 | − | 8.65992i | 0.0719621 | − | 0.288184i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.531796 | − | 1.98469i | −0.0176580 | − | 0.0659005i | 0.956535 | − | 0.291619i | \(-0.0941938\pi\) |
−0.974193 | + | 0.225718i | \(0.927527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.75071 | −0.290243 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1855 | 1.23201 | 0.616006 | − | 0.787742i | \(-0.288750\pi\) | ||||
0.616006 | + | 0.787742i | \(0.288750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.22066 | + | 19.4838i | 0.172779 | + | 0.644819i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.03640 | + | 6.24639i | −0.199339 | + | 0.206274i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.39087 | + | 1.38037i | −0.0788676 | + | 0.0455342i | −0.538915 | − | 0.842360i | \(-0.681166\pi\) |
0.460048 | + | 0.887894i | \(0.347832\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.7309 | − | 27.2467i | 0.518351 | − | 0.897811i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.9069 | − | 37.9069i | 1.24772 | − | 1.24772i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.17860 | + | 0.851703i | −0.104399 | + | 0.0279736i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.2568 | + | 31.6216i | 0.598985 | + | 1.03747i | 0.992971 | + | 0.118356i | \(0.0377623\pi\) |
−0.393987 | + | 0.919116i | \(0.628904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.7299 | + | 20.6287i | 1.26932 | + | 0.676078i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.766245 | + | 2.85967i | −0.0250857 | + | 0.0936212i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.5719 | − | 40.5719i | −1.32543 | − | 1.32543i | −0.909313 | − | 0.416112i | \(-0.863392\pi\) |
−0.416112 | − | 0.909313i | \(-0.636608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.29073i | 0.172656i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8917 | + | 16.6806i | 0.941842 | + | 0.543773i | 0.890537 | − | 0.454910i | \(-0.150329\pi\) |
0.0513045 | + | 0.998683i | \(0.483662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.9637 | − | 8.02874i | −0.975751 | − | 0.261452i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.7887 | − | 13.3408i | −1.61792 | − | 0.433519i | −0.667527 | − | 0.744585i | \(-0.732647\pi\) |
−0.950388 | + | 0.311066i | \(0.899314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.7464 | + | 21.2155i | 1.19284 | + | 0.688685i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.3965i | 0.661402i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3822 | + | 17.3822i | 0.563066 | + | 0.563066i | 0.930177 | − | 0.367111i | \(-0.119653\pi\) |
−0.367111 | + | 0.930177i | \(0.619653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.15758 | − | 11.7843i | 0.102070 | − | 0.380931i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.5666 | + | 37.5877i | 0.728715 | + | 1.21377i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.2970 | − | 24.7631i | −0.461193 | − | 0.798809i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8346 | + | 3.43903i | −0.413590 | + | 0.110821i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.77615 | − | 7.77615i | 0.250064 | − | 0.250064i | −0.570933 | − | 0.820997i | \(-0.693418\pi\) |
0.820997 | + | 0.570933i | \(0.193418\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.1804 | − | 19.3650i | 0.359165 | − | 0.622093i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.9856 | − | 12.6934i | 0.705551 | − | 0.407350i | −0.103861 | − | 0.994592i | \(-0.533120\pi\) |
0.809411 | + | 0.587242i | \(0.199786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.21724 | − | 0.348567i | 0.0390230 | − | 0.0111745i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.8663 | + | 48.0179i | 0.411631 | + | 1.53623i | 0.791489 | + | 0.611183i | \(0.209306\pi\) |
−0.379859 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 76.4782 | 2.44426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.3052 | −0.456729 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.06316 | − | 11.4319i | −0.0976997 | − | 0.364620i | 0.899715 | − | 0.436477i | \(-0.143774\pi\) |
−0.997415 | + | 0.0718572i | \(0.977107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.8271 | − | 6.25036i | 0.694765 | − | 0.198951i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.45846 | + | 4.88349i | −0.268963 | + | 0.155286i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2866 | − | 19.5490i | 0.358532 | − | 0.620995i | −0.629184 | − | 0.777256i | \(-0.716611\pi\) |
0.987716 | + | 0.156261i | \(0.0499441\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.11587 | + | 4.11587i | −0.130613 | + | 0.130613i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0962 | + | 4.31297i | −0.509773 | + | 0.136593i | −0.504532 | − | 0.863393i | \(-0.668335\pi\) |
−0.00524094 | + | 0.999986i | \(0.501668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.84986 | + | 4.93609i | 0.0901654 | + | 0.156171i |
(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 | 2100.2.ce.d.493.4 | yes | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.d.157.4 | yes | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.d.157.2 | ✓ | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.d.493.2 | yes | 24 | |
7.5 | odd | 6 | inner | 2100.2.ce.d.1993.4 | yes | 24 | |
35.12 | even | 12 | inner | 2100.2.ce.d.1657.4 | yes | 24 | |
35.19 | odd | 6 | inner | 2100.2.ce.d.1993.2 | yes | 24 | |
35.33 | even | 12 | inner | 2100.2.ce.d.1657.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.d.157.2 | ✓ | 24 | 5.3 | odd | 4 | inner | |
2100.2.ce.d.157.4 | yes | 24 | 5.2 | odd | 4 | inner | |
2100.2.ce.d.493.2 | yes | 24 | 5.4 | even | 2 | inner | |
2100.2.ce.d.493.4 | yes | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.d.1657.2 | yes | 24 | 35.33 | even | 12 | inner | |
2100.2.ce.d.1657.4 | yes | 24 | 35.12 | even | 12 | inner | |
2100.2.ce.d.1993.2 | yes | 24 | 35.19 | odd | 6 | inner | |
2100.2.ce.d.1993.4 | yes | 24 | 7.5 | odd | 6 | inner |