Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.c.249.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.59808 | + | 1.50000i | −1.50000 | + | 0.866025i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59808 | − | 0.500000i | −0.981981 | − | 0.188982i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.00000i | − | 1.66410i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||
0.554700 | − | 0.832050i | \(-0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.50000 | − | 2.59808i | 1.63663 | − | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.79423 | + | 4.50000i | 1.62521 | + | 0.938315i | 0.985496 | + | 0.169701i | \(0.0542803\pi\) |
0.639713 | + | 0.768613i | \(0.279053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.00000i | 1.73205i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.19615 | − | 3.00000i | −0.904534 | − | 0.522233i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92820 | + | 4.00000i | 1.13899 | + | 0.657596i | 0.946180 | − | 0.323640i | \(-0.104907\pi\) |
0.192809 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.00000 | + | 15.5885i | 1.44115 | + | 2.49615i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000i | 0.152499i | 0.997089 | + | 0.0762493i | \(0.0242945\pi\) | ||||
−0.997089 | + | 0.0762493i | \(0.975706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.92820 | + | 4.00000i | 1.01058 | + | 0.583460i | 0.911362 | − | 0.411606i | \(-0.135032\pi\) |
0.0992202 | + | 0.995066i | \(0.468365\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.50000 | + | 2.59808i | 0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.46410 | − | 2.00000i | 0.475831 | − | 0.274721i | −0.242846 | − | 0.970065i | \(-0.578081\pi\) |
0.718677 | + | 0.695344i | \(0.244748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | − | 6.92820i | −0.520756 | − | 0.901975i | −0.999709 | − | 0.0241347i | \(-0.992317\pi\) |
0.478953 | − | 0.877841i | \(-0.341016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | + | 6.06218i | −0.448129 | + | 0.776182i | −0.998264 | − | 0.0588933i | \(-0.981243\pi\) |
0.550135 | + | 0.835076i | \(0.314576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.3923 | + | 12.0000i | −1.30931 | + | 1.51186i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.59808 | − | 1.50000i | 0.317406 | − | 0.183254i | −0.332830 | − | 0.942987i | \(-0.608004\pi\) |
0.650236 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −27.0000 | −3.25042 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1244 | − | 7.00000i | 1.41905 | − | 0.819288i | 0.422833 | − | 0.906208i | \(-0.361036\pi\) |
0.996215 | + | 0.0869195i | \(0.0277023\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.73205 | − | 5.00000i | −0.197386 | − | 0.569803i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.00000i | − | 0.109764i | −0.998493 | − | 0.0548821i | \(-0.982522\pi\) | ||
0.998493 | − | 0.0548821i | \(-0.0174783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.79423 | − | 4.50000i | 0.835629 | − | 0.482451i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.50000 | − | 11.2583i | 0.688999 | − | 1.19338i | −0.283164 | − | 0.959072i | \(-0.591384\pi\) |
0.972162 | − | 0.234309i | \(-0.0752827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 15.5885i | −0.314485 | + | 1.63411i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19615 | + | 3.00000i | 0.538816 | + | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0000 | 1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2583 | − | 6.50000i | −1.10932 | − | 0.640464i | −0.170664 | − | 0.985329i | \(-0.554591\pi\) |
−0.938652 | + | 0.344865i | \(0.887925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9904 | − | 7.50000i | −1.25583 | − | 0.725052i | −0.283567 | − | 0.958952i | \(-0.591518\pi\) |
−0.972261 | + | 0.233900i | \(0.924851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50000 | + | 7.79423i | 0.431022 | + | 0.746552i | 0.996962 | − | 0.0778949i | \(-0.0248199\pi\) |
−0.565940 | + | 0.824447i | \(0.691487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.0000 | −2.27798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.00000i | − | 0.376288i | −0.982141 | − | 0.188144i | \(-0.939753\pi\) | ||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −31.1769 | − | 18.0000i | −2.88231 | − | 1.66410i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.00000 | − | 1.73205i | 0.458349 | − | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.9904 | + | 7.50000i | −1.17130 | + | 0.676252i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0000i | − | 1.41977i | −0.704317 | − | 0.709885i | \(-0.748747\pi\) | ||
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.50000 | − | 2.59808i | −0.132068 | − | 0.228748i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.0000 | −2.02116 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3923 | − | 6.00000i | 0.869048 | − | 0.501745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.7846 | + | 3.00000i | −1.71429 | + | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000i | 0.970143i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73205 | − | 1.00000i | 0.138233 | − | 0.0798087i | −0.429289 | − | 0.903167i | \(-0.641236\pi\) |
0.567521 | + | 0.823359i | \(0.307902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | + | 10.3923i | −0.475831 | + | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.0000 | − | 15.5885i | −1.41860 | − | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.92820 | − | 4.00000i | −0.542659 | − | 0.313304i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.00000i | 0.696441i | 0.937413 | + | 0.348220i | \(0.113214\pi\) | ||||
−0.937413 | + | 0.348220i | \(0.886786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.8564 | + | 8.00000i | 1.05348 | + | 0.608229i | 0.923622 | − | 0.383304i | \(-0.125214\pi\) |
0.129861 | + | 0.991532i | \(0.458547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.7846 | + | 12.0000i | 1.56227 | + | 0.901975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | 0.0743294 | 0.0371647 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371647 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 21.0000i | − | 1.55236i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | − | 2.00000i | −0.253320 | − | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50000 | − | 23.3827i | 0.327327 | − | 1.70084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.73205 | − | 1.00000i | 0.124676 | − | 0.0719816i | −0.436365 | − | 0.899770i | \(-0.643734\pi\) |
0.561041 | + | 0.827788i | \(0.310401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.0000i | − | 0.997459i | −0.866758 | − | 0.498729i | \(-0.833800\pi\) | ||
0.866758 | − | 0.498729i | \(-0.166200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | + | 17.3205i | 0.708881 | + | 1.22782i | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | + | 7.79423i | −0.317406 | + | 0.549762i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.79423 | + | 1.50000i | 0.547048 | + | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 46.7654 | − | 27.0000i | 3.25042 | − | 1.87663i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.7846 | + | 12.0000i | −1.42414 | + | 0.822226i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73205 | + | 5.00000i | 0.117579 | + | 0.339422i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.0000 | + | 36.3731i | −1.41905 | + | 2.45786i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.46410 | − | 2.00000i | 0.229920 | − | 0.132745i | −0.380615 | − | 0.924734i | \(-0.624288\pi\) |
0.610535 | + | 0.791989i | \(0.290954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | + | 10.3923i | 0.789542 | + | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.5885 | + | 9.00000i | 1.02123 | + | 0.589610i | 0.914461 | − | 0.404674i | \(-0.132615\pi\) |
0.106773 | + | 0.994283i | \(0.465948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0000i | 0.779484i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0000 | 1.68180 | 0.840900 | − | 0.541190i | \(-0.182026\pi\) | ||||
0.840900 | + | 0.541190i | \(0.182026\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.50000 | + | 2.59808i | 0.0950586 | + | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.0000 | 1.89358 | 0.946792 | − | 0.321847i | \(-0.104304\pi\) | ||||
0.946792 | + | 0.321847i | \(0.104304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000i | 1.13165i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.92820 | + | 4.00000i | 0.432169 | + | 0.249513i | 0.700270 | − | 0.713878i | \(-0.253063\pi\) |
−0.268101 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | − | 13.8564i | −0.994192 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | + | 15.5885i | −0.557086 | + | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.7224 | − | 8.50000i | 0.907824 | − | 0.524132i | 0.0280936 | − | 0.999605i | \(-0.491056\pi\) |
0.879730 | + | 0.475473i | \(0.157723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.0000i | 2.38676i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.50000 | + | 7.79423i | 0.274370 | + | 0.475223i | 0.969976 | − | 0.243201i | \(-0.0781974\pi\) |
−0.695606 | + | 0.718423i | \(0.744864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.5885 | − | 45.0000i | −0.943456 | − | 2.72352i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5885 | + | 9.00000i | −0.936620 | + | 0.540758i | −0.888899 | − | 0.458103i | \(-0.848529\pi\) |
−0.0477206 | + | 0.998861i | \(0.515196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46410 | + | 2.00000i | −0.205919 | + | 0.118888i | −0.599414 | − | 0.800439i | \(-0.704600\pi\) |
0.393494 | + | 0.919327i | \(0.371266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.9904 | − | 2.50000i | −0.766798 | − | 0.147570i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.0000 | − | 25.9808i | −0.879316 | − | 1.52302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.00000i | 0.233682i | 0.993151 | + | 0.116841i | \(0.0372769\pi\) | ||||
−0.993151 | + | 0.116841i | \(0.962723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.5885 | + | 9.00000i | −0.904534 | + | 0.522233i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.0000 | − | 46.7654i | 1.56145 | − | 2.70451i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 2.59808i | 0.0288195 | − | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.79423 | − | 4.50000i | −0.447767 | − | 0.258518i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.00000i | − | 0.0570730i | −0.999593 | − | 0.0285365i | \(-0.990915\pi\) | ||
0.999593 | − | 0.0285365i | \(-0.00908469\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.0000 | 2.21863 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | − | 20.7846i | −0.680458 | − | 1.17859i | −0.974841 | − | 0.222900i | \(-0.928448\pi\) |
0.294384 | − | 0.955687i | \(-0.404886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46410 | + | 2.00000i | 0.195803 | + | 0.113047i | 0.594696 | − | 0.803951i | \(-0.297272\pi\) |
−0.398894 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.66025 | + | 5.00000i | 0.486408 | + | 0.280828i | 0.723083 | − | 0.690761i | \(-0.242724\pi\) |
−0.236675 | + | 0.971589i | \(0.576058\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00000 | − | 5.19615i | −0.167968 | − | 0.290929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.0000 | 2.51166 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.3827 | − | 13.5000i | −1.29307 | − | 0.746552i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | − | 13.8564i | −0.882109 | − | 0.763928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | + | 8.66025i | −0.274825 | + | 0.476011i | −0.970091 | − | 0.242742i | \(-0.921953\pi\) |
0.695266 | + | 0.718752i | \(0.255287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 41.5692 | − | 24.0000i | 2.27798 | − | 1.31519i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 28.0000i | − | 1.52526i | −0.646837 | − | 0.762629i | \(-0.723908\pi\) | ||
0.646837 | − | 0.762629i | \(-0.276092\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | + | 10.3923i | 0.325875 | + | 0.564433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | − | 3.46410i | 0.108306 | − | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6506 | + | 12.5000i | −1.16227 | + | 0.671035i | −0.951846 | − | 0.306576i | \(-0.900817\pi\) |
−0.210421 | + | 0.977611i | \(0.567483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0000 | 0.909989 | 0.454995 | − | 0.890494i | \(-0.349641\pi\) | ||||
0.454995 | + | 0.890494i | \(0.349641\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54.0000 | 2.88231 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.1769 | + | 18.0000i | −1.65938 | + | 0.958043i | −0.686378 | + | 0.727245i | \(0.740800\pi\) |
−0.973002 | + | 0.230799i | \(0.925866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.3923 | + | 12.0000i | −0.550019 | + | 0.635107i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.00000 | + | 8.66025i | −0.263890 | + | 0.457071i | −0.967272 | − | 0.253741i | \(-0.918339\pi\) |
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.0000i | 1.10221i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.866025 | + | 0.500000i | −0.0452062 | + | 0.0260998i | −0.522433 | − | 0.852680i | \(-0.674975\pi\) |
0.477227 | + | 0.878780i | \(0.341642\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.0000 | − | 25.9808i | 0.780869 | − | 1.35250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0000 | + | 3.46410i | −0.519174 | + | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7128 | − | 16.0000i | −1.43492 | − | 0.828449i | −0.437425 | − | 0.899255i | \(-0.644109\pi\) |
−0.997490 | + | 0.0708063i | \(0.977443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.0000i | 0.927047i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0000 | + | 41.5692i | 1.22956 | + | 2.12966i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.79423 | + | 4.50000i | 0.398266 | + | 0.229939i | 0.685736 | − | 0.727851i | \(-0.259481\pi\) |
−0.287469 | + | 0.957790i | \(0.592814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.19615 | + | 3.00000i | 0.264135 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.00000 | − | 8.66025i | −0.253510 | − | 0.439092i | 0.710980 | − | 0.703213i | \(-0.248252\pi\) |
−0.964490 | + | 0.264120i | \(0.914918\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.66025 | + | 5.00000i | 0.434646 | + | 0.250943i | 0.701324 | − | 0.712843i | \(-0.252593\pi\) |
−0.266678 | + | 0.963786i | \(0.585926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5000 | − | 25.1147i | 0.724095 | − | 1.25417i | −0.235250 | − | 0.971935i | \(-0.575591\pi\) |
0.959345 | − | 0.282235i | \(-0.0910758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3923 | + | 6.00000i | −0.517678 | + | 0.298881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0000i | 0.793091i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50000 | + | 2.59808i | 0.0741702 | + | 0.128467i | 0.900725 | − | 0.434389i | \(-0.143036\pi\) |
−0.826555 | + | 0.562856i | \(0.809703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | + | 31.1769i | −0.887875 | + | 1.53784i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92820 | + | 20.0000i | 0.340915 | + | 0.984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.9808 | − | 15.0000i | 1.27228 | − | 0.734553i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000 | 1.17248 | 0.586238 | − | 0.810139i | \(-0.300608\pi\) | ||||
0.586238 | + | 0.810139i | \(0.300608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 41.5692 | − | 24.0000i | 2.02116 | − | 1.16692i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1244 | − | 14.0000i | 0.586739 | − | 0.677507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | + | 31.1769i | −0.869048 | + | 1.50524i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.00000i | − | 0.192228i | −0.995370 | − | 0.0961139i | \(-0.969359\pi\) | ||
0.995370 | − | 0.0961139i | \(-0.0306413\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00000 | − | 3.46410i | 0.0954548 | − | 0.165333i | −0.814344 | − | 0.580383i | \(-0.802903\pi\) |
0.909798 | + | 0.415051i | \(0.136236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.0000 | − | 25.9808i | 1.57143 | − | 1.23718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0429 | − | 18.5000i | −1.52241 | − | 0.878962i | −0.999649 | − | 0.0264796i | \(-0.991570\pi\) |
−0.522757 | − | 0.852482i | \(-0.675096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.0000i | 1.27706i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00000 | + | 8.66025i | 0.235441 | + | 0.407795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.9808 | − | 15.0000i | −1.22068 | − | 0.704761i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2487 | + | 14.0000i | 1.13431 | + | 0.654892i | 0.945015 | − | 0.327028i | \(-0.106047\pi\) |
0.189292 | + | 0.981921i | \(0.439381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.00000 | − | 15.5885i | −0.420084 | − | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.00000 | −0.0931493 | −0.0465746 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465746 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000i | 0.790057i | 0.918669 | + | 0.395029i | \(0.129265\pi\) | ||||
−0.918669 | + | 0.395029i | \(0.870735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.33013 | + | 2.50000i | 0.200374 | + | 0.115686i | 0.596830 | − | 0.802368i | \(-0.296427\pi\) |
−0.396456 | + | 0.918054i | \(0.629760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.50000 | + | 2.59808i | −0.346318 | + | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | + | 5.19615i | −0.138233 | + | 0.239426i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.73205 | + | 1.00000i | −0.0796398 | + | 0.0459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 24.0000i | − | 1.09888i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.0000 | − | 25.9808i | −0.685367 | − | 1.18709i | −0.973321 | − | 0.229447i | \(-0.926308\pi\) |
0.287954 | − | 0.957644i | \(-0.407025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | − | 41.5692i | 1.09431 | − | 1.89539i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 70.1481 | + | 13.5000i | 3.19185 | + | 0.614271i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | + | 16.0000i | −1.25579 | + | 0.725029i | −0.972253 | − | 0.233933i | \(-0.924840\pi\) |
−0.283535 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.19615 | − | 3.00000i | 0.234023 | − | 0.135113i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.7846 | − | 4.00000i | −0.932317 | − | 0.179425i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00000 | + | 5.19615i | −0.134298 | + | 0.232612i | −0.925329 | − | 0.379165i | \(-0.876211\pi\) |
0.791031 | + | 0.611776i | \(0.209545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5000 | − | 23.3827i | −0.603136 | − | 1.04466i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.0000i | 1.20387i | 0.798545 | + | 0.601935i | \(0.205603\pi\) | ||||
−0.798545 | + | 0.601935i | \(0.794397\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 59.7558 | − | 34.5000i | 2.65385 | − | 1.53220i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.5000 | + | 35.5070i | −0.908647 | + | 1.57382i | −0.0927004 | + | 0.995694i | \(0.529550\pi\) |
−0.815946 | + | 0.578128i | \(0.803783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0000 | + | 12.1244i | −1.54831 | + | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000i | 0.703679i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.0000 | −2.10697 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.00000 | − | 12.1244i | −0.306676 | − | 0.531178i | 0.670957 | − | 0.741496i | \(-0.265883\pi\) |
−0.977633 | + | 0.210318i | \(0.932550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.46410 | − | 2.00000i | −0.151475 | − | 0.0874539i | 0.422347 | − | 0.906434i | \(-0.361206\pi\) |
−0.573822 | + | 0.818980i | \(0.694540\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46410 | + | 2.00000i | 0.150899 | + | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.0000 | + | 50.2295i | 1.26087 | + | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −48.0000 | −2.08302 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 30.0000i | − | 1.29944i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.5885 | + | 9.00000i | 0.672692 | + | 0.388379i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | + | 13.8564i | 0.0861461 | + | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.5000 | + | 28.5788i | −0.709390 | + | 1.22870i | 0.255693 | + | 0.966758i | \(0.417696\pi\) |
−0.965084 | + | 0.261942i | \(0.915637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.59808 | + | 1.50000i | −0.111494 | + | 0.0643712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0000i | 0.641354i | 0.947189 | + | 0.320677i | \(0.103910\pi\) | ||||
−0.947189 | + | 0.320677i | \(0.896090\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.0000 | + | 36.3731i | 0.896258 | + | 1.55236i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | + | 8.00000i | −0.294617 | + | 0.340195i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.73205 | − | 1.00000i | 0.0733893 | − | 0.0423714i | −0.462856 | − | 0.886433i | \(-0.653175\pi\) |
0.536246 | + | 0.844062i | \(0.319842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2583 | + | 6.50000i | −0.474482 | + | 0.273942i | −0.718114 | − | 0.695925i | \(-0.754994\pi\) |
0.243632 | + | 0.969868i | \(0.421661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.79423 | + | 22.5000i | 0.327327 | + | 0.944911i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0000 | − | 25.9808i | 0.628833 | − | 1.08917i | −0.358954 | − | 0.933355i | \(-0.616866\pi\) |
0.987786 | − | 0.155815i | \(-0.0498003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | − | 20.7846i | −0.502184 | − | 0.869809i | −0.999997 | − | 0.00252413i | \(-0.999197\pi\) |
0.497812 | − | 0.867285i | \(-0.334137\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 18.0000i | − | 0.751961i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0526 | + | 11.0000i | −0.793168 | + | 0.457936i | −0.841077 | − | 0.540916i | \(-0.818078\pi\) |
0.0479084 | + | 0.998852i | \(0.484744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.00000 | + | 5.19615i | −0.124676 | + | 0.215945i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.500000 | + | 2.59808i | −0.0207435 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.92820 | + | 4.00000i | 0.286937 | + | 0.165663i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 20.0000i | − | 0.825488i | −0.910847 | − | 0.412744i | \(-0.864570\pi\) | ||
0.910847 | − | 0.412744i | \(-0.135430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.0000 | + | 36.3731i | 0.863825 | + | 1.49619i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1769 | + | 18.0000i | 1.28028 | + | 0.739171i | 0.976900 | − | 0.213697i | \(-0.0685507\pi\) |
0.303383 | + | 0.952869i | \(0.401884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −51.9615 | − | 30.0000i | −2.12664 | − | 1.22782i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 18.0000i | − | 0.733017i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.866025 | + | 0.500000i | 0.0351509 | + | 0.0202944i | 0.517472 | − | 0.855700i | \(-0.326873\pi\) |
−0.482322 | + | 0.875994i | \(0.660206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.5000 | + | 7.79423i | −0.911746 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | − | 41.5692i | 0.970936 | − | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.19615 | + | 3.00000i | −0.209871 | + | 0.121169i | −0.601251 | − | 0.799060i | \(-0.705331\pi\) |
0.391381 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 20.0000i | − | 0.805170i | −0.915383 | − | 0.402585i | \(-0.868112\pi\) | ||
0.915383 | − | 0.402585i | \(-0.131888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.00000 | − | 8.66025i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663842i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −40.5000 | + | 70.1481i | −1.62521 | + | 2.81494i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.5167 | + | 26.0000i | −0.902111 | + | 1.04167i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.3923 | + | 6.00000i | −0.413057 | + | 0.238479i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5885 | − | 39.0000i | 0.617637 | − | 1.54524i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | − | 41.5692i | 0.949425 | − | 1.64445i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5000 | + | 26.8468i | 0.612213 | + | 1.06038i | 0.990867 | + | 0.134846i | \(0.0430539\pi\) |
−0.378653 | + | 0.925539i | \(0.623613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.866025 | + | 0.500000i | −0.0340470 | + | 0.0196570i | −0.516927 | − | 0.856030i | \(-0.672924\pi\) |
0.482880 | + | 0.875687i | \(0.339591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | − | 13.8564i | 0.314027 | − | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | − | 10.3923i | −0.470317 | − | 0.407307i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4449 | + | 17.0000i | 1.15227 | + | 0.665261i | 0.949439 | − | 0.313953i | \(-0.101653\pi\) |
0.202828 | + | 0.979214i | \(0.434987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 84.0000i | − | 3.27715i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5000 | − | 26.8468i | −0.602880 | − | 1.04422i | −0.992383 | − | 0.123194i | \(-0.960686\pi\) |
0.389503 | − | 0.921025i | \(-0.372647\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.1769 | − | 18.0000i | −1.21081 | − | 0.699062i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3827 | − | 13.5000i | −0.905381 | − | 0.522722i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.0000 | − | 41.5692i | −0.927894 | − | 1.60716i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0000 | −0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000i | 0.616755i | 0.951264 | + | 0.308377i | \(0.0997859\pi\) | ||||
−0.951264 | + | 0.308377i | \(0.900214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.19615 | + | 3.00000i | 0.199704 | + | 0.115299i | 0.596518 | − | 0.802600i | \(-0.296551\pi\) |
−0.396813 | + | 0.917899i | \(0.629884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.00000 | − | 25.9808i | 0.191882 | − | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 10.3923i | −0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.1147 | − | 14.5000i | 0.960989 | − | 0.554827i | 0.0645115 | − | 0.997917i | \(-0.479451\pi\) |
0.896477 | + | 0.443090i | \(0.146118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 42.0000i | − | 1.60240i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.0000 | − | 20.7846i | −0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0000 | − | 22.5167i | 0.494543 | − | 0.856574i | −0.505437 | − | 0.862864i | \(-0.668669\pi\) |
0.999980 | + | 0.00628943i | \(0.00200200\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.1769 | − | 6.00000i | −1.18431 | − | 0.227921i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.66025 | + | 5.00000i | −0.328031 | + | 0.189389i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −54.0000 | −2.04247 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0000 | −1.09531 | −0.547657 | − | 0.836703i | \(-0.684480\pi\) | ||||
−0.547657 | + | 0.836703i | \(0.684480\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.59808 | − | 7.50000i | −0.0977107 | − | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | − | 26.8468i | 0.582115 | − | 1.00825i | −0.413114 | − | 0.910679i | \(-0.635559\pi\) |
0.995228 | − | 0.0975728i | \(-0.0311079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.0000 | − | 20.7846i | −0.450035 | − | 0.779484i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 18.0000i | − | 0.674105i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −67.5500 | + | 39.0000i | −2.52270 | + | 1.45648i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.0000 | + | 22.5167i | 0.968291 | + | 0.838564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.9808 | + | 15.0000i | 0.966235 | + | 0.557856i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.00000i | − | 0.111264i | −0.998451 | − | 0.0556319i | \(-0.982283\pi\) | ||
0.998451 | − | 0.0556319i | \(-0.0177173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00000 | − | 1.73205i | −0.0369863 | − | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4449 | − | 17.0000i | −1.08757 | − | 0.627909i | −0.154642 | − | 0.987971i | \(-0.549422\pi\) |
−0.932929 | + | 0.360061i | \(0.882756\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.19615 | + | 3.00000i | 0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.00000i | − | 0.110059i | −0.998485 | − | 0.0550297i | \(-0.982475\pi\) | ||
0.998485 | − | 0.0550297i | \(-0.0175253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.19615 | − | 3.00000i | −0.190117 | − | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | + | 25.9808i | 1.09618 | + | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | \(-0.952232\pi\) |
0.623856 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −77.9423 | + | 45.0000i | −2.84037 | + | 1.63989i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000i | 1.38113i | 0.723269 | + | 0.690567i | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.0000 | − | 46.7654i | −0.980038 | − | 1.69748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.79423 | − | 22.5000i | −0.282170 | − | 0.814555i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.5692 | + | 24.0000i | −1.50098 | + | 0.866590i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0000 | −0.864339 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.5885 | + | 9.00000i | −0.560678 | + | 0.323708i | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.192740 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 62.3538 | + | 12.0000i | 2.23693 | + | 0.430498i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | + | 13.8564i | 0.286263 | + | 0.495821i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 27.0000i | − | 0.964901i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.52628 | − | 5.50000i | 0.339575 | − | 0.196054i | −0.320509 | − | 0.947245i | \(-0.603854\pi\) |
0.660084 | + | 0.751192i | \(0.270521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.5000 | + | 44.1673i | −0.907824 | + | 1.57240i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | + | 10.3923i | −0.0711118 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.3731 | + | 21.0000i | 1.29165 | + | 0.745732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 36.0000i | − | 1.27519i | −0.770374 | − | 0.637593i | \(-0.779930\pi\) | ||
0.770374 | − | 0.637593i | \(-0.220070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.0000 | − | 67.5500i | −1.37800 | − | 2.38676i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.2487 | + | 14.0000i | 0.855718 | + | 0.494049i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.3827 | − | 13.5000i | −0.823110 | − | 0.475223i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.5000 | + | 38.9711i | 0.791058 | + | 1.37015i | 0.925312 | + | 0.379206i | \(0.123803\pi\) |
−0.134255 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.0000 | 1.75574 | 0.877869 | − | 0.478901i | \(-0.158965\pi\) | ||||
0.877869 | + | 0.478901i | \(0.158965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 72.0000i | 2.52515i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 72.0000 | + | 62.3538i | 2.51588 | + | 2.17882i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.4545 | − | 9.50000i | 0.573567 | − | 0.331149i | −0.185006 | − | 0.982737i | \(-0.559230\pi\) |
0.758573 | + | 0.651588i | \(0.225897\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.0000i | − | 0.799788i | −0.916561 | − | 0.399894i | \(-0.869047\pi\) | ||
0.916561 | − | 0.399894i | \(-0.130953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.00000 | − | 8.66025i | −0.173657 | − | 0.300783i | 0.766039 | − | 0.642795i | \(-0.222225\pi\) |
−0.939696 | + | 0.342012i | \(0.888892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0000 | − | 46.7654i | 0.936620 | − | 1.62227i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.8564 | + | 2.00000i | −0.480096 | + | 0.0692959i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.5885 | − | 9.00000i | 0.538816 | − | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0000 | −0.483334 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57.1577 | − | 33.0000i | 1.96861 | − | 1.13658i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.1244 | + | 14.0000i | −0.416598 | + | 0.481046i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.00000 | − | 10.3923i | 0.205919 | − | 0.356663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000 | + | 62.3538i | 1.23406 | + | 2.13746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.0000i | − | 1.36957i | −0.728743 | − | 0.684787i | \(-0.759895\pi\) | ||
0.728743 | − | 0.684787i | \(-0.240105\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.7654 | − | 27.0000i | 1.59747 | − | 0.922302i | 0.605503 | − | 0.795843i | \(-0.292972\pi\) |
0.991972 | − | 0.126459i | \(-0.0403613\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.0000 | + | 31.1769i | −0.614152 | + | 1.06374i | 0.376381 | + | 0.926465i | \(0.377169\pi\) |
−0.990533 | + | 0.137277i | \(0.956165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.5000 | − | 12.9904i | 1.27800 | − | 0.442711i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.0429 | − | 18.5000i | −1.09075 | − | 0.629747i | −0.156977 | − | 0.987602i | \(-0.550175\pi\) |
−0.933777 | + | 0.357855i | \(0.883508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 39.0000i | − | 1.32451i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.00000 | − | 15.5885i | −0.304953 | − | 0.528195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 51.9615 | + | 30.0000i | 1.75863 | + | 1.01535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.7128 | + | 16.0000i | 0.935795 | + | 0.540282i | 0.888640 | − | 0.458606i | \(-0.151651\pi\) |
0.0471555 | + | 0.998888i | \(0.484984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.0000 | −1.04442 | −0.522208 | − | 0.852818i | \(-0.674892\pi\) | ||||
−0.522208 | + | 0.852818i | \(0.674892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.0000i | − | 1.21150i | −0.795656 | − | 0.605748i | \(-0.792874\pi\) | ||
0.795656 | − | 0.605748i | \(-0.207126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.8993 | + | 26.5000i | 1.54115 | + | 0.889783i | 0.998767 | + | 0.0496513i | \(0.0158110\pi\) |
0.542383 | + | 0.840132i | \(0.317522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | + | 41.5692i | −0.268311 | + | 1.39419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | − | 15.5885i | 0.301511 | − | 0.522233i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 162.000i | 5.40902i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000 | + | 5.19615i | 0.100056 | + | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.00000 | + | 6.92820i | −0.133259 | + | 0.230812i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.59808 | + | 7.50000i | 0.0864586 | + | 0.249584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0429 | − | 18.5000i | 1.06397 | − | 0.614282i | 0.137441 | − | 0.990510i | \(-0.456112\pi\) |
0.926527 | + | 0.376228i | \(0.122779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.73205 | − | 1.00000i | 0.0573225 | − | 0.0330952i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.92820 | + | 8.00000i | −0.228789 | + | 0.264183i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | − | 27.7128i | 0.527791 | − | 0.914161i | −0.471684 | − | 0.881768i | \(-0.656354\pi\) |
0.999475 | − | 0.0323936i | \(-0.0103130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50000 | + | 2.59808i | 0.0494267 | + | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −67.5500 | + | 39.0000i | −2.21863 | + | 1.28093i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.50000 | + | 4.33013i | −0.0820223 | + | 0.142067i | −0.904118 | − | 0.427282i | \(-0.859471\pi\) |
0.822096 | + | 0.569349i | \(0.192805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 62.3538 | + | 36.0000i | 2.04137 | + | 1.17859i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.0000i | 1.69877i | 0.527777 | + | 0.849383i | \(0.323026\pi\) | ||||
−0.527777 | + | 0.849383i | \(0.676974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0000 | − | 32.9090i | −0.619382 | − | 1.07280i | −0.989599 | − | 0.143856i | \(-0.954050\pi\) |
0.370216 | − | 0.928946i | \(-0.379284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.9711 | + | 22.5000i | 1.26908 | + | 0.732701i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.1147 | + | 14.5000i | 0.816119 | + | 0.471187i | 0.849076 | − | 0.528270i | \(-0.177159\pi\) |
−0.0329571 | + | 0.999457i | \(0.510492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.0000 | − | 72.7461i | −1.36338 | − | 2.36144i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.0000 | −0.972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 60.0000i | − | 1.94359i | −0.235826 | − | 0.971795i | \(-0.575780\pi\) | ||
0.235826 | − | 0.971795i | \(-0.424220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.5885 | + | 9.00000i | 0.503903 | + | 0.290929i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.0000 | + | 10.3923i | −0.968751 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −77.9423 | + | 45.0000i | −2.51166 | + | 1.45010i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 37.0000i | − | 1.18984i | −0.803785 | − | 0.594920i | \(-0.797184\pi\) | ||
0.803785 | − | 0.594920i | \(-0.202816\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | − | 10.3923i | 0.192549 | − | 0.333505i | −0.753545 | − | 0.657396i | \(-0.771658\pi\) |
0.946094 | + | 0.323891i | \(0.104991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.9808 | + | 5.00000i | 0.832905 | + | 0.160293i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.19615 | − | 3.00000i | 0.166240 | − | 0.0959785i | −0.414572 | − | 0.910017i | \(-0.636069\pi\) |
0.580812 | + | 0.814038i | \(0.302735\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.0000 | 0.830964 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.0000 | 1.72409 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.4545 | + | 9.50000i | −0.524816 | + | 0.303003i | −0.738903 | − | 0.673812i | \(-0.764656\pi\) |
0.214087 | + | 0.976815i | \(0.431323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 62.3538 | + | 12.0000i | 1.98474 | + | 0.381964i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50000 | + | 7.79423i | −0.143092 | + | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | + | 32.9090i | 0.603555 | + | 1.04539i | 0.992278 | + | 0.124033i | \(0.0395829\pi\) |
−0.388723 | + | 0.921355i | \(0.627084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30.0000i | − | 0.952021i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.6410 | − | 20.0000i | 1.09709 | − | 0.633406i | 0.161636 | − | 0.986850i | \(-0.448323\pi\) |
0.935456 | + | 0.353444i | \(0.114990\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.0000 | + | 62.3538i | −1.13899 | + | 1.97279i |
(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 | 700.2.r.c.149.1 | 4 | ||
5.2 | odd | 4 | 140.2.i.b.121.1 | yes | 2 | ||
5.3 | odd | 4 | 700.2.i.a.401.1 | 2 | |||
5.4 | even | 2 | inner | 700.2.r.c.149.2 | 4 | ||
7.2 | even | 3 | 4900.2.e.c.2549.1 | 2 | |||
7.4 | even | 3 | inner | 700.2.r.c.249.2 | 4 | ||
7.5 | odd | 6 | 4900.2.e.b.2549.2 | 2 | |||
15.2 | even | 4 | 1260.2.s.b.541.1 | 2 | |||
20.7 | even | 4 | 560.2.q.a.401.1 | 2 | |||
35.2 | odd | 12 | 980.2.a.a.1.1 | 1 | |||
35.4 | even | 6 | inner | 700.2.r.c.249.1 | 4 | ||
35.9 | even | 6 | 4900.2.e.c.2549.2 | 2 | |||
35.12 | even | 12 | 980.2.a.i.1.1 | 1 | |||
35.17 | even | 12 | 980.2.i.a.361.1 | 2 | |||
35.18 | odd | 12 | 700.2.i.a.501.1 | 2 | |||
35.19 | odd | 6 | 4900.2.e.b.2549.1 | 2 | |||
35.23 | odd | 12 | 4900.2.a.v.1.1 | 1 | |||
35.27 | even | 4 | 980.2.i.a.961.1 | 2 | |||
35.32 | odd | 12 | 140.2.i.b.81.1 | ✓ | 2 | ||
35.33 | even | 12 | 4900.2.a.a.1.1 | 1 | |||
105.2 | even | 12 | 8820.2.a.w.1.1 | 1 | |||
105.32 | even | 12 | 1260.2.s.b.361.1 | 2 | |||
105.47 | odd | 12 | 8820.2.a.k.1.1 | 1 | |||
140.47 | odd | 12 | 3920.2.a.d.1.1 | 1 | |||
140.67 | even | 12 | 560.2.q.a.81.1 | 2 | |||
140.107 | even | 12 | 3920.2.a.bi.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.i.b.81.1 | ✓ | 2 | 35.32 | odd | 12 | ||
140.2.i.b.121.1 | yes | 2 | 5.2 | odd | 4 | ||
560.2.q.a.81.1 | 2 | 140.67 | even | 12 | |||
560.2.q.a.401.1 | 2 | 20.7 | even | 4 | |||
700.2.i.a.401.1 | 2 | 5.3 | odd | 4 | |||
700.2.i.a.501.1 | 2 | 35.18 | odd | 12 | |||
700.2.r.c.149.1 | 4 | 1.1 | even | 1 | trivial | ||
700.2.r.c.149.2 | 4 | 5.4 | even | 2 | inner | ||
700.2.r.c.249.1 | 4 | 35.4 | even | 6 | inner | ||
700.2.r.c.249.2 | 4 | 7.4 | even | 3 | inner | ||
980.2.a.a.1.1 | 1 | 35.2 | odd | 12 | |||
980.2.a.i.1.1 | 1 | 35.12 | even | 12 | |||
980.2.i.a.361.1 | 2 | 35.17 | even | 12 | |||
980.2.i.a.961.1 | 2 | 35.27 | even | 4 | |||
1260.2.s.b.361.1 | 2 | 105.32 | even | 12 | |||
1260.2.s.b.541.1 | 2 | 15.2 | even | 4 | |||
3920.2.a.d.1.1 | 1 | 140.47 | odd | 12 | |||
3920.2.a.bi.1.1 | 1 | 140.107 | even | 12 | |||
4900.2.a.a.1.1 | 1 | 35.33 | even | 12 | |||
4900.2.a.v.1.1 | 1 | 35.23 | odd | 12 | |||
4900.2.e.b.2549.1 | 2 | 35.19 | odd | 6 | |||
4900.2.e.b.2549.2 | 2 | 7.5 | odd | 6 | |||
4900.2.e.c.2549.1 | 2 | 7.2 | even | 3 | |||
4900.2.e.c.2549.2 | 2 | 35.9 | even | 6 | |||
8820.2.a.k.1.1 | 1 | 105.47 | odd | 12 | |||
8820.2.a.w.1.1 | 1 | 105.2 | even | 12 |