Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 274x^{12} + 1236x^{10} + 2703x^{8} + 2676x^{6} + 946x^{4} + 64x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{46}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(2.24296i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.3.h.g.65.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.75782 | − | 1.18087i | −0.919272 | − | 0.393623i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.68481 | 0.736961 | 0.368481 | − | 0.929635i | \(-0.379878\pi\) | ||||
0.368481 | + | 0.929635i | \(0.379878\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.43855 | −0.776935 | −0.388468 | − | 0.921462i | \(-0.626995\pi\) | ||||
−0.388468 | + | 0.921462i | \(0.626995\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.21110 | + | 6.51323i | 0.690123 | + | 0.723693i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.16436 | −0.105851 | −0.0529256 | − | 0.998598i | \(-0.516855\pi\) | ||||
−0.0529256 | + | 0.998598i | \(0.516855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14.4222i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.1620 | − | 4.35127i | −0.677468 | − | 0.290085i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.71276i | 0.100750i | 0.998730 | + | 0.0503752i | \(0.0160417\pi\) | ||||
−0.998730 | + | 0.0503752i | \(0.983958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 28.8394i | − | 1.51786i | −0.651171 | − | 0.758931i | \(-0.725722\pi\) | ||
0.651171 | − | 0.758931i | \(-0.274278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.9985 | + | 6.42221i | 0.714215 | + | 0.305819i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.4225i | 1.54011i | 0.637978 | + | 0.770055i | \(0.279771\pi\) | ||||
−0.637978 | + | 0.770055i | \(0.720229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4222 | −0.456888 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.43781 | − | 25.2968i | −0.349549 | − | 0.936918i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.6818 | −1.16144 | −0.580721 | − | 0.814102i | \(-0.697229\pi\) | ||||
−0.580721 | + | 0.814102i | \(0.697229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55.5336 | −1.79141 | −0.895703 | − | 0.444654i | \(-0.853327\pi\) | ||||
−0.895703 | + | 0.444654i | \(0.853327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.21110 | + | 1.37496i | 0.0973061 | + | 0.0416655i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.0400 | −0.572571 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.4222i | 0.822222i | 0.911585 | + | 0.411111i | \(0.134859\pi\) | ||||
−0.911585 | + | 0.411111i | \(0.865141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.0307 | + | 39.7738i | −0.436685 | + | 1.01984i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 63.4196i | − | 1.54682i | −0.633907 | − | 0.773409i | \(-0.718550\pi\) | ||
0.633907 | − | 0.773409i | \(-0.281450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 43.0098i | − | 1.00023i | −0.865960 | − | 0.500114i | \(-0.833291\pi\) | ||
0.865960 | − | 0.500114i | \(-0.166709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 22.8867 | + | 24.0000i | 0.508594 | + | 0.533333i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 61.5301i | − | 1.30915i | −0.755996 | − | 0.654576i | \(-0.772847\pi\) | ||
0.755996 | − | 0.654576i | \(-0.227153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.4222 | −0.396372 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.02254 | − | 4.72347i | 0.0396577 | − | 0.0926171i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −56.3093 | −1.06244 | −0.531219 | − | 0.847234i | \(-0.678266\pi\) | ||||
−0.531219 | + | 0.847234i | \(0.678266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.29046 | −0.0780083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −34.0555 | + | 79.5338i | −0.597465 | + | 1.39533i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −49.6407 | −0.841368 | −0.420684 | − | 0.907207i | \(-0.638210\pi\) | ||||
−0.420684 | + | 0.907207i | \(0.638210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.73338i | − | 0.0775965i | −0.999247 | − | 0.0387982i | \(-0.987647\pi\) | ||
0.999247 | − | 0.0387982i | \(-0.0123530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −33.7794 | − | 35.4225i | −0.536181 | − | 0.562262i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 53.1430i | − | 0.817585i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.08521i | 0.105749i | 0.998601 | + | 0.0528747i | \(0.0168384\pi\) | ||||
−0.998601 | + | 0.0528747i | \(0.983162\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41.8293 | − | 97.6888i | 0.606222 | − | 1.41578i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 96.9527i | 1.36553i | 0.730638 | + | 0.682765i | \(0.239223\pi\) | ||||
−0.730638 | + | 0.682765i | \(0.760777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 68.5332 | 0.938811 | 0.469406 | − | 0.882983i | \(-0.344468\pi\) | ||||
0.469406 | + | 0.882983i | \(0.344468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 31.5003 | + | 13.4881i | 0.420005 | + | 0.179842i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.33245 | 0.0822396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.72900 | 0.123152 | 0.0615760 | − | 0.998102i | \(-0.480387\pi\) | ||||
0.0615760 | + | 0.998102i | \(0.480387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.84441 | + | 80.9087i | −0.0474619 | + | 0.998873i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 38.9156 | 0.468863 | 0.234431 | − | 0.972133i | \(-0.424677\pi\) | ||||
0.234431 | + | 0.972133i | \(0.424677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.31118i | 0.0742492i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 92.8883 | + | 39.7738i | 1.06768 | + | 0.457170i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.675595i | 0.00759096i | 0.999993 | + | 0.00379548i | \(0.00120814\pi\) | ||||
−0.999993 | + | 0.00379548i | \(0.998792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 78.4358i | 0.861932i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 153.151 | + | 65.5778i | 1.64679 | + | 0.705138i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 106.268i | − | 1.11861i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 86.1110 | 0.887743 | 0.443871 | − | 0.896091i | \(-0.353605\pi\) | ||||
0.443871 | + | 0.896091i | \(0.353605\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.23199 | − | 7.58378i | −0.0730504 | − | 0.0766038i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109.452 | −1.08369 | −0.541843 | − | 0.840480i | \(-0.682273\pi\) | ||||
−0.541843 | + | 0.840480i | \(0.682273\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 160.014 | 1.55353 | 0.776767 | − | 0.629788i | \(-0.216858\pi\) | ||||
0.776767 | + | 0.629788i | \(0.216858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 55.2666 | + | 23.6646i | 0.526349 | + | 0.225377i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 184.345 | 1.72285 | 0.861423 | − | 0.507887i | \(-0.169573\pi\) | ||||
0.861423 | + | 0.507887i | \(0.169573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 68.7334i | − | 0.630582i | −0.948995 | − | 0.315291i | \(-0.897898\pi\) | ||
0.948995 | − | 0.315291i | \(-0.102102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.9246 | − | 83.8989i | 0.323645 | − | 0.755846i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 71.3078i | − | 0.631042i | −0.948919 | − | 0.315521i | \(-0.897821\pi\) | ||
0.948919 | − | 0.315521i | \(-0.102179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 130.525i | 1.13500i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 93.9352 | − | 89.5778i | 0.802865 | − | 0.765622i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.31491i | − | 0.0782766i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.644 | −0.988796 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −74.8901 | + | 174.900i | −0.608863 | + | 1.42195i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −134.209 | −1.07367 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 88.1648 | 0.694211 | 0.347106 | − | 0.937826i | \(-0.387165\pi\) | ||||
0.347106 | + | 0.937826i | \(0.387165\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −50.7889 | + | 118.613i | −0.393712 | + | 0.919482i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.56071 | −0.0729825 | −0.0364913 | − | 0.999334i | \(-0.511618\pi\) | ||||
−0.0364913 | + | 0.999334i | \(0.511618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 156.844i | 1.17928i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −34.7765 | − | 93.2138i | −0.257604 | − | 0.690472i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 150.504i | − | 1.09857i | −0.835636 | − | 0.549284i | \(-0.814901\pi\) | ||
0.835636 | − | 0.549284i | \(-0.185099\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 51.5907i | 0.371156i | 0.982630 | + | 0.185578i | \(0.0594158\pi\) | ||||
−0.982630 | + | 0.185578i | \(0.940584\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −72.6590 | + | 169.689i | −0.515312 | + | 1.20347i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.7927i | 0.117431i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −124.111 | −0.855938 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 53.5629 | + | 22.9351i | 0.364373 | + | 0.156021i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25.7936 | −0.173112 | −0.0865558 | − | 0.996247i | \(-0.527586\pi\) | ||||
−0.0865558 | + | 0.996247i | \(0.527586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.3156 | 0.108051 | 0.0540253 | − | 0.998540i | \(-0.482795\pi\) | ||||
0.0540253 | + | 0.998540i | \(0.482795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.1556 | + | 10.6381i | −0.0729124 | + | 0.0695302i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −204.630 | −1.32020 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 251.489i | − | 1.60184i | −0.598772 | − | 0.800919i | \(-0.704345\pi\) | ||
0.598772 | − | 0.800919i | \(-0.295655\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 155.291 | + | 66.4938i | 0.976670 | + | 0.418200i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 192.647i | − | 1.19657i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 99.6915i | 0.611604i | 0.952095 | + | 0.305802i | \(0.0989246\pi\) | ||||
−0.952095 | + | 0.305802i | \(0.901075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.8323 | + | 5.06646i | 0.0717108 | + | 0.0307058i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 158.483i | − | 0.948999i | −0.880256 | − | 0.474499i | \(-0.842629\pi\) | ||
0.880256 | − | 0.474499i | \(-0.157371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −39.0000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 187.838 | − | 179.124i | 1.09847 | − | 1.04751i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −117.340 | −0.678269 | −0.339134 | − | 0.940738i | \(-0.610134\pi\) | ||||
−0.339134 | + | 0.940738i | \(0.610134\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 62.1202 | 0.354973 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 136.900 | + | 58.6191i | 0.773446 | + | 0.331181i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 144.265 | 0.805948 | 0.402974 | − | 0.915212i | \(-0.367977\pi\) | ||||
0.402974 | + | 0.915212i | \(0.367977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 289.800i | 1.60110i | 0.599263 | + | 0.800552i | \(0.295460\pi\) | ||||
−0.599263 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.58950 | + | 13.0538i | −0.0305437 | + | 0.0713323i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 112.100i | 0.605946i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.99427i | − | 0.0106646i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 51.3280 | + | 137.578i | 0.271577 | + | 0.727925i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 151.005i | 0.790602i | 0.918552 | + | 0.395301i | \(0.129360\pi\) | ||||
−0.918552 | + | 0.395301i | \(0.870640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.22205 | −0.0115132 | −0.00575661 | − | 0.999983i | \(-0.501832\pi\) | ||||
−0.00575661 | + | 0.999983i | \(0.501832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −62.7549 | + | 146.559i | −0.321820 | + | 0.751583i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 174.742 | 0.887013 | 0.443507 | − | 0.896271i | \(-0.353734\pi\) | ||||
0.443507 | + | 0.896271i | \(0.353734\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −140.556 | −0.706312 | −0.353156 | − | 0.935564i | \(-0.614891\pi\) | ||||
−0.353156 | + | 0.935564i | \(0.614891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.36669 | − | 19.5397i | 0.0416253 | − | 0.0972124i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 183.180 | 0.902366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 233.689i | − | 1.13995i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −230.715 | + | 220.013i | −1.11457 | + | 1.06286i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.5796i | 0.160668i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 295.479i | − | 1.40038i | −0.713959 | − | 0.700188i | \(-0.753100\pi\) | ||
0.713959 | − | 0.700188i | \(-0.246900\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 114.488 | − | 267.378i | 0.537504 | − | 1.25529i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 158.483i | − | 0.737129i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 302.022 | 1.39181 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −189.002 | − | 80.9287i | −0.863023 | − | 0.369537i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.7017 | 0.111773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.43282 | −0.0333310 | −0.0166655 | − | 0.999861i | \(-0.505305\pi\) | ||||
−0.0166655 | + | 0.999861i | \(0.505305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −70.9445 | − | 74.3955i | −0.315309 | − | 0.330647i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −305.995 | −1.34799 | −0.673997 | − | 0.738734i | \(-0.735424\pi\) | ||||
−0.673997 | + | 0.738734i | \(0.735424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 62.6443i | − | 0.273556i | −0.990602 | − | 0.136778i | \(-0.956325\pi\) | ||
0.990602 | − | 0.136778i | \(-0.0436747\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.4637 | − | 7.47779i | −0.0756006 | − | 0.0323714i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 270.130i | 1.15936i | 0.814845 | + | 0.579679i | \(0.196822\pi\) | ||||
−0.814845 | + | 0.579679i | \(0.803178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 226.727i | − | 0.964794i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.8308 | − | 11.4887i | −0.113210 | − | 0.0484754i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 344.910i | 1.44314i | 0.692342 | + | 0.721570i | \(0.256579\pi\) | ||||
−0.692342 | + | 0.721570i | \(0.743421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9109 | 0.0992152 | 0.0496076 | − | 0.998769i | \(-0.484203\pi\) | ||||
0.0496076 | + | 0.998769i | \(0.484203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 106.145 | − | 218.592i | 0.436809 | − | 0.899554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −71.5671 | −0.292110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −415.928 | −1.68392 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −107.322 | − | 45.9542i | −0.431013 | − | 0.184555i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −395.470 | −1.57558 | −0.787788 | − | 0.615946i | \(-0.788774\pi\) | ||||
−0.787788 | + | 0.615946i | \(0.788774\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 41.2447i | − | 0.163023i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.45267 | − | 17.4051i | 0.0292262 | − | 0.0682552i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 451.825i | 1.75807i | 0.476753 | + | 0.879037i | \(0.341814\pi\) | ||||
−0.476753 | + | 0.879037i | \(0.658186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 165.453i | − | 0.638813i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −209.201 | − | 219.378i | −0.801538 | − | 0.840527i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 167.798i | − | 0.638014i | −0.947752 | − | 0.319007i | \(-0.896651\pi\) | ||
0.947752 | − | 0.319007i | \(-0.103349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −207.489 | −0.782976 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.797788 | − | 1.86317i | 0.00298797 | − | 0.00697815i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 452.084 | 1.68061 | 0.840306 | − | 0.542113i | \(-0.182375\pi\) | ||||
0.840306 | + | 0.542113i | \(0.182375\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −207.813 | −0.766837 | −0.383419 | − | 0.923575i | \(-0.625253\pi\) | ||||
−0.383419 | + | 0.923575i | \(0.625253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 92.6224 | − | 216.312i | 0.339276 | − | 0.792350i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.2996 | 0.0483622 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 216.111i | 0.780184i | 0.920776 | + | 0.390092i | \(0.127557\pi\) | ||||
−0.920776 | + | 0.390092i | \(0.872443\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −344.925 | − | 361.703i | −1.23629 | − | 1.29643i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 499.107i | − | 1.77618i | −0.459669 | − | 0.888090i | \(-0.652032\pi\) | ||
0.459669 | − | 0.888090i | \(-0.347968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 206.468i | 0.729569i | 0.931092 | + | 0.364785i | \(0.118857\pi\) | ||||
−0.931092 | + | 0.364785i | \(0.881143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −125.488 | + | 293.066i | −0.440309 | + | 1.02830i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 344.910i | 1.20178i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 286.066 | 0.989849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −237.478 | − | 101.686i | −0.816077 | − | 0.349436i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 74.6785 | 0.254876 | 0.127438 | − | 0.991847i | \(-0.459325\pi\) | ||||
0.127438 | + | 0.991847i | \(0.459325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −182.916 | −0.620055 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9891 | + | 29.4547i | 0.0370002 | + | 0.0991740i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 510.871 | 1.70860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 233.911i | 0.777113i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 301.849 | + | 129.249i | 0.996202 | + | 0.426563i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 17.4416i | − | 0.0571856i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 293.485i | − | 0.955977i | −0.878366 | − | 0.477988i | \(-0.841366\pi\) | ||
0.878366 | − | 0.477988i | \(-0.158634\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −441.289 | − | 188.955i | −1.42812 | − | 0.611506i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 44.7374i | 0.143850i | 0.997410 | + | 0.0719251i | \(0.0229143\pi\) | ||||
−0.997410 | + | 0.0719251i | \(0.977086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 69.2666 | 0.221299 | 0.110650 | − | 0.993859i | \(-0.464707\pi\) | ||||
0.110650 | + | 0.993859i | \(0.464707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −124.470 | − | 130.525i | −0.395144 | − | 0.414365i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0916 | −0.0381438 | −0.0190719 | − | 0.999818i | \(-0.506071\pi\) | ||||
−0.0190719 | + | 0.999818i | \(0.506071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.2179 | 0.122940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −508.389 | − | 217.687i | −1.58377 | − | 0.678151i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.3949 | 0.152925 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 164.733i | 0.506872i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −81.1650 | + | 189.554i | −0.248211 | + | 0.579676i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 334.635i | 1.01713i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 468.516i | − | 1.41545i | −0.706486 | − | 0.707727i | \(-0.749721\pi\) | ||
0.706486 | − | 0.707727i | \(-0.250279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −198.147 | + | 188.955i | −0.595036 | + | 0.567434i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.1076i | 0.0779332i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −302.111 | −0.896472 | −0.448236 | − | 0.893915i | \(-0.647948\pi\) | ||||
−0.448236 | + | 0.893915i | \(0.647948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −84.2050 | + | 196.654i | −0.248392 | + | 0.580099i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 64.6613 | 0.189623 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 372.117 | 1.08489 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 154.133 | − | 359.964i | 0.446762 | − | 1.04337i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −419.740 | −1.20963 | −0.604813 | − | 0.796368i | \(-0.706752\pi\) | ||||
−0.604813 | + | 0.796368i | \(0.706752\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.0446i | − | 0.0774916i | −0.999249 | − | 0.0387458i | \(-0.987664\pi\) | ||
0.999249 | − | 0.0387458i | \(-0.0123363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −364.836 | + | 136.114i | −1.03942 | + | 0.387789i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 47.9572i | 0.135856i | 0.997690 | + | 0.0679281i | \(0.0216388\pi\) | ||||
−0.997690 | + | 0.0679281i | \(0.978361\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 357.252i | 1.00634i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9997 | + | 25.6888i | −0.0308114 | + | 0.0719575i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.1076i | − | 0.0727232i | −0.999339 | − | 0.0363616i | \(-0.988423\pi\) | ||
0.999339 | − | 0.0363616i | \(-0.0115768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −470.711 | −1.30391 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 329.957 | + | 141.284i | 0.908972 | + | 0.389212i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 252.532 | 0.691868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 101.338 | 0.276126 | 0.138063 | − | 0.990423i | \(-0.455912\pi\) | ||||
0.138063 | + | 0.990423i | \(0.455912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 413.066 | − | 393.905i | 1.11942 | − | 1.06749i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 306.241 | 0.825446 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 286.644i | − | 0.768483i | −0.923233 | − | 0.384242i | \(-0.874463\pi\) | ||
0.923233 | − | 0.384242i | \(-0.125537\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 370.123 | + | 158.483i | 0.986995 | + | 0.422621i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 485.766i | 1.28850i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 257.560i | 0.679579i | 0.940502 | + | 0.339789i | \(0.110356\pi\) | ||||
−0.940502 | + | 0.339789i | \(0.889644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −243.142 | − | 104.111i | −0.638169 | − | 0.273257i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 311.325i | − | 0.812859i | −0.913682 | − | 0.406429i | \(-0.866774\pi\) | ||
0.913682 | − | 0.406429i | \(-0.133226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.3338 | 0.0606074 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 280.133 | − | 267.138i | 0.723858 | − | 0.690280i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.1287 | −0.0337500 | −0.0168750 | − | 0.999858i | \(-0.505372\pi\) | ||||
−0.0168750 | + | 0.999858i | \(0.505372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −60.6702 | −0.155167 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.3667 | + | 11.2899i | 0.0670908 | + | 0.0287276i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.8495 | 0.0907582 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 498.244i | − | 1.25502i | −0.778607 | − | 0.627511i | \(-0.784074\pi\) | ||
0.778607 | − | 0.627511i | \(-0.215926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 185.213 | − | 432.548i | 0.464192 | − | 1.08408i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 523.495i | 1.30547i | 0.757585 | + | 0.652736i | \(0.226379\pi\) | ||||
−0.757585 | + | 0.652736i | \(0.773621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 800.916i | 1.98739i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.1659 | + | 298.133i | −0.0349775 | + | 0.736131i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 35.4225i | − | 0.0870332i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 581.822 | 1.42255 | 0.711274 | − | 0.702915i | \(-0.248119\pi\) | ||||
0.711274 | + | 0.702915i | \(0.248119\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −177.725 | + | 415.062i | −0.432421 | + | 1.00988i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 269.973 | 0.653688 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 143.396 | 0.345534 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 60.9218 | − | 142.278i | 0.146095 | − | 0.341194i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −256.600 | −0.612410 | −0.306205 | − | 0.951966i | \(-0.599059\pi\) | ||||
−0.306205 | + | 0.951966i | \(0.599059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 72.1110i | 0.171285i | 0.996326 | + | 0.0856425i | \(0.0272943\pi\) | ||||
−0.996326 | + | 0.0856425i | \(0.972706\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 400.760 | − | 382.170i | 0.947423 | − | 0.903475i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 19.5635i | − | 0.0460317i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.7427i | 0.0602874i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.8300 | − | 46.3112i | 0.0462237 | − | 0.107951i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 714.091i | − | 1.65682i | −0.560119 | − | 0.828412i | \(-0.689245\pi\) | ||
0.560119 | − | 0.828412i | \(-0.310755\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −192.200 | −0.443880 | −0.221940 | − | 0.975060i | \(-0.571239\pi\) | ||||
−0.221940 | + | 0.975060i | \(0.571239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 342.275 | + | 146.559i | 0.786840 | + | 0.336917i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1021.56 | 2.33768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 504.093 | 1.14827 | 0.574137 | − | 0.818759i | \(-0.305338\pi\) | ||||
0.574137 | + | 0.818759i | \(0.305338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −120.633 | − | 126.501i | −0.273545 | − | 0.286851i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 97.6254 | 0.220373 | 0.110187 | − | 0.993911i | \(-0.464855\pi\) | ||||
0.110187 | + | 0.993911i | \(0.464855\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48944i | 0.00559424i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 71.1341 | + | 30.4589i | 0.159137 | + | 0.0681407i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 306.869i | 0.683450i | 0.939800 | + | 0.341725i | \(0.111011\pi\) | ||||
−0.939800 | + | 0.341725i | \(0.888989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 73.8435i | 0.163733i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −44.9955 | − | 19.2666i | −0.0993279 | − | 0.0425312i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 289.021i | 0.635211i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 117.378 | 0.256844 | 0.128422 | − | 0.991720i | \(-0.459009\pi\) | ||||
0.128422 | + | 0.991720i | \(0.459009\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 43.3273 | − | 16.1647i | 0.0943949 | − | 0.0352172i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −604.144 | −1.31051 | −0.655254 | − | 0.755409i | \(-0.727438\pi\) | ||||
−0.655254 | + | 0.755409i | \(0.727438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 523.249 | 1.13013 | 0.565063 | − | 0.825048i | \(-0.308852\pi\) | ||||
0.565063 | + | 0.825048i | \(0.308852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 564.333 | + | 241.641i | 1.21362 | + | 0.519659i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −219.340 | −0.469679 | −0.234840 | − | 0.972034i | \(-0.575456\pi\) | ||||
−0.234840 | + | 0.972034i | \(0.575456\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 38.5332i | − | 0.0821604i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −296.975 | + | 693.560i | −0.630520 | + | 1.47253i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.0791i | 0.105875i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 329.409i | 0.693494i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −349.743 | − | 366.755i | −0.733213 | − | 0.768879i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 302.010i | − | 0.630501i | −0.949008 | − | 0.315251i | \(-0.897911\pi\) | ||
0.949008 | − | 0.315251i | \(-0.102089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 438.755 | 0.912173 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −227.491 | + | 531.285i | −0.470995 | + | 1.09997i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 317.302 | 0.654232 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 208.115 | 0.427340 | 0.213670 | − | 0.976906i | \(-0.431458\pi\) | ||||
0.213670 | + | 0.976906i | \(0.431458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 117.722 | − | 274.931i | 0.240741 | − | 0.562231i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 584.291 | 1.19000 | 0.595001 | − | 0.803725i | \(-0.297152\pi\) | ||||
0.595001 | + | 0.803725i | \(0.297152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 57.6888i | − | 0.117016i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.6485 | − | 27.9447i | −0.0538353 | − | 0.0564540i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 527.282i | − | 1.06093i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 352.161i | − | 0.705733i | −0.935674 | − | 0.352867i | \(-0.885207\pi\) | ||
0.935674 | − | 0.352867i | \(-0.114793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −187.147 | + | 437.066i | −0.373547 | + | 0.872388i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 130.538i | 0.259519i | 0.991545 | + | 0.129760i | \(0.0414205\pi\) | ||||
−0.991545 | + | 0.129760i | \(0.958579\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −403.310 | −0.798634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 107.555 | + | 46.0538i | 0.212140 | + | 0.0908360i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 738.353 | 1.45059 | 0.725297 | − | 0.688436i | \(-0.241702\pi\) | ||||
0.725297 | + | 0.688436i | \(0.241702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −372.721 | −0.729396 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −729.544 | + | 272.181i | −1.42211 | + | 0.530567i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 589.621 | 1.14489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 71.6435i | 0.138575i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 323.603 | + | 138.564i | 0.623513 | + | 0.266982i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 318.449i | 0.611227i | 0.952156 | + | 0.305613i | \(0.0988615\pi\) | ||||
−0.952156 | + | 0.305613i | \(0.901139\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 817.186i | 1.56250i | 0.624220 | + | 0.781249i | \(0.285417\pi\) | ||||
−0.624220 | + | 0.781249i | \(0.714583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −171.316 | − | 73.3557i | −0.326316 | − | 0.139725i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 95.1155i | − | 0.180485i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −725.755 | −1.37194 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −308.323 | − | 323.321i | −0.580647 | − | 0.608892i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −914.650 | −1.71604 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 679.274 | 1.26967 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −397.855 | − | 170.357i | −0.740885 | − | 0.317239i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.6145 | 0.0419564 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 322.022i | 0.595235i | 0.954685 | + | 0.297617i | \(0.0961919\pi\) | ||||
−0.954685 | + | 0.297617i | \(0.903808\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 342.215 | − | 799.215i | 0.630231 | − | 1.47185i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 253.269i | − | 0.464714i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 276.716i | − | 0.505880i | −0.967482 | − | 0.252940i | \(-0.918602\pi\) | ||
0.967482 | − | 0.252940i | \(-0.0813975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8296 | − | 29.3995i | 0.0561560 | − | 0.0535511i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 971.364i | 1.76291i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.9116 | −0.0956811 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 132.375 | − | 309.151i | 0.238514 | − | 0.557029i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −579.033 | −1.03956 | −0.519778 | − | 0.854301i | \(-0.673985\pi\) | ||||
−0.519778 | + | 0.854301i | \(0.673985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −620.296 | −1.10965 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.35497 | + | 5.49984i | −0.00419781 | + | 0.00980364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 494.751 | 0.878776 | 0.439388 | − | 0.898297i | \(-0.355195\pi\) | ||||
0.439388 | + | 0.898297i | \(0.355195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 262.755i | − | 0.465054i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.9080 | − | 440.026i | 0.0368748 | − | 0.776060i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 229.386i | − | 0.403138i | −0.979474 | − | 0.201569i | \(-0.935396\pi\) | ||
0.979474 | − | 0.201569i | \(-0.0646041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 451.354i | − | 0.790462i | −0.918582 | − | 0.395231i | \(-0.870665\pi\) | ||
0.918582 | − | 0.395231i | \(-0.129335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 178.317 | − | 416.444i | 0.311199 | − | 0.726779i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 404.603i | − | 0.703658i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 792.644 | 1.37373 | 0.686867 | − | 0.726783i | \(-0.258986\pi\) | ||||
0.686867 | + | 0.726783i | \(0.258986\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.12801 | + | 2.62395i | 0.0105838 | + | 0.00453186i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −211.644 | −0.364276 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 65.5645 | 0.112461 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 346.133 | − | 330.077i | 0.591680 | − | 0.564234i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −930.546 | −1.58526 | −0.792629 | − | 0.609704i | \(-0.791288\pi\) | ||||
−0.792629 | + | 0.609704i | \(0.791288\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1601.55i | 2.71911i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −481.905 | − | 206.347i | −0.815407 | − | 0.349148i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 147.392i | − | 0.248554i | −0.992248 | − | 0.124277i | \(-0.960339\pi\) | ||
0.992248 | − | 0.124277i | \(-0.0396611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 34.3236i | − | 0.0576868i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 387.628 | + | 165.978i | 0.649293 | + | 0.278020i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 423.233i | 0.706566i | 0.935516 | + | 0.353283i | \(0.114935\pi\) | ||||
−0.935516 | + | 0.353283i | \(0.885065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 145.156 | 0.241523 | 0.120762 | − | 0.992682i | \(-0.461466\pi\) | ||||
0.120762 | + | 0.992682i | \(0.461466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.1476 | + | 44.0069i | −0.0765300 | + | 0.0729800i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −440.866 | −0.728704 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −503.791 | −0.829968 | −0.414984 | − | 0.909829i | \(-0.636213\pi\) | ||||
−0.414984 | + | 0.909829i | \(0.636213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −505.177 | − | 216.312i | −0.829520 | − | 0.355192i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −887.400 | −1.45237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 245.400i | − | 0.400326i | −0.979763 | − | 0.200163i | \(-0.935853\pi\) | ||
0.979763 | − | 0.200163i | \(-0.0641471\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −275.956 | + | 644.471i | −0.448708 | + | 1.04792i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 87.0366i | − | 0.141064i | −0.997510 | − | 0.0705321i | \(-0.977530\pi\) | ||
0.997510 | − | 0.0705321i | \(-0.0224697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 203.477i | − | 0.328718i | −0.986401 | − | 0.164359i | \(-0.947444\pi\) | ||
0.986401 | − | 0.164359i | \(-0.0525556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 896.076 | − | 334.311i | 1.44296 | − | 0.538343i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.67426i | − | 0.00589768i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −208.978 | −0.334365 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 39.6530 | − | 92.6063i | 0.0632425 | − | 0.147697i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.1059 | −0.0828392 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −975.796 | −1.54643 | −0.773214 | − | 0.634145i | \(-0.781352\pi\) | ||||
−0.773214 | + | 0.634145i | \(0.781352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −348.922 | + | 814.877i | −0.551219 | + | 1.28733i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 324.870 | 0.511607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 280.111i | 0.439735i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −631.475 | + | 602.183i | −0.988224 | + | 0.942383i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 797.821i | − | 1.24465i | −0.782759 | − | 0.622325i | \(-0.786188\pi\) | ||
0.782759 | − | 0.622325i | \(-0.213812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 94.7058i | − | 0.147287i | −0.997285 | − | 0.0736437i | \(-0.976537\pi\) | ||
0.997285 | − | 0.0736437i | \(-0.0234628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −187.147 | + | 437.066i | −0.290151 | + | 0.677622i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 367.344i | − | 0.567765i | −0.958859 | − | 0.283882i | \(-0.908378\pi\) | ||
0.958859 | − | 0.283882i | \(-0.0916225\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.7998 | 0.0890599 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −832.921 | − | 356.648i | −1.27945 | − | 0.547846i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 680.024 | 1.04138 | 0.520692 | − | 0.853745i | \(-0.325674\pi\) | ||||
0.520692 | + | 0.853745i | \(0.325674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.2294 | −0.0537853 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 425.667 | + | 446.373i | 0.647895 | + | 0.679411i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −687.246 | −1.04286 | −0.521431 | − | 0.853293i | \(-0.674602\pi\) | ||||
−0.521431 | + | 0.853293i | \(0.674602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1121.58i | − | 1.69679i | −0.529364 | − | 0.848395i | \(-0.677569\pi\) | ||
0.529364 | − | 0.848395i | \(-0.322431\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −68.1229 | − | 29.1695i | −0.102749 | − | 0.0439962i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 577.941i | 0.869085i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1193.10i | − | 1.78875i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.4984 | + | 8.77718i | 0.0306403 | + | 0.0131198i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.51138i | 0.00821369i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 563.177 | 0.836816 | 0.418408 | − | 0.908259i | \(-0.362588\pi\) | ||||
0.418408 | + | 0.908259i | \(0.362588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 107.801 | + | 288.945i | 0.159705 | + | 0.428067i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −998.773 | −1.47529 | −0.737646 | − | 0.675188i | \(-0.764063\pi\) | ||||
−0.737646 | + | 0.675188i | \(0.764063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −468.319 | −0.689719 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 843.877 | + | 361.339i | 1.23917 | + | 0.530601i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 147.020 | 0.215257 | 0.107628 | − | 0.994191i | \(-0.465674\pi\) | ||||
0.107628 | + | 0.994191i | \(0.465674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 554.577i | − | 0.809601i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −73.9746 | + | 172.761i | −0.107678 | + | 0.251472i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 812.104i | 1.17867i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 862.689i | − | 1.24846i | −0.781239 | − | 0.624232i | \(-0.785412\pi\) | ||
0.781239 | − | 0.624232i | \(-0.214588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 39.3315 | + | 41.2447i | 0.0567554 | + | 0.0595162i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 190.102i | 0.273528i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 108.622 | 0.155843 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 318.988 | − | 744.970i | 0.456349 | − | 1.06576i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 468.489 | 0.668315 | 0.334158 | − | 0.942517i | \(-0.391548\pi\) | ||||
0.334158 | + | 0.942517i | \(0.391548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 877.358 | 1.24802 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −267.734 | + | 625.270i | −0.379765 | + | 0.886908i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 595.261 | 0.841954 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1020.60i | − | 1.43949i | −0.694238 | − | 0.719745i | \(-0.744259\pi\) | ||
0.694238 | − | 0.719745i | \(-0.255741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 60.4278 | + | 63.3673i | 0.0849899 | + | 0.0891241i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1967.14i | − | 2.75896i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 61.8778i | 0.0865424i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 407.294 | − | 951.199i | 0.568052 | − | 1.32664i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 477.286i | 0.663819i | 0.943311 | + | 0.331909i | \(0.107693\pi\) | ||||
−0.943311 | + | 0.331909i | \(0.892307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −870.244 | −1.20700 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −65.9418 | − | 28.2356i | −0.0912058 | − | 0.0390534i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 384.721 | 0.530649 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1042.27 | −1.43365 | −0.716827 | − | 0.697251i | \(-0.754406\pi\) | ||||
−0.716827 | + | 0.697251i | \(0.754406\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −550.855 | + | 477.493i | −0.755631 | + | 0.654997i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.6654 | 0.100773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 952.333i | 1.29923i | 0.760265 | + | 0.649613i | \(0.225069\pi\) | ||||
−0.760265 | + | 0.649613i | \(0.774931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 197.369 | + | 84.5112i | 0.268529 | + | 0.114981i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.24976i | − | 0.0111937i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 25.2442i | − | 0.0341599i | −0.999854 | − | 0.0170800i | \(-0.994563\pi\) | ||
0.999854 | − | 0.0170800i | \(-0.00543698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1147.05 | + | 491.156i | 1.54798 | + | 0.662828i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 706.613i | − | 0.951027i | −0.879708 | − | 0.475514i | \(-0.842262\pi\) | ||
0.879708 | − | 0.475514i | \(-0.157738\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −95.0446 | −0.127577 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 241.709 | + | 253.466i | 0.323573 | + | 0.339313i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1002.57 | −1.33854 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1414.08 | −1.88293 | −0.941466 | − | 0.337108i | \(-0.890551\pi\) | ||||
−0.941466 | + | 0.337108i | \(0.890551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1090.63 | + | 466.997i | 1.44838 | + | 0.620182i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 60.1200 | 0.0796291 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 309.177i | 0.408425i | 0.978927 | + | 0.204212i | \(0.0654633\pi\) | ||||
−0.978927 | + | 0.204212i | \(0.934537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48.7046 | + | 113.745i | −0.0641694 | + | 0.149862i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 400.757i | 0.526618i | 0.964712 | + | 0.263309i | \(0.0848139\pi\) | ||||
−0.964712 | + | 0.263309i | \(0.915186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 373.810i | 0.489921i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.1062 | + | 39.1994i | −0.0537336 | + | 0.0512410i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 715.928i | 0.933414i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 804.533 | 1.04621 | 0.523104 | − | 0.852269i | \(-0.324774\pi\) | ||||
0.523104 | + | 0.852269i | \(0.324774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 533.546 | − | 1246.05i | 0.692018 | − | 1.61615i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 122.227 | 0.158120 | 0.0790599 | − | 0.996870i | \(-0.474808\pi\) | ||||
0.0790599 | + | 0.996870i | \(0.474808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 634.316 | 0.818472 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −195.378 | + | 456.288i | −0.251451 | + | 0.587243i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1828.98 | −2.34786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 112.888i | − | 0.144543i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 317.883 | + | 852.042i | 0.405981 | + | 1.08818i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 926.687i | − | 1.18049i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 574.295i | 0.729727i | 0.931061 | + | 0.364863i | \(0.118884\pi\) | ||||
−0.931061 | + | 0.364863i | \(0.881116\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −198.147 | + | 462.755i | −0.251137 | + | 0.586509i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 387.811i | 0.490279i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.2658 | −0.0860856 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 572.216 | + | 245.017i | 0.719768 | + | 0.308197i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1000.03 | −1.25474 | −0.627371 | − | 0.778721i | \(-0.715869\pi\) | ||||
−0.627371 | + | 0.778721i | \(0.715869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 105.386 | 0.131898 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.40031 | + | 4.19619i | −0.00549352 | + | 0.00523869i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −79.7976 | −0.0993744 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 709.867i | − | 0.881822i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1246.77 | − | 533.852i | −1.54494 | − | 0.661527i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 583.032i | − | 0.720682i | −0.932821 | − | 0.360341i | \(-0.882660\pi\) | ||
0.932821 | − | 0.360341i | \(-0.117340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 911.183i | − | 1.12353i | −0.827297 | − | 0.561765i | \(-0.810122\pi\) | ||
0.827297 | − | 0.561765i | \(-0.189878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 573.110 | + | 245.400i | 0.704932 | + | 0.301844i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 367.344i | 0.450728i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1240.38 | −1.51821 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −510.871 | + | 487.173i | −0.623774 | + | 0.594839i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −914.486 | −1.11387 | −0.556934 | − | 0.830557i | \(-0.688022\pi\) | ||||
−0.556934 | + | 0.830557i | \(0.688022\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 686.707 | 0.834395 | 0.417197 | − | 0.908816i | \(-0.363012\pi\) | ||||
0.417197 | + | 0.908816i | \(0.363012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.6779 | − | 15.7051i | −0.0444580 | − | 0.0190365i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1107.30 | 1.33893 | 0.669466 | − | 0.742843i | \(-0.266523\pi\) | ||||
0.669466 | + | 0.742843i | \(0.266523\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 366.866i | − | 0.442541i | −0.975212 | − | 0.221270i | \(-0.928980\pi\) | ||
0.975212 | − | 0.221270i | \(-0.0710203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 255.199 | − | 595.995i | 0.307098 | − | 0.717202i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 33.2655i | − | 0.0399346i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 583.978i | − | 0.699375i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 524.115 | + | 1404.82i | 0.626183 | + | 1.67840i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1085.11i | − | 1.29334i | −0.762771 | − | 0.646668i | \(-0.776162\pi\) | ||
0.762771 | − | 0.646668i | \(-0.223838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 293.466 | 0.348949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −589.379 | + | 1376.44i | −0.699145 | + | 1.63279i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −143.707 | −0.170068 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 650.691 | 0.768230 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 243.812 | − | 569.401i | 0.287175 | − | 0.670673i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1077.63 | −1.26631 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1039.75i | 1.21894i | 0.792810 | + | 0.609469i | \(0.208617\pi\) | ||||
−0.792810 | + | 0.609469i | \(0.791383\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 692.145 | − | 660.039i | 0.809527 | − | 0.771975i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1216.69i | − | 1.41971i | −0.704346 | − | 0.709857i | \(-0.748760\pi\) | ||
0.704346 | − | 0.709857i | \(-0.251240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 318.230i | 0.370466i | 0.982695 | + | 0.185233i | \(0.0593040\pi\) | ||||
−0.982695 | + | 0.185233i | \(0.940696\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 407.294 | − | 951.199i | 0.473047 | − | 1.10476i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 464.296i | 0.538003i | 0.963140 | + | 0.269001i | \(0.0866936\pi\) | ||||
−0.963140 | + | 0.269001i | \(0.913306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −432.377 | −0.499858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −788.919 | − | 337.807i | −0.909941 | − | 0.389627i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.3281 | −0.0130358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 102.184 | 0.117318 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 534.844 | + | 560.861i | 0.612651 | + | 0.642453i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 729.901 | 0.834172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1239.89i | 1.41378i | 0.707321 | + | 0.706892i | \(0.249903\pi\) | ||||
−0.707321 | + | 0.706892i | \(0.750097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −205.950 | − | 88.1855i | −0.234300 | − | 0.100325i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.3084i | 0.0559687i | 0.999608 | + | 0.0279843i | \(0.00890885\pi\) | ||||
−0.999608 | + | 0.0279843i | \(0.991091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1359.44i | 1.53957i | 0.638303 | + | 0.769785i | \(0.279637\pi\) | ||||
−0.638303 | + | 0.769785i | \(0.720363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 504.450 | + | 216.000i | 0.570000 | + | 0.244068i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1353.53i | − | 1.52597i | −0.646417 | − | 0.762984i | \(-0.723733\pi\) | ||
0.646417 | − | 0.762984i | \(-0.276267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −479.489 | −0.539357 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.47629 | − | 94.2072i | 0.00502390 | − | 0.105732i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1774.49 | −1.98711 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 531.587 | 0.593952 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1408.89 | − | 603.271i | −1.57067 | − | 0.672543i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1870.47 | 2.08061 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 96.4441i | − | 0.107041i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 276.218 | − | 645.083i | 0.305889 | − | 0.714378i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1067.86i | 1.17995i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1442.68i | 1.59061i | 0.606213 | + | 0.795303i | \(0.292688\pi\) | ||||
−0.606213 | + | 0.795303i | \(0.707312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −679.819 | − | 712.888i | −0.747876 | − | 0.784255i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 128.701i | − | 0.141274i | −0.997502 | − | 0.0706372i | \(-0.977497\pi\) | ||
0.997502 | − | 0.0706372i | \(-0.0225033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.3120 | −0.0496297 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.5962 | + | 48.1007i | −0.0225095 | + | 0.0525691i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51.9964 | 0.0567027 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −837.294 | −0.911092 | −0.455546 | − | 0.890212i | \(-0.650556\pi\) | ||||
−0.455546 | + | 0.890212i | \(0.650556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −346.567 | + | 809.377i | −0.376294 | + | 0.878803i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1398.27 | 1.51492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 347.489i | − | 0.375663i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 993.864 | + | 1042.21i | 1.07213 | + | 1.12428i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 671.610i | − | 0.722939i | −0.932384 | − | 0.361469i | \(-0.882275\pi\) | ||
0.932384 | − | 0.361469i | \(-0.117725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 560.125i | 0.601638i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.8290 | − | 123.378i | 0.0566227 | − | 0.132238i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.34851i | − | 0.00785937i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −598.511 | −0.638753 | −0.319376 | − | 0.947628i | \(-0.603473\pi\) | ||||
−0.319376 | + | 0.947628i | \(0.603473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −191.025 | − | 81.7947i | −0.203434 | − | 0.0871083i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 308.432 | 0.327770 | 0.163885 | − | 0.986479i | \(-0.447597\pi\) | ||||
0.163885 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2246.48 | 2.38227 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 189.134 | + | 506.947i | 0.200141 | + | 0.536452i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 119.140 | 0.125808 | 0.0629040 | − | 0.998020i | \(-0.479964\pi\) | ||||
0.0629040 | + | 0.998020i | \(0.479964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 988.400i | − | 1.04152i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.3464 | + | 14.2786i | 0.0350645 | + | 0.0150143i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1061.63i | − | 1.11399i | −0.830516 | − | 0.556995i | \(-0.811954\pi\) | ||
0.830516 | − | 0.556995i | \(-0.188046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 556.424i | 0.582643i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −108.156 | − | 46.3112i | −0.113015 | − | 0.0483920i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 818.522i | 0.853516i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2122.98 | 2.20913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1144.98 | + | 1200.68i | 1.18898 | + | 1.24681i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.18783 | −0.00848479 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −167.506 | −0.173223 | −0.0866114 | − | 0.996242i | \(-0.527604\pi\) | ||||
−0.0866114 | + | 0.996242i | \(0.527604\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −136.222 | − | 58.3288i | −0.140580 | − | 0.0601949i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1724.86 | −1.77638 | −0.888189 | − | 0.459479i | \(-0.848036\pi\) | ||||
−0.888189 | + | 0.459479i | \(0.848036\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 280.579i | − | 0.288364i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 194.528 | − | 454.304i | 0.199516 | − | 0.465953i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 166.328i | 0.170243i | 0.996371 | + | 0.0851216i | \(0.0271279\pi\) | ||||
−0.996371 | + | 0.0851216i | \(0.972872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.786639i | − | 0.000803512i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 447.677 | − | 426.910i | 0.456347 | − | 0.435178i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1532.48i | − | 1.55899i | −0.626411 | − | 0.779493i | \(-0.715477\pi\) | ||
0.626411 | − | 0.779493i | \(-0.284523\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 643.889 | 0.653694 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 395.159 | − | 922.861i | 0.400364 | − | 0.935016i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1523.52 | 1.54046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −152.339 | −0.153722 | −0.0768612 | − | 0.997042i | \(-0.524490\pi\) | ||||
−0.0768612 | + | 0.997042i | \(0.524490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −553.255 | + | 1292.08i | −0.557155 | + | 1.30119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −517.922 | −0.520524 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 626.688i | 0.628574i | 0.949328 | + | 0.314287i | \(0.101765\pi\) | ||||
−0.949328 | + | 0.314287i | \(0.898235\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 769.584 | − | 287.119i | 0.770355 | − | 0.287406i |
(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 | 384.3.h.g.65.2 | yes | 16 | |
3.2 | odd | 2 | inner | 384.3.h.g.65.13 | yes | 16 | |
4.3 | odd | 2 | inner | 384.3.h.g.65.16 | yes | 16 | |
8.3 | odd | 2 | inner | 384.3.h.g.65.1 | ✓ | 16 | |
8.5 | even | 2 | inner | 384.3.h.g.65.15 | yes | 16 | |
12.11 | even | 2 | inner | 384.3.h.g.65.3 | yes | 16 | |
16.3 | odd | 4 | 768.3.e.o.257.4 | 8 | |||
16.5 | even | 4 | 768.3.e.p.257.4 | 8 | |||
16.11 | odd | 4 | 768.3.e.p.257.5 | 8 | |||
16.13 | even | 4 | 768.3.e.o.257.5 | 8 | |||
24.5 | odd | 2 | inner | 384.3.h.g.65.4 | yes | 16 | |
24.11 | even | 2 | inner | 384.3.h.g.65.14 | yes | 16 | |
48.5 | odd | 4 | 768.3.e.p.257.3 | 8 | |||
48.11 | even | 4 | 768.3.e.p.257.6 | 8 | |||
48.29 | odd | 4 | 768.3.e.o.257.6 | 8 | |||
48.35 | even | 4 | 768.3.e.o.257.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.h.g.65.1 | ✓ | 16 | 8.3 | odd | 2 | inner | |
384.3.h.g.65.2 | yes | 16 | 1.1 | even | 1 | trivial | |
384.3.h.g.65.3 | yes | 16 | 12.11 | even | 2 | inner | |
384.3.h.g.65.4 | yes | 16 | 24.5 | odd | 2 | inner | |
384.3.h.g.65.13 | yes | 16 | 3.2 | odd | 2 | inner | |
384.3.h.g.65.14 | yes | 16 | 24.11 | even | 2 | inner | |
384.3.h.g.65.15 | yes | 16 | 8.5 | even | 2 | inner | |
384.3.h.g.65.16 | yes | 16 | 4.3 | odd | 2 | inner | |
768.3.e.o.257.3 | 8 | 48.35 | even | 4 | |||
768.3.e.o.257.4 | 8 | 16.3 | odd | 4 | |||
768.3.e.o.257.5 | 8 | 16.13 | even | 4 | |||
768.3.e.o.257.6 | 8 | 48.29 | odd | 4 | |||
768.3.e.p.257.3 | 8 | 48.5 | odd | 4 | |||
768.3.e.p.257.4 | 8 | 16.5 | even | 4 | |||
768.3.e.p.257.5 | 8 | 16.11 | odd | 4 | |||
768.3.e.p.257.6 | 8 | 48.11 | even | 4 |