Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,4,Mod(49,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.f (of order \(2\), degree \(1\), 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: | \(14.1604584014\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.49 |
Dual form | 240.4.f.e.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | + | 10.0000i | 0.447214 | + | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00000i | − | 0.215980i | −0.994152 | − | 0.107990i | \(-0.965559\pi\) | ||
0.994152 | − | 0.107990i | \(-0.0344414\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.0000i | 0.341354i | 0.985327 | + | 0.170677i | \(0.0545955\pi\) | ||||
−0.985327 | + | 0.170677i | \(0.945405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 30.0000 | − | 15.0000i | 0.516398 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 108.000i | 1.54081i | 0.637552 | + | 0.770407i | \(0.279947\pi\) | ||||
−0.637552 | + | 0.770407i | \(0.720053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.0000 | 0.386384 | 0.193192 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193192 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 28.0000i | − | 0.253844i | −0.991913 | − | 0.126922i | \(-0.959490\pi\) | ||
0.991913 | − | 0.126922i | \(-0.0405097\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −75.0000 | + | 100.000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 238.000 | 1.52398 | 0.761991 | − | 0.647587i | \(-0.224222\pi\) | ||||
0.761991 | + | 0.647587i | \(0.224222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 180.000 | 1.04287 | 0.521435 | − | 0.853291i | \(-0.325397\pi\) | ||||
0.521435 | + | 0.853291i | \(0.325397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 84.0000i | − | 0.443107i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 40.0000 | − | 20.0000i | 0.193178 | − | 0.0965891i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 40.0000i | − | 0.177729i | −0.996044 | − | 0.0888643i | \(-0.971676\pi\) | ||
0.996044 | − | 0.0888643i | \(-0.0283238\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 48.0000 | 0.197081 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 422.000 | 1.60745 | 0.803724 | − | 0.595003i | \(-0.202849\pi\) | ||||
0.803724 | + | 0.595003i | \(0.202849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 276.000i | 0.978828i | 0.872052 | + | 0.489414i | \(0.162789\pi\) | ||||
−0.872052 | + | 0.489414i | \(0.837211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45.0000 | − | 90.0000i | −0.149071 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 60.0000i | − | 0.186211i | −0.995656 | − | 0.0931053i | \(-0.970321\pi\) | ||
0.995656 | − | 0.0931053i | \(-0.0296793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 327.000 | 0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 324.000 | 0.889590 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 220.000i | − | 0.570176i | −0.958501 | − | 0.285088i | \(-0.907977\pi\) | ||
0.958501 | − | 0.285088i | \(-0.0920228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 140.000 | + | 280.000i | 0.343229 | + | 0.686458i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 96.0000i | − | 0.223079i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −804.000 | −1.77410 | −0.887050 | − | 0.461674i | \(-0.847249\pi\) | ||||
−0.887050 | + | 0.461674i | \(0.847249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.000 | −0.751430 | −0.375715 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375715 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.0000i | 0.0719932i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −160.000 | + | 80.0000i | −0.305316 | + | 0.152658i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 884.000i | 1.61191i | 0.591979 | + | 0.805954i | \(0.298347\pi\) | ||||
−0.591979 | + | 0.805954i | \(0.701653\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −84.0000 | −0.146557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64.0000 | 0.106978 | 0.0534888 | − | 0.998568i | \(-0.482966\pi\) | ||||
0.0534888 | + | 0.998568i | \(0.482966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 152.000i | 0.243702i | 0.992548 | + | 0.121851i | \(0.0388830\pi\) | ||||
−0.992548 | + | 0.121851i | \(0.961117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 300.000 | + | 225.000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 112.000i | − | 0.165761i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −932.000 | −1.32732 | −0.663659 | − | 0.748035i | \(-0.730998\pi\) | ||||
−0.663659 | + | 0.748035i | \(0.730998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1292.00i | − | 1.70862i | −0.519764 | − | 0.854310i | \(-0.673980\pi\) | ||
0.519764 | − | 0.854310i | \(-0.326020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1080.00 | + | 540.000i | −1.37815 | + | 0.689073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 714.000i | − | 0.879872i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1146.00 | 1.36490 | 0.682448 | − | 0.730934i | \(-0.260915\pi\) | ||||
0.682448 | + | 0.730934i | \(0.260915\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 64.0000 | 0.0737255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 540.000i | − | 0.602101i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 160.000 | + | 320.000i | 0.172796 | + | 0.345593i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 824.000i | 0.862521i | 0.902227 | + | 0.431260i | \(0.141931\pi\) | ||||
−0.902227 | + | 0.431260i | \(0.858069\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −252.000 | −0.255828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1290.00 | −1.27089 | −0.635445 | − | 0.772147i | \(-0.719183\pi\) | ||||
−0.635445 | + | 0.772147i | \(0.719183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1604.00i | − | 1.53444i | −0.641387 | − | 0.767218i | \(-0.721641\pi\) | ||
0.641387 | − | 0.767218i | \(-0.278359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −60.0000 | − | 120.000i | −0.0557657 | − | 0.111531i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 892.000i | − | 0.805915i | −0.915219 | − | 0.402957i | \(-0.867982\pi\) | ||
0.915219 | − | 0.402957i | \(-0.132018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −966.000 | −0.848863 | −0.424431 | − | 0.905460i | \(-0.639526\pi\) | ||||
−0.424431 | + | 0.905460i | \(0.639526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −120.000 | −0.102612 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1124.00i | − | 0.935726i | −0.883801 | − | 0.467863i | \(-0.845024\pi\) | ||
0.883801 | − | 0.467863i | \(-0.154976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 280.000 | − | 140.000i | 0.227045 | − | 0.113522i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 144.000i | − | 0.113785i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 432.000 | 0.332785 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1266.00i | − | 0.928060i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1375.00 | − | 250.000i | −0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1884.00i | 1.31636i | 0.752860 | + | 0.658181i | \(0.228674\pi\) | ||||
−0.752860 | + | 0.658181i | \(0.771326\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 828.000 | 0.565127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 588.000 | 0.392166 | 0.196083 | − | 0.980587i | \(-0.437178\pi\) | ||||
0.196083 | + | 0.980587i | \(0.437178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 128.000i | − | 0.0834512i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −270.000 | + | 135.000i | −0.172133 | + | 0.0860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1060.00i | 0.661036i | 0.943800 | + | 0.330518i | \(0.107223\pi\) | ||||
−0.943800 | + | 0.330518i | \(0.892777\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2864.00 | −1.74764 | −0.873818 | − | 0.486254i | \(-0.838363\pi\) | ||||
−0.873818 | + | 0.486254i | \(0.838363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −180.000 | −0.107509 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 448.000i | 0.261984i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1190.00 | + | 2380.00i | 0.681546 | + | 1.36309i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 981.000i | − | 0.550418i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −342.000 | −0.188038 | −0.0940192 | − | 0.995570i | \(-0.529972\pi\) | ||||
−0.0940192 | + | 0.995570i | \(0.529972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1636.00 | −0.881694 | −0.440847 | − | 0.897582i | \(-0.645322\pi\) | ||||
−0.440847 | + | 0.897582i | \(0.645322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 972.000i | − | 0.513605i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 900.000 | + | 1800.00i | 0.466385 | + | 0.932771i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2072.00i | − | 1.05327i | −0.850091 | − | 0.526636i | \(-0.823453\pi\) | ||
0.850091 | − | 0.526636i | \(-0.176547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −660.000 | −0.329191 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −112.000 | −0.0548251 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 772.000i | 0.370968i | 0.982647 | + | 0.185484i | \(0.0593852\pi\) | ||||
−0.982647 | + | 0.185484i | \(0.940615\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 840.000 | − | 420.000i | 0.396327 | − | 0.198163i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1044.00i | 0.483755i | 0.970307 | + | 0.241878i | \(0.0777633\pi\) | ||||
−0.970307 | + | 0.241878i | \(0.922237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1941.00 | 0.883477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −288.000 | −0.128795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4404.00i | − | 1.93543i | −0.252041 | − | 0.967717i | \(-0.581102\pi\) | ||
0.252041 | − | 0.967717i | \(-0.418898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 400.000 | + | 300.000i | 0.172784 | + | 0.129588i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2412.00i | 1.02428i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3452.00 | 1.44142 | 0.720711 | − | 0.693235i | \(-0.243815\pi\) | ||||
0.720711 | + | 0.693235i | \(0.243815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 526.000 | 0.216007 | 0.108004 | − | 0.994151i | \(-0.465554\pi\) | ||||
0.108004 | + | 0.994151i | \(0.465554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1074.00i | 0.433838i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 400.000 | − | 200.000i | 0.158965 | − | 0.0794827i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3024.00i | 1.18255i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 108.000 | 0.0415653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −72.0000 | −0.0272761 | −0.0136381 | − | 0.999907i | \(-0.504341\pi\) | ||||
−0.0136381 | + | 0.999907i | \(0.504341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 208.000i | − | 0.0775760i | −0.999247 | − | 0.0387880i | \(-0.987650\pi\) | ||
0.999247 | − | 0.0387880i | \(-0.0123497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 240.000 | + | 480.000i | 0.0881372 | + | 0.176274i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 372.000i | 0.134538i | 0.997735 | + | 0.0672688i | \(0.0214285\pi\) | ||||
−0.997735 | + | 0.0672688i | \(0.978571\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4348.00 | 1.54885 | 0.774426 | − | 0.632665i | \(-0.218039\pi\) | ||||
0.774426 | + | 0.632665i | \(0.218039\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2652.00 | 0.930635 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 952.000i | − | 0.329149i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2110.00 | + | 4220.00i | 0.718872 | + | 1.43774i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 252.000i | 0.0846145i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 896.000 | 0.296544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 416.000 | 0.135728 | 0.0678640 | − | 0.997695i | \(-0.478382\pi\) | ||||
0.0678640 | + | 0.997695i | \(0.478382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 192.000i | − | 0.0617635i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2760.00 | + | 1380.00i | −0.875490 | + | 0.437745i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 720.000i | − | 0.225239i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 456.000 | 0.140701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1728.00 | −0.525963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5748.00i | − | 1.72607i | −0.505141 | − | 0.863037i | \(-0.668559\pi\) | ||
0.505141 | − | 0.863037i | \(-0.331441\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 675.000 | − | 900.000i | 0.200000 | − | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1148.00i | − | 0.335663i | −0.985816 | − | 0.167831i | \(-0.946324\pi\) | ||
0.985816 | − | 0.167831i | \(-0.0536764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3234.00 | −0.933226 | −0.466613 | − | 0.884462i | \(-0.654526\pi\) | ||||
−0.466613 | + | 0.884462i | \(0.654526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −336.000 | −0.0957021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 228.000i | 0.0641063i | 0.999486 | + | 0.0320532i | \(0.0102046\pi\) | ||||
−0.999486 | + | 0.0320532i | \(0.989795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 600.000 | − | 300.000i | 0.166552 | − | 0.0832759i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2796.00i | 0.766328i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4760.00 | 1.28828 | 0.644140 | − | 0.764908i | \(-0.277216\pi\) | ||||
0.644140 | + | 0.764908i | \(0.277216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3230.00 | 0.863330 | 0.431665 | − | 0.902034i | \(-0.357926\pi\) | ||||
0.431665 | + | 0.902034i | \(0.357926\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1635.00 | + | 3270.00i | 0.426352 | + | 0.852705i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 512.000i | 0.131894i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3876.00 | −0.986472 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1708.00 | −0.429514 | −0.214757 | − | 0.976668i | \(-0.568896\pi\) | ||||
−0.214757 | + | 0.976668i | \(0.568896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 784.000i | − | 0.194821i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1620.00 | + | 3240.00i | 0.397837 | + | 0.795673i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6372.00i | 1.54659i | 0.634044 | + | 0.773297i | \(0.281394\pi\) | ||||
−0.634044 | + | 0.773297i | \(0.718606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −160.000 | −0.0383858 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2142.00 | −0.507994 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 3036.00i | − | 0.711817i | −0.934521 | − | 0.355908i | \(-0.884172\pi\) | ||
0.934521 | − | 0.355908i | \(-0.115828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2200.00 | − | 1100.00i | 0.509981 | − | 0.254990i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3438.00i | − | 0.788023i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 114.000 | 0.0258390 | 0.0129195 | − | 0.999917i | \(-0.495887\pi\) | ||||
0.0129195 | + | 0.999917i | \(0.495887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5236.00 | 1.17367 | 0.586835 | − | 0.809707i | \(-0.300374\pi\) | ||||
0.586835 | + | 0.809707i | \(0.300374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 192.000i | − | 0.0425655i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2100.00 | + | 2800.00i | −0.460490 | + | 0.613987i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5712.00i | − | 1.23899i | −0.785000 | − | 0.619496i | \(-0.787337\pi\) | ||
0.785000 | − | 0.619496i | \(-0.212663\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1620.00 | −0.347623 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3222.00 | 0.684016 | 0.342008 | − | 0.939697i | \(-0.388893\pi\) | ||||
0.342008 | + | 0.939697i | \(0.388893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4620.00i | − | 0.970426i | −0.874396 | − | 0.485213i | \(-0.838742\pi\) | ||
0.874396 | − | 0.485213i | \(-0.161258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 960.000 | − | 480.000i | 0.199528 | − | 0.0997640i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1688.00i | − | 0.347176i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6751.00 | −1.37411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2472.00 | 0.497977 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5404.00i | 1.07749i | 0.842468 | + | 0.538746i | \(0.181102\pi\) | ||||
−0.842468 | + | 0.538746i | \(0.818898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4020.00 | − | 8040.00i | −0.793402 | − | 1.58680i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 756.000i | 0.147702i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 448.000 | 0.0866505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1104.00 | 0.211407 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3870.00i | 0.733748i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1790.00 | − | 3580.00i | −0.336050 | − | 0.672099i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9700.00i | 1.80328i | 0.432483 | + | 0.901642i | \(0.357638\pi\) | ||||
−0.432483 | + | 0.901642i | \(0.642362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4812.00 | −0.885907 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9672.00 | −1.76350 | −0.881750 | − | 0.471716i | \(-0.843635\pi\) | ||||
−0.881750 | + | 0.471716i | \(0.843635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4048.00i | − | 0.731011i | −0.930809 | − | 0.365506i | \(-0.880896\pi\) | ||
0.930809 | − | 0.365506i | \(-0.119104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −360.000 | + | 180.000i | −0.0643927 | + | 0.0321964i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 84.0000i | − | 0.0148830i | −0.999972 | − | 0.00744150i | \(-0.997631\pi\) | ||
0.999972 | − | 0.00744150i | \(-0.00236872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6664.00 | 1.16963 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2676.00 | −0.465295 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3456.00i | 0.595347i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1600.00 | − | 1200.00i | −0.273083 | − | 0.204812i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2898.00i | 0.490091i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −240.000 | −0.0402177 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5416.00 | −0.899366 | −0.449683 | − | 0.893188i | \(-0.648463\pi\) | ||||
−0.449683 | + | 0.893188i | \(0.648463\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 360.000i | 0.0592429i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8840.00 | + | 4420.00i | −1.44173 | + | 0.720867i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8216.00i | − | 1.32805i | −0.747709 | − | 0.664027i | \(-0.768846\pi\) | ||
0.747709 | − | 0.664027i | \(-0.231154\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3372.00 | −0.540242 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5040.00 | 0.800385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2680.00i | − | 0.421885i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −420.000 | − | 840.000i | −0.0655421 | − | 0.131084i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3836.00i | − | 0.593450i | −0.954963 | − | 0.296725i | \(-0.904105\pi\) | ||
0.954963 | − | 0.296725i | \(-0.0958945\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2038.00 | 0.312583 | 0.156292 | − | 0.987711i | \(-0.450046\pi\) | ||||
0.156292 | + | 0.987711i | \(0.450046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −432.000 | −0.0656936 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5292.00i | − | 0.797917i | −0.916969 | − | 0.398959i | \(-0.869372\pi\) | ||
0.916969 | − | 0.398959i | \(-0.130628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 320.000 | + | 640.000i | 0.0478418 | + | 0.0956836i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 1296.00i | − | 0.192133i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3896.00 | −0.572766 | −0.286383 | − | 0.958115i | \(-0.592453\pi\) | ||||
−0.286383 | + | 0.958115i | \(0.592453\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5835.00 | −0.850707 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1641.00i | 0.237273i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1520.00 | + | 760.000i | −0.217974 | + | 0.108987i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7652.00i | − | 1.08837i | −0.838966 | − | 0.544184i | \(-0.816839\pi\) | ||
0.838966 | − | 0.544184i | \(-0.183161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3798.00 | −0.535816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −880.000 | −0.123146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1576.00i | 0.218773i | 0.993999 | + | 0.109386i | \(0.0348886\pi\) | ||||
−0.993999 | + | 0.109386i | \(0.965111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −750.000 | + | 4125.00i | −0.103280 | + | 0.568038i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3808.00i | 0.520217i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5416.00 | −0.734040 | −0.367020 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367020 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5652.00 | 0.760002 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8292.00i | 1.10627i | 0.833092 | + | 0.553135i | \(0.186569\pi\) | ||||
−0.833092 | + | 0.553135i | \(0.813431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1120.00 | − | 560.000i | 0.148261 | − | 0.0741305i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2484.00i | − | 0.326276i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9642.00 | 1.25673 | 0.628366 | − | 0.777918i | \(-0.283724\pi\) | ||||
0.628366 | + | 0.777918i | \(0.283724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3024.00 | 0.391126 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1764.00i | − | 0.226417i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4660.00 | − | 9320.00i | −0.593595 | − | 1.18719i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13032.0i | − | 1.64750i | −0.566954 | − | 0.823750i | \(-0.691878\pi\) | ||
0.566954 | − | 0.823750i | \(-0.308122\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −384.000 | −0.0481806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13358.0 | −1.66351 | −0.831754 | − | 0.555144i | \(-0.812663\pi\) | ||||
−0.831754 | + | 0.555144i | \(0.812663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2880.00i | 0.355988i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | + | 810.000i | 0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1120.00i | − | 0.136404i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6410.00 | −0.774949 | −0.387474 | − | 0.921880i | \(-0.626652\pi\) | ||||
−0.387474 | + | 0.921880i | \(0.626652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3180.00 | 0.381649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3216.00i | 0.383170i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12920.0 | − | 6460.00i | 1.52824 | − | 0.764118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8592.00i | 1.00900i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7644.00 | 0.891250 | 0.445625 | − | 0.895220i | \(-0.352981\pi\) | ||||
0.445625 | + | 0.895220i | \(0.352981\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14674.0 | 1.69873 | 0.849367 | − | 0.527803i | \(-0.176984\pi\) | ||||
0.849367 | + | 0.527803i | \(0.176984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 540.000i | 0.0620702i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10800.0 | − | 8100.00i | −1.23265 | − | 0.924489i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1432.00i | 0.162294i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1344.00 | 0.151256 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9704.00 | 1.08451 | 0.542257 | − | 0.840213i | \(-0.317570\pi\) | ||||
0.542257 | + | 0.840213i | \(0.317570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1296.00i | − | 0.143838i | −0.997410 | − | 0.0719189i | \(-0.977088\pi\) | ||
0.997410 | − | 0.0719189i | \(-0.0229123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7140.00 | − | 3570.00i | 0.786981 | − | 0.393491i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 896.000i | − | 0.0980812i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15684.0 | −1.70514 | −0.852570 | − | 0.522613i | \(-0.824957\pi\) | ||||
−0.852570 | + | 0.522613i | \(0.824957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2943.00 | −0.317784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5772.00i | − | 0.619043i | −0.950892 | − | 0.309521i | \(-0.899831\pi\) | ||
0.950892 | − | 0.309521i | \(-0.100169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5730.00 | + | 11460.0i | 0.610400 | + | 1.22080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1026.00i | 0.108564i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4782.00 | 0.502620 | 0.251310 | − | 0.967907i | \(-0.419139\pi\) | ||||
0.251310 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11816.0 | 1.23369 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4908.00i | 0.509046i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 320.000 | + | 640.000i | 0.0329711 | + | 0.0659421i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15000.0i | 1.53538i | 0.640819 | + | 0.767692i | \(0.278595\pi\) | ||||
−0.640819 | + | 0.767692i | \(0.721405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2916.00 | −0.296530 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3762.00 | −0.380073 | −0.190037 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190037 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5036.00i | 0.505492i | 0.967533 | + | 0.252746i | \(0.0813337\pi\) | ||||
−0.967533 | + | 0.252746i | \(0.918666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5400.00 | − | 2700.00i | 0.538535 | − | 0.269268i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2268.00i | − | 0.224733i | −0.993667 | − | 0.112367i | \(-0.964157\pi\) | ||
0.993667 | − | 0.112367i | \(-0.0358431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3536.00 | 0.348139 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6216.00 | −0.608106 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7728.00i | 0.751234i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2400.00 | + | 3200.00i | −0.231831 | + | 0.309108i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1980.00i | 0.190059i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16208.0 | 1.54606 | 0.773030 | − | 0.634370i | \(-0.218740\pi\) | ||||
0.773030 | + | 0.634370i | \(0.218740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 640.000 | 0.0606684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 336.000i | 0.0316533i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8240.00 | + | 4120.00i | −0.771462 | + | 0.385731i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11572.0i | − | 1.07675i | −0.842705 | − | 0.538375i | \(-0.819038\pi\) | ||
0.842705 | − | 0.538375i | \(-0.180962\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2316.00 | 0.214178 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5636.00 | −0.518023 | −0.259011 | − | 0.965874i | \(-0.583397\pi\) | ||||
−0.259011 | + | 0.965874i | \(0.583397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25704.0i | 2.34817i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1260.00 | − | 2520.00i | −0.114410 | − | 0.228819i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 256.000i | − | 0.0231050i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5560.00 | −0.498797 | −0.249399 | − | 0.968401i | \(-0.580233\pi\) | ||||
−0.249399 | + | 0.968401i | \(0.580233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3132.00 | 0.279296 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15172.0i | 1.34490i | 0.740141 | + | 0.672451i | \(0.234759\pi\) | ||||
−0.740141 | + | 0.672451i | \(0.765241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6450.00 | − | 12900.0i | −0.568359 | − | 1.13672i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5823.00i | − | 0.510076i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17342.0 | 1.51016 | 0.755079 | − | 0.655634i | \(-0.227598\pi\) | ||||
0.755079 | + | 0.655634i | \(0.227598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 608.000 | 0.0526347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 864.000i | 0.0743597i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16040.0 | − | 8020.00i | 1.37244 | − | 0.686220i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1680.00i | − | 0.142914i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13212.0 | −1.11742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4886.00 | −0.410863 | −0.205431 | − | 0.978672i | \(-0.565860\pi\) | ||||
−0.205431 | + | 0.978672i | \(0.565860\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18548.0i | 1.55076i | 0.631495 | + | 0.775380i | \(0.282442\pi\) | ||||
−0.631495 | + | 0.775380i | \(0.717558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 900.000 | − | 1200.00i | 0.0748176 | − | 0.0997567i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19440.0i | 1.60687i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11383.0 | 0.935563 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7236.00 | 0.591367 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6752.00i | 0.548708i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8920.00 | − | 4460.00i | 0.720832 | − | 0.360416i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10356.0i | − | 0.832206i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9156.00 | 0.731682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15770.0 | −1.25324 | −0.626622 | − | 0.779323i | \(-0.715563\pi\) | ||||
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1578.00i | − | 0.124712i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4830.00 | − | 9660.00i | −0.379623 | − | 0.759246i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7700.00i | 0.601880i | 0.953643 | + | 0.300940i | \(0.0973004\pi\) | ||||
−0.953643 | + | 0.300940i | \(0.902700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3222.00 | 0.250477 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7616.00 | 0.588843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3728.00i | 0.286674i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −600.000 | − | 1200.00i | −0.0458893 | − | 0.0917787i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 19236.0i | − | 1.46330i | −0.681683 | − | 0.731648i | \(-0.738752\pi\) | ||
0.681683 | − | 0.731648i | \(-0.261248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4416.00 | −0.334127 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9072.00 | 0.682745 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8388.00i | 0.627908i | 0.949438 | + | 0.313954i | \(0.101654\pi\) | ||||
−0.949438 | + | 0.313954i | \(0.898346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11240.0 | − | 5620.00i | 0.836939 | − | 0.418469i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 324.000i | − | 0.0239977i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16758.0 | 1.23468 | 0.617339 | − | 0.786697i | \(-0.288211\pi\) | ||||
0.617339 | + | 0.786697i | \(0.288211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8056.00 | −0.590426 | −0.295213 | − | 0.955432i | \(-0.595391\pi\) | ||||
−0.295213 | + | 0.955432i | \(0.595391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 216.000i | 0.0157479i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2800.00 | + | 2100.00i | 0.203075 | + | 0.152306i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5728.00i | 0.413275i | 0.978418 | + | 0.206638i | \(0.0662521\pi\) | ||||
−0.978418 | + | 0.206638i | \(0.933748\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −624.000 | −0.0447885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5168.00 | −0.369027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6160.00i | − | 0.437601i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1440.00 | − | 720.000i | 0.101772 | − | 0.0508860i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12172.0i | − | 0.855864i | −0.903811 | − | 0.427932i | \(-0.859242\pi\) | ||
0.903811 | − | 0.427932i | \(-0.140758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5760.00 | 0.402948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1116.00 | 0.0776753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10708.0i | − | 0.741526i | −0.928728 | − | 0.370763i | \(-0.879096\pi\) | ||
0.928728 | − | 0.370763i | \(-0.120904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2160.00 | + | 4320.00i | 0.148826 | + | 0.297652i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 13044.0i | − | 0.894230i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9416.00 | −0.642283 | −0.321141 | − | 0.947031i | \(-0.604066\pi\) | ||||
−0.321141 | + | 0.947031i | \(0.604066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9270.00 | 0.629170 | 0.314585 | − | 0.949229i | \(-0.398135\pi\) | ||||
0.314585 | + | 0.949229i | \(0.398135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7956.00i | − | 0.537302i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2735.00 | − | 5470.00i | −0.183791 | − | 0.367582i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7996.00i | 0.534675i | 0.963603 | + | 0.267337i | \(0.0861438\pi\) | ||||
−0.963603 | + | 0.267337i | \(0.913856\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2856.00 | −0.190034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 960.000 | 0.0635637 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 232.000i | 0.0152861i | 0.999971 | + | 0.00764306i | \(0.00243289\pi\) | ||||
−0.999971 | + | 0.00764306i | \(0.997567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12660.0 | − | 6330.00i | 0.830082 | − | 0.415041i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3740.00i | 0.244030i | 0.992528 | + | 0.122015i | \(0.0389357\pi\) | ||||
−0.992528 | + | 0.122015i | \(0.961064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26000.0 | −1.68825 | −0.844126 | − | 0.536145i | \(-0.819880\pi\) | ||||
−0.844126 | + | 0.536145i | \(0.819880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 756.000 | 0.0488522 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4584.00i | − | 0.294790i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4375.00 | − | 15000.0i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2688.00i | − | 0.171210i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4320.00 | 0.273847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11660.0 | −0.735622 | −0.367811 | − | 0.929901i | \(-0.619893\pi\) | ||||
−0.367811 | + | 0.929901i | \(0.619893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1248.00i | − | 0.0783626i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18840.0 | + | 9420.00i | −1.17739 | + | 0.588695i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5232.00i | 0.325431i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −576.000 | −0.0356592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7602.00 | −0.468426 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29268.0i | 1.79505i | 0.440963 | + | 0.897525i | \(0.354637\pi\) | ||||
−0.440963 | + | 0.897525i | \(0.645363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4140.00 | + | 8280.00i | 0.252732 | + | 0.505465i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17836.0i | − | 1.08378i | −0.840449 | − | 0.541890i | \(-0.817709\pi\) | ||
0.840449 | − | 0.541890i | \(-0.182291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22512.0 | −1.36159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2160.00 | −0.130042 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19188.0i | 1.14990i | 0.818189 | + | 0.574950i | \(0.194978\pi\) | ||||
−0.818189 | + | 0.574950i | \(0.805022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2940.00 | + | 5880.00i | 0.175382 | + | 0.350764i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1368.00i | − | 0.0812340i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13860.0 | 0.819285 | 0.409643 | − | 0.912246i | \(-0.365653\pi\) | ||||
0.409643 | + | 0.912246i | \(0.365653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16558.0 | −0.974329 | −0.487165 | − | 0.873310i | \(-0.661969\pi\) | ||||
−0.487165 | + | 0.873310i | \(0.661969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5184.00i | 0.303665i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1280.00 | − | 640.000i | 0.0746410 | − | 0.0373205i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6664.00i | − | 0.386853i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17244.0 | −0.996549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10024.0 | −0.576710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4640.00i | 0.265764i | 0.991132 | + | 0.132882i | \(0.0424231\pi\) | ||||
−0.991132 | + | 0.132882i | \(0.957577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2700.00 | − | 2025.00i | −0.153960 | − | 0.115470i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 34260.0i | − | 1.94493i | −0.233045 | − | 0.972466i | \(-0.574869\pi\) | ||
0.233045 | − | 0.972466i | \(-0.425131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3296.00 | 0.186287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3444.00 | −0.193795 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19420.0i | − | 1.08797i | −0.839094 | − | 0.543987i | \(-0.816914\pi\) | ||
0.839094 | − | 0.543987i | \(-0.183086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10600.0 | + | 5300.00i | −0.591248 | + | 0.295624i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9702.00i | 0.538798i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3520.00 | 0.194632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4608.00 | −0.253685 | −0.126843 | − | 0.991923i | \(-0.540484\pi\) | ||||
−0.126843 | + | 0.991923i | \(0.540484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1008.00i | 0.0552536i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14320.0 | − | 28640.0i | −0.781566 | − | 1.56313i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45576.0i | 2.47678i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 684.000 | 0.0370118 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2318.00 | −0.124893 | −0.0624463 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624463 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1280.00i | − | 0.0686716i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −900.000 | − | 1800.00i | −0.0480794 | − | 0.0961588i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5160.00i | 0.274486i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16834.0 | −0.891698 | −0.445849 | − | 0.895108i | \(-0.647098\pi\) | ||||
−0.445849 | + | 0.895108i | \(0.647098\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8388.00 | 0.442440 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5040.00i | − | 0.264726i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4480.00 | + | 2240.00i | −0.234325 | + | 0.117163i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 14280.0i | − | 0.743789i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7400.00 | −0.383830 | −0.191915 | − | 0.981412i | \(-0.561470\pi\) | ||||
−0.191915 | + | 0.981412i | \(0.561470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6416.00 | −0.331407 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 9690.00i | − | 0.498444i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17850.0 | + | 23800.0i | −0.914389 | + | 1.21919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20340.0i | − | 1.03765i | −0.854882 | − | 0.518823i | \(-0.826370\pi\) | ||
0.854882 | − | 0.518823i | \(-0.173630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29808.0 | −1.50819 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4896.00i | − | 0.246709i | −0.992363 | − | 0.123355i | \(-0.960635\pi\) | ||
0.992363 | − | 0.123355i | \(-0.0393653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9810.00 | − | 4905.00i | 0.492309 | − | 0.246155i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24752.0i | 1.23711i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26040.0 | 1.29621 | 0.648103 | − | 0.761552i | \(-0.275562\pi\) | ||||
0.648103 | + | 0.761552i | \(0.275562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1536.00 | 0.0761489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6780.00i | − | 0.334770i | −0.985892 | − | 0.167385i | \(-0.946468\pi\) | ||
0.985892 | − | 0.167385i | \(-0.0535323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1710.00 | − | 3420.00i | −0.0840934 | − | 0.168187i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11628.0i | 0.569540i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3568.00 | −0.174061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20692.0 | 1.00541 | 0.502704 | − | 0.864458i | \(-0.332338\pi\) | ||||
0.502704 | + | 0.864458i | \(0.332338\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5124.00i | 0.247980i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8180.00 | − | 16360.0i | −0.394306 | − | 0.788611i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10816.0i | − | 0.519305i | −0.965702 | − | 0.259653i | \(-0.916392\pi\) | ||
0.965702 | − | 0.259653i | \(-0.0836081\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2352.00 | −0.112480 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13978.0 | 0.665837 | 0.332919 | − | 0.942956i | \(-0.391967\pi\) | ||||
0.332919 | + | 0.942956i | \(0.391967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3864.00i | 0.183337i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9720.00 | − | 4860.00i | 0.459382 | − | 0.229691i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12864.0i | − | 0.605596i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2926.00 | −0.137210 | −0.0686048 | − | 0.997644i | \(-0.521855\pi\) | ||||
−0.0686048 | + | 0.997644i | \(0.521855\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19116.0 | 0.892926 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13916.0i | − | 0.647508i | −0.946141 | − | 0.323754i | \(-0.895055\pi\) | ||
0.946141 | − | 0.323754i | \(-0.104945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13500.0 | + | 18000.0i | −0.625722 | + | 0.834296i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 480.000i | 0.0221620i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13504.0 | 0.621092 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1792.00 | 0.0821035 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6426.00i | 0.293291i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20720.0 | − | 10360.0i | 0.942075 | − | 0.471037i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29996.0i | − | 1.35863i | −0.733847 | − | 0.679315i | \(-0.762277\pi\) | ||
0.733847 | − | 0.679315i | \(-0.237723\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9108.00 | −0.410968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4496.00 | −0.202098 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5728.00i | − | 0.256503i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3300.00 | − | 6600.00i | −0.147219 | − | 0.294438i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8940.00i | − | 0.397329i | −0.980068 | − | 0.198664i | \(-0.936340\pi\) | ||
0.980068 | − | 0.198664i | \(-0.0636604\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6480.00 | 0.286916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10314.0 | −0.454965 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4256.00i | 0.187037i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −560.000 | − | 1120.00i | −0.0245185 | − | 0.0490370i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 342.000i | − | 0.0149182i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10698.0 | 0.464922 | 0.232461 | − | 0.972606i | \(-0.425322\pi\) | ||||
0.232461 | + | 0.972606i | \(0.425322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6408.00 | 0.277454 | 0.138727 | − | 0.990331i | \(-0.455699\pi\) | ||||
0.138727 | + | 0.990331i | \(0.455699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15708.0i | − | 0.677618i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7720.00 | + | 3860.00i | −0.331803 | + | 0.165902i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8832.00i | 0.378204i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −576.000 | −0.0245752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23130.0 | 0.983243 | 0.491622 | − | 0.870809i | \(-0.336404\pi\) | ||||
0.491622 | + | 0.870809i | \(0.336404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11852.0i | 0.501986i | 0.967989 | + | 0.250993i | \(0.0807572\pi\) | ||||
−0.967989 | + | 0.250993i | \(0.919243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8400.00 | + | 6300.00i | 0.354485 | + | 0.265864i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32628.0i | 1.37193i | 0.727634 | + | 0.685965i | \(0.240620\pi\) | ||||
−0.727634 | + | 0.685965i | \(0.759380\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36694.0 | −1.53732 | −0.768658 | − | 0.639660i | \(-0.779075\pi\) | ||||
−0.768658 | + | 0.639660i | \(0.779075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17136.0 | −0.715332 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35316.0i | 1.46894i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10440.0 | + | 5220.00i | −0.432684 | + | 0.216342i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4860.00i | 0.200700i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1704.00 | −0.0701175 | −0.0350588 | − | 0.999385i | \(-0.511162\pi\) | ||||
−0.0350588 | + | 0.999385i | \(0.511162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32255.0 | 1.32252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 9666.00i | − | 0.394917i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9705.00 | + | 19410.0i | 0.395103 | + | 0.790206i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2188.00i | 0.0887610i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13860.0 | −0.560276 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1120.00 | −0.0451153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31880.0i | − | 1.27966i | −0.768516 | − | 0.639830i | \(-0.779005\pi\) | ||
0.768516 | − | 0.639830i | \(-0.220995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1440.00 | − | 2880.00i | −0.0575988 | − | 0.115198i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7972.00i | − | 0.317758i | −0.987298 | − | 0.158879i | \(-0.949212\pi\) | ||
0.987298 | − | 0.158879i | \(-0.0507879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6008.00 | −0.238638 | −0.119319 | − | 0.992856i | \(-0.538071\pi\) | ||||
−0.119319 | + | 0.992856i | \(0.538071\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5064.00 | −0.200442 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1716.00i | 0.0676863i | 0.999427 | + | 0.0338432i | \(0.0107747\pi\) | ||||
−0.999427 | + | 0.0338432i | \(0.989225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44040.0 | − | 22020.0i | 1.73110 | − | 0.865552i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20253.0i | 0.793342i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26096.0 | −1.01870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14144.0 | −0.550231 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7416.00i | − | 0.287507i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1000.00 | + | 5500.00i | −0.0386356 | + | 0.212496i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 9032.00i | − | 0.347764i | −0.984767 | − | 0.173882i | \(-0.944369\pi\) | ||
0.984767 | − | 0.173882i | \(-0.0556311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16212.0 | 0.622090 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27838.0 | 1.06457 | 0.532285 | − | 0.846565i | \(-0.321334\pi\) | ||||
0.532285 | + | 0.846565i | \(0.321334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4316.00i | − | 0.164490i | −0.996612 | − | 0.0822452i | \(-0.973791\pi\) | ||
0.996612 | − | 0.0822452i | \(-0.0262091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24120.0 | + | 12060.0i | −0.916141 | + | 0.458071i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43524.0i | 1.64757i | 0.566904 | + | 0.823784i | \(0.308141\pi\) | ||||
−0.566904 | + | 0.823784i | \(0.691859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7536.00 | 0.284307 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2268.00 | 0.0852759 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1920.00i | − | 0.0719489i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17260.0 | + | 34520.0i | 0.644624 | + | 1.28925i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1344.00i | − | 0.0500277i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42840.0 | 1.58931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23760.0 | 0.878535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3312.00i | − | 0.122056i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2630.00 | + | 5260.00i | 0.0966013 | + | 0.193203i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 10556.0i | − | 0.386446i | −0.981155 | − | 0.193223i | \(-0.938106\pi\) | ||
0.981155 | − | 0.193223i | \(-0.0618940\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11610.0 | 0.423630 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47472.0 | 1.72647 | 0.863237 | − | 0.504799i | \(-0.168433\pi\) | ||||
0.863237 | + | 0.504799i | \(0.168433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 36176.0i | − | 1.31134i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10740.0 | + | 5370.00i | −0.388037 | + | 0.194018i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2352.00i | − | 0.0847000i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11964.0 | 0.429441 | 0.214720 | − | 0.976676i | \(-0.431116\pi\) | ||||
0.214720 | + | 0.976676i | \(0.431116\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29100.0 | 1.04113 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1024.00i | 0.0365172i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4000.00 | + | 3000.00i | 0.142183 | + | 0.106637i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14436.0i | 0.511478i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15214.0 | 0.537304 | 0.268652 | − | 0.963237i | \(-0.413422\pi\) | ||||
0.268652 | + | 0.963237i | \(0.413422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10464.0 | 0.368361 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29016.0i | 1.01816i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30240.0 | + | 15120.0i | −1.05770 | + | 0.528852i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39712.0i | 1.38456i | 0.721628 | + | 0.692281i | \(0.243394\pi\) | ||||
−0.721628 | + | 0.692281i | \(0.756606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12144.0 | −0.422049 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36034.0 | −1.24833 | −0.624163 | − | 0.781294i | \(-0.714560\pi\) | ||||
−0.624163 | + | 0.781294i | \(0.714560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 11816.0i | − | 0.408040i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 540.000 | + | 1080.00i | 0.0185886 | + | 0.0371771i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2532.00i | 0.0868838i | 0.999056 | + | 0.0434419i | \(0.0138323\pi\) | ||||
−0.999056 | + | 0.0434419i | \(0.986168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2432.00 | −0.0831887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −252.000 | −0.00859270 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 55284.0i | − | 1.87914i | −0.342351 | − | 0.939572i | \(-0.611223\pi\) | ||
0.342351 | − | 0.939572i | \(-0.388777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −360.000 | − | 720.000i | −0.0121982 | − | 0.0243965i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 19992.0i | − | 0.675287i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4240.00 | 0.142770 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2609.00 | 0.0875768 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8028.00i | 0.268638i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2080.00 | − | 1040.00i | 0.0693861 | − | 0.0346930i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4372.00i | − | 0.145392i | −0.997354 | − | 0.0726960i | \(-0.976840\pi\) | ||
0.997354 | − | 0.0726960i | \(-0.0231603\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10368.0 | 0.343724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24300.0 | −0.803114 | −0.401557 | − | 0.915834i | \(-0.631531\pi\) | ||||
−0.401557 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11456.0i | 0.377454i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3600.00 | + | 4800.00i | −0.118248 | + | 0.157665i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46204.0i | 1.51300i | 0.653996 | + | 0.756498i | \(0.273091\pi\) | ||||
−0.653996 | + | 0.756498i | \(0.726909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32088.0 | 1.04754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8694.00 | 0.282954 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 25468.0i | − | 0.826351i | −0.910651 | − | 0.413176i | \(-0.864420\pi\) | ||
0.910651 | − | 0.413176i | \(-0.135580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3720.00 | + | 1860.00i | −0.120334 | + | 0.0601670i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 720.000i | 0.0232197i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7728.00 | 0.248469 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11668.0 | −0.374012 | −0.187006 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187006 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16248.0i | 0.519249i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21740.0 | + | 43480.0i | 0.692668 | + | 1.38534i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 7224.00i | − | 0.229475i | −0.993396 | − | 0.114737i | \(-0.963397\pi\) | ||
0.993396 | − | 0.114737i | \(-0.0366027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1080.00 | 0.0342039 |
(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 | 240.4.f.e.49.1 | 2 | ||
3.2 | odd | 2 | 720.4.f.b.289.1 | 2 | |||
4.3 | odd | 2 | 120.4.f.c.49.2 | yes | 2 | ||
5.2 | odd | 4 | 1200.4.a.l.1.1 | 1 | |||
5.3 | odd | 4 | 1200.4.a.z.1.1 | 1 | |||
5.4 | even | 2 | inner | 240.4.f.e.49.2 | 2 | ||
8.3 | odd | 2 | 960.4.f.b.769.1 | 2 | |||
8.5 | even | 2 | 960.4.f.a.769.2 | 2 | |||
12.11 | even | 2 | 360.4.f.a.289.1 | 2 | |||
15.14 | odd | 2 | 720.4.f.b.289.2 | 2 | |||
20.3 | even | 4 | 600.4.a.f.1.1 | 1 | |||
20.7 | even | 4 | 600.4.a.k.1.1 | 1 | |||
20.19 | odd | 2 | 120.4.f.c.49.1 | ✓ | 2 | ||
40.19 | odd | 2 | 960.4.f.b.769.2 | 2 | |||
40.29 | even | 2 | 960.4.f.a.769.1 | 2 | |||
60.23 | odd | 4 | 1800.4.a.u.1.1 | 1 | |||
60.47 | odd | 4 | 1800.4.a.o.1.1 | 1 | |||
60.59 | even | 2 | 360.4.f.a.289.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.f.c.49.1 | ✓ | 2 | 20.19 | odd | 2 | ||
120.4.f.c.49.2 | yes | 2 | 4.3 | odd | 2 | ||
240.4.f.e.49.1 | 2 | 1.1 | even | 1 | trivial | ||
240.4.f.e.49.2 | 2 | 5.4 | even | 2 | inner | ||
360.4.f.a.289.1 | 2 | 12.11 | even | 2 | |||
360.4.f.a.289.2 | 2 | 60.59 | even | 2 | |||
600.4.a.f.1.1 | 1 | 20.3 | even | 4 | |||
600.4.a.k.1.1 | 1 | 20.7 | even | 4 | |||
720.4.f.b.289.1 | 2 | 3.2 | odd | 2 | |||
720.4.f.b.289.2 | 2 | 15.14 | odd | 2 | |||
960.4.f.a.769.1 | 2 | 40.29 | even | 2 | |||
960.4.f.a.769.2 | 2 | 8.5 | even | 2 | |||
960.4.f.b.769.1 | 2 | 8.3 | odd | 2 | |||
960.4.f.b.769.2 | 2 | 40.19 | odd | 2 | |||
1200.4.a.l.1.1 | 1 | 5.2 | odd | 4 | |||
1200.4.a.z.1.1 | 1 | 5.3 | odd | 4 | |||
1800.4.a.o.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.a.u.1.1 | 1 | 60.23 | odd | 4 |