Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,4,Mod(289,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.7369626429\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.361 |
Dual form | 504.4.s.e.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.50000 | + | 6.06218i | 0.313050 | + | 0.542218i | 0.979021 | − | 0.203760i | \(-0.0653161\pi\) |
−0.665971 | + | 0.745977i | \(0.731983\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.5000 | + | 6.06218i | −0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.50000 | − | 6.06218i | 0.0959354 | − | 0.166165i | −0.814063 | − | 0.580776i | \(-0.802749\pi\) |
0.909999 | + | 0.414611i | \(0.136082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −52.0000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.0000 | − | 62.3538i | 0.513605 | − | 0.889590i | −0.486271 | − | 0.873808i | \(-0.661643\pi\) |
0.999875 | − | 0.0157814i | \(-0.00502359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0000 | − | 17.3205i | −0.120745 | − | 0.209137i | 0.799317 | − | 0.600910i | \(-0.205195\pi\) |
−0.920062 | + | 0.391773i | \(0.871862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.0000 | − | 41.5692i | −0.217580 | − | 0.376860i | 0.736487 | − | 0.676451i | \(-0.236483\pi\) |
−0.954068 | + | 0.299591i | \(0.903150\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.0000 | − | 65.8179i | 0.304000 | − | 0.526543i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 243.000 | 1.55600 | 0.777999 | − | 0.628265i | \(-0.216235\pi\) | ||||
0.777999 | + | 0.628265i | \(0.216235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −47.5000 | + | 82.2724i | −0.275202 | + | 0.476663i | −0.970186 | − | 0.242362i | \(-0.922078\pi\) |
0.694984 | + | 0.719025i | \(0.255411\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −98.0000 | − | 84.8705i | −0.473286 | − | 0.409878i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −176.000 | − | 304.841i | −0.782006 | − | 1.35447i | −0.930771 | − | 0.365602i | \(-0.880863\pi\) |
0.148765 | − | 0.988873i | \(-0.452470\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 296.000 | 1.12750 | 0.563749 | − | 0.825946i | \(-0.309358\pi\) | ||||
0.563749 | + | 0.825946i | \(0.309358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 158.000 | 0.560344 | 0.280172 | − | 0.959950i | \(-0.409609\pi\) | ||||
0.280172 | + | 0.959950i | \(0.409609\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −71.0000 | − | 122.976i | −0.220349 | − | 0.381656i | 0.734565 | − | 0.678539i | \(-0.237386\pi\) |
−0.954914 | + | 0.296882i | \(0.904053\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 269.500 | − | 212.176i | 0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −187.500 | + | 324.760i | −0.485945 | + | 0.841682i | −0.999870 | − | 0.0161535i | \(-0.994858\pi\) |
0.513924 | + | 0.857836i | \(0.328191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49.0000 | 0.120130 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 139.500 | − | 241.621i | 0.307820 | − | 0.533159i | −0.670066 | − | 0.742302i | \(-0.733734\pi\) |
0.977885 | + | 0.209143i | \(0.0670674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −123.000 | − | 213.042i | −0.258173 | − | 0.447168i | 0.707580 | − | 0.706634i | \(-0.249787\pi\) |
−0.965752 | + | 0.259465i | \(0.916454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −182.000 | − | 315.233i | −0.347297 | − | 0.601536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 365.000 | − | 632.199i | 0.665550 | − | 1.15277i | −0.313586 | − | 0.949560i | \(-0.601530\pi\) |
0.979136 | − | 0.203207i | \(-0.0651363\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −338.000 | −0.564975 | −0.282487 | − | 0.959271i | \(-0.591160\pi\) | ||||
−0.282487 | + | 0.959271i | \(0.591160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 271.000 | − | 469.386i | 0.434495 | − | 0.752568i | −0.562759 | − | 0.826621i | \(-0.690260\pi\) |
0.997254 | + | 0.0740532i | \(0.0235935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.5000 | + | 127.306i | −0.0362602 | + | 0.188413i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 152.500 | + | 264.138i | 0.217185 | + | 0.376175i | 0.953946 | − | 0.299978i | \(-0.0969793\pi\) |
−0.736761 | + | 0.676153i | \(0.763646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1123.00 | −1.48512 | −0.742562 | − | 0.669778i | \(-0.766389\pi\) | ||||
−0.742562 | + | 0.669778i | \(0.766389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 504.000 | 0.643135 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −213.000 | − | 368.927i | −0.253685 | − | 0.439395i | 0.710853 | − | 0.703341i | \(-0.248309\pi\) |
−0.964537 | + | 0.263946i | \(0.914976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 910.000 | − | 315.233i | 1.04828 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 70.0000 | − | 121.244i | 0.0755984 | − | 0.130940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −369.000 | −0.386250 | −0.193125 | − | 0.981174i | \(-0.561862\pi\) | ||||
−0.193125 | + | 0.981174i | \(0.561862\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 635.000 | − | 1099.85i | 0.625593 | − | 1.08356i | −0.362833 | − | 0.931854i | \(-0.618191\pi\) |
0.988426 | − | 0.151704i | \(-0.0484761\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −916.000 | − | 1586.56i | −0.876273 | − | 1.51775i | −0.855400 | − | 0.517968i | \(-0.826689\pi\) |
−0.0208734 | − | 0.999782i | \(-0.506645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −499.500 | − | 865.159i | −0.451294 | − | 0.781665i | 0.547172 | − | 0.837020i | \(-0.315704\pi\) |
−0.998467 | + | 0.0553553i | \(0.982371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 833.000 | − | 1442.80i | 0.731990 | − | 1.26784i | −0.224041 | − | 0.974580i | \(-0.571925\pi\) |
0.956031 | − | 0.293264i | \(-0.0947417\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1832.00 | 1.52513 | 0.762567 | − | 0.646910i | \(-0.223939\pi\) | ||||
0.762567 | + | 0.646910i | \(0.223939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 168.000 | − | 290.985i | 0.136227 | − | 0.235952i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −252.000 | + | 1309.43i | −0.194124 | + | 1.00870i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 641.000 | + | 1110.24i | 0.481593 | + | 0.834143i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1407.00 | 1.00677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1931.00 | −1.34920 | −0.674601 | − | 0.738183i | \(-0.735684\pi\) | ||||
−0.674601 | + | 0.738183i | \(0.735684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 489.500 | + | 847.839i | 0.326472 | + | 0.565466i | 0.981809 | − | 0.189871i | \(-0.0608068\pi\) |
−0.655337 | + | 0.755336i | \(0.727473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 280.000 | + | 242.487i | 0.182549 | + | 0.158092i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −243.000 | + | 420.888i | −0.151539 | + | 0.262474i | −0.931794 | − | 0.362989i | \(-0.881756\pi\) |
0.780254 | + | 0.625463i | \(0.215090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2630.00 | −1.60485 | −0.802423 | − | 0.596755i | \(-0.796456\pi\) | ||||
−0.802423 | + | 0.596755i | \(0.796456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −182.000 | + | 315.233i | −0.106431 | + | 0.184344i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 850.500 | + | 1473.11i | 0.487105 | + | 0.843690i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −939.000 | − | 1626.40i | −0.516281 | − | 0.894225i | −0.999821 | − | 0.0189029i | \(-0.993983\pi\) |
0.483540 | − | 0.875322i | \(-0.339351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1051.50 | + | 1821.25i | −0.566688 | + | 0.981532i | 0.430203 | + | 0.902732i | \(0.358442\pi\) |
−0.996890 | + | 0.0787997i | \(0.974891\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −665.000 | −0.344607 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −702.000 | + | 1215.90i | −0.356852 | + | 0.618085i | −0.987433 | − | 0.158038i | \(-0.949483\pi\) |
0.630581 | + | 0.776123i | \(0.282816\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 672.000 | + | 581.969i | 0.328950 | + | 0.284879i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 768.000 | + | 1330.22i | 0.369045 | + | 0.639205i | 0.989417 | − | 0.145103i | \(-0.0463513\pi\) |
−0.620371 | + | 0.784308i | \(0.713018\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3634.00 | 1.68388 | 0.841938 | − | 0.539574i | \(-0.181415\pi\) | ||||
0.841938 | + | 0.539574i | \(0.181415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 507.000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 429.000 | + | 743.050i | 0.188533 | + | 0.326549i | 0.944761 | − | 0.327759i | \(-0.106293\pi\) |
−0.756228 | + | 0.654308i | \(0.772960\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −266.000 | + | 1382.18i | −0.114901 | + | 0.597044i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1210.00 | + | 2095.78i | −0.505249 | + | 0.875118i | 0.494732 | + | 0.869046i | \(0.335266\pi\) |
−0.999982 | + | 0.00607215i | \(0.998067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2672.00 | −1.09728 | −0.548641 | − | 0.836058i | \(-0.684855\pi\) | ||||
−0.548641 | + | 0.836058i | \(0.684855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1232.00 | − | 2133.89i | 0.489613 | − | 0.848035i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −252.000 | − | 436.477i | −0.0985458 | − | 0.170686i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −856.000 | − | 1482.64i | −0.324283 | − | 0.561674i | 0.657084 | − | 0.753817i | \(-0.271790\pi\) |
−0.981367 | + | 0.192143i | \(0.938456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1697.50 | − | 2940.16i | 0.633102 | − | 1.09657i | −0.353812 | − | 0.935317i | \(-0.615115\pi\) |
0.986914 | − | 0.161248i | \(-0.0515521\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −510.000 | −0.184447 | −0.0922233 | − | 0.995738i | \(-0.529397\pi\) | ||||
−0.0922233 | + | 0.995738i | \(0.529397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −138.000 | + | 239.023i | −0.0491586 | + | 0.0851452i | −0.889558 | − | 0.456823i | \(-0.848987\pi\) |
0.840399 | + | 0.541968i | \(0.182321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4252.50 | + | 1473.11i | −1.47028 | + | 0.509320i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1036.00 | + | 1794.40i | 0.352963 | + | 0.611350i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −140.000 | −0.0463349 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3198.00 | 1.04341 | 0.521705 | − | 0.853126i | \(-0.325296\pi\) | ||||
0.521705 | + | 0.853126i | \(0.325296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 553.000 | + | 957.824i | 0.175415 | + | 0.303828i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 332.500 | − | 1727.72i | 0.104016 | − | 0.540485i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1872.00 | + | 3242.40i | −0.569793 | + | 0.986911i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5091.00 | −1.52878 | −0.764391 | − | 0.644752i | \(-0.776960\pi\) | ||||
−0.764391 | + | 0.644752i | \(0.776960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1947.50 | + | 3373.17i | −0.569428 | + | 0.986278i | 0.427195 | + | 0.904160i | \(0.359502\pi\) |
−0.996623 | + | 0.0821183i | \(0.973831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3214.00 | + | 5566.81i | 0.927455 | + | 1.60640i | 0.787565 | + | 0.616231i | \(0.211341\pi\) |
0.139889 | + | 0.990167i | \(0.455325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1912.00 | − | 3311.68i | −0.537593 | − | 0.931139i | −0.999033 | − | 0.0439676i | \(-0.986000\pi\) |
0.461439 | − | 0.887172i | \(-0.347333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 497.000 | − | 860.829i | 0.137960 | − | 0.238955i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −568.000 | −0.153727 | −0.0768637 | − | 0.997042i | \(-0.524491\pi\) | ||||
−0.0768637 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1767.50 | + | 3061.40i | −0.472426 | + | 0.818266i | −0.999502 | − | 0.0315522i | \(-0.989955\pi\) |
0.527076 | + | 0.849818i | \(0.323288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2229.50 | + | 891.140i | 0.581378 | + | 0.232379i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 520.000 | + | 900.666i | 0.133955 | + | 0.232016i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4335.00 | −1.09013 | −0.545065 | − | 0.838394i | \(-0.683495\pi\) | ||||
−0.545065 | + | 0.838394i | \(0.683495\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −336.000 | −0.0834946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1787.00 | + | 3095.17i | 0.433735 | + | 0.751252i | 0.997191 | − | 0.0748943i | \(-0.0238619\pi\) |
−0.563456 | + | 0.826146i | \(0.690529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4928.00 | + | 4267.77i | 1.18228 | + | 1.02389i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2733.00 | − | 4733.69i | 0.640776 | − | 1.10986i | −0.344484 | − | 0.938792i | \(-0.611946\pi\) |
0.985260 | − | 0.171064i | \(-0.0547205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2625.00 | −0.608500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2907.50 | + | 5035.94i | −0.659009 | + | 1.14144i | 0.321864 | + | 0.946786i | \(0.395691\pi\) |
−0.980873 | + | 0.194651i | \(0.937643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1618.50 | + | 2803.32i | 0.362793 | + | 0.628376i | 0.988419 | − | 0.151747i | \(-0.0484899\pi\) |
−0.625626 | + | 0.780123i | \(0.715157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −266.000 | − | 460.726i | −0.0583287 | − | 0.101028i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1588.00 | − | 2750.50i | 0.344454 | − | 0.596611i | −0.640801 | − | 0.767707i | \(-0.721397\pi\) |
0.985254 | + | 0.171096i | \(0.0547308\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3282.00 | 0.696753 | 0.348377 | − | 0.937355i | \(-0.386733\pi\) | ||||
0.348377 | + | 0.937355i | \(0.386733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1091.00 | + | 1889.67i | −0.229163 | + | 0.396923i | −0.957560 | − | 0.288233i | \(-0.906932\pi\) |
0.728397 | + | 0.685155i | \(0.240266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5180.00 | + | 1794.40i | −1.06539 | + | 0.369060i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −135.500 | − | 234.693i | −0.0275799 | − | 0.0477698i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3021.00 | −0.602351 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1953.00 | 0.385451 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1248.00 | + | 2161.60i | 0.241384 | + | 0.418089i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2765.00 | + | 957.824i | −0.529475 | + | 0.183415i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 861.000 | − | 1491.30i | 0.161642 | − | 0.279972i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1304.00 | −0.242421 | −0.121210 | − | 0.992627i | \(-0.538678\pi\) | ||||
−0.121210 | + | 0.992627i | \(0.538678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3104.00 | − | 5376.29i | 0.565954 | − | 0.980261i | −0.431006 | − | 0.902349i | \(-0.641841\pi\) |
0.996960 | − | 0.0779121i | \(-0.0248254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1668.50 | − | 2889.93i | −0.301307 | − | 0.521880i | 0.675125 | − | 0.737703i | \(-0.264090\pi\) |
−0.976432 | + | 0.215824i | \(0.930756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4318.50 | + | 7479.86i | 0.765146 | + | 1.32527i | 0.940170 | + | 0.340707i | \(0.110666\pi\) |
−0.175024 | + | 0.984564i | \(0.556000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 850.500 | − | 1473.11i | 0.149275 | − | 0.258553i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1440.00 | −0.248061 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1976.00 | + | 3422.53i | −0.337258 | + | 0.584148i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1988.00 | + | 1721.66i | 0.333137 | + | 0.288505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −970.000 | − | 1680.09i | −0.161076 | − | 0.278991i | 0.774179 | − | 0.632967i | \(-0.218163\pi\) |
−0.935255 | + | 0.353975i | \(0.884830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5110.00 | 0.833400 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5527.00 | −0.893397 | −0.446699 | − | 0.894684i | \(-0.647400\pi\) | ||||
−0.446699 | + | 0.894684i | \(0.647400\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 332.500 | + | 575.907i | 0.0528032 | + | 0.0914578i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3430.00 | + | 5346.84i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4782.00 | − | 8282.67i | 0.739802 | − | 1.28137i | −0.212783 | − | 0.977100i | \(-0.568253\pi\) |
0.952584 | − | 0.304275i | \(-0.0984141\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −918.000 | −0.140801 | −0.0704003 | − | 0.997519i | \(-0.522428\pi\) | ||||
−0.0704003 | + | 0.997519i | \(0.522428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5740.00 | − | 9941.97i | 0.865466 | − | 1.49903i | −0.00111843 | − | 0.999999i | \(-0.500356\pi\) |
0.866584 | − | 0.499031i | \(-0.166311\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1183.00 | − | 2049.02i | −0.176865 | − | 0.306339i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1827.00 | + | 3164.46i | 0.268594 | + | 0.465219i | 0.968499 | − | 0.249017i | \(-0.0801076\pi\) |
−0.699905 | + | 0.714236i | \(0.746774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3229.50 | − | 5593.66i | 0.470841 | − | 0.815521i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3794.00 | 0.544074 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5033.50 | − | 8718.28i | 0.715931 | − | 1.24003i | −0.246669 | − | 0.969100i | \(-0.579336\pi\) |
0.962599 | − | 0.270928i | \(-0.0873307\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1312.50 | − | 6819.95i | 0.183670 | − | 0.954378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4400.00 | − | 7621.02i | −0.610786 | − | 1.05791i | −0.991108 | − | 0.133059i | \(-0.957520\pi\) |
0.380322 | − | 0.924854i | \(-0.375813\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12636.0 | −1.72623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1136.00 | 0.153964 | 0.0769821 | − | 0.997032i | \(-0.475472\pi\) | ||||
0.0769821 | + | 0.997032i | \(0.475472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2145.00 | + | 3715.25i | 0.286173 | + | 0.495667i | 0.972893 | − | 0.231256i | \(-0.0742834\pi\) |
−0.686720 | + | 0.726922i | \(0.740950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −857.500 | + | 297.047i | −0.113512 | + | 0.0393218i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −431.000 | + | 746.514i | −0.0561763 | + | 0.0973001i | −0.892746 | − | 0.450560i | \(-0.851224\pi\) |
0.836570 | + | 0.547861i | \(0.184558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3456.00 | −0.447001 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1067.50 | + | 1848.96i | −0.135979 | + | 0.235523i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4570.00 | + | 7915.47i | 0.577737 | + | 1.00067i | 0.995738 | + | 0.0922238i | \(0.0293975\pi\) |
−0.418001 | + | 0.908447i | \(0.637269\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7116.00 | − | 12325.3i | −0.886175 | − | 1.53490i | −0.844361 | − | 0.535774i | \(-0.820020\pi\) |
−0.0418135 | − | 0.999125i | \(-0.513314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2470.00 | − | 4278.17i | 0.305309 | − | 0.528810i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2464.00 | −0.300088 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5000.50 | − | 8661.12i | 0.604545 | − | 1.04710i | −0.387578 | − | 0.921837i | \(-0.626688\pi\) |
0.992123 | − | 0.125266i | \(-0.0399783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −976.500 | + | 5074.04i | −0.116345 | + | 0.604546i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3930.50 | − | 6807.83i | −0.464917 | − | 0.805260i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10256.0 | 1.19580 | 0.597898 | − | 0.801572i | \(-0.296003\pi\) | ||||
0.597898 | + | 0.801572i | \(0.296003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4502.00 | −0.521174 | −0.260587 | − | 0.965450i | \(-0.583916\pi\) | ||||
−0.260587 | + | 0.965450i | \(0.583916\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2736.00 | − | 4738.89i | −0.312272 | − | 0.540871i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3444.00 | + | 2982.59i | 0.390320 | + | 0.338027i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6178.00 | − | 10700.6i | 0.690450 | − | 1.19589i | −0.281241 | − | 0.959637i | \(-0.590746\pi\) |
0.971691 | − | 0.236257i | \(-0.0759206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 862.000 | 0.0956699 | 0.0478350 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478350 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −480.000 | + | 831.384i | −0.0525435 | + | 0.0910080i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 682.500 | + | 1182.12i | 0.0742003 | + | 0.128519i | 0.900738 | − | 0.434362i | \(-0.143026\pi\) |
−0.826538 | + | 0.562881i | \(0.809693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4465.50 | + | 7734.47i | 0.478922 | + | 0.829517i | 0.999708 | − | 0.0241705i | \(-0.00769445\pi\) |
−0.520786 | + | 0.853687i | \(0.674361\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1491.00 | − | 2582.49i | 0.158832 | − | 0.275105i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11228.0 | −1.18014 | −0.590069 | − | 0.807353i | \(-0.700900\pi\) | ||||
−0.590069 | + | 0.807353i | \(0.700900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1036.00 | − | 1794.40i | 0.108167 | − | 0.187351i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5096.00 | + | 4413.27i | 0.525064 | + | 0.454719i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6075.50 | − | 10523.1i | −0.621882 | − | 1.07713i | −0.989135 | − | 0.147010i | \(-0.953035\pi\) |
0.367253 | − | 0.930121i | \(-0.380298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18534.0 | −1.87248 | −0.936241 | − | 0.351358i | \(-0.885720\pi\) | ||||
−0.936241 | + | 0.351358i | \(0.885720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17096.0 | 1.71602 | 0.858011 | − | 0.513631i | \(-0.171700\pi\) | ||||
0.858011 | + | 0.513631i | \(0.171700\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1070.00 | − | 1853.29i | −0.106025 | − | 0.183641i | 0.808131 | − | 0.589002i | \(-0.200479\pi\) |
−0.914157 | + | 0.405361i | \(0.867146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2555.00 | + | 13276.2i | −0.251554 | + | 1.30711i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 553.000 | − | 957.824i | 0.0537568 | − | 0.0931095i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1520.00 | −0.146826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6633.00 | + | 11488.7i | −0.632713 | + | 1.09589i | 0.354282 | + | 0.935139i | \(0.384725\pi\) |
−0.986995 | + | 0.160752i | \(0.948608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9152.00 | + | 15851.7i | 0.867558 | + | 1.50265i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1291.50 | − | 2236.94i | −0.120915 | − | 0.209432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9591.50 | − | 16613.0i | 0.892469 | − | 1.54580i | 0.0555627 | − | 0.998455i | \(-0.482305\pi\) |
0.836906 | − | 0.547346i | \(-0.184362\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21693.0 | 1.99387 | 0.996936 | − | 0.0782185i | \(-0.0249232\pi\) | ||||
0.996936 | + | 0.0782185i | \(0.0249232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8748.00 | − | 15152.0i | 0.799169 | − | 1.38420i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5915.00 | − | 2049.02i | 0.533851 | − | 0.184931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9829.00 | − | 17024.3i | −0.881776 | − | 1.52728i | −0.849364 | − | 0.527807i | \(-0.823014\pi\) |
−0.0324122 | − | 0.999475i | \(-0.510319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19436.0 | −1.72288 | −0.861440 | − | 0.507860i | \(-0.830437\pi\) | ||||
−0.861440 | + | 0.507860i | \(0.830437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8890.00 | 0.783366 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1544.50 | + | 2675.15i | 0.134497 | + | 0.232955i | 0.925405 | − | 0.378980i | \(-0.123725\pi\) |
−0.790908 | + | 0.611934i | \(0.790392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1897.00 | + | 9857.10i | −0.164224 | + | 0.853332i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6412.00 | − | 11105.9i | 0.548634 | − | 0.950262i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −994.000 | −0.0845572 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 975.000 | − | 1688.75i | 0.0819876 | − | 0.142007i | −0.822116 | − | 0.569320i | \(-0.807207\pi\) |
0.904104 | + | 0.427313i | \(0.140540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6566.00 | − | 11372.6i | −0.548970 | − | 0.950843i | −0.998345 | − | 0.0575005i | \(-0.981687\pi\) |
0.449376 | − | 0.893343i | \(-0.351646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3420.00 | + | 5923.61i | 0.282690 | + | 0.489633i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4931.50 | − | 8541.61i | 0.405318 | − | 0.702031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15392.0 | −1.25085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3496.50 | − | 6056.12i | 0.282555 | − | 0.489399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −343.000 | − | 2376.37i | −0.0274101 | − | 0.189903i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1465.00 | − | 2537.45i | −0.116424 | − | 0.201652i | 0.801924 | − | 0.597426i | \(-0.203810\pi\) |
−0.918348 | + | 0.395774i | \(0.870476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11662.0 | 0.916597 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19824.0 | 1.54957 | 0.774783 | − | 0.632227i | \(-0.217859\pi\) | ||||
0.774783 | + | 0.632227i | \(0.217859\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2430.00 | − | 4208.88i | −0.187879 | − | 0.325416i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4270.00 | − | 3697.93i | −0.328352 | − | 0.284362i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9584.50 | + | 16600.8i | −0.729099 | + | 1.26284i | 0.228165 | + | 0.973622i | \(0.426727\pi\) |
−0.957264 | + | 0.289215i | \(0.906606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8216.00 | −0.621645 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3633.50 | − | 6293.41i | 0.271996 | − | 0.471111i | −0.697377 | − | 0.716705i | \(-0.745650\pi\) |
0.969373 | + | 0.245594i | \(0.0789829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6412.00 | + | 11105.9i | 0.477442 | + | 0.826954i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2446.00 | − | 4236.60i | −0.180214 | − | 0.312139i | 0.761739 | − | 0.647883i | \(-0.224346\pi\) |
−0.941953 | + | 0.335744i | \(0.891012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11063.0 | + | 19161.7i | −0.810809 | + | 1.40436i | 0.101489 | + | 0.994837i | \(0.467639\pi\) |
−0.912298 | + | 0.409526i | \(0.865694\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3648.00 | −0.264578 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 548.500 | − | 950.030i | 0.0395743 | − | 0.0685446i | −0.845560 | − | 0.533881i | \(-0.820733\pi\) |
0.885134 | + | 0.465336i | \(0.154066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19652.5 | − | 6807.83i | 1.40331 | − | 0.486121i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1312.50 | + | 2273.32i | 0.0932388 | + | 0.161494i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9969.00 | −0.700962 | −0.350481 | − | 0.936570i | \(-0.613982\pi\) | ||||
−0.350481 | + | 0.936570i | \(0.613982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1900.00 | 0.132917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3212.00 | − | 5563.35i | −0.222430 | − | 0.385260i | 0.733115 | − | 0.680104i | \(-0.238066\pi\) |
−0.955545 | + | 0.294844i | \(0.904732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8820.00 | + | 3055.34i | −0.607705 | + | 0.210515i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8523.00 | − | 14762.3i | 0.581370 | − | 1.00696i | −0.413948 | − | 0.910301i | \(-0.635850\pi\) |
0.995317 | − | 0.0966609i | \(-0.0308162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18877.0 | −1.28121 | −0.640606 | − | 0.767869i | \(-0.721317\pi\) | ||||
−0.640606 | + | 0.767869i | \(0.721317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4487.00 | + | 7771.71i | −0.301525 | + | 0.522256i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6891.50 | + | 11936.4i | 0.460819 | + | 0.798163i | 0.999002 | − | 0.0446657i | \(-0.0142223\pi\) |
−0.538183 | + | 0.842828i | \(0.680889\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3692.00 | + | 6394.73i | 0.244456 | + | 0.423409i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9096.00 | + | 15754.7i | −0.599321 | + | 1.03806i | 0.393600 | + | 0.919282i | \(0.371229\pi\) |
−0.992921 | + | 0.118773i | \(0.962104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13054.0 | 0.851757 | 0.425879 | − | 0.904780i | \(-0.359965\pi\) | ||||
0.425879 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3623.00 | + | 6275.22i | −0.235251 | + | 0.407468i | −0.959346 | − | 0.282234i | \(-0.908925\pi\) |
0.724094 | + | 0.689701i | \(0.242258\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5964.00 | + | 5164.98i | 0.383535 | + | 0.332151i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 174.500 | + | 302.243i | 0.0111680 | + | 0.0193435i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25344.0 | −1.60657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2817.00 | 0.177723 | 0.0888613 | − | 0.996044i | \(-0.471677\pi\) | ||||
0.0888613 | + | 0.996044i | \(0.471677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6758.50 | − | 11706.1i | −0.422367 | − | 0.731561i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14014.0 | + | 11033.2i | −0.871672 | + | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7893.00 | − | 13671.1i | 0.486357 | − | 0.842395i | −0.513520 | − | 0.858078i | \(-0.671659\pi\) |
0.999877 | + | 0.0156827i | \(0.00499217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17426.0 | −1.06876 | −0.534381 | − | 0.845244i | \(-0.679455\pi\) | ||||
−0.534381 | + | 0.845244i | \(0.679455\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12917.0 | + | 22372.9i | −0.784884 | + | 1.35946i | 0.144185 | + | 0.989551i | \(0.453944\pi\) |
−0.929069 | + | 0.369907i | \(0.879389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −976.500 | − | 1691.35i | −0.0590616 | − | 0.102298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13991.5 | + | 24234.0i | 0.838483 | + | 1.45230i | 0.891162 | + | 0.453684i | \(0.149891\pi\) |
−0.0526789 | + | 0.998612i | \(0.516776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3426.50 | + | 5934.87i | −0.204404 | + | 0.354038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28296.0 | 1.67262 | 0.836309 | − | 0.548258i | \(-0.184709\pi\) | ||||
0.836309 | + | 0.548258i | \(0.184709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10627.0 | + | 18406.5i | −0.625329 | + | 1.08310i | 0.363148 | + | 0.931731i | \(0.381702\pi\) |
−0.988477 | + | 0.151370i | \(0.951631\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −490.000 | + | 2546.11i | −0.0285735 | + | 0.148472i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5832.00 | − | 10101.3i | −0.338555 | − | 0.586394i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1722.00 | −0.0990716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28259.0 | −1.61858 | −0.809290 | − | 0.587409i | \(-0.800148\pi\) | ||||
−0.809290 | + | 0.587409i | \(0.800148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15889.5 | + | 27521.4i | 0.902043 | + | 1.56238i | 0.824838 | + | 0.565369i | \(0.191266\pi\) |
0.0772049 | + | 0.997015i | \(0.475400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6457.50 | − | 2236.94i | 0.364972 | − | 0.126430i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4873.50 | + | 8441.15i | −0.273030 | + | 0.472901i | −0.969636 | − | 0.244552i | \(-0.921359\pi\) |
0.696606 | + | 0.717453i | \(0.254692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3402.00 | −0.189757 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9750.00 | − | 16887.5i | 0.539108 | − | 0.933762i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12256.0 | + | 21228.0i | 0.674733 | + | 1.16867i | 0.976547 | + | 0.215304i | \(0.0690744\pi\) |
−0.301814 | + | 0.953367i | \(0.597592\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9205.00 | − | 15943.5i | −0.502396 | − | 0.870176i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10656.0 | − | 18456.7i | 0.579089 | − | 1.00301i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14325.0 | −0.771823 | −0.385911 | − | 0.922536i | \(-0.626113\pi\) | ||||
−0.385911 | + | 0.922536i | \(0.626113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3520.00 | + | 6096.82i | −0.188847 | + | 0.327092i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4445.00 | + | 23096.9i | −0.236452 | + | 1.22864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6039.00 | − | 10459.9i | −0.319886 | − | 0.554059i | 0.660578 | − | 0.750758i | \(-0.270311\pi\) |
−0.980464 | + | 0.196698i | \(0.936978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4560.00 | 0.239514 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2548.00 | −0.133272 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5329.00 | − | 9230.10i | −0.276409 | − | 0.478755i | 0.694081 | − | 0.719897i | \(-0.255811\pi\) |
−0.970490 | + | 0.241143i | \(0.922478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25648.0 | + | 22211.8i | 1.32480 | + | 1.14731i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9234.00 | − | 15993.8i | 0.473024 | − | 0.819301i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19099.0 | 0.974337 | 0.487168 | − | 0.873308i | \(-0.338030\pi\) | ||||
0.487168 | + | 0.873308i | \(0.338030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5688.00 | − | 9851.90i | 0.287795 | − | 0.498476i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −703.000 | − | 1217.63i | −0.0354241 | − | 0.0613564i | 0.847770 | − | 0.530364i | \(-0.177945\pi\) |
−0.883194 | + | 0.469008i | \(0.844612\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2555.00 | − | 4425.39i | −0.127700 | − | 0.221182i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3365.00 | + | 5828.35i | −0.167501 | + | 0.290121i | −0.937541 | − | 0.347875i | \(-0.886903\pi\) |
0.770039 | + | 0.637996i | \(0.220237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1166.00 | 0.0575725 | 0.0287863 | − | 0.999586i | \(-0.490836\pi\) | ||||
0.0287863 | + | 0.999586i | \(0.490836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6573.00 | − | 11384.8i | 0.323243 | − | 0.559873i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13986.0 | + | 12112.2i | 0.682293 | + | 0.590883i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8483.50 | + | 14693.9i | 0.412207 | + | 0.713963i | 0.995131 | − | 0.0985636i | \(-0.0314248\pi\) |
−0.582924 | + | 0.812527i | \(0.698091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14721.0 | −0.709605 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11878.0 | 0.570295 | 0.285147 | − | 0.958484i | \(-0.407957\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13662.0 | + | 23663.3i | 0.650785 | + | 1.12719i | 0.982933 | + | 0.183965i | \(0.0588933\pi\) |
−0.332148 | + | 0.943227i | \(0.607773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5831.00 | + | 30298.8i | −0.276666 | + | 1.43760i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7254.00 | + | 12564.3i | −0.341495 | + | 0.591487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11971.0 | −0.561359 | −0.280680 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280680 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −169.000 | + | 292.717i | −0.00786353 | + | 0.0136200i | −0.869930 | − | 0.493175i | \(-0.835836\pi\) |
0.862067 | + | 0.506795i | \(0.169170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3610.00 | + | 6252.70i | 0.167323 | + | 0.289811i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2960.00 | − | 5126.87i | −0.136140 | − | 0.235801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1183.00 | + | 2049.02i | −0.0542011 | + | 0.0938791i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9828.00 | −0.446849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7057.00 | + | 12223.1i | −0.319638 | + | 0.553629i | −0.980412 | − | 0.196956i | \(-0.936895\pi\) |
0.660775 | + | 0.750584i | \(0.270228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32060.0 | + | 11105.9i | −1.44112 | + | 0.499217i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6396.00 | + | 11078.2i | 0.286417 | + | 0.496089i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1563.00 | −0.0694659 | −0.0347329 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347329 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10224.0 | −0.452690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1897.00 | − | 3285.70i | −0.0833670 | − | 0.144396i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1176.00 | + | 6110.68i | −0.0514889 | + | 0.267544i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15784.0 | + | 27338.7i | −0.685953 | + | 1.18811i | 0.287183 | + | 0.957876i | \(0.407281\pi\) |
−0.973136 | + | 0.230230i | \(0.926052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2626.00 | 0.113701 | 0.0568504 | − | 0.998383i | \(-0.481894\pi\) | ||||
0.0568504 | + | 0.998383i | \(0.481894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5376.00 | + | 9311.51i | −0.231059 | + | 0.400206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1580.00 | − | 2736.64i | −0.0676588 | − | 0.117188i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 180.500 | + | 312.635i | 0.00767295 | + | 0.0132899i | 0.869836 | − | 0.493340i | \(-0.164224\pi\) |
−0.862163 | + | 0.506630i | \(0.830891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14772.0 | − | 25585.9i | 0.625662 | − | 1.08368i | −0.362751 | − | 0.931886i | \(-0.618162\pi\) |
0.988413 | − | 0.151792i | \(-0.0485043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24163.0 | −1.01600 | −0.507999 | − | 0.861358i | \(-0.669615\pi\) | ||||
−0.507999 | + | 0.861358i | \(0.669615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19598.0 | − | 33944.7i | 0.821070 | − | 1.42213i | −0.0838169 | − | 0.996481i | \(-0.526711\pi\) |
0.904886 | − | 0.425653i | \(-0.139956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3528.00 | − | 24442.7i | −0.146744 | − | 1.01667i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12719.0 | + | 22030.0i | 0.527137 | + | 0.913028i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6528.00 | −0.268619 | −0.134310 | − | 0.990939i | \(-0.542882\pi\) | ||||
−0.134310 | + | 0.990939i | \(0.542882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34660.0 | 1.42113 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1774.50 | + | 3073.52i | 0.0722422 | + | 0.125127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17948.0 | − | 15543.4i | −0.728100 | − | 0.630553i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8448.00 | + | 14632.4i | −0.340298 | + | 0.589414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1046.00 | 0.0419864 | 0.0209932 | − | 0.999780i | \(-0.493317\pi\) | ||||
0.0209932 | + | 0.999780i | \(0.493317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16455.0 | − | 28500.9i | 0.655883 | − | 1.13602i | −0.325788 | − | 0.945443i | \(-0.605630\pi\) |
0.981672 | − | 0.190581i | \(-0.0610371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11341.0 | − | 19643.2i | −0.450466 | − | 0.780229i | 0.547949 | − | 0.836512i | \(-0.315409\pi\) |
−0.998415 | + | 0.0562823i | \(0.982075\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3725.00 | − | 6451.89i | −0.146930 | − | 0.254490i | 0.783161 | − | 0.621818i | \(-0.213606\pi\) |
−0.930091 | + | 0.367328i | \(0.880272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3003.00 | + | 5201.35i | −0.118041 | + | 0.204452i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2135.00 | 0.0833428 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18980.0 | + | 32874.3i | −0.738361 | + | 1.27888i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24622.5 | + | 8529.48i | −0.951306 | + | 0.329542i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5040.00 | − | 8729.54i | −0.194058 | − | 0.336118i | 0.752533 | − | 0.658554i | \(-0.228832\pi\) |
−0.946591 | + | 0.322436i | \(0.895498\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32958.0 | 1.26037 | 0.630183 | − | 0.776446i | \(-0.282980\pi\) | ||||
0.630183 | + | 0.776446i | \(0.282980\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19784.0 | −0.754003 | −0.377001 | − | 0.926213i | \(-0.623045\pi\) | ||||
−0.377001 | + | 0.926213i | \(0.623045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5740.00 | − | 9941.97i | −0.217283 | − | 0.376346i | 0.736693 | − | 0.676227i | \(-0.236386\pi\) |
−0.953976 | + | 0.299881i | \(0.903053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33792.5 | − | 11706.1i | 1.27488 | − | 0.441630i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1420.00 | + | 2459.51i | −0.0532122 | + | 0.0921662i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16940.0 | −0.632672 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11542.5 | + | 19992.2i | −0.428213 | + | 0.741688i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13500.0 | + | 23382.7i | 0.499168 | + | 0.864584i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9352.00 | − | 16198.1i | −0.343504 | − | 0.594966i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22676.0 | − | 39276.0i | 0.830148 | − | 1.43786i | −0.0677725 | − | 0.997701i | \(-0.521589\pi\) |
0.897920 | − | 0.440158i | \(-0.145077\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39906.0 | 1.45131 | 0.725656 | − | 0.688058i | \(-0.241537\pi\) | ||||
0.725656 | + | 0.688058i | \(0.241537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3930.50 | + | 6807.83i | −0.142476 | + | 0.246776i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13706.0 | − | 11869.7i | −0.493579 | − | 0.427452i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8764.00 | − | 15179.7i | −0.314579 | − | 0.544866i | 0.664769 | − | 0.747049i | \(-0.268530\pi\) |
−0.979348 | + | 0.202183i | \(0.935197\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17576.0 | 0.626783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26752.0 | −0.950919 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8533.00 | + | 14779.6i | 0.301355 | + | 0.521962i | 0.976443 | − | 0.215775i | \(-0.0692278\pi\) |
−0.675088 | + | 0.737737i | \(0.735894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6370.00 | − | 2546.11i | −0.224241 | − | 0.0896300i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1764.00 | − | 3055.34i | 0.0616994 | − | 0.106867i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30821.0 | −1.07458 | −0.537288 | − | 0.843399i | \(-0.680551\pi\) | ||||
−0.537288 | + | 0.843399i | \(0.680551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2089.50 | − | 3619.12i | 0.0723866 | − | 0.125377i | −0.827560 | − | 0.561377i | \(-0.810272\pi\) |
0.899947 | + | 0.436000i | \(0.143605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7104.00 | − | 12304.5i | −0.245321 | − | 0.424909i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4888.00 | + | 8466.26i | 0.167728 | + | 0.290514i | 0.937621 | − | 0.347660i | \(-0.113024\pi\) |
−0.769893 | + | 0.638174i | \(0.779690\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14092.0 | + | 24408.1i | −0.482029 | + | 0.834899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14778.0 | −0.502315 | −0.251158 | − | 0.967946i | \(-0.580811\pi\) | ||||
−0.251158 | + | 0.967946i | \(0.580811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5992.00 | − | 10378.4i | 0.203033 | − | 0.351664i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1701.00 | − | 8838.66i | 0.0572765 | − | 0.297617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10383.0 | + | 17983.9i | 0.348528 | + | 0.603668i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23765.0 | 0.792769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8759.00 | 0.291283 | 0.145641 | − | 0.989337i | \(-0.453475\pi\) | ||||
0.145641 | + | 0.989337i | \(0.453475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16789.5 | − | 29080.3i | −0.554893 | − | 0.961102i | −0.997912 | − | 0.0645901i | \(-0.979426\pi\) |
0.443019 | − | 0.896512i | \(-0.353907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46025.0 | − | 15943.5i | 1.51644 | − | 0.525309i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21317.0 | − | 36922.1i | 0.698046 | − | 1.20905i | −0.271097 | − | 0.962552i | \(-0.587386\pi\) |
0.969143 | − | 0.246500i | \(-0.0792804\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2982.00 | −0.0973495 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14574.0 | − | 25242.9i | 0.472877 | − | 0.819048i | −0.526641 | − | 0.850088i | \(-0.676549\pi\) |
0.999518 | + | 0.0310404i | \(0.00988204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1785.00 | − | 3091.71i | −0.0577409 | − | 0.100010i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3792.00 | − | 6567.94i | −0.121920 | − | 0.211171i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22398.5 | − | 38795.3i | 0.717974 | − | 1.24357i | −0.243828 | − | 0.969819i | \(-0.578403\pi\) |
0.961801 | − | 0.273748i | \(-0.0882635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1932.00 | −0.0615563 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5327.00 | + | 9226.63i | −0.169215 | + | 0.293090i | −0.938144 | − | 0.346245i | \(-0.887457\pi\) |
0.768929 | + | 0.639334i | \(0.220790\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 504.4.s.e.361.1 | 2 | ||
3.2 | odd | 2 | 168.4.q.a.25.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 504.4.s.e.289.1 | 2 | ||
12.11 | even | 2 | 336.4.q.a.193.1 | 2 | |||
21.2 | odd | 6 | 168.4.q.a.121.1 | yes | 2 | ||
21.11 | odd | 6 | 1176.4.a.f.1.1 | 1 | |||
21.17 | even | 6 | 1176.4.a.i.1.1 | 1 | |||
84.11 | even | 6 | 2352.4.a.bg.1.1 | 1 | |||
84.23 | even | 6 | 336.4.q.a.289.1 | 2 | |||
84.59 | odd | 6 | 2352.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.a.25.1 | ✓ | 2 | 3.2 | odd | 2 | ||
168.4.q.a.121.1 | yes | 2 | 21.2 | odd | 6 | ||
336.4.q.a.193.1 | 2 | 12.11 | even | 2 | |||
336.4.q.a.289.1 | 2 | 84.23 | even | 6 | |||
504.4.s.e.289.1 | 2 | 7.2 | even | 3 | inner | ||
504.4.s.e.361.1 | 2 | 1.1 | even | 1 | trivial | ||
1176.4.a.f.1.1 | 1 | 21.11 | odd | 6 | |||
1176.4.a.i.1.1 | 1 | 21.17 | even | 6 | |||
2352.4.a.c.1.1 | 1 | 84.59 | odd | 6 | |||
2352.4.a.bg.1.1 | 1 | 84.11 | even | 6 |