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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(-8.34231i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.361 |
Dual form | 504.4.s.j.289.3 |
$q$-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 | ||||||||
\(5\) | 0.363171 | + | 0.629031i | 0.0324830 | + | 0.0562622i | 0.881810 | − | 0.471605i | \(-0.156325\pi\) |
−0.849327 | + | 0.527867i | \(0.822992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.1420 | − | 3.72380i | −0.979578 | − | 0.201066i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.2447 | + | 55.8495i | −0.883832 | + | 1.53084i | −0.0367856 | + | 0.999323i | \(0.511712\pi\) |
−0.847046 | + | 0.531519i | \(0.821621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.8475 | 1.53284 | 0.766420 | − | 0.642340i | \(-0.222036\pi\) | ||||
0.766420 | + | 0.642340i | \(0.222036\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.4517 | − | 42.3515i | 0.348847 | − | 0.604221i | −0.637198 | − | 0.770700i | \(-0.719907\pi\) |
0.986045 | + | 0.166479i | \(0.0532399\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.1984 | − | 29.7885i | −0.207663 | − | 0.359682i | 0.743315 | − | 0.668941i | \(-0.233252\pi\) |
−0.950978 | + | 0.309259i | \(0.899919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.451675 | − | 0.782324i | −0.00409482 | − | 0.00709243i | 0.863971 | − | 0.503542i | \(-0.167970\pi\) |
−0.868066 | + | 0.496450i | \(0.834637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.2362 | − | 107.796i | 0.497890 | − | 0.862370i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −226.686 | −1.45154 | −0.725769 | − | 0.687939i | \(-0.758516\pi\) | ||||
−0.725769 | + | 0.687939i | \(0.758516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 137.898 | − | 238.846i | 0.798940 | − | 1.38380i | −0.121367 | − | 0.992608i | \(-0.538728\pi\) |
0.920307 | − | 0.391197i | \(-0.127939\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.24627 | − | 12.7643i | −0.0205072 | − | 0.0616444i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −147.605 | − | 255.658i | −0.655839 | − | 1.13595i | −0.981683 | − | 0.190522i | \(-0.938982\pi\) |
0.325844 | − | 0.945423i | \(-0.394352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −186.604 | −0.710798 | −0.355399 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355399 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −455.317 | −1.61477 | −0.807386 | − | 0.590023i | \(-0.799119\pi\) | ||||
−0.807386 | + | 0.590023i | \(0.799119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 141.167 | + | 244.509i | 0.438114 | + | 0.758835i | 0.997544 | − | 0.0700420i | \(-0.0223133\pi\) |
−0.559430 | + | 0.828877i | \(0.688980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 315.267 | + | 135.115i | 0.919145 | + | 0.393920i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 178.107 | − | 308.491i | 0.461602 | − | 0.799518i | −0.537439 | − | 0.843303i | \(-0.680608\pi\) |
0.999041 | + | 0.0437844i | \(0.0139415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.8414 | −0.114838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 364.685 | − | 631.653i | 0.804711 | − | 1.39380i | −0.111776 | − | 0.993733i | \(-0.535654\pi\) |
0.916486 | − | 0.400066i | \(-0.131013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −137.176 | − | 237.596i | −0.287928 | − | 0.498706i | 0.685387 | − | 0.728179i | \(-0.259633\pi\) |
−0.973315 | + | 0.229473i | \(0.926300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26.0929 | + | 45.1943i | 0.0497912 | + | 0.0862409i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −96.6361 | + | 167.379i | −0.176209 | + | 0.305202i | −0.940579 | − | 0.339575i | \(-0.889717\pi\) |
0.764370 | + | 0.644778i | \(0.223050\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −40.5277 | −0.0677429 | −0.0338715 | − | 0.999426i | \(-0.510784\pi\) | ||||
−0.0338715 | + | 0.999426i | \(0.510784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 103.236 | − | 178.810i | 0.165519 | − | 0.286687i | −0.771320 | − | 0.636447i | \(-0.780403\pi\) |
0.936839 | + | 0.349760i | \(0.113737\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 792.958 | − | 893.151i | 1.17358 | − | 1.32187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −468.870 | − | 812.107i | −0.667747 | − | 1.15657i | −0.978533 | − | 0.206092i | \(-0.933925\pi\) |
0.310785 | − | 0.950480i | \(-0.399408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −911.607 | −1.20556 | −0.602782 | − | 0.797906i | \(-0.705941\pi\) | ||||
−0.602782 | + | 0.797906i | \(0.705941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.5206 | 0.0453264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −474.988 | − | 822.703i | −0.565715 | − | 0.979846i | −0.996983 | − | 0.0776226i | \(-0.975267\pi\) |
0.431268 | − | 0.902224i | \(-0.358066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1303.46 | − | 267.546i | −1.50154 | − | 0.308203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.4919 | − | 21.6367i | 0.0134910 | − | 0.0233671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.4687 | 0.0413138 | 0.0206569 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206569 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −158.437 | + | 274.421i | −0.156090 | + | 0.270356i | −0.933455 | − | 0.358694i | \(-0.883222\pi\) |
0.777365 | + | 0.629049i | \(0.216556\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 161.317 | + | 279.409i | 0.154321 | + | 0.267291i | 0.932811 | − | 0.360365i | \(-0.117348\pi\) |
−0.778491 | + | 0.627656i | \(0.784014\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 340.726 | + | 590.154i | 0.307843 | + | 0.533200i | 0.977890 | − | 0.209119i | \(-0.0670595\pi\) |
−0.670047 | + | 0.742318i | \(0.733726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 227.984 | − | 394.879i | 0.200338 | − | 0.346996i | −0.748299 | − | 0.663361i | \(-0.769129\pi\) |
0.948637 | + | 0.316365i | \(0.102463\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 796.025 | 0.662688 | 0.331344 | − | 0.943510i | \(-0.392498\pi\) | ||||
0.331344 | + | 0.943510i | \(0.392498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.328071 | − | 0.568235i | 0.000266024 | − | 0.000460767i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −601.312 | + | 677.290i | −0.463212 | + | 0.521740i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1413.95 | − | 2449.03i | −1.06232 | − | 1.83999i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 181.202 | 0.129658 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2333.92 | 1.63072 | 0.815362 | − | 0.578952i | \(-0.196538\pi\) | ||||
0.815362 | + | 0.578952i | \(0.196538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −943.489 | − | 1634.17i | −0.629259 | − | 1.08991i | −0.987701 | − | 0.156357i | \(-0.950025\pi\) |
0.358441 | − | 0.933552i | \(-0.383308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 201.088 | + | 604.468i | 0.131102 | + | 0.394091i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1473.63 | − | 2552.40i | 0.918983 | − | 1.59173i | 0.118021 | − | 0.993011i | \(-0.462345\pi\) |
0.800963 | − | 0.598714i | \(-0.204322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 955.433 | 0.583013 | 0.291506 | − | 0.956569i | \(-0.405844\pi\) | ||||
0.291506 | + | 0.956569i | \(0.405844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2316.70 | + | 4012.65i | −1.35477 | + | 2.34654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −82.3259 | − | 142.593i | −0.0471503 | − | 0.0816667i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1091.87 | + | 1891.17i | 0.600332 | + | 1.03981i | 0.992771 | + | 0.120027i | \(0.0382981\pi\) |
−0.392439 | + | 0.919778i | \(0.628369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −202.360 | + | 350.497i | −0.109058 | + | 0.188894i | −0.915389 | − | 0.402570i | \(-0.868117\pi\) |
0.806331 | + | 0.591465i | \(0.201450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 200.322 | 0.103808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 464.791 | − | 805.042i | 0.236270 | − | 0.409231i | −0.723371 | − | 0.690459i | \(-0.757408\pi\) |
0.959641 | + | 0.281228i | \(0.0907418\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28108 | + | 15.8749i | 0.00258514 | + | 0.00777092i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 712.840 | + | 1234.68i | 0.342540 | + | 0.593296i | 0.984904 | − | 0.173104i | \(-0.0553796\pi\) |
−0.642364 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4185.15 | −1.93926 | −0.969631 | − | 0.244572i | \(-0.921353\pi\) | ||||
−0.969631 | + | 0.244572i | \(0.921353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2965.07 | 1.34960 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1117.78 | + | 1936.05i | 0.491231 | + | 0.850837i | 0.999949 | − | 0.0100961i | \(-0.00321376\pi\) |
−0.508718 | + | 0.860933i | \(0.669880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1530.50 | + | 1723.89i | −0.661115 | + | 0.744650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −470.740 | + | 815.345i | −0.196563 | + | 0.340457i | −0.947412 | − | 0.320017i | \(-0.896311\pi\) |
0.750849 | + | 0.660474i | \(0.229645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −467.540 | −0.192000 | −0.0960000 | − | 0.995381i | \(-0.530605\pi\) | ||||
−0.0960000 | + | 0.995381i | \(0.530605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 107.211 | − | 185.696i | 0.0426072 | − | 0.0737979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1576.88 | + | 2731.23i | 0.616645 | + | 1.06806i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 137.701 | + | 238.506i | 0.0521660 | + | 0.0903542i | 0.890929 | − | 0.454142i | \(-0.150054\pi\) |
−0.838763 | + | 0.544496i | \(0.816721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −820.148 | + | 1420.54i | −0.305884 | + | 0.529806i | −0.977458 | − | 0.211131i | \(-0.932285\pi\) |
0.671574 | + | 0.740937i | \(0.265619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1303.88 | −0.471560 | −0.235780 | − | 0.971806i | \(-0.575764\pi\) | ||||
−0.235780 | + | 0.971806i | \(0.575764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 663.678 | − | 1149.52i | 0.236417 | − | 0.409485i | −0.723267 | − | 0.690569i | \(-0.757360\pi\) |
0.959683 | + | 0.281083i | \(0.0906937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4112.55 | + | 844.135i | 1.42189 | + | 0.291855i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −67.7693 | − | 117.380i | −0.0230889 | − | 0.0399911i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2218.23 | 0.734155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4753.28 | −1.55085 | −0.775426 | − | 0.631439i | \(-0.782465\pi\) | ||||
−0.775426 | + | 0.631439i | \(0.782465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −165.358 | − | 286.408i | −0.0524527 | − | 0.0908507i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3391.16 | + | 3819.64i | −1.06086 | + | 1.19490i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1756.79 | − | 3042.85i | 0.534727 | − | 0.926174i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 513.149 | 0.154094 | 0.0770470 | − | 0.997027i | \(-0.475451\pi\) | ||||
0.0770470 | + | 0.997027i | \(0.475451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1654.67 | − | 2865.97i | 0.483808 | − | 0.837980i | −0.516019 | − | 0.856577i | \(-0.672587\pi\) |
0.999827 | + | 0.0185972i | \(0.00592001\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2954.73 | + | 5117.75i | 0.852639 | + | 1.47681i | 0.878819 | + | 0.477156i | \(0.158332\pi\) |
−0.0261800 | + | 0.999657i | \(0.508334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −176.786 | − | 306.202i | −0.0497065 | − | 0.0860943i | 0.840102 | − | 0.542429i | \(-0.182495\pi\) |
−0.889808 | + | 0.456335i | \(0.849162\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −102.536 | + | 177.597i | −0.0284625 | + | 0.0492985i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1652.55 | 0.447259 | 0.223629 | − | 0.974674i | \(-0.428209\pi\) | ||||
0.223629 | + | 0.974674i | \(0.428209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1553.47 | − | 2690.69i | 0.415220 | − | 0.719182i | −0.580232 | − | 0.814451i | \(-0.697038\pi\) |
0.995452 | + | 0.0952696i | \(0.0303713\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.5044 | + | 247.382i | 0.00769374 | + | 0.0645088i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1235.66 | − | 2140.23i | −0.318313 | − | 0.551335i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1771.77 | −0.445551 | −0.222776 | − | 0.974870i | \(-0.571512\pi\) | ||||
−0.222776 | + | 0.974870i | \(0.571512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58.2566 | 0.0144765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 739.063 | + | 1280.09i | 0.179383 | + | 0.310701i | 0.941669 | − | 0.336539i | \(-0.109257\pi\) |
−0.762286 | + | 0.647240i | \(0.775923\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1725.82 | + | 5187.81i | 0.414044 | + | 1.24461i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −715.987 | + | 1240.13i | −0.167869 | + | 0.290758i | −0.937671 | − | 0.347525i | \(-0.887022\pi\) |
0.769801 | + | 0.638284i | \(0.220355\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 258.734 | 0.0599769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 142.699 | − | 247.162i | 0.0323439 | − | 0.0560213i | −0.849400 | − | 0.527749i | \(-0.823036\pi\) |
0.881744 | + | 0.471728i | \(0.156369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2624.66 | + | 4546.05i | 0.588328 | + | 1.01901i | 0.994452 | + | 0.105196i | \(0.0335470\pi\) |
−0.406123 | + | 0.913818i | \(0.633120\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4013.58 | + | 6951.72i | 0.880102 | + | 1.52438i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3573.93 | + | 6190.24i | −0.775224 | + | 1.34273i | 0.159445 | + | 0.987207i | \(0.449029\pi\) |
−0.934669 | + | 0.355520i | \(0.884304\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4228.36 | −0.897661 | −0.448831 | − | 0.893617i | \(-0.648159\pi\) | ||||
−0.448831 | + | 0.893617i | \(0.648159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4171.19 | + | 7224.71i | −0.876154 | + | 1.51754i | −0.0206255 | + | 0.999787i | \(0.506566\pi\) |
−0.855528 | + | 0.517756i | \(0.826768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3385.38 | + | 694.878i | 0.696282 | + | 0.142918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1260.73 | + | 2183.65i | 0.256611 | + | 0.444464i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5038.84 | −1.00468 | −0.502342 | − | 0.864669i | \(-0.667528\pi\) | ||||
−0.502342 | + | 0.864669i | \(0.667528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 529.772 | 0.104558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −32.4517 | − | 56.2081i | −0.00627670 | − | 0.0108716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8260.38 | + | 1695.51i | 1.58180 | + | 0.324677i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 99.6369 | − | 172.576i | 0.0187055 | − | 0.0323990i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4869.67 | −0.905300 | −0.452650 | − | 0.891688i | \(-0.649521\pi\) | ||||
−0.452650 | + | 0.891688i | \(0.649521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −726.421 | + | 1258.20i | −0.132449 | + | 0.229408i | −0.924620 | − | 0.380891i | \(-0.875617\pi\) |
0.792171 | + | 0.610299i | \(0.208951\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2848.14 | − | 4933.12i | −0.514333 | − | 0.890850i | −0.999862 | − | 0.0166299i | \(-0.994706\pi\) |
0.485529 | − | 0.874221i | \(-0.338627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1735.73 | − | 3006.38i | −0.307535 | − | 0.532666i | 0.670288 | − | 0.742101i | \(-0.266171\pi\) |
−0.977822 | + | 0.209435i | \(0.932837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7309.44 | − | 12660.3i | 1.28291 | − | 2.22207i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1682.12 | −0.289770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4471.52 | − | 7744.90i | 0.763185 | − | 1.32188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1650.56 | − | 4961.56i | −0.276590 | − | 0.831428i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3127.19 | − | 5416.45i | −0.519293 | − | 0.899441i | −0.999749 | − | 0.0224223i | \(-0.992862\pi\) |
0.480456 | − | 0.877019i | \(-0.340471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −140.382 | −0.0228951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8006.96 | 1.29426 | 0.647132 | − | 0.762378i | \(-0.275968\pi\) | ||||
0.647132 | + | 0.762378i | \(0.275968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8892.94 | + | 15403.0i | 1.41226 | + | 2.44610i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5216.44 | − | 3625.25i | −0.821169 | − | 0.570685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3817.80 | − | 6612.62i | 0.590634 | − | 1.02301i | −0.403513 | − | 0.914974i | \(-0.632211\pi\) |
0.994147 | − | 0.108034i | \(-0.0344556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10358.0 | −1.58869 | −0.794345 | − | 0.607468i | \(-0.792185\pi\) | ||||
−0.794345 | + | 0.607468i | \(0.792185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1692.12 | − | 2930.83i | 0.255134 | − | 0.441905i | −0.709798 | − | 0.704405i | \(-0.751214\pi\) |
0.964932 | + | 0.262500i | \(0.0845471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7185 | − | 25.4931i | −0.00220049 | − | 0.00381137i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4097.31 | − | 7096.74i | −0.602361 | − | 1.04332i | −0.992463 | − | 0.122548i | \(-0.960894\pi\) |
0.390102 | − | 0.920772i | \(-0.372440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2837.93 | − | 4915.44i | 0.413752 | − | 0.716640i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 149.970 | 0.0215062 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −402.755 | + | 697.592i | −0.0572851 | + | 0.0992208i | −0.893246 | − | 0.449569i | \(-0.851578\pi\) |
0.835961 | + | 0.548789i | \(0.184911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4379.99 | + | 4933.41i | −0.612931 | + | 0.690377i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3952.86 | − | 6846.55i | −0.548716 | − | 0.950404i | −0.998363 | − | 0.0571977i | \(-0.981783\pi\) |
0.449647 | − | 0.893206i | \(-0.351550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16286.8 | −2.22497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3324.24 | 0.450540 | 0.225270 | − | 0.974296i | \(-0.427674\pi\) | ||||
0.225270 | + | 0.974296i | \(0.427674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4235.38 | − | 7335.90i | −0.565060 | − | 0.978712i | −0.997044 | − | 0.0768310i | \(-0.975520\pi\) |
0.431984 | − | 0.901881i | \(-0.357814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 849.798 | + | 174.428i | 0.112493 | + | 0.0230901i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3954.20 | + | 6848.88i | −0.515388 | + | 0.892678i | 0.484452 | + | 0.874818i | \(0.339019\pi\) |
−0.999840 | + | 0.0178606i | \(0.994314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.1769 | −0.00571386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 340.560 | − | 589.868i | 0.0433809 | − | 0.0751379i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4890.79 | + | 8471.10i | 0.618292 | + | 1.07091i | 0.989797 | + | 0.142482i | \(0.0455083\pi\) |
−0.371506 | + | 0.928431i | \(0.621158\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −397.827 | − | 689.056i | −0.0495424 | − | 0.0858100i | 0.840191 | − | 0.542291i | \(-0.182443\pi\) |
−0.889733 | + | 0.456481i | \(0.849110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9907.60 | − | 17160.5i | 1.22465 | − | 2.12115i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19037.9 | 2.31860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4292.36 | + | 7434.59i | −0.518933 | + | 0.898818i | 0.480825 | + | 0.876817i | \(0.340337\pi\) |
−0.999758 | + | 0.0220017i | \(0.992996\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8968.27 | + | 10101.4i | −1.06852 | + | 1.20353i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −331.069 | − | 573.428i | −0.0391603 | − | 0.0678277i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7447.09 | 0.868292 | 0.434146 | − | 0.900843i | \(-0.357050\pi\) | ||||
0.434146 | + | 0.900843i | \(0.357050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4446.76 | −0.514779 | −0.257390 | − | 0.966308i | \(-0.582862\pi\) | ||||
−0.257390 | + | 0.966308i | \(0.582862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3043.56 | − | 5271.60i | −0.347375 | − | 0.601671i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1603.89 | + | 4821.30i | 0.181775 | + | 0.546414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4481.85 | + | 7762.79i | −0.500889 | + | 0.867565i | 0.499110 | + | 0.866538i | \(0.333660\pi\) |
−0.999999 | + | 0.00102683i | \(0.999673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16173.6 | −1.79504 | −0.897520 | − | 0.440973i | \(-0.854633\pi\) | ||||
−0.897520 | + | 0.440973i | \(0.854633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.5362 | + | 26.9095i | −0.00170068 | + | 0.00294567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3149.21 | + | 5454.60i | 0.342378 | + | 0.593015i | 0.984874 | − | 0.173274i | \(-0.0554345\pi\) |
−0.642496 | + | 0.766289i | \(0.722101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8392.35 | − | 14536.0i | −0.900074 | − | 1.55897i | −0.827397 | − | 0.561618i | \(-0.810179\pi\) |
−0.0726770 | − | 0.997356i | \(-0.523154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 345.004 | − | 597.564i | 0.0367522 | − | 0.0636567i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2733.88 | −0.287349 | −0.143674 | − | 0.989625i | \(-0.545892\pi\) | ||||
−0.143674 | + | 0.989625i | \(0.545892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6017.01 | − | 10421.8i | 0.628226 | − | 1.08812i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −305.084 | − | 917.081i | −0.0314342 | − | 0.0944910i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4614.60 | − | 7992.72i | −0.472345 | − | 0.818126i | 0.527154 | − | 0.849770i | \(-0.323259\pi\) |
−0.999499 | + | 0.0316437i | \(0.989926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19726.7 | 1.99298 | 0.996491 | − | 0.0837048i | \(-0.0266753\pi\) | ||||
0.996491 | + | 0.0837048i | \(0.0266753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 368.924 | 0.0370310 | 0.0185155 | − | 0.999829i | \(-0.494106\pi\) | ||||
0.0185155 | + | 0.999829i | \(0.494106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6654.78 | − | 11526.4i | −0.659414 | − | 1.14214i | −0.980768 | − | 0.195179i | \(-0.937471\pi\) |
0.321353 | − | 0.946959i | \(-0.395862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2376.46 | − | 2676.73i | 0.233976 | − | 0.263540i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14681.6 | − | 25429.2i | 1.42719 | − | 2.47196i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4281.46 | −0.413572 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5781.39 | − | 10013.7i | 0.551479 | − | 0.955189i | −0.446689 | − | 0.894689i | \(-0.647397\pi\) |
0.998168 | − | 0.0605002i | \(-0.0192696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10605.0 | − | 18368.4i | −1.00530 | − | 1.74122i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3339 | + | 24.8270i | 0.00134200 | + | 0.00232440i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1314.06 | + | 2276.02i | −0.122271 | + | 0.211779i | −0.920663 | − | 0.390359i | \(-0.872351\pi\) |
0.798392 | + | 0.602138i | \(0.205684\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12319.9 | 1.13236 | 0.566181 | − | 0.824281i | \(-0.308420\pi\) | ||||
0.566181 | + | 0.824281i | \(0.308420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5542.86 | + | 9600.51i | −0.506365 | + | 0.877049i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 735.254 | + | 150.917i | 0.0663595 | + | 0.0136208i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1652.90 | + | 2862.91i | 0.148285 | + | 0.256837i | 0.930594 | − | 0.366054i | \(-0.119291\pi\) |
−0.782309 | + | 0.622891i | \(0.785958\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3072.72 | 0.272377 | 0.136189 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136189 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −230.159 | −0.0202811 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6784.91 | + | 11751.8i | 0.590836 | + | 1.02336i | 0.994120 | + | 0.108284i | \(0.0345355\pi\) |
−0.403284 | + | 0.915075i | \(0.632131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2538.77 | + | 2859.55i | −0.219782 | + | 0.247552i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −117.171 | + | 202.947i | −0.0100256 | + | 0.0173648i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18207.6 | −1.54888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5366.68 | + | 9295.36i | −0.451283 | + | 0.781645i | −0.998466 | − | 0.0553681i | \(-0.982367\pi\) |
0.547183 | + | 0.837013i | \(0.315700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4174.07 | − | 7229.71i | −0.348986 | − | 0.604461i | 0.637084 | − | 0.770794i | \(-0.280140\pi\) |
−0.986070 | + | 0.166334i | \(0.946807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6743.65 | − | 11680.3i | −0.557416 | − | 0.965473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6083.09 | − | 10536.2i | 0.499966 | − | 0.865967i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13407.1 | −1.08954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −247.483 | + | 428.654i | −0.0199993 | + | 0.0346399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17711.8 | + | 13250.7i | −1.41540 | + | 1.05891i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11553.6 | + | 20011.5i | 0.918170 | + | 1.59032i | 0.802192 | + | 0.597066i | \(0.203667\pi\) |
0.115978 | + | 0.993252i | \(0.463000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 331.188 | 0.0260304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13935.2 | 1.08926 | 0.544630 | − | 0.838676i | \(-0.316670\pi\) | ||||
0.544630 | + | 0.838676i | \(0.316670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3898.65 | + | 6752.65i | 0.301430 | + | 0.522092i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5482.13 | + | 16479.3i | 0.421562 | + | 1.26721i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7523.76 | + | 13031.5i | −0.572337 | + | 0.991317i | 0.423988 | + | 0.905668i | \(0.360630\pi\) |
−0.996325 | + | 0.0856492i | \(0.972704\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32713.4 | −2.47519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7721.08 | − | 13373.3i | 0.577983 | − | 1.00110i | −0.417727 | − | 0.908572i | \(-0.637173\pi\) |
0.995710 | − | 0.0925239i | \(-0.0294934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 289.093 | + | 500.724i | 0.0215261 | + | 0.0372843i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6681.06 | − | 11571.9i | −0.492240 | − | 0.852585i | 0.507720 | − | 0.861522i | \(-0.330489\pi\) |
−0.999960 | + | 0.00893696i | \(0.997155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11092.6 | − | 19213.0i | 0.812981 | − | 1.40812i | −0.0977876 | − | 0.995207i | \(-0.531177\pi\) |
0.910769 | − | 0.412917i | \(-0.135490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −112.442 | −0.00815507 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9475.68 | − | 16412.4i | 0.683671 | − | 1.18415i | −0.290182 | − | 0.956971i | \(-0.593716\pi\) |
0.973853 | − | 0.227181i | \(-0.0729508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16538.4 | + | 3394.64i | 1.18094 | + | 0.242399i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11486.0 | + | 19894.4i | 0.815957 | + | 1.41328i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19579.5 | −1.37672 | −0.688359 | − | 0.725371i | \(-0.741668\pi\) | ||||
−0.688359 | + | 0.725371i | \(0.741668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9486.48 | −0.663640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2806.51 | + | 4861.01i | 0.194350 | + | 0.336624i | 0.946687 | − | 0.322154i | \(-0.104407\pi\) |
−0.752337 | + | 0.658778i | \(0.771074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −644.415 | − | 132.272i | −0.0444007 | − | 0.00911362i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10962.8 | − | 18988.0i | 0.747790 | − | 1.29521i | −0.201090 | − | 0.979573i | \(-0.564448\pi\) |
0.948880 | − | 0.315637i | \(-0.102218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2067.51 | −0.140326 | −0.0701628 | − | 0.997536i | \(-0.522352\pi\) | ||||
−0.0701628 | + | 0.997536i | \(0.522352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1027.01 | − | 1778.83i | 0.0690146 | − | 0.119537i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5083.61 | + | 8805.07i | 0.339930 | + | 0.588775i | 0.984419 | − | 0.175838i | \(-0.0562634\pi\) |
−0.644490 | + | 0.764613i | \(0.722930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10142.5 | + | 17567.3i | 0.671558 | + | 1.16317i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9093.05 | − | 15749.6i | 0.599127 | − | 1.03772i | −0.393824 | − | 0.919186i | \(-0.628848\pi\) |
0.992950 | − | 0.118532i | \(-0.0378188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6584.41 | −0.429625 | −0.214812 | − | 0.976655i | \(-0.568914\pi\) | ||||
−0.214812 | + | 0.976655i | \(0.568914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3889.86 | − | 6737.43i | 0.252579 | − | 0.437480i | −0.711656 | − | 0.702528i | \(-0.752054\pi\) |
0.964235 | + | 0.265048i | \(0.0853878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5553.66 | + | 16694.3i | 0.357147 | + | 1.07358i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7713.72 | − | 13360.6i | −0.493678 | − | 0.855075i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14436.7 | −0.915150 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3787.78 | 0.238969 | 0.119484 | − | 0.992836i | \(-0.461876\pi\) | ||||
0.119484 | + | 0.992836i | \(0.461876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 847.612 | + | 1468.11i | 0.0529708 | + | 0.0917481i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22651.1 | + | 9707.66i | 1.40890 | + | 0.603817i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9965.44 | + | 17260.6i | −0.614058 | + | 1.06358i | 0.376491 | + | 0.926420i | \(0.377131\pi\) |
−0.990549 | + | 0.137159i | \(0.956203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3185.18 | 0.195352 | 0.0976759 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976759 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8471.50 | + | 14673.1i | −0.514759 | + | 0.891589i | 0.485094 | + | 0.874462i | \(0.338785\pi\) |
−0.999853 | + | 0.0171270i | \(0.994548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23518.3 | + | 40734.9i | 1.42246 | + | 2.46377i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10039.4 | − | 17388.7i | −0.601640 | − | 1.04207i | −0.992573 | − | 0.121652i | \(-0.961181\pi\) |
0.390932 | − | 0.920419i | \(-0.372153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 685.295 | − | 1186.97i | 0.0408805 | − | 0.0708070i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9442.46 | 0.558158 | 0.279079 | − | 0.960268i | \(-0.409971\pi\) | ||||
0.279079 | + | 0.960268i | \(0.409971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −380.995 | + | 659.902i | −0.0224190 | + | 0.0388309i | −0.877017 | − | 0.480459i | \(-0.840470\pi\) |
0.854598 | + | 0.519290i | \(0.173803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −307.200 | + | 346.016i | −0.0179138 | + | 0.0201773i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 102.389 | + | 177.342i | 0.00594378 | + | 0.0102949i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17692.8 | 1.01792 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16111.6 | −0.922818 | −0.461409 | − | 0.887188i | \(-0.652656\pi\) | ||||
−0.461409 | + | 0.887188i | \(0.652656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15620.7 | + | 27055.9i | 0.886786 | + | 1.53596i | 0.843653 | + | 0.536889i | \(0.180401\pi\) |
0.0431329 | + | 0.999069i | \(0.486266\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −716.042 | − | 146.974i | −0.0404700 | − | 0.00830682i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15056.8 | + | 26079.1i | −0.843530 | + | 1.46104i | 0.0433614 | + | 0.999059i | \(0.486193\pi\) |
−0.886892 | + | 0.461978i | \(0.847140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2140.72 | 0.119405 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12796.6 | − | 22164.3i | 0.707562 | − | 1.22553i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4875.43 | + | 8444.49i | 0.268408 | + | 0.464896i | 0.968451 | − | 0.249204i | \(-0.0801691\pi\) |
−0.700043 | + | 0.714101i | \(0.746836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 346.986 | + | 600.997i | 0.0189380 | + | 0.0328016i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4562.79 | + | 7902.99i | −0.247960 | + | 0.429479i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11851.6 | −0.638559 | −0.319280 | − | 0.947661i | \(-0.603441\pi\) | ||||
−0.319280 | + | 0.947661i | \(0.603441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5077.13 | + | 8793.85i | −0.272386 | + | 0.471787i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3896.26 | − | 4388.57i | 0.207262 | − | 0.233450i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −661.196 | − | 1145.22i | −0.0350236 | − | 0.0606627i | 0.847982 | − | 0.530025i | \(-0.177817\pi\) |
−0.883006 | + | 0.469362i | \(0.844484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −249.140 | −0.0130861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3365.44 | −0.176028 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3650.78 | + | 6323.33i | 0.189362 | + | 0.327984i | 0.945038 | − | 0.326962i | \(-0.106025\pi\) |
−0.755676 | + | 0.654946i | \(0.772691\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1886.15 | − | 5669.76i | −0.0974257 | − | 0.292861i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14108.1 | + | 24435.9i | −0.722705 | + | 1.25176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6088.72 | −0.310616 | −0.155308 | − | 0.987866i | \(-0.549637\pi\) | ||||
−0.155308 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11133.3 | + | 19283.4i | −0.563309 | + | 0.975680i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13289.2 | + | 23017.6i | 0.669644 | + | 1.15986i | 0.978004 | + | 0.208587i | \(0.0668865\pi\) |
−0.308360 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6232.01 | − | 10794.2i | −0.311478 | − | 0.539495i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12609.9 | + | 21841.0i | −0.627689 | + | 1.08719i | 0.360325 | + | 0.932827i | \(0.382666\pi\) |
−0.988014 | + | 0.154363i | \(0.950668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2634.28 | −0.130071 | −0.0650353 | − | 0.997883i | \(-0.520716\pi\) | ||||
−0.0650353 | + | 0.997883i | \(0.520716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −793.071 | + | 1373.64i | −0.0390012 | + | 0.0675520i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3983.84 | − | 11975.4i | −0.194347 | − | 0.584207i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2883.64 | − | 4994.62i | −0.140114 | − | 0.242685i | 0.787425 | − | 0.616410i | \(-0.211414\pi\) |
−0.927539 | + | 0.373725i | \(0.878080\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −293.965 | −0.0141702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33378.7 | 1.60260 | 0.801302 | − | 0.598260i | \(-0.204141\pi\) | ||||
0.801302 | + | 0.598260i | \(0.204141\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1813.04 | + | 3140.28i | 0.0863637 | + | 0.149586i | 0.905971 | − | 0.423339i | \(-0.139142\pi\) |
−0.819608 | + | 0.572925i | \(0.805809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5606.54 | + | 6314.95i | −0.266016 | + | 0.299628i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26201.7 | − | 45382.7i | 1.23349 | − | 2.13647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3426.15 | 0.160663 | 0.0803316 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803316 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6554.09 | − | 11352.0i | 0.304960 | − | 0.528207i | −0.672292 | − | 0.740286i | \(-0.734690\pi\) |
0.977252 | + | 0.212079i | \(0.0680235\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17164.4 | − | 29729.7i | −0.795568 | − | 1.37796i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3209.30 | + | 5558.67i | 0.147606 | + | 0.255661i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1306.80 | − | 2263.45i | 0.0598734 | − | 0.103704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 675.194 | 0.0306990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19659.9 | + | 34051.9i | −0.890468 | + | 1.54234i | −0.0511538 | + | 0.998691i | \(0.516290\pi\) |
−0.839315 | + | 0.543646i | \(0.817043\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14441.5 | − | 2964.24i | −0.649154 | − | 0.133244i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9855.77 | − | 17070.7i | −0.441348 | − | 0.764437i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14597.8 | 0.648785 | 0.324393 | − | 0.945923i | \(-0.394840\pi\) | ||||
0.324393 | + | 0.945923i | \(0.394840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13807.1 | 0.611339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6657.65 | + | 11531.4i | 0.292582 | + | 0.506767i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.06786 | + | 9.08727i | −0.000353236 | + | 0.000397868i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13413.7 | − | 23233.2i | 0.582943 | − | 1.00969i | −0.412185 | − | 0.911100i | \(-0.635234\pi\) |
0.995128 | − | 0.0985870i | \(-0.0314323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5177.09 | −0.224158 | −0.112079 | − | 0.993699i | \(-0.535751\pi\) | ||||
−0.112079 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −517.766 | + | 896.796i | −0.0222534 | + | 0.0385441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7830.74 | + | 13563.2i | 0.335328 | + | 0.580805i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10178.4 | + | 17629.5i | 0.432678 | + | 0.749420i | 0.997103 | − | 0.0760646i | \(-0.0242355\pi\) |
−0.564425 | + | 0.825484i | \(0.690902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7869 | + | 49.8603i | −0.00121926 | + | 0.00211181i | −0.866634 | − | 0.498944i | \(-0.833721\pi\) |
0.865415 | + | 0.501056i | \(0.167055\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12296.6 | 0.517044 | 0.258522 | − | 0.966005i | \(-0.416765\pi\) | ||||
0.258522 | + | 0.966005i | \(0.416765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11435.9 | + | 19807.5i | −0.479112 | + | 0.829846i | −0.999713 | − | 0.0239540i | \(-0.992374\pi\) |
0.520601 | + | 0.853800i | \(0.325708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13431.1 | − | 10048.2i | 0.558656 | − | 0.417948i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1519.93 | − | 2632.59i | −0.0629931 | − | 0.109107i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37571.3 | −1.54601 | −0.773007 | − | 0.634398i | \(-0.781248\pi\) | ||||
−0.773007 | + | 0.634398i | \(0.781248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26997.6 | 1.10696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1076.83 | + | 1865.12i | 0.0438390 | + | 0.0759313i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16532.2 | + | 49695.6i | 0.670663 | + | 2.01601i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −133.339 | + | 230.949i | −0.00537108 | + | 0.00930298i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38354.5 | −1.53955 | −0.769774 | − | 0.638317i | \(-0.779631\pi\) | ||||
−0.769774 | + | 0.638317i | \(0.779631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18272.8 | − | 31649.5i | 0.728341 | − | 1.26152i | −0.229243 | − | 0.973369i | \(-0.573625\pi\) |
0.957584 | − | 0.288154i | \(-0.0930416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9282.13 | + | 16077.1i | 0.368687 | + | 0.638585i | 0.989361 | − | 0.145484i | \(-0.0464740\pi\) |
−0.620673 | + | 0.784069i | \(0.713141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18728.9 | + | 32439.3i | 0.738746 | + | 1.27955i | 0.953060 | + | 0.302781i | \(0.0979150\pi\) |
−0.214314 | + | 0.976765i | \(0.568752\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −811.888 | + | 1406.23i | −0.0319133 | + | 0.0552755i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60474.4 | 2.36071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6943.06 | + | 12025.7i | −0.270100 | + | 0.467826i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3287.38 | − | 674.762i | −0.127010 | − | 0.0260698i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13564.4 | + | 23494.2i | 0.522277 | + | 0.904611i | 0.999664 | + | 0.0259177i | \(0.00825080\pi\) |
−0.477387 | + | 0.878693i | \(0.658416\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23647.8 | −0.904329 | −0.452165 | − | 0.891935i | \(-0.649348\pi\) | ||||
−0.452165 | + | 0.891935i | \(0.649348\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4488.47 | −0.171063 | −0.0855316 | − | 0.996335i | \(-0.527259\pi\) | ||||
−0.0855316 | + | 0.996335i | \(0.527259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20513.4 | − | 35530.3i | −0.776520 | − | 1.34497i | −0.933936 | − | 0.357439i | \(-0.883650\pi\) |
0.157417 | − | 0.987532i | \(-0.449683\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42342.0 | − | 8691.06i | −1.59742 | − | 0.327884i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4855.71 | − | 8410.33i | 0.181960 | − | 0.315163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −683.836 | −0.0255398 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31259.5 | + | 54143.0i | −1.15969 | + | 2.00864i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8710.04 | − | 15086.2i | −0.322057 | − | 0.557819i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −169.797 | − | 294.097i | −0.00623673 | − | 0.0108023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 368.152 | − | 637.659i | 0.0134777 | − | 0.0233441i | −0.859208 | − | 0.511627i | \(-0.829043\pi\) |
0.872686 | + | 0.488283i | \(0.162376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1287.54 | −0.0468256 | −0.0234128 | − | 0.999726i | \(-0.507453\pi\) | ||||
−0.0234128 | + | 0.999726i | \(0.507453\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29394.5 | − | 50912.8i | 1.06552 | − | 1.84553i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11031.5 | + | 33160.5i | 0.397264 | + | 1.19417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17140.0 | − | 29687.3i | −0.615230 | − | 1.06561i | −0.990344 | − | 0.138631i | \(-0.955730\pi\) |
0.375114 | − | 0.926979i | \(-0.377603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2911.81 | −0.103839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36745.4 | −1.30614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15737.9 | − | 27258.9i | −0.555806 | − | 0.962685i | −0.997840 | − | 0.0656866i | \(-0.979076\pi\) |
0.442034 | − | 0.896998i | \(-0.354257\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1397.22 | − | 11715.1i | −0.0491858 | − | 0.412402i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1145.35 | + | 1983.81i | −0.0400609 | + | 0.0693876i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52560.6 | 1.83253 | 0.916264 | − | 0.400575i | \(-0.131190\pi\) | ||||
0.916264 | + | 0.400575i | \(0.131190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7988.37 | − | 13836.3i | 0.276741 | − | 0.479330i | −0.693832 | − | 0.720137i | \(-0.744079\pi\) |
0.970573 | + | 0.240807i | \(0.0774122\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.2846 | + | 145.985i | 0.00291059 | + | 0.00504129i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4252.22 | − | 7365.06i | −0.145912 | − | 0.252727i | 0.783801 | − | 0.621012i | \(-0.213278\pi\) |
−0.929713 | + | 0.368285i | \(0.879945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7417.27 | − | 12847.1i | 0.253714 | − | 0.439446i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29417.5 | −0.999923 | −0.499961 | − | 0.866048i | \(-0.666652\pi\) | ||||
−0.499961 | + | 0.866048i | \(0.666652\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −100.018 | + | 173.237i | −0.00338902 | + | 0.00586995i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36239.3 | + | 40818.2i | −1.22026 | + | 1.37444i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23136.0 | − | 40072.7i | −0.776610 | − | 1.34513i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1191.42 | −0.0397441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3461.97 | 0.115129 | 0.0575643 | − | 0.998342i | \(-0.481667\pi\) | ||||
0.0575643 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21779.4 | − | 37723.0i | −0.719809 | − | 1.24675i | −0.961075 | − | 0.276287i | \(-0.910896\pi\) |
0.241266 | − | 0.970459i | \(-0.422437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17333.5 | − | 3557.84i | −0.571106 | − | 0.117224i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2752.47 | + | 4767.42i | −0.0901325 | + | 0.156114i | −0.907567 | − | 0.419908i | \(-0.862062\pi\) |
0.817434 | + | 0.576022i | \(0.195396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61263.4 | 1.99999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15394.9 | + | 26664.7i | −0.499511 | + | 0.865179i | −1.00000 | 0.000564108i | \(-0.999820\pi\) | |
0.500488 | + | 0.865743i | \(0.333154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −473.530 | − | 820.178i | −0.0153177 | − | 0.0265310i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 205.655 | + | 356.206i | 0.00661220 | + | 0.0114527i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10814.6 | − | 18731.4i | 0.346656 | − | 0.600426i | −0.638997 | − | 0.769209i | \(-0.720650\pi\) |
0.985653 | + | 0.168783i | \(0.0539838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 964.114 | 0.0307181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19097.9 | − | 33078.5i | 0.606656 | − | 1.05076i | −0.385131 | − | 0.922862i | \(-0.625844\pi\) |
0.991787 | − | 0.127898i | \(-0.0408229\pi\) | |||||||
\(998\) | 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.j.361.3 | 8 | ||
3.2 | odd | 2 | 168.4.q.f.25.2 | ✓ | 8 | ||
7.2 | even | 3 | inner | 504.4.s.j.289.3 | 8 | ||
12.11 | even | 2 | 336.4.q.m.193.2 | 8 | |||
21.2 | odd | 6 | 168.4.q.f.121.2 | yes | 8 | ||
21.11 | odd | 6 | 1176.4.a.bd.1.3 | 4 | |||
21.17 | even | 6 | 1176.4.a.ba.1.2 | 4 | |||
84.11 | even | 6 | 2352.4.a.cm.1.3 | 4 | |||
84.23 | even | 6 | 336.4.q.m.289.2 | 8 | |||
84.59 | odd | 6 | 2352.4.a.cp.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.2 | ✓ | 8 | 3.2 | odd | 2 | ||
168.4.q.f.121.2 | yes | 8 | 21.2 | odd | 6 | ||
336.4.q.m.193.2 | 8 | 12.11 | even | 2 | |||
336.4.q.m.289.2 | 8 | 84.23 | even | 6 | |||
504.4.s.j.289.3 | 8 | 7.2 | even | 3 | inner | ||
504.4.s.j.361.3 | 8 | 1.1 | even | 1 | trivial | ||
1176.4.a.ba.1.2 | 4 | 21.17 | even | 6 | |||
1176.4.a.bd.1.3 | 4 | 21.11 | odd | 6 | |||
2352.4.a.cm.1.3 | 4 | 84.11 | even | 6 | |||
2352.4.a.cp.1.2 | 4 | 84.59 | odd | 6 |