Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.8957735523\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 136.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.136 |
Dual form | 405.4.e.k.271.1 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 2.59808i | 0.530330 | − | 0.918559i | −0.469044 | − | 0.883175i | \(-0.655401\pi\) |
0.999374 | − | 0.0353837i | \(-0.0112653\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0000 | + | 17.3205i | −0.539949 | + | 0.935220i | 0.458957 | + | 0.888459i | \(0.348223\pi\) |
−0.998906 | + | 0.0467610i | \(0.985110\pi\) | |||||||
\(8\) | 21.0000 | 0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −15.0000 | −0.474342 | ||||||||
\(11\) | −12.0000 | + | 20.7846i | −0.328921 | + | 0.569709i | −0.982298 | − | 0.187324i | \(-0.940018\pi\) |
0.653377 | + | 0.757033i | \(0.273352\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.0000 | − | 64.0859i | −0.789381 | − | 1.36725i | −0.926347 | − | 0.376672i | \(-0.877068\pi\) |
0.136966 | − | 0.990576i | \(-0.456265\pi\) | |||||||
\(14\) | 30.0000 | + | 51.9615i | 0.572703 | + | 0.991950i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 35.5000 | − | 61.4878i | 0.554688 | − | 0.960747i | ||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −124.000 | −1.49724 | −0.748620 | − | 0.663000i | \(-0.769283\pi\) | ||||
−0.748620 | + | 0.663000i | \(0.769283\pi\) | |||||||
\(20\) | −2.50000 | + | 4.33013i | −0.0279508 | + | 0.0484123i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 36.0000 | + | 62.3538i | 0.348874 | + | 0.604267i | ||||
\(23\) | −60.0000 | − | 103.923i | −0.543951 | − | 0.942150i | −0.998672 | − | 0.0515165i | \(-0.983595\pi\) |
0.454721 | − | 0.890634i | \(-0.349739\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −222.000 | −1.67453 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 20.0000 | 0.134987 | ||||||||
\(29\) | −39.0000 | + | 67.5500i | −0.249728 | + | 0.432542i | −0.963450 | − | 0.267887i | \(-0.913675\pi\) |
0.713722 | + | 0.700429i | \(0.247008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −100.000 | − | 173.205i | −0.579372 | − | 1.00350i | −0.995551 | − | 0.0942192i | \(-0.969965\pi\) |
0.416180 | − | 0.909282i | \(-0.363369\pi\) | |||||||
\(32\) | −22.5000 | − | 38.9711i | −0.124296 | − | 0.215287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −81.0000 | + | 140.296i | −0.408570 | + | 0.707664i | ||||
\(35\) | 100.000 | 0.482945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −70.0000 | −0.311025 | −0.155513 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155513 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(38\) | −186.000 | + | 322.161i | −0.794031 | + | 1.37530i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −52.5000 | − | 90.9327i | −0.207524 | − | 0.359443i | ||||
\(41\) | 165.000 | + | 285.788i | 0.628504 | + | 1.08860i | 0.987852 | + | 0.155397i | \(0.0496658\pi\) |
−0.359348 | + | 0.933204i | \(0.617001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −46.0000 | + | 79.6743i | −0.163138 | + | 0.282563i | −0.935992 | − | 0.352020i | \(-0.885495\pi\) |
0.772854 | + | 0.634583i | \(0.218828\pi\) | |||||||
\(44\) | 24.0000 | 0.0822304 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −360.000 | −1.15389 | ||||||||
\(47\) | −12.0000 | + | 20.7846i | −0.0372421 | + | 0.0645053i | −0.884046 | − | 0.467401i | \(-0.845191\pi\) |
0.846804 | + | 0.531906i | \(0.178524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −28.5000 | − | 49.3634i | −0.0830904 | − | 0.143917i | ||||
\(50\) | 37.5000 | + | 64.9519i | 0.106066 | + | 0.183712i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −37.0000 | + | 64.0859i | −0.0986726 | + | 0.170906i | ||||
\(53\) | −450.000 | −1.16627 | −0.583134 | − | 0.812376i | \(-0.698174\pi\) | ||||
−0.583134 | + | 0.812376i | \(0.698174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 120.000 | 0.294196 | ||||||||
\(56\) | −210.000 | + | 363.731i | −0.501115 | + | 0.867956i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 117.000 | + | 202.650i | 0.264877 | + | 0.458780i | ||||
\(59\) | 12.0000 | + | 20.7846i | 0.0264791 | + | 0.0458631i | 0.878961 | − | 0.476893i | \(-0.158237\pi\) |
−0.852482 | + | 0.522756i | \(0.824904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 161.000 | − | 278.860i | 0.337933 | − | 0.585318i | −0.646110 | − | 0.763244i | \(-0.723605\pi\) |
0.984044 | + | 0.177926i | \(0.0569388\pi\) | |||||||
\(62\) | −600.000 | −1.22903 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | −185.000 | + | 320.429i | −0.353022 | + | 0.611452i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 98.0000 | + | 169.741i | 0.178696 | + | 0.309510i | 0.941434 | − | 0.337197i | \(-0.109479\pi\) |
−0.762738 | + | 0.646707i | \(0.776146\pi\) | |||||||
\(68\) | 27.0000 | + | 46.7654i | 0.0481505 | + | 0.0833990i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 150.000 | − | 259.808i | 0.256120 | − | 0.443614i | ||||
\(71\) | 288.000 | 0.481399 | 0.240699 | − | 0.970600i | \(-0.422623\pi\) | ||||
0.240699 | + | 0.970600i | \(0.422623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −430.000 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(74\) | −105.000 | + | 181.865i | −0.164946 | + | 0.285695i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62.0000 | + | 107.387i | 0.0935775 | + | 0.162081i | ||||
\(77\) | −240.000 | − | 415.692i | −0.355202 | − | 0.615228i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 260.000 | − | 450.333i | 0.370282 | − | 0.641347i | −0.619327 | − | 0.785133i | \(-0.712594\pi\) |
0.989609 | + | 0.143786i | \(0.0459277\pi\) | |||||||
\(80\) | −355.000 | −0.496128 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 990.000 | 1.33326 | ||||||||
\(83\) | 78.0000 | − | 135.100i | 0.103152 | − | 0.178664i | −0.809830 | − | 0.586665i | \(-0.800441\pi\) |
0.912982 | + | 0.408001i | \(0.133774\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 135.000 | + | 233.827i | 0.172268 | + | 0.298377i | ||||
\(86\) | 138.000 | + | 239.023i | 0.173034 | + | 0.299704i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −252.000 | + | 436.477i | −0.305265 | + | 0.528734i | ||||
\(89\) | −1026.00 | −1.22198 | −0.610988 | − | 0.791640i | \(-0.709227\pi\) | ||||
−0.610988 | + | 0.791640i | \(0.709227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1480.00 | 1.70490 | ||||||||
\(92\) | −60.0000 | + | 103.923i | −0.0679938 | + | 0.117769i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 36.0000 | + | 62.3538i | 0.0395012 | + | 0.0684182i | ||||
\(95\) | 310.000 | + | 536.936i | 0.334793 | + | 0.579878i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 143.000 | − | 247.683i | 0.149685 | − | 0.259262i | −0.781426 | − | 0.623998i | \(-0.785507\pi\) |
0.931111 | + | 0.364736i | \(0.118841\pi\) | |||||||
\(98\) | −171.000 | −0.176261 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 25.0000 | 0.0250000 | ||||||||
\(101\) | −867.000 | + | 1501.69i | −0.854156 | + | 1.47944i | 0.0232704 | + | 0.999729i | \(0.492592\pi\) |
−0.877426 | + | 0.479712i | \(0.840741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −226.000 | − | 391.443i | −0.216198 | − | 0.374467i | 0.737444 | − | 0.675408i | \(-0.236032\pi\) |
−0.953643 | + | 0.300941i | \(0.902699\pi\) | |||||||
\(104\) | −777.000 | − | 1345.80i | −0.732607 | − | 1.26891i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −675.000 | + | 1169.13i | −0.618508 | + | 1.07129i | ||||
\(107\) | 1404.00 | 1.26850 | 0.634251 | − | 0.773127i | \(-0.281308\pi\) | ||||
0.634251 | + | 0.773127i | \(0.281308\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1474.00 | −1.29526 | −0.647631 | − | 0.761954i | \(-0.724240\pi\) | ||||
−0.647631 | + | 0.761954i | \(0.724240\pi\) | |||||||
\(110\) | 180.000 | − | 311.769i | 0.156021 | − | 0.270237i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 710.000 | + | 1229.76i | 0.599006 | + | 1.03751i | ||||
\(113\) | 543.000 | + | 940.504i | 0.452046 | + | 0.782966i | 0.998513 | − | 0.0545145i | \(-0.0173611\pi\) |
−0.546467 | + | 0.837480i | \(0.684028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −300.000 | + | 519.615i | −0.243262 | + | 0.421342i | ||||
\(116\) | 78.0000 | 0.0624321 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 72.0000 | 0.0561707 | ||||||||
\(119\) | 540.000 | − | 935.307i | 0.415981 | − | 0.720500i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 377.500 | + | 653.849i | 0.283621 | + | 0.491247i | ||||
\(122\) | −483.000 | − | 836.581i | −0.358433 | − | 0.620823i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −100.000 | + | 173.205i | −0.0724215 | + | 0.125438i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1244.00 | 0.869190 | 0.434595 | − | 0.900626i | \(-0.356891\pi\) | ||||
0.434595 | + | 0.900626i | \(0.356891\pi\) | |||||||
\(128\) | 829.500 | − | 1436.74i | 0.572798 | − | 0.992115i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 555.000 | + | 961.288i | 0.374436 | + | 0.648543i | ||||
\(131\) | 1164.00 | + | 2016.11i | 0.776329 | + | 1.34464i | 0.934044 | + | 0.357157i | \(0.116254\pi\) |
−0.157715 | + | 0.987485i | \(0.550413\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1240.00 | − | 2147.74i | 0.808433 | − | 1.40025i | ||||
\(134\) | 588.000 | 0.379071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1134.00 | −0.714998 | ||||||||
\(137\) | 1059.00 | − | 1834.24i | 0.660412 | − | 1.14387i | −0.320095 | − | 0.947385i | \(-0.603715\pi\) |
0.980507 | − | 0.196482i | \(-0.0629518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1162.00 | − | 2012.64i | −0.709062 | − | 1.22813i | −0.965206 | − | 0.261492i | \(-0.915785\pi\) |
0.256144 | − | 0.966639i | \(-0.417548\pi\) | |||||||
\(140\) | −50.0000 | − | 86.6025i | −0.0301841 | − | 0.0522804i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 432.000 | − | 748.246i | 0.255300 | − | 0.442193i | ||||
\(143\) | 1776.00 | 1.03858 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 390.000 | 0.223364 | ||||||||
\(146\) | −645.000 | + | 1117.17i | −0.365620 | + | 0.633273i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 35.0000 | + | 60.6218i | 0.0194391 | + | 0.0336695i | ||||
\(149\) | 129.000 | + | 223.435i | 0.0709268 | + | 0.122849i | 0.899308 | − | 0.437316i | \(-0.144071\pi\) |
−0.828381 | + | 0.560165i | \(0.810738\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 404.000 | − | 699.749i | 0.217729 | − | 0.377117i | −0.736384 | − | 0.676563i | \(-0.763468\pi\) |
0.954113 | + | 0.299446i | \(0.0968018\pi\) | |||||||
\(152\) | −2604.00 | −1.38955 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1440.00 | −0.753497 | ||||||||
\(155\) | −500.000 | + | 866.025i | −0.259103 | + | 0.448780i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1189.00 | − | 2059.41i | −0.604411 | − | 1.04687i | −0.992144 | − | 0.125099i | \(-0.960075\pi\) |
0.387733 | − | 0.921772i | \(-0.373258\pi\) | |||||||
\(158\) | −780.000 | − | 1351.00i | −0.392743 | − | 0.680252i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −112.500 | + | 194.856i | −0.0555869 | + | 0.0962794i | ||||
\(161\) | 2400.00 | 1.17482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −52.0000 | −0.0249874 | −0.0124937 | − | 0.999922i | \(-0.503977\pi\) | ||||
−0.0124937 | + | 0.999922i | \(0.503977\pi\) | |||||||
\(164\) | 165.000 | − | 285.788i | 0.0785630 | − | 0.136075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −234.000 | − | 405.300i | −0.109409 | − | 0.189502i | ||||
\(167\) | −1860.00 | − | 3221.61i | −0.861863 | − | 1.49279i | −0.870129 | − | 0.492825i | \(-0.835964\pi\) |
0.00826564 | − | 0.999966i | \(-0.497369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1639.50 | + | 2839.70i | −0.746245 | + | 1.29253i | ||||
\(170\) | 810.000 | 0.365436 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 92.0000 | 0.0407845 | ||||||||
\(173\) | 213.000 | − | 368.927i | 0.0936075 | − | 0.162133i | −0.815419 | − | 0.578871i | \(-0.803493\pi\) |
0.909027 | + | 0.416738i | \(0.136827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −250.000 | − | 433.013i | −0.107990 | − | 0.187044i | ||||
\(176\) | 852.000 | + | 1475.71i | 0.364897 | + | 0.632021i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1539.00 | + | 2665.63i | −0.648050 | + | 1.12246i | ||||
\(179\) | 1440.00 | 0.601289 | 0.300644 | − | 0.953736i | \(-0.402798\pi\) | ||||
0.300644 | + | 0.953736i | \(0.402798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3130.00 | −1.28537 | −0.642683 | − | 0.766133i | \(-0.722179\pi\) | ||||
−0.642683 | + | 0.766133i | \(0.722179\pi\) | |||||||
\(182\) | 2220.00 | − | 3845.15i | 0.904161 | − | 1.56605i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1260.00 | − | 2182.38i | −0.504828 | − | 0.874389i | ||||
\(185\) | 175.000 | + | 303.109i | 0.0695473 | + | 0.120460i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 648.000 | − | 1122.37i | 0.253403 | − | 0.438908i | ||||
\(188\) | 24.0000 | 0.00931053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1860.00 | 0.710203 | ||||||||
\(191\) | 1788.00 | − | 3096.91i | 0.677357 | − | 1.17322i | −0.298417 | − | 0.954436i | \(-0.596459\pi\) |
0.975774 | − | 0.218781i | \(-0.0702080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1333.00 | − | 2308.82i | −0.497158 | − | 0.861102i | 0.502837 | − | 0.864381i | \(-0.332290\pi\) |
−0.999995 | + | 0.00327888i | \(0.998956\pi\) | |||||||
\(194\) | −429.000 | − | 743.050i | −0.158765 | − | 0.274989i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.5000 | + | 49.3634i | −0.0103863 | + | 0.0179896i | ||||
\(197\) | 2718.00 | 0.982992 | 0.491496 | − | 0.870880i | \(-0.336450\pi\) | ||||
0.491496 | + | 0.870880i | \(0.336450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3832.00 | −1.36504 | −0.682521 | − | 0.730866i | \(-0.739116\pi\) | ||||
−0.682521 | + | 0.730866i | \(0.739116\pi\) | |||||||
\(200\) | −262.500 | + | 454.663i | −0.0928078 | + | 0.160748i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2601.00 | + | 4505.06i | 0.905969 | + | 1.56918i | ||||
\(203\) | −780.000 | − | 1351.00i | −0.269681 | − | 0.467101i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 825.000 | − | 1428.94i | 0.281076 | − | 0.486837i | ||||
\(206\) | −1356.00 | −0.458626 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5254.00 | −1.75144 | ||||||||
\(209\) | 1488.00 | − | 2577.29i | 0.492474 | − | 0.852990i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −550.000 | − | 952.628i | −0.179448 | − | 0.310813i | 0.762244 | − | 0.647290i | \(-0.224098\pi\) |
−0.941692 | + | 0.336477i | \(0.890765\pi\) | |||||||
\(212\) | 225.000 | + | 389.711i | 0.0728918 | + | 0.126252i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2106.00 | − | 3647.70i | 0.672725 | − | 1.16519i | ||||
\(215\) | 460.000 | 0.145915 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4000.00 | 1.25133 | ||||||||
\(218\) | −2211.00 | + | 3829.56i | −0.686917 | + | 1.18977i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −60.0000 | − | 103.923i | −0.0183873 | − | 0.0318477i | ||||
\(221\) | 1998.00 | + | 3460.64i | 0.608145 | + | 1.05334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −982.000 | + | 1700.87i | −0.294886 | + | 0.510758i | −0.974958 | − | 0.222387i | \(-0.928615\pi\) |
0.680072 | + | 0.733145i | \(0.261948\pi\) | |||||||
\(224\) | 900.000 | 0.268454 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3258.00 | 0.958933 | ||||||||
\(227\) | 330.000 | − | 571.577i | 0.0964884 | − | 0.167123i | −0.813740 | − | 0.581228i | \(-0.802572\pi\) |
0.910229 | + | 0.414106i | \(0.135906\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 953.000 | + | 1650.64i | 0.275004 | + | 0.476322i | 0.970136 | − | 0.242561i | \(-0.0779873\pi\) |
−0.695132 | + | 0.718882i | \(0.744654\pi\) | |||||||
\(230\) | 900.000 | + | 1558.85i | 0.258018 | + | 0.446901i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −819.000 | + | 1418.55i | −0.231767 | + | 0.401433i | ||||
\(233\) | 1458.00 | 0.409943 | 0.204972 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204972 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 120.000 | 0.0333104 | ||||||||
\(236\) | 12.0000 | − | 20.7846i | 0.00330989 | − | 0.00573289i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1620.00 | − | 2805.92i | −0.441214 | − | 0.764206i | ||||
\(239\) | 588.000 | + | 1018.45i | 0.159140 | + | 0.275639i | 0.934559 | − | 0.355808i | \(-0.115794\pi\) |
−0.775419 | + | 0.631448i | \(0.782461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −433.000 | + | 749.978i | −0.115734 | + | 0.200458i | −0.918073 | − | 0.396411i | \(-0.870255\pi\) |
0.802339 | + | 0.596869i | \(0.203589\pi\) | |||||||
\(242\) | 2265.00 | 0.601652 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −322.000 | −0.0844834 | ||||||||
\(245\) | −142.500 | + | 246.817i | −0.0371591 | + | 0.0643615i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4588.00 | + | 7946.65i | 1.18189 | + | 2.04710i | ||||
\(248\) | −2100.00 | − | 3637.31i | −0.537702 | − | 0.931327i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 187.500 | − | 324.760i | 0.0474342 | − | 0.0821584i | ||||
\(251\) | −432.000 | −0.108636 | −0.0543179 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543179 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2880.00 | 0.715668 | ||||||||
\(254\) | 1866.00 | − | 3232.01i | 0.460958 | − | 0.798402i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −756.500 | − | 1310.30i | −0.184692 | − | 0.319897i | ||||
\(257\) | 1263.00 | + | 2187.58i | 0.306552 | + | 0.530963i | 0.977606 | − | 0.210445i | \(-0.0674914\pi\) |
−0.671054 | + | 0.741409i | \(0.734158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 700.000 | − | 1212.44i | 0.167938 | − | 0.290877i | ||||
\(260\) | 370.000 | 0.0882555 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6984.00 | 1.64684 | ||||||||
\(263\) | 2724.00 | − | 4718.11i | 0.638666 | − | 1.10620i | −0.347060 | − | 0.937843i | \(-0.612820\pi\) |
0.985726 | − | 0.168358i | \(-0.0538466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1125.00 | + | 1948.56i | 0.260786 | + | 0.451694i | ||||
\(266\) | −3720.00 | − | 6443.23i | −0.857473 | − | 1.48519i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 98.0000 | − | 169.741i | 0.0223370 | − | 0.0386887i | ||||
\(269\) | 2574.00 | 0.583418 | 0.291709 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291709 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3184.00 | −0.713706 | −0.356853 | − | 0.934161i | \(-0.616150\pi\) | ||||
−0.356853 | + | 0.934161i | \(0.616150\pi\) | |||||||
\(272\) | −1917.00 | + | 3320.34i | −0.427335 | + | 0.740166i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3177.00 | − | 5502.73i | −0.700473 | − | 1.21325i | ||||
\(275\) | −300.000 | − | 519.615i | −0.0657843 | − | 0.113942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1981.00 | + | 3431.19i | −0.429699 | + | 0.744261i | −0.996846 | − | 0.0793553i | \(-0.974714\pi\) |
0.567147 | + | 0.823617i | \(0.308047\pi\) | |||||||
\(278\) | −6972.00 | −1.50415 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2100.00 | 0.448211 | ||||||||
\(281\) | −4143.00 | + | 7175.89i | −0.879540 | + | 1.52341i | −0.0276929 | + | 0.999616i | \(0.508816\pi\) |
−0.851847 | + | 0.523791i | \(0.824517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1358.00 | + | 2352.12i | 0.285246 | + | 0.494061i | 0.972669 | − | 0.232197i | \(-0.0745912\pi\) |
−0.687423 | + | 0.726258i | \(0.741258\pi\) | |||||||
\(284\) | −144.000 | − | 249.415i | −0.0300874 | − | 0.0521129i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2664.00 | − | 4614.18i | 0.550789 | − | 0.953994i | ||||
\(287\) | −6600.00 | −1.35744 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 585.000 | − | 1013.25i | 0.118456 | − | 0.205173i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 215.000 | + | 372.391i | 0.0430888 | + | 0.0746320i | ||||
\(293\) | 3009.00 | + | 5211.74i | 0.599958 | + | 1.03916i | 0.992827 | + | 0.119563i | \(0.0381493\pi\) |
−0.392869 | + | 0.919595i | \(0.628517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 60.0000 | − | 103.923i | 0.0118418 | − | 0.0205106i | ||||
\(296\) | −1470.00 | −0.288655 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 774.000 | 0.150458 | ||||||||
\(299\) | −4440.00 | + | 7690.31i | −0.858769 | + | 1.48743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −920.000 | − | 1593.49i | −0.176172 | − | 0.305140i | ||||
\(302\) | −1212.00 | − | 2099.25i | −0.230936 | − | 0.399993i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4402.00 | + | 7624.49i | −0.830500 | + | 1.43847i | ||||
\(305\) | −1610.00 | −0.302257 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9236.00 | 1.71702 | 0.858512 | − | 0.512793i | \(-0.171389\pi\) | ||||
0.858512 | + | 0.512793i | \(0.171389\pi\) | |||||||
\(308\) | −240.000 | + | 415.692i | −0.0444002 | + | 0.0769034i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1500.00 | + | 2598.08i | 0.274820 | + | 0.476003i | ||||
\(311\) | 768.000 | + | 1330.22i | 0.140030 | + | 0.242539i | 0.927508 | − | 0.373804i | \(-0.121947\pi\) |
−0.787478 | + | 0.616343i | \(0.788613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3671.00 | − | 6358.36i | 0.662930 | − | 1.14823i | −0.316912 | − | 0.948455i | \(-0.602646\pi\) |
0.979842 | − | 0.199774i | \(-0.0640208\pi\) | |||||||
\(314\) | −7134.00 | −1.28215 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −520.000 | −0.0925705 | ||||||||
\(317\) | −1947.00 | + | 3372.30i | −0.344967 | + | 0.597500i | −0.985348 | − | 0.170558i | \(-0.945443\pi\) |
0.640381 | + | 0.768057i | \(0.278776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −936.000 | − | 1621.20i | −0.164282 | − | 0.284545i | ||||
\(320\) | −1082.50 | − | 1874.94i | −0.189105 | − | 0.327539i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3600.00 | − | 6235.38i | 0.623044 | − | 1.07914i | ||||
\(323\) | 6696.00 | 1.15348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1850.00 | 0.315752 | ||||||||
\(326\) | −78.0000 | + | 135.100i | −0.0132516 | + | 0.0229524i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3465.00 | + | 6001.56i | 0.583301 | + | 1.01031i | ||||
\(329\) | −240.000 | − | 415.692i | −0.0402177 | − | 0.0696591i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1846.00 | + | 3197.37i | −0.306542 | + | 0.530946i | −0.977603 | − | 0.210456i | \(-0.932505\pi\) |
0.671062 | + | 0.741402i | \(0.265839\pi\) | |||||||
\(332\) | −156.000 | −0.0257880 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11160.0 | −1.82829 | ||||||||
\(335\) | 490.000 | − | 848.705i | 0.0799151 | − | 0.138417i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4499.00 | + | 7792.50i | 0.727229 | + | 1.25960i | 0.958050 | + | 0.286601i | \(0.0925255\pi\) |
−0.230821 | + | 0.972996i | \(0.574141\pi\) | |||||||
\(338\) | 4918.50 | + | 8519.09i | 0.791512 | + | 1.37094i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 135.000 | − | 233.827i | 0.0215335 | − | 0.0372972i | ||||
\(341\) | 4800.00 | 0.762271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5720.00 | −0.900440 | ||||||||
\(344\) | −966.000 | + | 1673.16i | −0.151405 | + | 0.262241i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −639.000 | − | 1106.78i | −0.0992857 | − | 0.171968i | ||||
\(347\) | 2622.00 | + | 4541.44i | 0.405638 | + | 0.702585i | 0.994395 | − | 0.105724i | \(-0.0337161\pi\) |
−0.588758 | + | 0.808310i | \(0.700383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3151.00 | + | 5457.69i | −0.483293 | + | 0.837088i | −0.999816 | − | 0.0191856i | \(-0.993893\pi\) |
0.516523 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(350\) | −1500.00 | −0.229081 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1080.00 | 0.163535 | ||||||||
\(353\) | 1707.00 | − | 2956.61i | 0.257378 | − | 0.445792i | −0.708161 | − | 0.706051i | \(-0.750475\pi\) |
0.965539 | + | 0.260259i | \(0.0838081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −720.000 | − | 1247.08i | −0.107644 | − | 0.186445i | ||||
\(356\) | 513.000 | + | 888.542i | 0.0763734 | + | 0.132283i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2160.00 | − | 3741.23i | 0.318881 | − | 0.552319i | ||||
\(359\) | −4824.00 | −0.709195 | −0.354597 | − | 0.935019i | \(-0.615382\pi\) | ||||
−0.354597 | + | 0.935019i | \(0.615382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8517.00 | 1.24173 | ||||||||
\(362\) | −4695.00 | + | 8131.98i | −0.681668 | + | 1.18068i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −740.000 | − | 1281.72i | −0.106556 | − | 0.184561i | ||||
\(365\) | 1075.00 | + | 1861.95i | 0.154159 | + | 0.267011i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1754.00 | − | 3038.02i | 0.249477 | − | 0.432107i | −0.713904 | − | 0.700244i | \(-0.753075\pi\) |
0.963381 | + | 0.268137i | \(0.0864080\pi\) | |||||||
\(368\) | −8520.00 | −1.20689 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1050.00 | 0.147532 | ||||||||
\(371\) | 4500.00 | − | 7794.23i | 0.629726 | − | 1.09072i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5401.00 | − | 9354.81i | −0.749740 | − | 1.29859i | −0.947947 | − | 0.318428i | \(-0.896845\pi\) |
0.198207 | − | 0.980160i | \(-0.436488\pi\) | |||||||
\(374\) | −1944.00 | − | 3367.11i | −0.268775 | − | 0.465532i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −252.000 | + | 436.477i | −0.0345636 | + | 0.0598659i | ||||
\(377\) | 5772.00 | 0.788523 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1460.00 | 0.197876 | 0.0989382 | − | 0.995094i | \(-0.468455\pi\) | ||||
0.0989382 | + | 0.995094i | \(0.468455\pi\) | |||||||
\(380\) | 310.000 | − | 536.936i | 0.0418491 | − | 0.0724848i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5364.00 | − | 9290.72i | −0.718445 | − | 1.24438i | ||||
\(383\) | −2436.00 | − | 4219.28i | −0.324997 | − | 0.562911i | 0.656515 | − | 0.754313i | \(-0.272030\pi\) |
−0.981512 | + | 0.191402i | \(0.938697\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1200.00 | + | 2078.46i | −0.158851 | + | 0.275138i | ||||
\(386\) | −7998.00 | −1.05463 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −286.000 | −0.0374213 | ||||||||
\(389\) | −7023.00 | + | 12164.2i | −0.915373 | + | 1.58547i | −0.109020 | + | 0.994040i | \(0.534771\pi\) |
−0.806354 | + | 0.591434i | \(0.798562\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3240.00 | + | 5611.84i | 0.419064 | + | 0.725839i | ||||
\(392\) | −598.500 | − | 1036.63i | −0.0771143 | − | 0.133566i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4077.00 | − | 7061.57i | 0.521310 | − | 0.902936i | ||||
\(395\) | −2600.00 | −0.331190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2734.00 | −0.345631 | −0.172816 | − | 0.984954i | \(-0.555286\pi\) | ||||
−0.172816 | + | 0.984954i | \(0.555286\pi\) | |||||||
\(398\) | −5748.00 | + | 9955.83i | −0.723923 | + | 1.25387i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 887.500 | + | 1537.20i | 0.110937 | + | 0.192149i | ||||
\(401\) | −7971.00 | − | 13806.2i | −0.992650 | − | 1.71932i | −0.601130 | − | 0.799151i | \(-0.705283\pi\) |
−0.391520 | − | 0.920170i | \(-0.628051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7400.00 | + | 12817.2i | −0.914690 | + | 1.58429i | ||||
\(404\) | 1734.00 | 0.213539 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4680.00 | −0.572080 | ||||||||
\(407\) | 840.000 | − | 1454.92i | 0.102303 | − | 0.177194i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4357.00 | − | 7546.55i | −0.526748 | − | 0.912354i | −0.999514 | − | 0.0311660i | \(-0.990078\pi\) |
0.472767 | − | 0.881188i | \(-0.343255\pi\) | |||||||
\(410\) | −2475.00 | − | 4286.83i | −0.298126 | − | 0.516369i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −226.000 | + | 391.443i | −0.0270248 | + | 0.0468083i | ||||
\(413\) | −480.000 | −0.0571895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −780.000 | −0.0922619 | ||||||||
\(416\) | −1665.00 | + | 2883.86i | −0.196234 | + | 0.339887i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4464.00 | − | 7731.87i | −0.522348 | − | 0.904733i | ||||
\(419\) | 5988.00 | + | 10371.5i | 0.698169 | + | 1.20926i | 0.969101 | + | 0.246666i | \(0.0793351\pi\) |
−0.270931 | + | 0.962599i | \(0.587332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5527.00 | + | 9573.04i | −0.639833 | + | 1.10822i | 0.345637 | + | 0.938368i | \(0.387663\pi\) |
−0.985469 | + | 0.169854i | \(0.945670\pi\) | |||||||
\(422\) | −3300.00 | −0.380667 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9450.00 | −1.08239 | ||||||||
\(425\) | 675.000 | − | 1169.13i | 0.0770407 | − | 0.133438i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3220.00 | + | 5577.20i | 0.364934 | + | 0.632084i | ||||
\(428\) | −702.000 | − | 1215.90i | −0.0792814 | − | 0.137319i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 690.000 | − | 1195.12i | 0.0773832 | − | 0.134032i | ||||
\(431\) | −720.000 | −0.0804668 | −0.0402334 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402334 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15622.0 | −1.73382 | −0.866912 | − | 0.498462i | \(-0.833898\pi\) | ||||
−0.866912 | + | 0.498462i | \(0.833898\pi\) | |||||||
\(434\) | 6000.00 | − | 10392.3i | 0.663616 | − | 1.14942i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 737.000 | + | 1276.52i | 0.0809539 | + | 0.140216i | ||||
\(437\) | 7440.00 | + | 12886.5i | 0.814424 | + | 1.41062i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4940.00 | − | 8556.33i | 0.537069 | − | 0.930231i | −0.461991 | − | 0.886885i | \(-0.652865\pi\) |
0.999060 | − | 0.0433464i | \(-0.0138019\pi\) | |||||||
\(440\) | 2520.00 | 0.273037 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11988.0 | 1.29007 | ||||||||
\(443\) | −8058.00 | + | 13956.9i | −0.864215 | + | 1.49686i | 0.00361002 | + | 0.999993i | \(0.498851\pi\) |
−0.867825 | + | 0.496870i | \(0.834482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2565.00 | + | 4442.71i | 0.273242 | + | 0.473269i | ||||
\(446\) | 2946.00 | + | 5102.62i | 0.312774 | + | 0.541740i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4330.00 | + | 7499.78i | −0.456637 | + | 0.790918i | ||||
\(449\) | −9018.00 | −0.947852 | −0.473926 | − | 0.880565i | \(-0.657164\pi\) | ||||
−0.473926 | + | 0.880565i | \(0.657164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7920.00 | −0.826914 | ||||||||
\(452\) | 543.000 | − | 940.504i | 0.0565057 | − | 0.0978707i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −990.000 | − | 1714.73i | −0.102341 | − | 0.177261i | ||||
\(455\) | −3700.00 | − | 6408.59i | −0.381228 | − | 0.660306i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1835.00 | − | 3178.31i | 0.187829 | − | 0.325329i | −0.756697 | − | 0.653765i | \(-0.773188\pi\) |
0.944526 | + | 0.328437i | \(0.106522\pi\) | |||||||
\(458\) | 5718.00 | 0.583372 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 600.000 | 0.0608155 | ||||||||
\(461\) | 8781.00 | − | 15209.1i | 0.887141 | − | 1.53657i | 0.0439008 | − | 0.999036i | \(-0.486021\pi\) |
0.843240 | − | 0.537537i | \(-0.180645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −586.000 | − | 1014.98i | −0.0588202 | − | 0.101879i | 0.835116 | − | 0.550074i | \(-0.185401\pi\) |
−0.893936 | + | 0.448195i | \(0.852067\pi\) | |||||||
\(464\) | 2769.00 | + | 4796.05i | 0.277042 | + | 0.479851i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2187.00 | − | 3788.00i | 0.217405 | − | 0.376557i | ||||
\(467\) | −6876.00 | −0.681335 | −0.340667 | − | 0.940184i | \(-0.610653\pi\) | ||||
−0.340667 | + | 0.940184i | \(0.610653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3920.00 | −0.385946 | ||||||||
\(470\) | 180.000 | − | 311.769i | 0.0176655 | − | 0.0305975i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 252.000 | + | 436.477i | 0.0245747 | + | 0.0425646i | ||||
\(473\) | −1104.00 | − | 1912.18i | −0.107319 | − | 0.185882i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1550.00 | − | 2684.68i | 0.149724 | − | 0.259329i | ||||
\(476\) | −1080.00 | −0.103995 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3528.00 | 0.337588 | ||||||||
\(479\) | 1140.00 | − | 1974.54i | 0.108743 | − | 0.188349i | −0.806518 | − | 0.591209i | \(-0.798651\pi\) |
0.915261 | + | 0.402861i | \(0.131984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2590.00 | + | 4486.01i | 0.245517 | + | 0.425248i | ||||
\(482\) | 1299.00 | + | 2249.93i | 0.122755 | + | 0.212618i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 377.500 | − | 653.849i | 0.0354527 | − | 0.0614058i | ||||
\(485\) | −1430.00 | −0.133882 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3076.00 | −0.286215 | −0.143108 | − | 0.989707i | \(-0.545710\pi\) | ||||
−0.143108 | + | 0.989707i | \(0.545710\pi\) | |||||||
\(488\) | 3381.00 | − | 5856.06i | 0.313628 | − | 0.543220i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 427.500 | + | 740.452i | 0.0394132 | + | 0.0682657i | ||||
\(491\) | −9456.00 | − | 16378.3i | −0.869131 | − | 1.50538i | −0.862886 | − | 0.505398i | \(-0.831346\pi\) |
−0.00624491 | − | 0.999981i | \(-0.501988\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2106.00 | − | 3647.70i | 0.192392 | − | 0.333233i | ||||
\(494\) | 27528.0 | 2.50717 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14200.0 | −1.28548 | ||||||||
\(497\) | −2880.00 | + | 4988.31i | −0.259931 | + | 0.450214i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4978.00 | − | 8622.15i | −0.446585 | − | 0.773508i | 0.551576 | − | 0.834125i | \(-0.314027\pi\) |
−0.998161 | + | 0.0606167i | \(0.980693\pi\) | |||||||
\(500\) | −62.5000 | − | 108.253i | −0.00559017 | − | 0.00968246i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −648.000 | + | 1122.37i | −0.0576129 | + | 0.0997884i | ||||
\(503\) | 10656.0 | 0.944588 | 0.472294 | − | 0.881441i | \(-0.343426\pi\) | ||||
0.472294 | + | 0.881441i | \(0.343426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8670.00 | 0.763980 | ||||||||
\(506\) | 4320.00 | − | 7482.46i | 0.379540 | − | 0.657383i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −622.000 | − | 1077.34i | −0.0543244 | − | 0.0940926i | ||||
\(509\) | −1383.00 | − | 2395.43i | −0.120433 | − | 0.208596i | 0.799506 | − | 0.600659i | \(-0.205095\pi\) |
−0.919939 | + | 0.392063i | \(0.871762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4300.00 | − | 7447.82i | 0.372252 | − | 0.644759i | ||||
\(512\) | 8733.00 | 0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7578.00 | 0.650294 | ||||||||
\(515\) | −1130.00 | + | 1957.22i | −0.0966869 | + | 0.167467i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −288.000 | − | 498.831i | −0.0244995 | − | 0.0424343i | ||||
\(518\) | −2100.00 | − | 3637.31i | −0.178125 | − | 0.308521i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3885.00 | + | 6729.02i | −0.327632 | + | 0.567475i | ||||
\(521\) | −10530.0 | −0.885466 | −0.442733 | − | 0.896654i | \(-0.645991\pi\) | ||||
−0.442733 | + | 0.896654i | \(0.645991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12692.0 | 1.06115 | 0.530576 | − | 0.847637i | \(-0.321976\pi\) | ||||
0.530576 | + | 0.847637i | \(0.321976\pi\) | |||||||
\(524\) | 1164.00 | − | 2016.11i | 0.0970412 | − | 0.168080i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8172.00 | − | 14154.3i | −0.677407 | − | 1.17330i | ||||
\(527\) | 5400.00 | + | 9353.07i | 0.446352 | + | 0.773105i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1116.50 | + | 1933.83i | −0.0917646 | + | 0.158941i | ||||
\(530\) | 6750.00 | 0.553210 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2480.00 | −0.202108 | ||||||||
\(533\) | 12210.0 | − | 21148.3i | 0.992259 | − | 1.71864i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3510.00 | − | 6079.50i | −0.283646 | − | 0.491289i | ||||
\(536\) | 2058.00 | + | 3564.56i | 0.165843 | + | 0.287249i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3861.00 | − | 6687.45i | 0.309404 | − | 0.535904i | ||||
\(539\) | 1368.00 | 0.109321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18110.0 | 1.43920 | 0.719602 | − | 0.694386i | \(-0.244324\pi\) | ||||
0.719602 | + | 0.694386i | \(0.244324\pi\) | |||||||
\(542\) | −4776.00 | + | 8272.27i | −0.378500 | + | 0.655580i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1215.00 | + | 2104.44i | 0.0957586 | + | 0.165859i | ||||
\(545\) | 3685.00 | + | 6382.61i | 0.289629 | + | 0.501653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1810.00 | + | 3135.01i | −0.141481 | + | 0.245052i | −0.928054 | − | 0.372445i | \(-0.878520\pi\) |
0.786574 | + | 0.617496i | \(0.211853\pi\) | |||||||
\(548\) | −2118.00 | −0.165103 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1800.00 | −0.139550 | ||||||||
\(551\) | 4836.00 | − | 8376.20i | 0.373903 | − | 0.647619i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5200.00 | + | 9006.66i | 0.399867 | + | 0.692590i | ||||
\(554\) | 5943.00 | + | 10293.6i | 0.455765 | + | 0.789408i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1162.00 | + | 2012.64i | −0.0886327 | + | 0.153516i | ||||
\(557\) | 14166.0 | 1.07762 | 0.538809 | − | 0.842428i | \(-0.318875\pi\) | ||||
0.538809 | + | 0.842428i | \(0.318875\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6808.00 | 0.515112 | ||||||||
\(560\) | 3550.00 | − | 6148.78i | 0.267884 | − | 0.463988i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12429.0 | + | 21527.7i | 0.932893 | + | 1.61582i | ||||
\(563\) | −6702.00 | − | 11608.2i | −0.501697 | − | 0.868965i | −0.999998 | − | 0.00196107i | \(-0.999376\pi\) |
0.498301 | − | 0.867004i | \(-0.333958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2715.00 | − | 4702.52i | 0.202161 | − | 0.350153i | ||||
\(566\) | 8148.00 | 0.605099 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6048.00 | 0.446775 | ||||||||
\(569\) | −9327.00 | + | 16154.8i | −0.687185 | + | 1.19024i | 0.285560 | + | 0.958361i | \(0.407820\pi\) |
−0.972745 | + | 0.231878i | \(0.925513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3842.00 | + | 6654.54i | 0.281581 | + | 0.487712i | 0.971774 | − | 0.235913i | \(-0.0758079\pi\) |
−0.690193 | + | 0.723625i | \(0.742475\pi\) | |||||||
\(572\) | −888.000 | − | 1538.06i | −0.0649111 | − | 0.112429i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9900.00 | + | 17147.3i | −0.719892 | + | 1.24689i | ||||
\(575\) | 3000.00 | 0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1726.00 | −0.124531 | −0.0622654 | − | 0.998060i | \(-0.519833\pi\) | ||||
−0.0622654 | + | 0.998060i | \(0.519833\pi\) | |||||||
\(578\) | −2995.50 | + | 5188.36i | −0.215565 | + | 0.373369i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −195.000 | − | 337.750i | −0.0139602 | − | 0.0241798i | ||||
\(581\) | 1560.00 | + | 2702.00i | 0.111394 | + | 0.192939i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5400.00 | − | 9353.07i | 0.383611 | − | 0.664434i | ||||
\(584\) | −9030.00 | −0.639836 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18054.0 | 1.27270 | ||||||||
\(587\) | 5298.00 | − | 9176.41i | 0.372524 | − | 0.645231i | −0.617429 | − | 0.786627i | \(-0.711826\pi\) |
0.989953 | + | 0.141396i | \(0.0451589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12400.0 | + | 21477.4i | 0.867459 | + | 1.50248i | ||||
\(590\) | −180.000 | − | 311.769i | −0.0125601 | − | 0.0217548i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2485.00 | + | 4304.15i | −0.172522 | + | 0.298816i | ||||
\(593\) | −2862.00 | −0.198193 | −0.0990963 | − | 0.995078i | \(-0.531595\pi\) | ||||
−0.0990963 | + | 0.995078i | \(0.531595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5400.00 | −0.372065 | ||||||||
\(596\) | 129.000 | − | 223.435i | 0.00886585 | − | 0.0153561i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13320.0 | + | 23070.9i | 0.910862 | + | 1.57766i | ||||
\(599\) | −11796.0 | − | 20431.3i | −0.804627 | − | 1.39365i | −0.916543 | − | 0.399937i | \(-0.869032\pi\) |
0.111916 | − | 0.993718i | \(-0.464301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4787.00 | − | 8291.33i | 0.324902 | − | 0.562746i | −0.656591 | − | 0.754247i | \(-0.728002\pi\) |
0.981492 | + | 0.191501i | \(0.0613355\pi\) | |||||||
\(602\) | −5520.00 | −0.373718 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −808.000 | −0.0544322 | ||||||||
\(605\) | 1887.50 | − | 3269.25i | 0.126839 | − | 0.219692i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8722.00 | − | 15106.9i | −0.583221 | − | 1.01017i | −0.995095 | − | 0.0989273i | \(-0.968459\pi\) |
0.411874 | − | 0.911241i | \(-0.364874\pi\) | |||||||
\(608\) | 2790.00 | + | 4832.42i | 0.186101 | + | 0.322336i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2415.00 | + | 4182.90i | −0.160296 | + | 0.277641i | ||||
\(611\) | 1776.00 | 0.117593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2374.00 | −0.156419 | −0.0782096 | − | 0.996937i | \(-0.524920\pi\) | ||||
−0.0782096 | + | 0.996937i | \(0.524920\pi\) | |||||||
\(614\) | 13854.0 | − | 23995.8i | 0.910589 | − | 1.57719i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5040.00 | − | 8729.54i | −0.329655 | − | 0.570979i | ||||
\(617\) | −6081.00 | − | 10532.6i | −0.396778 | − | 0.687239i | 0.596549 | − | 0.802577i | \(-0.296538\pi\) |
−0.993326 | + | 0.115338i | \(0.963205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4402.00 | + | 7624.49i | −0.285834 | + | 0.495079i | −0.972811 | − | 0.231600i | \(-0.925604\pi\) |
0.686977 | + | 0.726679i | \(0.258937\pi\) | |||||||
\(620\) | 1000.00 | 0.0647758 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4608.00 | 0.297048 | ||||||||
\(623\) | 10260.0 | − | 17770.8i | 0.659805 | − | 1.14281i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −11013.0 | − | 19075.1i | −0.703144 | − | 1.21788i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1189.00 | + | 2059.41i | −0.0755514 | + | 0.130859i | ||||
\(629\) | 3780.00 | 0.239616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12688.0 | −0.800478 | −0.400239 | − | 0.916411i | \(-0.631073\pi\) | ||||
−0.400239 | + | 0.916411i | \(0.631073\pi\) | |||||||
\(632\) | 5460.00 | − | 9457.00i | 0.343651 | − | 0.595220i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5841.00 | + | 10116.9i | 0.365892 | + | 0.633744i | ||||
\(635\) | −3110.00 | − | 5386.68i | −0.194357 | − | 0.336636i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2109.00 | + | 3652.90i | −0.131180 | + | 0.227210i | ||||
\(638\) | −5616.00 | −0.348495 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8295.00 | −0.512326 | ||||||||
\(641\) | −4575.00 | + | 7924.13i | −0.281906 | + | 0.488275i | −0.971854 | − | 0.235583i | \(-0.924300\pi\) |
0.689948 | + | 0.723859i | \(0.257633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12646.0 | − | 21903.5i | −0.775598 | − | 1.34338i | −0.934458 | − | 0.356074i | \(-0.884115\pi\) |
0.158860 | − | 0.987301i | \(-0.449218\pi\) | |||||||
\(644\) | −1200.00 | − | 2078.46i | −0.0734264 | − | 0.127178i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10044.0 | − | 17396.7i | 0.611727 | − | 1.05954i | ||||
\(647\) | 2736.00 | 0.166249 | 0.0831246 | − | 0.996539i | \(-0.473510\pi\) | ||||
0.0831246 | + | 0.996539i | \(0.473510\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −576.000 | −0.0348382 | ||||||||
\(650\) | 2775.00 | − | 4806.44i | 0.167453 | − | 0.290037i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.0000 | + | 45.0333i | 0.00156172 | + | 0.00270497i | ||||
\(653\) | 11109.0 | + | 19241.4i | 0.665741 | + | 1.15310i | 0.979084 | + | 0.203457i | \(0.0652177\pi\) |
−0.313343 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5820.00 | − | 10080.5i | 0.347185 | − | 0.601342i | ||||
\(656\) | 23430.0 | 1.39449 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1440.00 | −0.0853147 | ||||||||
\(659\) | 7260.00 | − | 12574.7i | 0.429149 | − | 0.743309i | −0.567648 | − | 0.823271i | \(-0.692147\pi\) |
0.996798 | + | 0.0799625i | \(0.0254801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5309.00 | + | 9195.46i | 0.312400 | + | 0.541092i | 0.978881 | − | 0.204429i | \(-0.0655339\pi\) |
−0.666482 | + | 0.745521i | \(0.732201\pi\) | |||||||
\(662\) | 5538.00 | + | 9592.10i | 0.325137 | + | 0.563153i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1638.00 | − | 2837.10i | 0.0957330 | − | 0.165814i | ||||
\(665\) | −12400.0 | −0.723085 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9360.00 | 0.543359 | ||||||||
\(668\) | −1860.00 | + | 3221.61i | −0.107733 | + | 0.186599i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1470.00 | − | 2546.11i | −0.0847628 | − | 0.146813i | ||||
\(671\) | 3864.00 | + | 6692.64i | 0.222307 | + | 0.385047i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −685.000 | + | 1186.45i | −0.0392345 | + | 0.0679561i | −0.884976 | − | 0.465637i | \(-0.845825\pi\) |
0.845741 | + | 0.533593i | \(0.179159\pi\) | |||||||
\(674\) | 26994.0 | 1.54269 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3279.00 | 0.186561 | ||||||||
\(677\) | −6879.00 | + | 11914.8i | −0.390519 | + | 0.676399i | −0.992518 | − | 0.122098i | \(-0.961038\pi\) |
0.601999 | + | 0.798497i | \(0.294371\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2860.00 | + | 4953.67i | 0.161645 | + | 0.279977i | ||||
\(680\) | 2835.00 | + | 4910.36i | 0.159878 | + | 0.276917i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7200.00 | − | 12470.8i | 0.404255 | − | 0.700191i | ||||
\(683\) | −11988.0 | −0.671608 | −0.335804 | − | 0.941932i | \(-0.609008\pi\) | ||||
−0.335804 | + | 0.941932i | \(0.609008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10590.0 | −0.590691 | ||||||||
\(686\) | −8580.00 | + | 14861.0i | −0.477530 | + | 0.827107i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3266.00 | + | 5656.88i | 0.180981 | + | 0.313469i | ||||
\(689\) | 16650.0 | + | 28838.6i | 0.920631 | + | 1.59458i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16498.0 | + | 28575.4i | −0.908268 | + | 1.57317i | −0.0917997 | + | 0.995777i | \(0.529262\pi\) |
−0.816469 | + | 0.577390i | \(0.804071\pi\) | |||||||
\(692\) | −426.000 | −0.0234019 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15732.0 | 0.860488 | ||||||||
\(695\) | −5810.00 | + | 10063.2i | −0.317102 | + | 0.549237i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8910.00 | − | 15432.6i | −0.484204 | − | 0.838666i | ||||
\(698\) | 9453.00 | + | 16373.1i | 0.512609 | + | 0.887865i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −250.000 | + | 433.013i | −0.0134987 | + | 0.0233805i | ||||
\(701\) | 25902.0 | 1.39558 | 0.697792 | − | 0.716300i | \(-0.254166\pi\) | ||||
0.697792 | + | 0.716300i | \(0.254166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8680.00 | 0.465679 | ||||||||
\(704\) | −5196.00 | + | 8999.74i | −0.278170 | + | 0.481804i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5121.00 | − | 8869.83i | −0.272991 | − | 0.472834i | ||||
\(707\) | −17340.0 | − | 30033.8i | −0.922401 | − | 1.59765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13697.0 | − | 23723.9i | 0.725531 | − | 1.25666i | −0.233224 | − | 0.972423i | \(-0.574927\pi\) |
0.958755 | − | 0.284234i | \(-0.0917392\pi\) | |||||||
\(710\) | −4320.00 | −0.228347 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21546.0 | −1.13409 | ||||||||
\(713\) | −12000.0 | + | 20784.6i | −0.630299 | + | 1.09171i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4440.00 | − | 7690.31i | −0.232233 | − | 0.402239i | ||||
\(716\) | −720.000 | − | 1247.08i | −0.0375805 | − | 0.0650914i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7236.00 | + | 12533.1i | −0.376107 | + | 0.651437i | ||||
\(719\) | −34848.0 | −1.80753 | −0.903763 | − | 0.428033i | \(-0.859207\pi\) | ||||
−0.903763 | + | 0.428033i | \(0.859207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9040.00 | 0.466945 | ||||||||
\(722\) | 12775.5 | − | 22127.8i | 0.658525 | − | 1.14060i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1565.00 | + | 2710.66i | 0.0803353 | + | 0.139145i | ||||
\(725\) | −975.000 | − | 1688.75i | −0.0499456 | − | 0.0865084i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14014.0 | + | 24273.0i | −0.714925 | + | 1.23829i | 0.248063 | + | 0.968744i | \(0.420206\pi\) |
−0.962988 | + | 0.269543i | \(0.913127\pi\) | |||||||
\(728\) | 31080.0 | 1.58228 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6450.00 | 0.327021 | ||||||||
\(731\) | 2484.00 | − | 4302.41i | 0.125683 | − | 0.217689i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9001.00 | − | 15590.2i | −0.453560 | − | 0.785589i | 0.545044 | − | 0.838407i | \(-0.316513\pi\) |
−0.998604 | + | 0.0528183i | \(0.983180\pi\) | |||||||
\(734\) | −5262.00 | − | 9114.05i | −0.264610 | − | 0.458318i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2700.00 | + | 4676.54i | −0.135222 | + | 0.234211i | ||||
\(737\) | −4704.00 | −0.235107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15284.0 | 0.760800 | 0.380400 | − | 0.924822i | \(-0.375786\pi\) | ||||
0.380400 | + | 0.924822i | \(0.375786\pi\) | |||||||
\(740\) | 175.000 | − | 303.109i | 0.00869342 | − | 0.0150574i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13500.0 | − | 23382.7i | −0.667925 | − | 1.15688i | ||||
\(743\) | −9384.00 | − | 16253.6i | −0.463345 | − | 0.802538i | 0.535780 | − | 0.844358i | \(-0.320018\pi\) |
−0.999125 | + | 0.0418201i | \(0.986684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 645.000 | − | 1117.17i | 0.0317194 | − | 0.0549397i | ||||
\(746\) | −32406.0 | −1.59044 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1296.00 | −0.0633509 | ||||||||
\(749\) | −14040.0 | + | 24318.0i | −0.684927 | + | 1.18633i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4348.00 | − | 7530.96i | −0.211266 | − | 0.365923i | 0.740845 | − | 0.671676i | \(-0.234425\pi\) |
−0.952111 | + | 0.305753i | \(0.901092\pi\) | |||||||
\(752\) | 852.000 | + | 1475.71i | 0.0413155 | + | 0.0715605i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8658.00 | − | 14996.1i | 0.418177 | − | 0.724305i | ||||
\(755\) | −4040.00 | −0.194743 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38662.0 | −1.85627 | −0.928134 | − | 0.372247i | \(-0.878587\pi\) | ||||
−0.928134 | + | 0.372247i | \(0.878587\pi\) | |||||||
\(758\) | 2190.00 | − | 3793.19i | 0.104940 | − | 0.181761i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6510.00 | + | 11275.7i | 0.310714 | + | 0.538172i | ||||
\(761\) | 11937.0 | + | 20675.5i | 0.568615 | + | 0.984870i | 0.996703 | + | 0.0811330i | \(0.0258538\pi\) |
−0.428088 | + | 0.903737i | \(0.640813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14740.0 | − | 25530.4i | 0.699376 | − | 1.21135i | ||||
\(764\) | −3576.00 | −0.169339 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14616.0 | −0.689422 | ||||||||
\(767\) | 888.000 | − | 1538.06i | 0.0418042 | − | 0.0724070i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11809.0 | − | 20453.8i | −0.553763 | − | 0.959145i | −0.997999 | − | 0.0632352i | \(-0.979858\pi\) |
0.444236 | − | 0.895910i | \(-0.353475\pi\) | |||||||
\(770\) | 3600.00 | + | 6235.38i | 0.168487 | + | 0.291828i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1333.00 | + | 2308.82i | −0.0621447 | + | 0.107638i | ||||
\(773\) | −11538.0 | −0.536860 | −0.268430 | − | 0.963299i | \(-0.586505\pi\) | ||||
−0.268430 | + | 0.963299i | \(0.586505\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5000.00 | 0.231749 | ||||||||
\(776\) | 3003.00 | − | 5201.35i | 0.138919 | − | 0.240615i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21069.0 | + | 36492.6i | 0.970900 | + | 1.68165i | ||||
\(779\) | −20460.0 | − | 35437.8i | −0.941021 | − | 1.62990i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3456.00 | + | 5985.97i | −0.158342 | + | 0.274257i | ||||
\(782\) | 19440.0 | 0.888968 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4047.00 | −0.184357 | ||||||||
\(785\) | −5945.00 | + | 10297.0i | −0.270301 | + | 0.468175i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7442.00 | + | 12889.9i | 0.337076 | + | 0.583832i | 0.983881 | − | 0.178823i | \(-0.0572288\pi\) |
−0.646806 | + | 0.762655i | \(0.723895\pi\) | |||||||
\(788\) | −1359.00 | − | 2353.86i | −0.0614370 | − | 0.106412i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3900.00 | + | 6755.00i | −0.175640 | + | 0.304218i | ||||
\(791\) | −21720.0 | −0.976327 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23828.0 | −1.06703 | ||||||||
\(794\) | −4101.00 | + | 7103.14i | −0.183299 | + | 0.317482i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1916.00 | + | 3318.61i | 0.0853151 | + | 0.147770i | ||||
\(797\) | −5667.00 | − | 9815.53i | −0.251864 | − | 0.436241i | 0.712175 | − | 0.702002i | \(-0.247710\pi\) |
−0.964039 | + | 0.265761i | \(0.914377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 648.000 | − | 1122.37i | 0.0286916 | − | 0.0496953i | ||||
\(800\) | 1125.00 | 0.0497184 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −47826.0 | −2.10573 | ||||||||
\(803\) | 5160.00 | − | 8937.38i | 0.226765 | − | 0.392769i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6000.00 | − | 10392.3i | −0.262698 | − | 0.455007i | ||||
\(806\) | 22200.0 | + | 38451.5i | 0.970176 | + | 1.68039i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18207.0 | + | 31535.4i | −0.792723 | + | 1.37304i | ||||
\(809\) | −44730.0 | −1.94391 | −0.971955 | − | 0.235167i | \(-0.924436\pi\) | ||||
−0.971955 | + | 0.235167i | \(0.924436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42748.0 | −1.85091 | −0.925453 | − | 0.378862i | \(-0.876316\pi\) | ||||
−0.925453 | + | 0.378862i | \(0.876316\pi\) | |||||||
\(812\) | −780.000 | + | 1351.00i | −0.0337101 | + | 0.0583877i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2520.00 | − | 4364.77i | −0.108509 | − | 0.187942i | ||||
\(815\) | 130.000 | + | 225.167i | 0.00558736 | + | 0.00967760i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5704.00 | − | 9879.62i | 0.244257 | − | 0.423065i | ||||
\(818\) | −26142.0 | −1.11740 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1650.00 | −0.0702689 | ||||||||
\(821\) | −15843.0 | + | 27440.9i | −0.673477 | + | 1.16650i | 0.303435 | + | 0.952852i | \(0.401867\pi\) |
−0.976912 | + | 0.213644i | \(0.931467\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5518.00 | − | 9557.46i | −0.233713 | − | 0.404802i | 0.725185 | − | 0.688554i | \(-0.241754\pi\) |
−0.958898 | + | 0.283752i | \(0.908421\pi\) | |||||||
\(824\) | −4746.00 | − | 8220.31i | −0.200649 | − | 0.347534i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −720.000 | + | 1247.08i | −0.0303293 | + | 0.0525319i | ||||
\(827\) | −25884.0 | −1.08836 | −0.544181 | − | 0.838968i | \(-0.683159\pi\) | ||||
−0.544181 | + | 0.838968i | \(0.683159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15950.0 | 0.668234 | 0.334117 | − | 0.942532i | \(-0.391562\pi\) | ||||
0.334117 | + | 0.942532i | \(0.391562\pi\) | |||||||
\(830\) | −1170.00 | + | 2026.50i | −0.0489293 | + | 0.0847480i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16021.0 | − | 27749.2i | −0.667582 | − | 1.15629i | ||||
\(833\) | 1539.00 | + | 2665.63i | 0.0640134 | + | 0.110875i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9300.00 | + | 16108.1i | −0.385437 | + | 0.667596i | ||||
\(836\) | −2976.00 | −0.123119 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35928.0 | 1.48104 | ||||||||
\(839\) | 6900.00 | − | 11951.2i | 0.283927 | − | 0.491775i | −0.688422 | − | 0.725311i | \(-0.741696\pi\) |
0.972348 | + | 0.233535i | \(0.0750294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9152.50 | + | 15852.6i | 0.375272 | + | 0.649990i | ||||
\(842\) | 16581.0 | + | 28719.1i | 0.678645 | + | 1.17545i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −550.000 | + | 952.628i | −0.0224310 | + | 0.0388517i | ||||
\(845\) | 16395.0 | 0.667462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15100.0 | −0.612565 | ||||||||
\(848\) | −15975.0 | + | 27669.5i | −0.646915 | + | 1.12049i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2025.00 | − | 3507.40i | −0.0817140 | − | 0.141533i | ||||
\(851\) | 4200.00 | + | 7274.61i | 0.169182 | + | 0.293032i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13931.0 | − | 24129.2i | 0.559189 | − | 0.968544i | −0.438375 | − | 0.898792i | \(-0.644446\pi\) |
0.997564 | − | 0.0697520i | \(-0.0222208\pi\) | |||||||
\(854\) | 19320.0 | 0.774141 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29484.0 | 1.17727 | ||||||||
\(857\) | −3657.00 | + | 6334.11i | −0.145765 | + | 0.252473i | −0.929658 | − | 0.368423i | \(-0.879898\pi\) |
0.783893 | + | 0.620896i | \(0.213231\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14390.0 | + | 24924.2i | 0.571572 | + | 0.989992i | 0.996405 | + | 0.0847201i | \(0.0269996\pi\) |
−0.424833 | + | 0.905272i | \(0.639667\pi\) | |||||||
\(860\) | −230.000 | − | 398.372i | −0.00911969 | − | 0.0157958i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1080.00 | + | 1870.61i | −0.0426740 | + | 0.0739135i | ||||
\(863\) | 32688.0 | 1.28935 | 0.644677 | − | 0.764455i | \(-0.276992\pi\) | ||||
0.644677 | + | 0.764455i | \(0.276992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2130.00 | −0.0837251 | ||||||||
\(866\) | −23433.0 | + | 40587.1i | −0.919499 | + | 1.59262i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2000.00 | − | 3464.10i | −0.0782079 | − | 0.135460i | ||||
\(869\) | 6240.00 | + | 10808.0i | 0.243587 | + | 0.421906i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7252.00 | − | 12560.8i | 0.282118 | − | 0.488642i | ||||
\(872\) | −30954.0 | −1.20210 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44640.0 | 1.72766 | ||||||||
\(875\) | −1250.00 | + | 2165.06i | −0.0482945 | + | 0.0836486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18325.0 | − | 31739.8i | −0.705577 | − | 1.22210i | −0.966483 | − | 0.256731i | \(-0.917354\pi\) |
0.260906 | − | 0.965364i | \(-0.415979\pi\) | |||||||
\(878\) | −14820.0 | − | 25669.0i | −0.569648 | − | 0.986659i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4260.00 | − | 7378.54i | 0.163187 | − | 0.282648i | ||||
\(881\) | 2646.00 | 0.101187 | 0.0505936 | − | 0.998719i | \(-0.483889\pi\) | ||||
0.0505936 | + | 0.998719i | \(0.483889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10892.0 | 0.415113 | 0.207557 | − | 0.978223i | \(-0.433449\pi\) | ||||
0.207557 | + | 0.978223i | \(0.433449\pi\) | |||||||
\(884\) | 1998.00 | − | 3460.64i | 0.0760181 | − | 0.131667i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24174.0 | + | 41870.6i | 0.916638 | + | 1.58766i | ||||
\(887\) | −21732.0 | − | 37640.9i | −0.822648 | − | 1.42487i | −0.903703 | − | 0.428159i | \(-0.859162\pi\) |
0.0810549 | − | 0.996710i | \(-0.474171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12440.0 | + | 21546.7i | −0.469319 | + | 0.812884i | ||||
\(890\) | 15390.0 | 0.579634 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1964.00 | 0.0737215 | ||||||||
\(893\) | 1488.00 | − | 2577.29i | 0.0557604 | − | 0.0965798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3600.00 | − | 6235.38i | −0.134452 | − | 0.232878i | ||||
\(896\) | 16590.0 | + | 28734.7i | 0.618564 | + | 1.07138i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13527.0 | + | 23429.5i | −0.502675 | + | 0.870658i | ||||
\(899\) | 15600.0 | 0.578742 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24300.0 | 0.898502 | ||||||||
\(902\) | −11880.0 | + | 20576.8i | −0.438537 | + | 0.759569i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11403.0 | + | 19750.6i | 0.419533 | + | 0.726653i | ||||
\(905\) | 7825.00 | + | 13553.3i | 0.287416 | + | 0.497820i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7442.00 | − | 12889.9i | 0.272445 | − | 0.471888i | −0.697042 | − | 0.717030i | \(-0.745501\pi\) |
0.969487 | + | 0.245141i | \(0.0788344\pi\) | |||||||
\(908\) | −660.000 | −0.0241221 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22200.0 | −0.808706 | ||||||||
\(911\) | −624.000 | + | 1080.80i | −0.0226938 | + | 0.0393068i | −0.877149 | − | 0.480218i | \(-0.840558\pi\) |
0.854455 | + | 0.519525i | \(0.173891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1872.00 | + | 3242.40i | 0.0678578 | + | 0.117533i | ||||
\(914\) | −5505.00 | − | 9534.94i | −0.199222 | − | 0.345063i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 953.000 | − | 1650.64i | 0.0343756 | − | 0.0595402i | ||||
\(917\) | −46560.0 | −1.67671 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6640.00 | −0.238339 | −0.119169 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119169 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(920\) | −6300.00 | + | 10911.9i | −0.225766 | + | 0.391038i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26343.0 | − | 45627.4i | −0.940955 | − | 1.62978i | ||||
\(923\) | −10656.0 | − | 18456.7i | −0.380007 | − | 0.658192i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 875.000 | − | 1515.54i | 0.0311025 | − | 0.0538711i | ||||
\(926\) | −3516.00 | −0.124776 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3510.00 | 0.124161 | ||||||||
\(929\) | 14973.0 | − | 25934.0i | 0.528792 | − | 0.915895i | −0.470644 | − | 0.882323i | \(-0.655978\pi\) |
0.999436 | − | 0.0335721i | \(-0.0106883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3534.00 | + | 6121.07i | 0.124406 | + | 0.215478i | ||||
\(932\) | −729.000 | − | 1262.67i | −0.0256214 | − | 0.0443776i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10314.0 | + | 17864.4i | −0.361332 | + | 0.625846i | ||||
\(935\) | −6480.00 | −0.226651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45002.0 | 1.56900 | 0.784499 | − | 0.620130i | \(-0.212920\pi\) | ||||
0.784499 | + | 0.620130i | \(0.212920\pi\) | |||||||
\(938\) | −5880.00 | + | 10184.5i | −0.204679 | + | 0.354514i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −60.0000 | − | 103.923i | −0.00208190 | − | 0.00360595i | ||||
\(941\) | 3045.00 | + | 5274.09i | 0.105488 | + | 0.182710i | 0.913937 | − | 0.405855i | \(-0.133026\pi\) |
−0.808450 | + | 0.588566i | \(0.799693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19800.0 | − | 34294.6i | 0.683750 | − | 1.18429i | ||||
\(944\) | 1704.00 | 0.0587505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6624.00 | −0.227658 | ||||||||
\(947\) | 28194.0 | − | 48833.4i | 0.967457 | − | 1.67568i | 0.264594 | − | 0.964360i | \(-0.414762\pi\) |
0.702863 | − | 0.711325i | \(-0.251905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15910.0 | + | 27556.9i | 0.544215 | + | 0.942609i | ||||
\(950\) | −4650.00 | − | 8054.04i | −0.158806 | − | 0.275060i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11340.0 | − | 19641.5i | 0.386063 | − | 0.668680i | ||||
\(953\) | −10854.0 | −0.368936 | −0.184468 | − | 0.982839i | \(-0.559056\pi\) | ||||
−0.184468 | + | 0.982839i | \(0.559056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17880.0 | −0.605846 | ||||||||
\(956\) | 588.000 | − | 1018.45i | 0.0198926 | − | 0.0344549i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3420.00 | − | 5923.61i | −0.115339 | − | 0.199774i | ||||
\(959\) | 21180.0 | + | 36684.8i | 0.713178 | + | 1.23526i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5104.50 | + | 8841.25i | −0.171344 | + | 0.296776i | ||||
\(962\) | 15540.0 | 0.520821 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 866.000 | 0.0289336 | ||||||||
\(965\) | −6665.00 | + | 11544.1i | −0.222336 | + | 0.385097i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21158.0 | + | 36646.7i | 0.703615 | + | 1.21870i | 0.967189 | + | 0.254057i | \(0.0817652\pi\) |
−0.263574 | + | 0.964639i | \(0.584901\pi\) | |||||||
\(968\) | 7927.50 | + | 13730.8i | 0.263223 | + | 0.455915i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2145.00 | + | 3715.25i | −0.0710019 | + | 0.122979i | ||||
\(971\) | −24480.0 | −0.809063 | −0.404532 | − | 0.914524i | \(-0.632565\pi\) | ||||
−0.404532 | + | 0.914524i | \(0.632565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46480.0 | 1.53143 | ||||||||
\(974\) | −4614.00 | + | 7991.68i | −0.151789 | + | 0.262906i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11431.0 | − | 19799.1i | −0.374895 | − | 0.649337i | ||||
\(977\) | −3453.00 | − | 5980.77i | −0.113072 | − | 0.195846i | 0.803935 | − | 0.594717i | \(-0.202736\pi\) |
−0.917007 | + | 0.398870i | \(0.869402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12312.0 | − | 21325.0i | 0.401934 | − | 0.696170i | ||||
\(980\) | 285.000 | 0.00928979 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −56736.0 | −1.84371 | ||||||||
\(983\) | 3480.00 | − | 6027.54i | 0.112914 | − | 0.195573i | −0.804030 | − | 0.594589i | \(-0.797315\pi\) |
0.916944 | + | 0.399016i | \(0.130648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6795.00 | − | 11769.3i | −0.219804 | − | 0.380711i | ||||
\(986\) | −6318.00 | − | 10943.1i | −0.204063 | − | 0.353447i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4588.00 | − | 7946.65i | 0.147737 | − | 0.255887i | ||||
\(989\) | 11040.0 | 0.354956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47792.0 | 1.53195 | 0.765975 | − | 0.642870i | \(-0.222256\pi\) | ||||
0.765975 | + | 0.642870i | \(0.222256\pi\) | |||||||
\(992\) | −4500.00 | + | 7794.23i | −0.144027 | + | 0.249463i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8640.00 | + | 14964.9i | 0.275698 | + | 0.477524i | ||||
\(995\) | 9580.00 | + | 16593.0i | 0.305233 | + | 0.528678i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4969.00 | + | 8606.56i | −0.157843 | + | 0.273393i | −0.934091 | − | 0.357036i | \(-0.883787\pi\) |
0.776247 | + | 0.630428i | \(0.217121\pi\) | |||||||
\(998\) | −29868.0 | −0.947350 | ||||||||
\(999\) | 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 | 405.4.e.k.136.1 | 2 | ||
3.2 | odd | 2 | 405.4.e.d.136.1 | 2 | |||
9.2 | odd | 6 | 15.4.a.b.1.1 | ✓ | 1 | ||
9.4 | even | 3 | inner | 405.4.e.k.271.1 | 2 | ||
9.5 | odd | 6 | 405.4.e.d.271.1 | 2 | |||
9.7 | even | 3 | 45.4.a.b.1.1 | 1 | |||
36.7 | odd | 6 | 720.4.a.r.1.1 | 1 | |||
36.11 | even | 6 | 240.4.a.f.1.1 | 1 | |||
45.2 | even | 12 | 75.4.b.a.49.2 | 2 | |||
45.7 | odd | 12 | 225.4.b.d.199.1 | 2 | |||
45.29 | odd | 6 | 75.4.a.a.1.1 | 1 | |||
45.34 | even | 6 | 225.4.a.g.1.1 | 1 | |||
45.38 | even | 12 | 75.4.b.a.49.1 | 2 | |||
45.43 | odd | 12 | 225.4.b.d.199.2 | 2 | |||
63.20 | even | 6 | 735.4.a.i.1.1 | 1 | |||
63.34 | odd | 6 | 2205.4.a.c.1.1 | 1 | |||
72.11 | even | 6 | 960.4.a.l.1.1 | 1 | |||
72.29 | odd | 6 | 960.4.a.bi.1.1 | 1 | |||
99.65 | even | 6 | 1815.4.a.a.1.1 | 1 | |||
180.47 | odd | 12 | 1200.4.f.m.49.1 | 2 | |||
180.83 | odd | 12 | 1200.4.f.m.49.2 | 2 | |||
180.119 | even | 6 | 1200.4.a.o.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.b.1.1 | ✓ | 1 | 9.2 | odd | 6 | ||
45.4.a.b.1.1 | 1 | 9.7 | even | 3 | |||
75.4.a.a.1.1 | 1 | 45.29 | odd | 6 | |||
75.4.b.a.49.1 | 2 | 45.38 | even | 12 | |||
75.4.b.a.49.2 | 2 | 45.2 | even | 12 | |||
225.4.a.g.1.1 | 1 | 45.34 | even | 6 | |||
225.4.b.d.199.1 | 2 | 45.7 | odd | 12 | |||
225.4.b.d.199.2 | 2 | 45.43 | odd | 12 | |||
240.4.a.f.1.1 | 1 | 36.11 | even | 6 | |||
405.4.e.d.136.1 | 2 | 3.2 | odd | 2 | |||
405.4.e.d.271.1 | 2 | 9.5 | odd | 6 | |||
405.4.e.k.136.1 | 2 | 1.1 | even | 1 | trivial | ||
405.4.e.k.271.1 | 2 | 9.4 | even | 3 | inner | ||
720.4.a.r.1.1 | 1 | 36.7 | odd | 6 | |||
735.4.a.i.1.1 | 1 | 63.20 | even | 6 | |||
960.4.a.l.1.1 | 1 | 72.11 | even | 6 | |||
960.4.a.bi.1.1 | 1 | 72.29 | odd | 6 | |||
1200.4.a.o.1.1 | 1 | 180.119 | even | 6 | |||
1200.4.f.m.49.1 | 2 | 180.47 | odd | 12 | |||
1200.4.f.m.49.2 | 2 | 180.83 | odd | 12 | |||
1815.4.a.a.1.1 | 1 | 99.65 | even | 6 | |||
2205.4.a.c.1.1 | 1 | 63.34 | odd | 6 |