Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(107,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.be (of order \(6\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 179.23 | ||
Character | \(\chi\) | \(=\) | 252.179 |
Dual form | 252.4.be.a.107.23 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.151648 | − | 2.82436i | −0.0536158 | − | 0.998562i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.95401 | + | 0.856618i | −0.994251 | + | 0.107077i | ||||
\(5\) | 14.8202 | − | 8.55643i | 1.32556 | − | 0.765311i | 0.340948 | − | 0.940082i | \(-0.389252\pi\) |
0.984609 | + | 0.174771i | \(0.0559186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.3319 | + | 14.6489i | −0.611863 | + | 0.790964i | ||||
\(8\) | 3.62561 | + | 22.3351i | 0.160231 | + | 0.987080i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −26.4139 | − | 40.5599i | −0.835281 | − | 1.28262i | ||||
\(11\) | −29.5475 | + | 51.1777i | −0.809900 | + | 1.40279i | 0.103033 | + | 0.994678i | \(0.467145\pi\) |
−0.912933 | + | 0.408110i | \(0.866188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −42.9268 | −0.915827 | −0.457913 | − | 0.888997i | \(-0.651403\pi\) | ||||
−0.457913 | + | 0.888997i | \(0.651403\pi\) | |||||||
\(14\) | 43.0921 | + | 29.7838i | 0.822632 | + | 0.568575i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.5324 | − | 13.6271i | 0.977069 | − | 0.212923i | ||||
\(17\) | −81.2955 | − | 46.9360i | −1.15983 | − | 0.669627i | −0.208565 | − | 0.978009i | \(-0.566879\pi\) |
−0.951263 | + | 0.308382i | \(0.900212\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −75.1664 | + | 43.3973i | −0.907597 | + | 0.524002i | −0.879657 | − | 0.475608i | \(-0.842228\pi\) |
−0.0279400 | + | 0.999610i | \(0.508895\pi\) | |||||||
\(20\) | −110.550 | + | 80.7532i | −1.23599 | + | 0.902848i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 149.025 | + | 75.6916i | 1.44419 | + | 0.733523i | ||||
\(23\) | −50.9747 | − | 88.2909i | −0.462129 | − | 0.800431i | 0.536938 | − | 0.843622i | \(-0.319581\pi\) |
−0.999067 | + | 0.0431908i | \(0.986248\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 83.9251 | − | 145.363i | 0.671401 | − | 1.16290i | ||||
\(26\) | 6.50977 | + | 121.241i | 0.0491028 | + | 0.914510i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 77.5852 | − | 126.224i | 0.523651 | − | 0.851933i | ||||
\(29\) | 302.226i | 1.93524i | 0.252415 | + | 0.967619i | \(0.418775\pi\) | ||||
−0.252415 | + | 0.967619i | \(0.581225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 37.3298 | + | 21.5524i | 0.216278 | + | 0.124868i | 0.604226 | − | 0.796813i | \(-0.293482\pi\) |
−0.387947 | + | 0.921681i | \(0.626816\pi\) | |||||||
\(32\) | −47.9707 | − | 174.547i | −0.265003 | − | 0.964247i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −120.236 | + | 236.726i | −0.606478 | + | 1.19406i | ||||
\(35\) | −42.5982 | + | 314.059i | −0.205726 | + | 1.51673i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 43.7307 | + | 75.7438i | 0.194305 | + | 0.336546i | 0.946672 | − | 0.322198i | \(-0.104422\pi\) |
−0.752368 | + | 0.658744i | \(0.771088\pi\) | |||||||
\(38\) | 133.968 | + | 205.716i | 0.571909 | + | 0.878197i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 244.841 | + | 299.987i | 0.967818 | + | 1.18580i | ||||
\(41\) | 423.830i | 1.61442i | 0.590266 | + | 0.807209i | \(0.299023\pi\) | ||||
−0.590266 | + | 0.807209i | \(0.700977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 214.086i | − | 0.759252i | −0.925140 | − | 0.379626i | \(-0.876053\pi\) | ||
0.925140 | − | 0.379626i | \(-0.123947\pi\) | |||||||
\(44\) | 191.181 | − | 432.379i | 0.655037 | − | 1.48144i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −241.635 | + | 157.360i | −0.774502 | + | 0.504380i | ||||
\(47\) | −51.0341 | − | 88.3937i | −0.158385 | − | 0.274331i | 0.775901 | − | 0.630854i | \(-0.217295\pi\) |
−0.934286 | + | 0.356523i | \(0.883962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −86.1780 | − | 331.998i | −0.251248 | − | 0.967923i | ||||
\(50\) | −423.283 | − | 214.991i | −1.19723 | − | 0.608086i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 341.440 | − | 36.7719i | 0.910561 | − | 0.0980643i | ||||
\(53\) | 224.794 | + | 129.785i | 0.582602 | + | 0.336365i | 0.762167 | − | 0.647381i | \(-0.224136\pi\) |
−0.179565 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1011.28i | 2.47930i | ||||||||
\(56\) | −368.268 | − | 199.987i | −0.878784 | − | 0.477220i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 853.594 | − | 45.8320i | 1.93245 | − | 0.103759i | ||||
\(59\) | 185.741 | − | 321.714i | 0.409855 | − | 0.709890i | −0.585018 | − | 0.811020i | \(-0.698912\pi\) |
0.994873 | + | 0.101130i | \(0.0322458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −226.821 | − | 392.865i | −0.476089 | − | 0.824610i | 0.523536 | − | 0.852004i | \(-0.324613\pi\) |
−0.999625 | + | 0.0273937i | \(0.991279\pi\) | |||||||
\(62\) | 55.2106 | − | 108.701i | 0.113093 | − | 0.222662i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −485.710 | + | 161.956i | −0.948652 | + | 0.316321i | ||||
\(65\) | −636.183 | + | 367.300i | −1.21398 | + | 0.700892i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −159.170 | − | 91.8966i | −0.290234 | − | 0.167566i | 0.347814 | − | 0.937564i | \(-0.386924\pi\) |
−0.638047 | + | 0.769997i | \(0.720258\pi\) | |||||||
\(68\) | 686.831 | + | 303.690i | 1.22486 | + | 0.541585i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 893.475 | + | 72.6860i | 1.52558 | + | 0.124109i | ||||
\(71\) | 1002.00 | 1.67486 | 0.837432 | − | 0.546542i | \(-0.184056\pi\) | ||||
0.837432 | + | 0.546542i | \(0.184056\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 216.995 | − | 375.846i | 0.347909 | − | 0.602595i | −0.637969 | − | 0.770062i | \(-0.720225\pi\) |
0.985878 | + | 0.167467i | \(0.0535586\pi\) | |||||||
\(74\) | 207.296 | − | 134.998i | 0.325644 | − | 0.212070i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 560.699 | − | 409.571i | 0.846271 | − | 0.618172i | ||||
\(77\) | −414.867 | − | 1012.78i | −0.614007 | − | 1.49891i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −111.598 | + | 64.4311i | −0.158934 | + | 0.0917604i | −0.577357 | − | 0.816492i | \(-0.695916\pi\) |
0.418424 | + | 0.908252i | \(0.362583\pi\) | |||||||
\(80\) | 810.142 | − | 737.010i | 1.13221 | − | 1.03000i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1197.05 | − | 64.2731i | 1.61210 | − | 0.0865583i | ||||
\(83\) | −802.817 | −1.06169 | −0.530847 | − | 0.847468i | \(-0.678126\pi\) | ||||
−0.530847 | + | 0.847468i | \(0.678126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1606.42 | −2.04989 | ||||||||
\(86\) | −604.656 | + | 32.4658i | −0.758159 | + | 0.0407079i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1250.18 | − | 474.394i | −1.51443 | − | 0.574666i | ||||
\(89\) | −401.231 | + | 231.651i | −0.477869 | + | 0.275898i | −0.719528 | − | 0.694463i | \(-0.755642\pi\) |
0.241659 | + | 0.970361i | \(0.422309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 486.440 | − | 628.828i | 0.560360 | − | 0.724386i | ||||
\(92\) | 481.085 | + | 658.600i | 0.545180 | + | 0.746346i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −241.916 | + | 157.544i | −0.265444 | + | 0.172866i | ||||
\(95\) | −742.653 | + | 1286.31i | −0.802048 | + | 1.38919i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −652.945 | −0.683469 | −0.341734 | − | 0.939797i | \(-0.611014\pi\) | ||||
−0.341734 | + | 0.939797i | \(0.611014\pi\) | |||||||
\(98\) | −924.611 | + | 293.745i | −0.953060 | + | 0.302782i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −543.021 | + | 1228.11i | −0.543021 | + | 1.22811i | ||||
\(101\) | −229.378 | − | 132.432i | −0.225980 | − | 0.130470i | 0.382736 | − | 0.923858i | \(-0.374982\pi\) |
−0.608716 | + | 0.793388i | \(0.708315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1250.99 | + | 722.261i | −1.19674 | + | 0.690937i | −0.959826 | − | 0.280594i | \(-0.909468\pi\) |
−0.236911 | + | 0.971531i | \(0.576135\pi\) | |||||||
\(104\) | −155.636 | − | 958.772i | −0.146744 | − | 0.903994i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 332.470 | − | 654.582i | 0.304645 | − | 0.599798i | ||||
\(107\) | 534.555 | + | 925.876i | 0.482966 | + | 0.836521i | 0.999809 | − | 0.0195590i | \(-0.00622622\pi\) |
−0.516843 | + | 0.856080i | \(0.672893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −344.726 | + | 597.083i | −0.302924 | + | 0.524680i | −0.976797 | − | 0.214167i | \(-0.931296\pi\) |
0.673873 | + | 0.738847i | \(0.264630\pi\) | |||||||
\(110\) | 2856.23 | − | 153.359i | 2.47573 | − | 0.132930i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −508.987 | + | 1070.45i | −0.429417 | + | 0.903106i | ||||
\(113\) | − | 189.378i | − | 0.157656i | −0.996888 | − | 0.0788282i | \(-0.974882\pi\) | ||
0.996888 | − | 0.0788282i | \(-0.0251179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1510.91 | − | 872.324i | −1.22516 | − | 0.707345i | ||||
\(116\) | −258.892 | − | 2403.90i | −0.207220 | − | 1.92411i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −936.802 | − | 475.813i | −0.730844 | − | 0.371205i | ||||
\(119\) | 1608.79 | − | 659.015i | 1.23931 | − | 0.507662i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1080.61 | − | 1871.66i | −0.811875 | − | 1.40621i | ||||
\(122\) | −1075.19 | + | 700.200i | −0.797898 | + | 0.519616i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −315.384 | − | 139.450i | −0.228405 | − | 0.100992i | ||||
\(125\) | − | 733.291i | − | 0.524700i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1180.84i | − | 0.825058i | −0.910944 | − | 0.412529i | \(-0.864646\pi\) | ||
0.910944 | − | 0.412529i | \(-0.135354\pi\) | |||||||
\(128\) | 531.080 | + | 1347.26i | 0.366729 | + | 0.930328i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1133.86 | + | 1741.11i | 0.764972 | + | 1.17466i | ||||
\(131\) | −230.038 | − | 398.438i | −0.153424 | − | 0.265738i | 0.779060 | − | 0.626949i | \(-0.215697\pi\) |
−0.932484 | + | 0.361211i | \(0.882363\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 216.053 | − | 1592.87i | 0.140859 | − | 1.03849i | ||||
\(134\) | −235.411 | + | 463.488i | −0.151764 | + | 0.298800i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 753.572 | − | 1985.91i | 0.475135 | − | 1.25214i | ||||
\(137\) | 191.954 | + | 110.825i | 0.119706 | + | 0.0691125i | 0.558658 | − | 0.829398i | \(-0.311317\pi\) |
−0.438951 | + | 0.898511i | \(0.644650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 330.244i | − | 0.201518i | −0.994911 | − | 0.100759i | \(-0.967873\pi\) | ||
0.994911 | − | 0.100759i | \(-0.0321270\pi\) | |||||||
\(140\) | 69.7973 | − | 2534.52i | 0.0421354 | − | 1.53004i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −151.951 | − | 2830.00i | −0.0897991 | − | 1.67245i | ||||
\(143\) | 1268.38 | − | 2196.89i | 0.741728 | − | 1.28471i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2585.97 | + | 4479.04i | 1.48106 | + | 2.56527i | ||||
\(146\) | −1094.43 | − | 555.875i | −0.620382 | − | 0.315100i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −412.718 | − | 565.006i | −0.229224 | − | 0.313805i | ||||
\(149\) | −750.128 | + | 433.087i | −0.412435 | + | 0.238120i | −0.691836 | − | 0.722055i | \(-0.743198\pi\) |
0.279400 | + | 0.960175i | \(0.409864\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1988.27 | + | 1147.93i | 1.07154 | + | 0.618656i | 0.928603 | − | 0.371075i | \(-0.121011\pi\) |
0.142941 | + | 0.989731i | \(0.454344\pi\) | |||||||
\(152\) | −1241.81 | − | 1521.50i | −0.662656 | − | 0.811910i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2797.53 | + | 1325.32i | −1.46384 | + | 0.693489i | ||||
\(155\) | 737.646 | 0.382252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1068.94 | − | 1851.46i | 0.543381 | − | 0.941163i | −0.455326 | − | 0.890325i | \(-0.650477\pi\) |
0.998707 | − | 0.0508385i | \(-0.0161894\pi\) | |||||||
\(158\) | 198.900 | + | 305.422i | 0.100150 | + | 0.153785i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2204.44 | − | 2176.37i | −1.08923 | − | 1.07536i | ||||
\(161\) | 1871.00 | + | 253.778i | 0.915872 | + | 0.124227i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −330.930 | + | 191.063i | −0.159021 | + | 0.0918110i | −0.577399 | − | 0.816462i | \(-0.695932\pi\) |
0.418378 | + | 0.908273i | \(0.362599\pi\) | |||||||
\(164\) | −363.061 | − | 3371.15i | −0.172868 | − | 1.60514i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 121.746 | + | 2267.44i | 0.0569235 | + | 1.06017i | ||||
\(167\) | −794.247 | −0.368028 | −0.184014 | − | 0.982924i | \(-0.558909\pi\) | ||||
−0.184014 | + | 0.982924i | \(0.558909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −354.291 | −0.161261 | ||||||||
\(170\) | 243.611 | + | 4537.10i | 0.109906 | + | 2.04694i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 183.390 | + | 1702.84i | 0.0812986 | + | 0.754886i | ||||
\(173\) | −26.6193 | + | 15.3687i | −0.0116984 | + | 0.00675409i | −0.505838 | − | 0.862629i | \(-0.668817\pi\) |
0.494139 | + | 0.869383i | \(0.335483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1178.37 | + | 2876.64i | 0.509007 | + | 1.24259i | ||||
\(176\) | −1150.27 | + | 3602.91i | −0.492642 | + | 1.54307i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 715.111 | + | 1098.09i | 0.301122 | + | 0.462390i | ||||
\(179\) | −1473.69 | + | 2552.50i | −0.615355 | + | 1.06583i | 0.374967 | + | 0.927038i | \(0.377654\pi\) |
−0.990322 | + | 0.138788i | \(0.955679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1320.02 | 0.542080 | 0.271040 | − | 0.962568i | \(-0.412632\pi\) | ||||
0.271040 | + | 0.962568i | \(0.412632\pi\) | |||||||
\(182\) | −1849.80 | − | 1278.52i | −0.753388 | − | 0.520716i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1787.17 | − | 1458.63i | 0.716042 | − | 0.584412i | ||||
\(185\) | 1296.19 | + | 748.358i | 0.515125 | + | 0.297407i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4804.15 | − | 2773.68i | 1.87869 | − | 1.08466i | ||||
\(188\) | 481.646 | + | 659.367i | 0.186849 | + | 0.255794i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3745.63 | + | 1902.45i | 1.43019 | + | 0.726412i | ||||
\(191\) | 565.044 | + | 978.684i | 0.214058 | + | 0.370760i | 0.952981 | − | 0.303031i | \(-0.0979984\pi\) |
−0.738923 | + | 0.673790i | \(0.764665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1278.39 | + | 2214.23i | −0.476789 | + | 0.825823i | −0.999646 | − | 0.0265973i | \(-0.991533\pi\) |
0.522857 | + | 0.852420i | \(0.324866\pi\) | |||||||
\(194\) | 99.0179 | + | 1844.15i | 0.0366447 | + | 0.682486i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 969.856 | + | 2566.89i | 0.353446 | + | 0.935455i | ||||
\(197\) | 1494.38i | 0.540456i | 0.962796 | + | 0.270228i | \(0.0870992\pi\) | ||||
−0.962796 | + | 0.270228i | \(0.912901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1996.88 | − | 1152.90i | −0.711331 | − | 0.410687i | 0.100223 | − | 0.994965i | \(-0.468044\pi\) |
−0.811554 | + | 0.584278i | \(0.801378\pi\) | |||||||
\(200\) | 3550.96 | + | 1347.44i | 1.25545 | + | 0.476394i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −339.250 | + | 667.930i | −0.118166 | + | 0.232650i | ||||
\(203\) | −4427.26 | − | 3424.78i | −1.53070 | − | 1.18410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3626.47 | + | 6281.24i | 1.23553 | + | 2.14000i | ||||
\(206\) | 2229.64 | + | 3423.72i | 0.754107 | + | 1.15797i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2684.32 | + | 584.967i | −0.894826 | + | 0.195001i | ||||
\(209\) | − | 5129.12i | − | 1.69755i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1353.94i | − | 0.441749i | −0.975302 | − | 0.220875i | \(-0.929109\pi\) | ||
0.975302 | − | 0.220875i | \(-0.0708911\pi\) | |||||||
\(212\) | −1899.19 | − | 839.749i | −0.615269 | − | 0.272048i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2533.94 | − | 1650.18i | 0.809423 | − | 0.527122i | ||||
\(215\) | −1831.81 | − | 3172.79i | −0.581063 | − | 1.00643i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −738.733 | + | 302.610i | −0.231099 | + | 0.0946661i | ||||
\(218\) | 1738.65 | + | 883.083i | 0.540167 | + | 0.274357i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −866.284 | − | 8043.76i | −0.265477 | − | 2.46505i | ||||
\(221\) | 3489.76 | + | 2014.81i | 1.06220 | + | 0.613262i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4101.54i | 1.23166i | 0.787881 | + | 0.615828i | \(0.211178\pi\) | ||||
−0.787881 | + | 0.615828i | \(0.788822\pi\) | |||||||
\(224\) | 3100.52 | + | 1275.23i | 0.924831 | + | 0.380379i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −534.871 | + | 28.7188i | −0.157430 | + | 0.00845287i | ||||
\(227\) | −216.589 | + | 375.143i | −0.0633282 | + | 0.109688i | −0.895951 | − | 0.444153i | \(-0.853505\pi\) |
0.832623 | + | 0.553840i | \(0.186838\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1354.84 | − | 2346.66i | −0.390963 | − | 0.677169i | 0.601613 | − | 0.798787i | \(-0.294525\pi\) |
−0.992577 | + | 0.121619i | \(0.961191\pi\) | |||||||
\(230\) | −2234.63 | + | 4399.64i | −0.640640 | + | 1.26132i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6750.23 | + | 1095.75i | −1.91023 | + | 0.310085i | ||||
\(233\) | 235.372 | − | 135.892i | 0.0661792 | − | 0.0382086i | −0.466545 | − | 0.884497i | \(-0.654502\pi\) |
0.532724 | + | 0.846289i | \(0.321168\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1512.67 | − | 873.341i | −0.419897 | − | 0.242428i | ||||
\(236\) | −1201.80 | + | 2718.02i | −0.331486 | + | 0.749695i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2105.26 | − | 4443.86i | −0.573378 | − | 1.21030i | ||||
\(239\) | −6354.33 | −1.71978 | −0.859890 | − | 0.510479i | \(-0.829468\pi\) | ||||
−0.859890 | + | 0.510479i | \(0.829468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1169.63 | − | 2025.85i | 0.312623 | − | 0.541479i | −0.666306 | − | 0.745678i | \(-0.732126\pi\) |
0.978929 | + | 0.204199i | \(0.0654590\pi\) | |||||||
\(242\) | −5122.38 | + | 3335.85i | −1.36066 | + | 0.886102i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2140.67 | + | 2930.55i | 0.561649 | + | 0.768891i | ||||
\(245\) | −4117.89 | − | 4182.89i | −1.07381 | − | 1.09075i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3226.65 | − | 1862.91i | 0.831202 | − | 0.479895i | ||||
\(248\) | −346.030 | + | 911.904i | −0.0886006 | + | 0.233492i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2071.08 | + | 111.202i | −0.523945 | + | 0.0281322i | ||||
\(251\) | 5180.74 | 1.30281 | 0.651406 | − | 0.758730i | \(-0.274180\pi\) | ||||
0.651406 | + | 0.758730i | \(0.274180\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6024.70 | 1.49711 | ||||||||
\(254\) | −3335.11 | + | 179.072i | −0.823872 | + | 0.0442361i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3724.60 | − | 1704.27i | 0.909327 | − | 0.416082i | ||||
\(257\) | 3138.15 | − | 1811.81i | 0.761683 | − | 0.439758i | −0.0682169 | − | 0.997671i | \(-0.521731\pi\) |
0.829900 | + | 0.557913i | \(0.188398\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1605.11 | − | 217.713i | −0.385084 | − | 0.0522318i | ||||
\(260\) | 4745.56 | − | 3466.47i | 1.13195 | − | 0.826852i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1090.45 | + | 710.132i | −0.257130 | + | 0.167451i | ||||
\(263\) | −683.315 | + | 1183.54i | −0.160209 | + | 0.277490i | −0.934944 | − | 0.354796i | \(-0.884550\pi\) |
0.774735 | + | 0.632287i | \(0.217884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4441.99 | 1.02970 | ||||||||
\(266\) | −4531.61 | − | 368.656i | −1.04455 | − | 0.0849764i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1344.76 | + | 594.598i | 0.306508 | + | 0.135526i | ||||
\(269\) | 6423.13 | + | 3708.39i | 1.45585 | + | 0.840538i | 0.998804 | − | 0.0489025i | \(-0.0155724\pi\) |
0.457051 | + | 0.889440i | \(0.348906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1610.08 | + | 929.582i | −0.360906 | + | 0.208369i | −0.669478 | − | 0.742832i | \(-0.733482\pi\) |
0.308572 | + | 0.951201i | \(0.400149\pi\) | |||||||
\(272\) | −5723.21 | − | 1827.20i | −1.27581 | − | 0.407317i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 283.900 | − | 558.955i | 0.0625949 | − | 0.123240i | ||||
\(275\) | 4959.55 | + | 8590.19i | 1.08754 | + | 1.88367i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1280.47 | + | 2217.83i | −0.277746 | + | 0.481071i | −0.970824 | − | 0.239792i | \(-0.922921\pi\) |
0.693078 | + | 0.720863i | \(0.256254\pi\) | |||||||
\(278\) | −932.728 | + | 50.0810i | −0.201228 | + | 0.0108045i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7168.97 | + | 187.223i | −1.53010 | + | 0.0399596i | ||||
\(281\) | 6441.96i | 1.36760i | 0.729670 | + | 0.683799i | \(0.239674\pi\) | ||||
−0.729670 | + | 0.683799i | \(0.760326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2799.87 | + | 1616.51i | 0.588110 | + | 0.339545i | 0.764350 | − | 0.644802i | \(-0.223060\pi\) |
−0.176240 | + | 0.984347i | \(0.556393\pi\) | |||||||
\(284\) | −7969.90 | + | 858.330i | −1.66523 | + | 0.179340i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6397.17 | − | 3249.20i | −1.32263 | − | 0.671780i | ||||
\(287\) | −6208.63 | − | 4802.78i | −1.27695 | − | 0.987802i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1949.48 | + | 3376.59i | 0.396799 | + | 0.687277i | ||||
\(290\) | 12258.3 | − | 7982.96i | 2.48217 | − | 1.61647i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1404.02 | + | 3175.36i | −0.281384 | + | 0.636384i | ||||
\(293\) | 1715.41i | 0.342033i | 0.985268 | + | 0.171016i | \(0.0547051\pi\) | ||||
−0.985268 | + | 0.171016i | \(0.945295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6357.14i | − | 1.25467i | ||||||
\(296\) | −1533.19 | + | 1251.35i | −0.301064 | + | 0.245719i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1336.95 | + | 2052.95i | 0.259890 | + | 0.399075i | ||||
\(299\) | 2188.18 | + | 3790.04i | 0.423230 | + | 0.733056i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3136.12 | + | 2425.99i | 0.600541 | + | 0.464558i | ||||
\(302\) | 2940.64 | − | 5789.67i | 0.560314 | − | 1.10317i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4108.96 | + | 3738.04i | −0.775213 | + | 0.705234i | ||||
\(305\) | −6723.05 | − | 3881.55i | −1.26217 | − | 0.728712i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7776.45i | 1.44569i | 0.691012 | + | 0.722843i | \(0.257165\pi\) | ||||
−0.691012 | + | 0.722843i | \(0.742835\pi\) | |||||||
\(308\) | 4167.42 | + | 7700.24i | 0.770976 | + | 1.42455i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −111.863 | − | 2083.38i | −0.0204948 | − | 0.381703i | ||||
\(311\) | 2639.63 | − | 4571.97i | 0.481285 | − | 0.833610i | −0.518484 | − | 0.855087i | \(-0.673504\pi\) |
0.999769 | + | 0.0214770i | \(0.00683688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3791.20 | − | 6566.56i | −0.684637 | − | 1.18583i | −0.973551 | − | 0.228472i | \(-0.926627\pi\) |
0.288913 | − | 0.957355i | \(-0.406706\pi\) | |||||||
\(314\) | −5391.29 | − | 2738.30i | −0.968943 | − | 0.492138i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 832.458 | − | 608.082i | 0.148194 | − | 0.108251i | ||||
\(317\) | 865.378 | − | 499.626i | 0.153326 | − | 0.0885230i | −0.421374 | − | 0.906887i | \(-0.638452\pi\) |
0.574700 | + | 0.818364i | \(0.305119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15467.2 | − | 8930.00i | −2.71473 | − | 1.56735i | ||||
\(320\) | −5812.54 | + | 6556.17i | −1.01541 | + | 1.14532i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 433.025 | − | 5322.86i | 0.0749427 | − | 0.921215i | ||||
\(323\) | 8147.59 | 1.40354 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3602.64 | + | 6239.95i | −0.614887 | + | 1.06502i | ||||
\(326\) | 589.815 | + | 905.692i | 0.100205 | + | 0.153870i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9466.27 | + | 1536.64i | −1.59356 | + | 0.258680i | ||||
\(329\) | 1873.18 | + | 254.073i | 0.313896 | + | 0.0425760i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4142.90 | − | 2391.90i | 0.687959 | − | 0.397193i | −0.114888 | − | 0.993378i | \(-0.536651\pi\) |
0.802847 | + | 0.596185i | \(0.203318\pi\) | |||||||
\(332\) | 6385.61 | − | 687.708i | 1.05559 | − | 0.113683i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 120.446 | + | 2243.24i | 0.0197321 | + | 0.367499i | ||||
\(335\) | −3145.23 | −0.512962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 582.478 | 0.0941532 | 0.0470766 | − | 0.998891i | \(-0.485010\pi\) | ||||
0.0470766 | + | 0.998891i | \(0.485010\pi\) | |||||||
\(338\) | 53.7276 | + | 1000.64i | 0.00864615 | + | 0.161029i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12777.5 | − | 1376.09i | 2.03810 | − | 0.219497i | ||||
\(341\) | −2206.00 | + | 1273.64i | −0.350328 | + | 0.202262i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5839.94 | + | 2499.74i | 0.919321 | + | 0.393508i | ||||
\(344\) | 4781.62 | − | 776.192i | 0.749442 | − | 0.121655i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 47.4434 | + | 72.8518i | 0.00737159 | + | 0.0113195i | ||||
\(347\) | 4960.07 | − | 8591.09i | 0.767350 | − | 1.32909i | −0.171646 | − | 0.985159i | \(-0.554908\pi\) |
0.938995 | − | 0.343930i | \(-0.111758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9238.72 | −1.41701 | −0.708506 | − | 0.705705i | \(-0.750631\pi\) | ||||
−0.708506 | + | 0.705705i | \(0.750631\pi\) | |||||||
\(350\) | 7945.95 | − | 3764.37i | 1.21351 | − | 0.574897i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10350.4 | + | 2702.40i | 1.56726 | + | 0.409200i | ||||
\(353\) | −1995.34 | − | 1152.01i | −0.300853 | − | 0.173698i | 0.341973 | − | 0.939710i | \(-0.388905\pi\) |
−0.642826 | + | 0.766012i | \(0.722238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14849.8 | − | 8573.53i | 2.22013 | − | 1.28179i | ||||
\(356\) | 2992.96 | − | 2186.25i | 0.445580 | − | 0.325481i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7432.66 | + | 3775.14i | 1.09729 | + | 0.557325i | ||||
\(359\) | −3076.29 | − | 5328.29i | −0.452257 | − | 0.783333i | 0.546269 | − | 0.837610i | \(-0.316048\pi\) |
−0.998526 | + | 0.0542774i | \(0.982714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 337.156 | − | 583.971i | 0.0491553 | − | 0.0851394i | ||||
\(362\) | −200.179 | − | 3728.22i | −0.0290640 | − | 0.541300i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3330.48 | + | 5418.40i | −0.479573 | + | 0.780223i | ||||
\(365\) | − | 7426.81i | − | 1.06503i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4297.82 | − | 2481.35i | −0.611293 | − | 0.352930i | 0.162178 | − | 0.986761i | \(-0.448148\pi\) |
−0.773471 | + | 0.633831i | \(0.781481\pi\) | |||||||
\(368\) | −4390.72 | − | 4826.40i | −0.621962 | − | 0.683678i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1917.06 | − | 3774.40i | 0.269361 | − | 0.530329i | ||||
\(371\) | −4448.54 | + | 1822.28i | −0.622525 | + | 0.255008i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1427.95 | − | 2473.29i | −0.198222 | − | 0.343330i | 0.749730 | − | 0.661743i | \(-0.230183\pi\) |
−0.947952 | + | 0.318414i | \(0.896850\pi\) | |||||||
\(374\) | −8562.41 | − | 13148.0i | −1.18383 | − | 1.81783i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1789.25 | − | 1460.33i | 0.245408 | − | 0.200295i | ||||
\(377\) | − | 12973.6i | − | 1.77234i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13658.0i | 1.85109i | 0.378637 | + | 0.925545i | \(0.376393\pi\) | ||||
−0.378637 | + | 0.925545i | \(0.623607\pi\) | |||||||
\(380\) | 4805.19 | − | 10867.5i | 0.648686 | − | 1.46708i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2678.47 | − | 1744.30i | 0.358749 | − | 0.233629i | ||||
\(383\) | 3411.17 | + | 5908.33i | 0.455099 | + | 0.788254i | 0.998694 | − | 0.0510933i | \(-0.0162706\pi\) |
−0.543595 | + | 0.839348i | \(0.682937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14814.2 | − | 11459.7i | −1.96104 | − | 1.51699i | ||||
\(386\) | 6447.65 | + | 3274.84i | 0.850199 | + | 0.431826i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5193.52 | − | 559.324i | 0.679539 | − | 0.0731840i | ||||
\(389\) | −8474.16 | − | 4892.56i | −1.10452 | − | 0.637693i | −0.167113 | − | 0.985938i | \(-0.553445\pi\) |
−0.937404 | + | 0.348244i | \(0.886778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9570.20i | 1.23782i | ||||||||
\(392\) | 7102.74 | − | 3128.48i | 0.915159 | − | 0.403093i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4220.66 | − | 226.620i | 0.539679 | − | 0.0289770i | ||||
\(395\) | −1102.60 | + | 1909.76i | −0.140450 | + | 0.243267i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6754.48 | − | 11699.1i | −0.853898 | − | 1.47899i | −0.877664 | − | 0.479277i | \(-0.840899\pi\) |
0.0237661 | − | 0.999718i | \(-0.492434\pi\) | |||||||
\(398\) | −2953.37 | + | 5814.73i | −0.371958 | + | 0.732327i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3267.17 | − | 10233.5i | 0.408396 | − | 1.27919i | ||||
\(401\) | 857.321 | − | 494.974i | 0.106764 | − | 0.0616405i | −0.445667 | − | 0.895199i | \(-0.647033\pi\) |
0.552431 | + | 0.833558i | \(0.313700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1602.45 | − | 925.174i | −0.198074 | − | 0.114358i | ||||
\(404\) | 1937.92 | + | 856.872i | 0.238651 | + | 0.105522i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9001.42 | + | 13023.5i | −1.10033 | + | 1.59199i | ||||
\(407\) | −5168.53 | −0.629470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2964.96 | + | 5135.45i | −0.358454 | + | 0.620860i | −0.987703 | − | 0.156344i | \(-0.950029\pi\) |
0.629249 | + | 0.777204i | \(0.283363\pi\) | |||||||
\(410\) | 17190.5 | − | 11195.0i | 2.07068 | − | 1.34849i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9331.70 | − | 6816.49i | 1.11587 | − | 0.815108i | ||||
\(413\) | 2607.94 | + | 6366.51i | 0.310722 | + | 0.758536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11897.9 | + | 6869.25i | −1.40734 | + | 0.812526i | ||||
\(416\) | 2059.23 | + | 7492.76i | 0.242697 | + | 0.883084i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14486.5 | + | 777.823i | −1.69511 | + | 0.0910157i | ||||
\(419\) | 16065.6 | 1.87316 | 0.936581 | − | 0.350452i | \(-0.113972\pi\) | ||||
0.936581 | + | 0.350452i | \(0.113972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2720.79 | −0.314972 | −0.157486 | − | 0.987521i | \(-0.550339\pi\) | ||||
−0.157486 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(422\) | −3824.01 | + | 205.323i | −0.441114 | + | 0.0236847i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2083.74 | + | 5491.35i | −0.238669 | + | 0.628970i | ||||
\(425\) | −13645.5 | + | 7878.22i | −1.55742 | + | 0.899176i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8325.32 | + | 1129.23i | 0.943538 | + | 0.127979i | ||||
\(428\) | −5044.97 | − | 6906.51i | −0.569761 | − | 0.779997i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8683.32 | + | 5654.85i | −0.973829 | + | 0.634188i | ||||
\(431\) | −6131.45 | + | 10620.0i | −0.685247 | + | 1.18688i | 0.288112 | + | 0.957597i | \(0.406972\pi\) |
−0.973359 | + | 0.229286i | \(0.926361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11603.6 | 1.28783 | 0.643916 | − | 0.765096i | \(-0.277309\pi\) | ||||
0.643916 | + | 0.765096i | \(0.277309\pi\) | |||||||
\(434\) | 966.708 | + | 2040.56i | 0.106920 | + | 0.225691i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2230.48 | − | 5044.50i | 0.245001 | − | 0.554100i | ||||
\(437\) | 7663.17 | + | 4424.34i | 0.838854 | + | 0.484313i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1082.48 | − | 624.968i | 0.117685 | − | 0.0679455i | −0.440002 | − | 0.897997i | \(-0.645022\pi\) |
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(440\) | −22587.1 | + | 3666.52i | −2.44727 | + | 0.397260i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5161.33 | − | 10161.9i | 0.555429 | − | 1.09355i | ||||
\(443\) | 8070.42 | + | 13978.4i | 0.865547 | + | 1.49917i | 0.866503 | + | 0.499171i | \(0.166362\pi\) |
−0.000956502 | 1.00000i | \(0.500304\pi\) | ||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3964.21 | + | 6866.21i | −0.422295 | + | 0.731437i | ||||
\(446\) | 11584.2 | − | 621.991i | 1.22988 | − | 0.0660362i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3131.52 | − | 8950.36i | 0.330246 | − | 0.943895i | ||||
\(449\) | 7440.67i | 0.782065i | 0.920377 | + | 0.391032i | \(0.127882\pi\) | ||||
−0.920377 | + | 0.391032i | \(0.872118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21690.7 | − | 12523.1i | −2.26469 | − | 1.30752i | ||||
\(452\) | 162.225 | + | 1506.31i | 0.0168814 | + | 0.156750i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1092.38 | + | 554.835i | 0.112925 | + | 0.0573561i | ||||
\(455\) | 1828.60 | − | 13481.5i | 0.188409 | − | 1.38906i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1959.56 | + | 3394.06i | 0.200578 | + | 0.347412i | 0.948715 | − | 0.316133i | \(-0.102385\pi\) |
−0.748136 | + | 0.663545i | \(0.769051\pi\) | |||||||
\(458\) | −6422.35 | + | 4182.43i | −0.655233 | + | 0.426708i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12765.0 | + | 5644.20i | 1.29385 | + | 0.572091i | ||||
\(461\) | − | 149.785i | − | 0.0151328i | −0.999971 | − | 0.00756638i | \(-0.997592\pi\) | ||
0.999971 | − | 0.00756638i | \(-0.00240848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12047.3i | − | 1.20925i | −0.796509 | − | 0.604627i | \(-0.793322\pi\) | ||
0.796509 | − | 0.604627i | \(-0.206678\pi\) | |||||||
\(464\) | 4118.46 | + | 18898.9i | 0.412057 | + | 1.89086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −419.502 | − | 644.168i | −0.0417019 | − | 0.0640354i | ||||
\(467\) | −2768.05 | − | 4794.40i | −0.274283 | − | 0.475071i | 0.695671 | − | 0.718360i | \(-0.255107\pi\) |
−0.969954 | + | 0.243289i | \(0.921774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3149.87 | − | 1290.29i | 0.310122 | − | 0.127037i | ||||
\(470\) | −2237.23 | + | 4404.76i | −0.219566 | + | 0.432291i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7858.92 | + | 2982.14i | 0.766390 | + | 0.290814i | ||||
\(473\) | 10956.4 | + | 6325.70i | 1.06507 | + | 0.614918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14568.5i | 1.40726i | ||||||||
\(476\) | −12231.8 | + | 6619.92i | −1.17782 | + | 0.637445i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 963.624 | + | 17946.9i | 0.0922074 | + | 1.71731i | ||||
\(479\) | −458.120 | + | 793.487i | −0.0436995 | + | 0.0756897i | −0.887048 | − | 0.461678i | \(-0.847248\pi\) |
0.843348 | + | 0.537367i | \(0.180581\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1877.22 | − | 3251.44i | −0.177950 | − | 0.308218i | ||||
\(482\) | −5899.10 | − | 2996.22i | −0.557462 | − | 0.283142i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10198.4 | + | 13961.6i | 0.957780 | + | 1.31119i | ||||
\(485\) | −9676.76 | + | 5586.88i | −0.905977 | + | 0.523066i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3979.10 | − | 2297.33i | −0.370246 | − | 0.213762i | 0.303320 | − | 0.952889i | \(-0.401905\pi\) |
−0.673566 | + | 0.739127i | \(0.735238\pi\) | |||||||
\(488\) | 7952.30 | − | 6490.43i | 0.737671 | − | 0.602065i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11189.5 | + | 12264.7i | −1.03161 | + | 1.13074i | ||||
\(491\) | −225.794 | −0.0207535 | −0.0103767 | − | 0.999946i | \(-0.503303\pi\) | ||||
−0.0103767 | + | 0.999946i | \(0.503303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14185.3 | − | 24569.6i | 1.29589 | − | 2.24454i | ||||
\(494\) | −5750.84 | − | 8830.71i | −0.523770 | − | 0.804276i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2628.02 | + | 839.025i | 0.237906 | + | 0.0759543i | ||||
\(497\) | −11354.5 | + | 14678.1i | −1.02479 | + | 1.32476i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14898.0 | + | 8601.36i | −1.33653 | + | 0.771643i | −0.986290 | − | 0.165019i | \(-0.947232\pi\) |
−0.350235 | + | 0.936662i | \(0.613898\pi\) | |||||||
\(500\) | 628.150 | + | 5832.60i | 0.0561835 | + | 0.521684i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −785.651 | − | 14632.3i | −0.0698512 | − | 1.30094i | ||||
\(503\) | −3932.26 | −0.348570 | −0.174285 | − | 0.984695i | \(-0.555761\pi\) | ||||
−0.174285 | + | 0.984695i | \(0.555761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4532.57 | −0.399400 | ||||||||
\(506\) | −913.635 | − | 17015.9i | −0.0802689 | − | 1.49496i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1011.53 | + | 9392.39i | 0.0883450 | + | 0.820315i | ||||
\(509\) | −18643.2 | + | 10763.6i | −1.62346 | + | 0.937308i | −0.637480 | + | 0.770467i | \(0.720023\pi\) |
−0.985984 | + | 0.166841i | \(0.946643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3046.76 | + | 7437.76i | 0.263759 | + | 0.643889i | ||||
\(512\) | −5378.30 | − | 10261.2i | −0.464237 | − | 0.885711i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5593.10 | − | 8588.50i | −0.479963 | − | 0.737009i | ||||
\(515\) | −12360.0 | + | 21408.1i | −1.05756 | + | 1.83175i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6031.72 | 0.513104 | ||||||||
\(518\) | −371.488 | + | 4566.42i | −0.0315101 | + | 0.387330i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10510.2 | − | 12877.5i | −0.886353 | − | 1.08599i | ||||
\(521\) | 9708.07 | + | 5604.96i | 0.816350 | + | 0.471320i | 0.849156 | − | 0.528142i | \(-0.177111\pi\) |
−0.0328062 | + | 0.999462i | \(0.510444\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8559.92 | − | 4942.07i | 0.715677 | − | 0.413197i | −0.0974822 | − | 0.995237i | \(-0.531079\pi\) |
0.813160 | + | 0.582041i | \(0.197746\pi\) | |||||||
\(524\) | 2171.03 | + | 2972.12i | 0.180996 | + | 0.247782i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3446.35 | + | 1750.44i | 0.285681 | + | 0.145101i | ||||
\(527\) | −2023.16 | − | 3504.22i | −0.167230 | − | 0.289651i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 886.650 | − | 1535.72i | 0.0728734 | − | 0.126220i | ||||
\(530\) | −673.621 | − | 12545.8i | −0.0552079 | − | 1.02821i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −354.005 | + | 12854.8i | −0.0288497 | + | 1.04761i | ||||
\(533\) | − | 18193.7i | − | 1.47853i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15844.4 | + | 9147.76i | 1.28040 | + | 0.739238i | ||||
\(536\) | 1475.43 | − | 3888.24i | 0.118897 | − | 0.313333i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9499.78 | − | 18703.6i | 0.761272 | − | 1.49883i | ||||
\(539\) | 19537.2 | + | 5399.29i | 1.56128 | + | 0.431473i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5817.56 | − | 10076.3i | −0.462323 | − | 0.800767i | 0.536753 | − | 0.843739i | \(-0.319651\pi\) |
−0.999076 | + | 0.0429726i | \(0.986317\pi\) | |||||||
\(542\) | 2869.64 | + | 4406.48i | 0.227420 | + | 0.349215i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4292.75 | + | 16441.5i | −0.338328 | + | 1.29581i | ||||
\(545\) | 11798.5i | 0.927325i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22662.9i | − | 1.77147i | −0.464187 | − | 0.885737i | \(-0.653653\pi\) | ||
0.464187 | − | 0.885737i | \(-0.346347\pi\) | |||||||
\(548\) | −1621.74 | − | 717.070i | −0.126419 | − | 0.0558973i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23509.7 | − | 15310.2i | 1.82265 | − | 1.18696i | ||||
\(551\) | −13115.8 | − | 22717.2i | −1.01407 | − | 1.75642i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 320.770 | − | 2364.91i | 0.0246664 | − | 0.181856i | ||||
\(554\) | 6458.13 | + | 3280.16i | 0.495270 | + | 0.251554i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 282.893 | + | 2626.76i | 0.0215780 | + | 0.200359i | ||||
\(557\) | 21756.9 | + | 12561.3i | 1.65506 | + | 0.955548i | 0.974946 | + | 0.222440i | \(0.0714020\pi\) |
0.680112 | + | 0.733109i | \(0.261931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9190.03i | 0.695343i | ||||||||
\(560\) | 1615.95 | + | 20219.4i | 0.121940 | + | 1.52576i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18194.4 | − | 976.912i | 1.36563 | − | 0.0733248i | ||||
\(563\) | −6462.85 | + | 11194.0i | −0.483795 | + | 0.837958i | −0.999827 | − | 0.0186119i | \(-0.994075\pi\) |
0.516032 | + | 0.856569i | \(0.327409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1620.40 | − | 2806.62i | −0.120656 | − | 0.208983i | ||||
\(566\) | 4141.00 | − | 8152.98i | 0.307525 | − | 0.605469i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3632.85 | + | 22379.7i | 0.268365 | + | 1.65322i | ||||
\(569\) | 5077.65 | − | 2931.58i | 0.374106 | − | 0.215990i | −0.301145 | − | 0.953578i | \(-0.597369\pi\) |
0.675251 | + | 0.737588i | \(0.264035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9167.78 | + | 5293.02i | 0.671908 | + | 0.387926i | 0.796799 | − | 0.604244i | \(-0.206525\pi\) |
−0.124891 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(572\) | −8206.78 | + | 18560.6i | −0.599900 | + | 1.35675i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12623.3 | + | 18263.7i | −0.917917 | + | 1.32807i | ||||
\(575\) | −17112.2 | −1.24110 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12153.9 | + | 21051.1i | −0.876901 | + | 1.51884i | −0.0221772 | + | 0.999754i | \(0.507060\pi\) |
−0.854724 | + | 0.519083i | \(0.826274\pi\) | |||||||
\(578\) | 9241.07 | − | 6018.07i | 0.665013 | − | 0.433077i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24405.7 | − | 33411.1i | −1.74723 | − | 2.39193i | ||||
\(581\) | 9097.41 | − | 11760.4i | 0.649611 | − | 0.839762i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13284.2 | + | 7669.65i | −0.943698 | + | 0.544844i | ||||
\(584\) | 9181.29 | + | 3483.92i | 0.650555 | + | 0.246859i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4844.95 | − | 260.140i | 0.341541 | − | 0.0183383i | ||||
\(587\) | 1958.28 | 0.137695 | 0.0688474 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688474 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3741.26 | −0.261725 | ||||||||
\(590\) | −17954.8 | + | 964.049i | −1.25286 | + | 0.0672699i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3766.75 | + | 4140.52i | 0.261508 | + | 0.287457i | ||||
\(593\) | 20986.1 | − | 12116.3i | 1.45328 | − | 0.839051i | 0.454614 | − | 0.890689i | \(-0.349777\pi\) |
0.998666 | + | 0.0516373i | \(0.0164440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18203.7 | − | 23532.2i | 1.25425 | − | 1.62139i | ||||
\(596\) | 5595.53 | − | 4087.35i | 0.384567 | − | 0.280913i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10372.6 | − | 6754.97i | 0.709310 | − | 0.461925i | ||||
\(599\) | 3792.08 | − | 6568.08i | 0.258665 | − | 0.448020i | −0.707220 | − | 0.706994i | \(-0.750051\pi\) |
0.965884 | + | 0.258973i | \(0.0833842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21603.1 | 1.46624 | 0.733120 | − | 0.680099i | \(-0.238063\pi\) | ||||
0.733120 | + | 0.680099i | \(0.238063\pi\) | |||||||
\(602\) | 6376.29 | − | 9225.41i | 0.431691 | − | 0.624584i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16798.0 | − | 7427.44i | −1.13163 | − | 0.500361i | ||||
\(605\) | −32029.5 | − | 18492.3i | −2.15237 | − | 1.24267i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20178.7 | + | 11650.2i | −1.34931 | + | 0.779022i | −0.988151 | − | 0.153484i | \(-0.950951\pi\) |
−0.361155 | + | 0.932506i | \(0.617617\pi\) | |||||||
\(608\) | 11180.7 | + | 11038.3i | 0.745784 | + | 0.736286i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9943.36 | + | 19576.9i | −0.659991 | + | 1.29942i | ||||
\(611\) | 2190.73 | + | 3794.46i | 0.145053 | + | 0.251240i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5466.30 | + | 9467.90i | −0.360166 | + | 0.623825i | −0.987988 | − | 0.154531i | \(-0.950613\pi\) |
0.627822 | + | 0.778357i | \(0.283947\pi\) | |||||||
\(614\) | 21963.5 | − | 1179.29i | 1.44361 | − | 0.0775116i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21116.2 | − | 12938.0i | 1.38117 | − | 0.846246i | ||||
\(617\) | 16801.8i | 1.09630i | 0.836381 | + | 0.548148i | \(0.184667\pi\) | ||||
−0.836381 | + | 0.548148i | \(0.815333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14271.0 | + | 8239.36i | 0.926655 | + | 0.535004i | 0.885752 | − | 0.464159i | \(-0.153643\pi\) |
0.0409028 | + | 0.999163i | \(0.486977\pi\) | |||||||
\(620\) | −5867.24 | + | 631.881i | −0.380055 | + | 0.0409306i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13313.2 | − | 6761.93i | −0.858216 | − | 0.435898i | ||||
\(623\) | 1153.27 | − | 8502.60i | 0.0741651 | − | 0.546789i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4216.29 | + | 7302.82i | 0.269842 | + | 0.467381i | ||||
\(626\) | −17971.4 | + | 11703.5i | −1.14741 | + | 0.747232i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6916.37 | + | 15642.2i | −0.439480 | + | 0.993936i | ||||
\(629\) | − | 8210.17i | − | 0.520447i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27965.1i | 1.76430i | 0.470967 | + | 0.882151i | \(0.343905\pi\) | ||||
−0.470967 | + | 0.882151i | \(0.656095\pi\) | |||||||
\(632\) | −1843.68 | − | 2258.95i | −0.116041 | − | 0.142177i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1542.36 | − | 2368.37i | −0.0966164 | − | 0.148360i | ||||
\(635\) | −10103.8 | − | 17500.2i | −0.631426 | − | 1.09366i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3699.35 | + | 14251.6i | 0.230100 | + | 0.886450i | ||||
\(638\) | −22876.0 | + | 45039.2i | −1.41954 | + | 2.79486i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19398.4 | + | 15422.5i | 1.19811 | + | 0.952541i | ||||
\(641\) | −13378.0 | − | 7723.82i | −0.824338 | − | 0.475932i | 0.0275718 | − | 0.999620i | \(-0.491222\pi\) |
−0.851910 | + | 0.523688i | \(0.824556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 750.600i | 0.0460354i | 0.999735 | + | 0.0230177i | \(0.00732741\pi\) | ||||
−0.999735 | + | 0.0230177i | \(0.992673\pi\) | |||||||
\(644\) | −15099.3 | − | 415.816i | −0.923908 | − | 0.0254432i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1235.57 | − | 23011.7i | −0.0752520 | − | 1.40152i | ||||
\(647\) | 3864.07 | − | 6692.77i | 0.234795 | − | 0.406677i | −0.724418 | − | 0.689361i | \(-0.757891\pi\) |
0.959213 | + | 0.282684i | \(0.0912248\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10976.4 | + | 19011.6i | 0.663884 | + | 1.14988i | ||||
\(650\) | 18170.2 | + | 9228.86i | 1.09645 | + | 0.556901i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2468.55 | − | 1803.20i | 0.148276 | − | 0.108311i | ||||
\(653\) | 23229.0 | − | 13411.3i | 1.39207 | − | 0.803711i | 0.398523 | − | 0.917158i | \(-0.369523\pi\) |
0.993544 | + | 0.113448i | \(0.0361894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6818.41 | − | 3936.61i | −0.406744 | − | 0.234834i | ||||
\(656\) | 5775.57 | + | 26503.1i | 0.343747 | + | 1.57740i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 433.530 | − | 5329.06i | 0.0256850 | − | 0.315727i | ||||
\(659\) | 17914.2 | 1.05893 | 0.529467 | − | 0.848331i | \(-0.322392\pi\) | ||||
0.529467 | + | 0.848331i | \(0.322392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9620.57 | + | 16663.3i | −0.566107 | + | 0.980527i | 0.430838 | + | 0.902429i | \(0.358218\pi\) |
−0.996946 | + | 0.0780975i | \(0.975115\pi\) | |||||||
\(662\) | −7383.86 | − | 11338.3i | −0.433507 | − | 0.665674i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2910.70 | − | 17931.0i | −0.170116 | − | 1.04798i | ||||
\(665\) | −10427.4 | − | 25455.3i | −0.608054 | − | 1.48438i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26683.8 | − | 15405.9i | 1.54902 | − | 0.894330i | ||||
\(668\) | 6317.45 | − | 680.367i | 0.365912 | − | 0.0394075i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 476.968 | + | 8883.25i | 0.0275028 | + | 0.512224i | ||||
\(671\) | 26807.9 | 1.54234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11564.3 | −0.662363 | −0.331181 | − | 0.943567i | \(-0.607447\pi\) | ||||
−0.331181 | + | 0.943567i | \(0.607447\pi\) | |||||||
\(674\) | −88.3318 | − | 1645.13i | −0.00504809 | − | 0.0940177i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2818.03 | − | 303.492i | 0.160334 | − | 0.0172674i | ||||
\(677\) | −2193.88 | + | 1266.64i | −0.124546 | + | 0.0719067i | −0.560979 | − | 0.827830i | \(-0.689575\pi\) |
0.436433 | + | 0.899737i | \(0.356242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7399.07 | − | 9564.89i | 0.418189 | − | 0.540599i | ||||
\(680\) | −5824.25 | − | 35879.5i | −0.328455 | − | 2.02340i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3931.74 | + | 6037.40i | 0.220754 | + | 0.338979i | ||||
\(683\) | −14481.5 | + | 25082.7i | −0.811303 | + | 1.40522i | 0.100650 | + | 0.994922i | \(0.467908\pi\) |
−0.911953 | + | 0.410295i | \(0.865426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3793.06 | 0.211570 | ||||||||
\(686\) | 6174.54 | − | 16873.2i | 0.343652 | − | 0.939097i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2917.37 | − | 13387.3i | −0.161662 | − | 0.741841i | ||||
\(689\) | −9649.71 | − | 5571.26i | −0.533562 | − | 0.308052i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15172.3 | − | 8759.75i | 0.835286 | − | 0.482253i | −0.0203730 | − | 0.999792i | \(-0.506485\pi\) |
0.855659 | + | 0.517540i | \(0.173152\pi\) | |||||||
\(692\) | 198.565 | − | 145.045i | 0.0109080 | − | 0.00796789i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25016.5 | − | 12706.2i | −1.36832 | − | 0.694986i | ||||
\(695\) | −2825.71 | − | 4894.28i | −0.154224 | − | 0.267123i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19892.9 | − | 34455.5i | 1.08106 | − | 1.87245i | ||||
\(698\) | 1401.04 | + | 26093.5i | 0.0759742 | + | 1.41497i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11836.9 | − | 21871.4i | −0.639134 | − | 1.18094i | ||||
\(701\) | 18033.4i | 0.971630i | 0.874062 | + | 0.485815i | \(0.161477\pi\) | ||||
−0.874062 | + | 0.485815i | \(0.838523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6574.16 | − | 3795.59i | −0.352701 | − | 0.203632i | ||||
\(704\) | 6062.94 | − | 29642.9i | 0.324582 | − | 1.58695i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2951.10 | + | 5810.25i | −0.157317 | + | 0.309733i | ||||
\(707\) | 4539.26 | − | 1859.43i | 0.241466 | − | 0.0989126i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6073.89 | + | 10520.3i | 0.321734 | + | 0.557260i | 0.980846 | − | 0.194785i | \(-0.0624009\pi\) |
−0.659112 | + | 0.752045i | \(0.729068\pi\) | |||||||
\(710\) | −26466.7 | − | 40641.0i | −1.39898 | − | 2.14821i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6628.64 | − | 8121.64i | −0.348903 | − | 0.427488i | ||||
\(713\) | − | 4394.51i | − | 0.230821i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 43411.2i | − | 2.27061i | ||||||
\(716\) | 9535.20 | − | 21565.0i | 0.497692 | − | 1.12559i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14582.5 | + | 9496.57i | −0.757958 | + | 0.493606i | ||||
\(719\) | −16020.2 | − | 27747.8i | −0.830949 | − | 1.43925i | −0.897287 | − | 0.441449i | \(-0.854465\pi\) |
0.0663375 | − | 0.997797i | \(-0.478869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3595.77 | − | 26510.2i | 0.185733 | − | 1.36933i | ||||
\(722\) | −1700.47 | − | 863.691i | −0.0876525 | − | 0.0445198i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10499.5 | + | 1130.76i | −0.538963 | + | 0.0580445i | ||||
\(725\) | 43932.3 | + | 25364.3i | 2.25049 | + | 1.29932i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5922.68i | 0.302146i | 0.988523 | + | 0.151073i | \(0.0482729\pi\) | ||||
−0.988523 | + | 0.151073i | \(0.951727\pi\) | |||||||
\(728\) | 15808.6 | + | 8584.79i | 0.804814 | + | 0.437051i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20976.0 | + | 1126.26i | −1.06350 | + | 0.0571026i | ||||
\(731\) | −10048.3 | + | 17404.2i | −0.508415 | + | 0.880601i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3318.01 | + | 5746.96i | 0.167194 | + | 0.289589i | 0.937432 | − | 0.348167i | \(-0.113196\pi\) |
−0.770238 | + | 0.637757i | \(0.779863\pi\) | |||||||
\(734\) | −6356.46 | + | 12514.9i | −0.319648 | + | 0.629336i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12965.6 | + | 13132.9i | −0.649348 | + | 0.657724i | ||||
\(737\) | 9406.11 | − | 5430.62i | 0.470120 | − | 0.271424i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27402.8 | − | 15821.0i | −1.36405 | − | 0.787532i | −0.373886 | − | 0.927475i | \(-0.621975\pi\) |
−0.990160 | + | 0.139942i | \(0.955308\pi\) | |||||||
\(740\) | −10951.0 | − | 4842.10i | −0.544008 | − | 0.240539i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5821.37 | + | 12287.9i | 0.288018 | + | 0.607957i | ||||
\(743\) | −1062.56 | −0.0524650 | −0.0262325 | − | 0.999656i | \(-0.508351\pi\) | ||||
−0.0262325 | + | 0.999656i | \(0.508351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7411.35 | + | 12836.8i | −0.364471 | + | 0.631283i | ||||
\(746\) | −6768.91 | + | 4408.12i | −0.332208 | + | 0.216344i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −35836.3 | + | 26177.2i | −1.75174 | + | 1.27959i | ||||
\(749\) | −19620.5 | − | 2661.28i | −0.957167 | − | 0.129828i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13065.1 | + | 7543.11i | −0.634821 | + | 0.366514i | −0.782617 | − | 0.622504i | \(-0.786116\pi\) |
0.147796 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(752\) | −4395.84 | − | 4832.03i | −0.213165 | − | 0.234316i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36642.0 | + | 1967.42i | −1.76979 | + | 0.0950255i | ||||
\(755\) | 39288.7 | 1.89386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21390.4 | 1.02701 | 0.513504 | − | 0.858087i | \(-0.328347\pi\) | ||||
0.513504 | + | 0.858087i | \(0.328347\pi\) | |||||||
\(758\) | 38575.0 | − | 2071.21i | 1.84843 | − | 0.0992476i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31422.4 | − | 11923.5i | −1.49975 | − | 0.569095i | ||||
\(761\) | 32800.0 | − | 18937.1i | 1.56242 | − | 0.902061i | 0.565403 | − | 0.824815i | \(-0.308721\pi\) |
0.997012 | − | 0.0772461i | \(-0.0246127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4840.20 | − | 11815.9i | −0.229655 | − | 0.560635i | ||||
\(764\) | −5332.72 | − | 7300.43i | −0.252527 | − | 0.345707i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16169.9 | − | 10530.4i | 0.762720 | − | 0.496707i | ||||
\(767\) | −7973.28 | + | 13810.1i | −0.375357 | + | 0.650137i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8846.40 | −0.414836 | −0.207418 | − | 0.978252i | \(-0.566506\pi\) | ||||
−0.207418 | + | 0.978252i | \(0.566506\pi\) | |||||||
\(770\) | −30119.8 | + | 43578.3i | −1.40967 | + | 2.03955i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8271.55 | − | 18707.1i | 0.385621 | − | 0.872129i | ||||
\(773\) | 8387.68 | + | 4842.63i | 0.390277 | + | 0.225326i | 0.682280 | − | 0.731091i | \(-0.260989\pi\) |
−0.292003 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6265.82 | − | 3617.57i | 0.290419 | − | 0.167674i | ||||
\(776\) | −2367.32 | − | 14583.6i | −0.109513 | − | 0.674638i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12533.3 | + | 24676.0i | −0.577556 | + | 1.13712i | ||||
\(779\) | −18393.1 | − | 31857.8i | −0.845958 | − | 1.46524i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29606.5 | + | 51280.0i | −1.35647 | + | 2.34948i | ||||
\(782\) | 27029.7 | − | 1451.30i | 1.23604 | − | 0.0663664i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9913.08 | − | 19586.2i | −0.451580 | − | 0.892231i | ||||
\(785\) | − | 36585.3i | − | 1.66342i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4876.52 | + | 2815.46i | 0.220876 | + | 0.127523i | 0.606356 | − | 0.795194i | \(-0.292631\pi\) |
−0.385480 | + | 0.922716i | \(0.625964\pi\) | |||||||
\(788\) | −1280.11 | − | 11886.3i | −0.0578706 | − | 0.537349i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5561.06 | + | 2824.53i | 0.250448 | + | 0.127205i | ||||
\(791\) | 2774.17 | + | 2146.00i | 0.124701 | + | 0.0964641i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9736.68 | + | 16864.4i | 0.436015 | + | 0.755200i | ||||
\(794\) | −32018.1 | + | 20851.2i | −1.43108 | + | 0.931967i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16870.8 | + | 7459.59i | 0.751216 | + | 0.332158i | ||||
\(797\) | − | 14199.7i | − | 0.631091i | −0.948910 | − | 0.315545i | \(-0.897813\pi\) | ||
0.948910 | − | 0.315545i | \(-0.102187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9581.35i | 0.424235i | ||||||||
\(800\) | −29398.6 | − | 7675.77i | −1.29925 | − | 0.339224i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1528.00 | − | 2346.32i | −0.0672761 | − | 0.103306i | ||||
\(803\) | 12823.3 | + | 22210.6i | 0.563542 | + | 0.976084i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29900.0 | − | 12248.0i | 1.30911 | − | 0.536257i | ||||
\(806\) | −2370.01 | + | 4666.19i | −0.103573 | + | 0.203920i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2126.23 | − | 5603.33i | 0.0925750 | − | 0.243966i | ||||
\(809\) | −21567.0 | − | 12451.7i | −0.937276 | − | 0.541137i | −0.0481708 | − | 0.998839i | \(-0.515339\pi\) |
−0.889105 | + | 0.457702i | \(0.848673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18557.0i | − | 0.803482i | −0.915753 | − | 0.401741i | \(-0.868405\pi\) | ||
0.915753 | − | 0.401741i | \(-0.131595\pi\) | |||||||
\(812\) | 38148.2 | + | 23448.2i | 1.64869 | + | 1.01339i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 783.798 | + | 14597.8i | 0.0337495 | + | 0.628565i | ||||
\(815\) | −3269.63 | + | 5663.17i | −0.140528 | + | 0.243401i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9290.76 | + | 16092.1i | 0.397849 | + | 0.689095i | ||||
\(818\) | 14954.0 | + | 7595.32i | 0.639186 | + | 0.324650i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34225.6 | − | 46854.5i | −1.45757 | − | 1.99540i | ||||
\(821\) | −5318.09 | + | 3070.40i | −0.226069 | + | 0.130521i | −0.608757 | − | 0.793357i | \(-0.708332\pi\) |
0.382688 | + | 0.923878i | \(0.374998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17282.2 | − | 9977.86i | −0.731978 | − | 0.422608i | 0.0871672 | − | 0.996194i | \(-0.472219\pi\) |
−0.819145 | + | 0.573586i | \(0.805552\pi\) | |||||||
\(824\) | −20667.4 | − | 25322.4i | −0.873764 | − | 1.07057i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17585.8 | − | 8331.23i | 0.740786 | − | 0.350945i | ||||
\(827\) | −10464.3 | −0.439998 | −0.219999 | − | 0.975500i | \(-0.570605\pi\) | ||||
−0.219999 | + | 0.975500i | \(0.570605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6805.40 | − | 11787.3i | 0.285116 | − | 0.493835i | −0.687521 | − | 0.726164i | \(-0.741301\pi\) |
0.972637 | + | 0.232329i | \(0.0746345\pi\) | |||||||
\(830\) | 21205.5 | + | 32562.2i | 0.886813 | + | 1.36175i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20850.0 | − | 6952.27i | 0.868801 | − | 0.289695i | ||||
\(833\) | −8576.74 | + | 31034.8i | −0.356743 | + | 1.29087i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11770.9 | + | 6795.92i | −0.487842 | + | 0.281656i | ||||
\(836\) | 4393.70 | + | 40797.1i | 0.181770 | + | 1.68780i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2436.32 | − | 45374.9i | −0.100431 | − | 1.87047i | ||||
\(839\) | 7552.99 | 0.310797 | 0.155398 | − | 0.987852i | \(-0.450334\pi\) | ||||
0.155398 | + | 0.987852i | \(0.450334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −66951.4 | −2.74515 | ||||||||
\(842\) | 412.603 | + | 7684.48i | 0.0168875 | + | 0.314519i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1159.81 | + | 10769.2i | 0.0473013 | + | 0.439209i | ||||
\(845\) | −5250.66 | + | 3031.47i | −0.213761 | + | 0.123415i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39663.0 | + | 5379.79i | 1.60902 | + | 0.218243i | ||||
\(848\) | 15825.5 | + | 5052.48i | 0.640862 | + | 0.204603i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24320.2 | + | 37345.0i | 0.981385 | + | 1.50697i | ||||
\(851\) | 4458.32 | − | 7722.04i | 0.179588 | − | 0.311055i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29075.2 | 1.16707 | 0.583537 | − | 0.812086i | \(-0.301668\pi\) | ||||
0.583537 | + | 0.812086i | \(0.301668\pi\) | |||||||
\(854\) | 1926.82 | − | 23684.9i | 0.0772065 | − | 0.949042i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18741.4 | + | 15296.2i | −0.748327 | + | 0.610762i | ||||
\(857\) | −18567.6 | − | 10720.0i | −0.740091 | − | 0.427292i | 0.0820116 | − | 0.996631i | \(-0.473866\pi\) |
−0.822102 | + | 0.569340i | \(0.807199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12966.8 | + | 7486.41i | −0.515044 | + | 0.297361i | −0.734905 | − | 0.678170i | \(-0.762773\pi\) |
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(860\) | 17288.1 | + | 23667.3i | 0.685489 | + | 0.938426i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30924.4 | + | 15706.9i | 1.22192 | + | 0.620626i | ||||
\(863\) | −19006.1 | − | 32919.6i | −0.749683 | − | 1.29849i | −0.947975 | − | 0.318346i | \(-0.896873\pi\) |
0.198291 | − | 0.980143i | \(-0.436461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −263.002 | + | 455.532i | −0.0103380 | + | 0.0179059i | ||||
\(866\) | −1759.66 | − | 32772.6i | −0.0690481 | − | 1.28598i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5616.67 | − | 3039.78i | 0.219634 | − | 0.118867i | ||||
\(869\) | − | 7615.11i | − | 0.297267i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6832.64 | + | 3944.82i | 0.265804 | + | 0.153462i | ||||
\(872\) | −14585.7 | − | 5534.68i | −0.566439 | − | 0.214940i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11333.8 | − | 22314.5i | 0.438640 | − | 0.863615i | ||||
\(875\) | 10741.9 | + | 8309.55i | 0.415019 | + | 0.321045i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12119.5 | − | 20991.7i | −0.466645 | − | 0.808253i | 0.532629 | − | 0.846349i | \(-0.321204\pi\) |
−0.999274 | + | 0.0380957i | \(0.987871\pi\) | |||||||
\(878\) | −1929.29 | − | 2962.53i | −0.0741576 | − | 0.113873i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13780.9 | + | 63238.0i | 0.527901 | + | 2.42245i | ||||
\(881\) | 27664.5i | 1.05793i | 0.848642 | + | 0.528967i | \(0.177421\pi\) | ||||
−0.848642 | + | 0.528967i | \(0.822579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25947.6i | 0.988909i | 0.869204 | + | 0.494454i | \(0.164632\pi\) | ||||
−0.869204 | + | 0.494454i | \(0.835368\pi\) | |||||||
\(884\) | −29483.5 | − | 13036.4i | −1.12176 | − | 0.495998i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38256.1 | − | 24913.6i | 1.45061 | − | 0.944681i | ||||
\(887\) | 17565.5 | + | 30424.3i | 0.664928 | + | 1.15169i | 0.979305 | + | 0.202391i | \(0.0648711\pi\) |
−0.314377 | + | 0.949298i | \(0.601796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17297.9 | + | 13381.1i | 0.652591 | + | 0.504822i | ||||
\(890\) | 19993.8 | + | 10155.1i | 0.753027 | + | 0.382471i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3513.45 | − | 32623.7i | −0.131882 | − | 1.22457i | ||||
\(893\) | 7672.10 | + | 4429.49i | 0.287500 | + | 0.165988i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50438.1i | 1.88375i | ||||||||
\(896\) | −25753.9 | − | 7487.23i | −0.960244 | − | 0.279164i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21015.1 | − | 1128.37i | 0.780940 | − | 0.0419310i | ||||
\(899\) | −6513.68 | + | 11282.0i | −0.241650 | + | 0.418550i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12183.2 | − | 21101.9i | −0.450478 | − | 0.780251i | ||||
\(902\) | −32080.4 | + | 63161.3i | −1.18421 | + | 2.33153i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4229.77 | − | 686.611i | 0.155619 | − | 0.0252614i | ||||
\(905\) | 19563.0 | − | 11294.7i | 0.718558 | − | 0.414860i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10367.0 | + | 5985.40i | 0.379527 | + | 0.219120i | 0.677613 | − | 0.735419i | \(-0.263015\pi\) |
−0.298085 | + | 0.954539i | \(0.596348\pi\) | |||||||
\(908\) | 1401.39 | − | 3169.42i | 0.0512190 | − | 0.115838i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −38354.0 | − | 3120.18i | −1.39717 | − | 0.113662i | ||||
\(911\) | −39587.4 | −1.43973 | −0.719863 | − | 0.694116i | \(-0.755795\pi\) | ||||
−0.719863 | + | 0.694116i | \(0.755795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23721.2 | − | 41086.3i | 0.859866 | − | 1.48933i | ||||
\(914\) | 9288.87 | − | 6049.20i | 0.336158 | − | 0.218917i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12786.6 | + | 17504.8i | 0.461225 | + | 0.631412i | ||||
\(917\) | 8443.41 | + | 1145.24i | 0.304063 | + | 0.0412424i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1701.62 | − | 982.433i | 0.0610788 | − | 0.0352639i | −0.469150 | − | 0.883119i | \(-0.655440\pi\) |
0.530228 | + | 0.847855i | \(0.322106\pi\) | |||||||
\(920\) | 14005.4 | − | 36909.0i | 0.501898 | − | 1.32267i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −423.048 | + | 22.7147i | −0.0151110 | + | 0.000811355i | ||||
\(923\) | −43012.6 | −1.53389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14680.4 | 0.521826 | ||||||||
\(926\) | −34025.9 | + | 1826.95i | −1.20752 | + | 0.0648351i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 52752.7 | − | 14498.0i | 1.86605 | − | 0.512845i | ||||
\(929\) | 1300.11 | − | 750.617i | 0.0459151 | − | 0.0265091i | −0.476867 | − | 0.878976i | \(-0.658228\pi\) |
0.522782 | + | 0.852467i | \(0.324894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20885.5 | + | 21215.2i | 0.735225 | + | 0.746830i | ||||
\(932\) | −1755.75 | + | 1282.51i | −0.0617075 | + | 0.0450752i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13121.3 | + | 8545.02i | −0.459682 | + | 0.299359i | ||||
\(935\) | 47465.6 | − | 82212.9i | 1.66020 | − | 2.87556i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23460.4 | −0.817949 | −0.408975 | − | 0.912546i | \(-0.634114\pi\) | ||||
−0.408975 | + | 0.912546i | \(0.634114\pi\) | |||||||
\(938\) | −4121.92 | − | 8700.68i | −0.143481 | − | 0.302865i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12779.9 | + | 5650.78i | 0.443441 | + | 0.196072i | ||||
\(941\) | −18966.8 | − | 10950.5i | −0.657068 | − | 0.379358i | 0.134091 | − | 0.990969i | \(-0.457189\pi\) |
−0.791159 | + | 0.611611i | \(0.790522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37420.3 | − | 21604.6i | 1.29223 | − | 0.746070i | ||||
\(944\) | 7230.84 | − | 22648.6i | 0.249305 | − | 0.780880i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16204.5 | − | 31904.2i | 0.556929 | − | 1.09651i | ||||
\(947\) | 13504.2 | + | 23390.0i | 0.463388 | + | 0.802611i | 0.999127 | − | 0.0417720i | \(-0.0133003\pi\) |
−0.535739 | + | 0.844383i | \(0.679967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9314.89 | + | 16133.9i | −0.318624 | + | 0.551873i | ||||
\(950\) | 41146.7 | − | 2209.29i | 1.40524 | − | 0.0754514i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20552.0 | + | 33543.0i | 0.699678 | + | 1.14195i | ||||
\(953\) | 8447.65i | 0.287142i | 0.989640 | + | 0.143571i | \(0.0458585\pi\) | ||||
−0.989640 | + | 0.143571i | \(0.954141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16748.1 | + | 9669.52i | 0.567493 | + | 0.327642i | ||||
\(956\) | 50542.4 | − | 5443.24i | 1.70989 | − | 0.184149i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2310.57 | + | 1173.56i | 0.0779238 | + | 0.0395785i | ||||
\(959\) | −3798.66 | + | 1556.06i | −0.127909 | + | 0.0523960i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13966.5 | − | 24190.7i | −0.468816 | − | 0.812013i | ||||
\(962\) | −8898.55 | + | 5795.01i | −0.298234 | + | 0.194219i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7567.83 | + | 17115.5i | −0.252846 | + | 0.571841i | ||||
\(965\) | 43753.7i | 1.45957i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6959.11i | 0.231427i | 0.993283 | + | 0.115714i | \(0.0369155\pi\) | ||||
−0.993283 | + | 0.115714i | \(0.963085\pi\) | |||||||
\(968\) | 37885.9 | − | 30921.3i | 1.25795 | − | 1.02670i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17246.8 | + | 26483.4i | 0.570888 | + | 0.876629i | ||||
\(971\) | 18808.0 | + | 32576.4i | 0.621604 | + | 1.07665i | 0.989187 | + | 0.146659i | \(0.0468521\pi\) |
−0.367583 | + | 0.929991i | \(0.619815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4837.70 | + | 3742.28i | 0.159393 | + | 0.123301i | ||||
\(974\) | −5885.07 | + | 11586.8i | −0.193603 | + | 0.381175i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19537.3 | − | 21475.9i | −0.640750 | − | 0.704330i | ||||
\(977\) | −24837.9 | − | 14340.2i | −0.813343 | − | 0.469584i | 0.0347724 | − | 0.999395i | \(-0.488929\pi\) |
−0.848116 | + | 0.529811i | \(0.822263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27378.8i | − | 0.893799i | ||||||
\(980\) | 36336.8 | + | 29743.2i | 1.18443 | + | 0.969503i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.2413 | + | 637.724i | 0.00111271 | + | 0.0207236i | ||||
\(983\) | −24634.8 | + | 42668.7i | −0.799316 | + | 1.38446i | 0.120747 | + | 0.992683i | \(0.461471\pi\) |
−0.920062 | + | 0.391772i | \(0.871862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12786.5 | + | 22146.9i | 0.413617 | + | 0.716406i | ||||
\(986\) | −71544.5 | − | 36338.3i | −2.31079 | − | 1.17368i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24069.0 | + | 17581.6i | −0.775037 | + | 0.566138i | ||||
\(989\) | −18901.8 | + | 10913.0i | −0.607729 | + | 0.350872i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6061.31 | − | 3499.50i | −0.194293 | − | 0.112175i | 0.399698 | − | 0.916647i | \(-0.369115\pi\) |
−0.593991 | + | 0.804472i | \(0.702448\pi\) | |||||||
\(992\) | 1971.17 | − | 7549.70i | 0.0630895 | − | 0.241636i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 43178.2 | + | 29843.3i | 1.37780 | + | 0.952285i | ||||
\(995\) | −39458.8 | −1.25721 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9573.57 | + | 16581.9i | −0.304110 | + | 0.526735i | −0.977063 | − | 0.212951i | \(-0.931693\pi\) |
0.672952 | + | 0.739686i | \(0.265026\pi\) | |||||||
\(998\) | 26552.6 | + | 40772.9i | 0.842192 | + | 1.29323i | ||||
\(999\) | 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 | 252.4.be.a.179.23 | yes | 96 | |
3.2 | odd | 2 | inner | 252.4.be.a.179.26 | yes | 96 | |
4.3 | odd | 2 | inner | 252.4.be.a.179.40 | yes | 96 | |
7.2 | even | 3 | inner | 252.4.be.a.107.9 | ✓ | 96 | |
12.11 | even | 2 | inner | 252.4.be.a.179.9 | yes | 96 | |
21.2 | odd | 6 | inner | 252.4.be.a.107.40 | yes | 96 | |
28.23 | odd | 6 | inner | 252.4.be.a.107.26 | yes | 96 | |
84.23 | even | 6 | inner | 252.4.be.a.107.23 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.be.a.107.9 | ✓ | 96 | 7.2 | even | 3 | inner | |
252.4.be.a.107.23 | yes | 96 | 84.23 | even | 6 | inner | |
252.4.be.a.107.26 | yes | 96 | 28.23 | odd | 6 | inner | |
252.4.be.a.107.40 | yes | 96 | 21.2 | odd | 6 | inner | |
252.4.be.a.179.9 | yes | 96 | 12.11 | even | 2 | inner | |
252.4.be.a.179.23 | yes | 96 | 1.1 | even | 1 | trivial | |
252.4.be.a.179.26 | yes | 96 | 3.2 | odd | 2 | inner | |
252.4.be.a.179.40 | yes | 96 | 4.3 | odd | 2 | inner |