Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,4,Mod(431,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.431");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.3209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.16 | ||
Character | \(\chi\) | \(=\) | 480.431 |
Dual form | 480.4.b.a.431.15 |
$q$-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 \(\left(\mathbb{Z}/480\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.49310 | + | 4.97701i | 0.287346 | + | 0.957827i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.5956i | 0.788089i | 0.919091 | + | 0.394044i | \(0.128924\pi\) | ||||
−0.919091 | + | 0.394044i | \(0.871076\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.5413 | + | 14.8623i | −0.834864 | + | 0.550456i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 58.0556i | − | 1.59131i | −0.605750 | − | 0.795655i | \(-0.707127\pi\) | ||
0.605750 | − | 0.795655i | \(-0.292873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 43.9441i | − | 0.937532i | −0.883322 | − | 0.468766i | \(-0.844699\pi\) | ||
0.883322 | − | 0.468766i | \(-0.155301\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.46548 | − | 24.8851i | −0.128505 | − | 0.428353i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 78.8045i | − | 1.12429i | −0.827039 | − | 0.562144i | \(-0.809977\pi\) | ||
0.827039 | − | 0.562144i | \(-0.190023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −103.306 | −1.24737 | −0.623687 | − | 0.781674i | \(-0.714366\pi\) | ||||
−0.623687 | + | 0.781674i | \(0.714366\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −72.6425 | + | 21.7926i | −0.754852 | + | 0.226454i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 163.945 | 1.48630 | 0.743151 | − | 0.669123i | \(-0.233330\pi\) | ||||
0.743151 | + | 0.669123i | \(0.233330\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −107.626 | − | 89.9977i | −0.767137 | − | 0.641484i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 247.735 | 1.58632 | 0.793160 | − | 0.609013i | \(-0.208434\pi\) | ||||
0.793160 | + | 0.609013i | \(0.208434\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 153.271i | 0.888009i | 0.896025 | + | 0.444004i | \(0.146443\pi\) | ||||
−0.896025 | + | 0.444004i | \(0.853557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 288.943 | − | 86.6825i | 1.52420 | − | 0.457257i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 72.9780i | − | 0.352444i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 153.638i | − | 0.682646i | −0.939946 | − | 0.341323i | \(-0.889125\pi\) | ||
0.939946 | − | 0.341323i | \(-0.110875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 218.711 | − | 65.6128i | 0.897993 | − | 0.269396i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 27.0586i | − | 0.103070i | −0.998671 | − | 0.0515348i | \(-0.983589\pi\) | ||
0.998671 | − | 0.0515348i | \(-0.0164113\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −246.934 | −0.875746 | −0.437873 | − | 0.899037i | \(-0.644268\pi\) | ||||
−0.437873 | + | 0.899037i | \(0.644268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 112.707 | − | 74.3116i | 0.373363 | − | 0.246171i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −411.901 | −1.27834 | −0.639170 | − | 0.769065i | \(-0.720722\pi\) | ||||
−0.639170 | + | 0.769065i | \(0.720722\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 129.968 | 0.378916 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 392.211 | − | 117.663i | 1.07687 | − | 0.323060i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 80.1737 | 0.207787 | 0.103893 | − | 0.994588i | \(-0.466870\pi\) | ||||
0.103893 | + | 0.994588i | \(0.466870\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 290.278i | 0.711656i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −154.246 | − | 514.157i | −0.358428 | − | 1.19477i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 513.612i | − | 1.13333i | −0.823947 | − | 0.566666i | \(-0.808233\pi\) | ||
0.823947 | − | 0.566666i | \(-0.191767\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 27.0460i | − | 0.0567686i | −0.999597 | − | 0.0283843i | \(-0.990964\pi\) | ||
0.999597 | − | 0.0283843i | \(-0.00903622\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −216.924 | − | 329.004i | −0.433808 | − | 0.657947i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 219.721i | 0.419277i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 453.089 | 0.826173 | 0.413087 | − | 0.910692i | \(-0.364451\pi\) | ||||
0.413087 | + | 0.910692i | \(0.364451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 244.786 | + | 815.958i | 0.427084 | + | 1.42362i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 446.258 | 0.745930 | 0.372965 | − | 0.927845i | \(-0.378341\pi\) | ||||
0.372965 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 524.821 | 0.841447 | 0.420724 | − | 0.907189i | \(-0.361776\pi\) | ||||
0.420724 | + | 0.907189i | \(0.361776\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 37.3274 | + | 124.425i | 0.0574693 | + | 0.191565i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 847.356 | 1.25409 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 93.4259i | − | 0.133054i | −0.997785 | − | 0.0665268i | \(-0.978808\pi\) | ||
0.997785 | − | 0.0665268i | \(-0.0211918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 287.223 | − | 670.033i | 0.393996 | − | 0.919112i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1249.95i | − | 1.65301i | −0.562933 | − | 0.826503i | \(-0.690327\pi\) | ||
0.562933 | − | 0.826503i | \(-0.309673\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 394.023i | 0.502797i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 369.892 | + | 1232.98i | 0.455823 | + | 1.51942i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 267.674i | 0.318803i | 0.987214 | + | 0.159401i | \(0.0509564\pi\) | ||||
−0.987214 | + | 0.159401i | \(0.949044\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 641.391 | 0.738858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −762.832 | + | 228.848i | −0.850559 | + | 0.255166i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 516.532 | 0.557843 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −897.223 | −0.939167 | −0.469584 | − | 0.882888i | \(-0.655596\pi\) | ||||
−0.469584 | + | 0.882888i | \(0.655596\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 862.840 | + | 1308.65i | 0.875946 | + | 1.32853i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1086.03 | −1.06994 | −0.534972 | − | 0.844870i | \(-0.679678\pi\) | ||||
−0.534972 | + | 0.844870i | \(0.679678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 602.598i | − | 0.576464i | −0.957561 | − | 0.288232i | \(-0.906933\pi\) | ||
0.957561 | − | 0.288232i | \(-0.0930674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 363.213 | − | 108.963i | 0.337580 | − | 0.101273i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 209.243i | 0.189050i | 0.995522 | + | 0.0945249i | \(0.0301332\pi\) | ||||
−0.995522 | + | 0.0945249i | \(0.969867\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 866.438i | − | 0.761374i | −0.924704 | − | 0.380687i | \(-0.875688\pi\) | ||
0.924704 | − | 0.380687i | \(-0.124312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 764.657 | − | 229.396i | 0.653856 | − | 0.196156i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1455.92i | − | 1.21205i | −0.795445 | − | 0.606026i | \(-0.792763\pi\) | ||
0.795445 | − | 0.606026i | \(-0.207237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −819.727 | −0.664695 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 653.112 | + | 990.560i | 0.516070 | + | 0.782712i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1150.20 | 0.886039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2039.45 | −1.53227 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 134.671 | − | 40.4011i | 0.0987228 | − | 0.0296167i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1710.12i | − | 1.19487i | −0.801917 | − | 0.597435i | \(-0.796186\pi\) | ||
0.801917 | − | 0.597435i | \(-0.203814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −368.696 | − | 1228.99i | −0.251642 | − | 0.838813i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 994.011i | − | 0.662955i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) | ||
0.943463 | − | 0.331478i | \(-0.107547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1507.82i | − | 0.983041i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 538.131 | + | 449.988i | 0.343074 | + | 0.286880i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 218.135i | − | 0.136033i | −0.997684 | − | 0.0680166i | \(-0.978333\pi\) | ||
0.997684 | − | 0.0680166i | \(-0.0216671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −871.961 | −0.532078 | −0.266039 | − | 0.963962i | \(-0.585715\pi\) | ||||
−0.266039 | + | 0.963962i | \(0.585715\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −615.008 | − | 2050.04i | −0.367326 | − | 1.22443i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2551.20 | −1.49190 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1238.68 | −0.709424 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 194.055 | + | 646.854i | 0.108880 | + | 0.362936i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2649.54 | 1.45677 | 0.728385 | − | 0.685168i | \(-0.240271\pi\) | ||||
0.728385 | + | 0.685168i | \(0.240271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 717.633i | − | 0.386756i | −0.981124 | − | 0.193378i | \(-0.938056\pi\) | ||
0.981124 | − | 0.193378i | \(-0.0619443\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1171.22 | + | 1776.36i | 0.618871 | + | 0.938628i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 766.355i | − | 0.397130i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3251.75i | 1.65298i | 0.562951 | + | 0.826490i | \(0.309666\pi\) | ||||
−0.562951 | + | 0.826490i | \(0.690334\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 119.707 | + | 399.026i | 0.0597068 | + | 0.199024i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2392.88i | 1.17134i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 180.616 | 0.0867912 | 0.0433956 | − | 0.999058i | \(-0.486182\pi\) | ||||
0.0433956 | + | 0.999058i | \(0.486182\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1444.72 | + | 433.413i | −0.681643 | + | 0.204492i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3583.90 | −1.66066 | −0.830332 | − | 0.557269i | \(-0.811849\pi\) | ||||
−0.830332 | + | 0.557269i | \(0.811849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 265.912 | 0.121034 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2328.66 | − | 1535.37i | 1.04139 | − | 0.686625i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 529.974 | 0.232909 | 0.116454 | − | 0.993196i | \(-0.462847\pi\) | ||||
0.116454 | + | 0.993196i | \(0.462847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 364.890i | 0.157618i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2556.26 | − | 766.872i | 1.08554 | − | 0.325659i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2272.25i | 0.948805i | 0.880308 | + | 0.474402i | \(0.157336\pi\) | ||||
−0.880308 | + | 0.474402i | \(0.842664\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 768.299i | − | 0.315509i | −0.987478 | − | 0.157755i | \(-0.949574\pi\) | ||
0.987478 | − | 0.157755i | \(-0.0504255\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 134.608 | − | 40.3823i | 0.0543745 | − | 0.0163123i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 768.189i | 0.305288i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4575.04 | −1.78909 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1313.57 | − | 1570.87i | 0.505546 | − | 0.604572i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1338.21 | 0.506962 | 0.253481 | − | 0.967340i | \(-0.418424\pi\) | ||||
0.253481 | + | 0.967340i | \(0.418424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −858.809 | −0.320303 | −0.160151 | − | 0.987092i | \(-0.551198\pi\) | ||||
−0.160151 | + | 0.987092i | \(0.551198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1093.55 | + | 328.064i | −0.401595 | + | 0.120478i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3040.41 | −1.09960 | −0.549798 | − | 0.835298i | \(-0.685295\pi\) | ||||
−0.549798 | + | 0.835298i | \(0.685295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1636.95i | − | 0.583118i | −0.956553 | − | 0.291559i | \(-0.905826\pi\) | ||
0.956553 | − | 0.291559i | \(-0.0941740\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 676.505 | + | 2255.03i | 0.237398 | + | 0.791331i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3615.85i | 1.25016i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 135.293i | 0.0460941i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3695.55 | + | 2436.61i | −1.24086 | + | 0.818144i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5997.51i | 1.98496i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6036.05 | −1.96938 | −0.984689 | − | 0.174322i | \(-0.944227\pi\) | ||||
−0.984689 | + | 0.174322i | \(0.944227\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 666.305 | + | 2221.03i | 0.214340 | + | 0.714472i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1234.67 | 0.391646 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2237.08 | −0.699830 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 783.608 | + | 2612.04i | 0.241787 | + | 0.805961i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3463.00 | −1.05406 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1524.61i | − | 0.457828i | −0.973447 | − | 0.228914i | \(-0.926483\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735175\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −563.533 | + | 371.558i | −0.166973 | + | 0.110091i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 472.571i | 0.138174i | 0.997611 | + | 0.0690872i | \(0.0220087\pi\) | ||||
−0.997611 | + | 0.0690872i | \(0.977991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3068.70i | − | 0.885526i | −0.896639 | − | 0.442763i | \(-0.853998\pi\) | ||
0.896639 | − | 0.442763i | \(-0.146002\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1265.18 | + | 4217.30i | 0.360359 | + | 1.20120i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 141.515i | − | 0.0397895i | −0.999802 | − | 0.0198947i | \(-0.993667\pi\) | ||
0.999802 | − | 0.0198947i | \(-0.00633311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2059.51 | 0.571691 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 464.982 | − | 139.494i | 0.127442 | − | 0.0382325i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3911.18 | −1.05855 | −0.529274 | − | 0.848451i | \(-0.677536\pi\) | ||||
−0.529274 | + | 0.848451i | \(0.677536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4114.37 | 1.09971 | 0.549855 | − | 0.835260i | \(-0.314683\pi\) | ||||
0.549855 | + | 0.835260i | \(0.314683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3763.61 | + | 429.092i | 0.993563 | + | 0.113277i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −649.841 | −0.169456 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4539.71i | 1.16945i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6221.00 | − | 1866.29i | 1.58329 | − | 0.474985i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5279.91i | 1.32775i | 0.747844 | + | 0.663874i | \(0.231089\pi\) | ||||
−0.747844 | + | 0.663874i | \(0.768911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9517.94i | − | 2.36517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1961.06 | + | 588.313i | −0.481592 | + | 0.144477i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2278.07i | − | 0.552928i | −0.961024 | − | 0.276464i | \(-0.910837\pi\) | ||
0.961024 | − | 0.276464i | \(-0.0891626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2242.44 | 0.537985 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5584.28 | + | 3681.92i | −1.32436 | + | 0.873199i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6017.98 | 1.41097 | 0.705484 | − | 0.708726i | \(-0.250730\pi\) | ||||
0.705484 | + | 0.708726i | \(0.250730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −400.869 | −0.0929252 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1332.22 | + | 399.663i | −0.305358 | + | 0.0916067i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3008.84 | −0.681979 | −0.340989 | − | 0.940067i | \(-0.610762\pi\) | ||||
−0.340989 | + | 0.940067i | \(0.610762\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2907.26i | − | 0.651673i | −0.945426 | − | 0.325836i | \(-0.894354\pi\) | ||
0.945426 | − | 0.325836i | \(-0.105646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 957.659 | + | 3192.21i | 0.212308 | + | 0.707698i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1451.39i | − | 0.318262i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7971.57i | 1.72912i | 0.502532 | + | 0.864558i | \(0.332402\pi\) | ||||
−0.502532 | + | 0.864558i | \(0.667598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2277.96 | − | 3454.93i | −0.488810 | − | 0.741367i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 913.436i | − | 0.193918i | −0.995288 | − | 0.0969591i | \(-0.969088\pi\) | ||
0.995288 | − | 0.0969591i | \(-0.0309116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1838.40 | 0.386154 | 0.193077 | − | 0.981184i | \(-0.438153\pi\) | ||||
0.193077 | + | 0.981184i | \(0.438153\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 771.231 | + | 2570.79i | 0.160294 | + | 0.534317i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 394.937 | 0.0812279 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1297.15 | −0.264024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1339.64 | − | 4465.49i | −0.269866 | − | 0.899559i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −742.598 | −0.148065 | −0.0740324 | − | 0.997256i | \(-0.523587\pi\) | ||||
−0.0740324 | + | 0.997256i | \(0.523587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2568.06i | 0.506842i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5224.87 | + | 6248.31i | −1.02080 | + | 1.22075i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 7204.44i | − | 1.39346i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3604.15i | − | 0.690166i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1621.55 | − | 5405.20i | −0.307445 | − | 1.02482i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 135.230i | 0.0253877i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8317.65 | −1.54630 | −0.773149 | − | 0.634225i | \(-0.781319\pi\) | ||||
−0.773149 | + | 0.634225i | \(0.781319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2999.14 | − | 899.736i | 0.552152 | − | 0.165645i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3016.33 | 0.549970 | 0.274985 | − | 0.961449i | \(-0.411327\pi\) | ||||
0.274985 | + | 0.961449i | \(0.411327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9400.48 | −1.69759 | −0.848797 | − | 0.528720i | \(-0.822672\pi\) | ||||
−0.848797 | + | 0.528720i | \(0.822672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1084.62 | + | 1645.02i | 0.194005 | + | 0.294243i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5801.88 | 1.02797 | 0.513985 | − | 0.857799i | \(-0.328169\pi\) | ||||
0.513985 | + | 0.857799i | \(0.328169\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14382.4i | − | 2.52433i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1041.41 | + | 312.420i | −0.181077 | + | 0.0543228i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8141.01i | 1.40241i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1098.60i | − | 0.187506i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4312.28 | − | 1293.68i | 0.729264 | − | 0.218778i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6011.95i | − | 1.00745i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5997.26 | 0.995888 | 0.497944 | − | 0.867209i | \(-0.334088\pi\) | ||||
0.497944 | + | 0.867209i | \(0.334088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2283.41 | + | 3463.20i | 0.375766 | + | 0.569916i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2265.44 | −0.369476 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8013.40 | −1.29531 | −0.647653 | − | 0.761936i | \(-0.724249\pi\) | ||||
−0.647653 | + | 0.761936i | \(0.724249\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7246.16 | − | 2173.83i | 1.16094 | − | 0.348279i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8898.23 | 1.41310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6903.26i | 1.08671i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1223.93 | − | 4079.79i | −0.190998 | − | 0.636663i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 249.070i | − | 0.0385325i | −0.999814 | − | 0.0192662i | \(-0.993867\pi\) | ||
0.999814 | − | 0.0192662i | \(-0.00613301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8681.38i | − | 1.33153i | −0.746162 | − | 0.665764i | \(-0.768106\pi\) | ||
0.746162 | − | 0.665764i | \(-0.231894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3954.87 | + | 4729.55i | −0.601411 | + | 0.719215i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6747.03i | − | 1.01730i | −0.860972 | − | 0.508652i | \(-0.830144\pi\) | ||
0.860972 | − | 0.508652i | \(-0.169856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2231.29 | −0.333590 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1717.36 | + | 5724.56i | 0.254600 | + | 0.848672i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1559.98 | 0.229339 | 0.114669 | − | 0.993404i | \(-0.463419\pi\) | ||||
0.114669 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3813.21 | 0.555942 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3045.09 | − | 10150.4i | −0.440292 | − | 1.46765i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2624.10 | −0.376307 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13670.5i | 1.94440i | 0.234144 | + | 0.972202i | \(0.424771\pi\) | ||||
−0.234144 | + | 0.972202i | \(0.575229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 402.154 | + | 609.938i | 0.0567352 | + | 0.0860491i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1170.18i | 0.163755i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10962.3i | 1.52173i | 0.648909 | + | 0.760866i | \(0.275226\pi\) | ||||
−0.648909 | + | 0.760866i | \(0.724774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −186.637 | − | 622.127i | −0.0257010 | − | 0.0856706i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 10886.5i | − | 1.48723i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 221.741 | 0.0300529 | 0.0150265 | − | 0.999887i | \(-0.495217\pi\) | ||||
0.0150265 | + | 0.999887i | \(0.495217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8511.29 | − | 2553.37i | 1.14448 | − | 0.343342i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 567.176 | 0.0756694 | 0.0378347 | − | 0.999284i | \(-0.487954\pi\) | ||||
0.0378347 | + | 0.999284i | \(0.487954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4236.78 | −0.560848 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5566.22 | − | 3670.01i | 0.731129 | − | 0.482060i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10143.0 | −1.32204 | −0.661019 | − | 0.750369i | \(-0.729876\pi\) | ||||
−0.661019 | + | 0.750369i | \(0.729876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12919.6i | − | 1.67103i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4947.21 | − | 1484.15i | 0.634996 | − | 0.190498i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 467.129i | 0.0595034i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4548.29i | − | 0.574992i | −0.957782 | − | 0.287496i | \(-0.907177\pi\) | ||
0.957782 | − | 0.287496i | \(-0.0928228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7504.44 | − | 2251.32i | 0.941583 | − | 0.282473i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 141.751i | 0.0176526i | 0.999961 | + | 0.00882632i | \(0.00280954\pi\) | ||||
−0.999961 | + | 0.00882632i | \(0.997190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6735.36 | 0.832537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1436.12 | + | 3350.16i | −0.176201 | + | 0.411039i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8919.53 | −1.08630 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10767.4 | 1.30175 | 0.650873 | − | 0.759186i | \(-0.274403\pi\) | ||||
0.650873 | + | 0.759186i | \(0.274403\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1085.66 | − | 325.697i | 0.130296 | − | 0.0390886i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7496.48 | 0.893167 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6249.73i | 0.739246i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1301.92 | − | 4339.76i | −0.152891 | − | 0.509638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1276.55i | − | 0.148840i | −0.997227 | − | 0.0744198i | \(-0.976290\pi\) | ||
0.997227 | − | 0.0744198i | \(-0.0237105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14268.0i | 1.65173i | 0.563869 | + | 0.825864i | \(0.309312\pi\) | ||||
−0.563869 | + | 0.825864i | \(0.690688\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9284.81 | − | 6121.81i | 1.06724 | − | 0.703670i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1970.11i | − | 0.224858i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 394.753 | 0.0447387 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3809.19 | − | 12697.4i | −0.428693 | − | 1.42899i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15402.6 | 1.72139 | 0.860695 | − | 0.509120i | \(-0.170029\pi\) | ||||
0.860695 | + | 0.509120i | \(0.170029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9528.41 | 1.05752 | 0.528760 | − | 0.848771i | \(-0.322657\pi\) | ||||
0.528760 | + | 0.848771i | \(0.322657\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1849.46 | − | 6164.91i | −0.203850 | − | 0.679505i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16936.6 | −1.85398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2811.08i | − | 0.305616i | −0.988256 | − | 0.152808i | \(-0.951168\pi\) | ||
0.988256 | − | 0.152808i | \(-0.0488317\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2929.66 | + | 1931.63i | −0.316344 | + | 0.208577i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 4207.40i | − | 0.451241i | −0.974215 | − | 0.225620i | \(-0.927559\pi\) | ||
0.974215 | − | 0.225620i | \(-0.0724409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 1338.37i | − | 0.142573i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3956.02 | + | 13186.8i | 0.418598 | + | 1.39533i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5099.95i | − | 0.536040i | −0.963413 | − | 0.268020i | \(-0.913631\pi\) | ||
0.963413 | − | 0.268020i | \(-0.0863693\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1570.91 | −0.164016 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3571.67 | − | 1071.49i | 0.370445 | − | 0.111133i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3206.96 | −0.330427 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8660.31 | 0.886460 | 0.443230 | − | 0.896408i | \(-0.353833\pi\) | ||||
0.443230 | + | 0.896408i | \(0.353833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7092.22 | + | 8481.44i | −0.721213 | + | 0.862483i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11202.5 | 1.13179 | 0.565893 | − | 0.824479i | \(-0.308532\pi\) | ||||
0.565893 | + | 0.824479i | \(0.308532\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2975.15i | 0.298633i | 0.988789 | + | 0.149316i | \(0.0477073\pi\) | ||||
−0.988789 | + | 0.149316i | \(0.952293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3814.16 | − | 1144.24i | 0.380381 | − | 0.114114i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 13454.8i | − | 1.33322i | −0.745406 | − | 0.666611i | \(-0.767744\pi\) | ||
0.745406 | − | 0.666611i | \(-0.232256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6613.11i | 0.651098i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16184.0 | + | 4855.17i | −1.58327 | + | 0.474978i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14335.9i | 1.39358i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2582.66 | −0.249475 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1807.22 | + | 1191.57i | −0.173474 | + | 0.114378i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11128.5 | 1.06153 | 0.530765 | − | 0.847519i | \(-0.321905\pi\) | ||||
0.530765 | + | 0.847519i | \(0.321905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6751.48 | −0.640002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11909.4 | + | 3572.80i | −1.12194 | + | 0.336580i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4486.12 | 0.420008 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2167.65i | 0.201695i | 0.994902 | + | 0.100848i | \(0.0321555\pi\) | ||||
−0.994902 | + | 0.100848i | \(0.967845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 269.677 | + | 898.930i | 0.0249391 | + | 0.0831309i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4706.59i | − | 0.432597i | −0.976327 | − | 0.216299i | \(-0.930601\pi\) | ||
0.976327 | − | 0.216299i | \(-0.0693985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 19522.7i | − | 1.78348i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4314.20 | − | 6543.25i | −0.391735 | − | 0.594136i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6513.40i | 0.587859i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21594.1 | 1.93724 | 0.968620 | − | 0.248546i | \(-0.0799528\pi\) | ||||
0.968620 | + | 0.248546i | \(0.0799528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5351.11 | − | 17837.1i | −0.477186 | − | 1.59063i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3910.09 | −0.346605 | −0.173303 | − | 0.984869i | \(-0.555444\pi\) | ||||
−0.173303 | + | 0.984869i | \(0.555444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5430.17 | 0.478494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 397.032 | + | 1323.45i | 0.0347787 | + | 0.115930i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18113.4 | 1.57733 | 0.788667 | − | 0.614821i | \(-0.210772\pi\) | ||||
0.788667 | + | 0.614821i | \(0.210772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7660.08i | 0.663135i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11118.5 | + | 9297.33i | 0.956906 | + | 0.800170i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3012.99i | 0.257802i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23913.2i | 2.03424i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 791.302 | + | 2637.69i | 0.0669254 | + | 0.223086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16469.0i | − | 1.38487i | −0.721480 | − | 0.692436i | \(-0.756538\pi\) | ||
0.721480 | − | 0.692436i | \(-0.243462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −380.198 | −0.0317876 | −0.0158938 | − | 0.999874i | \(-0.505059\pi\) | ||||
−0.0158938 | + | 0.999874i | \(0.505059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1816.06 | + | 544.816i | −0.150970 | + | 0.0452909i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12078.4 | 0.998378 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14711.1 | 1.20910 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7633.47 | + | 11577.5i | 0.623850 | + | 0.946179i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1189.07 | −0.0966310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1046.22i | − | 0.0845456i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11309.0 | + | 3392.69i | −0.908791 | + | 0.272636i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 7545.38i | − | 0.602973i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5985.34i | 0.475656i | 0.971307 | + | 0.237828i | \(0.0764354\pi\) | ||||
−0.971307 | + | 0.237828i | \(0.923565\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3823.83 | − | 1147.14i | 0.302203 | − | 0.0906605i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4332.19i | 0.340497i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6496.76 | −0.507827 | −0.253914 | − | 0.967227i | \(-0.581718\pi\) | ||||
−0.253914 | + | 0.967227i | \(0.581718\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 401.966 | + | 609.653i | 0.0312486 | + | 0.0473941i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25592.6 | −1.97873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1363.61 | 0.104858 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3823.29 | + | 1146.98i | −0.292413 | + | 0.0877235i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22280.1 | −1.69486 | −0.847431 | − | 0.530905i | \(-0.821852\pi\) | ||||
−0.847431 | + | 0.530905i | \(0.821852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10851.3i | 0.821040i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6830.97 | − | 22770.0i | −0.514089 | − | 1.71364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10370.5i | − | 0.776317i | −0.921593 | − | 0.388158i | \(-0.873111\pi\) | ||
0.921593 | − | 0.388158i | \(-0.126889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7279.62i | 0.542046i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9779.53 | + | 4192.20i | 0.724342 | + | 0.310504i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15791.9i | 1.16350i | 0.813368 | + | 0.581750i | \(0.197632\pi\) | ||||
−0.813368 | + | 0.581750i | \(0.802368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14459.2 | −1.05972 | −0.529858 | − | 0.848087i | \(-0.677755\pi\) | ||||
−0.529858 | + | 0.848087i | \(0.677755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1998.08 | + | 6660.31i | 0.145674 | + | 0.485582i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4098.63 | 0.297261 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1179.27 | −0.0850845 | −0.0425423 | − | 0.999095i | \(-0.513546\pi\) | ||||
−0.0425423 | + | 0.999095i | \(0.513546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1282.28 | − | 4274.30i | −0.0920378 | − | 0.306795i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18243.7 | 1.30271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4654.53i | − | 0.330654i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3265.56 | − | 4952.80i | −0.230794 | − | 0.350039i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3761.00i | − | 0.264451i | −0.991220 | − | 0.132226i | \(-0.957788\pi\) | ||
0.991220 | − | 0.132226i | \(-0.0422124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15833.9i | − | 1.10768i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4539.63 | − | 15132.2i | −0.315965 | − | 1.05322i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7912.85i | − | 0.547962i | −0.961735 | − | 0.273981i | \(-0.911659\pi\) | ||
0.961735 | − | 0.273981i | \(-0.0883406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5751.00 | −0.396249 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8147.14 | − | 2444.13i | 0.558526 | − | 0.167557i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13018.4 | −0.888012 | −0.444006 | − | 0.896024i | \(-0.646443\pi\) | ||||
−0.444006 | + | 0.896024i | \(0.646443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6784.23 | 0.460457 | 0.230228 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230228 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10213.2 | + | 6733.95i | −0.689742 | + | 0.454772i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10197.2 | 0.685251 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16589.8i | − | 1.10932i | −0.832077 | − | 0.554661i | \(-0.812848\pi\) | ||
0.832077 | − | 0.554661i | \(-0.187152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17996.1 | + | 5398.80i | −1.19744 | + | 0.359229i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18100.7i | 1.19848i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16207.7i | − | 1.06790i | −0.845516 | − | 0.533950i | \(-0.820707\pi\) | ||
0.845516 | − | 0.533950i | \(-0.179293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −673.356 | + | 202.006i | −0.0441502 | + | 0.0132450i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17461.9i | 1.13936i | 0.821865 | + | 0.569682i | \(0.192934\pi\) | ||||
−0.821865 | + | 0.569682i | \(0.807066\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5700.52 | −0.370151 | −0.185075 | − | 0.982724i | \(-0.559253\pi\) | ||||
−0.185075 | + | 0.982724i | \(0.559253\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17644.8 | − | 14754.7i | −1.14020 | − | 0.953439i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3906.87 | −0.251245 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29849.7 | + | 8954.86i | −1.90125 | + | 0.570371i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12107.3 | −0.767491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8186.74i | − | 0.516496i | −0.966079 | − | 0.258248i | \(-0.916855\pi\) | ||
0.966079 | − | 0.258248i | \(-0.0831452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9012.39 | − | 30041.5i | −0.565893 | − | 1.88632i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8550.60i | 0.534363i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5711.34i | − | 0.355246i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10059.2 | + | 6632.42i | −0.622750 | + | 0.410602i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27307.8i | 1.68267i | 0.540510 | + | 0.841337i | \(0.318231\pi\) | ||||
−0.540510 | + | 0.841337i | \(0.681769\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11306.2 | 0.693427 | 0.346714 | − | 0.937971i | \(-0.387298\pi\) | ||||
0.346714 | + | 0.937971i | \(0.387298\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1843.48 | + | 6144.97i | 0.112538 | + | 0.375129i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4998.32 | −0.303716 | −0.151858 | − | 0.988402i | \(-0.548526\pi\) | ||||
−0.151858 | + | 0.988402i | \(0.548526\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29818.1 | −1.80348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3340.18 | − | 11134.0i | −0.201094 | − | 0.670316i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23047.6 | −1.38120 | −0.690599 | − | 0.723238i | \(-0.742653\pi\) | ||||
−0.690599 | + | 0.723238i | \(0.742653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4970.06i | 0.296483i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11830.2 | + | 7800.05i | −0.702494 | + | 0.463180i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18811.4i | 1.11197i | 0.831191 | + | 0.555986i | \(0.187659\pi\) | ||||
−0.831191 | + | 0.555986i | \(0.812341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30855.3i | 1.81563i | 0.419370 | + | 0.907815i | \(0.362251\pi\) | ||||
−0.419370 | + | 0.907815i | \(0.637749\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5170.58 | − | 17235.4i | −0.302879 | − | 1.00960i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7539.10i | 0.439629i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40615.0 | 2.35775 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7588.02 | − | 2276.39i | 0.438520 | − | 0.131555i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1570.17 | −0.0903365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12293.3 | 0.704117 | 0.352058 | − | 0.935978i | \(-0.385482\pi\) | ||||
0.352058 | + | 0.935978i | \(0.385482\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2690.66 | − | 2249.94i | −0.153427 | − | 0.128297i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 296.947 | 0.0168576 | 0.00842881 | − | 0.999964i | \(-0.497317\pi\) | ||||
0.00842881 | + | 0.999964i | \(0.497317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13095.5i | − | 0.740147i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2351.99 | + | 705.593i | −0.132347 | + | 0.0397039i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6305.85i | 0.353275i | 0.984276 | + | 0.176638i | \(0.0565220\pi\) | ||||
−0.984276 | + | 0.176638i | \(0.943478\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1090.68i | 0.0608359i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15273.0 | − | 4581.86i | 0.848181 | − | 0.254453i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 3523.17i | − | 0.194807i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27248.7 | 1.50013 | 0.750064 | − | 0.661365i | \(-0.230022\pi\) | ||||
0.750064 | + | 0.661365i | \(0.230022\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19100.5 | + | 12593.7i | −1.04700 | + | 0.690323i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4359.81 | 0.237952 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2132.34 | −0.115880 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 704.321 | − | 211.295i | 0.0381114 | − | 0.0114334i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17919.3 | 0.965481 | 0.482741 | − | 0.875763i | \(-0.339641\pi\) | ||||
0.482741 | + | 0.875763i | \(0.339641\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15871.8i | 0.851515i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3075.04 | + | 10250.2i | 0.164273 | + | 0.547581i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 15851.3i | − | 0.843211i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12485.0i | 0.661329i | 0.943748 | + | 0.330665i | \(0.107273\pi\) | ||||
−0.943748 | + | 0.330665i | \(0.892727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1388.52 | + | 2105.94i | 0.0732402 | + | 0.111082i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25128.1i | 1.31985i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12756.0 | 0.667200 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5839.76 | − | 19466.0i | −0.304170 | − | 1.01391i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7727.83 | 0.400834 | 0.200417 | − | 0.979711i | \(-0.435770\pi\) | ||||
0.200417 | + | 0.979711i | \(0.435770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8795.28 | 0.454304 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6143.15 | + | 20477.3i | 0.315998 | + | 1.05333i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6193.38 | 0.317264 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12917.1i | 0.658964i | 0.944162 | + | 0.329482i | \(0.106874\pi\) | ||||
−0.944162 | + | 0.329482i | \(0.893126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3483.84 | + | 19372.2i | 0.176997 | + | 0.984211i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19459.5i | 0.984591i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5574.53i | − | 0.280900i | −0.990088 | − | 0.140450i | \(-0.955145\pi\) | ||
0.990088 | − | 0.140450i | \(-0.0448550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −970.275 | − | 3234.27i | −0.0486927 | − | 0.162310i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 26304.3i | − | 1.31470i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17289.1 | −0.860607 | −0.430304 | − | 0.902684i | \(-0.641594\pi\) | ||||
−0.430304 | + | 0.902684i | \(0.641594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22594.2 | + | 6778.22i | −1.12013 | + | 0.336038i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13359.7 | −0.659649 | −0.329824 | − | 0.944042i | \(-0.606990\pi\) | ||||
−0.329824 | + | 0.944042i | \(0.606990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13247.7 | −0.651487 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18577.1 | + | 28175.5i | 0.909907 | + | 1.38003i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3054.03 | −0.148988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8468.05i | 0.411456i | 0.978609 | + | 0.205728i | \(0.0659563\pi\) | ||||
−0.978609 | + | 0.205728i | \(0.934044\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −26278.2 | + | 7883.41i | −1.27175 | + | 0.381524i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3588.16i | 0.172962i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6277.34i | − | 0.301392i | −0.988580 | − | 0.150696i | \(-0.951849\pi\) | ||
0.988580 | − | 0.150696i | \(-0.0481515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47370.9 | − | 14211.2i | 2.26542 | − | 0.679623i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11037.7i | 0.525778i | 0.964826 | + | 0.262889i | \(0.0846752\pi\) | ||||
−0.964826 | + | 0.262889i | \(0.915325\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12646.2 | 0.600030 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5856.09 | − | 8881.79i | −0.276768 | − | 0.419767i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22570.3 | −1.06254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5492.77 | 0.257574 | 0.128787 | − | 0.991672i | \(-0.458892\pi\) | ||||
0.128787 | + | 0.991672i | \(0.458892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11338.0 | − | 3401.38i | 0.529609 | − | 0.158882i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21115.4 | −0.982497 | −0.491248 | − | 0.871020i | \(-0.663459\pi\) | ||||
−0.491248 | + | 0.871020i | \(0.663459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3831.77i | 0.177602i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3348.17 | + | 11160.6i | 0.154588 | + | 0.515297i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2795.33i | 0.128566i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 25907.7i | − | 1.18701i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26662.8 | − | 22295.6i | −1.21692 | − | 1.01760i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 16258.7i | − | 0.739235i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38018.5 | −1.72200 | −0.861000 | − | 0.508605i | \(-0.830161\pi\) | ||||
−0.861000 | + | 0.508605i | \(0.830161\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8985.42 | + | 29951.6i | 0.405436 | + | 1.35146i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21250.1 | 0.955205 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1188.51 | −0.0532224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −598.535 | − | 1995.13i | −0.0267017 | − | 0.0890062i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5023.82 | −0.223278 | −0.111639 | − | 0.993749i | \(-0.535610\pi\) | ||||
−0.111639 | + | 0.993749i | \(0.535610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32459.7i | 1.43722i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3978.26 | − | 6033.74i | −0.175487 | − | 0.266157i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 30468.8i | − | 1.33900i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 11964.4i | − | 0.523839i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4492.49 | − | 14975.0i | −0.195964 | − | 0.653218i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9928.57i | − | 0.431483i | −0.976450 | − | 0.215742i | \(-0.930783\pi\) | ||
0.976450 | − | 0.215742i | \(-0.0692169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16918.7 | −0.732549 | −0.366274 | − | 0.930507i | \(-0.619367\pi\) | ||||
−0.366274 | + | 0.930507i | \(0.619367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14469.5 | − | 4340.81i | 0.624190 | − | 0.187256i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −903.082 | −0.0388142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25509.9 | 1.09238 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14457.8 | + | 9532.56i | −0.616846 | + | 0.406709i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18362.5 | −0.780579 | −0.390289 | − | 0.920692i | \(-0.627625\pi\) | ||||
−0.390289 | + | 0.920692i | \(0.627625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35007.5i | 1.48273i | 0.671103 | + | 0.741364i | \(0.265821\pi\) | ||||
−0.671103 | + | 0.741364i | \(0.734179\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7223.59 | − | 2167.06i | 0.304840 | − | 0.0914514i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21104.7i | 0.887404i | 0.896174 | + | 0.443702i | \(0.146335\pi\) | ||||
−0.896174 | + | 0.443702i | \(0.853665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44840.3i | 1.87861i | 0.343085 | + | 0.939304i | \(0.388528\pi\) | ||||
−0.343085 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39674.6 | + | 11902.3i | −1.65619 | + | 0.496855i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10242.1i | − | 0.426011i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17919.5 | 0.742671 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13794.0 | − | 16496.0i | 0.569643 | − | 0.681224i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19998.2 | −0.822900 | −0.411450 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411450 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36983.8 | 1.51641 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4546.18 | − | 1363.85i | 0.185740 | − | 0.0557217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1329.56 | −0.0541281 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 29767.0i | − | 1.20756i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2744.91 | + | 9149.75i | 0.110960 | + | 0.369869i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 25188.2i | − | 1.01462i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27500.9i | 1.10388i | 0.833882 | + | 0.551942i | \(0.186113\pi\) | ||||
−0.833882 | + | 0.551942i | \(0.813887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11643.3 | + | 7676.86i | −0.465723 | + | 0.307068i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1250.31i | 0.0498365i | 0.999689 | + | 0.0249183i | \(0.00793255\pi\) | ||||
−0.999689 | + | 0.0249183i | \(0.992067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15260.3 | −0.606142 | −0.303071 | − | 0.952968i | \(-0.598012\pi\) | ||||
−0.303071 | + | 0.952968i | \(0.598012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 589.679 | + | 1965.61i | 0.0233406 | + | 0.0778023i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15513.7 | 0.611926 | 0.305963 | − | 0.952043i | \(-0.401022\pi\) | ||||
0.305963 | + | 0.952043i | \(0.401022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2649.87 | −0.104160 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1936.77 | − | 6455.93i | −0.0758664 | − | 0.252889i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5423.89 | −0.211730 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 19910.6i | − | 0.774564i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20224.6 | − | 13334.8i | 0.784077 | − | 0.516970i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1824.45i | − | 0.0704888i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 17948.8i | − | 0.691091i | −0.938402 | − | 0.345545i | \(-0.887694\pi\) | ||
0.938402 | − | 0.345545i | \(-0.112306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1108.77 | − | 3695.92i | −0.0425459 | − | 0.141821i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50006.7i | 1.91234i | 0.292817 | + | 0.956169i | \(0.405407\pi\) | ||||
−0.292817 | + | 0.956169i | \(0.594593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2670.53 | 0.101779 | 0.0508894 | − | 0.998704i | \(-0.483794\pi\) | ||||
0.0508894 | + | 0.998704i | \(0.483794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12781.3 | + | 3834.36i | −0.485467 | + | 0.145639i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27123.1 | −1.02672 | −0.513362 | − | 0.858172i | \(-0.671600\pi\) | ||||
−0.513362 | + | 0.858172i | \(0.671600\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24960.2 | 0.941664 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38899.1 | − | 16674.9i | −1.46259 | − | 0.626970i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42552.0 | 1.59457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11361.3i | − | 0.424318i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35856.6 | − | 10756.9i | 1.33469 | − | 0.400405i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37970.6i | 1.40867i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6318.05i | − | 0.233612i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17937.9 | − | 5381.34i | 0.661059 | − | 0.198317i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3841.49i | 0.141100i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33013.5 | 1.20860 | 0.604298 | − | 0.796759i | \(-0.293454\pi\) | ||||
0.604298 | + | 0.796759i | \(0.293454\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24480.6 | − | 16141.0i | 0.893258 | − | 0.588957i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47241.1 | 1.71808 | 0.859038 | − | 0.511912i | \(-0.171062\pi\) | ||||
0.859038 | + | 0.511912i | \(0.171062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −72566.3 | −2.63044 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −673.041 | + | 201.911i | −0.0243170 | + | 0.00729506i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14508.2 | 0.522468 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50644.8i | 1.81787i | 0.416942 | + | 0.908933i | \(0.363102\pi\) | ||||
−0.416942 | + | 0.908933i | \(0.636898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12419.0 | − | 41397.1i | −0.444323 | − | 1.48108i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19610.4i | − | 0.699333i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 3840.94i | − | 0.136529i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8956.00 | + | 13583.4i | 0.317318 | + | 0.481269i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 36463.1i | − | 1.28774i | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||
0.765133 | − | 0.643872i | \(-0.222673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13426.5 | −0.472650 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4503.67 | + | 15012.3i | 0.158032 | + | 0.526776i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22875.2 | 0.800106 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1429.44 | −0.0498376 | −0.0249188 | − | 0.999689i | \(-0.507933\pi\) | ||||
−0.0249188 | + | 0.999689i | \(0.507933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14035.8 | − | 46786.3i | −0.487797 | − | 1.62600i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8397.60 | 0.290918 | 0.145459 | − | 0.989364i | \(-0.453534\pi\) | ||||
0.145459 | + | 0.989364i | \(0.453534\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4436.14i | − | 0.153193i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6567.85 | + | 7854.36i | −0.226087 | + | 0.270373i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 43156.1i | − | 1.48087i | −0.672127 | − | 0.740436i | \(-0.734619\pi\) | ||
0.672127 | − | 0.740436i | \(-0.265381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 23062.8i | − | 0.788883i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8662.77 | + | 28876.1i | 0.295383 | + | 0.984616i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20652.4i | − | 0.701991i | −0.936377 | − | 0.350995i | \(-0.885843\pi\) | ||
0.936377 | − | 0.350995i | \(-0.114157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6691.07 | −0.226720 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 71581.5 | − | 21474.3i | 2.41787 | − | 0.725356i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3183.81 | 0.107206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6299.02 | 0.211440 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3109.84 | − | 4716.63i | −0.104064 | − | 0.157831i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4294.05 | 0.143244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27587.9i | − | 0.917443i | −0.888580 | − | 0.458721i | \(-0.848308\pi\) | ||
0.888580 | − | 0.458721i | \(-0.151692\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40517.9 | + | 12155.3i | −1.34326 | + | 0.402977i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 13285.7i | − | 0.439093i | −0.975602 | − | 0.219547i | \(-0.929542\pi\) | ||
0.975602 | − | 0.219547i | \(-0.0704578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12726.8i | − | 0.419324i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5467.77 | − | 1640.32i | 0.179599 | − | 0.0538793i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20541.2i | − | 0.672642i | −0.941747 | − | 0.336321i | \(-0.890817\pi\) | ||
0.941747 | − | 0.336321i | \(-0.109183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15540.0 | 0.507314 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12877.3 | + | 19530.7i | 0.419103 | + | 0.635644i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28203.9 | −0.915123 | −0.457562 | − | 0.889178i | \(-0.651277\pi\) | ||||
−0.457562 | + | 0.889178i | \(0.651277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15202.1 | 0.491754 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29921.6 | − | 8976.42i | 0.964958 | − | 0.289486i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40483.7 | −1.30162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 30236.1i | − | 0.969206i | −0.874734 | − | 0.484603i | \(-0.838964\pi\) | ||
0.874734 | − | 0.484603i | \(-0.161036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8954.48 | + | 29848.4i | 0.286165 | + | 0.953888i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8184.76i | 0.260778i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 848.710i | 0.0269598i | 0.999909 | + | 0.0134799i | \(0.00429091\pi\) | ||||
−0.999909 | + | 0.0134799i | \(0.995709\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13827.0 | + | 16535.5i | −0.437906 | + | 0.523683i |
(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 | 480.4.b.a.431.16 | 24 | ||
3.2 | odd | 2 | 480.4.b.b.431.15 | 24 | |||
4.3 | odd | 2 | 120.4.b.b.11.19 | yes | 24 | ||
8.3 | odd | 2 | 480.4.b.b.431.16 | 24 | |||
8.5 | even | 2 | 120.4.b.a.11.5 | ✓ | 24 | ||
12.11 | even | 2 | 120.4.b.a.11.6 | yes | 24 | ||
24.5 | odd | 2 | 120.4.b.b.11.20 | yes | 24 | ||
24.11 | even | 2 | inner | 480.4.b.a.431.15 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.b.a.11.5 | ✓ | 24 | 8.5 | even | 2 | ||
120.4.b.a.11.6 | yes | 24 | 12.11 | even | 2 | ||
120.4.b.b.11.19 | yes | 24 | 4.3 | odd | 2 | ||
120.4.b.b.11.20 | yes | 24 | 24.5 | odd | 2 | ||
480.4.b.a.431.15 | 24 | 24.11 | even | 2 | inner | ||
480.4.b.a.431.16 | 24 | 1.1 | even | 1 | trivial | ||
480.4.b.b.431.15 | 24 | 3.2 | odd | 2 | |||
480.4.b.b.431.16 | 24 | 8.3 | odd | 2 |