Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Character | \(\chi\) | \(=\) | 256.33 |
Dual form | 256.4.g.b.225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −3.54796 | + | 8.56554i | −0.682806 | + | 1.64844i | 0.0759878 | + | 0.997109i | \(0.475789\pi\) |
−0.758794 | + | 0.651331i | \(0.774211\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.55322 | − | 3.12865i | 0.675581 | − | 0.279835i | −0.0183975 | − | 0.999831i | \(-0.505856\pi\) |
0.693978 | + | 0.719996i | \(0.255856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.16166 | − | 7.16166i | 0.386693 | − | 0.386693i | −0.486813 | − | 0.873506i | \(-0.661841\pi\) |
0.873506 | + | 0.486813i | \(0.161841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −41.6886 | − | 41.6886i | −1.54402 | − | 1.54402i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.758120 | − | 1.83026i | −0.0207802 | − | 0.0501678i | 0.913149 | − | 0.407626i | \(-0.133643\pi\) |
−0.933929 | + | 0.357458i | \(0.883643\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −71.0832 | − | 29.4436i | −1.51653 | − | 0.628168i | −0.539639 | − | 0.841896i | \(-0.681439\pi\) |
−0.976893 | + | 0.213728i | \(0.931439\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 75.7978i | 1.30473i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 98.5470i | − | 1.40595i | −0.711214 | − | 0.702975i | \(-0.751854\pi\) | ||
0.711214 | − | 0.702975i | \(-0.248146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −89.5748 | − | 37.1031i | −1.08157 | − | 0.448002i | −0.230512 | − | 0.973070i | \(-0.574040\pi\) |
−0.851060 | + | 0.525068i | \(0.824040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.9342 | + | 86.7528i | 0.373404 | + | 0.901477i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.9355 | + | 24.9355i | 0.226062 | + | 0.226062i | 0.811045 | − | 0.584984i | \(-0.198899\pi\) |
−0.584984 | + | 0.811045i | \(0.698899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −41.1256 | + | 41.1256i | −0.329005 | + | 0.329005i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 273.726 | − | 113.381i | 1.95106 | − | 0.808154i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 57.8528 | − | 139.669i | 0.370448 | − | 0.894341i | −0.623226 | − | 0.782042i | \(-0.714178\pi\) |
0.993674 | − | 0.112299i | \(-0.0358216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.0545 | 0.336351 | 0.168176 | − | 0.985757i | \(-0.446212\pi\) | ||||
0.168176 | + | 0.985757i | \(0.446212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.3670 | 0.0968874 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.6873 | − | 76.4999i | 0.153032 | − | 0.369453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 202.968 | − | 84.0720i | 0.901829 | − | 0.373550i | 0.116906 | − | 0.993143i | \(-0.462702\pi\) |
0.784923 | + | 0.619593i | \(0.212702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 504.401 | − | 504.401i | 2.07100 | − | 2.07100i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −45.3618 | − | 45.3618i | −0.172788 | − | 0.172788i | 0.615415 | − | 0.788203i | \(-0.288988\pi\) |
−0.788203 | + | 0.615415i | \(0.788988\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −89.7175 | − | 216.597i | −0.318181 | − | 0.768157i | −0.999351 | − | 0.0360314i | \(-0.988528\pi\) |
0.681170 | − | 0.732126i | \(-0.261472\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −445.312 | − | 184.454i | −1.47518 | − | 0.611041i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.38416i | − | 0.0136063i | −0.999977 | − | 0.00680315i | \(-0.997834\pi\) | ||
0.999977 | − | 0.00680315i | \(-0.00216553\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 240.421i | 0.700937i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 844.109 | + | 349.641i | 2.31762 | + | 0.959992i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.98141 | − | 21.6830i | −0.0232772 | − | 0.0561961i | 0.911814 | − | 0.410604i | \(-0.134682\pi\) |
−0.935091 | + | 0.354408i | \(0.884682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.4525 | − | 11.4525i | −0.0280774 | − | 0.0280774i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 635.616 | − | 635.616i | 1.47701 | − | 1.47701i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −287.366 | + | 119.031i | −0.634099 | + | 0.262652i | −0.676494 | − | 0.736448i | \(-0.736501\pi\) |
0.0423945 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28.2072 | − | 68.0983i | 0.0592060 | − | 0.142936i | −0.891508 | − | 0.453005i | \(-0.850352\pi\) |
0.950714 | + | 0.310069i | \(0.100352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −597.119 | −1.19413 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −629.026 | −1.20032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −293.521 | + | 708.622i | −0.535213 | + | 1.29212i | 0.392818 | + | 0.919616i | \(0.371500\pi\) |
−0.928031 | + | 0.372502i | \(0.878500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −302.057 | + | 125.116i | −0.527005 | + | 0.218293i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −579.730 | + | 579.730i | −0.969032 | + | 0.969032i | −0.999535 | − | 0.0305030i | \(-0.990289\pi\) |
0.0305030 | + | 0.999535i | \(0.490289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −258.894 | − | 258.894i | −0.415085 | − | 0.415085i | 0.468420 | − | 0.883506i | \(-0.344823\pi\) |
−0.883506 | + | 0.468420i | \(0.844823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −206.351 | − | 498.176i | −0.317698 | − | 0.766991i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.5371 | − | 7.67833i | −0.0274351 | − | 0.0113640i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 834.510i | − | 1.18848i | −0.804289 | − | 0.594239i | \(-0.797453\pi\) | ||
0.804289 | − | 0.594239i | \(-0.202547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1155.05i | 1.58443i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −234.905 | − | 97.3009i | −0.310653 | − | 0.128677i | 0.221910 | − | 0.975067i | \(-0.428771\pi\) |
−0.532563 | + | 0.846391i | \(0.678771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −308.319 | − | 744.347i | −0.393434 | − | 0.949833i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 991.082 | + | 991.082i | 1.22132 | + | 1.22132i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 179.539 | − | 179.539i | 0.213833 | − | 0.213833i | −0.592061 | − | 0.805893i | \(-0.701685\pi\) |
0.805893 | + | 0.592061i | \(0.201685\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −719.939 | + | 298.208i | −0.829342 | + | 0.343525i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −205.975 | + | 497.268i | −0.229663 | + | 0.554455i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −792.661 | −0.856056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −624.033 | −0.653205 | −0.326603 | − | 0.945162i | \(-0.605904\pi\) | ||||
−0.326603 | + | 0.945162i | \(0.605904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −44.6962 | + | 107.906i | −0.0453751 | + | 0.109545i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1513.83 | − | 627.049i | 1.49140 | − | 0.617760i | 0.519782 | − | 0.854299i | \(-0.326013\pi\) |
0.971622 | + | 0.236540i | \(0.0760133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 146.406 | − | 146.406i | 0.140056 | − | 0.140056i | −0.633603 | − | 0.773659i | \(-0.718425\pi\) |
0.773659 | + | 0.633603i | \(0.218425\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 542.838 | + | 542.838i | 0.504529 | + | 0.504529i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −375.001 | − | 905.331i | −0.338810 | − | 0.817960i | −0.997831 | − | 0.0658347i | \(-0.979029\pi\) |
0.659021 | − | 0.752125i | \(-0.270971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 330.443 | + | 136.874i | 0.290373 | + | 0.120277i | 0.523115 | − | 0.852262i | \(-0.324770\pi\) |
−0.232742 | + | 0.972539i | \(0.574770\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2036.81i | 1.74167i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 743.066i | 0.618600i | 0.950965 | + | 0.309300i | \(0.100095\pi\) | ||||
−0.950965 | + | 0.309300i | \(0.899905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 266.358 | + | 110.329i | 0.215983 | + | 0.0894630i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1735.89 | + | 4190.82i | 1.37165 | + | 3.31147i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −705.760 | − | 705.760i | −0.543672 | − | 0.543672i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 938.384 | − | 938.384i | 0.705022 | − | 0.705022i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 549.491 | − | 227.606i | 0.402812 | − | 0.166850i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −573.044 | + | 1383.45i | −0.410037 | + | 0.989917i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −316.036 | −0.220816 | −0.110408 | − | 0.993886i | \(-0.535216\pi\) | ||||
−0.110408 | + | 0.993886i | \(0.535216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2173.59 | 1.48352 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 126.926 | − | 306.426i | 0.0846532 | − | 0.204371i | −0.875884 | − | 0.482521i | \(-0.839721\pi\) |
0.960538 | + | 0.278150i | \(0.0897212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −907.224 | + | 375.785i | −0.591476 | + | 0.244997i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1712.78 | − | 1712.78i | 1.09195 | − | 1.09195i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −465.127 | − | 465.127i | −0.290062 | − | 0.290062i | 0.547043 | − | 0.837105i | \(-0.315754\pi\) |
−0.837105 | + | 0.547043i | \(0.815754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −158.069 | − | 381.612i | −0.0964548 | − | 0.232863i | 0.868286 | − | 0.496064i | \(-0.165222\pi\) |
−0.964741 | + | 0.263201i | \(0.915222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.5528 | + | 15.5549i | 0.0224292 | + | 0.00929046i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 152.423i | 0.0891345i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1235.95i | − | 0.707864i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2059.34 | − | 853.006i | −1.15545 | − | 0.478604i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −316.900 | − | 765.063i | −0.174238 | − | 0.420647i | 0.812502 | − | 0.582959i | \(-0.198105\pi\) |
−0.986740 | + | 0.162312i | \(0.948105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1447.99 | − | 1447.99i | −0.780369 | − | 0.780369i | 0.199524 | − | 0.979893i | \(-0.436060\pi\) |
−0.979893 | + | 0.199524i | \(0.936060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4108.29 | + | 4108.29i | −2.17082 | + | 2.17082i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 438.498 | − | 181.632i | 0.227233 | − | 0.0941228i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1154.08 | − | 2786.21i | 0.586662 | − | 1.41633i | −0.300013 | − | 0.953935i | \(-0.596991\pi\) |
0.886675 | − | 0.462393i | \(-0.153009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 217.593 | 0.108530 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 357.160 | 0.174833 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1315.01 | + | 3174.72i | −0.631899 | + | 1.52554i | 0.205333 | + | 0.978692i | \(0.434172\pi\) |
−0.837232 | + | 0.546848i | \(0.815828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 138.730 | − | 57.4638i | 0.0654552 | − | 0.0271125i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2616.84 | + | 2616.84i | −1.21256 | + | 1.21256i | −0.242376 | + | 0.970182i | \(0.577927\pi\) |
−0.970182 | + | 0.242376i | \(0.922073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2632.38 | + | 2632.38i | 1.19817 | + | 1.19817i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2187.47 | + | 5281.03i | 0.978247 | + | 2.36170i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1699.43 | − | 703.925i | −0.746849 | − | 0.309355i | −0.0233941 | − | 0.999726i | \(-0.507447\pi\) |
−0.723455 | + | 0.690371i | \(0.757447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 589.055i | 0.254448i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2883.76i | − | 1.22461i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1726.10 | − | 714.972i | −0.720751 | − | 0.298545i | −0.00800596 | − | 0.999968i | \(-0.502548\pi\) |
−0.712745 | + | 0.701423i | \(0.752548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1087.42 | − | 2625.26i | −0.446559 | − | 1.07809i | −0.973602 | − | 0.228251i | \(-0.926699\pi\) |
0.527043 | − | 0.849839i | \(-0.323301\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 483.221 | + | 483.221i | 0.195195 | + | 0.195195i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1270.03 | − | 1270.03i | 0.504726 | − | 0.504726i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −180.367 | + | 74.7105i | −0.0705334 | + | 0.0292159i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1148.33 | − | 2772.32i | 0.441953 | − | 1.06697i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1649.64 | 0.624940 | 0.312470 | − | 0.949928i | \(-0.398844\pi\) | ||||
0.312470 | + | 0.949928i | \(0.398844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1928.59 | −0.719291 | −0.359645 | − | 0.933089i | \(-0.617102\pi\) | ||||
−0.359645 | + | 0.933089i | \(0.617102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2231.76 | − | 5387.95i | 0.819588 | − | 1.97866i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3725.06 | + | 1542.97i | −1.34720 | + | 0.558030i | −0.935513 | − | 0.353293i | \(-0.885062\pi\) |
−0.411692 | + | 0.911323i | \(0.635062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 361.648 | − | 361.648i | 0.128827 | − | 0.128827i | −0.639753 | − | 0.768580i | \(-0.720964\pi\) |
0.768580 | + | 0.639753i | \(0.220964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5028.33 | − | 5028.33i | −1.76453 | − | 1.76453i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −585.940 | − | 1414.58i | −0.202586 | − | 0.489086i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −484.549 | − | 200.707i | −0.165085 | − | 0.0683803i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2079.06i | − | 0.698089i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 192.074i | 0.0635696i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5549.04 | + | 2298.49i | 1.81048 | + | 0.749927i | 0.981721 | + | 0.190325i | \(0.0609543\pi\) |
0.828762 | + | 0.559601i | \(0.189046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2908.84 | − | 7022.56i | −0.935730 | − | 2.25905i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1355.31 | − | 1355.31i | −0.429914 | − | 0.429914i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 415.767 | − | 415.767i | 0.130065 | − | 0.130065i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3136.11 | − | 1299.02i | 0.967666 | − | 0.400820i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2901.58 | + | 7005.03i | −0.883174 | + | 2.13217i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2968.26 | 0.891344 | 0.445672 | − | 0.895196i | \(-0.352965\pi\) | ||||
0.445672 | + | 0.895196i | \(0.352965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3428.94 | 1.01598 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 947.980 | − | 2288.63i | 0.277179 | − | 0.669169i | −0.722576 | − | 0.691291i | \(-0.757042\pi\) |
0.999755 | + | 0.0221219i | \(0.00704218\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5763.17 | − | 2387.18i | 1.66306 | − | 0.688862i | 0.664756 | − | 0.747061i | \(-0.268536\pi\) |
0.998305 | + | 0.0581984i | \(0.0185356\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 131.538 | − | 131.538i | 0.0374657 | − | 0.0374657i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3036.23 | + | 3036.23i | 0.853691 | + | 0.853691i | 0.990586 | − | 0.136895i | \(-0.0437122\pi\) |
−0.136895 | + | 0.990586i | \(0.543712\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.7165 | − | 33.1146i | −0.00380751 | − | 0.00919215i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7148.03 | + | 2960.81i | 1.95913 | + | 0.811500i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6291.50i | − | 1.70278i | −0.524537 | − | 0.851388i | \(-0.675761\pi\) | ||
0.524537 | − | 0.851388i | \(-0.324239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 795.320i | 0.212577i | 0.994335 | + | 0.106289i | \(0.0338967\pi\) | ||||
−0.994335 | + | 0.106289i | \(0.966103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2503.05 | − | 1036.80i | −0.660786 | − | 0.273706i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 752.193 | + | 1815.95i | 0.196146 | + | 0.473539i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5274.81 | + | 5274.81i | 1.35882 | + | 1.35882i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1666.87 | − | 1666.87i | 0.424231 | − | 0.424231i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6040.73 | + | 2502.15i | −1.51907 | + | 0.629221i | −0.977406 | − | 0.211372i | \(-0.932207\pi\) |
−0.541668 | + | 0.840593i | \(0.682207\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.7345 | − | 64.5428i | 0.00664341 | − | 0.0160386i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7469.64 | 1.83438 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3591.20 | −0.871645 | −0.435823 | − | 0.900033i | \(-0.643543\pi\) | ||||
−0.435823 | + | 0.900033i | \(0.643543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 851.491 | − | 2055.68i | 0.204282 | − | 0.493181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8234.41 | + | 3410.80i | −1.95286 | + | 0.808902i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2616.63 | + | 2616.63i | −0.613491 | + | 0.613491i | −0.943854 | − | 0.330363i | \(-0.892829\pi\) |
0.330363 | + | 0.943854i | \(0.392829\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −135.677 | − | 135.677i | −0.0314513 | − | 0.0314513i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 900.853 | + | 2174.85i | 0.206484 | + | 0.498497i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6877.53 | + | 2848.77i | 1.55885 | + | 0.645697i | 0.984889 | − | 0.173186i | \(-0.0554061\pi\) |
0.573961 | + | 0.818883i | \(0.305406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6338.06i | − | 1.42070i | −0.703848 | − | 0.710350i | \(-0.748537\pi\) | ||
0.703848 | − | 0.710350i | \(-0.251463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7224.70i | − | 1.60168i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 106.449 | + | 44.0926i | 0.0233422 | + | 0.00966867i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −655.560 | − | 1582.66i | −0.142198 | − | 0.343296i | 0.836695 | − | 0.547669i | \(-0.184485\pi\) |
−0.978893 | + | 0.204373i | \(0.934485\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2420.21 | − | 2420.21i | −0.519334 | − | 0.519334i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3436.47 | + | 3436.47i | −0.729547 | + | 0.729547i | −0.970529 | − | 0.240983i | \(-0.922530\pi\) |
0.240983 | + | 0.970529i | \(0.422530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5101.55 | − | 2113.13i | 1.07158 | − | 0.443861i | 0.224029 | − | 0.974582i | \(-0.428079\pi\) |
0.847546 | + | 0.530722i | \(0.178079\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2812.33 | − | 6789.57i | 0.584520 | − | 1.41116i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −649.732 | −0.133632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4798.52 | −0.976698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2214.05 | − | 5345.18i | 0.446013 | − | 1.07677i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2820.64 | + | 1168.35i | −0.562402 | + | 0.232954i | −0.645727 | − | 0.763568i | \(-0.723446\pi\) |
0.0833258 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1798.13 | + | 1798.13i | −0.354886 | + | 0.354886i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −415.034 | − | 415.034i | −0.0810866 | − | 0.0810866i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1038.30 | − | 2506.69i | −0.200825 | − | 0.484835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2193.72 | − | 908.669i | −0.420080 | − | 0.174003i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15191.5i | 2.88030i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 602.612i | − | 0.113133i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −424.120 | − | 175.676i | −0.0788463 | − | 0.0326592i | 0.342912 | − | 0.939368i | \(-0.388587\pi\) |
−0.421758 | + | 0.906708i | \(0.638587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 734.603 | + | 1773.49i | 0.135243 | + | 0.326506i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3761.67 | − | 3761.67i | −0.685868 | − | 0.685868i | 0.275448 | − | 0.961316i | \(-0.411174\pi\) |
−0.961316 | + | 0.275448i | \(0.911174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 718.221 | − | 718.221i | 0.129700 | − | 0.129700i | −0.639277 | − | 0.768977i | \(-0.720766\pi\) |
0.768977 | + | 0.639277i | \(0.220766\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4510.17 | + | 1868.18i | −0.806729 | + | 0.334158i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1315.47 | + | 3175.83i | −0.233073 | + | 0.562689i | −0.996536 | − | 0.0831634i | \(-0.973498\pi\) |
0.763463 | + | 0.645852i | \(0.223498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −299.491 | −0.0525651 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9085.14 | 1.57970 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3656.40 | + | 8827.33i | −0.629869 | + | 1.52064i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4134.23 | − | 1712.45i | 0.705617 | − | 0.292276i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2344.80 | + | 2344.80i | −0.396537 | + | 0.396537i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.3979 | − | 31.3979i | −0.00526147 | − | 0.00526147i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −515.566 | − | 1244.69i | −0.0856136 | − | 0.206689i | 0.875274 | − | 0.483626i | \(-0.160681\pi\) |
−0.960888 | + | 0.276937i | \(0.910681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11966.3 | − | 4956.60i | −1.96921 | − | 0.815675i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6270.70i | 1.02270i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4770.86i | 0.771173i | 0.922672 | + | 0.385587i | \(0.126001\pi\) | ||||
−0.922672 | + | 0.385587i | \(0.873999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6364.77 | − | 2636.37i | −1.01972 | − | 0.422384i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.0123 | − | 106.255i | −0.00698944 | − | 0.0168740i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4178.26 | + | 4178.26i | 0.657741 | + | 0.657741i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1890.06 | + | 1890.06i | −0.294949 | + | 0.294949i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2534.53 | + | 1049.84i | −0.392105 | + | 0.162415i | −0.570021 | − | 0.821630i | \(-0.693065\pi\) |
0.177915 | + | 0.984046i | \(0.443065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1115.54 | + | 2693.15i | −0.171099 | + | 0.413069i | −0.986048 | − | 0.166464i | \(-0.946765\pi\) |
0.814949 | + | 0.579533i | \(0.196765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22795.6 | −3.46650 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2416.71 | 0.364387 | 0.182193 | − | 0.983263i | \(-0.441680\pi\) | ||||
0.182193 | + | 0.983263i | \(0.441680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2565.06 | + | 6192.60i | −0.383490 | + | 0.925828i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8549.23 | − | 3541.21i | 1.26743 | − | 0.524988i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8445.07 | − | 8445.07i | 1.24154 | − | 1.24154i | 0.282182 | − | 0.959361i | \(-0.408942\pi\) |
0.959361 | − | 0.282182i | \(-0.0910582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1796.96 | + | 1796.96i | 0.261986 | + | 0.261986i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4708.42 | + | 11367.1i | 0.680793 | + | 1.64358i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2765.47 | − | 1145.49i | −0.396579 | − | 0.164268i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1632.32i | − | 0.232170i | −0.993239 | − | 0.116085i | \(-0.962966\pi\) | ||
0.993239 | − | 0.116085i | \(-0.0370345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3782.14i | 0.533578i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −219.608 | − | 90.9648i | −0.0307318 | − | 0.0127295i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5198.39 | + | 12550.0i | 0.721615 | + | 1.74213i | 0.668700 | + | 0.743533i | \(0.266851\pi\) |
0.0529149 | + | 0.998599i | \(0.483149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9816.87 | − | 9816.87i | −1.35184 | − | 1.35184i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8224.72 | + | 8224.72i | −1.12359 | + | 1.12359i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4404.78 | − | 1824.52i | 0.596987 | − | 0.247280i | −0.0636663 | − | 0.997971i | \(-0.520279\pi\) |
0.660653 | + | 0.750691i | \(0.270279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1121.28 | − | 2707.02i | 0.150775 | − | 0.364002i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7295.56 | 0.973331 | 0.486665 | − | 0.873589i | \(-0.338213\pi\) | ||||
0.486665 | + | 0.873589i | \(0.338213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −164.038 | −0.0217147 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5289.44 | + | 12769.8i | −0.694773 | + | 1.67733i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2614.79 | − | 1083.08i | 0.340810 | − | 0.141168i | −0.205712 | − | 0.978612i | \(-0.565951\pi\) |
0.546523 | + | 0.837444i | \(0.315951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2457.32 | − | 2457.32i | 0.317832 | − | 0.317832i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2174.38 | + | 2174.38i | 0.279091 | + | 0.279091i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2610.89 | − | 6303.24i | −0.332577 | − | 0.802913i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1867.07 | + | 773.367i | 0.236034 | + | 0.0977687i | 0.497566 | − | 0.867426i | \(-0.334227\pi\) |
−0.261531 | + | 0.965195i | \(0.584227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 9104.14i | − | 1.14230i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12147.1i | 1.51271i | 0.654162 | + | 0.756354i | \(0.273021\pi\) | ||||
−0.654162 | + | 0.756354i | \(0.726979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4126.70 | − | 1709.33i | −0.510088 | − | 0.211285i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3613.75 | + | 8724.36i | 0.443379 | + | 1.07041i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −307.748 | − | 307.748i | −0.0374803 | − | 0.0374803i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9049.93 | − | 9049.93i | 1.09411 | − | 1.09411i | 0.0990235 | − | 0.995085i | \(-0.468428\pi\) |
0.995085 | − | 0.0990235i | \(-0.0315719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5634.32 | − | 2333.81i | 0.676206 | − | 0.280094i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1205.56 | + | 2910.48i | −0.143636 | + | 0.346768i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2078.71 | −0.245879 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3829.54 | 0.449720 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5216.15 | − | 12592.9i | 0.608176 | − | 1.46827i | −0.256806 | − | 0.966463i | \(-0.582670\pi\) |
0.864982 | − | 0.501803i | \(-0.167330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12044.9 | + | 4989.15i | −1.39437 | + | 0.577568i | −0.948285 | − | 0.317421i | \(-0.897183\pi\) |
−0.446088 | + | 0.894989i | \(0.647183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −182.770 | + | 182.770i | −0.0210084 | + | 0.0210084i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4052.81 | + | 4052.81i | 0.462565 | + | 0.462565i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −285.686 | − | 689.708i | −0.0323778 | − | 0.0781670i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1305.58 | − | 540.791i | −0.146933 | − | 0.0608616i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3074.64i | 0.343620i | 0.985130 | + | 0.171810i | \(0.0549615\pi\) | ||||
−0.985130 | + | 0.171810i | \(0.945039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3478.83i | − | 0.386101i | −0.981189 | − | 0.193051i | \(-0.938162\pi\) | ||
0.981189 | − | 0.193051i | \(-0.0618381\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10586.6 | + | 4385.12i | 1.16687 | + | 0.483334i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1308.41 | − | 3158.78i | −0.143226 | − | 0.345778i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6595.03 | + | 6595.03i | 0.717001 | + | 0.717001i | 0.967990 | − | 0.250989i | \(-0.0807557\pi\) |
−0.250989 | + | 0.967990i | \(0.580756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10022.8 | − | 10022.8i | 1.08226 | − | 1.08226i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1177.46 | + | 487.720i | −0.126282 | + | 0.0523076i | −0.444930 | − | 0.895566i | \(-0.646771\pi\) |
0.318648 | + | 0.947873i | \(0.396771\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 794.385 | − | 1917.82i | 0.0846235 | − | 0.204299i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7677.53 | 0.812382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −517.491 | −0.0543918 | −0.0271959 | − | 0.999630i | \(-0.508658\pi\) | ||||
−0.0271959 | + | 0.999630i | \(0.508658\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.6344 | + | 117.414i | −0.00507784 | + | 0.0122590i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17540.2 | − | 7265.40i | 1.81923 | − | 0.753550i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4504.87 | + | 4504.87i | −0.464157 | + | 0.464157i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1142.85 | + | 1142.85i | 0.116981 | + | 0.116981i | 0.763174 | − | 0.646193i | \(-0.223640\pi\) |
−0.646193 | + | 0.763174i | \(0.723640\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11173.3 | − | 26974.8i | −1.13622 | − | 2.74309i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7860.73 | + | 3256.02i | 0.794166 | + | 0.328954i | 0.742617 | − | 0.669716i | \(-0.233584\pi\) |
0.0515489 | + | 0.998670i | \(0.483584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2545.63i | 0.255519i | 0.991805 | + | 0.127760i | \(0.0407786\pi\) | ||||
−0.991805 | + | 0.127760i | \(0.959221\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4400.40i | 0.438847i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7269.46 | + | 3011.11i | 0.720322 | + | 0.298367i | 0.712568 | − | 0.701603i | \(-0.247532\pi\) |
0.00775364 | + | 0.999970i | \(0.497532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2972.81 | + | 7177.01i | 0.292690 | + | 0.706617i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19770.7 | + | 19770.7i | 1.93415 | + | 1.93415i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −328.413 | + | 328.413i | −0.0319249 | + | 0.0319249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5209.71 | − | 2157.93i | 0.503237 | − | 0.208448i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −529.513 | + | 1278.36i | −0.0508276 | + | 0.122709i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19071.7 | −1.81922 | −0.909612 | − | 0.415459i | \(-0.863621\pi\) | ||||
−0.909612 | + | 0.415459i | \(0.863621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16903.0 | −1.60231 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1267.19 | + | 3059.27i | −0.119377 | + | 0.288202i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4713.46 | + | 1952.38i | −0.441293 | + | 0.182790i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4422.93 | − | 4422.93i | 0.411544 | − | 0.411544i | −0.470732 | − | 0.882276i | \(-0.656010\pi\) |
0.882276 | + | 0.470732i | \(0.156010\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −22527.6 | − | 22527.6i | −2.08330 | − | 2.08330i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1908.12 | + | 4606.60i | 0.175381 | + | 0.423408i | 0.986987 | − | 0.160797i | \(-0.0514065\pi\) |
−0.811606 | + | 0.584205i | \(0.801407\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13764.0 | − | 5701.22i | −1.25740 | − | 0.520832i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 954.878i | 0.0867042i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8303.65i | 0.749436i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9996.34 | + | 4140.62i | 0.896789 | + | 0.371462i | 0.782985 | − | 0.622041i | \(-0.213696\pi\) |
0.113804 | + | 0.993503i | \(0.463696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13130.2 | − | 31699.1i | −1.17089 | − | 2.82677i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6186.59 | − | 6186.59i | −0.548402 | − | 0.548402i | 0.377576 | − | 0.925978i | \(-0.376758\pi\) |
−0.925978 | + | 0.377576i | \(0.876758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9472.48 | − | 9472.48i | 0.834693 | − | 0.834693i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31887.3 | + | 13208.2i | −2.79323 | + | 1.15699i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1472.42 | + | 3554.75i | −0.128220 | + | 0.309551i | −0.974933 | − | 0.222500i | \(-0.928578\pi\) |
0.846713 | + | 0.532051i | \(0.178578\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3708.22 | −0.321021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28725.7 | −2.47226 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 647.783 | − | 1563.89i | 0.0554267 | − | 0.133812i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.02418 | + | 3.32372i | −0.000682598 | + | 0.000282741i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12059.0 | − | 12059.0i | 1.01991 | − | 1.01991i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.6914 | − | 41.6914i | −0.00350582 | − | 0.00350582i | 0.705352 | − | 0.708858i | \(-0.250789\pi\) |
−0.708858 | + | 0.705352i | \(0.750789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6675.06 | − | 16115.0i | −0.558088 | − | 1.34734i | −0.911278 | − | 0.411791i | \(-0.864903\pi\) |
0.353191 | − | 0.935551i | \(-0.385097\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5045.58 | − | 2089.95i | −0.419442 | − | 0.173739i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5721.10i | − | 0.472894i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10923.4i | − | 0.897792i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16942.1 | + | 7017.65i | 1.38460 | + | 0.573522i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1888.85 | + | 4560.08i | 0.153499 | + | 0.370579i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5664.92 | − | 5664.92i | −0.457787 | − | 0.457787i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12248.3 | − | 12248.3i | 0.984266 | − | 0.984266i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 440.035 | − | 182.268i | 0.0351644 | − | 0.0145656i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5953.02 | − | 14371.9i | 0.473087 | − | 1.14213i | −0.489704 | − | 0.871889i | \(-0.662895\pi\) |
0.962792 | − | 0.270245i | \(-0.0871048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 26344.9 | 2.08208 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2924.14 | 0.229828 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2956.49 | + | 7137.60i | −0.231098 | + | 0.557919i | −0.996307 | − | 0.0858625i | \(-0.972635\pi\) |
0.765209 | + | 0.643782i | \(0.222635\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4014.84 | + | 1663.00i | −0.312112 | + | 0.129281i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10364.3 | + | 10364.3i | −0.801333 | + | 0.801333i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5976.48 | − | 5976.48i | −0.459576 | − | 0.459576i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6372.47 | + | 15384.5i | 0.487381 | + | 1.17664i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6601.43 | + | 2734.40i | 0.502176 | + | 0.208008i | 0.619367 | − | 0.785101i | \(-0.287389\pi\) |
−0.117192 | + | 0.993109i | \(0.537389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18038.0i | 1.36481i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1810.01i | − | 0.136219i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17608.4 | − | 7293.65i | −1.31813 | − | 0.545987i | −0.390883 | − | 0.920440i | \(-0.627830\pi\) |
−0.927246 | + | 0.374453i | \(0.877830\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2324.79 | + | 5612.54i | 0.173106 | + | 0.417914i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8272.09 | + | 8272.09i | 0.612690 | + | 0.612690i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13651.2 | + | 13651.2i | −1.00578 | + | 1.00578i | −0.00579351 | + | 0.999983i | \(0.501844\pi\) |
−0.999983 | + | 0.00579351i | \(0.998156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15023.6 | − | 6222.97i | 1.10108 | − | 0.456083i | 0.243224 | − | 0.969970i | \(-0.421795\pi\) |
0.857858 | + | 0.513887i | \(0.171795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5852.85 | + | 14130.0i | −0.426713 | + | 1.03018i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2050.98 | −0.148751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17031.0 | 1.22879 | 0.614394 | − | 0.788999i | \(-0.289400\pi\) | ||||
0.614394 | + | 0.788999i | \(0.289400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6842.58 | − | 16519.4i | 0.491136 | − | 1.18571i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2379.15 | + | 985.475i | −0.169886 | + | 0.0703690i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.8767 | + | 32.8767i | −0.00233553 | + | 0.00233553i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26223.2 | + | 26223.2i | 1.85333 | + | 1.85333i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6926.72 | + | 16722.6i | 0.487046 | + | 1.17583i | 0.956199 | + | 0.292717i | \(0.0945594\pi\) |
−0.469153 | + | 0.883117i | \(0.655441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5200.22 | − | 2154.00i | −0.363788 | − | 0.150686i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 37381.5i | − | 2.60181i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23359.0i | − | 1.61760i | −0.588082 | − | 0.808801i | \(-0.700117\pi\) | ||
0.588082 | − | 0.808801i | \(-0.299883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7538.84 | − | 3122.69i | −0.519432 | − | 0.215156i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1814.60 | + | 4380.82i | 0.124399 | + | 0.300327i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8027.34 | − | 8027.34i | −0.547559 | − | 0.547559i | 0.378175 | − | 0.925734i | \(-0.376552\pi\) |
−0.925734 | + | 0.378175i | \(0.876552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11725.6 | − | 11725.6i | 0.795837 | − | 0.795837i | −0.186599 | − | 0.982436i | \(-0.559747\pi\) |
0.982436 | + | 0.186599i | \(0.0597466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 41777.9 | − | 17305.0i | 2.82144 | − | 1.16868i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4151.95 | − | 10023.7i | 0.279010 | − | 0.673589i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25799.6 | −1.72516 | −0.862580 | − | 0.505920i | \(-0.831153\pi\) | ||||
−0.862580 | + | 0.505920i | \(0.831153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14195.6 | 0.944555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −129.086 | + | 311.640i | −0.00854705 | + | 0.0206344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8320.05 | + | 3446.28i | −0.548195 | + | 0.227070i | −0.639551 | − | 0.768748i | \(-0.720880\pi\) |
0.0913562 | + | 0.995818i | \(0.470880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3438.32 | − | 3438.32i | 0.225442 | − | 0.225442i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14643.0 | − | 14643.0i | −0.955437 | − | 0.955437i | 0.0436114 | − | 0.999049i | \(-0.486114\pi\) |
−0.999049 | + | 0.0436114i | \(0.986114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 842.686 | + | 2034.42i | 0.0547180 | + | 0.132101i | 0.948874 | − | 0.315654i | \(-0.102224\pi\) |
−0.894156 | + | 0.447755i | \(0.852224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9652.70 | + | 3998.28i | 0.623751 | + | 0.258366i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2571.60i | − | 0.165376i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4972.32i | 0.318228i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1645.22 | − | 681.473i | −0.104791 | − | 0.0434057i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8285.04 | − | 20001.9i | −0.525193 | − | 1.26793i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16113.6 | + | 16113.6i | 1.01660 | + | 1.01660i | 0.999860 | + | 0.0167358i | \(0.00532743\pi\) |
0.0167358 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39375.6 | + | 39375.6i | −2.47242 | + | 2.47242i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2387.09 | + | 988.765i | −0.149179 | + | 0.0617921i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7078.87 | − | 17089.9i | 0.440306 | − | 1.06299i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48336.2 | 2.99241 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21358.0 | 1.31605 | 0.658026 | − | 0.752995i | \(-0.271392\pi\) | ||||
0.658026 | + | 0.752995i | \(0.271392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1217.22 | − | 2938.63i | 0.0746540 | − | 0.180231i | −0.882147 | − | 0.470974i | \(-0.843903\pi\) |
0.956801 | + | 0.290743i | \(0.0939026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16417.6 | − | 6800.39i | 1.00224 | − | 0.415139i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16654.8 | − | 16654.8i | 1.01200 | − | 1.01200i | 0.0120763 | − | 0.999927i | \(-0.496156\pi\) |
0.999927 | − | 0.0120763i | \(-0.00384410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 435.716 | + | 435.716i | 0.0263534 | + | 0.0263534i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2086.14 | + | 5036.39i | 0.125595 | + | 0.303213i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20645.8 | − | 8551.79i | −1.23727 | − | 0.512492i | −0.334406 | − | 0.942429i | \(-0.608536\pi\) |
−0.902859 | + | 0.429937i | \(0.858536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2711.61i | − | 0.161758i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21585.8i | 1.28180i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3783.98 | − | 1567.37i | −0.223676 | − | 0.0926498i | 0.268031 | − | 0.963410i | \(-0.413627\pi\) |
−0.491707 | + | 0.870760i | \(0.663627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9874.75 | + | 23839.8i | 0.581064 | + | 1.40281i | 0.891849 | + | 0.452333i | \(0.149408\pi\) |
−0.310785 | + | 0.950480i | \(0.600592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −49707.2 | − | 49707.2i | −2.91172 | − | 2.91172i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5676.77 | + | 5676.77i | −0.331031 | + | 0.331031i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4925.31 | − | 2040.13i | 0.285920 | − | 0.118432i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10531.3 | + | 25424.8i | −0.608615 | + | 1.46933i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −146.022 | −0.00840109 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8888.42 | 0.509099 | 0.254549 | − | 0.967060i | \(-0.418073\pi\) | ||||
0.254549 | + | 0.967060i | \(0.418073\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6594.28 | + | 15920.0i | −0.376020 | + | 0.907794i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12382.5 | − | 5128.98i | 0.702949 | − | 0.291171i | −0.00243434 | − | 0.999997i | \(-0.500775\pi\) |
0.705383 | + | 0.708826i | \(0.250775\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4469.11 | + | 4469.11i | −0.252590 | + | 0.252590i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16239.9 | + | 16239.9i | 0.913826 | + | 0.913826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3359.39 | + | 8110.29i | 0.188204 | + | 0.454365i | 0.989614 | − | 0.143751i | \(-0.0459163\pi\) |
−0.801410 | + | 0.598116i | \(0.795916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4968.43 | − | 2057.99i | −0.277130 | − | 0.114791i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 57834.3i | 3.21181i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1805.74i | 0.0998453i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19614.8 | − | 8124.74i | −1.07986 | − | 0.447293i | −0.229401 | − | 0.973332i | \(-0.573677\pi\) |
−0.850460 | + | 0.526039i | \(0.823677\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 452.688 | + | 1092.89i | 0.0248142 | + | 0.0599067i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2387.86 | − | 2387.86i | −0.130326 | − | 0.130326i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4470.27 | + | 4470.27i | −0.242932 | + | 0.242932i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36779.4 | + | 15234.5i | −1.99016 | + | 0.824353i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7415.56 | − | 17902.8i | 0.399546 | − | 0.964590i | −0.588227 | − | 0.808696i | \(-0.700174\pi\) |
0.987774 | − | 0.155895i | \(-0.0498260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21300.1 | −1.14274 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 332.310 | 0.0177525 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6350.83 | − | 15332.3i | 0.337832 | − | 0.815599i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4168.86 | − | 1726.80i | 0.220825 | − | 0.0914686i | −0.269528 | − | 0.962992i | \(-0.586868\pi\) |
0.490353 | + | 0.871524i | \(0.336868\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34789.6 | + | 34789.6i | −1.83504 | + | 1.83504i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1447.62 | + | 1447.62i | 0.0760362 | + | 0.0760362i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 476.877 | + | 1151.28i | 0.0249429 | + | 0.0602176i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 53890.1 | + | 22322.0i | 2.80692 | + | 1.16267i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13109.2i | 0.679961i | 0.940432 | + | 0.339981i | \(0.110420\pi\) | ||||
−0.940432 | + | 0.339981i | \(0.889580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2097.02i | − | 0.108318i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6812.35 | − | 2821.77i | −0.350420 | − | 0.145149i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3364.74 | + | 8123.21i | 0.172363 | + | 0.416122i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19846.0 | + | 19846.0i | 1.01245 | + | 1.01245i | 0.999922 | + | 0.0125242i | \(0.00398668\pi\) |
0.0125242 | + | 0.999922i | \(0.496013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4290.62 | + | 4290.62i | −0.217986 | + | 0.217986i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21345.0 | + | 8841.39i | −1.07999 | + | 0.447347i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1724.21 | − | 4162.60i | 0.0868827 | − | 0.209753i | −0.874466 | − | 0.485086i | \(-0.838788\pi\) |
0.961349 | + | 0.275333i | \(0.0887881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18223.4 | −0.914531 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1519.49 | 0.0759445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6958.79 | + | 16800.0i | −0.346391 | + | 0.836263i | 0.650649 | + | 0.759379i | \(0.274497\pi\) |
−0.997040 | + | 0.0768839i | \(0.975503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −63896.5 | + | 26466.8i | −3.16774 | + | 1.31212i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1100.04 | + | 1100.04i | −0.0543157 | + | 0.0543157i | −0.733743 | − | 0.679427i | \(-0.762228\pi\) |
0.679427 | + | 0.733743i | \(0.262228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4787.23 | − | 4787.23i | −0.235423 | − | 0.235423i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5736.53 | + | 13849.2i | 0.280975 | + | 0.678335i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9169.30 | − | 3798.05i | −0.447315 | − | 0.185284i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22547.4i | − | 1.09556i | −0.836623 | − | 0.547780i | \(-0.815473\pi\) | ||
0.836623 | − | 0.547780i | \(-0.184527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 60619.7i | − | 2.93374i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15467.2 | − | 6406.73i | −0.745576 | − | 0.308828i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1904.46 | − | 4597.78i | −0.0914383 | − | 0.220752i | 0.871543 | − | 0.490318i | \(-0.163120\pi\) |
−0.962982 | + | 0.269567i | \(0.913120\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 457.991 | + | 457.991i | 0.0219025 | + | 0.0219025i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7703.17 | − | 7703.17i | 0.366938 | − | 0.366938i | −0.499421 | − | 0.866359i | \(-0.666454\pi\) |
0.866359 | + | 0.499421i | \(0.166454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3346.76 | − | 1386.28i | 0.158796 | − | 0.0657753i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18177.4 | + | 43884.2i | −0.859093 | + | 2.07403i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23931.6 | 1.12662 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29833.1 | −1.39897 | −0.699485 | − | 0.714648i | \(-0.746587\pi\) | ||||
−0.699485 | + | 0.714648i | \(0.746587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12741.4 | − | 30760.6i | 0.595165 | − | 1.43685i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −736.895 | + | 305.232i | −0.0342876 | + | 0.0142024i | −0.399761 | − | 0.916619i | \(-0.630907\pi\) |
0.365474 | + | 0.930822i | \(0.380907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2387.53 | + | 2387.53i | −0.110661 | + | 0.110661i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14587.0 | + | 14587.0i | 0.673493 | + | 0.673493i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2380.21 | + | 5746.34i | 0.109474 | + | 0.264293i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1500.56 | + | 621.554i | 0.0687508 | + | 0.0284775i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 44790.4i | − | 2.04429i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 24655.6i | − | 1.12101i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23884.7 | − | 9893.38i | −1.08183 | − | 0.448108i | −0.230678 | − | 0.973030i | \(-0.574094\pi\) |
−0.851150 | + | 0.524922i | \(0.824094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13129.1 | − | 31696.5i | −0.592408 | − | 1.43020i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5321.59 | + | 5321.59i | 0.239208 | + | 0.239208i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4010.12 | + | 4010.12i | −0.179576 | + | 0.179576i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1643.53 | − | 680.771i | 0.0733206 | − | 0.0303704i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5927.29 | + | 14309.7i | −0.263432 | + | 0.635981i | −0.999146 | − | 0.0413107i | \(-0.986847\pi\) |
0.735714 | + | 0.677292i | \(0.236847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −432.046 | −0.0191298 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14969.5 | −0.660326 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −277.571 | + | 670.117i | −0.0121984 | + | 0.0294494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2697.71 | − | 1117.43i | 0.118114 | − | 0.0489244i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −48802.5 | + | 48802.5i | −2.12878 | + | 2.12878i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15747.5 | − | 15747.5i | −0.684367 | − | 0.684367i | 0.276614 | − | 0.960981i | \(-0.410788\pi\) |
−0.960981 | + | 0.276614i | \(0.910788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4881.91 | + | 11786.0i | 0.211377 | + | 0.510310i | 0.993635 | − | 0.112644i | \(-0.0359321\pi\) |
−0.782258 | + | 0.622955i | \(0.785932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54289.0 | + | 22487.2i | 2.34194 | + | 0.970063i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28093.5i | 1.20745i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22730.4i | 0.973363i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42445.1 | + | 17581.3i | 1.81093 | + | 0.750112i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −417.068 | − | 1006.89i | −0.0177293 | − | 0.0428024i | 0.914767 | − | 0.403982i | \(-0.132374\pi\) |
−0.932496 | + | 0.361180i | \(0.882374\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12509.6 | − | 12509.6i | −0.529837 | − | 0.529837i | 0.390687 | − | 0.920524i | \(-0.372237\pi\) |
−0.920524 | + | 0.390687i | \(0.872237\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −755.354 | + | 755.354i | −0.0318764 | + | 0.0318764i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25130.3 | + | 10409.3i | −1.05667 | + | 0.437687i | −0.842268 | − | 0.539059i | \(-0.818780\pi\) |
−0.214401 | + | 0.976746i | \(0.568780\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10061.9 | − | 24291.6i | 0.421549 | − | 1.01771i | −0.560341 | − | 0.828262i | \(-0.689330\pi\) |
0.981891 | − | 0.189448i | \(-0.0606700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15882.3 | 0.662996 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23692.8 | 0.985482 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11578.4 | + | 27952.8i | −0.479865 | + | 1.15850i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15891.0 | − | 6582.27i | 0.656240 | − | 0.271824i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −997.866 | + | 997.866i | −0.0410610 | + | 0.0410610i | −0.727339 | − | 0.686278i | \(-0.759243\pi\) |
0.686278 | + | 0.727339i | \(0.259243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1085.13 | + | 1085.13i | 0.0444926 | + | 0.0444926i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17242.8 | − | 41627.7i | −0.704475 | − | 1.70075i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28118.7 | + | 11647.1i | 1.14475 | + | 0.474171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13440.8i | − | 0.545254i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 51194.9i | 2.06950i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7157.49 | + | 2964.73i | 0.288314 | + | 0.119424i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3356.26 | + | 8102.73i | 0.134720 | + | 0.325243i | 0.976815 | − | 0.214087i | \(-0.0686776\pi\) |
−0.842095 | + | 0.539330i | \(0.818678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33044.9 | + | 33044.9i | 1.32177 | + | 1.32177i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22839.3 | − | 22839.3i | 0.910357 | − | 0.910357i | −0.0859432 | − | 0.996300i | \(-0.527390\pi\) |
0.996300 | + | 0.0859432i | \(0.0273904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7527.54 | + | 3118.01i | −0.298994 | + | 0.123848i | −0.527137 | − | 0.849780i | \(-0.676735\pi\) |
0.228143 | + | 0.973628i | \(0.426735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2305.23 | − | 5565.31i | 0.0912449 | − | 0.220285i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29479.1 | 1.16278 | 0.581392 | − | 0.813624i | \(-0.302508\pi\) | ||||
0.581392 | + | 0.813624i | \(0.302508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15038.5 | −0.591125 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17025.0 | − | 41101.9i | 0.666895 | − | 1.61003i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1527.37 | + | 632.659i | −0.0596233 | + | 0.0246968i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41728.8 | − | 41728.8i | 1.62334 | − | 1.62334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26015.1 | + | 26015.1i | 1.00856 | + | 1.00856i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5803.86 | + | 14011.8i | 0.224236 | + | 0.541353i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.5671 | + | 14.7324i | 0.00136946 | + | 0.000567248i | 0.383368 | − | 0.923596i | \(-0.374764\pi\) |
−0.381999 | + | 0.924163i | \(0.624764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 28305.6i | − | 1.08615i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50541.0i | 1.93277i | 0.257100 | + | 0.966385i | \(0.417233\pi\) | ||||
−0.257100 | + | 0.966385i | \(0.582767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17247.2 | + | 7144.04i | 0.657323 | + | 0.272272i | 0.686312 | − | 0.727308i | \(-0.259229\pi\) |
−0.0289887 | + | 0.999580i | \(0.509229\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9022.27 | − | 21781.7i | −0.342690 | − | 0.827326i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10744.8 | − | 10744.8i | −0.406736 | − | 0.406736i | 0.473863 | − | 0.880599i | \(-0.342859\pi\) |
−0.880599 | + | 0.473863i | \(0.842859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2263.34 | + | 2263.34i | −0.0853882 | + | 0.0853882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2114.05 | − | 875.668i | 0.0794875 | − | 0.0329248i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −162.666 | + | 392.711i | −0.00609565 | + | 0.0147162i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15274.5 | −0.570469 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25155.0 | 0.936345 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3358.62 | − | 8108.42i | 0.124601 | − | 0.300813i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2136.80 | + | 885.091i | −0.0790090 | + | 0.0327266i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15566.5 | − | 15566.5i | 0.573666 | − | 0.573666i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16427.0 | − | 16427.0i | −0.603374 | − | 0.603374i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15317.6 | − | 36980.0i | −0.560764 | − | 1.35380i | −0.909157 | − | 0.416454i | \(-0.863273\pi\) |
0.348393 | − | 0.937349i | \(-0.386727\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −89250.3 | − | 36968.7i | −3.25659 | − | 1.34893i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 18795.0i | − | 0.683540i | −0.939784 | − | 0.341770i | \(-0.888974\pi\) | ||
0.939784 | − | 0.341770i | \(-0.111026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 503.705i | 0.0182587i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5161.70 | + | 2138.05i | 0.186492 | + | 0.0772477i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1285.52 | − | 3103.52i | −0.0462940 | − | 0.111764i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6027.61 | − | 6027.61i | −0.216358 | − | 0.216358i | 0.590604 | − | 0.806962i | \(-0.298890\pi\) |
−0.806962 | + | 0.590604i | \(0.798890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3009.52 | − | 3009.52i | 0.107673 | − | 0.107673i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58278.4 | − | 24139.7i | 2.07828 | − | 0.860853i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4889.66 | + | 11804.7i | −0.173807 | + | 0.419606i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12206.9 | −0.432500 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5213.50 | 0.184122 | 0.0920611 | − | 0.995753i | \(-0.470654\pi\) | ||||
0.0920611 | + | 0.995753i | \(0.470654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8920.37 | − | 21535.7i | 0.314021 | − | 0.758113i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 45567.1 | − | 18874.5i | 1.59893 | − | 0.662297i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1128.61 | + | 1128.61i | −0.0394754 | + | 0.0394754i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18034.8 | + | 18034.8i | 0.628783 | + | 0.628783i | 0.947762 | − | 0.318979i | \(-0.103340\pi\) |
−0.318979 | + | 0.947762i | \(0.603340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3603.73 | + | 8700.17i | 0.125243 | + | 0.302363i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1253.64 | + | 519.275i | 0.0434299 | + | 0.0179892i | 0.404293 | − | 0.914630i | \(-0.367518\pi\) |
−0.360863 | + | 0.932619i | \(0.617518\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2262.24i | − | 0.0781217i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 24532.7i | − | 0.844497i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25052.1 | + | 10376.9i | 0.859646 | + | 0.356077i | 0.768569 | − | 0.639767i | \(-0.220969\pi\) |
0.0910771 | + | 0.995844i | \(0.470969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10780.2 | + | 26025.8i | 0.368747 | + | 0.890234i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22535.4 | − | 22535.4i | −0.768414 | − | 0.768414i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9648.15 | − | 9648.15i | 0.327948 | − | 0.327948i | −0.523858 | − | 0.851806i | \(-0.675508\pi\) |
0.851806 | + | 0.523858i | \(0.175508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12460.1 | − | 5161.13i | 0.422197 | − | 0.174880i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1062.58 | − | 2565.30i | 0.0358918 | − | 0.0866504i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6662.17 | −0.224330 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26420.7 | −0.886868 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22108.8 | + | 53375.2i | −0.739818 | + | 1.78608i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14567.1 | + | 6033.88i | −0.485939 | + | 0.201283i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12684.4 | + | 12684.4i | −0.421824 | + | 0.421824i | −0.885831 | − | 0.464007i | \(-0.846411\pi\) |
0.464007 | + | 0.885831i | \(0.346411\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −62638.1 | − | 62638.1i | −2.07660 | − | 2.07660i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10462.9 | + | 25259.7i | 0.345799 | + | 0.834832i | 0.997106 | + | 0.0760183i | \(0.0242208\pi\) |
−0.651308 | + | 0.758814i | \(0.725779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3865.01 | − | 1600.94i | −0.127345 | − | 0.0527480i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41487.6i | 1.36274i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 60560.6i | − | 1.98312i | −0.129654 | − | 0.991559i | \(-0.541387\pi\) | ||
0.129654 | − | 0.991559i | \(-0.458613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −464.717 | − | 192.492i | −0.0151710 | − | 0.00628404i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8069.62 | − | 19481.8i | −0.262633 | − | 0.634053i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36767.4 | + | 36767.4i | 1.19298 | + | 1.19298i | 0.976227 | + | 0.216751i | \(0.0695461\pi\) |
0.216751 | + | 0.976227i | \(0.430454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23308.8 | + | 23308.8i | −0.753989 | + | 0.753989i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 380.339 | − | 157.541i | 0.0122658 | − | 0.00508065i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3163.81 | − | 7638.12i | 0.101722 | − | 0.245579i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38103.0 | −1.22137 | −0.610687 | − | 0.791872i | \(-0.709107\pi\) | ||||
−0.610687 | + | 0.791872i | \(0.709107\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12490.6 | 0.399173 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1600.14 | − | 3863.07i | 0.0509827 | − | 0.123083i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −967.156 | + | 400.609i | −0.0307223 | + | 0.0127256i | −0.397992 | − | 0.917389i | \(-0.630293\pi\) |
0.367269 | + | 0.930115i | \(0.380293\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 46025.3 | − | 46025.3i | 1.45763 | − | 1.45763i |
(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 | 256.4.g.b.33.1 | 44 | ||
4.3 | odd | 2 | 256.4.g.a.33.11 | 44 | |||
8.3 | odd | 2 | 128.4.g.a.17.1 | 44 | |||
8.5 | even | 2 | 32.4.g.a.13.4 | yes | 44 | ||
32.5 | even | 8 | inner | 256.4.g.b.225.1 | 44 | ||
32.11 | odd | 8 | 128.4.g.a.113.1 | 44 | |||
32.21 | even | 8 | 32.4.g.a.5.4 | ✓ | 44 | ||
32.27 | odd | 8 | 256.4.g.a.225.11 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.4 | ✓ | 44 | 32.21 | even | 8 | ||
32.4.g.a.13.4 | yes | 44 | 8.5 | even | 2 | ||
128.4.g.a.17.1 | 44 | 8.3 | odd | 2 | |||
128.4.g.a.113.1 | 44 | 32.11 | odd | 8 | |||
256.4.g.a.33.11 | 44 | 4.3 | odd | 2 | |||
256.4.g.a.225.11 | 44 | 32.27 | odd | 8 | |||
256.4.g.b.33.1 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.b.225.1 | 44 | 32.5 | even | 8 | inner |