Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.5 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.i.895.20 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 13.1053i | − | 1.17218i | −0.810247 | − | 0.586089i | \(-0.800667\pi\) | ||
0.810247 | − | 0.586089i | \(-0.199333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.87442 | − | 15.6683i | 0.533169 | − | 0.846009i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 66.5093i | 1.82303i | 0.411270 | + | 0.911513i | \(0.365085\pi\) | ||||
−0.411270 | + | 0.911513i | \(0.634915\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.0750i | 0.705643i | 0.935691 | + | 0.352822i | \(0.114778\pi\) | ||||
−0.935691 | + | 0.352822i | \(0.885222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 39.3160i | 0.676757i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 86.2229i | 1.23013i | 0.788478 | + | 0.615063i | \(0.210869\pi\) | ||||
−0.788478 | + | 0.615063i | \(0.789131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.0063 | 0.253640 | 0.126820 | − | 0.991926i | \(-0.459523\pi\) | ||||
0.126820 | + | 0.991926i | \(0.459523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −29.6233 | + | 47.0049i | −0.307825 | + | 0.488444i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 218.669i | − | 1.98242i | −0.132307 | − | 0.991209i | \(-0.542239\pi\) | ||
0.132307 | − | 0.991209i | \(-0.457761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −46.7501 | −0.374001 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 133.471 | 0.854652 | 0.427326 | − | 0.904098i | \(-0.359456\pi\) | ||||
0.427326 | + | 0.904098i | \(0.359456\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −324.428 | −1.87965 | −0.939823 | − | 0.341662i | \(-0.889010\pi\) | ||||
−0.939823 | + | 0.341662i | \(0.889010\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 199.528i | − | 1.05253i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −205.339 | − | 129.408i | −0.991673 | − | 0.624968i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 73.1277 | 0.324922 | 0.162461 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162461 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 99.2251i | − | 0.407403i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 309.181i | − | 1.17771i | −0.808240 | − | 0.588854i | \(-0.799579\pi\) | ||
0.808240 | − | 0.588854i | \(-0.200421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 28.7269i | − | 0.101879i | −0.998702 | − | 0.0509396i | \(-0.983778\pi\) | ||
0.998702 | − | 0.0509396i | \(-0.0162216\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 117.948i | − | 0.390726i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −162.730 | −0.505036 | −0.252518 | − | 0.967592i | \(-0.581259\pi\) | ||||
−0.252518 | + | 0.967592i | \(0.581259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −147.992 | − | 309.431i | −0.431463 | − | 0.902131i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 258.669i | − | 0.710213i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −575.828 | −1.49238 | −0.746189 | − | 0.665734i | \(-0.768118\pi\) | ||||
−0.746189 | + | 0.665734i | \(0.768118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 871.627 | 2.13691 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −63.0188 | −0.146439 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −861.347 | −1.90064 | −0.950320 | − | 0.311273i | \(-0.899245\pi\) | ||||
−0.950320 | + | 0.311273i | \(0.899245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 367.037i | − | 0.770399i | −0.922833 | − | 0.385199i | \(-0.874133\pi\) | ||
0.922833 | − | 0.385199i | \(-0.125867\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 88.8698 | − | 141.015i | 0.177723 | − | 0.282003i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 433.460 | 0.827140 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 818.701i | 1.49284i | 0.665476 | + | 0.746419i | \(0.268229\pi\) | ||||
−0.665476 | + | 0.746419i | \(0.731771\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 656.006i | 1.14455i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 407.234i | − | 0.680701i | −0.940299 | − | 0.340351i | \(-0.889454\pi\) | ||
0.940299 | − | 0.340351i | \(-0.110546\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 515.657i | − | 0.826754i | −0.910560 | − | 0.413377i | \(-0.864349\pi\) | ||
0.910560 | − | 0.413377i | \(-0.135651\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 140.250 | 0.215929 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1042.09 | + | 656.740i | 1.54230 | + | 0.971981i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1135.55i | 1.61721i | 0.588355 | + | 0.808603i | \(0.299776\pi\) | ||||
−0.588355 | + | 0.808603i | \(0.700224\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −941.158 | −1.24464 | −0.622322 | − | 0.782761i | \(-0.713811\pi\) | ||||
−0.622322 | + | 0.782761i | \(0.713811\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1129.98 | 1.44193 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −400.412 | −0.493434 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 628.192i | 0.748182i | 0.927392 | + | 0.374091i | \(0.122045\pi\) | ||||
−0.927392 | + | 0.374091i | \(0.877955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 518.230 | + | 326.597i | 0.596981 | + | 0.376227i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 973.285 | 1.08521 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 275.294i | − | 0.297312i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 522.331i | − | 0.546750i | −0.961908 | − | 0.273375i | \(-0.911860\pi\) | ||
0.961908 | − | 0.273375i | \(-0.0881399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 598.583i | 0.607676i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1086.40i | 1.07031i | 0.844755 | + | 0.535153i | \(0.179746\pi\) | ||||
−0.844755 | + | 0.535153i | \(0.820254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 196.731 | 0.188199 | 0.0940995 | − | 0.995563i | \(-0.470003\pi\) | ||||
0.0940995 | + | 0.995563i | \(0.470003\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 616.016 | + | 388.223i | 0.572543 | + | 0.360826i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 870.161i | 0.786183i | 0.919499 | + | 0.393092i | \(0.128594\pi\) | ||||
−0.919499 | + | 0.393092i | \(0.871406\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −277.220 | −0.243604 | −0.121802 | − | 0.992554i | \(-0.538867\pi\) | ||||
−0.121802 | + | 0.992554i | \(0.538867\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −219.383 | −0.187594 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 958.381 | 0.797849 | 0.398924 | − | 0.916984i | \(-0.369384\pi\) | ||||
0.398924 | + | 0.916984i | \(0.369384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2865.73 | −2.32375 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 297.675i | 0.235214i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1350.97 | + | 851.402i | 1.04070 | + | 0.655864i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3092.48 | −2.32343 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 927.544i | 0.679950i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1025.49i | − | 0.733782i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 63.9927i | − | 0.0447121i | −0.999750 | − | 0.0223560i | \(-0.992883\pi\) | ||
0.999750 | − | 0.0223560i | \(-0.00711674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 86.1807i | 0.0588200i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 219.879 | 0.146648 | 0.0733240 | − | 0.997308i | \(-0.476639\pi\) | ||||
0.0733240 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 207.425 | − | 329.133i | 0.135233 | − | 0.214582i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 353.844i | 0.225586i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1493.47 | −0.931358 | −0.465679 | − | 0.884954i | \(-0.654190\pi\) | ||||
−0.465679 | + | 0.884954i | \(0.654190\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1149.51 | −0.701442 | −0.350721 | − | 0.936480i | \(-0.614064\pi\) | ||||
−0.350721 | + | 0.936480i | \(0.614064\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 488.191 | 0.291582 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2199.80 | −1.28641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1749.18i | − | 1.00180i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 443.975 | + | 928.293i | 0.249105 | + | 0.520845i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 229.427 | 0.126144 | 0.0630719 | − | 0.998009i | \(-0.479910\pi\) | ||||
0.0630719 | + | 0.998009i | \(0.479910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 407.635i | 0.219688i | 0.993949 | + | 0.109844i | \(0.0350351\pi\) | ||||
−0.993949 | + | 0.109844i | \(0.964965\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 776.007i | 0.410042i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4251.74i | 2.20328i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 167.822i | 0.0853101i | 0.999090 | + | 0.0426551i | \(0.0135817\pi\) | ||||
−0.999090 | + | 0.0426551i | \(0.986418\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1727.48 | 0.861625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3426.17 | − | 2159.23i | −1.67714 | − | 1.05696i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3096.94i | − | 1.48817i | −0.668086 | − | 0.744084i | \(-0.732886\pi\) | ||
0.668086 | − | 0.744084i | \(-0.267114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2614.88 | −1.23375 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3764.16 | −1.74419 | −0.872095 | − | 0.489337i | \(-0.837239\pi\) | ||||
−0.872095 | + | 0.489337i | \(0.837239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1103.04 | 0.502067 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 189.056 | 0.0845468 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3438.40i | 1.51108i | 0.655103 | + | 0.755539i | \(0.272625\pi\) | ||||
−0.655103 | + | 0.755539i | \(0.727375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −461.630 | + | 732.495i | −0.199405 | + | 0.316408i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2584.04 | 1.09734 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1128.66i | 0.471286i | 0.971840 | + | 0.235643i | \(0.0757196\pi\) | ||||
−0.971840 | + | 0.235643i | \(0.924280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1613.94i | − | 0.662781i | −0.943494 | − | 0.331391i | \(-0.892482\pi\) | ||
0.943494 | − | 0.331391i | \(-0.107518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1101.11i | 0.444790i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 958.364i | − | 0.380866i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5734.62 | −2.24255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −266.609 | + | 423.044i | −0.102608 | + | 0.162815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2819.97i | 1.06830i | 0.845388 | + | 0.534152i | \(0.179369\pi\) | ||||
−0.845388 | + | 0.534152i | \(0.820631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1749.41 | 0.652463 | 0.326232 | − | 0.945290i | \(-0.394221\pi\) | ||||
0.326232 | + | 0.945290i | \(0.394221\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1300.38 | −0.477549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3168.95 | −1.14608 | −0.573041 | − | 0.819527i | \(-0.694236\pi\) | ||||
−0.573041 | + | 0.819527i | \(0.694236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −978.805 | −0.348672 | −0.174336 | − | 0.984686i | \(-0.555778\pi\) | ||||
−0.174336 | + | 0.984686i | \(0.555778\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2456.10i | − | 0.861891i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1317.95 | − | 2091.26i | 0.455674 | − | 0.723043i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4051.93 | −1.38048 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1968.02i | − | 0.660806i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1397.11i | 0.462393i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1183.70i | − | 0.386204i | −0.981179 | − | 0.193102i | \(-0.938145\pi\) | ||
0.981179 | − | 0.193102i | \(-0.0618548\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1221.70i | 0.393003i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −376.476 | −0.119421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3203.54 | + | 5083.24i | −1.00217 | + | 1.59020i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1546.97i | 0.477327i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2851.83 | −0.868030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1724.50 | −0.517852 | −0.258926 | − | 0.965897i | \(-0.583369\pi\) | ||||
−0.258926 | + | 0.965897i | \(0.583369\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −420.751 | −0.124667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2296.41 | 0.671445 | 0.335723 | − | 0.941961i | \(-0.391020\pi\) | ||||
0.335723 | + | 0.941961i | \(0.391020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4404.32i | − | 1.27094i | −0.772125 | − | 0.635471i | \(-0.780806\pi\) | ||
0.772125 | − | 0.635471i | \(-0.219194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3126.26 | − | 1970.22i | −0.890446 | − | 0.561173i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4222.07 | 1.18711 | 0.593556 | − | 0.804793i | \(-0.297723\pi\) | ||||
0.593556 | + | 0.804793i | \(0.297723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2132.64i | 0.591992i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3406.65i | − | 0.933694i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4649.91i | − | 1.25848i | −0.777210 | − | 0.629242i | \(-0.783366\pi\) | ||
0.777210 | − | 0.629242i | \(-0.216634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.3928i | − | 0.00384697i | −0.999998 | − | 0.00192348i | \(-0.999388\pi\) | ||
0.999998 | − | 0.00192348i | \(-0.000612264\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4055.20 | + | 1939.48i | −1.05746 | + | 0.505751i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 694.783i | 0.178980i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2823.47 | 0.718596 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6957.71 | −1.74967 | −0.874834 | − | 0.484422i | \(-0.839030\pi\) | ||||
−0.874834 | + | 0.484422i | \(0.839030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14543.5 | 3.61400 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3389.94 | −0.832496 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4915.09i | 1.19298i | 0.802622 | + | 0.596488i | \(0.203438\pi\) | ||||
−0.802622 | + | 0.596488i | \(0.796562\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 722.093 | − | 1145.79i | 0.173238 | − | 0.274887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1201.24 | 0.284884 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6930.51i | 1.62492i | 0.583018 | + | 0.812459i | \(0.301872\pi\) | ||||
−0.583018 | + | 0.812459i | \(0.698128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7546.42i | 1.74933i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1884.57i | − | 0.431963i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 481.497i | 0.109135i | 0.998510 | + | 0.0545676i | \(0.0173780\pi\) | ||||
−0.998510 | + | 0.0545676i | \(0.982622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5156.02 | −1.15574 | −0.577871 | − | 0.816128i | \(-0.696116\pi\) | ||||
−0.577871 | + | 0.816128i | \(0.696116\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1554.69 | − | 979.790i | −0.344667 | − | 0.217215i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3109.31i | − | 0.681814i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2065.98 | 0.448134 | 0.224067 | − | 0.974574i | \(-0.428067\pi\) | ||||
0.224067 | + | 0.974574i | \(0.428067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2919.85 | −0.626549 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4260.27 | 0.904436 | 0.452218 | − | 0.891907i | \(-0.350633\pi\) | ||||
0.452218 | + | 0.891907i | \(0.350633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3195.17 | 0.671141 | 0.335571 | − | 0.942015i | \(-0.391071\pi\) | ||||
0.335571 | + | 0.942015i | \(0.391071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 825.883i | 0.171653i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4844.35 | − | 3052.98i | −0.996351 | − | 0.627916i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2521.40 | −0.513209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1566.99i | 0.315666i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6349.41i | 1.26599i | 0.774154 | + | 0.632997i | \(0.218176\pi\) | ||||
−0.774154 | + | 0.632997i | \(0.781824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11288.2i | 2.22789i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1795.75i | − | 0.350842i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7232.48 | 1.39888 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −450.102 | − | 283.661i | −0.0861908 | − | 0.0543188i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3259.20i | − | 0.617942i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4810.15 | −0.903044 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 684.156 | 0.127188 | 0.0635942 | − | 0.997976i | \(-0.479744\pi\) | ||||
0.0635942 | + | 0.997976i | \(0.479744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −590.193 | −0.108657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4151.64 | −0.756970 | −0.378485 | − | 0.925607i | \(-0.623555\pi\) | ||||
−0.378485 | + | 0.925607i | \(0.623555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2788.88i | 0.503632i | 0.967775 | + | 0.251816i | \(0.0810277\pi\) | ||||
−0.967775 | + | 0.251816i | \(0.918972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1848.05 | − | 1164.67i | −0.330558 | − | 0.208323i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1123.95 | −0.199139 | −0.0995697 | − | 0.995031i | \(-0.531747\pi\) | ||||
−0.0995697 | + | 0.995031i | \(0.531747\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8877.04i | 1.55805i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2610.48i | − | 0.453903i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1811.22i | 0.312010i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1546.26i | − | 0.263911i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 831.659 | 0.140645 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1606.87 | + | 2549.71i | −0.269269 | + | 0.427265i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4265.14i | − | 0.708258i | −0.935197 | − | 0.354129i | \(-0.884777\pi\) | ||
0.935197 | − | 0.354129i | \(-0.115223\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 658.149 | 0.108307 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10729.4 | 1.74987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5217.89 | 0.843433 | 0.421716 | − | 0.906728i | \(-0.361428\pi\) | ||||
0.421716 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2875.14 | −0.460638 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 21577.5i | − | 3.42664i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6309.59 | − | 736.671i | −0.993253 | − | 0.115966i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8597.19 | 1.34162 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2596.17i | 0.401642i | 0.979628 | + | 0.200821i | \(0.0643609\pi\) | ||||
−0.979628 | + | 0.200821i | \(0.935639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9467.68i | − | 1.45213i | −0.687626 | − | 0.726065i | \(-0.741347\pi\) | ||
0.687626 | − | 0.726065i | \(-0.258653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 893.026i | − | 0.135801i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2276.11i | 0.343188i | 0.985168 | + | 0.171594i | \(0.0548917\pi\) | ||||
−0.985168 | + | 0.171594i | \(0.945108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5336.94 | −0.797903 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4052.90 | − | 2554.20i | −0.600847 | − | 0.378663i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4663.75i | − | 0.685636i | −0.939402 | − | 0.342818i | \(-0.888619\pi\) | ||
0.939402 | − | 0.342818i | \(-0.111381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6417.74 | −0.935667 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9277.44 | 1.34143 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6757.86 | −0.969103 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4677.32 | 0.665270 | 0.332635 | − | 0.943056i | \(-0.392062\pi\) | ||||
0.332635 | + | 0.943056i | \(0.392062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2782.63i | − | 0.392569i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5685.97 | + | 9022.25i | −0.795689 | + | 1.26257i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −551.009 | −0.0764884 | −0.0382442 | − | 0.999268i | \(-0.512176\pi\) | ||||
−0.0382442 | + | 0.999268i | \(0.512176\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3076.48i | 0.423649i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4414.55i | 0.603080i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 573.945i | 0.0777878i | 0.999243 | + | 0.0388939i | \(0.0123834\pi\) | ||||
−0.999243 | + | 0.0388939i | \(0.987617\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 191.978i | 0.0258145i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10376.9 | −1.38443 | −0.692215 | − | 0.721692i | \(-0.743365\pi\) | ||||
−0.692215 | + | 0.721692i | \(0.743365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8606.81 | − | 13656.9i | 1.13933 | − | 1.80785i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 258.542i | − | 0.0339598i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8040.94 | −1.04805 | −0.524025 | − | 0.851703i | \(-0.675570\pi\) | ||||
−0.524025 | + | 0.851703i | \(0.675570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18854.3 | 2.43862 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −659.636 | −0.0846673 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14881.8 | 1.89565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6608.26i | 0.835413i | 0.908582 | + | 0.417706i | \(0.137166\pi\) | ||||
−0.908582 | + | 0.417706i | \(0.862834\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −622.274 | + | 987.398i | −0.0780768 | + | 0.123889i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −292.364 | −0.0364089 | −0.0182045 | − | 0.999834i | \(-0.505795\pi\) | ||||
−0.0182045 | + | 0.999834i | \(0.505795\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10730.5i | − | 1.32636i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1061.53i | − | 0.130242i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4863.67i | 0.592342i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1334.80i | − | 0.161374i | −0.996740 | − | 0.0806868i | \(-0.974289\pi\) | ||
0.996740 | − | 0.0806868i | \(-0.0257114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4480.42 | 0.537720 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8505.30 | + | 13495.8i | −1.01336 | + | 1.60796i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12334.2i | 1.45894i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3448.54 | 0.404978 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8852.36 | −1.03214 | −0.516069 | − | 0.856547i | \(-0.672605\pi\) | ||||
−0.516069 | + | 0.856547i | \(0.672605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6270.01 | 0.725847 | 0.362924 | − | 0.931819i | \(-0.381779\pi\) | ||||
0.362924 | + | 0.931819i | \(0.381779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1464.57 | −0.168345 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4030.93i | − | 0.460068i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5750.86 | − | 3624.28i | −0.651764 | − | 0.410752i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6599.39 | 0.742707 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 205.022i | 0.0229131i | 0.999934 | + | 0.0114566i | \(0.00364682\pi\) | ||||
−0.999934 | + | 0.0114566i | \(0.996353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12003.1i | 1.33217i | 0.745875 | + | 0.666086i | \(0.232032\pi\) | ||||
−0.745875 | + | 0.666086i | \(0.767968\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5247.54i | 0.578392i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4593.41i | − | 0.502821i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2757.16 | 0.299754 | 0.149877 | − | 0.988705i | \(-0.452112\pi\) | ||||
0.149877 | + | 0.988705i | \(0.452112\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1331.93 | − | 2784.88i | −0.143821 | − | 0.300710i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3626.94i | 0.388987i | 0.980904 | + | 0.194493i | \(0.0623063\pi\) | ||||
−0.980904 | + | 0.194493i | \(0.937694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8232.67 | 0.877002 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −688.282 | −0.0728291 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16303.5 | −1.71360 | −0.856801 | − | 0.515647i | \(-0.827552\pi\) | ||||
−0.856801 | + | 0.515647i | \(0.827552\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20563.4 | 2.14699 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 1222.90i | − | 0.126837i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4280.16 | − | 6791.58i | 0.441005 | − | 0.699768i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11048.3 | 1.13089 | 0.565447 | − | 0.824784i | \(-0.308704\pi\) | ||||
0.565447 | + | 0.824784i | \(0.308704\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2328.02i | − | 0.236738i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5823.95i | 0.588391i | 0.955745 | + | 0.294196i | \(0.0950518\pi\) | ||||
−0.955745 | + | 0.294196i | \(0.904948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15638.6i | − | 1.56974i | −0.619661 | − | 0.784869i | \(-0.712730\pi\) | ||
0.619661 | − | 0.784869i | \(-0.287270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 12755.2i | − | 1.27206i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 730.574 | 0.0723917 | 0.0361959 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361959 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12827.7 | + | 8084.19i | 1.26296 | + | 0.795935i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 503.467i | − | 0.0492538i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1910.60 | 0.185729 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −982.045 | −0.0948617 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5182.45 | −0.497459 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1211.82 | 0.115594 | 0.0577971 | − | 0.998328i | \(-0.481592\pi\) | ||||
0.0577971 | + | 0.998328i | \(0.481592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2418.70i | 0.229279i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10278.5 | + | 6477.68i | 0.968299 | + | 0.610238i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6845.33 | −0.640888 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5068.72i | − | 0.471634i | −0.971798 | − | 0.235817i | \(-0.924223\pi\) | ||
0.971798 | − | 0.235817i | \(-0.0757766\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9290.83i | 0.859194i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11619.0i | − | 1.06794i | −0.845503 | − | 0.533971i | \(-0.820699\pi\) | ||
0.845503 | − | 0.533971i | \(-0.179301\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11508.2i | 1.05133i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7844.64 | 0.712304 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6380.67 | − | 4021.20i | −0.575879 | − | 0.362928i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6132.84i | 0.550187i | 0.961417 | + | 0.275094i | \(0.0887089\pi\) | ||||
−0.961417 | + | 0.275094i | \(0.911291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11292.5 | 1.00701 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5868.53 | 0.520208 | 0.260104 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14237.7 | 1.25459 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3309.13 | −0.289869 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8716.70i | 0.759059i | 0.925180 | + | 0.379529i | \(0.123914\pi\) | ||||
−0.925180 | + | 0.379529i | \(0.876086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8079.47 | − | 5091.81i | −0.699442 | − | 0.440799i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −567.169 | −0.0488131 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 2578.23i | − | 0.220603i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10823.1i | − | 0.920693i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10315.2i | − | 0.872422i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6289.58i | − | 0.528890i | −0.964401 | − | 0.264445i | \(-0.914811\pi\) | ||
0.964401 | − | 0.264445i | \(-0.0851887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19253.1 | −1.60971 | −0.804854 | − | 0.593473i | \(-0.797757\pi\) | ||||
−0.804854 | + | 0.593473i | \(0.797757\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1384.89 | − | 2197.48i | 0.115127 | − | 0.182678i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27973.2i | − | 2.31220i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35649.1 | −2.92998 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7752.12 | −0.633547 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10226.2 | 0.831041 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11403.8 | 0.921546 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3385.99i | − | 0.272097i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20580.0 | − | 9842.82i | 1.64461 | − | 0.786568i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6806.51 | 0.540915 | 0.270457 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270457 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4841.83i | 0.382657i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3633.06i | 0.285547i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2333.60i | − | 0.182409i | −0.995832 | − | 0.0912044i | \(-0.970928\pi\) | ||
0.995832 | − | 0.0912044i | \(-0.0290717\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3303.34i | − | 0.256800i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2803.72 | 0.216774 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17792.1 | + | 11212.9i | 1.36817 | + | 0.862243i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2875.09i | 0.219893i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3035.04 | −0.230878 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 950.143 | 0.0718904 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17203.9 | 1.29474 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9471.73 | −0.709034 | −0.354517 | − | 0.935050i | \(-0.615355\pi\) | ||||
−0.354517 | + | 0.935050i | \(0.615355\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 12559.9i | − | 0.935220i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 799.828 | − | 1269.13i | 0.0592409 | − | 0.0940010i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4580.84 | −0.337502 | −0.168751 | − | 0.985659i | \(-0.553973\pi\) | ||||
−0.168751 | + | 0.985659i | \(0.553973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15298.8i | 1.12125i | 0.828068 | + | 0.560627i | \(0.189440\pi\) | ||||
−0.828068 | + | 0.560627i | \(0.810560\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8459.92i | − | 0.616786i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10222.8i | 0.741426i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22630.9i | − | 1.63282i | −0.577473 | − | 0.816410i | \(-0.695961\pi\) | ||
0.577473 | − | 0.816410i | \(-0.304039\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5248.23 | −0.376700 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9293.38 | + | 14746.3i | −0.663605 | + | 1.05298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 38297.9i | − | 2.72065i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3901.14 | 0.275713 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17070.7 | −1.20031 | −0.600157 | − | 0.799883i | \(-0.704895\pi\) | ||||
−0.600157 | + | 0.799883i | \(0.704895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6815.02 | −0.476754 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9506.84 | 0.661691 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2588.94i | 0.179283i | 0.995974 | + | 0.0896416i | \(0.0285722\pi\) | ||||
−0.995974 | + | 0.0896416i | \(0.971428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11157.9 | − | 17704.9i | 0.768790 | − | 1.21988i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2936.42 | 0.201306 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 432.117i | 0.0294755i | 0.999891 | + | 0.0147378i | \(0.00469134\pi\) | ||||
−0.999891 | + | 0.0147378i | \(0.995309\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11299.7i | 0.766927i | 0.923556 | + | 0.383463i | \(0.125269\pi\) | ||||
−0.923556 | + | 0.383463i | \(0.874731\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7368.31i | 0.497613i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40528.0i | 2.72347i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20570.8 | 1.37552 | 0.687761 | − | 0.725938i | \(-0.258594\pi\) | ||||
0.687761 | + | 0.725938i | \(0.258594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3953.84 | + | 6273.79i | −0.263083 | + | 0.417449i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5382.32i | − | 0.356375i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11492.6 | −0.757231 | −0.378615 | − | 0.925554i | \(-0.623600\pi\) | ||||
−0.378615 | + | 0.925554i | \(0.623600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12155.8 | 0.797022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26688.7 | −1.74140 | −0.870701 | − | 0.491812i | \(-0.836335\pi\) | ||||
−0.870701 | + | 0.491812i | \(0.836335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4597.10 | 0.298502 | 0.149251 | − | 0.988799i | \(-0.452314\pi\) | ||||
0.149251 | + | 0.988799i | \(0.452314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5904.06i | 0.381516i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9842.70 | + | 6203.03i | 0.632969 | + | 0.398907i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19283.2 | −1.23412 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 4191.33i | − | 0.266963i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6305.28i | 0.399695i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5107.87i | 0.322252i | 0.986934 | + | 0.161126i | \(0.0515126\pi\) | ||||
−0.986934 | + | 0.161126i | \(0.948487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3551.09i | 0.222975i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −838.647 | −0.0524105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10234.4 | − | 4894.83i | 0.636583 | − | 0.304459i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3665.11i | − | 0.226900i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1581.52 | 0.0974512 | 0.0487256 | − | 0.998812i | \(-0.484484\pi\) | ||||
0.0487256 | + | 0.998812i | \(0.484484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2210.56 | −0.135577 | −0.0677884 | − | 0.997700i | \(-0.521594\pi\) | ||||
−0.0677884 | + | 0.997700i | \(0.521594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1129.43 | 0.0689475 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12507.1 | −0.759976 | −0.379988 | − | 0.924991i | \(-0.624072\pi\) | ||||
−0.379988 | + | 0.924991i | \(0.624072\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 57287.5i | − | 3.46492i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9610.62 | − | 15249.7i | 0.578602 | − | 0.918101i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −990.222 | −0.0593421 | −0.0296710 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296710 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2881.59i | − | 0.171898i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4640.91i | − | 0.275585i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 25900.2i | − | 1.53100i | −0.643435 | − | 0.765501i | \(-0.722491\pi\) | ||
0.643435 | − | 0.765501i | \(-0.277509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22104.7i | − | 1.30071i | −0.759628 | − | 0.650357i | \(-0.774619\pi\) | ||
0.759628 | − | 0.650357i | \(-0.225381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8555.48 | 0.501157 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4313.40 | − | 2718.37i | −0.251528 | − | 0.158517i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29185.9i | − | 1.69428i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5173.49 | 0.298982 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24411.4 | 1.40446 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6847.62 | −0.392209 | −0.196104 | − | 0.980583i | \(-0.562829\pi\) | ||||
−0.196104 | + | 0.980583i | \(0.562829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1262.25 | 0.0719765 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8884.62i | − | 0.504378i | −0.967678 | − | 0.252189i | \(-0.918850\pi\) | ||
0.967678 | − | 0.252189i | \(-0.0811504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8184.05 | − | 5157.72i | −0.462555 | − | 0.291510i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6889.23 | −0.387659 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24173.3i | 1.35427i | 0.735859 | + | 0.677135i | \(0.236779\pi\) | ||||
−0.735859 | + | 0.677135i | \(0.763221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19572.5i | 1.09172i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13213.0i | 0.733778i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19045.5i | − | 1.05309i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11158.2 | 0.614296 | 0.307148 | − | 0.951662i | \(-0.400625\pi\) | ||||
0.307148 | + | 0.951662i | \(0.400625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9378.79 | + | 5910.66i | 0.514099 | + | 0.323994i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15064.8i | 0.822215i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26658.5 | 1.44873 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12666.2 | −0.685380 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4440.80 | −0.239268 | −0.119634 | − | 0.992818i | \(-0.538172\pi\) | ||||
−0.119634 | + | 0.992818i | \(0.538172\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1536.14 | 0.0824134 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6397.92i | − | 0.341786i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17022.1 | + | 10727.6i | 0.905489 | + | 0.570654i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19194.5 | −1.01673 | −0.508367 | − | 0.861140i | \(-0.669751\pi\) | ||||
−0.508367 | + | 0.861140i | \(0.669751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10219.9i | 0.539068i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 70942.3i | 3.72624i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28829.1i | 1.50790i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13949.7i | 0.726586i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35198.1 | 1.82569 | 0.912843 | − | 0.408310i | \(-0.133882\pi\) | ||||
0.912843 | + | 0.408310i | \(0.133882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1942.61 | − | 3082.44i | 0.100342 | − | 0.159218i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.1783i | 0.00222105i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6239.77 | −0.319641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13232.3 | 0.675047 | 0.337524 | − | 0.941317i | \(-0.390411\pi\) | ||||
0.337524 | + | 0.941317i | \(0.390411\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2476.92 | 0.125324 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20075.6i | − | 1.01161i | −0.862649 | − | 0.505804i | \(-0.831196\pi\) | ||
0.862649 | − | 0.505804i | \(-0.168804\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12165.6 | − | 5818.45i | 0.610523 | − | 0.291995i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54451.2 | −2.72149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15808.7i | 0.786917i | 0.919342 | + | 0.393459i | \(0.128722\pi\) | ||||
−0.919342 | + | 0.393459i | \(0.871278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2084.35i | − | 0.103334i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4785.70i | − | 0.236299i | −0.992996 | − | 0.118150i | \(-0.962304\pi\) | ||
0.992996 | − | 0.118150i | \(-0.0376962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3006.73i | − | 0.147863i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8470.42 | −0.414881 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13633.9 | + | 8592.33i | 0.665118 | + | 0.419168i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26285.5i | 1.27719i | 0.769543 | + | 0.638595i | \(0.220484\pi\) | ||||
−0.769543 | + | 0.638595i | \(0.779516\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20873.1 | 1.01017 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5342.20 | 0.257513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26989.1 | −1.29582 | −0.647910 | − | 0.761717i | \(-0.724357\pi\) | ||||
−0.647910 | + | 0.761717i | \(0.724357\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −43630.5 | −2.08654 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26835.7i | 1.27831i | 0.769079 | + | 0.639154i | \(0.220715\pi\) | ||||
−0.769079 | + | 0.639154i | \(0.779285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2737.38 | + | 4343.56i | −0.129882 | + | 0.206091i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10169.8 | 0.480642 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 28489.1i | − | 1.34117i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7482.83i | − | 0.350894i | −0.984489 | − | 0.175447i | \(-0.943863\pi\) | ||
0.984489 | − | 0.175447i | \(-0.0561371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 14745.3i | − | 0.688765i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 755.076i | − | 0.0351335i | −0.999846 | − | 0.0175668i | \(-0.994408\pi\) | ||
0.999846 | − | 0.0175668i | \(-0.00559196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15167.1 | 0.702989 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2166.28 | + | 3437.36i | −0.100019 | + | 0.158706i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 6494.74i | − | 0.298714i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27084.8 | 1.24094 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3603.71 | −0.164478 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2199.37 | 0.0999987 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38108.4 | 1.72607 | 0.863036 | − | 0.505143i | \(-0.168560\pi\) | ||||
0.863036 | + | 0.505143i | \(0.168560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 20791.5i | − | 0.938147i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9463.45 | − | 15016.2i | 0.425388 | − | 0.674987i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12139.8 | 0.543627 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 22639.3i | − | 1.00998i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 20013.0i | − | 0.889455i | −0.895666 | − | 0.444728i | \(-0.853301\pi\) | ||
0.895666 | − | 0.444728i | \(-0.146699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 14031.1i | − | 0.621257i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5653.72i | 0.249394i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34295.9 | 1.50720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28297.4 | + | 44901.1i | −1.23895 | + | 1.96591i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1444.49i | − | 0.0630093i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15288.5 | 0.664420 | 0.332210 | − | 0.943206i | \(-0.392206\pi\) | ||||
0.332210 | + | 0.943206i | \(0.392206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15348.1 | −0.664542 | −0.332271 | − | 0.943184i | \(-0.607815\pi\) | ||||
−0.332271 | + | 0.943184i | \(0.607815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15468.1 | 0.667268 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40586.5 | −1.74440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 603.444i | − | 0.0258407i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4664.07 | + | 2939.37i | 0.198994 | + | 0.125409i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15311.7 | 0.650891 | 0.325445 | − | 0.945561i | \(-0.394486\pi\) | ||||
0.325445 | + | 0.945561i | \(0.394486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30450.5i | − | 1.28972i | −0.764301 | − | 0.644859i | \(-0.776916\pi\) | ||
0.764301 | − | 0.644859i | \(-0.223084\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9327.94i | 0.393645i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8352.35i | 0.351197i | 0.984462 | + | 0.175598i | \(0.0561860\pi\) | ||||
−0.984462 | + | 0.175598i | \(0.943814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18715.9i | 0.784114i | 0.919941 | + | 0.392057i | \(0.128236\pi\) | ||||
−0.919941 | + | 0.392057i | \(0.871764\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6197.95 | −0.258730 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26680.0 | − | 12760.3i | 1.10973 | − | 0.530753i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49330.6i | 2.04450i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8759.56 | 0.361738 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19309.6 | 0.794566 | 0.397283 | − | 0.917696i | \(-0.369953\pi\) | ||||
0.397283 | + | 0.917696i | \(0.369953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6574.54 | −0.269570 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12780.8 | −0.522177 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 14455.7i | − | 0.588512i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30536.5 | + | 48453.9i | −1.23878 | + | 1.96564i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9585.50 | −0.387484 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 15990.7i | − | 0.644131i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27138.9i | − | 1.08935i | −0.838646 | − | 0.544677i | \(-0.816652\pi\) | ||
0.838646 | − | 0.544677i | \(-0.183348\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2477.65i | − | 0.0991039i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25760.4i | 1.02679i | 0.858152 | + | 0.513395i | \(0.171613\pi\) | ||||
−0.858152 | + | 0.513395i | \(0.828387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42892.5 | 1.70369 | 0.851846 | − | 0.523792i | \(-0.175483\pi\) | ||||
0.851846 | + | 0.523792i | \(0.175483\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14533.0 | + | 9158.95i | 0.575243 | + | 0.362528i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26017.9i | 1.02626i | 0.858312 | + | 0.513128i | \(0.171513\pi\) | ||||
−0.858312 | + | 0.513128i | \(0.828487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 45061.4 | 1.77125 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7564.19 | 0.296301 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −75524.5 | −2.94821 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27078.6 | −1.05341 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4700.98i | − | 0.182250i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16067.7 | − | 10126.1i | −0.620786 | − | 0.391230i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4450.82 | 0.171372 | 0.0856861 | − | 0.996322i | \(-0.472692\pi\) | ||||
0.0856861 | + | 0.996322i | \(0.472692\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 19048.2i | − | 0.730922i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15737.7i | − | 0.601837i | −0.953650 | − | 0.300918i | \(-0.902707\pi\) | ||
0.953650 | − | 0.300918i | \(-0.0972931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5677.78i | − | 0.216390i | −0.994130 | − | 0.108195i | \(-0.965493\pi\) | ||
0.994130 | − | 0.108195i | \(-0.0345071\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 33864.7i | − | 1.28627i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7460.00 | 0.282393 | 0.141196 | − | 0.989982i | \(-0.454905\pi\) | ||||
0.141196 | + | 0.989982i | \(0.454905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1002.66 | − | 631.891i | −0.0378268 | − | 0.0238391i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5387.25i | 0.202559i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3418.36 | −0.128097 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14791.5 | 0.552431 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21697.4 | −0.807644 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43301.7 | −1.60644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 49649.6i | − | 1.83581i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1350.30 | + | 850.984i | 0.0497623 | + | 0.0313610i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21151.3 | −0.776897 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34731.8i | 1.27150i | 0.771894 | + | 0.635751i | \(0.219309\pi\) | ||||
−0.771894 | + | 0.635751i | \(0.780691\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9777.61i | 0.356769i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1692.78i | − | 0.0615636i | −0.999526 | − | 0.0307818i | \(-0.990200\pi\) | ||
0.999526 | − | 0.0307818i | \(-0.00979970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 62595.7i | − | 2.26902i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14430.5 | 0.521373 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2171.17 | − | 3445.13i | 0.0781881 | − | 0.124066i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7532.50i | − | 0.270375i | −0.990820 | − | 0.135187i | \(-0.956836\pi\) | ||
0.990820 | − | 0.135187i | \(-0.0431636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2052.47 | −0.0734323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13469.3 | 0.480332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3418.73 | −0.121521 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1770.58 | 0.0627330 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 21633.4i | − | 0.764012i | −0.924160 | − | 0.382006i | \(-0.875233\pi\) | ||
0.924160 | − | 0.382006i | \(-0.124767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3108.75 | − | 6499.99i | −0.109436 | − | 0.228817i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12454.9 | 0.437037 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 75154.2i | 2.62867i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33386.1i | 1.16401i | 0.813185 | + | 0.582005i | \(0.197732\pi\) | ||||
−0.813185 | + | 0.582005i | \(0.802268\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 8366.63i | − | 0.290772i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 22939.9i | − | 0.794709i | −0.917665 | − | 0.397354i | \(-0.869928\pi\) | ||
0.917665 | − | 0.397354i | \(-0.130072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −67608.3 | −2.33471 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5544.14 | + | 3494.01i | 0.190848 | + | 0.120275i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3074.78i | − | 0.105509i | −0.998608 | − | 0.0527545i | \(-0.983200\pi\) | ||
0.998608 | − | 0.0527545i | \(-0.0168001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17055.4 | 0.583394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3371.84 | 0.114973 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26530.3 | 0.901786 | 0.450893 | − | 0.892578i | \(-0.351106\pi\) | ||||
0.450893 | + | 0.892578i | \(0.351106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36956.7 | 1.25224 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 26631.1i | − | 0.899543i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14747.2 | + | 23400.2i | −0.496571 | + | 0.787937i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 75462.6 | 2.53307 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7831.45i | 0.262061i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 22926.6i | − | 0.764803i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5995.46i | 0.199381i | 0.995019 | + | 0.0996903i | \(0.0317852\pi\) | ||||
−0.995019 | + | 0.0996903i | \(0.968215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5433.67i | − | 0.180139i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16996.3 | −0.561726 | −0.280863 | − | 0.959748i | \(-0.590621\pi\) | ||||
−0.280863 | + | 0.959748i | \(0.590621\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11350.8 | + | 18010.9i | −0.373987 | + | 0.593427i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4638.78i | 0.152369i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8989.54 | 0.294371 | 0.147186 | − | 0.989109i | \(-0.452979\pi\) | ||||
0.147186 | + | 0.989109i | \(0.452979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41780.6 | −1.36396 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2494.98 | −0.0812013 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1169.17 | 0.0379356 | 0.0189678 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189678 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41530.1i | 1.34341i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4820.61 | − | 7649.13i | 0.155463 | − | 0.246681i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6281.67 | −0.201967 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 55448.1i | − | 1.77736i | −0.458525 | − | 0.888681i | \(-0.651622\pi\) | ||
0.458525 | − | 0.888681i | \(-0.348378\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12795.4i | 0.408913i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12827.6i | 0.408705i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48292.0i | 1.53403i | 0.641631 | + | 0.767013i | \(0.278258\pi\) | ||||
−0.641631 | + | 0.767013i | \(0.721742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1974.45 | −0.0625313 |
(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 | 1344.4.b.i.895.5 | 24 | ||
4.3 | odd | 2 | 1344.4.b.j.895.5 | 24 | |||
7.6 | odd | 2 | 1344.4.b.j.895.20 | 24 | |||
8.3 | odd | 2 | 672.4.b.a.223.20 | yes | 24 | ||
8.5 | even | 2 | 672.4.b.b.223.20 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.i.895.20 | 24 | ||
56.13 | odd | 2 | 672.4.b.a.223.5 | ✓ | 24 | ||
56.27 | even | 2 | 672.4.b.b.223.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.5 | ✓ | 24 | 56.13 | odd | 2 | ||
672.4.b.a.223.20 | yes | 24 | 8.3 | odd | 2 | ||
672.4.b.b.223.5 | yes | 24 | 56.27 | even | 2 | ||
672.4.b.b.223.20 | yes | 24 | 8.5 | even | 2 | ||
1344.4.b.i.895.5 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.i.895.20 | 24 | 28.27 | even | 2 | inner | ||
1344.4.b.j.895.5 | 24 | 4.3 | odd | 2 | |||
1344.4.b.j.895.20 | 24 | 7.6 | odd | 2 |