Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,3,Mod(1151,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.c (of order \(2\), degree \(1\), 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: | \(50.1363686423\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.20 | ||
Character | \(\chi\) | \(=\) | 1840.1151 |
Dual form | 1840.3.c.b.1151.37 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.78315i | − 0.594382i | −0.954818 | − | 0.297191i | \(-0.903950\pi\) | ||||
0.954818 | − | 0.297191i | \(-0.0960498\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 11.2760i | − 1.61086i | −0.592691 | − | 0.805430i | \(-0.701934\pi\) | ||||
0.592691 | − | 0.805430i | \(-0.298066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.82039 | 0.646710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 20.5962i | − 1.87238i | −0.351488 | − | 0.936192i | \(-0.614324\pi\) | ||||
0.351488 | − | 0.936192i | \(-0.385676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.3818 | 1.49091 | 0.745455 | − | 0.666556i | \(-0.232232\pi\) | ||||
0.745455 | + | 0.666556i | \(0.232232\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 3.98723i | − 0.265816i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −27.1601 | −1.59765 | −0.798827 | − | 0.601560i | \(-0.794546\pi\) | ||||
−0.798827 | + | 0.601560i | \(0.794546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 29.7144i | − 1.56392i | −0.623330 | − | 0.781959i | \(-0.714221\pi\) | ||||
0.623330 | − | 0.781959i | \(-0.285779\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.1068 | −0.957466 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 26.4269i | − 0.978775i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.1117 | 0.417644 | 0.208822 | − | 0.977954i | \(-0.433037\pi\) | ||||
0.208822 | + | 0.977954i | \(0.433037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25345i | 0.169466i | 0.996404 | + | 0.0847331i | \(0.0270038\pi\) | ||||
−0.996404 | + | 0.0847331i | \(0.972996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36.7261 | −1.11291 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 25.2140i | − 0.720399i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.56136 | −0.0692261 | −0.0346130 | − | 0.999401i | \(-0.511020\pi\) | ||||
−0.0346130 | + | 0.999401i | \(0.511020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 34.5606i | − 0.886170i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17.2011 | 0.419539 | 0.209769 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209769 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.38042i | − 0.171638i | −0.996311 | − | 0.0858189i | \(-0.972649\pi\) | ||||
0.996311 | − | 0.0858189i | \(-0.0273506\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.0148 | 0.289218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 77.4615i | 1.64812i | 0.566505 | + | 0.824058i | \(0.308295\pi\) | ||||
−0.566505 | + | 0.824058i | \(0.691705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −78.1487 | −1.59487 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48.4304i | 0.949617i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 95.1341 | 1.79498 | 0.897492 | − | 0.441032i | \(-0.145387\pi\) | ||||
0.897492 | + | 0.441032i | \(0.145387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 46.0546i | − 0.837356i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −52.9852 | −0.929564 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22.2739i | 0.377524i | 0.982023 | + | 0.188762i | \(0.0604474\pi\) | ||||
−0.982023 | + | 0.188762i | \(0.939553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.6344 | −0.387449 | −0.193724 | − | 0.981056i | \(-0.562057\pi\) | ||||
−0.193724 | + | 0.981056i | \(0.562057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 65.6309i | − 1.04176i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 43.3391 | 0.666755 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 63.2193i | 0.943572i | 0.881713 | + | 0.471786i | \(0.156391\pi\) | ||||
−0.881713 | + | 0.471786i | \(0.843609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.55166 | 0.123937 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 20.7152i | − 0.291764i | −0.989302 | − | 0.145882i | \(-0.953398\pi\) | ||||
0.989302 | − | 0.145882i | \(-0.0466020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 114.966 | 1.57487 | 0.787436 | − | 0.616396i | \(-0.211408\pi\) | ||||
0.787436 | + | 0.616396i | \(0.211408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 8.91573i | − 0.118876i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −232.244 | −3.01615 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 150.947i | 1.91072i | 0.295444 | + | 0.955360i | \(0.404532\pi\) | ||||
−0.295444 | + | 0.955360i | \(0.595468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.26053 | 0.0649448 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 134.051i | 1.61508i | 0.589815 | + | 0.807538i | \(0.299200\pi\) | ||||
−0.589815 | + | 0.807538i | \(0.700800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60.7319 | −0.714493 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 21.5969i | − 0.248240i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 61.9897 | 0.696513 | 0.348257 | − | 0.937399i | \(-0.386774\pi\) | ||||
0.348257 | + | 0.937399i | \(0.386774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 218.550i | − 2.40165i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.36767 | 0.100728 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 66.4435i | − 0.699405i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −42.1692 | −0.434734 | −0.217367 | − | 0.976090i | \(-0.569747\pi\) | ||||
−0.217367 | + | 0.976090i | \(0.569747\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 119.878i | − 1.21089i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1829 | −0.160227 | −0.0801134 | − | 0.996786i | \(-0.525528\pi\) | ||||
−0.0801134 | + | 0.996786i | \(0.525528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 83.8777i | − 0.814347i | −0.913351 | − | 0.407173i | \(-0.866514\pi\) | ||||
0.913351 | − | 0.407173i | \(-0.133486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −44.9601 | −0.428192 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 154.676i | − 1.44557i | −0.691074 | − | 0.722784i | \(-0.742862\pi\) | ||||
0.691074 | − | 0.722784i | \(-0.257138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −185.589 | −1.70266 | −0.851328 | − | 0.524634i | \(-0.824202\pi\) | ||||
−0.851328 | + | 0.524634i | \(0.824202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.56729i | 0.0411467i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.06892 | −0.0271586 | −0.0135793 | − | 0.999908i | \(-0.504323\pi\) | ||||
−0.0135793 | + | 0.999908i | \(0.504323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7238i | 0.0932505i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 112.810 | 0.964187 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 306.258i | 2.57360i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −303.205 | −2.50582 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 30.6720i | − 0.249366i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 110.645i | − 0.871217i | −0.900136 | − | 0.435608i | \(-0.856533\pi\) | ||||
0.900136 | − | 0.435608i | \(-0.143467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1604 | −0.102018 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 215.393i | 1.64422i | 0.569327 | + | 0.822111i | \(0.307204\pi\) | ||||
−0.569327 | + | 0.822111i | \(0.692796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −335.061 | −2.51925 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 59.0924i | − 0.437721i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 72.3393 | 0.528024 | 0.264012 | − | 0.964519i | \(-0.414954\pi\) | ||||
0.264012 | + | 0.964519i | \(0.414954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 92.1524i | − 0.662967i | −0.943461 | − | 0.331483i | \(-0.892451\pi\) | ||||
0.943461 | − | 0.331483i | \(-0.107549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 138.125 | 0.979611 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 399.193i | − 2.79156i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.0826 | 0.186776 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 139.350i | 0.947962i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0258 | −0.0807103 | −0.0403552 | − | 0.999185i | \(-0.512849\pi\) | ||||
−0.0403552 | + | 0.999185i | \(0.512849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 45.6425i | − 0.302268i | −0.988513 | − | 0.151134i | \(-0.951707\pi\) | ||||
0.988513 | − | 0.151134i | \(-0.0482926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −158.083 | −1.03322 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.7471i | 0.0757876i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 142.807 | 0.909600 | 0.454800 | − | 0.890594i | \(-0.349711\pi\) | ||||
0.454800 | + | 0.890594i | \(0.349711\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 169.638i | − 1.06691i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 54.0779 | 0.335888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 13.6877i | − 0.0839733i | −0.999118 | − | 0.0419867i | \(-0.986631\pi\) | ||||
0.999118 | − | 0.0419867i | \(-0.0133687\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −82.1220 | −0.497709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 100.923i | − 0.604327i | −0.953256 | − | 0.302164i | \(-0.902291\pi\) | ||||
0.953256 | − | 0.302164i | \(-0.0977089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 206.655 | 1.22281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 172.950i | − 1.01140i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 218.056 | 1.26044 | 0.630219 | − | 0.776417i | \(-0.282965\pi\) | ||||
0.630219 | + | 0.776417i | \(0.282965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 56.3801i | − 0.322172i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 39.7176 | 0.224393 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 321.350i | 1.79525i | 0.440756 | + | 0.897627i | \(0.354710\pi\) | ||||
−0.440756 | + | 0.897627i | \(0.645290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −272.135 | −1.50351 | −0.751753 | − | 0.659445i | \(-0.770792\pi\) | ||||
−0.751753 | + | 0.659445i | \(0.770792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 42.1435i | 0.230292i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.72739 | −0.0309588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 559.396i | 2.99142i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −297.990 | −1.57667 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 106.689i | 0.558582i | 0.960207 | + | 0.279291i | \(0.0900994\pi\) | ||||
−0.960207 | + | 0.279291i | \(0.909901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 182.969 | 0.948023 | 0.474012 | − | 0.880519i | \(-0.342805\pi\) | ||||
0.474012 | + | 0.880519i | \(0.342805\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 77.2799i | − 0.396307i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 358.927 | 1.82197 | 0.910983 | − | 0.412444i | \(-0.135325\pi\) | ||||
0.910983 | + | 0.412444i | \(0.135325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 260.206i | − 1.30757i | −0.756681 | − | 0.653784i | \(-0.773180\pi\) | ||||
0.756681 | − | 0.653784i | \(-0.226820\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 112.729 | 0.560842 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 136.572i | − 0.672767i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38.4628 | 0.187623 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27.9136i | 0.134848i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −612.006 | −2.92826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 85.8730i | 0.406981i | 0.979077 | + | 0.203491i | \(0.0652286\pi\) | ||||
−0.979077 | + | 0.203491i | \(0.934771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −36.9383 | −0.173419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 16.5031i | − 0.0767587i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 59.2381 | 0.272986 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 205.000i | − 0.936075i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −526.413 | −2.38196 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.27585i | − 0.0326271i | −0.999867 | − | 0.0163136i | \(-0.994807\pi\) | ||||
0.999867 | − | 0.0163136i | \(-0.00519300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.1020 | 0.129342 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 158.670i | − 0.698987i | −0.936939 | − | 0.349493i | \(-0.886354\pi\) | ||||
0.936939 | − | 0.349493i | \(-0.113646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −170.421 | −0.744196 | −0.372098 | − | 0.928193i | \(-0.621362\pi\) | ||||
−0.372098 | + | 0.928193i | \(0.621362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 414.124i | 1.79274i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −441.884 | −1.89650 | −0.948248 | − | 0.317530i | \(-0.897147\pi\) | ||||
−0.948248 | + | 0.317530i | \(0.897147\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 173.209i | 0.737060i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 269.160 | 1.13570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 218.029i | 0.912257i | 0.889914 | + | 0.456128i | \(0.150764\pi\) | ||||
−0.889914 | + | 0.456128i | \(0.849236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −282.317 | −1.17144 | −0.585721 | − | 0.810513i | \(-0.699188\pi\) | ||||
−0.585721 | + | 0.810513i | \(0.699188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 247.222i | − 1.01738i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −174.746 | −0.713248 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 575.920i | − 2.33166i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 239.033 | 0.959972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 201.439i | − 0.802548i | −0.915958 | − | 0.401274i | \(-0.868568\pi\) | ||||
0.915958 | − | 0.401274i | \(-0.131432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 98.7761 | 0.390419 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 108.294i | 0.424681i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −453.755 | −1.76558 | −0.882791 | − | 0.469766i | \(-0.844338\pi\) | ||||
−0.882791 | + | 0.469766i | \(0.844338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.8820i | 0.111514i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 70.4948 | 0.270095 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 107.082i | − 0.407155i | −0.979059 | − | 0.203577i | \(-0.934743\pi\) | ||||
0.979059 | − | 0.203577i | \(-0.0652568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 212.726 | 0.802741 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 110.537i | − 0.413995i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −278.681 | −1.03599 | −0.517994 | − | 0.855384i | \(-0.673321\pi\) | ||||
−0.517994 | + | 0.855384i | \(0.673321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 306.814i | 1.13215i | 0.824352 | + | 0.566077i | \(0.191540\pi\) | ||||
−0.824352 | + | 0.566077i | \(0.808460\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −389.706 | −1.42750 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 102.981i | − 0.374477i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 384.344 | 1.38752 | 0.693762 | − | 0.720204i | \(-0.255952\pi\) | ||||
0.693762 | + | 0.720204i | \(0.255952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.5772i | 0.109596i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −95.5712 | −0.340111 | −0.170055 | − | 0.985434i | \(-0.554395\pi\) | ||||
−0.170055 | + | 0.985434i | \(0.554395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 159.227i | 0.562639i | 0.959614 | + | 0.281319i | \(0.0907721\pi\) | ||||
−0.959614 | + | 0.281319i | \(0.909228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −118.478 | −0.415714 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 193.960i | − 0.675818i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 448.672 | 1.55250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 75.1938i | 0.258398i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 68.9553 | 0.235342 | 0.117671 | − | 0.993053i | \(-0.462457\pi\) | ||||
0.117671 | + | 0.993053i | \(0.462457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 49.8059i | 0.168834i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −544.295 | −1.83264 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 92.9520i | 0.310876i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −83.2218 | −0.276484 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.8565i | 0.0952359i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −52.8481 | −0.173272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 284.390i | − 0.926350i | −0.886267 | − | 0.463175i | \(-0.846710\pi\) | ||||
0.886267 | − | 0.463175i | \(-0.153290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −149.566 | −0.484033 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 378.124i | − 1.21583i | −0.794001 | − | 0.607917i | \(-0.792005\pi\) | ||||
0.794001 | − | 0.607917i | \(-0.207995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.5344 | −0.107139 | −0.0535694 | − | 0.998564i | \(-0.517060\pi\) | ||||
−0.0535694 | + | 0.998564i | \(0.517060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 146.755i | − 0.465889i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 507.734 | 1.60168 | 0.800842 | − | 0.598876i | \(-0.204386\pi\) | ||||
0.800842 | + | 0.598876i | \(0.204386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 249.455i | − 0.781991i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −275.810 | −0.859220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 807.048i | 2.49860i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 96.9092 | 0.298182 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 330.933i | 1.01203i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 873.458 | 2.65489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 501.833i | 1.51611i | 0.652190 | + | 0.758056i | \(0.273850\pi\) | ||||
−0.652190 | + | 0.758056i | \(0.726150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.9082 | −0.0447692 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 141.363i | 0.421978i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 39.7559 | 0.117970 | 0.0589851 | − | 0.998259i | \(-0.481214\pi\) | ||||
0.0589851 | + | 0.998259i | \(0.481214\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.47234i | 0.0161426i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 108.201 | 0.317306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 328.681i | 0.958255i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.1221 | 0.0554264 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 52.8521i | − 0.152311i | −0.997096 | − | 0.0761557i | \(-0.975735\pi\) | ||||
0.997096 | − | 0.0761557i | \(-0.0242646\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 469.656 | 1.34572 | 0.672860 | − | 0.739770i | \(-0.265066\pi\) | ||||
0.672860 | + | 0.739770i | \(0.265066\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 512.202i | − 1.45926i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −355.526 | −1.00716 | −0.503578 | − | 0.863950i | \(-0.667983\pi\) | ||||
−0.503578 | + | 0.863950i | \(0.667983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 46.3207i | − 0.130481i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 546.103 | 1.52970 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 27.0403i | − 0.0753211i | −0.999291 | − | 0.0376606i | \(-0.988009\pi\) | ||||
0.999291 | − | 0.0376606i | \(-0.0119906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −521.948 | −1.44584 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 540.658i | 1.48942i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 257.071 | 0.704304 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 468.694i | − 1.27710i | −0.769582 | − | 0.638548i | \(-0.779536\pi\) | ||||
0.769582 | − | 0.638548i | \(-0.220464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 100.117 | 0.271320 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1072.73i | − 2.89147i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −139.574 | −0.374194 | −0.187097 | − | 0.982341i | \(-0.559908\pi\) | ||||
−0.187097 | + | 0.982341i | \(0.559908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 19.9362i | − 0.0531631i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 234.747 | 0.622670 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 517.047i | − 1.36424i | −0.731240 | − | 0.682120i | \(-0.761058\pi\) | ||||
0.731240 | − | 0.682120i | \(-0.238942\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −197.295 | −0.517835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7901i | 0.0464494i | 0.999730 | + | 0.0232247i | \(0.00739332\pi\) | ||||
−0.999730 | + | 0.0232247i | \(0.992607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −519.312 | −1.34886 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 42.9570i | − 0.111000i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 48.2931 | 0.124147 | 0.0620734 | − | 0.998072i | \(-0.480229\pi\) | ||||
0.0620734 | + | 0.998072i | \(0.480229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 130.255i | − 0.333134i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 384.077 | 0.977295 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 337.528i | 0.854500i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −343.875 | −0.866185 | −0.433092 | − | 0.901350i | \(-0.642578\pi\) | ||||
−0.433092 | + | 0.901350i | \(0.642578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 597.462i | 1.49740i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 266.765 | 0.665250 | 0.332625 | − | 0.943059i | \(-0.392066\pi\) | ||||
0.332625 | + | 0.943059i | \(0.392066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 101.822i | 0.252659i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.7629 | 0.0290442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 52.7545i | 0.129618i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 454.087 | 1.11024 | 0.555118 | − | 0.831771i | \(-0.312673\pi\) | ||||
0.555118 | + | 0.831771i | \(0.312673\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 128.991i | − 0.313848i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 251.161 | 0.608138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 299.748i | 0.722284i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −164.321 | −0.394055 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 635.903i | 1.51767i | 0.651284 | + | 0.758834i | \(0.274231\pi\) | ||||
−0.651284 | + | 0.758834i | \(0.725769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 329.846 | 0.783482 | 0.391741 | − | 0.920076i | \(-0.371873\pi\) | ||||
0.391741 | + | 0.920076i | \(0.371873\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 450.856i | 1.06585i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −135.801 | −0.319531 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 266.502i | 0.624126i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −711.819 | −1.65925 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 142.754i | 0.331215i | 0.986192 | + | 0.165607i | \(0.0529584\pi\) | ||||
−0.986192 | + | 0.165607i | \(0.947042\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 635.368 | 1.46736 | 0.733682 | − | 0.679493i | \(-0.237800\pi\) | ||||
0.733682 | + | 0.679493i | \(0.237800\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 48.2921i | − 0.111016i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 142.505 | 0.326099 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 154.754i | − 0.352515i | −0.984344 | − | 0.176258i | \(-0.943601\pi\) | ||||
0.984344 | − | 0.176258i | \(-0.0563992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −454.856 | −1.03142 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 219.706i | 0.495951i | 0.968766 | + | 0.247975i | \(0.0797652\pi\) | ||||
−0.968766 | + | 0.247975i | \(0.920235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 138.613 | 0.311490 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.4438i | 0.0479727i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 73.0500 | 0.162695 | 0.0813475 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813475 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 354.278i | − 0.785538i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −81.3873 | −0.179663 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 488.693i | − 1.07405i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 348.797 | 0.763232 | 0.381616 | − | 0.924321i | \(-0.375368\pi\) | ||||
0.381616 | + | 0.924321i | \(0.375368\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 717.758i | 1.56374i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 384.410 | 0.833860 | 0.416930 | − | 0.908939i | \(-0.363106\pi\) | ||||
0.416930 | + | 0.908939i | \(0.363106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 180.334i | 0.389490i | 0.980854 | + | 0.194745i | \(0.0623879\pi\) | ||||
−0.980854 | + | 0.194745i | \(0.937612\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9467 | 0.0450468 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 52.8643i | 0.113200i | 0.998397 | + | 0.0565998i | \(0.0180259\pi\) | ||||
−0.998397 | + | 0.0565998i | \(0.981974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 712.863 | 1.51996 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 254.646i | − 0.540649i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −152.009 | −0.321372 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 148.572i | − 0.312784i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 553.718 | 1.16083 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 189.099i | − 0.394780i | −0.980325 | − | 0.197390i | \(-0.936754\pi\) | ||||
0.980325 | − | 0.197390i | \(-0.0632465\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.6439 | −0.103210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 96.4288i | − 0.199645i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −94.2932 | −0.194419 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 104.030i | 0.213615i | 0.994280 | + | 0.106807i | \(0.0340628\pi\) | ||||
−0.994280 | + | 0.106807i | \(0.965937\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.4071 | −0.0499122 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 396.964i | − 0.808480i | −0.914653 | − | 0.404240i | \(-0.867536\pi\) | ||||
0.914653 | − | 0.404240i | \(-0.132464\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −328.955 | −0.667251 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 268.056i | − 0.541527i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −233.586 | −0.469991 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 626.983i | − 1.25648i | −0.778020 | − | 0.628239i | \(-0.783776\pi\) | ||||
0.778020 | − | 0.628239i | \(-0.216224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −179.960 | −0.359201 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 359.980i | − 0.715667i | −0.933785 | − | 0.357833i | \(-0.883516\pi\) | ||||
0.933785 | − | 0.357833i | \(-0.116484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.1861 | −0.0716556 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 368.497i | − 0.726818i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 395.425 | 0.776867 | 0.388433 | − | 0.921477i | \(-0.373016\pi\) | ||||
0.388433 | + | 0.921477i | \(0.373016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1296.36i | − 2.53690i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −785.261 | −1.53072 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 187.556i | − 0.364187i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1595.42 | 3.08591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 388.825i | − 0.749182i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −220.949 | −0.424086 | −0.212043 | − | 0.977260i | \(-0.568012\pi\) | ||||
−0.212043 | + | 0.977260i | \(0.568012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 619.464i | 1.18444i | 0.805775 | + | 0.592222i | \(0.201749\pi\) | ||||
−0.805775 | + | 0.592222i | \(0.798251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −100.534 | −0.191493 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 142.684i | − 0.270749i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 129.643i | 0.244148i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 333.389 | 0.625494 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 345.866i | − 0.646478i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 573.015 | 1.06707 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1609.57i | 2.98621i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −80.8928 | −0.149525 | −0.0747623 | − | 0.997201i | \(-0.523820\pi\) | ||||
−0.0747623 | + | 0.997201i | \(0.523820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 485.256i | 0.893657i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −414.991 | −0.761451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 902.721i | 1.65031i | 0.564905 | + | 0.825156i | \(0.308913\pi\) | ||||
−0.564905 | + | 0.825156i | \(0.691087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −137.561 | −0.250567 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 359.892i | − 0.653162i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1702.08 | 3.07790 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.2128i | 0.0184014i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −352.533 | −0.632914 | −0.316457 | − | 0.948607i | \(-0.602493\pi\) | ||||
−0.316457 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 143.046i | − 0.255896i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 997.485 | 1.77805 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 292.609i | − 0.519731i | −0.965645 | − | 0.259866i | \(-0.916322\pi\) | ||||
0.965645 | − | 0.259866i | \(-0.0836782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.86232 | −0.0121457 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 59.3178i | − 0.104617i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 190.490 | 0.334781 | 0.167390 | − | 0.985891i | \(-0.446466\pi\) | ||||
0.167390 | + | 0.985891i | \(0.446466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 57.4750i | − 0.100657i | −0.998733 | − | 0.0503284i | \(-0.983973\pi\) | ||||
0.998733 | − | 0.0503284i | \(-0.0160268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 190.242 | 0.332011 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.9792i | 0.0417029i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.5032 | 0.0823280 | 0.0411640 | − | 0.999152i | \(-0.486893\pi\) | ||||
0.0411640 | + | 0.999152i | \(0.486893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 326.259i | − 0.563488i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1511.57 | 2.60166 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1959.40i | − 3.36090i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 252.251 | 0.431198 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1030.76i | 1.75599i | 0.478672 | + | 0.877994i | \(0.341118\pi\) | ||||
−0.478672 | + | 0.877994i | \(0.658882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 156.103 | 0.265031 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 640.019i | − 1.08294i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 911.094 | 1.53641 | 0.768207 | − | 0.640201i | \(-0.221149\pi\) | ||||
0.768207 | + | 0.640201i | \(0.221149\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 684.814i | 1.15095i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −463.985 | −0.777195 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 911.862i | 1.52231i | 0.648572 | + | 0.761153i | \(0.275367\pi\) | ||||
−0.648572 | + | 0.761153i | \(0.724633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −227.152 | −0.377957 | −0.188978 | − | 0.981981i | \(-0.560518\pi\) | ||||
−0.188978 | + | 0.981981i | \(0.560518\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 367.961i | 0.610218i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −677.987 | −1.12064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 155.710i | 0.256524i | 0.991740 | + | 0.128262i | \(0.0409399\pi\) | ||||
−0.991740 | + | 0.128262i | \(0.959060\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −243.527 | −0.399880 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1501.35i | 2.45719i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −131.088 | −0.213847 | −0.106924 | − | 0.994267i | \(-0.534100\pi\) | ||||
−0.106924 | + | 0.994267i | \(0.534100\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 68.5847i | − 0.111520i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 540.179 | 0.875492 | 0.437746 | − | 0.899099i | \(-0.355777\pi\) | ||||
0.437746 | + | 0.899099i | \(0.355777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1050.32i | 1.69680i | 0.529353 | + | 0.848402i | \(0.322435\pi\) | ||||
−0.529353 | + | 0.848402i | \(0.677565\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 126.739 | 0.204089 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 698.997i | − 1.12199i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1091.29i | 1.74050i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 69.5670 | 0.110599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 339.913i | − 0.538689i | −0.963044 | − | 0.269344i | \(-0.913193\pi\) | ||||
0.963044 | − | 0.269344i | \(-0.0868070\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 153.124 | 0.241902 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 247.409i | − 0.389620i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1514.67 | −2.37781 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 120.571i | − 0.188687i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1064.68 | −1.66096 | −0.830480 | − | 0.557048i | \(-0.811934\pi\) | ||||
−0.830480 | + | 0.557048i | \(0.811934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 472.734i | 0.735201i | 0.929984 | + | 0.367600i | \(0.119821\pi\) | ||||
−0.929984 | + | 0.367600i | \(0.880179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −29.4275 | −0.0456240 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 661.303i | 1.02211i | 0.859549 | + | 0.511054i | \(0.170745\pi\) | ||||
−0.859549 | + | 0.511054i | \(0.829255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 458.758 | 0.706869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 105.630i | − 0.162258i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −91.5511 | −0.140201 | −0.0701004 | − | 0.997540i | \(-0.522332\pi\) | ||||
−0.0701004 | + | 0.997540i | \(0.522332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 481.634i | 0.735318i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 669.145 | 1.01849 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 803.989i | 1.22001i | 0.792396 | + | 0.610007i | \(0.208833\pi\) | ||||
−0.792396 | + | 0.610007i | \(0.791167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −882.772 | −1.33551 | −0.667755 | − | 0.744381i | \(-0.732745\pi\) | ||||
−0.667755 | + | 0.744381i | \(0.732745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 938.671i | 1.41579i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −749.219 | −1.12664 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.0856i | 0.0870849i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9739 | −0.0193930 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 486.779i | 0.725453i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −174.407 | −0.259149 | −0.129574 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129574 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 132.135i | − 0.195755i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 323.903 | 0.478439 | 0.239219 | − | 0.970966i | \(-0.423109\pi\) | ||||
0.239219 | + | 0.970966i | \(0.423109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 475.501i | 0.700296i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −282.932 | −0.415465 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7421i | 0.0245126i | 0.999925 | + | 0.0122563i | \(0.00390140\pi\) | ||||
−0.999925 | + | 0.0122563i | \(0.996099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 161.755 | 0.236139 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 303.885i | 0.442337i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1843.87 | 2.67616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1107.77i | − 1.60314i | −0.597904 | − | 0.801568i | \(-0.704000\pi\) | ||||
0.597904 | − | 0.801568i | \(-0.296000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1351.75 | −1.95058 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 206.059i | − 0.296488i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −467.184 | −0.670278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 787.943i | 1.12724i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 638.357 | 0.910637 | 0.455319 | − | 0.890329i | \(-0.349525\pi\) | ||||
0.455319 | + | 0.890329i | \(0.349525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 76.1095i | 0.108264i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 308.857 | 0.438095 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 182.479i | 0.258103i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −855.687 | −1.20689 | −0.603446 | − | 0.797404i | \(-0.706206\pi\) | ||||
−0.603446 | + | 0.797404i | \(0.706206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 878.570i | 1.23568i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.1947 | −0.0353362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 892.622i | − 1.24842i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 388.778 | 0.542229 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 359.613i | − 0.500158i | −0.968225 | − | 0.250079i | \(-0.919543\pi\) | ||||
0.968225 | − | 0.250079i | \(-0.0804566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −945.807 | −1.31180 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 503.413i | 0.696283i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 60.5584 | 0.0835289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 106.361i | 0.146301i | 0.997321 | + | 0.0731505i | \(0.0233053\pi\) | ||||
−0.997321 | + | 0.0731505i | \(0.976695\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −393.489 | −0.539765 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 200.453i | 0.274218i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −714.794 | −0.975162 | −0.487581 | − | 0.873078i | \(-0.662121\pi\) | ||||
−0.487581 | + | 0.873078i | \(0.662121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 311.597i | 0.423942i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1302.08 | 1.76673 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1131.01i | − 1.53046i | −0.643757 | − | 0.765230i | \(-0.722625\pi\) | ||||
0.643757 | − | 0.765230i | \(-0.277375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1026.95 | −1.38590 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 316.289i | − 0.425692i | −0.977086 | − | 0.212846i | \(-0.931727\pi\) | ||||
0.977086 | − | 0.212846i | \(-0.0682732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.8906 | −0.0360947 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 780.231i | 1.04449i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1744.13 | −2.32861 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 249.612i | − 0.332373i | −0.986094 | − | 0.166187i | \(-0.946855\pi\) | ||||
0.986094 | − | 0.166187i | \(-0.0531454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −359.196 | −0.477020 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 102.060i | − 0.135179i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 78.0177 | 0.103062 | 0.0515308 | − | 0.998671i | \(-0.483590\pi\) | ||||
0.0515308 | + | 0.998671i | \(0.483590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 176.132i | − 0.232058i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 380.576 | 0.500099 | 0.250050 | − | 0.968233i | \(-0.419553\pi\) | ||||
0.250050 | + | 0.968233i | \(0.419553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2092.71i | 2.74274i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −353.484 | −0.462070 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 431.709i | 0.562854i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 410.236 | 0.533467 | 0.266734 | − | 0.963770i | \(-0.414056\pi\) | ||||
0.266734 | + | 0.963770i | \(0.414056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 809.110i | 1.04943i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 560.359 | 0.724914 | 0.362457 | − | 0.932000i | \(-0.381938\pi\) | ||||
0.362457 | + | 0.932000i | \(0.381938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.2673i | 0.0338932i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.5008 | 0.0662816 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 511.121i | − 0.656124i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −426.656 | −0.546294 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 320.074i | − 0.408780i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 319.327 | 0.406785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 649.620i | − 0.825439i | −0.910858 | − | 0.412719i | \(-0.864579\pi\) | ||||
0.910858 | − | 0.412719i | \(-0.135421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −190.942 | −0.242005 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.6053i | 0.0437487i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −458.077 | −0.577651 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 379.322i | − 0.477134i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1116.25 | 1.40056 | 0.700282 | − | 0.713867i | \(-0.253058\pi\) | ||||
0.700282 | + | 0.713867i | \(0.253058\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 2103.86i | − 2.63312i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 360.804 | 0.450442 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2367.86i | − 2.94877i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 120.922 | 0.150214 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 496.928i | 0.615773i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 349.204 | 0.431649 | 0.215824 | − | 0.976432i | \(-0.430756\pi\) | ||||
0.215824 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 602.463i | 0.742864i | 0.928460 | + | 0.371432i | \(0.121133\pi\) | ||||
−0.928460 | + | 0.371432i | \(0.878867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 547.093 | 0.672932 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 30.6065i | − 0.0375540i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −219.305 | −0.268427 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1272.05i | − 1.55317i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 207.306 | 0.252504 | 0.126252 | − | 0.991998i | \(-0.459705\pi\) | ||||
0.126252 | + | 0.991998i | \(0.459705\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 388.053i | − 0.471510i | −0.971813 | − | 0.235755i | \(-0.924244\pi\) | ||||
0.971813 | − | 0.235755i | \(-0.0757563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −183.630 | −0.222582 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 177.374i | 0.214479i | 0.994233 | + | 0.107240i | \(0.0342012\pi\) | ||||
−0.994233 | + | 0.107240i | \(0.965799\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1521.76 | −1.83566 | −0.917828 | − | 0.396979i | \(-0.870059\pi\) | ||||
−0.917828 | + | 0.396979i | \(0.870059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 685.341i | − 0.824719i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2122.53 | 2.54805 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 225.670i | − 0.270263i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 138.833 | 0.165869 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 253.074i | − 0.301637i | −0.988561 | − | 0.150819i | \(-0.951809\pi\) | ||||
0.988561 | − | 0.150819i | \(-0.0481910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −694.307 | −0.825573 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 170.417i | 0.202156i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 462.096 | 0.546859 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3418.94i | 4.03653i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 283.925 | 0.334422 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 12.2839i | − 0.0144346i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1324.50 | −1.55275 | −0.776376 | − | 0.630270i | \(-0.782944\pi\) | ||||
−0.776376 | + | 0.630270i | \(0.782944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 386.727i | − 0.452313i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 652.655 | 0.761558 | 0.380779 | − | 0.924666i | \(-0.375656\pi\) | ||||
0.380779 | + | 0.924666i | \(0.375656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 557.810i | 0.649372i | 0.945822 | + | 0.324686i | \(0.105259\pi\) | ||||
−0.945822 | + | 0.324686i | \(0.894741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −345.859 | −0.401694 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 613.258i | 0.710612i | 0.934750 | + | 0.355306i | \(0.115623\pi\) | ||||
−0.934750 | + | 0.355306i | \(0.884377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 487.588 | 0.563685 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 800.048i | − 0.922778i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3108.94 | 3.57760 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1225.31i | 1.40678i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −245.441 | −0.281147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 126.070i | − 0.144080i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −817.583 | −0.932249 | −0.466125 | − | 0.884719i | \(-0.654350\pi\) | ||||
−0.466125 | + | 0.884719i | \(0.654350\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 122.957i | − 0.139883i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1211.48 | 1.37512 | 0.687558 | − | 0.726129i | \(-0.258683\pi\) | ||||
0.687558 | + | 0.726129i | \(0.258683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1591.37i | − 1.80224i | −0.433574 | − | 0.901118i | \(-0.642748\pi\) | ||||
0.433574 | − | 0.901118i | \(-0.357252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 88.8112 | 0.100352 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 609.859i | − 0.687552i | −0.939052 | − | 0.343776i | \(-0.888294\pi\) | ||||
0.939052 | − | 0.343776i | \(-0.111706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1247.63 | −1.40341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 108.347i | − 0.121602i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2301.73 | 2.57752 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 718.561i | 0.802862i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 165.747 | 0.184779 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.6282i | 0.0707766i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2583.85 | −2.86776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 148.397i | 0.164337i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −608.512 | −0.672389 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 73.5050i | 0.0810418i | 0.999179 | + | 0.0405209i | \(0.0129017\pi\) | ||||
−0.999179 | + | 0.0405209i | \(0.987098\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −94.1909 | −0.103620 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1275.16i | − 1.39973i | −0.714273 | − | 0.699867i | \(-0.753243\pi\) | ||||
0.714273 | − | 0.699867i | \(-0.246757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2760.95 | 3.02404 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 94.2357i | 0.102990i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2428.78 | 2.64861 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 310.848i | 0.338246i | 0.985595 | + | 0.169123i | \(0.0540935\pi\) | ||||
−0.985595 | + | 0.169123i | \(0.945907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −507.108 | −0.550606 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 401.499i | − 0.434994i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.8068 | −0.0138452 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 488.201i | − 0.526646i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −591.042 | −0.636213 | −0.318107 | − | 0.948055i | \(-0.603047\pi\) | ||||
−0.318107 | + | 0.948055i | \(0.603047\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2322.15i | 2.49425i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −674.250 | −0.722669 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1250.85i | 1.33781i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1458.34 | 1.55639 | 0.778197 | − | 0.628020i | \(-0.216135\pi\) | ||||
0.778197 | + | 0.628020i | \(0.216135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.7967i | 0.0636813i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1212.25 | −1.28826 | −0.644128 | − | 0.764918i | \(-0.722780\pi\) | ||||
−0.644128 | + | 0.764918i | \(0.722780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.4935i | 0.0874799i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −666.327 | −0.705108 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 422.808i | − 0.446471i | −0.974764 | − | 0.223236i | \(-0.928338\pi\) | ||||
0.974764 | − | 0.223236i | \(-0.0716620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2228.25 | 2.34799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 905.363i | − 0.952012i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 352.540 | 0.369927 | 0.184963 | − | 0.982745i | \(-0.440783\pi\) | ||||
0.184963 | + | 0.982745i | \(0.440783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 238.564i | 0.249805i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −444.815 | −0.464801 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 815.699i | − 0.850573i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 933.401 | 0.971281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 900.274i | − 0.934864i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 409.130 | 0.423969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 297.029i | 0.307166i | 0.988136 | + | 0.153583i | \(0.0490812\pi\) | ||||
−0.988136 | + | 0.153583i | \(0.950919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1439.08 | 1.48512 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 950.451i | 0.978837i | 0.872049 | + | 0.489419i | \(0.162791\pi\) | ||||
−0.872049 | + | 0.489419i | \(0.837209\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1039.11 | −1.06795 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 172.803i | − 0.177234i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −723.725 | −0.740762 | −0.370381 | − | 0.928880i | \(-0.620773\pi\) | ||||
−0.370381 | + | 0.928880i | \(0.620773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1276.75i | − 1.30414i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1080.20 | −1.10113 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 103.447i | 0.105236i | 0.998615 | + | 0.0526181i | \(0.0167566\pi\) | ||||
−0.998615 | + | 0.0526181i | \(0.983243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 802.586 | 0.814808 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1557.50i | − 1.57802i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.3953 | 0.0357889 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1451.61i | − 1.46479i | −0.680880 | − | 0.732395i | \(-0.738402\pi\) | ||||
0.680880 | − | 0.732395i | \(-0.261598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 894.841 | 0.901149 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 581.838i | − 0.584762i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −541.612 | −0.543242 | −0.271621 | − | 0.962404i | \(-0.587560\pi\) | ||||
−0.271621 | + | 0.962404i | \(0.587560\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 67.6890i | 0.0677567i |
(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 | 1840.3.c.b.1151.20 | ✓ | 56 | |
4.3 | odd | 2 | inner | 1840.3.c.b.1151.37 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.3.c.b.1151.20 | ✓ | 56 | 1.1 | even | 1 | trivial | |
1840.3.c.b.1151.37 | yes | 56 | 4.3 | odd | 2 | inner |