Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 363) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.1 | ||
Root | \(1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.d.604.4 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.34607i | − 1.67303i | −0.547942 | − | 0.836516i | \(-0.684589\pi\) | ||||
0.547942 | − | 0.836516i | \(-0.315411\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.19615 | −1.79904 | ||||||||
\(5\) | 8.66025 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.10634i | 1.15805i | 0.815310 | + | 0.579025i | \(0.196566\pi\) | ||||
−0.815310 | + | 0.579025i | \(0.803434\pi\) | |||||||
\(8\) | 10.6945i | 1.33682i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 28.9778i | − 2.89778i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.619174i | 0.0476288i | 0.999716 | + | 0.0238144i | \(0.00758107\pi\) | ||||
−0.999716 | + | 0.0238144i | \(0.992419\pi\) | |||||||
\(14\) | 27.1244 | 1.93745 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.00000 | 0.437500 | ||||||||
\(17\) | 25.2156i | 1.48327i | 0.670803 | + | 0.741636i | \(0.265950\pi\) | ||||
−0.670803 | + | 0.741636i | \(0.734050\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.10205i | − 0.268529i | −0.990946 | − | 0.134265i | \(-0.957133\pi\) | ||||
0.990946 | − | 0.134265i | \(-0.0428672\pi\) | |||||||
\(20\) | −62.3205 | −3.11603 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.26795 | 0.315998 | 0.157999 | − | 0.987439i | \(-0.449496\pi\) | ||||
0.157999 | + | 0.987439i | \(0.449496\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.0000 | 2.00000 | ||||||||
\(26\) | 2.07180 | 0.0796845 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 58.3345i | − 2.08337i | ||||||||
\(29\) | 21.8052i | 0.751902i | 0.926639 | + | 0.375951i | \(0.122684\pi\) | ||||
−0.926639 | + | 0.375951i | \(0.877316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15.4641 | −0.498842 | −0.249421 | − | 0.968395i | \(-0.580240\pi\) | ||||
−0.249421 | + | 0.968395i | \(0.580240\pi\) | |||||||
\(32\) | 19.3557i | 0.604865i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 84.3731 | 2.48156 | ||||||||
\(35\) | 70.2030i | 2.00580i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.8038 | −0.670374 | −0.335187 | − | 0.942152i | \(-0.608800\pi\) | ||||
−0.335187 | + | 0.942152i | \(0.608800\pi\) | |||||||
\(38\) | −17.0718 | −0.449258 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 92.6174i | 2.31543i | ||||||||
\(41\) | − 23.2466i | − 0.566990i | −0.958974 | − | 0.283495i | \(-0.908506\pi\) | ||||
0.958974 | − | 0.283495i | \(-0.0914939\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.4649i | 0.848022i | 0.905657 | + | 0.424011i | \(0.139378\pi\) | ||||
−0.905657 | + | 0.424011i | \(0.860622\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 24.3190i | − 0.528675i | ||||||||
\(47\) | 86.1051 | 1.83202 | 0.916012 | − | 0.401151i | \(-0.131390\pi\) | ||||
0.916012 | + | 0.401151i | \(0.131390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.7128 | −0.341078 | ||||||||
\(50\) | − 167.303i | − 3.34607i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 4.45567i | − 0.0856860i | ||||||||
\(53\) | 53.1051 | 1.00198 | 0.500992 | − | 0.865452i | \(-0.332969\pi\) | ||||
0.500992 | + | 0.865452i | \(0.332969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −86.6936 | −1.54810 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 72.9615 | 1.25796 | ||||||||
\(59\) | 66.4064 | 1.12553 | 0.562766 | − | 0.826616i | \(-0.309737\pi\) | ||||
0.562766 | + | 0.826616i | \(0.309737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.632i | 1.64971i | 0.565346 | + | 0.824854i | \(0.308743\pi\) | ||||
−0.565346 | + | 0.824854i | \(0.691257\pi\) | |||||||
\(62\) | 51.7439i | 0.834579i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 92.7654 | 1.44946 | ||||||||
\(65\) | 5.36220i | 0.0824955i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 74.0141 | 1.10469 | 0.552344 | − | 0.833616i | \(-0.313734\pi\) | ||||
0.552344 | + | 0.833616i | \(0.313734\pi\) | |||||||
\(68\) | − 181.455i | − 2.66846i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 234.904 | 3.35577 | ||||||||
\(71\) | 66.8372 | 0.941369 | 0.470684 | − | 0.882302i | \(-0.344007\pi\) | ||||
0.470684 | + | 0.882302i | \(0.344007\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.1571i | 0.591193i | 0.955313 | + | 0.295596i | \(0.0955184\pi\) | ||||
−0.955313 | + | 0.295596i | \(0.904482\pi\) | |||||||
\(74\) | 82.9953i | 1.12156i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 36.7151i | 0.483094i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 99.7528i | − 1.26269i | −0.775500 | − | 0.631347i | \(-0.782502\pi\) | ||||
0.775500 | − | 0.631347i | \(-0.217498\pi\) | |||||||
\(80\) | 60.6218 | 0.757772 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −77.7846 | −0.948593 | ||||||||
\(83\) | − 20.5569i | − 0.247673i | −0.992303 | − | 0.123837i | \(-0.960480\pi\) | ||||
0.992303 | − | 0.123837i | \(-0.0395198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 218.374i | 2.56910i | ||||||||
\(86\) | 122.014 | 1.41877 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.0141 | −0.191169 | −0.0955847 | − | 0.995421i | \(-0.530472\pi\) | ||||
−0.0955847 | + | 0.995421i | \(0.530472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01924 | −0.0551565 | ||||||||
\(92\) | −52.3013 | −0.568492 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 288.113i | − 3.06504i | ||||||||
\(95\) | − 44.1851i | − 0.465106i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −161.158 | −1.66142 | −0.830710 | − | 0.556706i | \(-0.812065\pi\) | ||||
−0.830710 | + | 0.556706i | \(0.812065\pi\) | |||||||
\(98\) | 55.9222i | 0.570634i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −359.808 | −3.59808 | ||||||||
\(101\) | − 107.250i | − 1.06188i | −0.847409 | − | 0.530940i | \(-0.821839\pi\) | ||||
0.847409 | − | 0.530940i | \(-0.178161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −102.550 | −0.995631 | −0.497815 | − | 0.867283i | \(-0.665864\pi\) | ||||
−0.497815 | + | 0.867283i | \(0.665864\pi\) | |||||||
\(104\) | −6.62178 | −0.0636709 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 177.693i | − 1.67635i | ||||||||
\(107\) | − 3.89091i | − 0.0363636i | −0.999835 | − | 0.0181818i | \(-0.994212\pi\) | ||||
0.999835 | − | 0.0181818i | \(-0.00578777\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 42.3348i | 0.388393i | 0.980963 | + | 0.194196i | \(0.0622099\pi\) | ||||
−0.980963 | + | 0.194196i | \(0.937790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 56.7444i | 0.506646i | ||||||||
\(113\) | −129.813 | −1.14879 | −0.574393 | − | 0.818580i | \(-0.694762\pi\) | ||||
−0.574393 | + | 0.818580i | \(0.694762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 62.9423 | 0.547324 | ||||||||
\(116\) | − 156.913i | − 1.35270i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 222.200i | − 1.88305i | ||||||||
\(119\) | −204.406 | −1.71770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 336.722 | 2.76001 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 111.282 | 0.897436 | ||||||||
\(125\) | 216.506 | 1.73205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 12.3490i | − 0.0972361i | −0.998817 | − | 0.0486180i | \(-0.984518\pi\) | ||||
0.998817 | − | 0.0486180i | \(-0.0154817\pi\) | |||||||
\(128\) | − 232.976i | − 1.82013i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.9423 | 0.138018 | ||||||||
\(131\) | 18.2361i | 0.139207i | 0.997575 | + | 0.0696035i | \(0.0221734\pi\) | ||||
−0.997575 | + | 0.0696035i | \(0.977827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.3590 | 0.310970 | ||||||||
\(134\) | − 247.656i | − 1.84818i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −269.669 | −1.98286 | ||||||||
\(137\) | −51.6462 | −0.376979 | −0.188490 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188490 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 78.8714i | − 0.567420i | −0.958910 | − | 0.283710i | \(-0.908435\pi\) | ||||
0.958910 | − | 0.283710i | \(-0.0915654\pi\) | |||||||
\(140\) | − 505.191i | − 3.60851i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 223.642i | − 1.57494i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 188.838i | 1.30233i | ||||||||
\(146\) | 144.406 | 0.989085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 178.492 | 1.20603 | ||||||||
\(149\) | 156.656i | 1.05138i | 0.850676 | + | 0.525691i | \(0.176193\pi\) | ||||
−0.850676 | + | 0.525691i | \(0.823807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 152.884i | − 1.01247i | −0.862394 | − | 0.506237i | \(-0.831036\pi\) | ||||
0.862394 | − | 0.506237i | \(-0.168964\pi\) | |||||||
\(152\) | 54.5641 | 0.358974 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −133.923 | −0.864020 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −276.813 | −1.76314 | −0.881569 | − | 0.472055i | \(-0.843513\pi\) | ||||
−0.881569 | + | 0.472055i | \(0.843513\pi\) | |||||||
\(158\) | −333.779 | −2.11253 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 167.625i | 1.04766i | ||||||||
\(161\) | 58.9165i | 0.365941i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −100.158 | −0.614464 | −0.307232 | − | 0.951635i | \(-0.599403\pi\) | ||||
−0.307232 | + | 0.951635i | \(0.599403\pi\) | |||||||
\(164\) | 167.286i | 1.02004i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −68.7846 | −0.414365 | ||||||||
\(167\) | 68.4443i | 0.409846i | 0.978778 | + | 0.204923i | \(0.0656945\pi\) | ||||
−0.978778 | + | 0.204923i | \(0.934306\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.617 | 0.997731 | ||||||||
\(170\) | 730.692 | 4.29819 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 262.407i | − 1.52562i | ||||||||
\(173\) | 60.4050i | 0.349162i | 0.984643 | + | 0.174581i | \(0.0558571\pi\) | ||||
−0.984643 | + | 0.174581i | \(0.944143\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 405.317i | 2.31610i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 56.9302i | 0.319833i | ||||||||
\(179\) | 207.962 | 1.16180 | 0.580898 | − | 0.813976i | \(-0.302701\pi\) | ||||
0.580898 | + | 0.813976i | \(0.302701\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 314.650 | 1.73840 | 0.869199 | − | 0.494463i | \(-0.164635\pi\) | ||||
0.869199 | + | 0.494463i | \(0.164635\pi\) | |||||||
\(182\) | 16.7947i | 0.0922786i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 77.7273i | 0.422431i | ||||||||
\(185\) | −214.808 | −1.16112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −619.626 | −3.29588 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −147.846 | −0.778137 | ||||||||
\(191\) | −28.7077 | −0.150302 | −0.0751509 | − | 0.997172i | \(-0.523944\pi\) | ||||
−0.0751509 | + | 0.997172i | \(0.523944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 197.661i | 1.02415i | 0.858941 | + | 0.512074i | \(0.171123\pi\) | ||||
−0.858941 | + | 0.512074i | \(0.828877\pi\) | |||||||
\(194\) | 539.244i | 2.77961i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 120.268 | 0.613612 | ||||||||
\(197\) | − 184.514i | − 0.936620i | −0.883564 | − | 0.468310i | \(-0.844863\pi\) | ||||
0.883564 | − | 0.468310i | \(-0.155137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41.8423 | −0.210263 | −0.105131 | − | 0.994458i | \(-0.533526\pi\) | ||||
−0.105131 | + | 0.994458i | \(0.533526\pi\) | |||||||
\(200\) | 534.727i | 2.67363i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −358.865 | −1.77656 | ||||||||
\(203\) | −176.760 | −0.870740 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 201.321i | − 0.982056i | ||||||||
\(206\) | 343.139i | 1.66572i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.33422i | 0.0208376i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 299.122i | − 1.41764i | −0.705388 | − | 0.708821i | \(-0.749227\pi\) | ||||
0.705388 | − | 0.708821i | \(-0.250773\pi\) | |||||||
\(212\) | −382.153 | −1.80261 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.0192 | −0.0608376 | ||||||||
\(215\) | 315.796i | 1.46882i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 125.357i | − 0.577684i | ||||||||
\(218\) | 141.655 | 0.649794 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.6128 | −0.0706464 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 195.023 | 0.874543 | 0.437271 | − | 0.899330i | \(-0.355945\pi\) | ||||
0.437271 | + | 0.899330i | \(0.355945\pi\) | |||||||
\(224\) | −156.904 | −0.700463 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 434.362i | 1.92196i | ||||||||
\(227\) | − 418.580i | − 1.84396i | −0.387232 | − | 0.921982i | \(-0.626569\pi\) | ||||
0.387232 | − | 0.921982i | \(-0.373431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −185.942 | −0.811975 | −0.405988 | − | 0.913879i | \(-0.633072\pi\) | ||||
−0.405988 | + | 0.913879i | \(0.633072\pi\) | |||||||
\(230\) | − 210.609i | − 0.915691i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −233.196 | −1.00516 | ||||||||
\(233\) | 54.2233i | 0.232718i | 0.993207 | + | 0.116359i | \(0.0371223\pi\) | ||||
−0.993207 | + | 0.116359i | \(0.962878\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 745.692 | 3.17316 | ||||||||
\(236\) | −477.870 | −2.02487 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 683.957i | 2.87377i | ||||||||
\(239\) | − 258.110i | − 1.07996i | −0.841678 | − | 0.539980i | \(-0.818432\pi\) | ||||
0.841678 | − | 0.539980i | \(-0.181568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 244.178i | − 1.01319i | −0.862185 | − | 0.506594i | \(-0.830904\pi\) | ||||
0.862185 | − | 0.506594i | \(-0.169096\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 724.164i | − 2.96789i | ||||||||
\(245\) | −144.737 | −0.590764 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.15906 | 0.0127897 | ||||||||
\(248\) | − 165.381i | − 0.666860i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 724.444i | − 2.89778i | ||||||||
\(251\) | 151.019 | 0.601670 | 0.300835 | − | 0.953676i | \(-0.402735\pi\) | ||||
0.300835 | + | 0.953676i | \(0.402735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −41.3205 | −0.162679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −408.492 | −1.59567 | ||||||||
\(257\) | −55.2346 | −0.214921 | −0.107460 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107460 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 201.069i | − 0.776326i | ||||||||
\(260\) | − 38.5872i | − 0.148412i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 61.0192 | 0.232898 | ||||||||
\(263\) | 402.008i | 1.52855i | 0.644891 | + | 0.764274i | \(0.276903\pi\) | ||||
−0.644891 | + | 0.764274i | \(0.723097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 459.904 | 1.73549 | ||||||||
\(266\) | − 138.390i | − 0.520263i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −532.617 | −1.98738 | ||||||||
\(269\) | −435.267 | −1.61809 | −0.809046 | − | 0.587746i | \(-0.800016\pi\) | ||||
−0.809046 | + | 0.587746i | \(0.800016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 112.461i | 0.414985i | 0.978237 | + | 0.207492i | \(0.0665302\pi\) | ||||
−0.978237 | + | 0.207492i | \(0.933470\pi\) | |||||||
\(272\) | 176.509i | 0.648931i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 172.811i | 0.630699i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 304.438i | 1.09905i | 0.835476 | + | 0.549526i | \(0.185192\pi\) | ||||
−0.835476 | + | 0.549526i | \(0.814808\pi\) | |||||||
\(278\) | −263.909 | −0.949313 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −750.788 | −2.68139 | ||||||||
\(281\) | − 307.053i | − 1.09272i | −0.837552 | − | 0.546358i | \(-0.816014\pi\) | ||||
0.837552 | − | 0.546358i | \(-0.183986\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 505.726i | 1.78702i | 0.449044 | + | 0.893509i | \(0.351765\pi\) | ||||
−0.449044 | + | 0.893509i | \(0.648235\pi\) | |||||||
\(284\) | −480.970 | −1.69356 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 188.445 | 0.656602 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −346.827 | −1.20009 | ||||||||
\(290\) | 631.865 | 2.17885 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 310.565i | − 1.06358i | ||||||||
\(293\) | − 484.102i | − 1.65223i | −0.563504 | − | 0.826113i | \(-0.690547\pi\) | ||||
0.563504 | − | 0.826113i | \(-0.309453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 575.096 | 1.94948 | ||||||||
\(296\) | − 265.266i | − 0.896168i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 524.181 | 1.75900 | ||||||||
\(299\) | 4.50013i | 0.0150506i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −295.597 | −0.982051 | ||||||||
\(302\) | −511.559 | −1.69390 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 35.7144i | − 0.117481i | ||||||||
\(305\) | 871.500i | 2.85738i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 473.965i | 1.54386i | 0.635708 | + | 0.771929i | \(0.280708\pi\) | ||||
−0.635708 | + | 0.771929i | \(0.719292\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 448.115i | 1.44553i | ||||||||
\(311\) | 516.449 | 1.66061 | 0.830303 | − | 0.557312i | \(-0.188167\pi\) | ||||
0.830303 | + | 0.557312i | \(0.188167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −418.626 | −1.33746 | −0.668731 | − | 0.743505i | \(-0.733162\pi\) | ||||
−0.668731 | + | 0.743505i | \(0.733162\pi\) | |||||||
\(314\) | 926.234i | 2.94979i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 717.837i | 2.27163i | ||||||||
\(317\) | −70.5744 | −0.222632 | −0.111316 | − | 0.993785i | \(-0.535507\pi\) | ||||
−0.111316 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 803.372 | 2.51054 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 197.138 | 0.612231 | ||||||||
\(323\) | 128.651 | 0.398301 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.9587i | 0.0952575i | ||||||||
\(326\) | 335.134i | 1.02802i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 248.611 | 0.757962 | ||||||||
\(329\) | 697.998i | 2.12157i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −442.315 | −1.33630 | −0.668150 | − | 0.744027i | \(-0.732914\pi\) | ||||
−0.668150 | + | 0.744027i | \(0.732914\pi\) | |||||||
\(332\) | 147.930i | 0.445573i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 229.019 | 0.685686 | ||||||||
\(335\) | 640.981 | 1.91338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 442.956i | − 1.31441i | −0.753712 | − | 0.657205i | \(-0.771739\pi\) | ||||
0.753712 | − | 0.657205i | \(-0.228261\pi\) | |||||||
\(338\) | − 564.202i | − 1.66924i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 1571.45i | − 4.62191i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 261.731i | 0.763064i | ||||||||
\(344\) | −389.976 | −1.13365 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 202.119 | 0.584160 | ||||||||
\(347\) | − 469.153i | − 1.35202i | −0.736890 | − | 0.676012i | \(-0.763707\pi\) | ||||
0.736890 | − | 0.676012i | \(-0.236293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 251.591i | 0.720892i | 0.932780 | + | 0.360446i | \(0.117375\pi\) | ||||
−0.932780 | + | 0.360446i | \(0.882625\pi\) | |||||||
\(350\) | 1356.22 | 3.87491 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.7424 | −0.0842560 | −0.0421280 | − | 0.999112i | \(-0.513414\pi\) | ||||
−0.0421280 | + | 0.999112i | \(0.513414\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 578.827 | 1.63050 | ||||||||
\(356\) | 122.436 | 0.343921 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 695.853i | − 1.94372i | ||||||||
\(359\) | − 196.041i | − 0.546075i | −0.962003 | − | 0.273037i | \(-0.911972\pi\) | ||||
0.962003 | − | 0.273037i | \(-0.0880283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.969 | 0.927892 | ||||||||
\(362\) | − 1052.84i | − 2.90840i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 36.1192 | 0.0992286 | ||||||||
\(365\) | 373.751i | 1.02398i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 123.881 | 0.337550 | 0.168775 | − | 0.985655i | \(-0.446019\pi\) | ||||
0.168775 | + | 0.985655i | \(0.446019\pi\) | |||||||
\(368\) | 50.8756 | 0.138249 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 718.760i | 1.94260i | ||||||||
\(371\) | 430.488i | 1.16035i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 101.316i | − 0.271624i | −0.990735 | − | 0.135812i | \(-0.956636\pi\) | ||||
0.990735 | − | 0.135812i | \(-0.0433643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 920.854i | 2.44908i | ||||||||
\(377\) | −13.5012 | −0.0358122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −44.8653 | −0.118378 | −0.0591891 | − | 0.998247i | \(-0.518851\pi\) | ||||
−0.0591891 | + | 0.998247i | \(0.518851\pi\) | |||||||
\(380\) | 317.962i | 0.836743i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 96.0577i | 0.251460i | ||||||||
\(383\) | 102.340 | 0.267206 | 0.133603 | − | 0.991035i | \(-0.457345\pi\) | ||||
0.133603 | + | 0.991035i | \(0.457345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 661.386 | 1.71343 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1159.72 | 2.98896 | ||||||||
\(389\) | 141.109 | 0.362748 | 0.181374 | − | 0.983414i | \(-0.441946\pi\) | ||||
0.181374 | + | 0.983414i | \(0.441946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 183.266i | 0.468710i | ||||||||
\(392\) | − 178.736i | − 0.455959i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −617.396 | −1.56700 | ||||||||
\(395\) | − 863.885i | − 2.18705i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 485.431 | 1.22275 | 0.611374 | − | 0.791342i | \(-0.290617\pi\) | ||||
0.611374 | + | 0.791342i | \(0.290617\pi\) | |||||||
\(398\) | 140.007i | 0.351777i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 350.000 | 0.875000 | ||||||||
\(401\) | −230.023 | −0.573623 | −0.286812 | − | 0.957987i | \(-0.592595\pi\) | ||||
−0.286812 | + | 0.957987i | \(0.592595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.57497i | − 0.0237592i | ||||||||
\(404\) | 771.787i | 1.91036i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 591.451i | 1.45678i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 204.705i | − 0.500500i | −0.968181 | − | 0.250250i | \(-0.919487\pi\) | ||||
0.968181 | − | 0.250250i | \(-0.0805129\pi\) | |||||||
\(410\) | −673.634 | −1.64301 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 737.965 | 1.79118 | ||||||||
\(413\) | 538.313i | 1.30342i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 178.028i | − 0.428982i | ||||||||
\(416\) | −11.9845 | −0.0288090 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 68.6448 | 0.163830 | 0.0819150 | − | 0.996639i | \(-0.473896\pi\) | ||||
0.0819150 | + | 0.996639i | \(0.473896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.2436 | −0.0955904 | −0.0477952 | − | 0.998857i | \(-0.515219\pi\) | ||||
−0.0477952 | + | 0.998857i | \(0.515219\pi\) | |||||||
\(422\) | −1000.88 | −2.37176 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 567.935i | 1.33947i | ||||||||
\(425\) | 1260.78i | 2.96654i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −815.759 | −1.91044 | ||||||||
\(428\) | 27.9996i | 0.0654196i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1056.67 | 2.45738 | ||||||||
\(431\) | − 6.13004i | − 0.0142228i | −0.999975 | − | 0.00711141i | \(-0.997736\pi\) | ||||
0.999975 | − | 0.00711141i | \(-0.00226365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 266.173 | 0.614719 | 0.307359 | − | 0.951594i | \(-0.400555\pi\) | ||||
0.307359 | + | 0.951594i | \(0.400555\pi\) | |||||||
\(434\) | −419.454 | −0.966483 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 304.648i | − 0.698734i | ||||||||
\(437\) | − 37.0815i | − 0.0848546i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 382.432i | − 0.871144i | −0.900154 | − | 0.435572i | \(-0.856546\pi\) | ||||
0.900154 | − | 0.435572i | \(-0.143454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 52.2416i | 0.118194i | ||||||||
\(443\) | −469.965 | −1.06087 | −0.530435 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530435 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −147.346 | −0.331115 | ||||||||
\(446\) | − 652.560i | − 1.46314i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 751.988i | 1.67854i | ||||||||
\(449\) | −95.4627 | −0.212612 | −0.106306 | − | 0.994333i | \(-0.533902\pi\) | ||||
−0.106306 | + | 0.994333i | \(0.533902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 934.153 | 2.06671 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1400.60 | −3.08501 | ||||||||
\(455\) | −43.4679 | −0.0955338 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 32.4154i | − 0.0709309i | −0.999371 | − | 0.0354654i | \(-0.988709\pi\) | ||||
0.999371 | − | 0.0354654i | \(-0.0112914\pi\) | |||||||
\(458\) | 622.175i | 1.35846i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −452.942 | −0.984657 | ||||||||
\(461\) | 383.378i | 0.831622i | 0.909451 | + | 0.415811i | \(0.136502\pi\) | ||||
−0.909451 | + | 0.415811i | \(0.863498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −491.804 | −1.06221 | −0.531106 | − | 0.847306i | \(-0.678223\pi\) | ||||
−0.531106 | + | 0.847306i | \(0.678223\pi\) | |||||||
\(464\) | 152.636i | 0.328957i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 181.435 | 0.389345 | ||||||||
\(467\) | 788.396 | 1.68821 | 0.844107 | − | 0.536175i | \(-0.180131\pi\) | ||||
0.844107 | + | 0.536175i | \(0.180131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 599.984i | 1.27928i | ||||||||
\(470\) | − 2495.13i | − 5.30880i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 710.185i | 1.50463i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 255.103i | − 0.537058i | ||||||||
\(476\) | 1470.94 | 3.09021 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −863.654 | −1.80681 | ||||||||
\(479\) | − 370.105i | − 0.772662i | −0.922360 | − | 0.386331i | \(-0.873742\pi\) | ||||
0.922360 | − | 0.386331i | \(-0.126258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 15.3579i | − 0.0319291i | ||||||||
\(482\) | −817.037 | −1.69510 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1395.67 | −2.87766 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 388.732 | 0.798218 | 0.399109 | − | 0.916904i | \(-0.369320\pi\) | ||||
0.399109 | + | 0.916904i | \(0.369320\pi\) | |||||||
\(488\) | −1076.21 | −2.20536 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 484.300i | 0.988368i | ||||||||
\(491\) | 40.5643i | 0.0826156i | 0.999146 | + | 0.0413078i | \(0.0131524\pi\) | ||||
−0.999146 | + | 0.0413078i | \(0.986848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −549.831 | −1.11528 | ||||||||
\(494\) | − 10.5704i | − 0.0213976i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −108.249 | −0.218243 | ||||||||
\(497\) | 541.805i | 1.09015i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 203.678 | 0.408173 | 0.204086 | − | 0.978953i | \(-0.434578\pi\) | ||||
0.204086 | + | 0.978953i | \(0.434578\pi\) | |||||||
\(500\) | −1558.01 | −3.11603 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 505.320i | − 1.00661i | ||||||||
\(503\) | − 303.501i | − 0.603382i | −0.953406 | − | 0.301691i | \(-0.902449\pi\) | ||||
0.953406 | − | 0.301691i | \(-0.0975511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 928.812i | − 1.83923i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 88.8652i | 0.174931i | ||||||||
\(509\) | −639.895 | −1.25716 | −0.628580 | − | 0.777745i | \(-0.716364\pi\) | ||||
−0.628580 | + | 0.777745i | \(0.716364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −349.846 | −0.684630 | ||||||||
\(512\) | 434.937i | 0.849486i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 184.819i | 0.359569i | ||||||||
\(515\) | −888.109 | −1.72448 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −672.788 | −1.29882 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −57.3463 | −0.110281 | ||||||||
\(521\) | −70.3744 | −0.135076 | −0.0675379 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675379 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 135.046i | 0.258215i | 0.991631 | + | 0.129108i | \(0.0412112\pi\) | ||||
−0.991631 | + | 0.129108i | \(0.958789\pi\) | |||||||
\(524\) | − 131.230i | − 0.250439i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1345.15 | 2.55731 | ||||||||
\(527\) | − 389.937i | − 0.739918i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −476.177 | −0.900145 | ||||||||
\(530\) | − 1538.87i | − 2.90352i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −297.626 | −0.559447 | ||||||||
\(533\) | 14.3937 | 0.0270050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 33.6963i | − 0.0629837i | ||||||||
\(536\) | 791.546i | 1.47677i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1456.43i | 2.70712i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 463.429i | 0.856615i | 0.903633 | + | 0.428307i | \(0.140890\pi\) | ||||
−0.903633 | + | 0.428307i | \(0.859110\pi\) | |||||||
\(542\) | 376.301 | 0.694283 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −488.065 | −0.897179 | ||||||||
\(545\) | 366.630i | 0.672716i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 424.973i | − 0.776916i | −0.921467 | − | 0.388458i | \(-0.873008\pi\) | ||||
0.921467 | − | 0.388458i | \(-0.126992\pi\) | |||||||
\(548\) | 371.654 | 0.678200 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 111.251 | 0.201908 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 808.631 | 1.46226 | ||||||||
\(554\) | 1018.67 | 1.83875 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 567.571i | 1.02081i | ||||||||
\(557\) | 157.458i | 0.282690i | 0.989960 | + | 0.141345i | \(0.0451426\pi\) | ||||
−0.989960 | + | 0.141345i | \(0.954857\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.5781 | −0.0403902 | ||||||||
\(560\) | 491.421i | 0.877537i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1027.42 | −1.82815 | ||||||||
\(563\) | 1026.05i | 1.82248i | 0.411881 | + | 0.911238i | \(0.364872\pi\) | ||||
−0.411881 | + | 0.911238i | \(0.635128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1124.21 | −1.98976 | ||||||||
\(566\) | 1692.19 | 2.98974 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 714.792i | 1.25844i | ||||||||
\(569\) | 853.945i | 1.50078i | 0.660994 | + | 0.750391i | \(0.270135\pi\) | ||||
−0.660994 | + | 0.750391i | \(0.729865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 155.457i | − 0.272253i | −0.990691 | − | 0.136127i | \(-0.956535\pi\) | ||||
0.990691 | − | 0.136127i | \(-0.0434654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 630.549i | − 1.09852i | ||||||||
\(575\) | 363.397 | 0.631996 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 466.219 | 0.808005 | 0.404003 | − | 0.914758i | \(-0.367619\pi\) | ||||
0.404003 | + | 0.914758i | \(0.367619\pi\) | |||||||
\(578\) | 1160.51i | 2.00779i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 1358.91i | − 2.34295i | ||||||||
\(581\) | 166.641 | 0.286818 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −461.545 | −0.790316 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1619.84 | −2.76423 | ||||||||
\(587\) | 62.6025 | 0.106648 | 0.0533241 | − | 0.998577i | \(-0.483018\pi\) | ||||
0.0533241 | + | 0.998577i | \(0.483018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 78.8986i | 0.133954i | ||||||||
\(590\) | − 1924.31i | − 3.26154i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −173.627 | −0.293289 | ||||||||
\(593\) | 685.312i | 1.15567i | 0.816154 | + | 0.577835i | \(0.196102\pi\) | ||||
−0.816154 | + | 0.577835i | \(0.803898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1770.21 | −2.97514 | ||||||||
\(596\) | − 1127.32i | − 1.89148i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.0577 | 0.0251801 | ||||||||
\(599\) | −736.939 | −1.23028 | −0.615141 | − | 0.788417i | \(-0.710901\pi\) | ||||
−0.615141 | + | 0.788417i | \(0.710901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 725.519i | − 1.20719i | −0.797292 | − | 0.603594i | \(-0.793735\pi\) | ||||
0.797292 | − | 0.603594i | \(-0.206265\pi\) | |||||||
\(602\) | 989.088i | 1.64300i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1100.17i | 1.82148i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 733.163i | − 1.20785i | −0.797043 | − | 0.603923i | \(-0.793603\pi\) | ||||
0.797043 | − | 0.603923i | \(-0.206397\pi\) | |||||||
\(608\) | 98.7537 | 0.162424 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2916.10 | 4.78048 | ||||||||
\(611\) | 53.3141i | 0.0872570i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 262.717i | − 0.428575i | −0.976771 | − | 0.214288i | \(-0.931257\pi\) | ||||
0.976771 | − | 0.214288i | \(-0.0687430\pi\) | |||||||
\(614\) | 1585.92 | 2.58293 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 451.077 | 0.731081 | 0.365540 | − | 0.930795i | \(-0.380884\pi\) | ||||
0.365540 | + | 0.930795i | \(0.380884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −363.212 | −0.586772 | −0.293386 | − | 0.955994i | \(-0.594782\pi\) | ||||
−0.293386 | + | 0.955994i | \(0.594782\pi\) | |||||||
\(620\) | 963.731 | 1.55440 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 1728.07i | − 2.77825i | ||||||||
\(623\) | − 137.922i | − 0.221384i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 1.00000 | ||||||||
\(626\) | 1400.75i | 2.23762i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1991.99 | 3.17195 | ||||||||
\(629\) | − 625.444i | − 0.994347i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1151.68 | −1.82516 | −0.912582 | − | 0.408894i | \(-0.865914\pi\) | ||||
−0.912582 | + | 0.408894i | \(0.865914\pi\) | |||||||
\(632\) | 1066.81 | 1.68799 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 236.146i | 0.372471i | ||||||||
\(635\) | − 106.945i | − 0.168418i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 10.3481i | − 0.0162451i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 2017.63i | − 3.15255i | ||||||||
\(641\) | −582.324 | −0.908462 | −0.454231 | − | 0.890884i | \(-0.650086\pi\) | ||||
−0.454231 | + | 0.890884i | \(0.650086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −735.061 | −1.14317 | −0.571587 | − | 0.820541i | \(-0.693672\pi\) | ||||
−0.571587 | + | 0.820541i | \(0.693672\pi\) | |||||||
\(644\) | − 423.972i | − 0.658342i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − 430.476i | − 0.666371i | ||||||||
\(647\) | 164.074 | 0.253592 | 0.126796 | − | 0.991929i | \(-0.459531\pi\) | ||||
0.126796 | + | 0.991929i | \(0.459531\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 103.590 | 0.159369 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 720.750 | 1.10544 | ||||||||
\(653\) | −415.328 | −0.636031 | −0.318015 | − | 0.948086i | \(-0.603016\pi\) | ||||
−0.318015 | + | 0.948086i | \(0.603016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 157.929i | 0.241114i | ||||||||
\(656\) | − 162.726i | − 0.248058i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2335.55 | 3.54946 | ||||||||
\(659\) | − 267.591i | − 0.406056i | −0.979173 | − | 0.203028i | \(-0.934922\pi\) | ||||
0.979173 | − | 0.203028i | \(-0.0650783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −312.979 | −0.473494 | −0.236747 | − | 0.971571i | \(-0.576081\pi\) | ||||
−0.236747 | + | 0.971571i | \(0.576081\pi\) | |||||||
\(662\) | 1480.02i | 2.23567i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 219.846 | 0.331094 | ||||||||
\(665\) | 358.179 | 0.538615 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 158.479i | 0.237600i | ||||||||
\(668\) | − 492.536i | − 0.737329i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 2144.76i | − 3.20114i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1010.71i | 1.50179i | 0.660419 | + | 0.750897i | \(0.270379\pi\) | ||||
−0.660419 | + | 0.750897i | \(0.729621\pi\) | |||||||
\(674\) | −1482.16 | −2.19905 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1213.39 | −1.79496 | ||||||||
\(677\) | − 1104.82i | − 1.63193i | −0.578103 | − | 0.815964i | \(-0.696207\pi\) | ||||
0.578103 | − | 0.815964i | \(-0.303793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1306.40i | − 1.92401i | ||||||||
\(680\) | −2335.40 | −3.43442 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −697.322 | −1.02097 | −0.510484 | − | 0.859887i | \(-0.670534\pi\) | ||||
−0.510484 | + | 0.859887i | \(0.670534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −447.269 | −0.652947 | ||||||||
\(686\) | 875.769 | 1.27663 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 255.255i | 0.371010i | ||||||||
\(689\) | 32.8813i | 0.0477232i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8883 | 0.0172046 | 0.00860228 | − | 0.999963i | \(-0.497262\pi\) | ||||
0.00860228 | + | 0.999963i | \(0.497262\pi\) | |||||||
\(692\) | − 434.684i | − 0.628156i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1569.82 | −2.26198 | ||||||||
\(695\) | − 683.047i | − 0.982801i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 586.177 | 0.841000 | ||||||||
\(698\) | 841.841 | 1.20608 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 2916.72i | − 4.16675i | ||||||||
\(701\) | − 1075.30i | − 1.53395i | −0.641679 | − | 0.766973i | \(-0.721762\pi\) | ||||
0.641679 | − | 0.766973i | \(-0.278238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 126.551i | 0.180015i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 99.5199i | 0.140963i | ||||||||
\(707\) | 869.405 | 1.22971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 742.841 | 1.04773 | 0.523865 | − | 0.851801i | \(-0.324490\pi\) | ||||
0.523865 | + | 0.851801i | \(0.324490\pi\) | |||||||
\(710\) | − 1936.79i | − 2.72788i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 181.958i | − 0.255559i | ||||||||
\(713\) | −112.392 | −0.157633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1496.52 | −2.09012 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −655.965 | −0.913601 | ||||||||
\(719\) | 934.852 | 1.30021 | 0.650106 | − | 0.759844i | \(-0.274725\pi\) | ||||
0.650106 | + | 0.759844i | \(0.274725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 831.305i | − 1.15299i | ||||||||
\(722\) | − 1120.83i | − 1.55239i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2264.27 | −3.12744 | ||||||||
\(725\) | 1090.26i | 1.50380i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1351.59 | 1.85913 | 0.929565 | − | 0.368657i | \(-0.120182\pi\) | ||||
0.929565 | + | 0.368657i | \(0.120182\pi\) | |||||||
\(728\) | − 53.6784i | − 0.0737341i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1250.60 | 1.71315 | ||||||||
\(731\) | −919.486 | −1.25785 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 696.688i | − 0.950461i | −0.879861 | − | 0.475230i | \(-0.842365\pi\) | ||||
0.879861 | − | 0.475230i | \(-0.157635\pi\) | |||||||
\(734\) | − 414.513i | − 0.564732i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 140.676i | 0.191136i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 950.312i | 1.28594i | 0.765890 | + | 0.642971i | \(0.222299\pi\) | ||||
−0.765890 | + | 0.642971i | \(0.777701\pi\) | |||||||
\(740\) | 1545.79 | 2.08890 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1440.44 | 1.94130 | ||||||||
\(743\) | − 785.944i | − 1.05780i | −0.848685 | − | 0.528899i | \(-0.822605\pi\) | ||||
0.848685 | − | 0.528899i | \(-0.177395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1356.68i | 1.82105i | ||||||||
\(746\) | −339.009 | −0.454436 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.5411 | 0.0421109 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1115.51 | −1.48537 | −0.742686 | − | 0.669640i | \(-0.766448\pi\) | ||||
−0.742686 | + | 0.669640i | \(0.766448\pi\) | |||||||
\(752\) | 602.736 | 0.801510 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 45.1759i | 0.0599150i | ||||||||
\(755\) | − 1324.01i | − 1.75366i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −336.149 | −0.444054 | −0.222027 | − | 0.975041i | \(-0.571267\pi\) | ||||
−0.222027 | + | 0.975041i | \(0.571267\pi\) | |||||||
\(758\) | 150.122i | 0.198051i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 472.539 | 0.621761 | ||||||||
\(761\) | 107.035i | 0.140650i | 0.997524 | + | 0.0703252i | \(0.0224037\pi\) | ||||
−0.997524 | + | 0.0703252i | \(0.977596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −343.181 | −0.449778 | ||||||||
\(764\) | 206.585 | 0.270399 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 342.435i | − 0.447044i | ||||||||
\(767\) | 41.1171i | 0.0536077i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 39.4845i | − 0.0513453i | −0.999670 | − | 0.0256726i | \(-0.991827\pi\) | ||||
0.999670 | − | 0.0256726i | \(-0.00817276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1422.40i | − 1.84248i | ||||||||
\(773\) | 670.228 | 0.867048 | 0.433524 | − | 0.901142i | \(-0.357270\pi\) | ||||
0.433524 | + | 0.901142i | \(0.357270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −773.205 | −0.997684 | ||||||||
\(776\) | − 1723.51i | − 2.22101i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 472.160i | − 0.606889i | ||||||||
\(779\) | −118.605 | −0.152253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 613.219 | 0.784168 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −116.990 | −0.149222 | ||||||||
\(785\) | −2397.27 | −3.05385 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 149.600i | − 0.190089i | −0.995473 | − | 0.0950445i | \(-0.969701\pi\) | ||||
0.995473 | − | 0.0950445i | \(-0.0302993\pi\) | |||||||
\(788\) | 1327.79i | 1.68501i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2890.61 | −3.65901 | ||||||||
\(791\) | − 1052.31i | − 1.33035i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.3088 | −0.0785735 | ||||||||
\(794\) | − 1624.28i | − 2.04570i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 301.104 | 0.378271 | ||||||||
\(797\) | 379.528 | 0.476196 | 0.238098 | − | 0.971241i | \(-0.423476\pi\) | ||||
0.238098 | + | 0.971241i | \(0.423476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2171.19i | 2.71739i | ||||||||
\(800\) | 967.784i | 1.20973i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 769.672i | 0.959691i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 510.232i | 0.633828i | ||||||||
\(806\) | −32.0385 | −0.0397500 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1146.99 | 1.41954 | ||||||||
\(809\) | 70.1432i | 0.0867036i | 0.999060 | + | 0.0433518i | \(0.0138036\pi\) | ||||
−0.999060 | + | 0.0433518i | \(0.986196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.2954i | 0.0163938i | 0.999966 | + | 0.00819689i | \(0.00260918\pi\) | ||||
−0.999966 | + | 0.00819689i | \(0.997391\pi\) | |||||||
\(812\) | 1271.99 | 1.56649 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −867.391 | −1.06428 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 186.046 | 0.227719 | ||||||||
\(818\) | −684.955 | −0.837353 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1448.74i | 1.76676i | ||||||||
\(821\) | − 614.891i | − 0.748954i | −0.927236 | − | 0.374477i | \(-0.877822\pi\) | ||||
0.927236 | − | 0.374477i | \(-0.122178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1537.20 | 1.86780 | 0.933898 | − | 0.357540i | \(-0.116384\pi\) | ||||
0.933898 | + | 0.357540i | \(0.116384\pi\) | |||||||
\(824\) | − 1096.72i | − 1.33098i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1801.23 | 2.18067 | ||||||||
\(827\) | 1143.12i | 1.38225i | 0.722734 | + | 0.691127i | \(0.242885\pi\) | ||||
−0.722734 | + | 0.691127i | \(0.757115\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −940.623 | −1.13465 | −0.567324 | − | 0.823495i | \(-0.692021\pi\) | ||||
−0.567324 | + | 0.823495i | \(0.692021\pi\) | |||||||
\(830\) | −595.692 | −0.717701 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 57.4379i | 0.0690360i | ||||||||
\(833\) | − 421.424i | − 0.505911i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 592.745i | 0.709875i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 229.690i | − 0.274093i | ||||||||
\(839\) | −795.384 | −0.948015 | −0.474007 | − | 0.880521i | \(-0.657193\pi\) | ||||
−0.474007 | + | 0.880521i | \(0.657193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 365.535 | 0.434643 | ||||||||
\(842\) | 134.658i | 0.159926i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2152.53i | 2.55039i | ||||||||
\(845\) | 1460.26 | 1.72812 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 371.736 | 0.438368 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4218.65 | 4.96312 | ||||||||
\(851\) | −180.273 | −0.211837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1410.47i | − 1.65354i | −0.562543 | − | 0.826768i | \(-0.690177\pi\) | ||||
0.562543 | − | 0.826768i | \(-0.309823\pi\) | |||||||
\(854\) | 2729.58i | 3.19623i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 41.6115 | 0.0486115 | ||||||||
\(857\) | − 628.919i | − 0.733861i | −0.930248 | − | 0.366931i | \(-0.880409\pi\) | ||||
0.930248 | − | 0.366931i | \(-0.119591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −255.965 | −0.297981 | −0.148990 | − | 0.988839i | \(-0.547602\pi\) | ||||
−0.148990 | + | 0.988839i | \(0.547602\pi\) | |||||||
\(860\) | − 2272.51i | − 2.64246i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.5115 | −0.0237953 | ||||||||
\(863\) | −295.104 | −0.341951 | −0.170976 | − | 0.985275i | \(-0.554692\pi\) | ||||
−0.170976 | + | 0.985275i | \(0.554692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 523.123i | 0.604766i | ||||||||
\(866\) | − 890.633i | − 1.02844i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 902.090i | 1.03927i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.8276i | 0.0526149i | ||||||||
\(872\) | −452.751 | −0.519210 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −124.077 | −0.141964 | ||||||||
\(875\) | 1755.07i | 2.00580i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 241.360i | − 0.275211i | −0.990487 | − | 0.137605i | \(-0.956059\pi\) | ||||
0.990487 | − | 0.137605i | \(-0.0439406\pi\) | |||||||
\(878\) | −1279.64 | −1.45745 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 708.997 | 0.804764 | 0.402382 | − | 0.915472i | \(-0.368182\pi\) | ||||
0.402382 | + | 0.915472i | \(0.368182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 682.264 | 0.772666 | 0.386333 | − | 0.922359i | \(-0.373742\pi\) | ||||
0.386333 | + | 0.922359i | \(0.373742\pi\) | |||||||
\(884\) | 112.352 | 0.127096 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1572.53i | 1.77487i | ||||||||
\(887\) | 87.3115i | 0.0984347i | 0.998788 | + | 0.0492173i | \(0.0156727\pi\) | ||||
−0.998788 | + | 0.0492173i | \(0.984327\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 100.105 | 0.112604 | ||||||||
\(890\) | 493.030i | 0.553967i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1403.42 | −1.57334 | ||||||||
\(893\) | − 439.313i | − 0.491952i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1801.00 | 2.01229 | ||||||||
\(896\) | 1888.59 | 2.10780 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 319.424i | 0.355707i | ||||||||
\(899\) | − 337.197i | − 0.375081i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1339.08i | 1.48621i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 1388.29i | − 1.53572i | ||||||||
\(905\) | 2724.95 | 3.01099 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 590.750 | 0.651323 | 0.325661 | − | 0.945486i | \(-0.394413\pi\) | ||||
0.325661 | + | 0.945486i | \(0.394413\pi\) | |||||||
\(908\) | 3012.17i | 3.31736i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 145.446i | 0.159831i | ||||||||
\(911\) | −240.655 | −0.264166 | −0.132083 | − | 0.991239i | \(-0.542167\pi\) | ||||
−0.132083 | + | 0.991239i | \(0.542167\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −108.464 | −0.118670 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1338.07 | 1.46077 | ||||||||
\(917\) | −147.828 | −0.161209 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4874i | 0.0168524i | 0.999964 | + | 0.00842620i | \(0.00268217\pi\) | ||||
−0.999964 | + | 0.00842620i | \(0.997318\pi\) | |||||||
\(920\) | 673.138i | 0.731672i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1282.81 | 1.39133 | ||||||||
\(923\) | 41.3838i | 0.0448362i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1240.19 | −1.34075 | ||||||||
\(926\) | 1645.61i | 1.77711i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −422.054 | −0.454800 | ||||||||
\(929\) | −382.741 | −0.411992 | −0.205996 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205996 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 85.2696i | 0.0915893i | ||||||||
\(932\) | − 390.199i | − 0.418668i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 2638.02i | − 2.82444i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 720.608i | − 0.769059i | −0.923113 | − | 0.384529i | \(-0.874364\pi\) | ||||
0.923113 | − | 0.384529i | \(-0.125636\pi\) | |||||||
\(938\) | 2007.58 | 2.14028 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5366.11 | −5.70863 | ||||||||
\(941\) | − 93.3461i | − 0.0991988i | −0.998769 | − | 0.0495994i | \(-0.984206\pi\) | ||||
0.998769 | − | 0.0495994i | \(-0.0157945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 168.955i | − 0.179168i | ||||||||
\(944\) | 464.845 | 0.492420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 306.176 | 0.323311 | 0.161656 | − | 0.986847i | \(-0.448317\pi\) | ||||
0.161656 | + | 0.986847i | \(0.448317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.7217 | −0.0281578 | ||||||||
\(950\) | −853.590 | −0.898516 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 2186.03i | − 2.29625i | ||||||||
\(953\) | 1825.42i | 1.91545i | 0.287691 | + | 0.957723i | \(0.407112\pi\) | ||||
−0.287691 | + | 0.957723i | \(0.592888\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −248.616 | −0.260330 | ||||||||
\(956\) | 1857.40i | 1.94289i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1238.40 | −1.29269 | ||||||||
\(959\) | − 418.662i | − 0.436561i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −721.862 | −0.751157 | ||||||||
\(962\) | −51.3885 | −0.0534184 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1757.15i | 1.82277i | ||||||||
\(965\) | 1711.79i | 1.77388i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1563.66i | − 1.61702i | −0.588483 | − | 0.808510i | \(-0.700275\pi\) | ||||
0.588483 | − | 0.808510i | \(-0.299725\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4669.99i | 4.81442i | ||||||||
\(971\) | 107.545 | 0.110757 | 0.0553784 | − | 0.998465i | \(-0.482363\pi\) | ||||
0.0553784 | + | 0.998465i | \(0.482363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 639.359 | 0.657101 | ||||||||
\(974\) | − 1300.72i | − 1.33544i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 704.425i | 0.721747i | ||||||||
\(977\) | 265.623 | 0.271876 | 0.135938 | − | 0.990717i | \(-0.456595\pi\) | ||||
0.135938 | + | 0.990717i | \(0.456595\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1041.55 | 1.06281 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 135.731 | 0.138219 | ||||||||
\(983\) | 767.587 | 0.780862 | 0.390431 | − | 0.920632i | \(-0.372326\pi\) | ||||
0.390431 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 1597.94i | − 1.62227i | ||||||||
\(986\) | 1839.77i | 1.86589i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.7331 | −0.0230092 | ||||||||
\(989\) | 265.025i | 0.267973i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1137.26 | 1.14759 | 0.573796 | − | 0.818998i | \(-0.305470\pi\) | ||||
0.573796 | + | 0.818998i | \(0.305470\pi\) | |||||||
\(992\) | − 299.318i | − 0.301732i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1812.92 | 1.82386 | ||||||||
\(995\) | −362.365 | −0.364186 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 280.401i | 0.281245i | 0.990063 | + | 0.140622i | \(0.0449104\pi\) | ||||
−0.990063 | + | 0.140622i | \(0.955090\pi\) | |||||||
\(998\) | − 681.520i | − 0.682886i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.c.d.604.1 | 4 | ||
3.2 | odd | 2 | 363.3.c.b.241.4 | yes | 4 | ||
11.10 | odd | 2 | inner | 1089.3.c.d.604.4 | 4 | ||
33.2 | even | 10 | 363.3.g.c.40.1 | 16 | |||
33.5 | odd | 10 | 363.3.g.c.118.1 | 16 | |||
33.8 | even | 10 | 363.3.g.c.112.1 | 16 | |||
33.14 | odd | 10 | 363.3.g.c.112.4 | 16 | |||
33.17 | even | 10 | 363.3.g.c.118.4 | 16 | |||
33.20 | odd | 10 | 363.3.g.c.40.4 | 16 | |||
33.26 | odd | 10 | 363.3.g.c.94.1 | 16 | |||
33.29 | even | 10 | 363.3.g.c.94.4 | 16 | |||
33.32 | even | 2 | 363.3.c.b.241.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.c.b.241.1 | ✓ | 4 | 33.32 | even | 2 | ||
363.3.c.b.241.4 | yes | 4 | 3.2 | odd | 2 | ||
363.3.g.c.40.1 | 16 | 33.2 | even | 10 | |||
363.3.g.c.40.4 | 16 | 33.20 | odd | 10 | |||
363.3.g.c.94.1 | 16 | 33.26 | odd | 10 | |||
363.3.g.c.94.4 | 16 | 33.29 | even | 10 | |||
363.3.g.c.112.1 | 16 | 33.8 | even | 10 | |||
363.3.g.c.112.4 | 16 | 33.14 | odd | 10 | |||
363.3.g.c.118.1 | 16 | 33.5 | odd | 10 | |||
363.3.g.c.118.4 | 16 | 33.17 | even | 10 | |||
1089.3.c.d.604.1 | 4 | 1.1 | even | 1 | trivial | ||
1089.3.c.d.604.4 | 4 | 11.10 | odd | 2 | inner |