Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(159,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.159");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.e (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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 19x^{14} + 301x^{12} + 1102x^{10} + 3238x^{8} + 1102x^{6} + 301x^{4} + 19x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 159.10 | ||
Root | \(1.94376 - 3.36668i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.159 |
Dual form | 320.3.e.b.159.5 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.90845i | 0.636150i | 0.948066 | + | 0.318075i | \(0.103036\pi\) | ||||
−0.948066 | + | 0.318075i | \(0.896964\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.37937 | + | 2.41269i | −0.875875 | + | 0.482539i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.95502 | −0.565003 | −0.282501 | − | 0.959267i | \(-0.591164\pi\) | ||||
−0.282501 | + | 0.959267i | \(0.591164\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.35782 | 0.595313 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.18667 | −0.562425 | −0.281212 | − | 0.959646i | \(-0.590737\pi\) | ||||
−0.281212 | + | 0.959646i | \(0.590737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.94185 | −0.380142 | −0.190071 | − | 0.981770i | \(-0.560872\pi\) | ||||
−0.190071 | + | 0.981770i | \(0.560872\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.60451 | − | 8.35782i | −0.306967 | − | 0.557188i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 22.4311i | − | 1.31948i | −0.751494 | − | 0.659740i | \(-0.770667\pi\) | ||
0.751494 | − | 0.659740i | \(-0.229333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.3923 | −0.546963 | −0.273482 | − | 0.961877i | \(-0.588175\pi\) | ||||
−0.273482 | + | 0.961877i | \(0.588175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 7.54796i | − | 0.359427i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.6083 | −1.72210 | −0.861050 | − | 0.508520i | \(-0.830193\pi\) | ||||
−0.861050 | + | 0.508520i | \(0.830193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.3578 | − | 21.1322i | 0.534313 | − | 0.845287i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.4012i | 1.01486i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 30.4354i | − | 1.04950i | −0.851258 | − | 0.524748i | \(-0.824160\pi\) | ||
0.851258 | − | 0.524748i | \(-0.175840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 24.7156i | − | 0.797278i | −0.917108 | − | 0.398639i | \(-0.869483\pi\) | ||
0.917108 | − | 0.398639i | \(-0.130517\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 11.8070i | − | 0.357787i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.3205 | − | 9.54225i | 0.494872 | − | 0.272636i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.0264 | −0.649361 | −0.324680 | − | 0.945824i | \(-0.605257\pi\) | ||||
−0.324680 | + | 0.945824i | \(0.605257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 9.43127i | − | 0.241827i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 31.0735 | 0.757889 | 0.378945 | − | 0.925419i | \(-0.376287\pi\) | ||||
0.378945 | + | 0.925419i | \(0.376287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.2110i | 1.21421i | 0.794622 | + | 0.607105i | \(0.207669\pi\) | ||||
−0.794622 | + | 0.607105i | \(0.792331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23.4639 | + | 12.9268i | −0.521420 | + | 0.287262i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.1640 | −0.280086 | −0.140043 | − | 0.990145i | \(-0.544724\pi\) | ||||
−0.140043 | + | 0.990145i | \(0.544724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.3578 | −0.680772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.8087 | 0.839387 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17.9596 | 0.338860 | 0.169430 | − | 0.985542i | \(-0.445807\pi\) | ||||
0.169430 | + | 0.985542i | \(0.445807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27.0938 | − | 14.9265i | 0.492614 | − | 0.271392i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 19.8332i | − | 0.347951i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −104.421 | −1.76985 | −0.884924 | − | 0.465735i | \(-0.845790\pi\) | ||||
−0.884924 | + | 0.465735i | \(0.845790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.2849i | 0.939097i | 0.882907 | + | 0.469548i | \(0.155583\pi\) | ||||
−0.882907 | + | 0.469548i | \(0.844417\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.1903 | −0.336354 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.6422 | − | 11.9232i | 0.332957 | − | 0.183433i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 99.3796i | − | 1.48328i | −0.670799 | − | 0.741639i | \(-0.734049\pi\) | ||
0.670799 | − | 0.741639i | \(-0.265951\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 75.5905i | − | 1.09551i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7156i | 0.235431i | 0.993047 | + | 0.117716i | \(0.0375572\pi\) | ||||
−0.993047 | + | 0.117716i | \(0.962443\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 96.3357i | 1.31967i | 0.751412 | + | 0.659833i | \(0.229373\pi\) | ||||
−0.751412 | + | 0.659833i | \(0.770627\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 40.3297 | + | 25.4927i | 0.537729 | + | 0.339903i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.4684 | 0.317772 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 139.578i | 1.76681i | 0.468608 | + | 0.883406i | \(0.344756\pi\) | ||||
−0.468608 | + | 0.883406i | \(0.655244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.07345 | −0.0502895 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 91.7458i | − | 1.10537i | −0.833390 | − | 0.552686i | \(-0.813603\pi\) | ||
0.833390 | − | 0.552686i | \(-0.186397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.1195 | + | 98.2344i | 0.636700 | + | 1.15570i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 58.0844 | 0.667637 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −94.7156 | −1.06422 | −0.532110 | − | 0.846675i | \(-0.678601\pi\) | ||||
−0.532110 | + | 0.846675i | \(0.678601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.5451 | 0.214781 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 47.1686 | 0.507189 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45.5118 | − | 25.0735i | 0.479071 | − | 0.263931i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 143.796i | 1.48243i | 0.671267 | + | 0.741216i | \(0.265751\pi\) | ||||
−0.671267 | + | 0.741216i | \(0.734249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −33.1471 | −0.334819 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66.5595i | 0.659005i | 0.944155 | + | 0.329502i | \(0.106881\pi\) | ||||
−0.944155 | + | 0.329502i | \(0.893119\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 153.063 | 1.48605 | 0.743024 | − | 0.669264i | \(-0.233391\pi\) | ||||
0.743024 | + | 0.669264i | \(0.233391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 18.2109 | + | 33.0553i | 0.173437 | + | 0.314813i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 75.7953i | 0.708367i | 0.935176 | + | 0.354184i | \(0.115241\pi\) | ||||
−0.935176 | + | 0.354184i | \(0.884759\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 124.088i | − | 1.13842i | −0.822192 | − | 0.569211i | \(-0.807249\pi\) | ||
0.822192 | − | 0.569211i | \(-0.192751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 45.8531i | − | 0.413091i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.19589i | 0.0459814i | 0.999736 | + | 0.0229907i | \(0.00731881\pi\) | ||||
−0.999736 | + | 0.0229907i | \(0.992681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 173.460 | − | 95.5627i | 1.50834 | − | 0.830980i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −26.4775 | −0.226303 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 88.7156i | 0.745510i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −82.7251 | −0.683678 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 59.3021i | 0.482131i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.51340 | + | 124.774i | −0.0601072 | + | 0.998192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 109.383 | 0.861287 | 0.430644 | − | 0.902522i | \(-0.358287\pi\) | ||||
0.430644 | + | 0.902522i | \(0.358287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −99.6422 | −0.772420 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 139.062 | 1.06154 | 0.530771 | − | 0.847515i | \(-0.321902\pi\) | ||||
0.530771 | + | 0.847515i | \(0.321902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 41.1018 | 0.309036 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −66.1107 | − | 120.000i | −0.489709 | − | 0.888889i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.42829i | 0.0396226i | 0.999804 | + | 0.0198113i | \(0.00630654\pi\) | ||||
−0.999804 | + | 0.0198113i | \(0.993693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −191.765 | −1.37961 | −0.689803 | − | 0.723998i | \(-0.742303\pi\) | ||||
−0.689803 | + | 0.723998i | \(0.742303\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 25.1229i | − | 0.178177i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.5736 | 0.213801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 73.4313 | + | 133.288i | 0.506423 | + | 0.919227i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 63.6617i | − | 0.433073i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 184.959i | − | 1.24133i | −0.784075 | − | 0.620667i | \(-0.786862\pi\) | ||
0.784075 | − | 0.620667i | \(-0.213138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 121.431i | 0.804181i | 0.915600 | + | 0.402090i | \(0.131716\pi\) | ||||
−0.915600 | + | 0.402090i | \(0.868284\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 120.182i | − | 0.785503i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 59.6313 | + | 108.239i | 0.384718 | + | 0.698316i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 261.156 | 1.66341 | 0.831706 | − | 0.555216i | \(-0.187364\pi\) | ||||
0.831706 | + | 0.555216i | \(0.187364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34.2749i | 0.215566i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 156.652 | 0.972991 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 199.302i | − | 1.22271i | −0.791356 | − | 0.611356i | \(-0.790625\pi\) | ||
0.791356 | − | 0.611356i | \(-0.209375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.4866 | + | 51.7071i | 0.172646 | + | 0.313376i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −168.999 | −1.01197 | −0.505986 | − | 0.862542i | \(-0.668871\pi\) | ||||
−0.505986 | + | 0.862542i | \(0.668871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −144.578 | −0.855492 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −55.6801 | −0.325614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −295.307 | −1.70697 | −0.853487 | − | 0.521113i | \(-0.825517\pi\) | ||||
−0.853487 | + | 0.521113i | \(0.825517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −52.8304 | + | 83.5782i | −0.301888 | + | 0.477590i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 199.282i | − | 1.12589i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −241.258 | −1.34781 | −0.673906 | − | 0.738817i | \(-0.735385\pi\) | ||||
−0.673906 | + | 0.738817i | \(0.735385\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 137.833i | 0.761511i | 0.924676 | + | 0.380755i | \(0.124336\pi\) | ||||
−0.924676 | + | 0.380755i | \(0.875664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −109.325 | −0.597406 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 105.220 | − | 57.9682i | 0.568759 | − | 0.313342i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 138.774i | 0.742108i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 108.372i | − | 0.573398i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 340.294i | − | 1.78164i | −0.454354 | − | 0.890821i | \(-0.650130\pi\) | ||
0.454354 | − | 0.890821i | \(-0.349870\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 96.5680i | − | 0.500353i | −0.968200 | − | 0.250176i | \(-0.919511\pi\) | ||
0.968200 | − | 0.250176i | \(-0.0804886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.7548 | + | 41.3030i | 0.116691 | + | 0.211810i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −229.054 | −1.16271 | −0.581354 | − | 0.813651i | \(-0.697477\pi\) | ||||
−0.581354 | + | 0.813651i | \(0.697477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 51.5782i | 0.259187i | 0.991567 | + | 0.129593i | \(0.0413672\pi\) | ||||
−0.991567 | + | 0.129593i | \(0.958633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 189.661 | 0.943587 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 120.373i | 0.592968i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −136.082 | + | 74.9707i | −0.663816 | + | 0.365711i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −212.214 | −1.02519 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 64.2938 | 0.307626 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 77.7042 | 0.368266 | 0.184133 | − | 0.982901i | \(-0.441052\pi\) | ||||
0.184133 | + | 0.982901i | \(0.441052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.9010 | −0.149770 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −125.969 | − | 228.652i | −0.585904 | − | 1.06350i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 97.7508i | 0.450465i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −183.852 | −0.839506 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 110.851i | 0.501589i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 98.9917 | 0.443909 | 0.221954 | − | 0.975057i | \(-0.428756\pi\) | ||||
0.221954 | + | 0.975057i | \(0.428756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 71.5687 | − | 113.222i | 0.318083 | − | 0.503210i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 172.584i | 0.760280i | 0.924929 | + | 0.380140i | \(0.124124\pi\) | ||||
−0.924929 | + | 0.380140i | \(0.875876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 151.690i | − | 0.662401i | −0.943560 | − | 0.331201i | \(-0.892546\pi\) | ||
0.943560 | − | 0.331201i | \(-0.107454\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 46.6968i | 0.202151i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 289.007i | − | 1.24037i | −0.784454 | − | 0.620187i | \(-0.787057\pi\) | ||
0.784454 | − | 0.620187i | \(-0.212943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 57.6502 | − | 31.7608i | 0.245320 | − | 0.135152i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −266.378 | −1.12396 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.5593i | 0.0734699i | 0.999325 | + | 0.0367349i | \(0.0116957\pi\) | ||||
−0.999325 | + | 0.0367349i | \(0.988304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −101.936 | −0.422971 | −0.211485 | − | 0.977381i | \(-0.567830\pi\) | ||||
−0.211485 | + | 0.977381i | \(0.567830\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 238.837i | 0.982867i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 146.086 | − | 80.4822i | 0.596271 | − | 0.328499i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51.3572 | 0.207924 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 175.092 | 0.703182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 123.966 | 0.493889 | 0.246944 | − | 0.969030i | \(-0.420573\pi\) | ||||
0.246944 | + | 0.969030i | \(0.420573\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 245.044 | 0.968552 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −187.475 | + | 103.284i | −0.735198 | + | 0.405037i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 118.534i | − | 0.461223i | −0.973046 | − | 0.230612i | \(-0.925927\pi\) | ||
0.973046 | − | 0.230612i | \(-0.0740727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 95.0247 | 0.366891 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 163.067i | − | 0.624779i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −223.071 | −0.848177 | −0.424089 | − | 0.905621i | \(-0.639405\pi\) | ||||
−0.424089 | + | 0.905621i | \(0.639405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −78.6516 | + | 43.3309i | −0.296799 | + | 0.163513i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 180.760i | − | 0.677004i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 249.061i | − | 0.925877i | −0.886390 | − | 0.462938i | \(-0.846795\pi\) | ||
0.886390 | − | 0.462938i | \(-0.153205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 130.991i | − | 0.483360i | −0.970356 | − | 0.241680i | \(-0.922302\pi\) | ||
0.970356 | − | 0.241680i | \(-0.0776984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 37.3008i | 0.136633i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −82.6405 | + | 130.738i | −0.300511 | + | 0.475410i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 39.7756 | 0.143594 | 0.0717971 | − | 0.997419i | \(-0.477127\pi\) | ||||
0.0717971 | + | 0.997419i | \(0.477127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 132.422i | − | 0.474630i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 58.0640 | 0.206634 | 0.103317 | − | 0.994649i | \(-0.467054\pi\) | ||||
0.103317 | + | 0.994649i | \(0.467054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 241.288i | − | 0.852607i | −0.904580 | − | 0.426304i | \(-0.859816\pi\) | ||
0.904580 | − | 0.426304i | \(-0.140184\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 47.8514 | + | 86.8570i | 0.167900 | + | 0.304761i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −122.896 | −0.428209 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −214.156 | −0.741025 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −274.427 | −0.943049 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −87.8283 | −0.299755 | −0.149878 | − | 0.988705i | \(-0.547888\pi\) | ||||
−0.149878 | + | 0.988705i | \(0.547888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 457.299 | − | 251.936i | 1.55016 | − | 0.854020i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 169.522i | − | 0.570782i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 195.738 | 0.654642 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 206.496i | − | 0.686032i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −127.025 | −0.419226 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −138.211 | − | 250.872i | −0.453151 | − | 0.822531i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 138.914i | − | 0.452490i | −0.974070 | − | 0.226245i | \(-0.927355\pi\) | ||
0.974070 | − | 0.226245i | \(-0.0726450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 292.113i | 0.945350i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 330.863i | 1.06387i | 0.846786 | + | 0.531933i | \(0.178534\pi\) | ||||
−0.846786 | + | 0.531933i | \(0.821466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 385.575i | 1.23187i | 0.787797 | + | 0.615935i | \(0.211221\pi\) | ||||
−0.787797 | + | 0.615935i | \(0.788779\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 92.8001 | − | 51.1256i | 0.294604 | − | 0.162304i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 414.112 | 1.30635 | 0.653174 | − | 0.757208i | \(-0.273437\pi\) | ||||
0.653174 | + | 0.757208i | \(0.273437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 188.294i | 0.590263i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −144.652 | −0.450628 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 233.111i | 0.721707i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −66.0123 | + | 104.432i | −0.203115 | + | 0.321329i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 236.816 | 0.724207 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 52.0640 | 0.158249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 52.4704 | 0.158521 | 0.0792604 | − | 0.996854i | \(-0.474744\pi\) | ||||
0.0792604 | + | 0.996854i | \(0.474744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −128.729 | −0.386573 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 239.773 | + | 435.220i | 0.715739 | + | 1.29917i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 469.871i | 1.39428i | 0.716937 | + | 0.697138i | \(0.245544\pi\) | ||||
−0.716937 | + | 0.697138i | \(0.754456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.91611 | −0.0292511 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 152.908i | 0.448409i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 325.727 | 0.949641 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 182.377 | + | 331.039i | 0.528628 | + | 0.959533i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 267.604i | − | 0.771192i | −0.922668 | − | 0.385596i | \(-0.873996\pi\) | ||
0.922668 | − | 0.385596i | \(-0.126004\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 662.916i | 1.89947i | 0.313053 | + | 0.949736i | \(0.398648\pi\) | ||||
−0.313053 | + | 0.949736i | \(0.601352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 135.412i | − | 0.385790i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 366.925i | 1.03945i | 0.854335 | + | 0.519723i | \(0.173965\pi\) | ||||
−0.854335 | + | 0.519723i | \(0.826035\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.3297 | − | 73.2040i | −0.113605 | − | 0.206208i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −169.309 | −0.474256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 234.863i | − | 0.654213i | −0.944987 | − | 0.327107i | \(-0.893926\pi\) | ||
0.944987 | − | 0.327107i | \(-0.106074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −253.000 | −0.700831 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 157.877i | − | 0.434922i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −232.428 | − | 421.890i | −0.636790 | − | 1.15586i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 455.060 | 1.23994 | 0.619972 | − | 0.784624i | \(-0.287144\pi\) | ||||
0.619972 | + | 0.784624i | \(0.287144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 166.486 | 0.451181 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −71.0304 | −0.191457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 518.534 | 1.39017 | 0.695086 | − | 0.718926i | \(-0.255366\pi\) | ||||
0.695086 | + | 0.718926i | \(0.255366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −238.125 | − | 14.3389i | −0.635000 | − | 0.0382372i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 150.407i | 0.398957i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 563.918 | 1.48791 | 0.743955 | − | 0.668230i | \(-0.232948\pi\) | ||||
0.743955 | + | 0.668230i | \(0.232948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 208.753i | 0.547908i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −56.8436 | −0.148417 | −0.0742083 | − | 0.997243i | \(-0.523643\pi\) | ||||
−0.0742083 | + | 0.997243i | \(0.523643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −107.156 | + | 59.0348i | −0.278328 | + | 0.153337i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 279.737i | 0.722835i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 188.677i | 0.485031i | 0.970147 | + | 0.242516i | \(0.0779726\pi\) | ||||
−0.970147 | + | 0.242516i | \(0.922027\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 888.460i | 2.27228i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 265.393i | 0.675300i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −336.759 | − | 611.265i | −0.852555 | − | 1.54751i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −143.716 | −0.362005 | −0.181003 | − | 0.983483i | \(-0.557934\pi\) | ||||
−0.181003 | + | 0.983483i | \(0.557934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 78.4407i | 0.196593i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.28437 | 0.00320291 | 0.00160145 | − | 0.999999i | \(-0.499490\pi\) | ||||
0.00160145 | + | 0.999999i | \(0.499490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 122.141i | 0.303079i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.8392 | − | 9.82799i | 0.0440473 | − | 0.0242666i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 148.643 | 0.365217 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −76.3767 | −0.186740 | −0.0933700 | − | 0.995631i | \(-0.529764\pi\) | ||||
−0.0933700 | + | 0.995631i | \(0.529764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3596 | −0.0252059 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 412.987 | 0.999969 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 221.355 | + | 401.789i | 0.533384 | + | 0.968166i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 365.974i | − | 0.877636i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.3906 | 0.0796912 | 0.0398456 | − | 0.999206i | \(-0.487313\pi\) | ||||
0.0398456 | + | 0.999206i | \(0.487313\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 392.318i | − | 0.931871i | −0.884819 | − | 0.465935i | \(-0.845718\pi\) | ||
0.884819 | − | 0.465935i | \(-0.154282\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −70.5305 | −0.166739 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −474.019 | − | 299.631i | −1.11534 | − | 0.705014i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 226.563i | − | 0.530592i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 58.3482i | 0.136010i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 840.460i | − | 1.95002i | −0.222156 | − | 0.975011i | \(-0.571309\pi\) | ||
0.222156 | − | 0.975011i | \(-0.428691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 275.552i | 0.636380i | 0.948027 | + | 0.318190i | \(0.103075\pi\) | ||||
−0.948027 | + | 0.318190i | \(0.896925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −254.373 | + | 140.140i | −0.584766 | + | 0.322161i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 411.622 | 0.941926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 477.725i | − | 1.08821i | −0.839016 | − | 0.544106i | \(-0.816869\pi\) | ||
0.839016 | − | 0.544106i | \(-0.183131\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −178.725 | −0.405272 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 625.709i | − | 1.41244i | −0.707994 | − | 0.706218i | \(-0.750400\pi\) | ||
0.707994 | − | 0.706218i | \(-0.249600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 414.795 | − | 228.520i | 0.932124 | − | 0.513528i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 352.984 | 0.789674 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 104.377 | 0.232465 | 0.116232 | − | 0.993222i | \(-0.462918\pi\) | ||||
0.116232 | + | 0.993222i | \(0.462918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −192.241 | −0.426256 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −231.746 | −0.511580 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −85.5953 | + | 47.1563i | −0.188121 | + | 0.103640i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 198.564i | 0.434495i | 0.976117 | + | 0.217248i | \(0.0697079\pi\) | ||||
−0.976117 | + | 0.217248i | \(0.930292\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 614.640 | 1.33908 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 11.1338i | − | 0.0241515i | −0.999927 | − | 0.0120757i | \(-0.996156\pi\) | ||
0.999927 | − | 0.0120757i | \(-0.00384392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.9944 | −0.0345451 | −0.0172725 | − | 0.999851i | \(-0.505498\pi\) | ||||
−0.0172725 | + | 0.999851i | \(0.505498\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −206.569 | + | 113.803i | −0.444234 | + | 0.244738i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 539.567i | 1.15539i | 0.816253 | + | 0.577695i | \(0.196048\pi\) | ||||
−0.816253 | + | 0.577695i | \(0.803952\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 393.048i | 0.838056i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 498.403i | 1.05818i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 323.013i | − | 0.682902i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −138.819 | + | 219.612i | −0.292249 | + | 0.462341i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 96.2240 | 0.201728 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 127.744i | 0.266689i | 0.991070 | + | 0.133344i | \(0.0425716\pi\) | ||||
−0.991070 | + | 0.133344i | \(0.957428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 118.735 | 0.246849 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 298.962i | 0.618969i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −346.935 | − | 629.736i | −0.715331 | − | 1.29842i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −624.466 | −1.28227 | −0.641135 | − | 0.767428i | \(-0.721536\pi\) | ||||
−0.641135 | + | 0.767428i | \(0.721536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 380.358 | 0.777828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 424.601 | 0.864769 | 0.432384 | − | 0.901689i | \(-0.357672\pi\) | ||||
0.432384 | + | 0.901689i | \(0.357672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −682.701 | −1.38479 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 145.163 | − | 79.9737i | 0.293259 | − | 0.161563i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 66.1107i | − | 0.133019i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 591.631 | 1.18563 | 0.592816 | − | 0.805338i | \(-0.298016\pi\) | ||||
0.592816 | + | 0.805338i | \(0.298016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 322.527i | − | 0.643766i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.71879 | 0.0113694 | 0.00568468 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568468 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −160.588 | − | 291.489i | −0.317995 | − | 0.577205i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 275.920i | − | 0.544221i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 439.708i | 0.863867i | 0.901905 | + | 0.431933i | \(0.142168\pi\) | ||||
−0.901905 | + | 0.431933i | \(0.857832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 381.009i | − | 0.745615i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 284.761i | − | 0.555091i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −670.320 | + | 369.294i | −1.30159 | + | 0.717076i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 81.4416 | 0.157527 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 563.578i | − | 1.08589i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 80.5687 | 0.154642 | 0.0773212 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773212 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 585.089i | 1.11872i | 0.828926 | + | 0.559359i | \(0.188953\pi\) | ||||
−0.828926 | + | 0.559359i | \(0.811047\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −159.505 | − | 100.824i | −0.303819 | − | 0.192046i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −554.400 | −1.05199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1039.82 | 1.96563 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −559.469 | −1.05361 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −153.560 | −0.288105 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −182.871 | − | 331.936i | −0.341815 | − | 0.620441i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 460.430i | − | 0.857411i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 206.374 | 0.382883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 248.685i | − | 0.459676i | −0.973229 | − | 0.229838i | \(-0.926180\pi\) | ||
0.973229 | − | 0.229838i | \(-0.0738196\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −263.048 | −0.484435 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 299.386 | + | 543.427i | 0.549332 | + | 0.997114i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 47.9916i | − | 0.0877360i | −0.999037 | − | 0.0438680i | \(-0.986032\pi\) | ||
0.999037 | − | 0.0438680i | \(-0.0139681\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 306.922i | 0.559056i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 316.294i | 0.574036i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 552.034i | − | 0.998254i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 110.629 | + | 200.808i | 0.199332 | + | 0.361816i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1091.71 | −1.95998 | −0.979990 | − | 0.199045i | \(-0.936216\pi\) | ||||
−0.979990 | + | 0.199045i | \(0.936216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 258.019i | − | 0.461572i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −264.844 | −0.472092 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 427.231i | 0.758846i | 0.925223 | + | 0.379423i | \(0.123878\pi\) | ||||
−0.925223 | + | 0.379423i | \(0.876122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.5361 | − | 22.7548i | −0.0221878 | − | 0.0402739i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.1106 | 0.0284137 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 54.2298 | 0.0953072 | 0.0476536 | − | 0.998864i | \(-0.484826\pi\) | ||||
0.0476536 | + | 0.998864i | \(0.484826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1050.42 | −1.83961 | −0.919806 | − | 0.392373i | \(-0.871654\pi\) | ||||
−0.919806 | + | 0.392373i | \(0.871654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 649.434 | 1.13339 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −529.080 | + | 837.009i | −0.920140 | + | 1.45567i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 161.031i | − | 0.279083i | −0.990216 | − | 0.139542i | \(-0.955437\pi\) | ||
0.990216 | − | 0.139542i | \(-0.0445629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 184.295 | 0.318299 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 362.856i | 0.624538i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −111.110 | −0.190583 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 115.955 | − | 63.8821i | 0.198213 | − | 0.109200i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 186.363i | − | 0.317484i | −0.987320 | − | 0.158742i | \(-0.949256\pi\) | ||
0.987320 | − | 0.158742i | \(-0.0507439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 256.852i | 0.436082i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 437.137i | − | 0.739657i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1011.51i | − | 1.70576i | −0.522109 | − | 0.852879i | \(-0.674855\pi\) | ||
0.522109 | − | 0.852879i | \(-0.325145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −214.044 | − | 388.519i | −0.359737 | − | 0.652973i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −98.4344 | −0.164882 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 647.616i | − | 1.08116i | −0.841292 | − | 0.540581i | \(-0.818204\pi\) | ||
0.841292 | − | 0.540581i | \(-0.181796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.3767 | 0.0671825 | 0.0335913 | − | 0.999436i | \(-0.489306\pi\) | ||||
0.0335913 | + | 0.999436i | \(0.489306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 532.458i | − | 0.883014i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 362.284 | − | 199.590i | 0.598816 | − | 0.329901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −799.902 | −1.31780 | −0.658898 | − | 0.752233i | \(-0.728977\pi\) | ||||
−0.658898 | + | 0.752233i | \(0.728977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −229.725 | −0.377217 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 65.0546 | 0.106472 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −900.584 | −1.46914 | −0.734571 | − | 0.678532i | \(-0.762616\pi\) | ||||
−0.734571 | + | 0.678532i | \(0.762616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −143.078 | − | 259.706i | −0.232647 | − | 0.422287i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 255.001i | 0.413292i | 0.978416 | + | 0.206646i | \(0.0662549\pi\) | ||||
−0.978416 | + | 0.206646i | \(0.933745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −168.789 | −0.272679 | −0.136340 | − | 0.990662i | \(-0.543534\pi\) | ||||
−0.136340 | + | 0.990662i | \(0.543534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1085.31i | − | 1.74769i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 374.602 | 0.601288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −268.137 | − | 564.559i | −0.429020 | − | 0.903295i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 122.702i | 0.195696i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 538.939i | 0.856818i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 665.431i | 1.05457i | 0.849690 | + | 0.527283i | \(0.176789\pi\) | ||||
−0.849690 | + | 0.527283i | \(0.823211\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 148.295i | 0.234273i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −479.031 | + | 263.909i | −0.754380 | + | 0.415605i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 164.849 | 0.258790 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 89.5593i | 0.140155i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 552.633 | 0.862142 | 0.431071 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431071 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 901.490i | − | 1.40201i | −0.713159 | − | 0.701003i | \(-0.752736\pi\) | ||
0.713159 | − | 0.701003i | \(-0.247264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 436.370 | − | 240.406i | 0.676543 | − | 0.372723i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 67.8163 | 0.104817 | 0.0524083 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524083 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 646.019 | 0.995407 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −186.553 | −0.286563 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −124.351 | −0.190431 | −0.0952153 | − | 0.995457i | \(-0.530354\pi\) | ||||
−0.0952153 | + | 0.995457i | \(0.530354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −609.005 | + | 335.514i | −0.929778 | + | 0.512235i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 516.149i | 0.785615i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 260.582 | 0.395420 | 0.197710 | − | 0.980261i | \(-0.436650\pi\) | ||||
0.197710 | + | 0.980261i | \(0.436650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 447.965i | − | 0.677708i | −0.940839 | − | 0.338854i | \(-0.889961\pi\) | ||
0.940839 | − | 0.338854i | \(-0.110039\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −211.554 | −0.319086 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −180.000 | + | 99.1660i | −0.270677 | + | 0.149122i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1205.49i | 1.80734i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 188.921i | 0.282393i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 354.403i | − | 0.528171i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 288.775i | − | 0.429086i | −0.976715 | − | 0.214543i | \(-0.931174\pi\) | ||
0.976715 | − | 0.214543i | \(-0.0688261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 579.047 | + | 366.020i | 0.857847 | + | 0.542252i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 248.339 | 0.366823 | 0.183412 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183412 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 568.716i | − | 0.837578i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −329.367 | −0.483652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 451.900i | 0.661640i | 0.943694 | + | 0.330820i | \(0.107325\pi\) | ||||
−0.943694 | + | 0.330820i | \(0.892675\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.0968 | − | 23.7725i | −0.0191194 | − | 0.0347044i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 289.493 | 0.421387 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −88.7534 | −0.128815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 193.513 | 0.280048 | 0.140024 | − | 0.990148i | \(-0.455282\pi\) | ||||
0.140024 | + | 0.990148i | \(0.455282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 131.097 | 0.189174 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 839.811 | − | 462.670i | 1.20836 | − | 0.665713i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 697.013i | − | 1.00002i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 551.555 | 0.789064 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 928.025i | 1.32386i | 0.749566 | + | 0.661929i | \(0.230262\pi\) | ||||
−0.749566 | + | 0.661929i | \(0.769738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 249.689 | 0.355177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 60.6139 | + | 110.023i | 0.0859771 | + | 0.156060i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 263.244i | − | 0.372339i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 75.9885i | − | 0.107177i | −0.998563 | − | 0.0535885i | \(-0.982934\pi\) | ||
0.998563 | − | 0.0535885i | \(-0.0170659\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 747.834i | 1.05181i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 978.944i | 1.37299i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −133.893 | + | 73.7647i | −0.187263 | + | 0.103167i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.5111 | −0.0467379 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 395.578i | 0.550178i | 0.961419 | + | 0.275089i | \(0.0887074\pi\) | ||||
−0.961419 | + | 0.275089i | \(0.911293\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −605.367 | −0.839622 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 194.540i | − | 0.269073i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −643.166 | − | 406.550i | −0.887125 | − | 0.560759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 352.113 | 0.484337 | 0.242168 | − | 0.970234i | \(-0.422141\pi\) | ||||
0.242168 | + | 0.970234i | \(0.422141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −492.469 | −0.675540 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1171.15 | 1.60213 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −156.532 | −0.213550 | −0.106775 | − | 0.994283i | \(-0.534053\pi\) | ||||
−0.106775 | + | 0.994283i | \(0.534053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 153.596 | + | 278.799i | 0.208975 | + | 0.379318i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 614.829i | 0.834232i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 183.376 | 0.248140 | 0.124070 | − | 0.992273i | \(-0.460405\pi\) | ||||
0.124070 | + | 0.992273i | \(0.460405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 98.0126i | 0.132271i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1028.34 | 1.38404 | 0.692021 | − | 0.721878i | \(-0.256721\pi\) | ||||
0.692021 | + | 0.721878i | \(0.256721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 446.249 | + | 810.003i | 0.598991 | + | 1.08725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 491.557i | − | 0.658042i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 299.772i | − | 0.400230i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 740.038i | − | 0.985403i | −0.870198 | − | 0.492702i | \(-0.836009\pi\) | ||
0.870198 | − | 0.492702i | \(-0.163991\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 236.583i | 0.314188i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −292.976 | − | 531.793i | −0.388048 | − | 0.704361i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 934.857 | 1.23495 | 0.617475 | − | 0.786591i | \(-0.288156\pi\) | ||||
0.617475 | + | 0.786591i | \(0.288156\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 467.654i | 0.616144i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 436.735 | 0.573896 | 0.286948 | − | 0.957946i | \(-0.407359\pi\) | ||||
0.286948 | + | 0.957946i | \(0.407359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 490.770i | 0.643211i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 289.962 | + | 526.322i | 0.379036 | + | 0.688002i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 516.033 | 0.672793 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −768.275 | −0.999057 | −0.499529 | − | 0.866297i | \(-0.666493\pi\) | ||||
−0.499529 | + | 0.866297i | \(0.666493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 226.217 | 0.293407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 792.266 | 1.02492 | 0.512462 | − | 0.858710i | \(-0.328734\pi\) | ||||
0.512462 | + | 0.858710i | \(0.328734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −522.295 | − | 330.147i | −0.673929 | − | 0.425996i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 181.350i | 0.233398i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −322.925 | −0.414538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 103.414i | − | 0.132413i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 833.966 | 1.06509 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1143.70 | + | 630.089i | −1.45694 | + | 0.802661i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 965.852i | − | 1.22726i | −0.789594 | − | 0.613629i | \(-0.789709\pi\) | ||
0.789594 | − | 0.613629i | \(-0.210291\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 425.719i | − | 0.539568i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 20.5499i | − | 0.0259796i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 283.093i | − | 0.356990i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −82.6949 | − | 150.103i | −0.104019 | − | 0.188808i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 358.505 | 0.449818 | 0.224909 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224909 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 295.284i | 0.369567i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −507.469 | −0.633544 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 595.997i | − | 0.742213i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −686.036 | + | 377.952i | −0.852218 | + | 0.469506i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 475.320 | 0.588997 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 222.881 | 0.275502 | 0.137751 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137751 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1292.40 | −1.59358 | −0.796792 | − | 0.604253i | \(-0.793471\pi\) | ||||
−0.796792 | + | 0.604253i | \(0.793471\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 249.989 | 0.307490 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 480.854 | + | 872.817i | 0.590005 | + | 1.07094i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 542.593i | − | 0.664129i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 104.719 | 0.127862 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1276.69i | 1.55505i | 0.628855 | + | 0.777523i | \(0.283524\pi\) | ||||
−0.628855 | + | 0.777523i | \(0.716476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1177.68 | −1.43096 | −0.715482 | − | 0.698631i | \(-0.753793\pi\) | ||||
−0.715482 | + | 0.698631i | \(0.753793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −249.507 | − | 157.715i | −0.302432 | − | 0.191170i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 154.182i | 0.186435i | 0.995646 | + | 0.0932176i | \(0.0297152\pi\) | ||||
−0.995646 | + | 0.0932176i | \(0.970285\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 243.838i | 0.294135i | 0.989126 | + | 0.147067i | \(0.0469834\pi\) | ||||
−0.989126 | + | 0.147067i | \(0.953017\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 75.9097i | 0.0913474i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 748.254i | 0.898264i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 740.111 | − | 407.744i | 0.886360 | − | 0.488316i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 677.238 | 0.809125 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1521.51i | 1.81348i | 0.421694 | + | 0.906738i | \(0.361436\pi\) | ||||
−0.421694 | + | 0.906738i | \(0.638564\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −85.3127 | −0.101442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 110.812i | 0.131450i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 633.162 | − | 348.823i | 0.749304 | − | 0.412808i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 327.179 | 0.386280 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 460.486 | 0.542386 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 951.643 | 1.11826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 59.6651 | 0.0699474 | 0.0349737 | − | 0.999388i | \(-0.488865\pi\) | ||||
0.0349737 | + | 0.999388i | \(0.488865\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 243.844 | − | 134.339i | 0.285197 | − | 0.157122i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1263.47i | 1.47430i | 0.675730 | + | 0.737149i | \(0.263828\pi\) | ||||
−0.675730 | + | 0.737149i | \(0.736172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1067.99 | −1.24330 | −0.621649 | − | 0.783296i | \(-0.713537\pi\) | ||||
−0.621649 | + | 0.783296i | \(0.713537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 234.541i | − | 0.272406i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −439.103 | −0.508810 | −0.254405 | − | 0.967098i | \(-0.581880\pi\) | ||||
−0.254405 | + | 0.967098i | \(0.581880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1293.26 | − | 712.485i | 1.49510 | − | 0.823682i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 408.707i | − | 0.471403i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 863.525i | − | 0.993699i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 491.119i | 0.563856i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 770.432i | 0.882511i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.7156 | − | 493.484i | 0.0339607 | − | 0.563981i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −932.204 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 167.616i | − | 0.190689i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 223.073 | 0.253205 | 0.126602 | − | 0.991954i | \(-0.459593\pi\) | ||||
0.126602 | + | 0.991954i | \(0.459593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 790.958i | − | 0.895762i | −0.894093 | − | 0.447881i | \(-0.852179\pi\) | ||
0.894093 | − | 0.447881i | \(-0.147821\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 480.807 | + | 872.732i | 0.543285 | + | 0.986138i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −233.462 | −0.263204 | −0.131602 | − | 0.991303i | \(-0.542012\pi\) | ||||
−0.131602 | + | 0.991303i | \(0.542012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −432.614 | −0.486630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.2011 | 0.0282841 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 136.805 | 0.153197 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1056.56 | − | 582.083i | 1.18052 | − | 0.650372i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 373.556i | 0.416451i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −752.230 | −0.836741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 402.854i | − | 0.447118i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 394.087 | 0.436420 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −332.550 | − | 603.624i | −0.367458 | − | 0.666988i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1679.77i | 1.85201i | 0.377514 | + | 0.926004i | \(0.376779\pi\) | ||||
−0.377514 | + | 0.926004i | \(0.623221\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 356.613i | 0.392314i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 44.0903i | − | 0.0483977i | −0.999707 | − | 0.0241988i | \(-0.992297\pi\) | ||
0.999707 | − | 0.0241988i | \(-0.00770348\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 567.601i | 0.621688i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 478.777 | − | 263.769i | 0.523253 | − | 0.288272i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −549.993 | −0.599774 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 153.303i | − | 0.166815i | −0.996516 | − | 0.0834076i | \(-0.973420\pi\) | ||
0.996516 | − | 0.0834076i | \(-0.0265804\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 265.111 | 0.287851 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 82.6061i | − | 0.0894974i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −320.940 | + | 507.729i | −0.346962 | + | 0.548896i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 820.084 | 0.884664 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1413.68 | −1.52172 | −0.760861 | − | 0.648915i | \(-0.775223\pi\) | ||||
−0.760861 | + | 0.648915i | \(0.775223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 346.665 | 0.372357 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −631.435 | −0.676779 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −334.820 | − | 607.744i | −0.358096 | − | 0.649994i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 90.2102i | − | 0.0962755i | −0.998841 | − | 0.0481378i | \(-0.984671\pi\) | ||
0.998841 | − | 0.0481378i | \(-0.0153287\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −735.851 | −0.783654 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1347.77i | 1.43227i | 0.697961 | + | 0.716136i | \(0.254091\pi\) | ||||
−0.697961 | + | 0.716136i | \(0.745909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1230.77 | −1.30516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 261.469 | + | 474.602i | 0.276687 | + | 0.502225i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 910.489i | − | 0.961446i | −0.876873 | − | 0.480723i | \(-0.840374\pi\) | ||
0.876873 | − | 0.480723i | \(-0.159626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 476.076i | − | 0.501661i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 790.313i | 0.831033i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 86.1971i | − | 0.0904481i | −0.998977 | − | 0.0452241i | \(-0.985600\pi\) | ||
0.998977 | − | 0.0452241i | \(-0.0144002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 821.025 | + | 1490.27i | 0.859712 | + | 1.56050i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −359.349 | −0.375496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 21.4690i | − | 0.0223869i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 350.137 | 0.364347 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 406.097i | 0.421700i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 232.989 | + | 422.908i | 0.241440 | + | 0.438246i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −419.290 | −0.433599 | −0.216799 | − | 0.976216i | \(-0.569562\pi\) | ||||
−0.216799 | + | 0.976216i | \(0.569562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −444.881 | −0.459114 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 829.403 | 0.854174 | 0.427087 | − | 0.904210i | \(-0.359540\pi\) | ||||
0.427087 | + | 0.904210i | \(0.359540\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 758.435 | 0.779481 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −199.303 | − | 125.981i | −0.204413 | − | 0.129211i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1667.21i | − | 1.70646i | −0.521533 | − | 0.853231i | \(-0.674640\pi\) | ||
0.521533 | − | 0.853231i | \(-0.325360\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 585.975 | 0.598544 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 664.840i | − | 0.677717i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 776.192 | 0.789616 | 0.394808 | − | 0.918764i | \(-0.370811\pi\) | ||||
0.394808 | + | 0.918764i | \(0.370811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1003.11 | − | 552.636i | 1.01839 | − | 0.561052i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 99.3616i | 0.100670i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2067.99i | − | 2.09099i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1392.66i | − | 1.40531i | −0.711530 | − | 0.702655i | \(-0.751998\pi\) | ||
0.711530 | − | 0.702655i | \(-0.248002\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 100.137i | 0.100843i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −124.442 | − | 225.880i | −0.125068 | − | 0.227015i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1400.32 | −1.40453 | −0.702266 | − | 0.711915i | \(-0.747828\pi\) | ||||
−0.702266 | + | 0.711915i | \(0.747828\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 658.350i | − | 0.659009i |
(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 | 320.3.e.b.159.10 | yes | 16 | |
4.3 | odd | 2 | inner | 320.3.e.b.159.6 | yes | 16 | |
5.2 | odd | 4 | 1600.3.g.k.351.9 | 16 | |||
5.3 | odd | 4 | 1600.3.g.k.351.7 | 16 | |||
5.4 | even | 2 | inner | 320.3.e.b.159.8 | yes | 16 | |
8.3 | odd | 2 | inner | 320.3.e.b.159.11 | yes | 16 | |
8.5 | even | 2 | inner | 320.3.e.b.159.7 | yes | 16 | |
16.3 | odd | 4 | 1280.3.h.n.1279.12 | 16 | |||
16.5 | even | 4 | 1280.3.h.n.1279.9 | 16 | |||
16.11 | odd | 4 | 1280.3.h.n.1279.5 | 16 | |||
16.13 | even | 4 | 1280.3.h.n.1279.8 | 16 | |||
20.3 | even | 4 | 1600.3.g.k.351.10 | 16 | |||
20.7 | even | 4 | 1600.3.g.k.351.8 | 16 | |||
20.19 | odd | 2 | inner | 320.3.e.b.159.12 | yes | 16 | |
40.3 | even | 4 | 1600.3.g.k.351.5 | 16 | |||
40.13 | odd | 4 | 1600.3.g.k.351.12 | 16 | |||
40.19 | odd | 2 | inner | 320.3.e.b.159.5 | ✓ | 16 | |
40.27 | even | 4 | 1600.3.g.k.351.11 | 16 | |||
40.29 | even | 2 | inner | 320.3.e.b.159.9 | yes | 16 | |
40.37 | odd | 4 | 1600.3.g.k.351.6 | 16 | |||
80.19 | odd | 4 | 1280.3.h.n.1279.7 | 16 | |||
80.29 | even | 4 | 1280.3.h.n.1279.11 | 16 | |||
80.59 | odd | 4 | 1280.3.h.n.1279.10 | 16 | |||
80.69 | even | 4 | 1280.3.h.n.1279.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.3.e.b.159.5 | ✓ | 16 | 40.19 | odd | 2 | inner | |
320.3.e.b.159.6 | yes | 16 | 4.3 | odd | 2 | inner | |
320.3.e.b.159.7 | yes | 16 | 8.5 | even | 2 | inner | |
320.3.e.b.159.8 | yes | 16 | 5.4 | even | 2 | inner | |
320.3.e.b.159.9 | yes | 16 | 40.29 | even | 2 | inner | |
320.3.e.b.159.10 | yes | 16 | 1.1 | even | 1 | trivial | |
320.3.e.b.159.11 | yes | 16 | 8.3 | odd | 2 | inner | |
320.3.e.b.159.12 | yes | 16 | 20.19 | odd | 2 | inner | |
1280.3.h.n.1279.5 | 16 | 16.11 | odd | 4 | |||
1280.3.h.n.1279.6 | 16 | 80.69 | even | 4 | |||
1280.3.h.n.1279.7 | 16 | 80.19 | odd | 4 | |||
1280.3.h.n.1279.8 | 16 | 16.13 | even | 4 | |||
1280.3.h.n.1279.9 | 16 | 16.5 | even | 4 | |||
1280.3.h.n.1279.10 | 16 | 80.59 | odd | 4 | |||
1280.3.h.n.1279.11 | 16 | 80.29 | even | 4 | |||
1280.3.h.n.1279.12 | 16 | 16.3 | odd | 4 | |||
1600.3.g.k.351.5 | 16 | 40.3 | even | 4 | |||
1600.3.g.k.351.6 | 16 | 40.37 | odd | 4 | |||
1600.3.g.k.351.7 | 16 | 5.3 | odd | 4 | |||
1600.3.g.k.351.8 | 16 | 20.7 | even | 4 | |||
1600.3.g.k.351.9 | 16 | 5.2 | odd | 4 | |||
1600.3.g.k.351.10 | 16 | 20.3 | even | 4 | |||
1600.3.g.k.351.11 | 16 | 40.27 | even | 4 | |||
1600.3.g.k.351.12 | 16 | 40.13 | odd | 4 |