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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.6 | ||
Root | \(-1.32111 - 0.429256i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.l.604.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.38910i | − 0.694551i | −0.937763 | − | 0.347275i | \(-0.887107\pi\) | ||||
0.937763 | − | 0.347275i | \(-0.112893\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.07040 | 0.517599 | ||||||||
\(5\) | 4.37284 | 0.874568 | 0.437284 | − | 0.899323i | \(-0.355940\pi\) | ||||
0.437284 | + | 0.899323i | \(0.355940\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.612830i | − 0.0875472i | −0.999041 | − | 0.0437736i | \(-0.986062\pi\) | ||||
0.999041 | − | 0.0437736i | \(-0.0139380\pi\) | |||||||
\(8\) | − 8.43240i | − 1.05405i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 6.07432i | − 0.607432i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 8.94888i | − 0.688375i | −0.938901 | − | 0.344188i | \(-0.888154\pi\) | ||||
0.938901 | − | 0.344188i | \(-0.111846\pi\) | |||||||
\(14\) | −0.851284 | −0.0608060 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.43188 | −0.214492 | ||||||||
\(17\) | − 2.97439i | − 0.174964i | −0.996166 | − | 0.0874820i | \(-0.972118\pi\) | ||||
0.996166 | − | 0.0874820i | \(-0.0278820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 10.0047i | − 0.526565i | −0.964719 | − | 0.263283i | \(-0.915195\pi\) | ||||
0.964719 | − | 0.263283i | \(-0.0848051\pi\) | |||||||
\(20\) | 9.05351 | 0.452675 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.6467 | 1.24551 | 0.622755 | − | 0.782417i | \(-0.286013\pi\) | ||||
0.622755 | + | 0.782417i | \(0.286013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.87827 | −0.235131 | ||||||||
\(26\) | −12.4309 | −0.478112 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 1.26880i | − 0.0453143i | ||||||||
\(29\) | − 35.3868i | − 1.22023i | −0.792311 | − | 0.610117i | \(-0.791122\pi\) | ||||
0.792311 | − | 0.610117i | \(-0.208878\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −50.3715 | −1.62489 | −0.812443 | − | 0.583040i | \(-0.801863\pi\) | ||||
−0.812443 | + | 0.583040i | \(0.801863\pi\) | |||||||
\(32\) | − 28.9624i | − 0.905074i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.13173 | −0.121521 | ||||||||
\(35\) | − 2.67981i | − 0.0765659i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.74660 | 0.0472055 | 0.0236028 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236028 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(38\) | −13.8976 | −0.365726 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 36.8735i | − 0.921838i | ||||||||
\(41\) | 59.4772i | 1.45066i | 0.688400 | + | 0.725331i | \(0.258313\pi\) | ||||
−0.688400 | + | 0.725331i | \(0.741687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 43.6490i | − 1.01509i | −0.861625 | − | 0.507546i | \(-0.830553\pi\) | ||||
0.861625 | − | 0.507546i | \(-0.169447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 39.7932i | − 0.865070i | ||||||||
\(47\) | −41.5674 | −0.884412 | −0.442206 | − | 0.896913i | \(-0.645804\pi\) | ||||
−0.442206 | + | 0.896913i | \(0.645804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6244 | 0.992335 | ||||||||
\(50\) | 8.16552i | 0.163310i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 18.5277i | − 0.356302i | ||||||||
\(53\) | 65.6252 | 1.23821 | 0.619105 | − | 0.785308i | \(-0.287495\pi\) | ||||
0.619105 | + | 0.785308i | \(0.287495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.16763 | −0.0922791 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −49.1559 | −0.847515 | ||||||||
\(59\) | 56.3923 | 0.955801 | 0.477901 | − | 0.878414i | \(-0.341398\pi\) | ||||
0.477901 | + | 0.878414i | \(0.341398\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 85.5613i | 1.40264i | 0.712845 | + | 0.701322i | \(0.247407\pi\) | ||||
−0.712845 | + | 0.701322i | \(0.752593\pi\) | |||||||
\(62\) | 69.9711i | 1.12857i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −53.9592 | −0.843112 | ||||||||
\(65\) | − 39.1320i | − 0.602031i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 27.8960 | 0.416359 | 0.208179 | − | 0.978091i | \(-0.433246\pi\) | ||||
0.208179 | + | 0.978091i | \(0.433246\pi\) | |||||||
\(68\) | − 6.15816i | − 0.0905611i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.72253 | −0.0531789 | ||||||||
\(71\) | 117.876 | 1.66023 | 0.830116 | − | 0.557591i | \(-0.188274\pi\) | ||||
0.830116 | + | 0.557591i | \(0.188274\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 118.075i | − 1.61747i | −0.588176 | − | 0.808733i | \(-0.700154\pi\) | ||||
0.588176 | − | 0.808733i | \(-0.299846\pi\) | |||||||
\(74\) | − 2.42621i | − 0.0327866i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 20.7138i | − 0.272550i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 125.059i | − 1.58303i | −0.611150 | − | 0.791515i | \(-0.709293\pi\) | ||||
0.611150 | − | 0.791515i | \(-0.290707\pi\) | |||||||
\(80\) | −15.0071 | −0.187588 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 82.6199 | 1.00756 | ||||||||
\(83\) | 32.6748i | 0.393672i | 0.980436 | + | 0.196836i | \(0.0630666\pi\) | ||||
−0.980436 | + | 0.196836i | \(0.936933\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.0065i | − 0.153018i | ||||||||
\(86\) | −60.6329 | −0.705033 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −19.9195 | −0.223815 | −0.111908 | − | 0.993719i | \(-0.535696\pi\) | ||||
−0.111908 | + | 0.993719i | \(0.535696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.48414 | −0.0602653 | ||||||||
\(92\) | 59.3101 | 0.644675 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 57.7413i | 0.614269i | ||||||||
\(95\) | − 43.7491i | − 0.460517i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −175.072 | −1.80486 | −0.902432 | − | 0.430831i | \(-0.858220\pi\) | ||||
−0.902432 | + | 0.430831i | \(0.858220\pi\) | |||||||
\(98\) | − 67.5443i | − 0.689228i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −12.1704 | −0.121704 | ||||||||
\(101\) | 84.5611i | 0.837238i | 0.908162 | + | 0.418619i | \(0.137486\pi\) | ||||
−0.908162 | + | 0.418619i | \(0.862514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32.1822 | −0.312448 | −0.156224 | − | 0.987722i | \(-0.549932\pi\) | ||||
−0.156224 | + | 0.987722i | \(0.549932\pi\) | |||||||
\(104\) | −75.4605 | −0.725582 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 91.1600i | − 0.860000i | ||||||||
\(107\) | − 42.9460i | − 0.401365i | −0.979656 | − | 0.200682i | \(-0.935684\pi\) | ||||
0.979656 | − | 0.200682i | \(-0.0643159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 18.6259i | − 0.170879i | −0.996343 | − | 0.0854397i | \(-0.972770\pi\) | ||||
0.996343 | − | 0.0854397i | \(-0.0272295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.10316i | 0.0187782i | ||||||||
\(113\) | 168.265 | 1.48908 | 0.744538 | − | 0.667581i | \(-0.232670\pi\) | ||||
0.744538 | + | 0.667581i | \(0.232670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 125.268 | 1.08928 | ||||||||
\(116\) | − 73.2647i | − 0.631592i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 78.3346i | − 0.663853i | ||||||||
\(119\) | −1.82279 | −0.0153176 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 118.853 | 0.974208 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −104.289 | −0.841040 | ||||||||
\(125\) | −135.026 | −1.08021 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 95.5531i | 0.752386i | 0.926541 | + | 0.376193i | \(0.122767\pi\) | ||||
−0.926541 | + | 0.376193i | \(0.877233\pi\) | |||||||
\(128\) | − 40.8946i | − 0.319489i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −54.3584 | −0.418141 | ||||||||
\(131\) | 201.569i | 1.53869i | 0.638833 | + | 0.769346i | \(0.279418\pi\) | ||||
−0.638833 | + | 0.769346i | \(0.720582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.13120 | −0.0460993 | ||||||||
\(134\) | − 38.7504i | − 0.289182i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −25.0812 | −0.184421 | ||||||||
\(137\) | −131.931 | −0.963003 | −0.481501 | − | 0.876445i | \(-0.659908\pi\) | ||||
−0.481501 | + | 0.876445i | \(0.659908\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 55.9770i | − 0.402712i | −0.979518 | − | 0.201356i | \(-0.935465\pi\) | ||||
0.979518 | − | 0.201356i | \(-0.0645348\pi\) | |||||||
\(140\) | − 5.54826i | − 0.0396305i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 163.742i | − 1.15312i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 154.741i | − 1.06718i | ||||||||
\(146\) | −164.018 | −1.12341 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.61616 | 0.0244335 | ||||||||
\(149\) | 30.3800i | 0.203892i | 0.994790 | + | 0.101946i | \(0.0325070\pi\) | ||||
−0.994790 | + | 0.101946i | \(0.967493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 113.516i | 0.751764i | 0.926668 | + | 0.375882i | \(0.122660\pi\) | ||||
−0.926668 | + | 0.375882i | \(0.877340\pi\) | |||||||
\(152\) | −84.3639 | −0.555026 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −220.266 | −1.42107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3951 | 0.142644 | 0.0713221 | − | 0.997453i | \(-0.477278\pi\) | ||||
0.0713221 | + | 0.997453i | \(0.477278\pi\) | |||||||
\(158\) | −173.720 | −1.09949 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 126.648i | − 0.791549i | ||||||||
\(161\) | − 17.5556i | − 0.109041i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −127.335 | −0.781194 | −0.390597 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390597 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(164\) | 123.141i | 0.750862i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 45.3886 | 0.273425 | ||||||||
\(167\) | − 248.138i | − 1.48586i | −0.669370 | − | 0.742929i | \(-0.733436\pi\) | ||||
0.669370 | − | 0.742929i | \(-0.266564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.9175 | 0.526139 | ||||||||
\(170\) | −18.0674 | −0.106279 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 90.3706i | − 0.525411i | ||||||||
\(173\) | − 187.474i | − 1.08367i | −0.840486 | − | 0.541833i | \(-0.817731\pi\) | ||||
0.840486 | − | 0.541833i | \(-0.182269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.60238i | 0.0205850i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 27.6703i | 0.155451i | ||||||||
\(179\) | 23.0143 | 0.128572 | 0.0642858 | − | 0.997932i | \(-0.479523\pi\) | ||||
0.0642858 | + | 0.997932i | \(0.479523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −139.288 | −0.769546 | −0.384773 | − | 0.923011i | \(-0.625720\pi\) | ||||
−0.384773 | + | 0.923011i | \(0.625720\pi\) | |||||||
\(182\) | 7.61803i | 0.0418573i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 241.561i | − 1.31283i | ||||||||
\(185\) | 7.63762 | 0.0412844 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −86.0609 | −0.457771 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −60.7720 | −0.319852 | ||||||||
\(191\) | 87.5488 | 0.458370 | 0.229185 | − | 0.973383i | \(-0.426394\pi\) | ||||
0.229185 | + | 0.973383i | \(0.426394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 141.096i | 0.731067i | 0.930798 | + | 0.365534i | \(0.119113\pi\) | ||||
−0.930798 | + | 0.365534i | \(0.880887\pi\) | |||||||
\(194\) | 243.193i | 1.25357i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 100.672 | 0.513632 | ||||||||
\(197\) | 180.754i | 0.917532i | 0.888557 | + | 0.458766i | \(0.151708\pi\) | ||||
−0.888557 | + | 0.458766i | \(0.848292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 57.3438 | 0.288160 | 0.144080 | − | 0.989566i | \(-0.453978\pi\) | ||||
0.144080 | + | 0.989566i | \(0.453978\pi\) | |||||||
\(200\) | 49.5679i | 0.247840i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 117.464 | 0.581505 | ||||||||
\(203\) | −21.6861 | −0.106828 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 260.084i | 1.26870i | ||||||||
\(206\) | 44.7043i | 0.217011i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 30.7115i | 0.147651i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 54.7860i | − 0.259649i | −0.991537 | − | 0.129825i | \(-0.958559\pi\) | ||||
0.991537 | − | 0.129825i | \(-0.0414414\pi\) | |||||||
\(212\) | 135.870 | 0.640896 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −59.6564 | −0.278768 | ||||||||
\(215\) | − 190.870i | − 0.887767i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.8692i | 0.142254i | ||||||||
\(218\) | −25.8732 | −0.118684 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.6174 | −0.120441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 292.895 | 1.31343 | 0.656716 | − | 0.754138i | \(-0.271945\pi\) | ||||
0.656716 | + | 0.754138i | \(0.271945\pi\) | |||||||
\(224\) | −17.7490 | −0.0792367 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 233.738i | − 1.03424i | ||||||||
\(227\) | − 86.2266i | − 0.379853i | −0.981798 | − | 0.189927i | \(-0.939175\pi\) | ||||
0.981798 | − | 0.189927i | \(-0.0608250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 50.2263 | 0.219329 | 0.109664 | − | 0.993969i | \(-0.465022\pi\) | ||||
0.109664 | + | 0.993969i | \(0.465022\pi\) | |||||||
\(230\) | − 174.009i | − 0.756563i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −298.396 | −1.28619 | ||||||||
\(233\) | 427.125i | 1.83315i | 0.399860 | + | 0.916576i | \(0.369059\pi\) | ||||
−0.399860 | + | 0.916576i | \(0.630941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −181.767 | −0.773479 | ||||||||
\(236\) | 116.754 | 0.494722 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.53205i | 0.0106389i | ||||||||
\(239\) | 19.0899i | 0.0798741i | 0.999202 | + | 0.0399371i | \(0.0127157\pi\) | ||||
−0.999202 | + | 0.0399371i | \(0.987284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 53.8901i | 0.223611i | 0.993730 | + | 0.111805i | \(0.0356633\pi\) | ||||
−0.993730 | + | 0.111805i | \(0.964337\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 177.146i | 0.726007i | ||||||||
\(245\) | 212.627 | 0.867865 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −89.5312 | −0.362474 | ||||||||
\(248\) | 424.752i | 1.71271i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 187.565i | 0.750258i | ||||||||
\(251\) | −399.601 | −1.59204 | −0.796018 | − | 0.605273i | \(-0.793064\pi\) | ||||
−0.796018 | + | 0.605273i | \(0.793064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 132.733 | 0.522571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −272.644 | −1.06501 | ||||||||
\(257\) | 458.433 | 1.78379 | 0.891894 | − | 0.452245i | \(-0.149377\pi\) | ||||
0.891894 | + | 0.452245i | \(0.149377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.07037i | − 0.00413271i | ||||||||
\(260\) | − 81.0188i | − 0.311611i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 279.999 | 1.06870 | ||||||||
\(263\) | − 262.279i | − 0.997259i | −0.866815 | − | 0.498630i | \(-0.833837\pi\) | ||||
0.866815 | − | 0.498630i | \(-0.166163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 286.968 | 1.08290 | ||||||||
\(266\) | 8.51687i | 0.0320183i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 57.7558 | 0.215507 | ||||||||
\(269\) | −72.6738 | −0.270163 | −0.135081 | − | 0.990834i | \(-0.543130\pi\) | ||||
−0.135081 | + | 0.990834i | \(0.543130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 201.240i | 0.742583i | 0.928516 | + | 0.371292i | \(0.121085\pi\) | ||||
−0.928516 | + | 0.371292i | \(0.878915\pi\) | |||||||
\(272\) | 10.2077i | 0.0375284i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 183.266i | 0.668854i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 357.053i | 1.28900i | 0.764604 | + | 0.644500i | \(0.222934\pi\) | ||||
−0.764604 | + | 0.644500i | \(0.777066\pi\) | |||||||
\(278\) | −77.7577 | −0.279704 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.5972 | −0.0807043 | ||||||||
\(281\) | − 276.466i | − 0.983863i | −0.870634 | − | 0.491932i | \(-0.836291\pi\) | ||||
0.870634 | − | 0.491932i | \(-0.163709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 286.805i | 1.01345i | 0.862109 | + | 0.506723i | \(0.169143\pi\) | ||||
−0.862109 | + | 0.506723i | \(0.830857\pi\) | |||||||
\(284\) | 244.051 | 0.859334 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 36.4494 | 0.127001 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 280.153 | 0.969388 | ||||||||
\(290\) | −214.951 | −0.741209 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 244.462i | − 0.837198i | ||||||||
\(293\) | 149.014i | 0.508579i | 0.967128 | + | 0.254289i | \(0.0818416\pi\) | ||||
−0.967128 | + | 0.254289i | \(0.918158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 246.594 | 0.835913 | ||||||||
\(296\) | − 14.7281i | − 0.0497570i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 42.2009 | 0.141614 | ||||||||
\(299\) | − 256.356i | − 0.857379i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.7494 | −0.0888684 | ||||||||
\(302\) | 157.686 | 0.522138 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34.3350i | 0.112944i | ||||||||
\(305\) | 374.146i | 1.22671i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 277.276i | 0.903179i | 0.892226 | + | 0.451590i | \(0.149143\pi\) | ||||
−0.892226 | + | 0.451590i | \(0.850857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 305.973i | 0.987008i | ||||||||
\(311\) | −209.678 | −0.674205 | −0.337102 | − | 0.941468i | \(-0.609447\pi\) | ||||
−0.337102 | + | 0.941468i | \(0.609447\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 106.849 | 0.341370 | 0.170685 | − | 0.985326i | \(-0.445402\pi\) | ||||
0.170685 | + | 0.985326i | \(0.445402\pi\) | |||||||
\(314\) | − 31.1091i | − 0.0990737i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − 258.922i | − 0.819374i | ||||||||
\(317\) | 489.691 | 1.54477 | 0.772384 | − | 0.635156i | \(-0.219064\pi\) | ||||
0.772384 | + | 0.635156i | \(0.219064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −235.955 | −0.737359 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.3865 | −0.0757344 | ||||||||
\(323\) | −29.7580 | −0.0921299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 52.6040i | 0.161858i | ||||||||
\(326\) | 176.881i | 0.542579i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 501.535 | 1.52907 | ||||||||
\(329\) | 25.4737i | 0.0774278i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −333.988 | −1.00903 | −0.504514 | − | 0.863404i | \(-0.668328\pi\) | ||||
−0.504514 | + | 0.863404i | \(0.668328\pi\) | |||||||
\(332\) | 67.6497i | 0.203764i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −344.690 | −1.03200 | ||||||||
\(335\) | 121.985 | 0.364134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 501.440i | 1.48795i | 0.668206 | + | 0.743976i | \(0.267062\pi\) | ||||
−0.668206 | + | 0.743976i | \(0.732938\pi\) | |||||||
\(338\) | − 123.516i | − 0.365431i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 26.9286i | − 0.0792019i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 59.8272i | − 0.174423i | ||||||||
\(344\) | −368.065 | −1.06996 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −260.421 | −0.752661 | ||||||||
\(347\) | 203.786i | 0.587280i | 0.955916 | + | 0.293640i | \(0.0948667\pi\) | ||||
−0.955916 | + | 0.293640i | \(0.905133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 422.541i | 1.21072i | 0.795952 | + | 0.605359i | \(0.206971\pi\) | ||||
−0.795952 | + | 0.605359i | \(0.793029\pi\) | |||||||
\(350\) | 5.00408 | 0.0142974 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 314.375 | 0.890581 | 0.445290 | − | 0.895386i | \(-0.353100\pi\) | ||||
0.445290 | + | 0.895386i | \(0.353100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 515.455 | 1.45198 | ||||||||
\(356\) | −41.2413 | −0.115846 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 31.9692i | − 0.0892995i | ||||||||
\(359\) | − 414.902i | − 1.15571i | −0.816138 | − | 0.577857i | \(-0.803889\pi\) | ||||
0.816138 | − | 0.577857i | \(-0.196111\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 260.905 | 0.722729 | ||||||||
\(362\) | 193.485i | 0.534489i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.3543 | −0.0311933 | ||||||||
\(365\) | − 516.323i | − 1.41458i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 462.999 | 1.26158 | 0.630789 | − | 0.775954i | \(-0.282731\pi\) | ||||
0.630789 | + | 0.775954i | \(0.282731\pi\) | |||||||
\(368\) | −98.3121 | −0.267152 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 10.6094i | − 0.0286741i | ||||||||
\(371\) | − 40.2171i | − 0.108402i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 656.230i | 1.75933i | 0.475594 | + | 0.879665i | \(0.342233\pi\) | ||||
−0.475594 | + | 0.879665i | \(0.657767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 350.513i | 0.932215i | ||||||||
\(377\) | −316.672 | −0.839979 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −451.003 | −1.18998 | −0.594990 | − | 0.803733i | \(-0.702844\pi\) | ||||
−0.594990 | + | 0.803733i | \(0.702844\pi\) | |||||||
\(380\) | − 90.5780i | − 0.238363i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 121.614i | − 0.318362i | ||||||||
\(383\) | 315.916 | 0.824847 | 0.412424 | − | 0.910992i | \(-0.364682\pi\) | ||||
0.412424 | + | 0.910992i | \(0.364682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 195.997 | 0.507763 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −362.468 | −0.934196 | ||||||||
\(389\) | −214.374 | −0.551091 | −0.275545 | − | 0.961288i | \(-0.588858\pi\) | ||||
−0.275545 | + | 0.961288i | \(0.588858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 85.2065i | − 0.217919i | ||||||||
\(392\) | − 410.021i | − 1.04597i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 251.085 | 0.637272 | ||||||||
\(395\) | − 546.864i | − 1.38447i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 369.231 | 0.930052 | 0.465026 | − | 0.885297i | \(-0.346045\pi\) | ||||
0.465026 | + | 0.885297i | \(0.346045\pi\) | |||||||
\(398\) | − 79.6565i | − 0.200142i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.1735 | 0.0504338 | ||||||||
\(401\) | −111.431 | −0.277883 | −0.138941 | − | 0.990301i | \(-0.544370\pi\) | ||||
−0.138941 | + | 0.990301i | \(0.544370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 450.768i | 1.11853i | ||||||||
\(404\) | 175.075i | 0.433354i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 30.1242i | 0.0741975i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 203.166i | 0.496739i | 0.968665 | + | 0.248370i | \(0.0798947\pi\) | ||||
−0.968665 | + | 0.248370i | \(0.920105\pi\) | |||||||
\(410\) | 361.283 | 0.881179 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −66.6299 | −0.161723 | ||||||||
\(413\) | − 34.5589i | − 0.0836777i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 142.881i | 0.344293i | ||||||||
\(416\) | −259.181 | −0.623031 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 519.060 | 1.23881 | 0.619404 | − | 0.785073i | \(-0.287374\pi\) | ||||
0.619404 | + | 0.785073i | \(0.287374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 333.468 | 0.792085 | 0.396042 | − | 0.918232i | \(-0.370383\pi\) | ||||
0.396042 | + | 0.918232i | \(0.370383\pi\) | |||||||
\(422\) | −76.1033 | −0.180340 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 553.378i | − 1.30514i | ||||||||
\(425\) | 17.4843i | 0.0411394i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.4345 | 0.122798 | ||||||||
\(428\) | − 88.9153i | − 0.207746i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −265.138 | −0.616599 | ||||||||
\(431\) | 731.630i | 1.69752i | 0.528781 | + | 0.848759i | \(0.322649\pi\) | ||||
−0.528781 | + | 0.848759i | \(0.677351\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −373.113 | −0.861693 | −0.430846 | − | 0.902425i | \(-0.641785\pi\) | ||||
−0.430846 | + | 0.902425i | \(0.641785\pi\) | |||||||
\(434\) | 42.8804 | 0.0988028 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 38.5629i | − 0.0884470i | ||||||||
\(437\) | − 286.603i | − 0.655842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 294.954i | − 0.671878i | −0.941884 | − | 0.335939i | \(-0.890946\pi\) | ||||
0.941884 | − | 0.335939i | \(-0.109054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.9743i | 0.0836523i | ||||||||
\(443\) | 505.564 | 1.14123 | 0.570614 | − | 0.821219i | \(-0.306705\pi\) | ||||
0.570614 | + | 0.821219i | \(0.306705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −87.1050 | −0.195741 | ||||||||
\(446\) | − 406.861i | − 0.912245i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 33.0678i | 0.0738121i | ||||||||
\(449\) | −26.5854 | −0.0592103 | −0.0296051 | − | 0.999562i | \(-0.509425\pi\) | ||||
−0.0296051 | + | 0.999562i | \(0.509425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 348.376 | 0.770744 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −119.778 | −0.263827 | ||||||||
\(455\) | −23.9813 | −0.0527061 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 176.695i | 0.386642i | 0.981136 | + | 0.193321i | \(0.0619259\pi\) | ||||
−0.981136 | + | 0.193321i | \(0.938074\pi\) | |||||||
\(458\) | − 69.7695i | − 0.152335i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 259.353 | 0.563812 | ||||||||
\(461\) | − 155.031i | − 0.336292i | −0.985762 | − | 0.168146i | \(-0.946222\pi\) | ||||
0.985762 | − | 0.168146i | \(-0.0537781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −192.026 | −0.414744 | −0.207372 | − | 0.978262i | \(-0.566491\pi\) | ||||
−0.207372 | + | 0.978262i | \(0.566491\pi\) | |||||||
\(464\) | 121.443i | 0.261731i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 593.320 | 1.27322 | ||||||||
\(467\) | 323.120 | 0.691906 | 0.345953 | − | 0.938252i | \(-0.387556\pi\) | ||||
0.345953 | + | 0.938252i | \(0.387556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 17.0955i | − 0.0364510i | ||||||||
\(470\) | 252.494i | 0.537220i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 475.522i | − 1.00746i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 58.8106i | 0.123812i | ||||||||
\(476\) | −3.77390 | −0.00792837 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.5178 | 0.0554766 | ||||||||
\(479\) | 458.454i | 0.957105i | 0.878059 | + | 0.478553i | \(0.158838\pi\) | ||||
−0.878059 | + | 0.478553i | \(0.841162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 15.6302i | − 0.0324951i | ||||||||
\(482\) | 74.8589 | 0.155309 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −765.561 | −1.57848 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 246.917 | 0.507015 | 0.253508 | − | 0.967333i | \(-0.418416\pi\) | ||||
0.253508 | + | 0.967333i | \(0.418416\pi\) | |||||||
\(488\) | 721.487 | 1.47846 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 295.360i | − 0.602776i | ||||||||
\(491\) | 43.3100i | 0.0882078i | 0.999027 | + | 0.0441039i | \(0.0140433\pi\) | ||||
−0.999027 | + | 0.0441039i | \(0.985957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −105.254 | −0.213497 | ||||||||
\(494\) | 124.368i | 0.251757i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 172.869 | 0.348526 | ||||||||
\(497\) | − 72.2382i | − 0.145349i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −493.199 | −0.988375 | −0.494187 | − | 0.869355i | \(-0.664534\pi\) | ||||
−0.494187 | + | 0.869355i | \(0.664534\pi\) | |||||||
\(500\) | −279.557 | −0.559113 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 555.086i | 1.10575i | ||||||||
\(503\) | − 299.110i | − 0.594651i | −0.954776 | − | 0.297326i | \(-0.903905\pi\) | ||||
0.954776 | − | 0.297326i | \(-0.0960947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 369.772i | 0.732222i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 197.833i | 0.389434i | ||||||||
\(509\) | −541.162 | −1.06319 | −0.531593 | − | 0.847000i | \(-0.678406\pi\) | ||||
−0.531593 | + | 0.847000i | \(0.678406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −72.3599 | −0.141605 | ||||||||
\(512\) | 215.151i | 0.420217i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 636.811i | − 1.23893i | ||||||||
\(515\) | −140.728 | −0.273257 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.48686 | −0.00287038 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −329.977 | −0.634571 | ||||||||
\(521\) | −206.634 | −0.396609 | −0.198305 | − | 0.980140i | \(-0.563544\pi\) | ||||
−0.198305 | + | 0.980140i | \(0.563544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 56.3408i | 0.107726i | 0.998548 | + | 0.0538631i | \(0.0171535\pi\) | ||||
−0.998548 | + | 0.0538631i | \(0.982847\pi\) | |||||||
\(524\) | 417.327i | 0.796425i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −364.332 | −0.692647 | ||||||||
\(527\) | 149.824i | 0.284297i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 291.635 | 0.551295 | ||||||||
\(530\) | − 398.628i | − 0.752129i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.6940 | −0.0238609 | ||||||||
\(533\) | 532.254 | 0.998601 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 187.796i | − 0.351021i | ||||||||
\(536\) | − 235.230i | − 0.438863i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 100.951i | 0.187642i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 448.655i | − 0.829307i | −0.909979 | − | 0.414654i | \(-0.863903\pi\) | ||||
0.909979 | − | 0.414654i | \(-0.136097\pi\) | |||||||
\(542\) | 279.543 | 0.515762 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −86.1453 | −0.158355 | ||||||||
\(545\) | − 81.4479i | − 0.149446i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 829.805i | 1.51701i | 0.651666 | + | 0.758506i | \(0.274070\pi\) | ||||
−0.651666 | + | 0.758506i | \(0.725930\pi\) | |||||||
\(548\) | −273.150 | −0.498449 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −354.036 | −0.642533 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −76.6401 | −0.138590 | ||||||||
\(554\) | 495.983 | 0.895276 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 115.894i | − 0.208443i | ||||||||
\(557\) | 1010.81i | 1.81475i | 0.420325 | + | 0.907374i | \(0.361916\pi\) | ||||
−0.420325 | + | 0.907374i | \(0.638084\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −390.609 | −0.698764 | ||||||||
\(560\) | 9.19677i | 0.0164228i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −384.039 | −0.683343 | ||||||||
\(563\) | − 8.04144i | − 0.0142832i | −0.999974 | − | 0.00714159i | \(-0.997727\pi\) | ||||
0.999974 | − | 0.00714159i | \(-0.00227326\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 735.798 | 1.30230 | ||||||||
\(566\) | 398.402 | 0.703890 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 993.981i | − 1.74997i | ||||||||
\(569\) | 660.882i | 1.16148i | 0.814089 | + | 0.580740i | \(0.197237\pi\) | ||||
−0.814089 | + | 0.580740i | \(0.802763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 472.496i | − 0.827489i | −0.910393 | − | 0.413745i | \(-0.864221\pi\) | ||||
0.910393 | − | 0.413745i | \(-0.135779\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 50.6319i | − 0.0882090i | ||||||||
\(575\) | −168.393 | −0.292858 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −193.531 | −0.335409 | −0.167705 | − | 0.985837i | \(-0.553636\pi\) | ||||
−0.167705 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(578\) | − 389.161i | − 0.673289i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 320.375i | − 0.552370i | ||||||||
\(581\) | 20.0241 | 0.0344648 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −995.655 | −1.70489 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 206.995 | 0.353234 | ||||||||
\(587\) | −436.101 | −0.742932 | −0.371466 | − | 0.928446i | \(-0.621145\pi\) | ||||
−0.371466 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 503.953i | 0.855608i | ||||||||
\(590\) | − 342.545i | − 0.580584i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.99413 | −0.0101252 | ||||||||
\(593\) | 848.153i | 1.43027i | 0.698984 | + | 0.715137i | \(0.253636\pi\) | ||||
−0.698984 | + | 0.715137i | \(0.746364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.97079 | −0.0133963 | ||||||||
\(596\) | 62.8985i | 0.105534i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −356.105 | −0.595493 | ||||||||
\(599\) | −1018.56 | −1.70044 | −0.850220 | − | 0.526427i | \(-0.823531\pi\) | ||||
−0.850220 | + | 0.526427i | \(0.823531\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 585.339i | 0.973942i | 0.873418 | + | 0.486971i | \(0.161898\pi\) | ||||
−0.873418 | + | 0.486971i | \(0.838102\pi\) | |||||||
\(602\) | 37.1576i | 0.0617237i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 235.024i | 0.389112i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 994.914i | − 1.63907i | −0.573031 | − | 0.819534i | \(-0.694233\pi\) | ||||
0.573031 | − | 0.819534i | \(-0.305767\pi\) | |||||||
\(608\) | −289.761 | −0.476580 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 519.727 | 0.852011 | ||||||||
\(611\) | 371.982i | 0.608808i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 661.114i | − 1.07849i | −0.842149 | − | 0.539245i | \(-0.818710\pi\) | ||||
0.842149 | − | 0.539245i | \(-0.181290\pi\) | |||||||
\(614\) | 385.165 | 0.627304 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 118.682 | 0.192354 | 0.0961770 | − | 0.995364i | \(-0.469339\pi\) | ||||
0.0961770 | + | 0.995364i | \(0.469339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −107.767 | −0.174099 | −0.0870495 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870495 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(620\) | −456.039 | −0.735546 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 291.264i | 0.468270i | ||||||||
\(623\) | 12.2073i | 0.0195944i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −443.489 | −0.709583 | ||||||||
\(626\) | − 148.424i | − 0.237099i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 46.3668 | 0.0738325 | ||||||||
\(629\) | − 5.19508i | − 0.00825926i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −472.024 | −0.748057 | −0.374029 | − | 0.927417i | \(-0.622024\pi\) | ||||
−0.374029 | + | 0.927417i | \(0.622024\pi\) | |||||||
\(632\) | −1054.55 | −1.66859 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 680.231i | − 1.07292i | ||||||||
\(635\) | 417.838i | 0.658013i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 435.134i | − 0.683099i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 178.826i | − 0.279415i | ||||||||
\(641\) | 589.141 | 0.919096 | 0.459548 | − | 0.888153i | \(-0.348011\pi\) | ||||
0.459548 | + | 0.888153i | \(0.348011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 986.500 | 1.53421 | 0.767107 | − | 0.641519i | \(-0.221696\pi\) | ||||
0.767107 | + | 0.641519i | \(0.221696\pi\) | |||||||
\(644\) | − 36.3470i | − 0.0564394i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 41.3368i | 0.0639889i | ||||||||
\(647\) | −731.747 | −1.13098 | −0.565492 | − | 0.824754i | \(-0.691314\pi\) | ||||
−0.565492 | + | 0.824754i | \(0.691314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 73.0723 | 0.112419 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −263.633 | −0.404345 | ||||||||
\(653\) | 105.534 | 0.161615 | 0.0808073 | − | 0.996730i | \(-0.474250\pi\) | ||||
0.0808073 | + | 0.996730i | \(0.474250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 881.427i | 1.34569i | ||||||||
\(656\) | − 204.118i | − 0.311156i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 35.3856 | 0.0537775 | ||||||||
\(659\) | 592.799i | 0.899543i | 0.893144 | + | 0.449772i | \(0.148495\pi\) | ||||
−0.893144 | + | 0.449772i | \(0.851505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 531.402 | 0.803936 | 0.401968 | − | 0.915654i | \(-0.368326\pi\) | ||||
0.401968 | + | 0.915654i | \(0.368326\pi\) | |||||||
\(662\) | 463.944i | 0.700821i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 275.527 | 0.414950 | ||||||||
\(665\) | −26.8108 | −0.0403169 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1013.72i | − 1.51981i | ||||||||
\(668\) | − 513.745i | − 0.769079i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 169.449i | − 0.252910i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 475.091i | 0.705931i | 0.935636 | + | 0.352965i | \(0.114827\pi\) | ||||
−0.935636 | + | 0.352965i | \(0.885173\pi\) | |||||||
\(674\) | 696.551 | 1.03346 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 184.094 | 0.272329 | ||||||||
\(677\) | 209.774i | 0.309859i | 0.987926 | + | 0.154929i | \(0.0495150\pi\) | ||||
−0.987926 | + | 0.154929i | \(0.950485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 107.289i | 0.158011i | ||||||||
\(680\) | −109.676 | −0.161288 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 661.462 | 0.968466 | 0.484233 | − | 0.874939i | \(-0.339099\pi\) | ||||
0.484233 | + | 0.874939i | \(0.339099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −576.915 | −0.842211 | ||||||||
\(686\) | −83.1061 | −0.121146 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 149.798i | 0.217730i | ||||||||
\(689\) | − 587.272i | − 0.852354i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1052.83 | −1.52363 | −0.761817 | − | 0.647792i | \(-0.775693\pi\) | ||||
−0.761817 | + | 0.647792i | \(0.775693\pi\) | |||||||
\(692\) | − 388.145i | − 0.560904i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 283.080 | 0.407896 | ||||||||
\(695\) | − 244.778i | − 0.352199i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 176.908 | 0.253814 | ||||||||
\(698\) | 586.952 | 0.840906 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.45836i | 0.0106548i | ||||||||
\(701\) | − 879.048i | − 1.25399i | −0.779023 | − | 0.626996i | \(-0.784284\pi\) | ||||
0.779023 | − | 0.626996i | \(-0.215716\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 17.4743i | − 0.0248568i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 436.699i | − 0.618554i | ||||||||
\(707\) | 51.8216 | 0.0732978 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 724.871 | 1.02239 | 0.511193 | − | 0.859466i | \(-0.329204\pi\) | ||||
0.511193 | + | 0.859466i | \(0.329204\pi\) | |||||||
\(710\) | − 716.019i | − 1.00848i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 167.970i | 0.235912i | ||||||||
\(713\) | −1442.98 | −2.02381 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 47.6487 | 0.0665485 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −576.341 | −0.802703 | ||||||||
\(719\) | −737.609 | −1.02588 | −0.512941 | − | 0.858424i | \(-0.671444\pi\) | ||||
−0.512941 | + | 0.858424i | \(0.671444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7222i | 0.0273540i | ||||||||
\(722\) | − 362.424i | − 0.501972i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −288.381 | −0.398316 | ||||||||
\(725\) | 208.013i | 0.286915i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −764.559 | −1.05166 | −0.525832 | − | 0.850589i | \(-0.676246\pi\) | ||||
−0.525832 | + | 0.850589i | \(0.676246\pi\) | |||||||
\(728\) | 46.2445i | 0.0635226i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −717.225 | −0.982500 | ||||||||
\(731\) | −129.829 | −0.177605 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1064.74i | − 1.45257i | −0.687392 | − | 0.726287i | \(-0.741244\pi\) | ||||
0.687392 | − | 0.726287i | \(-0.258756\pi\) | |||||||
\(734\) | − 643.153i | − 0.876230i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 829.677i | − 1.12728i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1170.71i | − 1.58418i | −0.610402 | − | 0.792092i | \(-0.708992\pi\) | ||||
0.610402 | − | 0.792092i | \(-0.291008\pi\) | |||||||
\(740\) | 15.8129 | 0.0213688 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −55.8656 | −0.0752906 | ||||||||
\(743\) | − 696.700i | − 0.937685i | −0.883282 | − | 0.468843i | \(-0.844671\pi\) | ||||
0.883282 | − | 0.468843i | \(-0.155329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 132.847i | 0.178318i | ||||||||
\(746\) | 911.571 | 1.22194 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.3186 | −0.0351384 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 426.754 | 0.568247 | 0.284124 | − | 0.958788i | \(-0.408297\pi\) | ||||
0.284124 | + | 0.958788i | \(0.408297\pi\) | |||||||
\(752\) | 142.654 | 0.189700 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 439.890i | 0.583408i | ||||||||
\(755\) | 496.389i | 0.657468i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −928.212 | −1.22617 | −0.613086 | − | 0.790016i | \(-0.710072\pi\) | ||||
−0.613086 | + | 0.790016i | \(0.710072\pi\) | |||||||
\(758\) | 626.489i | 0.826502i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −368.910 | −0.485408 | ||||||||
\(761\) | − 48.2758i | − 0.0634373i | −0.999497 | − | 0.0317186i | \(-0.989902\pi\) | ||||
0.999497 | − | 0.0317186i | \(-0.0100981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.4145 | −0.0149600 | ||||||||
\(764\) | 181.261 | 0.237252 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 438.840i | − 0.572898i | ||||||||
\(767\) | − 504.648i | − 0.657950i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 435.589i | 0.566435i | 0.959056 | + | 0.283218i | \(0.0914019\pi\) | ||||
−0.959056 | + | 0.283218i | \(0.908598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 292.124i | 0.378400i | ||||||||
\(773\) | −351.292 | −0.454453 | −0.227226 | − | 0.973842i | \(-0.572966\pi\) | ||||
−0.227226 | + | 0.973842i | \(0.572966\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 296.097 | 0.382061 | ||||||||
\(776\) | 1476.28i | 1.90242i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 297.788i | 0.382761i | ||||||||
\(779\) | 595.053 | 0.763868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −118.360 | −0.151356 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −166.873 | −0.212848 | ||||||||
\(785\) | 97.9304 | 0.124752 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 430.733i | − 0.547310i | −0.961828 | − | 0.273655i | \(-0.911767\pi\) | ||||
0.961828 | − | 0.273655i | \(-0.0882327\pi\) | |||||||
\(788\) | 374.232i | 0.474913i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −759.650 | −0.961583 | ||||||||
\(791\) | − 103.118i | − 0.130364i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 765.678 | 0.965546 | ||||||||
\(794\) | − 512.899i | − 0.645968i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 118.724 | 0.149151 | ||||||||
\(797\) | 391.319 | 0.490990 | 0.245495 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245495 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 123.637i | 0.154740i | ||||||||
\(800\) | 170.249i | 0.212811i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 154.789i | 0.193004i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 76.7677i | − 0.0953636i | ||||||||
\(806\) | 626.163 | 0.776877 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 713.053 | 0.882491 | ||||||||
\(809\) | − 337.874i | − 0.417643i | −0.977954 | − | 0.208822i | \(-0.933037\pi\) | ||||
0.977954 | − | 0.208822i | \(-0.0669628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1478.21i | − 1.82270i | −0.411630 | − | 0.911351i | \(-0.635040\pi\) | ||||
0.411630 | − | 0.911351i | \(-0.364960\pi\) | |||||||
\(812\) | −44.8988 | −0.0552941 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −556.814 | −0.683207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −436.696 | −0.534512 | ||||||||
\(818\) | 282.219 | 0.345011 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 538.477i | 0.656679i | ||||||||
\(821\) | − 13.0232i | − 0.0158626i | −0.999969 | − | 0.00793131i | \(-0.997475\pi\) | ||||
0.999969 | − | 0.00793131i | \(-0.00252464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0793 | 0.0122470 | 0.00612350 | − | 0.999981i | \(-0.498051\pi\) | ||||
0.00612350 | + | 0.999981i | \(0.498051\pi\) | |||||||
\(824\) | 271.373i | 0.329336i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.0058 | −0.0581184 | ||||||||
\(827\) | − 12.5612i | − 0.0151888i | −0.999971 | − | 0.00759442i | \(-0.997583\pi\) | ||||
0.999971 | − | 0.00759442i | \(-0.00241740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −205.335 | −0.247690 | −0.123845 | − | 0.992302i | \(-0.539523\pi\) | ||||
−0.123845 | + | 0.992302i | \(0.539523\pi\) | |||||||
\(830\) | 198.477 | 0.239129 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 482.874i | 0.580378i | ||||||||
\(833\) | − 144.628i | − 0.173623i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1085.07i | − 1.29948i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 721.028i | − 0.860415i | ||||||||
\(839\) | −1108.32 | −1.32100 | −0.660499 | − | 0.750827i | \(-0.729655\pi\) | ||||
−0.660499 | + | 0.750827i | \(0.729655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −411.225 | −0.488972 | ||||||||
\(842\) | − 463.220i | − 0.550143i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − 113.429i | − 0.134394i | ||||||||
\(845\) | 388.822 | 0.460145 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −225.218 | −0.265587 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.2874 | 0.0285734 | ||||||||
\(851\) | 50.0345 | 0.0587950 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1392.87i | 1.63290i | 0.577413 | + | 0.816452i | \(0.304062\pi\) | ||||
−0.577413 | + | 0.816452i | \(0.695938\pi\) | |||||||
\(854\) | − 72.8369i | − 0.0852891i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −362.138 | −0.423059 | ||||||||
\(857\) | − 1297.45i | − 1.51395i | −0.653444 | − | 0.756974i | \(-0.726677\pi\) | ||||
0.653444 | − | 0.756974i | \(-0.273323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −406.557 | −0.473290 | −0.236645 | − | 0.971596i | \(-0.576048\pi\) | ||||
−0.236645 | + | 0.971596i | \(0.576048\pi\) | |||||||
\(860\) | − 395.176i | − 0.459507i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1016.31 | 1.17901 | ||||||||
\(863\) | 323.659 | 0.375040 | 0.187520 | − | 0.982261i | \(-0.439955\pi\) | ||||
0.187520 | + | 0.982261i | \(0.439955\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 819.794i | − 0.947739i | ||||||||
\(866\) | 518.292i | 0.598490i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 63.9114i | 0.0736306i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 249.638i | − 0.286611i | ||||||||
\(872\) | −157.061 | −0.180115 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −398.121 | −0.455516 | ||||||||
\(875\) | 82.7478i | 0.0945690i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 621.473i | − 0.708635i | −0.935125 | − | 0.354318i | \(-0.884713\pi\) | ||||
0.935125 | − | 0.354318i | \(-0.115287\pi\) | |||||||
\(878\) | −409.722 | −0.466654 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1346.48 | 1.52835 | 0.764176 | − | 0.645007i | \(-0.223146\pi\) | ||||
0.764176 | + | 0.645007i | \(0.223146\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 537.489 | 0.608708 | 0.304354 | − | 0.952559i | \(-0.401559\pi\) | ||||
0.304354 | + | 0.952559i | \(0.401559\pi\) | |||||||
\(884\) | −55.1086 | −0.0623401 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 702.280i | − 0.792641i | ||||||||
\(887\) | 467.641i | 0.527217i | 0.964630 | + | 0.263608i | \(0.0849127\pi\) | ||||
−0.964630 | + | 0.263608i | \(0.915087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.5578 | 0.0658693 | ||||||||
\(890\) | 120.998i | 0.135952i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 606.409 | 0.679831 | ||||||||
\(893\) | 415.871i | 0.465701i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 100.638 | 0.112445 | ||||||||
\(896\) | −25.0615 | −0.0279704 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.9299i | 0.0411246i | ||||||||
\(899\) | 1782.49i | 1.98274i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 195.195i | − 0.216642i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 1418.88i | − 1.56956i | ||||||||
\(905\) | −609.084 | −0.673021 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 163.842 | 0.180642 | 0.0903209 | − | 0.995913i | \(-0.471211\pi\) | ||||
0.0903209 | + | 0.995913i | \(0.471211\pi\) | |||||||
\(908\) | − 178.523i | − 0.196612i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 33.3124i | 0.0366071i | ||||||||
\(911\) | 964.379 | 1.05859 | 0.529297 | − | 0.848437i | \(-0.322456\pi\) | ||||
0.529297 | + | 0.848437i | \(0.322456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 245.448 | 0.268542 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 103.988 | 0.113524 | ||||||||
\(917\) | 123.527 | 0.134708 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1592.00i | − 1.73232i | −0.499769 | − | 0.866159i | \(-0.666582\pi\) | ||||
0.499769 | − | 0.866159i | \(-0.333418\pi\) | |||||||
\(920\) | − 1056.31i | − 1.14816i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −215.354 | −0.233572 | ||||||||
\(923\) | − 1054.86i | − 1.14286i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.2670 | −0.0110995 | ||||||||
\(926\) | 266.744i | 0.288061i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1024.89 | −1.10440 | ||||||||
\(929\) | −1071.44 | −1.15333 | −0.576665 | − | 0.816980i | \(-0.695646\pi\) | ||||
−0.576665 | + | 0.816980i | \(0.695646\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 486.475i | − 0.522529i | ||||||||
\(932\) | 884.317i | 0.948838i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 448.847i | − 0.480564i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 535.151i | 0.571132i | 0.958359 | + | 0.285566i | \(0.0921816\pi\) | ||||
−0.958359 | + | 0.285566i | \(0.907818\pi\) | |||||||
\(938\) | −23.7474 | −0.0253171 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −376.331 | −0.400352 | ||||||||
\(941\) | 1477.02i | 1.56963i | 0.619733 | + | 0.784813i | \(0.287241\pi\) | ||||
−0.619733 | + | 0.784813i | \(0.712759\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1703.83i | 1.80682i | ||||||||
\(944\) | −193.531 | −0.205012 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −425.172 | −0.448968 | −0.224484 | − | 0.974478i | \(-0.572070\pi\) | ||||
−0.224484 | + | 0.974478i | \(0.572070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1056.64 | −1.11342 | ||||||||
\(950\) | 81.6939 | 0.0859936 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.3705i | 0.0161455i | ||||||||
\(953\) | − 544.839i | − 0.571710i | −0.958273 | − | 0.285855i | \(-0.907723\pi\) | ||||
0.958273 | − | 0.285855i | \(-0.0922775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 382.837 | 0.400876 | ||||||||
\(956\) | 39.5237i | 0.0413428i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 636.839 | 0.664759 | ||||||||
\(959\) | 80.8515i | 0.0843081i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1576.29 | 1.64026 | ||||||||
\(962\) | −21.7119 | −0.0225695 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 111.574i | 0.115741i | ||||||||
\(965\) | 616.990i | 0.639368i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1196.81i | − 1.23765i | −0.785529 | − | 0.618824i | \(-0.787609\pi\) | ||||
0.785529 | − | 0.618824i | \(-0.212391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1063.44i | 1.09633i | ||||||||
\(971\) | 813.320 | 0.837611 | 0.418806 | − | 0.908076i | \(-0.362449\pi\) | ||||
0.418806 | + | 0.908076i | \(0.362449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.3044 | −0.0352563 | ||||||||
\(974\) | − 342.992i | − 0.352148i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 293.636i | − 0.300856i | ||||||||
\(977\) | 682.907 | 0.698983 | 0.349492 | − | 0.936939i | \(-0.386354\pi\) | ||||
0.349492 | + | 0.936939i | \(0.386354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 440.222 | 0.449206 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 60.1620 | 0.0612648 | ||||||||
\(983\) | 1471.66 | 1.49711 | 0.748556 | − | 0.663072i | \(-0.230748\pi\) | ||||
0.748556 | + | 0.663072i | \(0.230748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 790.407i | 0.802444i | ||||||||
\(986\) | 146.209i | 0.148285i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −185.365 | −0.187616 | ||||||||
\(989\) | − 1250.40i | − 1.26431i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −399.921 | −0.403553 | −0.201777 | − | 0.979432i | \(-0.564671\pi\) | ||||
−0.201777 | + | 0.979432i | \(0.564671\pi\) | |||||||
\(992\) | 1458.88i | 1.47064i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −100.346 | −0.100952 | ||||||||
\(995\) | 250.755 | 0.252016 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1250.46i | 1.25422i | 0.778931 | + | 0.627109i | \(0.215762\pi\) | ||||
−0.778931 | + | 0.627109i | \(0.784238\pi\) | |||||||
\(998\) | 685.104i | 0.686477i | ||||||||
\(999\) | 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.l.604.6 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.c.l.604.11 | 16 | ||
11.6 | odd | 10 | 99.3.k.b.19.2 | ✓ | 16 | ||
11.9 | even | 5 | 99.3.k.b.73.2 | yes | 16 | ||
11.10 | odd | 2 | inner | 1089.3.c.l.604.12 | 16 | ||
33.17 | even | 10 | 99.3.k.b.19.3 | yes | 16 | ||
33.20 | odd | 10 | 99.3.k.b.73.3 | yes | 16 | ||
33.32 | even | 2 | inner | 1089.3.c.l.604.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.k.b.19.2 | ✓ | 16 | 11.6 | odd | 10 | ||
99.3.k.b.19.3 | yes | 16 | 33.17 | even | 10 | ||
99.3.k.b.73.2 | yes | 16 | 11.9 | even | 5 | ||
99.3.k.b.73.3 | yes | 16 | 33.20 | odd | 10 | ||
1089.3.c.l.604.5 | 16 | 33.32 | even | 2 | inner | ||
1089.3.c.l.604.6 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.c.l.604.11 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.c.l.604.12 | 16 | 11.10 | odd | 2 | inner |