Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (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: | \(28.6104277578\) |
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: | \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + \cdots + 33124 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.6 | ||
Root | \(-0.207107 + 0.264184i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.e.601.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −0.853218 | − | 6.94781i | −0.121888 | − | 0.992544i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.88097 | 0.261906 | 0.130953 | − | 0.991389i | \(-0.458196\pi\) | ||||
0.130953 | + | 0.991389i | \(0.458196\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 13.8145i | 1.06266i | 0.847166 | + | 0.531328i | \(0.178307\pi\) | ||||
−0.847166 | + | 0.531328i | \(0.821693\pi\) | |||||||
\(14\) | 1.20663 | + | 9.82568i | 0.0861880 | + | 0.701834i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 24.1754i | − | 1.42208i | −0.703150 | − | 0.711041i | \(-0.748224\pi\) | ||
0.703150 | − | 0.711041i | \(-0.251776\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 6.53403i | 0.343896i | 0.985106 | + | 0.171948i | \(0.0550062\pi\) | ||||
−0.985106 | + | 0.171948i | \(0.944994\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.0340 | − | 1.47782i | 0.573045 | − | 0.0703722i | ||||
\(22\) | −4.07430 | −0.185196 | ||||||||
\(23\) | −28.8420 | −1.25400 | −0.627000 | − | 0.779019i | \(-0.715717\pi\) | ||||
−0.627000 | + | 0.779019i | \(0.715717\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 19.5367i | − | 0.751411i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −1.70644 | − | 13.8956i | −0.0609441 | − | 0.496272i | ||||
\(29\) | 32.9589 | 1.13651 | 0.568257 | − | 0.822851i | \(-0.307618\pi\) | ||||
0.568257 | + | 0.822851i | \(0.307618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.43276i | 0.0784762i | 0.999230 | + | 0.0392381i | \(0.0124931\pi\) | ||||
−0.999230 | + | 0.0392381i | \(0.987507\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 4.98998i | 0.151212i | ||||||||
\(34\) | 34.1892i | 1.00556i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −50.9799 | −1.37783 | −0.688917 | − | 0.724840i | \(-0.741914\pi\) | ||||
−0.688917 | + | 0.724840i | \(0.741914\pi\) | |||||||
\(38\) | − | 9.24052i | − | 0.243171i | ||||||
\(39\) | −23.9275 | −0.613525 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.5225i | 0.524940i | 0.964940 | + | 0.262470i | \(0.0845371\pi\) | ||||
−0.964940 | + | 0.262470i | \(0.915463\pi\) | |||||||
\(42\) | −17.0186 | + | 2.08995i | −0.405204 | + | 0.0497607i | ||||
\(43\) | −13.5554 | −0.315243 | −0.157621 | − | 0.987500i | \(-0.550383\pi\) | ||||
−0.157621 | + | 0.987500i | \(0.550383\pi\) | |||||||
\(44\) | 5.76193 | 0.130953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.7887 | 0.886712 | ||||||||
\(47\) | 40.7305i | 0.866605i | 0.901248 | + | 0.433303i | \(0.142652\pi\) | ||||
−0.901248 | + | 0.433303i | \(0.857348\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −47.5440 | + | 11.8560i | −0.970287 | + | 0.241959i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 41.8730 | 0.821040 | ||||||||
\(52\) | 27.6291i | 0.531328i | ||||||||
\(53\) | 17.2758 | 0.325959 | 0.162979 | − | 0.986629i | \(-0.447890\pi\) | ||||
0.162979 | + | 0.986629i | \(0.447890\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.41326 | + | 19.6514i | 0.0430940 | + | 0.350917i | ||||
\(57\) | −11.3173 | −0.198549 | ||||||||
\(58\) | −46.6109 | −0.803636 | ||||||||
\(59\) | − | 1.47488i | − | 0.0249980i | −0.999922 | − | 0.0124990i | \(-0.996021\pi\) | ||
0.999922 | − | 0.0124990i | \(-0.00397867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 111.568i | 1.82898i | 0.404609 | + | 0.914490i | \(0.367408\pi\) | ||||
−0.404609 | + | 0.914490i | \(0.632592\pi\) | |||||||
\(62\) | − | 3.44045i | − | 0.0554911i | ||||||
\(63\) | 2.55965 | + | 20.8434i | 0.0406294 | + | 0.330848i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 7.05690i | − | 0.106923i | ||||||
\(67\) | −120.293 | −1.79542 | −0.897709 | − | 0.440590i | \(-0.854769\pi\) | ||||
−0.897709 | + | 0.440590i | \(0.854769\pi\) | |||||||
\(68\) | − | 48.3508i | − | 0.711041i | ||||||
\(69\) | − | 49.9558i | − | 0.723997i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −90.3855 | −1.27304 | −0.636518 | − | 0.771262i | \(-0.719626\pi\) | ||||
−0.636518 | + | 0.771262i | \(0.719626\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | − | 21.4890i | − | 0.294370i | −0.989109 | − | 0.147185i | \(-0.952979\pi\) | ||
0.989109 | − | 0.147185i | \(-0.0470212\pi\) | |||||||
\(74\) | 72.0964 | 0.974276 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.0681i | 0.171948i | ||||||||
\(77\) | −2.45809 | − | 20.0164i | −0.0319233 | − | 0.259953i | ||||
\(78\) | 33.8385 | 0.433827 | ||||||||
\(79\) | 66.1324 | 0.837119 | 0.418559 | − | 0.908189i | \(-0.362535\pi\) | ||||
0.418559 | + | 0.908189i | \(0.362535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 30.4375i | − | 0.371189i | ||||||
\(83\) | − | 78.5172i | − | 0.945990i | −0.881065 | − | 0.472995i | \(-0.843173\pi\) | ||
0.881065 | − | 0.472995i | \(-0.156827\pi\) | |||||||
\(84\) | 24.0679 | − | 2.95563i | 0.286523 | − | 0.0351861i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 19.1703 | 0.222910 | ||||||||
\(87\) | 57.0865i | 0.656166i | ||||||||
\(88\) | −8.14861 | −0.0925978 | ||||||||
\(89\) | − | 90.9724i | − | 1.02216i | −0.859533 | − | 0.511081i | \(-0.829245\pi\) | ||
0.859533 | − | 0.511081i | \(-0.170755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 95.9807 | − | 11.7868i | 1.05473 | − | 0.129525i | ||||
\(92\) | −57.6840 | −0.627000 | ||||||||
\(93\) | −4.21367 | −0.0453083 | ||||||||
\(94\) | − | 57.6016i | − | 0.612783i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | 44.1972i | 0.455642i | 0.973703 | + | 0.227821i | \(0.0731600\pi\) | ||||
−0.973703 | + | 0.227821i | \(0.926840\pi\) | |||||||
\(98\) | 67.2374 | − | 16.7669i | 0.686096 | − | 0.171091i | ||||
\(99\) | −8.64290 | −0.0873020 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 180.052i | − | 1.78269i | −0.453326 | − | 0.891345i | \(-0.649763\pi\) | ||
0.453326 | − | 0.891345i | \(-0.350237\pi\) | |||||||
\(102\) | −59.2174 | −0.580563 | ||||||||
\(103\) | 107.208i | 1.04086i | 0.853906 | + | 0.520428i | \(0.174228\pi\) | ||||
−0.853906 | + | 0.520428i | \(0.825772\pi\) | |||||||
\(104\) | − | 39.0734i | − | 0.375706i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.4317 | −0.230488 | ||||||||
\(107\) | −33.1521 | −0.309833 | −0.154917 | − | 0.987928i | \(-0.549511\pi\) | ||||
−0.154917 | + | 0.987928i | \(0.549511\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | −108.819 | −0.998338 | −0.499169 | − | 0.866505i | \(-0.666361\pi\) | ||||
−0.499169 | + | 0.866505i | \(0.666361\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 88.2997i | − | 0.795493i | ||||||
\(112\) | −3.41287 | − | 27.7912i | −0.0304721 | − | 0.248136i | ||||
\(113\) | −157.658 | −1.39520 | −0.697600 | − | 0.716488i | \(-0.745749\pi\) | ||||
−0.697600 | + | 0.716488i | \(0.745749\pi\) | |||||||
\(114\) | 16.0050 | 0.140395 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 65.9178 | 0.568257 | ||||||||
\(117\) | − | 41.4436i | − | 0.354219i | ||||||
\(118\) | 2.08580i | 0.0176763i | ||||||||
\(119\) | −167.966 | + | 20.6269i | −1.41148 | + | 0.173335i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112.700 | −0.931405 | ||||||||
\(122\) | − | 157.781i | − | 1.29328i | ||||||
\(123\) | −37.2781 | −0.303074 | ||||||||
\(124\) | 4.86553i | 0.0392381i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.61990 | − | 29.4770i | −0.0287293 | − | 0.233945i | ||||
\(127\) | −28.2047 | −0.222085 | −0.111042 | − | 0.993816i | \(-0.535419\pi\) | ||||
−0.111042 | + | 0.993816i | \(0.535419\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | − | 23.4787i | − | 0.182006i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 157.620i | − | 1.20321i | −0.798795 | − | 0.601604i | \(-0.794529\pi\) | ||
0.798795 | − | 0.601604i | \(-0.205471\pi\) | |||||||
\(132\) | 9.97996i | 0.0756058i | ||||||||
\(133\) | 45.3972 | − | 5.57495i | 0.341332 | − | 0.0419169i | ||||
\(134\) | 170.120 | 1.26955 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 68.3784i | 0.502782i | ||||||||
\(137\) | −244.855 | −1.78726 | −0.893632 | − | 0.448800i | \(-0.851852\pi\) | ||||
−0.893632 | + | 0.448800i | \(0.851852\pi\) | |||||||
\(138\) | 70.6482i | 0.511943i | ||||||||
\(139\) | 238.245i | 1.71399i | 0.515325 | + | 0.856995i | \(0.327671\pi\) | ||||
−0.515325 | + | 0.856995i | \(0.672329\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70.5472 | −0.500335 | ||||||||
\(142\) | 127.824 | 0.900172 | ||||||||
\(143\) | 39.7992i | 0.278316i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 30.3900i | 0.208151i | ||||||||
\(147\) | −20.5352 | − | 82.3487i | −0.139695 | − | 0.560195i | ||||
\(148\) | −101.960 | −0.688917 | ||||||||
\(149\) | −10.8398 | −0.0727503 | −0.0363751 | − | 0.999338i | \(-0.511581\pi\) | ||||
−0.0363751 | + | 0.999338i | \(0.511581\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −112.999 | −0.748340 | −0.374170 | − | 0.927360i | \(-0.622072\pi\) | ||||
−0.374170 | + | 0.927360i | \(0.622072\pi\) | |||||||
\(152\) | − | 18.4810i | − | 0.121586i | ||||||
\(153\) | 72.5262i | 0.474027i | ||||||||
\(154\) | 3.47627 | + | 28.3075i | 0.0225732 | + | 0.183815i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −47.8549 | −0.306762 | ||||||||
\(157\) | − | 103.693i | − | 0.660462i | −0.943900 | − | 0.330231i | \(-0.892873\pi\) | ||
0.943900 | − | 0.330231i | \(-0.107127\pi\) | |||||||
\(158\) | −93.5253 | −0.591932 | ||||||||
\(159\) | 29.9226i | 0.188193i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.6085 | + | 200.389i | 0.152848 | + | 1.24465i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 199.576 | 1.22439 | 0.612196 | − | 0.790706i | \(-0.290287\pi\) | ||||
0.612196 | + | 0.790706i | \(0.290287\pi\) | |||||||
\(164\) | 43.0451i | 0.262470i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 111.040i | 0.668916i | ||||||||
\(167\) | 87.0777i | 0.521424i | 0.965417 | + | 0.260712i | \(0.0839572\pi\) | ||||
−0.965417 | + | 0.260712i | \(0.916043\pi\) | |||||||
\(168\) | −34.0372 | + | 4.17990i | −0.202602 | + | 0.0248803i | ||||
\(169\) | −21.8411 | −0.129237 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 19.6021i | − | 0.114632i | ||||||
\(172\) | −27.1109 | −0.157621 | ||||||||
\(173\) | − | 106.597i | − | 0.616166i | −0.951359 | − | 0.308083i | \(-0.900313\pi\) | ||
0.951359 | − | 0.308083i | \(-0.0996875\pi\) | |||||||
\(174\) | − | 80.7325i | − | 0.463980i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.5239 | 0.0654765 | ||||||||
\(177\) | 2.55458 | 0.0144326 | ||||||||
\(178\) | 128.654i | 0.722778i | ||||||||
\(179\) | −275.881 | −1.54123 | −0.770617 | − | 0.637298i | \(-0.780052\pi\) | ||||
−0.770617 | + | 0.637298i | \(0.780052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 186.431i | 1.03000i | 0.857189 | + | 0.515002i | \(0.172209\pi\) | ||||
−0.857189 | + | 0.515002i | \(0.827791\pi\) | |||||||
\(182\) | −135.737 | + | 16.6690i | −0.745808 | + | 0.0915882i | ||||
\(183\) | −193.241 | −1.05596 | ||||||||
\(184\) | 81.5775 | 0.443356 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.95903 | 0.0320378 | ||||||||
\(187\) | − | 69.6485i | − | 0.372452i | ||||||
\(188\) | 81.4609i | 0.433303i | ||||||||
\(189\) | −36.1019 | + | 4.43345i | −0.191015 | + | 0.0234574i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −177.076 | −0.927102 | −0.463551 | − | 0.886070i | \(-0.653425\pi\) | ||||
−0.463551 | + | 0.886070i | \(0.653425\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −153.453 | −0.795092 | −0.397546 | − | 0.917582i | \(-0.630138\pi\) | ||||
−0.397546 | + | 0.917582i | \(0.630138\pi\) | |||||||
\(194\) | − | 62.5043i | − | 0.322187i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −95.0881 | + | 23.7120i | −0.485143 | + | 0.120979i | ||||
\(197\) | 214.041 | 1.08650 | 0.543252 | − | 0.839570i | \(-0.317193\pi\) | ||||
0.543252 | + | 0.839570i | \(0.317193\pi\) | |||||||
\(198\) | 12.2229 | 0.0617319 | ||||||||
\(199\) | − | 178.176i | − | 0.895359i | −0.894194 | − | 0.447679i | \(-0.852251\pi\) | ||
0.894194 | − | 0.447679i | \(-0.147749\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 208.354i | − | 1.03658i | ||||||
\(202\) | 254.631i | 1.26055i | ||||||||
\(203\) | −28.1211 | − | 228.992i | −0.138528 | − | 1.12804i | ||||
\(204\) | 83.7460 | 0.410520 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 151.615i | − | 0.735996i | ||||||
\(207\) | 86.5260 | 0.418000 | ||||||||
\(208\) | 55.2581i | 0.265664i | ||||||||
\(209\) | 18.8243i | 0.0900686i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −398.012 | −1.88631 | −0.943156 | − | 0.332350i | \(-0.892158\pi\) | ||||
−0.943156 | + | 0.332350i | \(0.892158\pi\) | |||||||
\(212\) | 34.5517 | 0.162979 | ||||||||
\(213\) | − | 156.552i | − | 0.734987i | ||||||
\(214\) | 46.8842 | 0.219085 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 16.9024 | − | 2.07568i | 0.0778911 | − | 0.00956533i | ||||
\(218\) | 153.893 | 0.705932 | ||||||||
\(219\) | 37.2200 | 0.169954 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 333.972 | 1.51118 | ||||||||
\(222\) | 124.875i | 0.562499i | ||||||||
\(223\) | 6.96741i | 0.0312440i | 0.999878 | + | 0.0156220i | \(0.00497284\pi\) | ||||
−0.999878 | + | 0.0156220i | \(0.995027\pi\) | |||||||
\(224\) | 4.82653 | + | 39.3027i | 0.0215470 | + | 0.175459i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 222.961 | 0.986555 | ||||||||
\(227\) | − | 242.118i | − | 1.06660i | −0.845927 | − | 0.533299i | \(-0.820952\pi\) | ||
0.845927 | − | 0.533299i | \(-0.179048\pi\) | |||||||
\(228\) | −22.6345 | −0.0992743 | ||||||||
\(229\) | − | 225.586i | − | 0.985093i | −0.870286 | − | 0.492547i | \(-0.836066\pi\) | ||
0.870286 | − | 0.492547i | \(-0.163934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 34.6694 | − | 4.25754i | 0.150084 | − | 0.0184309i | ||||
\(232\) | −93.2218 | −0.401818 | ||||||||
\(233\) | 435.850 | 1.87060 | 0.935300 | − | 0.353856i | \(-0.115130\pi\) | ||||
0.935300 | + | 0.353856i | \(0.115130\pi\) | |||||||
\(234\) | 58.6101i | 0.250470i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 2.94977i | − | 0.0124990i | ||||||
\(237\) | 114.545i | 0.483311i | ||||||||
\(238\) | 237.540 | − | 29.1708i | 0.998066 | − | 0.122566i | ||||
\(239\) | −194.711 | −0.814690 | −0.407345 | − | 0.913274i | \(-0.633545\pi\) | ||||
−0.407345 | + | 0.913274i | \(0.633545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 245.810i | 1.01996i | 0.860186 | + | 0.509980i | \(0.170347\pi\) | ||||
−0.860186 | + | 0.509980i | \(0.829653\pi\) | |||||||
\(242\) | 159.382 | 0.658603 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 223.136i | 0.914490i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 52.7192 | 0.214306 | ||||||||
\(247\) | −90.2645 | −0.365443 | ||||||||
\(248\) | − | 6.88089i | − | 0.0277455i | ||||||
\(249\) | 135.996 | 0.546168 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 147.023i | − | 0.585749i | −0.956151 | − | 0.292875i | \(-0.905388\pi\) | ||
0.956151 | − | 0.292875i | \(-0.0946118\pi\) | |||||||
\(252\) | 5.11931 | + | 41.6868i | 0.0203147 | + | 0.165424i | ||||
\(253\) | −83.0928 | −0.328430 | ||||||||
\(254\) | 39.8875 | 0.157038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 421.734i | 1.64099i | 0.571654 | + | 0.820495i | \(0.306302\pi\) | ||||
−0.571654 | + | 0.820495i | \(0.693698\pi\) | |||||||
\(258\) | 33.2039i | 0.128697i | ||||||||
\(259\) | 43.4969 | + | 354.198i | 0.167942 | + | 1.36756i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −98.8767 | −0.378838 | ||||||||
\(262\) | 222.909i | 0.850796i | ||||||||
\(263\) | −68.6354 | −0.260971 | −0.130486 | − | 0.991450i | \(-0.541654\pi\) | ||||
−0.130486 | + | 0.991450i | \(0.541654\pi\) | |||||||
\(264\) | − | 14.1138i | − | 0.0534614i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −64.2013 | + | 7.88417i | −0.241358 | + | 0.0296397i | ||||
\(267\) | 157.569 | 0.590145 | ||||||||
\(268\) | −240.586 | −0.897709 | ||||||||
\(269\) | 93.2991i | 0.346837i | 0.984848 | + | 0.173418i | \(0.0554813\pi\) | ||||
−0.984848 | + | 0.173418i | \(0.944519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 288.317i | 1.06390i | 0.846776 | + | 0.531949i | \(0.178540\pi\) | ||||
−0.846776 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(272\) | − | 96.7016i | − | 0.355521i | ||||||
\(273\) | 20.4153 | + | 166.243i | 0.0747814 | + | 0.608950i | ||||
\(274\) | 346.278 | 1.26379 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 99.9116i | − | 0.361999i | ||||||
\(277\) | 385.440 | 1.39148 | 0.695740 | − | 0.718294i | \(-0.255077\pi\) | ||||
0.695740 | + | 0.718294i | \(0.255077\pi\) | |||||||
\(278\) | − | 336.929i | − | 1.21197i | ||||||
\(279\) | − | 7.29829i | − | 0.0261587i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 243.958 | 0.868179 | 0.434090 | − | 0.900870i | \(-0.357070\pi\) | ||||
0.434090 | + | 0.900870i | \(0.357070\pi\) | |||||||
\(282\) | 99.7688 | 0.353790 | ||||||||
\(283\) | − | 501.435i | − | 1.77185i | −0.463825 | − | 0.885927i | \(-0.653523\pi\) | ||
0.463825 | − | 0.885927i | \(-0.346477\pi\) | |||||||
\(284\) | −180.771 | −0.636518 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 56.2846i | − | 0.196799i | ||||||
\(287\) | 149.534 | − | 18.3634i | 0.521026 | − | 0.0639840i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −295.450 | −1.02232 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −76.5519 | −0.263065 | ||||||||
\(292\) | − | 42.9780i | − | 0.147185i | ||||||
\(293\) | 337.308i | 1.15122i | 0.817724 | + | 0.575611i | \(0.195236\pi\) | ||||
−0.817724 | + | 0.575611i | \(0.804764\pi\) | |||||||
\(294\) | 29.0411 | + | 116.459i | 0.0987793 | + | 0.396118i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 144.193 | 0.487138 | ||||||||
\(297\) | − | 14.9699i | − | 0.0504039i | ||||||
\(298\) | 15.3298 | 0.0514422 | ||||||||
\(299\) | − | 398.438i | − | 1.33257i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5657 | + | 94.1806i | 0.0384244 | + | 0.312892i | ||||
\(302\) | 159.805 | 0.529156 | ||||||||
\(303\) | 311.859 | 1.02924 | ||||||||
\(304\) | 26.1361i | 0.0859741i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 102.568i | − | 0.335188i | ||||||
\(307\) | 112.285i | 0.365751i | 0.983136 | + | 0.182875i | \(0.0585405\pi\) | ||||
−0.983136 | + | 0.182875i | \(0.941460\pi\) | |||||||
\(308\) | −4.91618 | − | 40.0328i | −0.0159616 | − | 0.129977i | ||||
\(309\) | −185.690 | −0.600938 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 146.478i | − | 0.470990i | −0.971876 | − | 0.235495i | \(-0.924329\pi\) | ||
0.971876 | − | 0.235495i | \(-0.0756711\pi\) | |||||||
\(312\) | 67.6771 | 0.216914 | ||||||||
\(313\) | 139.927i | 0.447052i | 0.974698 | + | 0.223526i | \(0.0717568\pi\) | ||||
−0.974698 | + | 0.223526i | \(0.928243\pi\) | |||||||
\(314\) | 146.643i | 0.467017i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 132.265 | 0.418559 | ||||||||
\(317\) | −39.7776 | −0.125481 | −0.0627407 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627407 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(318\) | − | 42.3170i | − | 0.133072i | ||||||
\(319\) | 94.9535 | 0.297660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 57.4212i | − | 0.178882i | ||||||
\(322\) | −34.8017 | − | 283.392i | −0.108080 | − | 0.880100i | ||||
\(323\) | 157.963 | 0.489049 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −282.243 | −0.865775 | ||||||||
\(327\) | − | 188.480i | − | 0.576391i | ||||||
\(328\) | − | 60.8749i | − | 0.185594i | ||||||
\(329\) | 282.987 | − | 34.7519i | 0.860144 | − | 0.105629i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6736 | −0.0413101 | −0.0206550 | − | 0.999787i | \(-0.506575\pi\) | ||||
−0.0206550 | + | 0.999787i | \(0.506575\pi\) | |||||||
\(332\) | − | 157.034i | − | 0.472995i | ||||||
\(333\) | 152.940 | 0.459278 | ||||||||
\(334\) | − | 123.147i | − | 0.368702i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 48.1358 | − | 5.91127i | 0.143261 | − | 0.0175931i | ||||
\(337\) | 364.873 | 1.08271 | 0.541354 | − | 0.840795i | \(-0.317912\pi\) | ||||
0.541354 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(338\) | 30.8880 | 0.0913846 | ||||||||
\(339\) | − | 273.071i | − | 0.805519i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.00871i | 0.0205534i | ||||||||
\(342\) | 27.7215i | 0.0810572i | ||||||||
\(343\) | 122.938 | + | 320.211i | 0.358421 | + | 0.933560i | ||||
\(344\) | 38.3406 | 0.111455 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 150.751i | 0.435695i | ||||||||
\(347\) | 469.783 | 1.35384 | 0.676920 | − | 0.736056i | \(-0.263314\pi\) | ||||
0.676920 | + | 0.736056i | \(0.263314\pi\) | |||||||
\(348\) | 114.173i | 0.328083i | ||||||||
\(349\) | 26.7504i | 0.0766487i | 0.999265 | + | 0.0383244i | \(0.0122020\pi\) | ||||
−0.999265 | + | 0.0383244i | \(0.987798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 71.7824 | 0.204508 | ||||||||
\(352\) | −16.2972 | −0.0462989 | ||||||||
\(353\) | 473.408i | 1.34110i | 0.741864 | + | 0.670550i | \(0.233942\pi\) | ||||
−0.741864 | + | 0.670550i | \(0.766058\pi\) | |||||||
\(354\) | −3.61272 | −0.0102054 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 181.945i | − | 0.511081i | ||||||
\(357\) | −35.7268 | − | 290.926i | −0.100075 | − | 0.814918i | ||||
\(358\) | 390.155 | 1.08982 | ||||||||
\(359\) | 98.8174 | 0.275257 | 0.137629 | − | 0.990484i | \(-0.456052\pi\) | ||||
0.137629 | + | 0.990484i | \(0.456052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 318.306 | 0.881735 | ||||||||
\(362\) | − | 263.653i | − | 0.728323i | ||||||
\(363\) | − | 195.202i | − | 0.537747i | ||||||
\(364\) | 191.961 | − | 23.5736i | 0.527366 | − | 0.0647626i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 273.284 | 0.746678 | ||||||||
\(367\) | − | 331.526i | − | 0.903341i | −0.892185 | − | 0.451671i | \(-0.850828\pi\) | ||
0.892185 | − | 0.451671i | \(-0.149172\pi\) | |||||||
\(368\) | −115.368 | −0.313500 | ||||||||
\(369\) | − | 64.5676i | − | 0.174980i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7400 | − | 120.029i | −0.0397306 | − | 0.323529i | ||||
\(372\) | −8.42734 | −0.0226541 | ||||||||
\(373\) | −416.519 | −1.11667 | −0.558337 | − | 0.829614i | \(-0.688560\pi\) | ||||
−0.558337 | + | 0.829614i | \(0.688560\pi\) | |||||||
\(374\) | 98.4979i | 0.263363i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 115.203i | − | 0.306391i | ||||||
\(377\) | 455.311i | 1.20772i | ||||||||
\(378\) | 51.0557 | − | 6.26984i | 0.135068 | − | 0.0165869i | ||||
\(379\) | −560.942 | −1.48006 | −0.740028 | − | 0.672576i | \(-0.765188\pi\) | ||||
−0.740028 | + | 0.672576i | \(0.765188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 48.8520i | − | 0.128221i | ||||||
\(382\) | 250.424 | 0.655560 | ||||||||
\(383\) | 135.702i | 0.354314i | 0.984183 | + | 0.177157i | \(0.0566900\pi\) | ||||
−0.984183 | + | 0.177157i | \(0.943310\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 217.015 | 0.562215 | ||||||||
\(387\) | 40.6663 | 0.105081 | ||||||||
\(388\) | 88.3945i | 0.227821i | ||||||||
\(389\) | 703.375 | 1.80816 | 0.904081 | − | 0.427361i | \(-0.140557\pi\) | ||||
0.904081 | + | 0.427361i | \(0.140557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 697.267i | 1.78329i | ||||||||
\(392\) | 134.475 | − | 33.5338i | 0.343048 | − | 0.0855454i | ||||
\(393\) | 273.006 | 0.694672 | ||||||||
\(394\) | −302.700 | −0.768274 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −17.2858 | −0.0436510 | ||||||||
\(397\) | − | 2.16495i | − | 0.00545326i | −0.999996 | − | 0.00272663i | \(-0.999132\pi\) | ||
0.999996 | − | 0.00272663i | \(-0.000867915\pi\) | |||||||
\(398\) | 251.979i | 0.633114i | ||||||||
\(399\) | 9.65610 | + | 78.6302i | 0.0242007 | + | 0.197068i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −227.907 | −0.568347 | −0.284174 | − | 0.958773i | \(-0.591719\pi\) | ||||
−0.284174 | + | 0.958773i | \(0.591719\pi\) | |||||||
\(402\) | 294.656i | 0.732976i | ||||||||
\(403\) | −33.6075 | −0.0833932 | ||||||||
\(404\) | − | 360.103i | − | 0.891345i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 39.7693 | + | 323.844i | 0.0979538 | + | 0.797644i | ||||
\(407\) | −146.871 | −0.360863 | ||||||||
\(408\) | −118.435 | −0.290281 | ||||||||
\(409\) | 219.271i | 0.536116i | 0.963403 | + | 0.268058i | \(0.0863818\pi\) | ||||
−0.963403 | + | 0.268058i | \(0.913618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 424.102i | − | 1.03188i | ||||||
\(412\) | 214.416i | 0.520428i | ||||||||
\(413\) | −10.2472 | + | 1.25840i | −0.0248117 | + | 0.00304697i | ||||
\(414\) | −122.366 | −0.295571 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 78.1468i | − | 0.187853i | ||||||
\(417\) | −412.652 | −0.989572 | ||||||||
\(418\) | − | 26.6216i | − | 0.0636881i | ||||||
\(419\) | 636.723i | 1.51963i | 0.650141 | + | 0.759813i | \(0.274710\pi\) | ||||
−0.650141 | + | 0.759813i | \(0.725290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 816.589 | 1.93964 | 0.969821 | − | 0.243819i | \(-0.0784003\pi\) | ||||
0.969821 | + | 0.243819i | \(0.0784003\pi\) | |||||||
\(422\) | 562.874 | 1.33382 | ||||||||
\(423\) | − | 122.191i | − | 0.288868i | ||||||
\(424\) | −48.8634 | −0.115244 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 221.398i | 0.519714i | ||||||||
\(427\) | 775.151 | − | 95.1916i | 1.81534 | − | 0.222931i | ||||
\(428\) | −66.3043 | −0.154917 | ||||||||
\(429\) | −68.9342 | −0.160686 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −288.911 | −0.670328 | −0.335164 | − | 0.942160i | \(-0.608792\pi\) | ||||
−0.335164 | + | 0.942160i | \(0.608792\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | 114.744i | 0.264997i | 0.991183 | + | 0.132498i | \(0.0423000\pi\) | ||||
−0.991183 | + | 0.132498i | \(0.957700\pi\) | |||||||
\(434\) | −23.9036 | + | 2.93545i | −0.0550773 | + | 0.00676371i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −217.638 | −0.499169 | ||||||||
\(437\) | − | 188.454i | − | 0.431246i | ||||||
\(438\) | −52.6371 | −0.120176 | ||||||||
\(439\) | − | 637.443i | − | 1.45203i | −0.687677 | − | 0.726017i | \(-0.741369\pi\) | ||
0.687677 | − | 0.726017i | \(-0.258631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 142.632 | − | 35.5679i | 0.323429 | − | 0.0806529i | ||||
\(442\) | −472.307 | −1.06857 | ||||||||
\(443\) | −184.901 | −0.417384 | −0.208692 | − | 0.977981i | \(-0.566921\pi\) | ||||
−0.208692 | + | 0.977981i | \(0.566921\pi\) | |||||||
\(444\) | − | 176.599i | − | 0.397747i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 9.85341i | − | 0.0220928i | ||||||
\(447\) | − | 18.7751i | − | 0.0420024i | ||||||
\(448\) | −6.82574 | − | 55.5825i | −0.0152360 | − | 0.124068i | ||||
\(449\) | 313.278 | 0.697723 | 0.348862 | − | 0.937174i | \(-0.386568\pi\) | ||||
0.348862 | + | 0.937174i | \(0.386568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 62.0057i | 0.137485i | ||||||||
\(452\) | −315.315 | −0.697600 | ||||||||
\(453\) | − | 195.721i | − | 0.432054i | ||||||
\(454\) | 342.406i | 0.754198i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 32.0101 | 0.0701976 | ||||||||
\(457\) | 174.826 | 0.382551 | 0.191275 | − | 0.981536i | \(-0.438738\pi\) | ||||
0.191275 | + | 0.981536i | \(0.438738\pi\) | |||||||
\(458\) | 319.027i | 0.696566i | ||||||||
\(459\) | −125.619 | −0.273680 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 379.263i | − | 0.822695i | −0.911479 | − | 0.411348i | \(-0.865058\pi\) | ||
0.911479 | − | 0.411348i | \(-0.134942\pi\) | |||||||
\(462\) | −49.0300 | + | 6.02107i | −0.106125 | + | 0.0130326i | ||||
\(463\) | 403.499 | 0.871489 | 0.435744 | − | 0.900071i | \(-0.356485\pi\) | ||||
0.435744 | + | 0.900071i | \(0.356485\pi\) | |||||||
\(464\) | 131.836 | 0.284128 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −616.385 | −1.32271 | ||||||||
\(467\) | 807.901i | 1.72998i | 0.501788 | + | 0.864991i | \(0.332676\pi\) | ||||
−0.501788 | + | 0.864991i | \(0.667324\pi\) | |||||||
\(468\) | − | 82.8872i | − | 0.177109i | ||||||
\(469\) | 102.636 | + | 835.772i | 0.218840 | + | 1.78203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 179.601 | 0.381318 | ||||||||
\(472\) | 4.17160i | 0.00883815i | ||||||||
\(473\) | −39.0528 | −0.0825640 | ||||||||
\(474\) | − | 161.991i | − | 0.341752i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −335.932 | + | 41.2538i | −0.705740 | + | 0.0866675i | ||||
\(477\) | −51.8275 | −0.108653 | ||||||||
\(478\) | 275.363 | 0.576073 | ||||||||
\(479\) | − | 439.564i | − | 0.917671i | −0.888521 | − | 0.458835i | \(-0.848267\pi\) | ||
0.888521 | − | 0.458835i | \(-0.151733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 704.263i | − | 1.46416i | ||||||
\(482\) | − | 347.628i | − | 0.721220i | ||||||
\(483\) | −347.083 | + | 42.6232i | −0.718599 | + | 0.0882467i | ||||
\(484\) | −225.400 | −0.465703 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | −37.9665 | −0.0779599 | −0.0389799 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389799 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(488\) | − | 315.561i | − | 0.646642i | ||||||
\(489\) | 345.675i | 0.706903i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.32753 | −0.0149237 | −0.00746184 | − | 0.999972i | \(-0.502375\pi\) | ||||
−0.00746184 | + | 0.999972i | \(0.502375\pi\) | |||||||
\(492\) | −74.5563 | −0.151537 | ||||||||
\(493\) | − | 796.794i | − | 1.61622i | ||||||
\(494\) | 127.653 | 0.258408 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.73105i | 0.0196191i | ||||||||
\(497\) | 77.1185 | + | 627.981i | 0.155168 | + | 1.26354i | ||||
\(498\) | −192.327 | −0.386199 | ||||||||
\(499\) | 397.886 | 0.797366 | 0.398683 | − | 0.917089i | \(-0.369467\pi\) | ||||
0.398683 | + | 0.917089i | \(0.369467\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −150.823 | −0.301044 | ||||||||
\(502\) | 207.922i | 0.414187i | ||||||||
\(503\) | 70.5081i | 0.140175i | 0.997541 | + | 0.0700876i | \(0.0223279\pi\) | ||||
−0.997541 | + | 0.0700876i | \(0.977672\pi\) | |||||||
\(504\) | −7.23979 | − | 58.9541i | −0.0143647 | − | 0.116972i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 117.511 | 0.232235 | ||||||||
\(507\) | − | 37.8299i | − | 0.0746152i | ||||||
\(508\) | −56.4095 | −0.111042 | ||||||||
\(509\) | − | 505.073i | − | 0.992285i | −0.868241 | − | 0.496143i | \(-0.834749\pi\) | ||
0.868241 | − | 0.496143i | \(-0.165251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −149.301 | + | 18.3348i | −0.292175 | + | 0.0358802i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 33.9518 | 0.0661829 | ||||||||
\(514\) | − | 596.422i | − | 1.16035i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 46.9574i | − | 0.0910028i | ||||||
\(517\) | 117.343i | 0.226969i | ||||||||
\(518\) | −61.5139 | − | 500.912i | −0.118753 | − | 0.967012i | ||||
\(519\) | 184.631 | 0.355744 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 214.185i | − | 0.411104i | −0.978646 | − | 0.205552i | \(-0.934101\pi\) | ||
0.978646 | − | 0.205552i | \(-0.0658990\pi\) | |||||||
\(522\) | 139.833 | 0.267879 | ||||||||
\(523\) | 121.732i | 0.232757i | 0.993205 | + | 0.116379i | \(0.0371286\pi\) | ||||
−0.993205 | + | 0.116379i | \(0.962871\pi\) | |||||||
\(524\) | − | 315.240i | − | 0.601604i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 97.0651 | 0.184534 | ||||||||
\(527\) | 58.8130 | 0.111600 | ||||||||
\(528\) | 19.9599i | 0.0378029i | ||||||||
\(529\) | 302.861 | 0.572515 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.42465i | 0.00833268i | ||||||||
\(532\) | 90.7944 | − | 11.1499i | 0.170666 | − | 0.0209585i | ||||
\(533\) | −297.324 | −0.557830 | ||||||||
\(534\) | −222.836 | −0.417296 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 340.240 | 0.634776 | ||||||||
\(537\) | − | 477.840i | − | 0.889832i | ||||||
\(538\) | − | 131.945i | − | 0.245251i | ||||||
\(539\) | −136.973 | + | 34.1567i | −0.254124 | + | 0.0633705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 600.626 | 1.11021 | 0.555107 | − | 0.831779i | \(-0.312677\pi\) | ||||
0.555107 | + | 0.831779i | \(0.312677\pi\) | |||||||
\(542\) | − | 407.741i | − | 0.752290i | ||||||
\(543\) | −322.908 | −0.594674 | ||||||||
\(544\) | 136.757i | 0.251391i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −28.8716 | − | 235.104i | −0.0528785 | − | 0.430593i | ||||
\(547\) | −1045.16 | −1.91071 | −0.955356 | − | 0.295457i | \(-0.904528\pi\) | ||||
−0.955356 | + | 0.295457i | \(0.904528\pi\) | |||||||
\(548\) | −489.711 | −0.893632 | ||||||||
\(549\) | − | 334.703i | − | 0.609660i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 215.354i | 0.390843i | ||||||||
\(552\) | 141.296i | 0.255972i | ||||||||
\(553\) | −56.4253 | − | 459.475i | −0.102035 | − | 0.830877i | ||||
\(554\) | −545.094 | −0.983924 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 476.489i | 0.856995i | ||||||||
\(557\) | −601.731 | −1.08031 | −0.540154 | − | 0.841566i | \(-0.681634\pi\) | ||||
−0.540154 | + | 0.841566i | \(0.681634\pi\) | |||||||
\(558\) | 10.3213i | 0.0184970i | ||||||||
\(559\) | − | 187.262i | − | 0.334995i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 120.635 | 0.215035 | ||||||||
\(562\) | −345.009 | −0.613896 | ||||||||
\(563\) | 363.871i | 0.646308i | 0.946346 | + | 0.323154i | \(0.104743\pi\) | ||||
−0.946346 | + | 0.323154i | \(0.895257\pi\) | |||||||
\(564\) | −141.094 | −0.250167 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 709.136i | 1.25289i | ||||||||
\(567\) | −7.67896 | − | 62.5303i | −0.0135431 | − | 0.110283i | ||||
\(568\) | 255.649 | 0.450086 | ||||||||
\(569\) | −902.900 | −1.58682 | −0.793410 | − | 0.608688i | \(-0.791696\pi\) | ||||
−0.793410 | + | 0.608688i | \(0.791696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −847.207 | −1.48372 | −0.741862 | − | 0.670552i | \(-0.766057\pi\) | ||||
−0.741862 | + | 0.670552i | \(0.766057\pi\) | |||||||
\(572\) | 79.5984i | 0.139158i | ||||||||
\(573\) | − | 306.705i | − | 0.535263i | ||||||
\(574\) | −211.474 | + | 25.9698i | −0.368421 | + | 0.0452435i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 306.535i | 0.531256i | 0.964076 | + | 0.265628i | \(0.0855793\pi\) | ||||
−0.964076 | + | 0.265628i | \(0.914421\pi\) | |||||||
\(578\) | 417.829 | 0.722888 | ||||||||
\(579\) | − | 265.788i | − | 0.459047i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −545.522 | + | 66.9923i | −0.938937 | + | 0.115305i | ||||
\(582\) | 108.261 | 0.186015 | ||||||||
\(583\) | 49.7711 | 0.0853707 | ||||||||
\(584\) | 60.7801i | 0.104075i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 477.025i | − | 0.814037i | ||||||
\(587\) | 467.524i | 0.796463i | 0.917285 | + | 0.398232i | \(0.130376\pi\) | ||||
−0.917285 | + | 0.398232i | \(0.869624\pi\) | |||||||
\(588\) | −41.0703 | − | 164.697i | −0.0698475 | − | 0.280098i | ||||
\(589\) | −15.8958 | −0.0269877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 370.730i | 0.627293i | ||||||||
\(592\) | −203.920 | −0.344459 | ||||||||
\(593\) | 744.542i | 1.25555i | 0.778395 | + | 0.627775i | \(0.216034\pi\) | ||||
−0.778395 | + | 0.627775i | \(0.783966\pi\) | |||||||
\(594\) | 21.1707i | 0.0356409i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6796 | −0.0363751 | ||||||||
\(597\) | 308.611 | 0.516936 | ||||||||
\(598\) | 563.477i | 0.942269i | ||||||||
\(599\) | 276.145 | 0.461011 | 0.230505 | − | 0.973071i | \(-0.425962\pi\) | ||||
0.230505 | + | 0.973071i | \(0.425962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 779.606i | 1.29718i | 0.761137 | + | 0.648591i | \(0.224641\pi\) | ||||
−0.761137 | + | 0.648591i | \(0.775359\pi\) | |||||||
\(602\) | −16.3564 | − | 133.191i | −0.0271702 | − | 0.221248i | ||||
\(603\) | 360.879 | 0.598472 | ||||||||
\(604\) | −225.999 | −0.374170 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −441.035 | −0.727780 | ||||||||
\(607\) | − | 567.539i | − | 0.934990i | −0.883996 | − | 0.467495i | \(-0.845157\pi\) | ||
0.883996 | − | 0.467495i | \(-0.154843\pi\) | |||||||
\(608\) | − | 36.9621i | − | 0.0607929i | ||||||
\(609\) | 396.626 | − | 48.7072i | 0.651274 | − | 0.0799790i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −562.672 | −0.920903 | ||||||||
\(612\) | 145.052i | 0.237014i | ||||||||
\(613\) | 801.088 | 1.30683 | 0.653416 | − | 0.756999i | \(-0.273335\pi\) | ||||
0.653416 | + | 0.756999i | \(0.273335\pi\) | |||||||
\(614\) | − | 158.796i | − | 0.258625i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.95253 | + | 56.6149i | 0.0112866 | + | 0.0919074i | ||||
\(617\) | −71.2583 | −0.115492 | −0.0577458 | − | 0.998331i | \(-0.518391\pi\) | ||||
−0.0577458 | + | 0.998331i | \(0.518391\pi\) | |||||||
\(618\) | 262.605 | 0.424928 | ||||||||
\(619\) | 821.793i | 1.32761i | 0.747904 | + | 0.663807i | \(0.231060\pi\) | ||||
−0.747904 | + | 0.663807i | \(0.768940\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 149.867i | 0.241332i | ||||||||
\(622\) | 207.151i | 0.333040i | ||||||||
\(623\) | −632.059 | + | 77.6193i | −1.01454 | + | 0.124590i | ||||
\(624\) | −95.7098 | −0.153381 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 197.887i | − | 0.316114i | ||||||
\(627\) | −32.6047 | −0.0520011 | ||||||||
\(628\) | − | 207.385i | − | 0.330231i | ||||||
\(629\) | 1232.46i | 1.95939i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −916.907 | −1.45310 | −0.726551 | − | 0.687113i | \(-0.758878\pi\) | ||||
−0.726551 | + | 0.687113i | \(0.758878\pi\) | |||||||
\(632\) | −187.051 | −0.295966 | ||||||||
\(633\) | − | 689.377i | − | 1.08906i | ||||||
\(634\) | 56.2540 | 0.0887287 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 59.8452i | 0.0940963i | ||||||||
\(637\) | −163.785 | − | 656.798i | −0.257119 | − | 1.03108i | ||||
\(638\) | −134.285 | −0.210477 | ||||||||
\(639\) | 271.156 | 0.424345 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 737.240 | 1.15014 | 0.575070 | − | 0.818104i | \(-0.304975\pi\) | ||||
0.575070 | + | 0.818104i | \(0.304975\pi\) | |||||||
\(642\) | 81.2058i | 0.126489i | ||||||||
\(643\) | 256.297i | 0.398596i | 0.979939 | + | 0.199298i | \(0.0638661\pi\) | ||||
−0.979939 | + | 0.199298i | \(0.936134\pi\) | |||||||
\(644\) | 49.2170 | + | 400.777i | 0.0764239 | + | 0.622325i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −223.393 | −0.345810 | ||||||||
\(647\) | − | 689.147i | − | 1.06514i | −0.846385 | − | 0.532571i | \(-0.821226\pi\) | ||
0.846385 | − | 0.532571i | \(-0.178774\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − | 4.24910i | − | 0.00654714i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.59518 | + | 29.2758i | 0.00552255 | + | 0.0449705i | ||||
\(652\) | 399.152 | 0.612196 | ||||||||
\(653\) | 395.775 | 0.606087 | 0.303044 | − | 0.952977i | \(-0.401997\pi\) | ||||
0.303044 | + | 0.952977i | \(0.401997\pi\) | |||||||
\(654\) | 266.551i | 0.407570i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 86.0902i | 0.131235i | ||||||||
\(657\) | 64.4670i | 0.0981233i | ||||||||
\(658\) | −400.205 | + | 49.1467i | −0.608214 | + | 0.0746910i | ||||
\(659\) | 47.8147 | 0.0725565 | 0.0362782 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362782 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 89.9129i | − | 0.136026i | −0.997684 | − | 0.0680128i | \(-0.978334\pi\) | ||
0.997684 | − | 0.0680128i | \(-0.0216659\pi\) | |||||||
\(662\) | 19.3374 | 0.0292106 | ||||||||
\(663\) | 578.456i | 0.872482i | ||||||||
\(664\) | 222.080i | 0.334458i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −216.289 | −0.324759 | ||||||||
\(667\) | −950.600 | −1.42519 | ||||||||
\(668\) | 174.155i | 0.260712i | ||||||||
\(669\) | −12.0679 | −0.0180387 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 321.423i | 0.479021i | ||||||||
\(672\) | −68.0743 | + | 8.35979i | −0.101301 | + | 0.0124402i | ||||
\(673\) | −833.478 | −1.23845 | −0.619226 | − | 0.785213i | \(-0.712553\pi\) | ||||
−0.619226 | + | 0.785213i | \(0.712553\pi\) | |||||||
\(674\) | −516.008 | −0.765590 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.6822 | −0.0646187 | ||||||||
\(677\) | 44.1092i | 0.0651540i | 0.999469 | + | 0.0325770i | \(0.0103714\pi\) | ||||
−0.999469 | + | 0.0325770i | \(0.989629\pi\) | |||||||
\(678\) | 386.181i | 0.569588i | ||||||||
\(679\) | 307.074 | − | 37.7099i | 0.452244 | − | 0.0555373i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 419.360 | 0.615800 | ||||||||
\(682\) | − | 9.91182i | − | 0.0145335i | ||||||
\(683\) | −130.146 | −0.190550 | −0.0952750 | − | 0.995451i | \(-0.530373\pi\) | ||||
−0.0952750 | + | 0.995451i | \(0.530373\pi\) | |||||||
\(684\) | − | 39.2042i | − | 0.0573161i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −173.861 | − | 452.847i | −0.253442 | − | 0.660127i | ||||
\(687\) | 390.727 | 0.568744 | ||||||||
\(688\) | −54.2218 | −0.0788107 | ||||||||
\(689\) | 238.657i | 0.346382i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 714.724i | − | 1.03433i | −0.855885 | − | 0.517167i | \(-0.826987\pi\) | ||
0.855885 | − | 0.517167i | \(-0.173013\pi\) | |||||||
\(692\) | − | 213.194i | − | 0.308083i | ||||||
\(693\) | 7.37428 | + | 60.0492i | 0.0106411 | + | 0.0866511i | ||||
\(694\) | −664.373 | −0.957310 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 161.465i | − | 0.231990i | ||||||
\(697\) | 520.316 | 0.746508 | ||||||||
\(698\) | − | 37.8308i | − | 0.0541988i | ||||||
\(699\) | 754.914i | 1.07999i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 463.854 | 0.661704 | 0.330852 | − | 0.943683i | \(-0.392664\pi\) | ||||
0.330852 | + | 0.943683i | \(0.392664\pi\) | |||||||
\(702\) | −101.516 | −0.144609 | ||||||||
\(703\) | − | 333.104i | − | 0.473832i | ||||||
\(704\) | 23.0477 | 0.0327383 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 669.500i | − | 0.948301i | ||||||
\(707\) | −1250.96 | + | 153.623i | −1.76940 | + | 0.217289i | ||||
\(708\) | 5.10915 | 0.00721632 | ||||||||
\(709\) | 970.049 | 1.36819 | 0.684097 | − | 0.729391i | \(-0.260197\pi\) | ||||
0.684097 | + | 0.729391i | \(0.260197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −198.397 | −0.279040 | ||||||||
\(712\) | 257.309i | 0.361389i | ||||||||
\(713\) | − | 70.1657i | − | 0.0984092i | ||||||
\(714\) | 50.5253 | + | 411.431i | 0.0707638 | + | 0.576234i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −551.762 | −0.770617 | ||||||||
\(717\) | − | 337.249i | − | 0.470362i | ||||||
\(718\) | −139.749 | −0.194636 | ||||||||
\(719\) | − | 1369.36i | − | 1.90453i | −0.305266 | − | 0.952267i | \(-0.598745\pi\) | ||
0.305266 | − | 0.952267i | \(-0.401255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 744.861 | − | 91.4719i | 1.03309 | − | 0.126868i | ||||
\(722\) | −450.153 | −0.623481 | ||||||||
\(723\) | −425.756 | −0.588874 | ||||||||
\(724\) | 372.862i | 0.515002i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 276.058i | 0.380245i | ||||||||
\(727\) | − | 1106.85i | − | 1.52249i | −0.648463 | − | 0.761246i | \(-0.724588\pi\) | ||
0.648463 | − | 0.761246i | \(-0.275412\pi\) | |||||||
\(728\) | −271.474 | + | 33.3381i | −0.372904 | + | 0.0457941i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 327.708i | 0.448301i | ||||||||
\(732\) | −386.482 | −0.527981 | ||||||||
\(733\) | 297.353i | 0.405665i | 0.979213 | + | 0.202833i | \(0.0650147\pi\) | ||||
−0.979213 | + | 0.202833i | \(0.934985\pi\) | |||||||
\(734\) | 468.849i | 0.638759i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 163.155 | 0.221678 | ||||||||
\(737\) | −346.560 | −0.470231 | ||||||||
\(738\) | 91.3124i | 0.123730i | ||||||||
\(739\) | −604.951 | −0.818608 | −0.409304 | − | 0.912398i | \(-0.634228\pi\) | ||||
−0.409304 | + | 0.912398i | \(0.634228\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 156.343i | − | 0.210989i | ||||||
\(742\) | 20.8456 | + | 169.747i | 0.0280938 | + | 0.228769i | ||||
\(743\) | 733.877 | 0.987722 | 0.493861 | − | 0.869541i | \(-0.335585\pi\) | ||||
0.493861 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(744\) | 11.9181 | 0.0160189 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 589.047 | 0.789608 | ||||||||
\(747\) | 235.552i | 0.315330i | ||||||||
\(748\) | − | 139.297i | − | 0.186226i | ||||||
\(749\) | 28.2860 | + | 230.335i | 0.0377650 | + | 0.307523i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −71.0036 | −0.0945455 | −0.0472727 | − | 0.998882i | \(-0.515053\pi\) | ||||
−0.0472727 | + | 0.998882i | \(0.515053\pi\) | |||||||
\(752\) | 162.922i | 0.216651i | ||||||||
\(753\) | 254.651 | 0.338182 | ||||||||
\(754\) | − | 643.908i | − | 0.853989i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −72.2037 | + | 8.86690i | −0.0955076 | + | 0.0117287i | ||||
\(757\) | −708.172 | −0.935497 | −0.467749 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(758\) | 793.291 | 1.04656 | ||||||||
\(759\) | − | 143.921i | − | 0.189619i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 797.652i | − | 1.04816i | −0.851668 | − | 0.524081i | \(-0.824409\pi\) | ||
0.851668 | − | 0.524081i | \(-0.175591\pi\) | |||||||
\(762\) | 69.0872i | 0.0906657i | ||||||||
\(763\) | 92.8462 | + | 756.052i | 0.121686 | + | 0.990894i | ||||
\(764\) | −354.153 | −0.463551 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 191.912i | − | 0.250538i | ||||||
\(767\) | 20.3748 | 0.0265643 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 261.829i | − | 0.340480i | −0.985403 | − | 0.170240i | \(-0.945546\pi\) | ||
0.985403 | − | 0.170240i | \(-0.0544543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −730.465 | −0.947426 | ||||||||
\(772\) | −306.906 | −0.397546 | ||||||||
\(773\) | − | 643.514i | − | 0.832489i | −0.909253 | − | 0.416245i | \(-0.863346\pi\) | ||
0.909253 | − | 0.416245i | \(-0.136654\pi\) | |||||||
\(774\) | −57.5109 | −0.0743035 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 125.009i | − | 0.161094i | ||||||
\(777\) | −613.490 | + | 75.3389i | −0.789562 | + | 0.0969613i | ||||
\(778\) | −994.722 | −1.27856 | ||||||||
\(779\) | −140.629 | −0.180525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −260.398 | −0.333416 | ||||||||
\(782\) | − | 986.084i | − | 1.26098i | ||||||
\(783\) | − | 171.259i | − | 0.218722i | ||||||
\(784\) | −190.176 | + | 47.4239i | −0.242572 | + | 0.0604897i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −386.089 | −0.491207 | ||||||||
\(787\) | 919.663i | 1.16857i | 0.811549 | + | 0.584284i | \(0.198625\pi\) | ||||
−0.811549 | + | 0.584284i | \(0.801375\pi\) | |||||||
\(788\) | 428.082 | 0.543252 | ||||||||
\(789\) | − | 118.880i | − | 0.150672i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 134.516 | + | 1095.37i | 0.170058 | + | 1.38480i | ||||
\(792\) | 24.4458 | 0.0308659 | ||||||||
\(793\) | −1541.26 | −1.94358 | ||||||||
\(794\) | 3.06170i | 0.00385604i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 356.353i | − | 0.447679i | ||||||
\(797\) | − | 246.244i | − | 0.308964i | −0.987996 | − | 0.154482i | \(-0.950629\pi\) | ||
0.987996 | − | 0.154482i | \(-0.0493708\pi\) | |||||||
\(798\) | −13.6558 | − | 111.200i | −0.0171125 | − | 0.139348i | ||||
\(799\) | 984.675 | 1.23238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 272.917i | 0.340721i | ||||||||
\(802\) | 322.309 | 0.401882 | ||||||||
\(803\) | − | 61.9091i | − | 0.0770973i | ||||||
\(804\) | − | 416.707i | − | 0.518292i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47.5281 | 0.0589679 | ||||||||
\(807\) | −161.599 | −0.200246 | ||||||||
\(808\) | 509.263i | 0.630276i | ||||||||
\(809\) | 609.838 | 0.753817 | 0.376908 | − | 0.926251i | \(-0.376987\pi\) | ||||
0.376908 | + | 0.926251i | \(0.376987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 605.726i | − | 0.746888i | −0.927653 | − | 0.373444i | \(-0.878177\pi\) | ||
0.927653 | − | 0.373444i | \(-0.121823\pi\) | |||||||
\(812\) | −56.2422 | − | 457.984i | −0.0692638 | − | 0.564020i | ||||
\(813\) | −499.379 | −0.614242 | ||||||||
\(814\) | 207.707 | 0.255169 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 167.492 | 0.205260 | ||||||||
\(817\) | − | 88.5717i | − | 0.108411i | ||||||
\(818\) | − | 310.097i | − | 0.379091i | ||||||
\(819\) | −287.942 | + | 35.3604i | −0.351577 | + | 0.0431751i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 890.751 | 1.08496 | 0.542480 | − | 0.840069i | \(-0.317486\pi\) | ||||
0.542480 | + | 0.840069i | \(0.317486\pi\) | |||||||
\(822\) | 599.770i | 0.729648i | ||||||||
\(823\) | −317.029 | −0.385211 | −0.192606 | − | 0.981276i | \(-0.561694\pi\) | ||||
−0.192606 | + | 0.981276i | \(0.561694\pi\) | |||||||
\(824\) | − | 303.230i | − | 0.367998i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.4918 | − | 1.77964i | 0.0175445 | − | 0.00215453i | ||||
\(827\) | −90.7251 | −0.109704 | −0.0548520 | − | 0.998494i | \(-0.517469\pi\) | ||||
−0.0548520 | + | 0.998494i | \(0.517469\pi\) | |||||||
\(828\) | 173.052 | 0.209000 | ||||||||
\(829\) | − | 1366.86i | − | 1.64880i | −0.566007 | − | 0.824400i | \(-0.691513\pi\) | ||
0.566007 | − | 0.824400i | \(-0.308487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 667.601i | 0.803371i | ||||||||
\(832\) | 110.516i | 0.132832i | ||||||||
\(833\) | 286.623 | + | 1149.40i | 0.344085 | + | 1.37983i | ||||
\(834\) | 583.578 | 0.699733 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 37.6487i | 0.0450343i | ||||||||
\(837\) | 12.6410 | 0.0151028 | ||||||||
\(838\) | − | 900.463i | − | 1.07454i | ||||||
\(839\) | 73.5993i | 0.0877227i | 0.999038 | + | 0.0438613i | \(0.0139660\pi\) | ||||
−0.999038 | + | 0.0438613i | \(0.986034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 245.289 | 0.291663 | ||||||||
\(842\) | −1154.83 | −1.37153 | ||||||||
\(843\) | 422.548i | 0.501244i | ||||||||
\(844\) | −796.024 | −0.943156 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 172.805i | 0.204261i | ||||||||
\(847\) | 96.1576 | + | 783.018i | 0.113527 | + | 0.924460i | ||||
\(848\) | 69.1033 | 0.0814897 | ||||||||
\(849\) | 868.510 | 1.02298 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1470.36 | 1.72780 | ||||||||
\(852\) | − | 313.105i | − | 0.367494i | ||||||
\(853\) | − | 822.046i | − | 0.963711i | −0.876251 | − | 0.481856i | \(-0.839963\pi\) | ||
0.876251 | − | 0.481856i | \(-0.160037\pi\) | |||||||
\(854\) | −1096.23 | + | 134.621i | −1.28364 | + | 0.157636i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 93.7684 | 0.109543 | ||||||||
\(857\) | 625.685i | 0.730087i | 0.930990 | + | 0.365044i | \(0.118946\pi\) | ||||
−0.930990 | + | 0.365044i | \(0.881054\pi\) | |||||||
\(858\) | 97.4877 | 0.113622 | ||||||||
\(859\) | − | 1396.65i | − | 1.62590i | −0.582332 | − | 0.812951i | \(-0.697860\pi\) | ||
0.582332 | − | 0.812951i | \(-0.302140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.8064 | + | 259.001i | 0.0369412 | + | 0.300814i | ||||
\(862\) | 408.582 | 0.473993 | ||||||||
\(863\) | −601.569 | −0.697068 | −0.348534 | − | 0.937296i | \(-0.613320\pi\) | ||||
−0.348534 | + | 0.937296i | \(0.613320\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 162.272i | − | 0.187381i | ||||||
\(867\) | − | 511.734i | − | 0.590236i | ||||||
\(868\) | 33.8047 | − | 4.15135i | 0.0389456 | − | 0.00478267i | ||||
\(869\) | 190.525 | 0.219246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1661.79i | − | 1.90791i | ||||||
\(872\) | 307.786 | 0.352966 | ||||||||
\(873\) | − | 132.592i | − | 0.151881i | ||||||
\(874\) | 266.515i | 0.304937i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 74.4401 | 0.0849772 | ||||||||
\(877\) | −570.762 | −0.650812 | −0.325406 | − | 0.945574i | \(-0.605501\pi\) | ||||
−0.325406 | + | 0.945574i | \(0.605501\pi\) | |||||||
\(878\) | 901.480i | 1.02674i | ||||||||
\(879\) | −584.234 | −0.664658 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1095.44i | 1.24341i | 0.783253 | + | 0.621703i | \(0.213559\pi\) | ||||
−0.783253 | + | 0.621703i | \(0.786441\pi\) | |||||||
\(882\) | −201.712 | + | 50.3007i | −0.228699 | + | 0.0570302i | ||||
\(883\) | 305.870 | 0.346399 | 0.173199 | − | 0.984887i | \(-0.444590\pi\) | ||||
0.173199 | + | 0.984887i | \(0.444590\pi\) | |||||||
\(884\) | 667.943 | 0.755592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 261.490 | 0.295135 | ||||||||
\(887\) | 637.527i | 0.718745i | 0.933194 | + | 0.359372i | \(0.117009\pi\) | ||||
−0.933194 | + | 0.359372i | \(0.882991\pi\) | |||||||
\(888\) | 249.749i | 0.281249i | ||||||||
\(889\) | 24.0648 | + | 195.961i | 0.0270695 | + | 0.220429i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.9287 | 0.0291007 | ||||||||
\(892\) | 13.9348i | 0.0156220i | ||||||||
\(893\) | −266.134 | −0.298022 | ||||||||
\(894\) | 26.5520i | 0.0297002i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.65306 | + | 78.6055i | 0.0107735 | + | 0.0877293i | ||||
\(897\) | 690.116 | 0.769360 | ||||||||
\(898\) | −443.042 | −0.493365 | ||||||||
\(899\) | 80.1812i | 0.0891893i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 417.650i | − | 0.463541i | ||||||
\(902\) | − | 87.6893i | − | 0.0972166i | ||||||
\(903\) | −163.126 | + | 20.0325i | −0.180649 | + | 0.0221843i | ||||
\(904\) | 445.923 | 0.493278 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 276.791i | 0.305509i | ||||||||
\(907\) | 785.727 | 0.866292 | 0.433146 | − | 0.901324i | \(-0.357403\pi\) | ||||
0.433146 | + | 0.901324i | \(0.357403\pi\) | |||||||
\(908\) | − | 484.235i | − | 0.533299i | ||||||
\(909\) | 540.155i | 0.594230i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −909.376 | −0.998217 | −0.499109 | − | 0.866539i | \(-0.666339\pi\) | ||||
−0.499109 | + | 0.866539i | \(0.666339\pi\) | |||||||
\(912\) | −45.2691 | −0.0496372 | ||||||||
\(913\) | − | 226.205i | − | 0.247761i | ||||||
\(914\) | −247.241 | −0.270504 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 451.173i | − | 0.492547i | ||||||
\(917\) | −1095.11 | + | 134.484i | −1.19424 | + | 0.146657i | ||||
\(918\) | 177.652 | 0.193521 | ||||||||
\(919\) | 270.279 | 0.294101 | 0.147050 | − | 0.989129i | \(-0.453022\pi\) | ||||
0.147050 | + | 0.989129i | \(0.453022\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −194.484 | −0.211166 | ||||||||
\(922\) | 536.358i | 0.581733i | ||||||||
\(923\) | − | 1248.63i | − | 1.35280i | ||||||
\(924\) | 69.3389 | − | 8.51508i | 0.0750421 | − | 0.00921546i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −570.634 | −0.616235 | ||||||||
\(927\) | − | 321.624i | − | 0.346952i | ||||||
\(928\) | −186.444 | −0.200909 | ||||||||
\(929\) | − | 1053.28i | − | 1.13378i | −0.823795 | − | 0.566889i | \(-0.808147\pi\) | ||
0.823795 | − | 0.566889i | \(-0.191853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −77.4674 | − | 310.654i | −0.0832088 | − | 0.333678i | ||||
\(932\) | 871.699 | 0.935300 | ||||||||
\(933\) | 253.707 | 0.271926 | ||||||||
\(934\) | − | 1142.55i | − | 1.22328i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 117.220i | 0.125235i | ||||||||
\(937\) | − | 1012.18i | − | 1.08024i | −0.841589 | − | 0.540119i | \(-0.818379\pi\) | ||
0.841589 | − | 0.540119i | \(-0.181621\pi\) | |||||||
\(938\) | −145.149 | − | 1181.96i | −0.154743 | − | 1.26009i | ||||
\(939\) | −242.361 | −0.258106 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1384.55i | 1.47136i | 0.677331 | + | 0.735679i | \(0.263137\pi\) | ||||
−0.677331 | + | 0.735679i | \(0.736863\pi\) | |||||||
\(942\) | −253.994 | −0.269633 | ||||||||
\(943\) | − | 620.753i | − | 0.658275i | ||||||
\(944\) | − | 5.89954i | − | 0.00624951i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55.2290 | 0.0583816 | ||||||||
\(947\) | 1216.79 | 1.28489 | 0.642444 | − | 0.766332i | \(-0.277920\pi\) | ||||
0.642444 | + | 0.766332i | \(0.277920\pi\) | |||||||
\(948\) | 229.089i | 0.241655i | ||||||||
\(949\) | 296.860 | 0.312814 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 68.8968i | − | 0.0724467i | ||||||
\(952\) | 475.080 | − | 58.3416i | 0.499033 | − | 0.0612832i | ||||
\(953\) | 30.5870 | 0.0320955 | 0.0160478 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160478 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(954\) | 73.2951 | 0.0768293 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −389.422 | −0.407345 | ||||||||
\(957\) | 164.464i | 0.171854i | ||||||||
\(958\) | 621.638i | 0.648891i | ||||||||
\(959\) | 208.915 | + | 1701.21i | 0.217847 | + | 1.77394i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 955.082 | 0.993841 | ||||||||
\(962\) | 995.978i | 1.03532i | ||||||||
\(963\) | 99.4564 | 0.103278 | ||||||||
\(964\) | 491.620i | 0.509980i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 490.850 | − | 60.2783i | 0.508126 | − | 0.0623999i | ||||
\(967\) | −1878.59 | −1.94270 | −0.971351 | − | 0.237650i | \(-0.923623\pi\) | ||||
−0.971351 | + | 0.237650i | \(0.923623\pi\) | |||||||
\(968\) | 318.764 | 0.329301 | ||||||||
\(969\) | 273.600i | 0.282353i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 712.009i | − | 0.733274i | −0.930364 | − | 0.366637i | \(-0.880509\pi\) | ||
0.930364 | − | 0.366637i | \(-0.119491\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1655.28 | − | 203.274i | 1.70121 | − | 0.208915i | ||||
\(974\) | 53.6927 | 0.0551260 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 446.271i | 0.457245i | ||||||||
\(977\) | −750.938 | −0.768616 | −0.384308 | − | 0.923205i | \(-0.625560\pi\) | ||||
−0.384308 | + | 0.923205i | \(0.625560\pi\) | |||||||
\(978\) | − | 488.859i | − | 0.499856i | ||||||
\(979\) | − | 262.089i | − | 0.267710i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 326.457 | 0.332779 | ||||||||
\(982\) | 10.3627 | 0.0105526 | ||||||||
\(983\) | − | 1525.09i | − | 1.55147i | −0.631059 | − | 0.775735i | \(-0.717379\pi\) | ||
0.631059 | − | 0.775735i | \(-0.282621\pi\) | |||||||
\(984\) | 105.438 | 0.107153 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1126.84i | 1.14284i | ||||||||
\(987\) | 60.1921 | + | 490.148i | 0.0609849 | + | 0.496604i | ||||
\(988\) | −180.529 | −0.182722 | ||||||||
\(989\) | 390.966 | 0.395314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1259.84 | 1.27128 | 0.635641 | − | 0.771985i | \(-0.280736\pi\) | ||||
0.635641 | + | 0.771985i | \(0.280736\pi\) | |||||||
\(992\) | − | 13.7618i | − | 0.0138728i | ||||||
\(993\) | − | 23.6834i | − | 0.0238504i | ||||||
\(994\) | −109.062 | − | 888.099i | −0.109720 | − | 0.893460i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 271.992 | 0.273084 | ||||||||
\(997\) | − | 1406.62i | − | 1.41086i | −0.708781 | − | 0.705428i | \(-0.750755\pi\) | ||
0.708781 | − | 0.705428i | \(-0.249245\pi\) | |||||||
\(998\) | −562.695 | −0.563823 | ||||||||
\(999\) | 264.899i | 0.265164i |
(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 | 1050.3.f.e.601.6 | 16 | ||
5.2 | odd | 4 | 210.3.h.a.139.6 | yes | 16 | ||
5.3 | odd | 4 | 210.3.h.a.139.11 | yes | 16 | ||
5.4 | even | 2 | inner | 1050.3.f.e.601.11 | 16 | ||
7.6 | odd | 2 | inner | 1050.3.f.e.601.2 | 16 | ||
15.2 | even | 4 | 630.3.h.e.559.14 | 16 | |||
15.8 | even | 4 | 630.3.h.e.559.3 | 16 | |||
20.3 | even | 4 | 1680.3.bd.a.769.14 | 16 | |||
20.7 | even | 4 | 1680.3.bd.a.769.4 | 16 | |||
35.13 | even | 4 | 210.3.h.a.139.14 | yes | 16 | ||
35.27 | even | 4 | 210.3.h.a.139.3 | ✓ | 16 | ||
35.34 | odd | 2 | inner | 1050.3.f.e.601.15 | 16 | ||
105.62 | odd | 4 | 630.3.h.e.559.11 | 16 | |||
105.83 | odd | 4 | 630.3.h.e.559.6 | 16 | |||
140.27 | odd | 4 | 1680.3.bd.a.769.13 | 16 | |||
140.83 | odd | 4 | 1680.3.bd.a.769.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.3 | ✓ | 16 | 35.27 | even | 4 | ||
210.3.h.a.139.6 | yes | 16 | 5.2 | odd | 4 | ||
210.3.h.a.139.11 | yes | 16 | 5.3 | odd | 4 | ||
210.3.h.a.139.14 | yes | 16 | 35.13 | even | 4 | ||
630.3.h.e.559.3 | 16 | 15.8 | even | 4 | |||
630.3.h.e.559.6 | 16 | 105.83 | odd | 4 | |||
630.3.h.e.559.11 | 16 | 105.62 | odd | 4 | |||
630.3.h.e.559.14 | 16 | 15.2 | even | 4 | |||
1050.3.f.e.601.2 | 16 | 7.6 | odd | 2 | inner | ||
1050.3.f.e.601.6 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.f.e.601.11 | 16 | 5.4 | even | 2 | inner | ||
1050.3.f.e.601.15 | 16 | 35.34 | odd | 2 | inner | ||
1680.3.bd.a.769.3 | 16 | 140.83 | odd | 4 | |||
1680.3.bd.a.769.4 | 16 | 20.7 | even | 4 | |||
1680.3.bd.a.769.13 | 16 | 140.27 | odd | 4 | |||
1680.3.bd.a.769.14 | 16 | 20.3 | even | 4 |