Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
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([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (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: | \(8\) |
Coefficient field: | 8.0.1105425137664.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 71x^{4} - 80x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.4 | ||
Root | \(0.979091 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.f.485.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.38464i | − 0.692322i | −0.938175 | − | 0.346161i | \(-0.887485\pi\) | ||||
0.938175 | − | 0.346161i | \(-0.112515\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.08276 | 0.520691 | ||||||||
\(5\) | 0.765629i | 0.153126i | 0.997065 | + | 0.0765629i | \(0.0243946\pi\) | ||||
−0.997065 | + | 0.0765629i | \(0.975605\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.89285 | 1.27041 | 0.635203 | − | 0.772345i | \(-0.280916\pi\) | ||||
0.635203 | + | 0.772345i | \(0.280916\pi\) | |||||||
\(8\) | − 8.42246i | − 1.05281i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.06012 | 0.106012 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.8510 | 0.834695 | 0.417347 | − | 0.908747i | \(-0.362960\pi\) | ||||
0.417347 | + | 0.908747i | \(0.362960\pi\) | |||||||
\(14\) | − 12.3134i | − 0.879530i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.33105 | −0.208191 | ||||||||
\(17\) | 20.8842i | 1.22849i | 0.789117 | + | 0.614243i | \(0.210538\pi\) | ||||
−0.789117 | + | 0.614243i | \(0.789462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.79091 | 0.515311 | 0.257655 | − | 0.966237i | \(-0.417050\pi\) | ||||
0.257655 | + | 0.966237i | \(0.417050\pi\) | |||||||
\(20\) | 1.59462i | 0.0797311i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 25.0413i | − 1.08875i | −0.838841 | − | 0.544377i | \(-0.816766\pi\) | ||||
0.838841 | − | 0.544377i | \(-0.183234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.4138 | 0.976553 | ||||||||
\(26\) | − 15.0248i | − 0.577877i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18.5217 | 0.661489 | ||||||||
\(29\) | 13.8464i | 0.477463i | 0.971086 | + | 0.238732i | \(0.0767316\pi\) | ||||
−0.971086 | + | 0.238732i | \(0.923268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.9172 | −0.610233 | −0.305117 | − | 0.952315i | \(-0.598695\pi\) | ||||
−0.305117 | + | 0.952315i | \(0.598695\pi\) | |||||||
\(32\) | − 29.0775i | − 0.908672i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 28.9172 | 0.850507 | ||||||||
\(35\) | 6.80862i | 0.194532i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.4138 | 0.416590 | 0.208295 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208295 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(38\) | − 13.5569i | − 0.356761i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.44848 | 0.161212 | ||||||||
\(41\) | 62.8819i | 1.53371i | 0.641823 | + | 0.766853i | \(0.278178\pi\) | ||||
−0.641823 | + | 0.766853i | \(0.721822\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −74.8971 | −1.74179 | −0.870896 | − | 0.491467i | \(-0.836461\pi\) | ||||
−0.870896 | + | 0.491467i | \(0.836461\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −34.6733 | −0.753768 | ||||||||
\(47\) | − 67.4678i | − 1.43548i | −0.696309 | − | 0.717742i | \(-0.745176\pi\) | ||||
0.696309 | − | 0.717742i | \(-0.254824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30.0828 | 0.613934 | ||||||||
\(50\) | − 33.8044i | − 0.676089i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 22.6001 | 0.434618 | ||||||||
\(53\) | 96.3372i | 1.81768i | 0.417141 | + | 0.908842i | \(0.363032\pi\) | ||||
−0.417141 | + | 0.908842i | \(0.636968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 74.8996i | − 1.33749i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 19.1724 | 0.330558 | ||||||||
\(59\) | − 8.48528i | − 0.143818i | −0.997411 | − | 0.0719092i | \(-0.977091\pi\) | ||||
0.997411 | − | 0.0719092i | \(-0.0229092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 93.4188 | 1.53146 | 0.765728 | − | 0.643165i | \(-0.222379\pi\) | ||||
0.765728 | + | 0.643165i | \(0.222379\pi\) | |||||||
\(62\) | 26.1936i | 0.422478i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −53.5862 | −0.837284 | ||||||||
\(65\) | 8.30786i | 0.127813i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 80.8276 | 1.20638 | 0.603191 | − | 0.797597i | \(-0.293896\pi\) | ||||
0.603191 | + | 0.797597i | \(0.293896\pi\) | |||||||
\(68\) | 43.4969i | 0.639661i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.42751 | 0.134679 | ||||||||
\(71\) | − 91.2656i | − 1.28543i | −0.766105 | − | 0.642716i | \(-0.777808\pi\) | ||||
0.766105 | − | 0.642716i | \(-0.222192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.9896 | 0.219035 | 0.109518 | − | 0.993985i | \(-0.465069\pi\) | ||||
0.109518 | + | 0.993985i | \(0.465069\pi\) | |||||||
\(74\) | − 21.3426i | − 0.288414i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.3921 | 0.268318 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 83.6279 | 1.05858 | 0.529290 | − | 0.848441i | \(-0.322458\pi\) | ||||
0.529290 | + | 0.848441i | \(0.322458\pi\) | |||||||
\(80\) | − 2.55035i | − 0.0318793i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87.0691 | 1.06182 | ||||||||
\(83\) | 98.8827i | 1.19136i | 0.803223 | + | 0.595679i | \(0.203117\pi\) | ||||
−0.803223 | + | 0.595679i | \(0.796883\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9896 | −0.188113 | ||||||||
\(86\) | 103.706i | 1.20588i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 113.722i | − 1.27778i | −0.769299 | − | 0.638889i | \(-0.779394\pi\) | ||||
0.769299 | − | 0.638889i | \(-0.220606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.4966 | 1.06040 | ||||||||
\(92\) | − 52.1552i | − 0.566904i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −93.4188 | −0.993817 | ||||||||
\(95\) | 7.49620i | 0.0789074i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −146.241 | −1.50764 | −0.753822 | − | 0.657079i | \(-0.771792\pi\) | ||||
−0.753822 | + | 0.657079i | \(0.771792\pi\) | |||||||
\(98\) | − 41.6539i | − 0.425040i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 50.8482 | 0.508482 | ||||||||
\(101\) | − 62.8819i | − 0.622593i | −0.950313 | − | 0.311297i | \(-0.899237\pi\) | ||||
0.950313 | − | 0.311297i | \(-0.100763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −45.4138 | −0.440911 | −0.220455 | − | 0.975397i | \(-0.570754\pi\) | ||||
−0.220455 | + | 0.975397i | \(0.570754\pi\) | |||||||
\(104\) | − 91.3923i | − 0.878773i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 133.393 | 1.25842 | ||||||||
\(107\) | − 117.456i | − 1.09772i | −0.835914 | − | 0.548860i | \(-0.815062\pi\) | ||||
0.835914 | − | 0.548860i | \(-0.184938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 113.001 | 1.03670 | 0.518351 | − | 0.855168i | \(-0.326546\pi\) | ||||
0.518351 | + | 0.855168i | \(0.326546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −29.6225 | −0.264487 | ||||||||
\(113\) | − 148.492i | − 1.31409i | −0.753850 | − | 0.657046i | \(-0.771806\pi\) | ||||
0.753850 | − | 0.657046i | \(-0.228194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.1724 | 0.166716 | ||||||||
\(116\) | 28.8388i | 0.248611i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.7491 | −0.0995686 | ||||||||
\(119\) | 185.720i | 1.56068i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − 129.352i | − 1.06026i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −39.4001 | −0.317743 | ||||||||
\(125\) | 37.8326i | 0.302661i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −89.9886 | −0.708572 | −0.354286 | − | 0.935137i | \(-0.615276\pi\) | ||||
−0.354286 | + | 0.935137i | \(0.615276\pi\) | |||||||
\(128\) | − 42.1123i | − 0.329002i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.5034 | 0.0884879 | ||||||||
\(131\) | 62.8819i | 0.480015i | 0.970771 | + | 0.240007i | \(0.0771499\pi\) | ||||
−0.970771 | + | 0.240007i | \(0.922850\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.0691 | 0.654655 | ||||||||
\(134\) | − 111.917i | − 0.835205i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 175.897 | 1.29336 | ||||||||
\(137\) | − 28.8695i | − 0.210726i | −0.994434 | − | 0.105363i | \(-0.966400\pi\) | ||||
0.994434 | − | 0.105363i | \(-0.0336005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −246.393 | −1.77261 | −0.886307 | − | 0.463098i | \(-0.846738\pi\) | ||||
−0.886307 | + | 0.463098i | \(0.846738\pi\) | |||||||
\(140\) | 14.1807i | 0.101291i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126.370 | −0.889932 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.6012 | −0.0731119 | ||||||||
\(146\) | − 22.1399i | − 0.151643i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.1033 | 0.216914 | ||||||||
\(149\) | − 216.339i | − 1.45194i | −0.687728 | − | 0.725969i | \(-0.741392\pi\) | ||||
0.687728 | − | 0.725969i | \(-0.258608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 74.6473 | 0.494353 | 0.247176 | − | 0.968970i | \(-0.420497\pi\) | ||||
0.247176 | + | 0.968970i | \(0.420497\pi\) | |||||||
\(152\) | − 82.4635i | − 0.542523i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 14.4836i | − 0.0934425i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 151.655 | 0.965957 | 0.482979 | − | 0.875632i | \(-0.339555\pi\) | ||||
0.482979 | + | 0.875632i | \(0.339555\pi\) | |||||||
\(158\) | − 115.795i | − 0.732878i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 22.2626 | 0.139141 | ||||||||
\(161\) | − 222.689i | − 1.38316i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −89.1724 | −0.547070 | −0.273535 | − | 0.961862i | \(-0.588193\pi\) | ||||
−0.273535 | + | 0.961862i | \(0.588193\pi\) | |||||||
\(164\) | 130.968i | 0.798586i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 136.917 | 0.824803 | ||||||||
\(167\) | 249.570i | 1.49443i | 0.664581 | + | 0.747216i | \(0.268610\pi\) | ||||
−0.664581 | + | 0.747216i | \(0.731390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −51.2551 | −0.303285 | ||||||||
\(170\) | 22.1399i | 0.130235i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −155.993 | −0.906935 | ||||||||
\(173\) | 166.845i | 0.964421i | 0.876055 | + | 0.482210i | \(0.160166\pi\) | ||||
−0.876055 | + | 0.482210i | \(0.839834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 217.108 | 1.24062 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −157.465 | −0.884634 | ||||||||
\(179\) | − 198.800i | − 1.11061i | −0.831646 | − | 0.555306i | \(-0.812601\pi\) | ||||
0.831646 | − | 0.555306i | \(-0.187399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −47.2620 | −0.261116 | −0.130558 | − | 0.991441i | \(-0.541677\pi\) | ||||
−0.130558 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(182\) | − 133.613i | − 0.734139i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −210.910 | −1.14625 | ||||||||
\(185\) | 11.8013i | 0.0637906i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 140.519i | − 0.747443i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.3796 | 0.0546293 | ||||||||
\(191\) | 94.5816i | 0.495192i | 0.968863 | + | 0.247596i | \(0.0796405\pi\) | ||||
−0.968863 | + | 0.247596i | \(0.920360\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −62.9859 | −0.326352 | −0.163176 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163176 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(194\) | 202.492i | 1.04377i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 62.6553 | 0.319670 | ||||||||
\(197\) | − 35.6475i | − 0.180952i | −0.995899 | − | 0.0904758i | \(-0.971161\pi\) | ||||
0.995899 | − | 0.0904758i | \(-0.0288388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −284.138 | −1.42783 | −0.713915 | − | 0.700232i | \(-0.753080\pi\) | ||||
−0.713915 | + | 0.700232i | \(0.753080\pi\) | |||||||
\(200\) | − 205.624i | − 1.02812i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −87.0691 | −0.431035 | ||||||||
\(203\) | 123.134i | 0.606573i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.1442 | −0.234850 | ||||||||
\(206\) | 62.8819i | 0.305252i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −36.1453 | −0.173776 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −89.7388 | −0.425302 | −0.212651 | − | 0.977128i | \(-0.568210\pi\) | ||||
−0.212651 | + | 0.977128i | \(0.568210\pi\) | |||||||
\(212\) | 200.648i | 0.946451i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −162.635 | −0.759975 | ||||||||
\(215\) | − 57.3434i | − 0.266713i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −168.228 | −0.775245 | ||||||||
\(218\) | − 156.466i | − 0.717732i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 226.616i | 1.02541i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5171 | 0.0785521 | 0.0392761 | − | 0.999228i | \(-0.487495\pi\) | ||||
0.0392761 | + | 0.999228i | \(0.487495\pi\) | |||||||
\(224\) | − 258.582i | − 1.15438i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −205.609 | −0.909775 | ||||||||
\(227\) | 28.3804i | 0.125024i | 0.998044 | + | 0.0625120i | \(0.0199112\pi\) | ||||
−0.998044 | + | 0.0625120i | \(0.980089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 190.000 | 0.829694 | 0.414847 | − | 0.909891i | \(-0.363835\pi\) | ||||
0.414847 | + | 0.909891i | \(0.363835\pi\) | |||||||
\(230\) | − 26.5469i | − 0.115421i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 116.621 | 0.502677 | ||||||||
\(233\) | 179.192i | 0.769064i | 0.923112 | + | 0.384532i | \(0.125637\pi\) | ||||
−0.923112 | + | 0.384532i | \(0.874363\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 51.6553 | 0.219810 | ||||||||
\(236\) | − 17.6728i | − 0.0748849i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 257.157 | 1.08049 | ||||||||
\(239\) | − 397.488i | − 1.66313i | −0.555427 | − | 0.831565i | \(-0.687445\pi\) | ||||
0.555427 | − | 0.831565i | \(-0.312555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 247.204 | 1.02574 | 0.512871 | − | 0.858466i | \(-0.328582\pi\) | ||||
0.512871 | + | 0.858466i | \(0.328582\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 194.569 | 0.797415 | ||||||||
\(245\) | 23.0322i | 0.0940091i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 106.241 | 0.430127 | ||||||||
\(248\) | 159.330i | 0.642458i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 52.3847 | 0.209539 | ||||||||
\(251\) | − 76.3675i | − 0.304253i | −0.988361 | − | 0.152127i | \(-0.951388\pi\) | ||||
0.988361 | − | 0.152127i | \(-0.0486121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 124.602i | 0.490560i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −272.655 | −1.06506 | ||||||||
\(257\) | 391.250i | 1.52237i | 0.648534 | + | 0.761186i | \(0.275383\pi\) | ||||
−0.648534 | + | 0.761186i | \(0.724617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 137.073 | 0.529238 | ||||||||
\(260\) | 17.3033i | 0.0665512i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 87.0691 | 0.332325 | ||||||||
\(263\) | 271.266i | 1.03143i | 0.856760 | + | 0.515715i | \(0.172474\pi\) | ||||
−0.856760 | + | 0.515715i | \(0.827526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −73.7586 | −0.278334 | ||||||||
\(266\) | − 120.560i | − 0.453232i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 168.345 | 0.628152 | ||||||||
\(269\) | 282.184i | 1.04901i | 0.851407 | + | 0.524506i | \(0.175750\pi\) | ||||
−0.851407 | + | 0.524506i | \(0.824250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 74.6473 | 0.275451 | 0.137726 | − | 0.990470i | \(-0.456021\pi\) | ||||
0.137726 | + | 0.990470i | \(0.456021\pi\) | |||||||
\(272\) | − 69.5665i | − 0.255759i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.9740 | −0.145890 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 265.887 | 0.959882 | 0.479941 | − | 0.877301i | \(-0.340658\pi\) | ||||
0.479941 | + | 0.877301i | \(0.340658\pi\) | |||||||
\(278\) | 341.167i | 1.22722i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 57.3453 | 0.204805 | ||||||||
\(281\) | 368.649i | 1.31192i | 0.754796 | + | 0.655960i | \(0.227736\pi\) | ||||
−0.754796 | + | 0.655960i | \(0.772264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 310.527 | 1.09727 | 0.548635 | − | 0.836062i | \(-0.315148\pi\) | ||||
0.548635 | + | 0.836062i | \(0.315148\pi\) | |||||||
\(284\) | − 190.085i | − 0.669312i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 559.200i | 1.94843i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −147.152 | −0.509176 | ||||||||
\(290\) | 14.6789i | 0.0506170i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 33.3025 | 0.114050 | ||||||||
\(293\) | − 396.677i | − 1.35385i | −0.736054 | − | 0.676923i | \(-0.763313\pi\) | ||||
0.736054 | − | 0.676923i | \(-0.236687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.49658 | 0.0220223 | ||||||||
\(296\) | − 129.822i | − 0.438588i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −299.552 | −1.00521 | ||||||||
\(299\) | − 271.724i | − 0.908777i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −666.049 | −2.21279 | ||||||||
\(302\) | − 103.360i | − 0.342251i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −32.6140 | −0.107283 | ||||||||
\(305\) | 71.5241i | 0.234505i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −370.893 | −1.20812 | −0.604061 | − | 0.796938i | \(-0.706452\pi\) | ||||
−0.604061 | + | 0.796938i | \(0.706452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.0546 | −0.0646922 | ||||||||
\(311\) | 155.003i | 0.498402i | 0.968452 | + | 0.249201i | \(0.0801679\pi\) | ||||
−0.968452 | + | 0.249201i | \(0.919832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −390.828 | −1.24865 | −0.624325 | − | 0.781164i | \(-0.714626\pi\) | ||||
−0.624325 | + | 0.781164i | \(0.714626\pi\) | |||||||
\(314\) | − 209.988i | − 0.668753i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 174.177 | 0.551193 | ||||||||
\(317\) | − 184.701i | − 0.582654i | −0.956624 | − | 0.291327i | \(-0.905903\pi\) | ||||
0.956624 | − | 0.291327i | \(-0.0940968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 41.0271i | − 0.128210i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −308.345 | −0.957592 | ||||||||
\(323\) | 204.476i | 0.633052i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 264.915 | 0.815123 | ||||||||
\(326\) | 123.472i | 0.378748i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 529.620 | 1.61470 | ||||||||
\(329\) | − 599.981i | − 1.82365i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −567.642 | −1.71493 | −0.857465 | − | 0.514543i | \(-0.827962\pi\) | ||||
−0.857465 | + | 0.514543i | \(0.827962\pi\) | |||||||
\(332\) | 205.949i | 0.620329i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 345.566 | 1.03463 | ||||||||
\(335\) | 61.8840i | 0.184728i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 82.5678 | 0.245008 | 0.122504 | − | 0.992468i | \(-0.460908\pi\) | ||||
0.122504 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(338\) | 70.9701i | 0.209971i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −33.3025 | −0.0979485 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −168.228 | −0.490461 | ||||||||
\(344\) | 630.818i | 1.83377i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 231.021 | 0.667689 | ||||||||
\(347\) | 132.572i | 0.382053i | 0.981585 | + | 0.191027i | \(0.0611817\pi\) | ||||
−0.981585 | + | 0.191027i | \(0.938818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −63.2357 | −0.181191 | −0.0905956 | − | 0.995888i | \(-0.528877\pi\) | ||||
−0.0905956 | + | 0.995888i | \(0.528877\pi\) | |||||||
\(350\) | − 300.618i | − 0.858908i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 487.270i | 1.38037i | 0.723634 | + | 0.690184i | \(0.242470\pi\) | ||||
−0.723634 | + | 0.690184i | \(0.757530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 69.8756 | 0.196833 | ||||||||
\(356\) | − 236.857i | − 0.665327i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −275.266 | −0.768901 | ||||||||
\(359\) | 626.527i | 1.74520i | 0.488434 | + | 0.872601i | \(0.337568\pi\) | ||||
−0.488434 | + | 0.872601i | \(0.662432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −265.138 | −0.734455 | ||||||||
\(362\) | 65.4410i | 0.180776i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 200.979 | 0.552141 | ||||||||
\(365\) | 12.2421i | 0.0335400i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −194.966 | −0.531242 | −0.265621 | − | 0.964078i | \(-0.585577\pi\) | ||||
−0.265621 | + | 0.964078i | \(0.585577\pi\) | |||||||
\(368\) | 83.4140i | 0.226668i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.3405 | 0.0441636 | ||||||||
\(371\) | 856.713i | 2.30920i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −602.195 | −1.61446 | −0.807232 | − | 0.590234i | \(-0.799035\pi\) | ||||
−0.807232 | + | 0.590234i | \(0.799035\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −568.244 | −1.51129 | ||||||||
\(377\) | 150.248i | 0.398536i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −334.138 | −0.881631 | −0.440815 | − | 0.897598i | \(-0.645311\pi\) | ||||
−0.440815 | + | 0.897598i | \(0.645311\pi\) | |||||||
\(380\) | 15.6128i | 0.0410863i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 130.962 | 0.342832 | ||||||||
\(383\) | − 310.225i | − 0.809987i | −0.914320 | − | 0.404993i | \(-0.867274\pi\) | ||||
0.914320 | − | 0.404993i | \(-0.132726\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 87.2131i | 0.225941i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −304.586 | −0.785016 | ||||||||
\(389\) | 413.609i | 1.06326i | 0.846976 | + | 0.531631i | \(0.178421\pi\) | ||||
−0.846976 | + | 0.531631i | \(0.821579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 522.970 | 1.33752 | ||||||||
\(392\) | − 253.371i | − 0.646354i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −49.3590 | −0.125277 | ||||||||
\(395\) | 64.0279i | 0.162096i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −375.414 | −0.945627 | −0.472813 | − | 0.881163i | \(-0.656762\pi\) | ||||
−0.472813 | + | 0.881163i | \(0.656762\pi\) | |||||||
\(398\) | 393.430i | 0.988518i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −81.3236 | −0.203309 | ||||||||
\(401\) | 415.750i | 1.03678i | 0.855144 | + | 0.518391i | \(0.173469\pi\) | ||||
−0.855144 | + | 0.518391i | \(0.826531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −205.272 | −0.509359 | ||||||||
\(404\) | − 130.968i | − 0.324179i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 170.497 | 0.419943 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 492.787 | 1.20486 | 0.602429 | − | 0.798173i | \(-0.294200\pi\) | ||||
0.602429 | + | 0.798173i | \(0.294200\pi\) | |||||||
\(410\) | 66.6626i | 0.162592i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −94.5862 | −0.229578 | ||||||||
\(413\) | − 75.4583i | − 0.182708i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −75.7074 | −0.182427 | ||||||||
\(416\) | − 315.521i | − 0.758464i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 703.323i | 1.67857i | 0.543688 | + | 0.839287i | \(0.317027\pi\) | ||||
−0.543688 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −220.255 | −0.523171 | −0.261586 | − | 0.965180i | \(-0.584245\pi\) | ||||
−0.261586 | + | 0.965180i | \(0.584245\pi\) | |||||||
\(422\) | 124.256i | 0.294446i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 811.396 | 1.91367 | ||||||||
\(425\) | 509.864i | 1.19968i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 830.759 | 1.94557 | ||||||||
\(428\) | − 244.633i | − 0.571572i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −79.4001 | −0.184651 | ||||||||
\(431\) | 244.032i | 0.566198i | 0.959091 | + | 0.283099i | \(0.0913626\pi\) | ||||
−0.959091 | + | 0.283099i | \(0.908637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 226.621 | 0.523374 | 0.261687 | − | 0.965153i | \(-0.415721\pi\) | ||||
0.261687 | + | 0.965153i | \(0.415721\pi\) | |||||||
\(434\) | 232.936i | 0.536719i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 235.353 | 0.539801 | ||||||||
\(437\) | − 245.178i | − 0.561047i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 192.138 | 0.437672 | 0.218836 | − | 0.975762i | \(-0.429774\pi\) | ||||
0.218836 | + | 0.975762i | \(0.429774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 313.782 | 0.709914 | ||||||||
\(443\) | − 535.597i | − 1.20902i | −0.796597 | − | 0.604511i | \(-0.793368\pi\) | ||||
0.796597 | − | 0.604511i | \(-0.206632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 87.0691 | 0.195661 | ||||||||
\(446\) | − 24.2550i | − 0.0543833i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −476.534 | −1.06369 | ||||||||
\(449\) | 83.0972i | 0.185072i | 0.995709 | + | 0.0925358i | \(0.0294973\pi\) | ||||
−0.995709 | + | 0.0925358i | \(0.970503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 309.274i | − 0.684236i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 39.2968 | 0.0865568 | ||||||||
\(455\) | 73.8806i | 0.162375i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −430.449 | −0.941901 | −0.470951 | − | 0.882160i | \(-0.656089\pi\) | ||||
−0.470951 | + | 0.882160i | \(0.656089\pi\) | |||||||
\(458\) | − 263.082i | − 0.574415i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 39.9315 | 0.0868076 | ||||||||
\(461\) | 713.044i | 1.54673i | 0.633959 | + | 0.773367i | \(0.281429\pi\) | ||||
−0.633959 | + | 0.773367i | \(0.718571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4138 | 0.0548894 | 0.0274447 | − | 0.999623i | \(-0.491263\pi\) | ||||
0.0274447 | + | 0.999623i | \(0.491263\pi\) | |||||||
\(464\) | − 46.1232i | − 0.0994034i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 248.117 | 0.532440 | ||||||||
\(467\) | − 242.757i | − 0.519823i | −0.965632 | − | 0.259911i | \(-0.916307\pi\) | ||||
0.965632 | − | 0.259911i | \(-0.0836933\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 718.788 | 1.53260 | ||||||||
\(470\) | − 71.5241i | − 0.152179i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −71.4669 | −0.151413 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 239.033 | 0.503228 | ||||||||
\(476\) | 386.812i | 0.812629i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −550.380 | −1.15142 | ||||||||
\(479\) | 160.953i | 0.336019i | 0.985785 | + | 0.168009i | \(0.0537339\pi\) | ||||
−0.985785 | + | 0.168009i | \(0.946266\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 167.256 | 0.347725 | ||||||||
\(482\) | − 342.289i | − 0.710143i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 111.967i | − 0.230859i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 244.138 | 0.501310 | 0.250655 | − | 0.968076i | \(-0.419354\pi\) | ||||
0.250655 | + | 0.968076i | \(0.419354\pi\) | |||||||
\(488\) | − 786.816i | − 1.61233i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 31.8914 | 0.0650845 | ||||||||
\(491\) | − 207.697i | − 0.423007i | −0.977377 | − | 0.211504i | \(-0.932164\pi\) | ||||
0.977377 | − | 0.211504i | \(-0.0678360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −289.172 | −0.586557 | ||||||||
\(494\) | − 147.107i | − 0.297786i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 63.0143 | 0.127045 | ||||||||
\(497\) | − 811.611i | − 1.63302i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −548.000 | −1.09820 | −0.549098 | − | 0.835758i | \(-0.685029\pi\) | ||||
−0.549098 | + | 0.835758i | \(0.685029\pi\) | |||||||
\(500\) | 78.7964i | 0.157593i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −105.742 | −0.210641 | ||||||||
\(503\) | − 229.498i | − 0.456258i | −0.973631 | − | 0.228129i | \(-0.926739\pi\) | ||||
0.973631 | − | 0.228129i | \(-0.0732607\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.1442 | 0.0953351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −187.425 | −0.368947 | ||||||||
\(509\) | 6.51047i | 0.0127907i | 0.999980 | + | 0.00639535i | \(0.00203572\pi\) | ||||
−0.999980 | + | 0.00639535i | \(0.997964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 142.193 | 0.278264 | ||||||||
\(512\) | 209.081i | 0.408362i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 541.741 | 1.05397 | ||||||||
\(515\) | − 34.7701i | − 0.0675148i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 189.797i | − 0.366403i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 69.9726 | 0.134563 | ||||||||
\(521\) | 478.716i | 0.918841i | 0.888219 | + | 0.459420i | \(0.151943\pi\) | ||||
−0.888219 | + | 0.459420i | \(0.848057\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −781.936 | −1.49510 | −0.747549 | − | 0.664207i | \(-0.768769\pi\) | ||||
−0.747549 | + | 0.664207i | \(0.768769\pi\) | |||||||
\(524\) | 130.968i | 0.249939i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 375.607 | 0.714081 | ||||||||
\(527\) | − 395.072i | − 0.749663i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −98.0691 | −0.185386 | ||||||||
\(530\) | 102.129i | 0.192697i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 181.344 | 0.340873 | ||||||||
\(533\) | 682.334i | 1.28018i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 89.9277 | 0.168089 | ||||||||
\(536\) | − 680.767i | − 1.27009i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 390.725 | 0.726254 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −646.572 | −1.19514 | −0.597571 | − | 0.801816i | \(-0.703867\pi\) | ||||
−0.597571 | + | 0.801816i | \(0.703867\pi\) | |||||||
\(542\) | − 103.360i | − 0.190701i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 607.262 | 1.11629 | ||||||||
\(545\) | 86.5165i | 0.158746i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −269.743 | −0.493131 | −0.246566 | − | 0.969126i | \(-0.579302\pi\) | ||||
−0.246566 | + | 0.969126i | \(0.579302\pi\) | |||||||
\(548\) | − 60.1283i | − 0.109723i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 135.569i | 0.246042i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 743.690 | 1.34483 | ||||||||
\(554\) | − 368.159i | − 0.664547i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −513.179 | −0.922983 | ||||||||
\(557\) | − 302.521i | − 0.543125i | −0.962421 | − | 0.271563i | \(-0.912460\pi\) | ||||
0.962421 | − | 0.271563i | \(-0.0875404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −812.711 | −1.45387 | ||||||||
\(560\) | − 22.6799i | − 0.0404997i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 510.448 | 0.908271 | ||||||||
\(563\) | 9.45383i | 0.0167919i | 0.999965 | + | 0.00839594i | \(0.00267254\pi\) | ||||
−0.999965 | + | 0.00839594i | \(0.997327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 113.690 | 0.201221 | ||||||||
\(566\) | − 429.969i | − 0.759663i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −768.681 | −1.35331 | ||||||||
\(569\) | − 91.7208i | − 0.161196i | −0.996747 | − | 0.0805982i | \(-0.974317\pi\) | ||||
0.996747 | − | 0.0805982i | \(-0.0256831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3533 | −0.0671687 | −0.0335843 | − | 0.999436i | \(-0.510692\pi\) | ||||
−0.0335843 | + | 0.999436i | \(0.510692\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 774.292 | 1.34894 | ||||||||
\(575\) | − 611.355i | − 1.06323i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −486.241 | −0.842706 | −0.421353 | − | 0.906897i | \(-0.638445\pi\) | ||||
−0.421353 | + | 0.906897i | \(0.638445\pi\) | |||||||
\(578\) | 203.753i | 0.352514i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −22.0798 | −0.0380687 | ||||||||
\(581\) | 879.349i | 1.51351i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 134.672i | − 0.230602i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −549.256 | −0.937296 | ||||||||
\(587\) | − 23.6025i | − 0.0402087i | −0.999798 | − | 0.0201044i | \(-0.993600\pi\) | ||||
0.999798 | − | 0.0201044i | \(-0.00639985\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −185.217 | −0.314460 | ||||||||
\(590\) | − 8.99544i | − 0.0152465i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −51.3442 | −0.0867300 | ||||||||
\(593\) | − 58.4893i | − 0.0986329i | −0.998783 | − | 0.0493165i | \(-0.984296\pi\) | ||||
0.998783 | − | 0.0493165i | \(-0.0157043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −142.193 | −0.238980 | ||||||||
\(596\) | − 450.582i | − 0.756010i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −376.241 | −0.629166 | ||||||||
\(599\) | − 570.460i | − 0.952353i | −0.879350 | − | 0.476177i | \(-0.842022\pi\) | ||||
0.879350 | − | 0.476177i | \(-0.157978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1017.38 | −1.69281 | −0.846404 | − | 0.532542i | \(-0.821237\pi\) | ||||
−0.846404 | + | 0.532542i | \(0.821237\pi\) | |||||||
\(602\) | 922.240i | 1.53196i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 155.473 | 0.257405 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −481.125 | −0.792628 | −0.396314 | − | 0.918115i | \(-0.629711\pi\) | ||||
−0.396314 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(608\) | − 284.695i | − 0.468249i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 99.0354 | 0.162353 | ||||||||
\(611\) | − 732.095i | − 1.19819i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 179.727 | 0.293193 | 0.146597 | − | 0.989196i | \(-0.453168\pi\) | ||||
0.146597 | + | 0.989196i | \(0.453168\pi\) | |||||||
\(614\) | 513.555i | 0.836409i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 972.784i | − 1.57664i | −0.615268 | − | 0.788318i | \(-0.710952\pi\) | ||||
0.615268 | − | 0.788318i | \(-0.289048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 236.497 | 0.382062 | 0.191031 | − | 0.981584i | \(-0.438817\pi\) | ||||
0.191031 | + | 0.981584i | \(0.438817\pi\) | |||||||
\(620\) | − 30.1659i | − 0.0486546i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 214.624 | 0.345054 | ||||||||
\(623\) | − 1011.32i | − 1.62330i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 581.380 | 0.930207 | ||||||||
\(626\) | 541.157i | 0.864468i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 315.862 | 0.502965 | ||||||||
\(629\) | 321.906i | 0.511774i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 612.931 | 0.971364 | 0.485682 | − | 0.874135i | \(-0.338571\pi\) | ||||
0.485682 | + | 0.874135i | \(0.338571\pi\) | |||||||
\(632\) | − 704.352i | − 1.11448i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −255.746 | −0.403384 | ||||||||
\(635\) | − 68.8979i | − 0.108501i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 326.429 | 0.512447 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32.2424 | 0.0503787 | ||||||||
\(641\) | 100.390i | 0.156614i | 0.996929 | + | 0.0783072i | \(0.0249515\pi\) | ||||
−0.996929 | + | 0.0783072i | \(0.975049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1129.10 | 1.75599 | 0.877997 | − | 0.478667i | \(-0.158880\pi\) | ||||
0.877997 | + | 0.478667i | \(0.158880\pi\) | |||||||
\(644\) | − 463.808i | − 0.720199i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 283.126 | 0.438276 | ||||||||
\(647\) | 607.210i | 0.938500i | 0.883065 | + | 0.469250i | \(0.155476\pi\) | ||||
−0.883065 | + | 0.469250i | \(0.844524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 366.813i | − 0.564327i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −185.725 | −0.284854 | ||||||||
\(653\) | 219.471i | 0.336097i | 0.985779 | + | 0.168049i | \(0.0537466\pi\) | ||||
−0.985779 | + | 0.168049i | \(0.946253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.1442 | −0.0735026 | ||||||||
\(656\) | − 209.463i | − 0.319303i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −830.759 | −1.26255 | ||||||||
\(659\) | 304.622i | 0.462248i | 0.972924 | + | 0.231124i | \(0.0742403\pi\) | ||||
−0.972924 | + | 0.231124i | \(0.925760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1084.14 | 1.64015 | 0.820074 | − | 0.572257i | \(-0.193932\pi\) | ||||
0.820074 | + | 0.572257i | \(0.193932\pi\) | |||||||
\(662\) | 785.981i | 1.18728i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 832.835 | 1.25427 | ||||||||
\(665\) | 66.6626i | 0.100244i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 346.733 | 0.519840 | ||||||||
\(668\) | 519.795i | 0.778137i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 85.6872 | 0.127891 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1135.22 | −1.68680 | −0.843402 | − | 0.537283i | \(-0.819451\pi\) | ||||
−0.843402 | + | 0.537283i | \(0.819451\pi\) | |||||||
\(674\) | − 114.327i | − 0.169624i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −106.752 | −0.157918 | ||||||||
\(677\) | − 837.328i | − 1.23682i | −0.785855 | − | 0.618410i | \(-0.787777\pi\) | ||||
0.785855 | − | 0.618410i | \(-0.212223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1300.50 | −1.91532 | ||||||||
\(680\) | 134.672i | 0.198046i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 50.7163i | − 0.0742553i | −0.999311 | − | 0.0371276i | \(-0.988179\pi\) | ||||
0.999311 | − | 0.0371276i | \(-0.0118208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.1033 | 0.0322676 | ||||||||
\(686\) | 232.936i | 0.339557i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 249.486 | 0.362625 | ||||||||
\(689\) | 1045.36i | 1.51721i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1090.28 | −1.57782 | −0.788912 | − | 0.614506i | \(-0.789355\pi\) | ||||
−0.788912 | + | 0.614506i | \(0.789355\pi\) | |||||||
\(692\) | 347.498i | 0.502165i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 183.566 | 0.264504 | ||||||||
\(695\) | − 188.646i | − 0.271433i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1313.24 | −1.88413 | ||||||||
\(698\) | 87.5590i | 0.125443i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 452.185 | 0.645979 | ||||||||
\(701\) | − 919.595i | − 1.31183i | −0.754834 | − | 0.655916i | \(-0.772282\pi\) | ||||
0.754834 | − | 0.655916i | \(-0.227718\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 150.915 | 0.214673 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 674.695 | 0.955659 | ||||||||
\(707\) | − 559.200i | − 0.790947i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −185.159 | −0.261155 | −0.130577 | − | 0.991438i | \(-0.541683\pi\) | ||||
−0.130577 | + | 0.991438i | \(0.541683\pi\) | |||||||
\(710\) | − 96.7528i | − 0.136271i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −957.821 | −1.34525 | ||||||||
\(713\) | 473.713i | 0.664394i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − 414.052i | − 0.578285i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 867.517 | 1.20824 | ||||||||
\(719\) | − 891.760i | − 1.24028i | −0.784492 | − | 0.620139i | \(-0.787076\pi\) | ||||
0.784492 | − | 0.620139i | \(-0.212924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −403.858 | −0.560136 | ||||||||
\(722\) | 367.122i | 0.508479i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −98.4355 | −0.135961 | ||||||||
\(725\) | 338.044i | 0.466268i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −410.000 | −0.563961 | −0.281981 | − | 0.959420i | \(-0.590991\pi\) | ||||
−0.281981 | + | 0.959420i | \(0.590991\pi\) | |||||||
\(728\) | − 812.738i | − 1.11640i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.9509 | 0.0232204 | ||||||||
\(731\) | − 1564.17i | − 2.13977i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −196.716 | −0.268371 | −0.134186 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134186 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(734\) | 269.958i | 0.367790i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −728.140 | −0.989321 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.9934 | 0.0419396 | 0.0209698 | − | 0.999780i | \(-0.493325\pi\) | ||||
0.0209698 | + | 0.999780i | \(0.493325\pi\) | |||||||
\(740\) | 24.5792i | 0.0332152i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1186.24 | 1.59871 | ||||||||
\(743\) | − 712.356i | − 0.958757i | −0.877608 | − | 0.479378i | \(-0.840862\pi\) | ||||
0.877608 | − | 0.479378i | \(-0.159138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 165.635 | 0.222329 | ||||||||
\(746\) | 833.825i | 1.11773i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 1044.52i | − 1.39455i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 787.345 | 1.04840 | 0.524198 | − | 0.851596i | \(-0.324365\pi\) | ||||
0.524198 | + | 0.851596i | \(0.324365\pi\) | |||||||
\(752\) | 224.738i | 0.298854i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 208.040 | 0.275915 | ||||||||
\(755\) | 57.1521i | 0.0756982i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1232.86 | −1.62862 | −0.814308 | − | 0.580433i | \(-0.802883\pi\) | ||||
−0.814308 | + | 0.580433i | \(0.802883\pi\) | |||||||
\(758\) | 462.662i | 0.610372i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 63.1364 | 0.0830742 | ||||||||
\(761\) | 763.225i | 1.00292i | 0.865180 | + | 0.501462i | \(0.167204\pi\) | ||||
−0.865180 | + | 0.501462i | \(0.832796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1004.90 | 1.31703 | ||||||||
\(764\) | 196.991i | 0.257842i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −429.551 | −0.560771 | ||||||||
\(767\) | − 92.0740i | − 0.120044i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1106.31 | 1.43863 | 0.719314 | − | 0.694685i | \(-0.244456\pi\) | ||||
0.719314 | + | 0.694685i | \(0.244456\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −131.185 | −0.169928 | ||||||||
\(773\) | − 908.828i | − 1.17572i | −0.808964 | − | 0.587858i | \(-0.799972\pi\) | ||||
0.808964 | − | 0.587858i | \(-0.200028\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −461.842 | −0.595925 | ||||||||
\(776\) | 1231.71i | 1.58726i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 572.700 | 0.736119 | ||||||||
\(779\) | 615.671i | 0.790335i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 724.127i | − 0.925993i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −100.207 | −0.127815 | ||||||||
\(785\) | 116.112i | 0.147913i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −434.230 | −0.551754 | −0.275877 | − | 0.961193i | \(-0.588968\pi\) | ||||
−0.275877 | + | 0.961193i | \(0.588968\pi\) | |||||||
\(788\) | − 74.2452i | − 0.0942198i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 88.6558 | 0.112223 | ||||||||
\(791\) | − 1320.52i | − 1.66943i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1013.69 | 1.27830 | ||||||||
\(794\) | 519.814i | 0.654678i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −591.792 | −0.743458 | ||||||||
\(797\) | − 423.314i | − 0.531134i | −0.964092 | − | 0.265567i | \(-0.914441\pi\) | ||||
0.964092 | − | 0.265567i | \(-0.0855591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1409.01 | 1.76347 | ||||||||
\(800\) | − 709.893i | − 0.887366i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 575.665 | 0.717787 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 170.497 | 0.211798 | ||||||||
\(806\) | 284.228i | 0.352640i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −529.620 | −0.655471 | ||||||||
\(809\) | 1192.46i | 1.47400i | 0.675893 | + | 0.736999i | \(0.263758\pi\) | ||||
−0.675893 | + | 0.736999i | \(0.736242\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 244.773 | 0.301816 | 0.150908 | − | 0.988548i | \(-0.451780\pi\) | ||||
0.150908 | + | 0.988548i | \(0.451780\pi\) | |||||||
\(812\) | 256.459i | 0.315837i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 68.2729i | − 0.0837705i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −733.311 | −0.897565 | ||||||||
\(818\) | − 682.334i | − 0.834149i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −100.273 | −0.122284 | ||||||||
\(821\) | 229.039i | 0.278976i | 0.990224 | + | 0.139488i | \(0.0445456\pi\) | ||||
−0.990224 | + | 0.139488i | \(0.955454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1353.31 | 1.64436 | 0.822181 | − | 0.569226i | \(-0.192757\pi\) | ||||
0.822181 | + | 0.569226i | \(0.192757\pi\) | |||||||
\(824\) | 382.496i | 0.464194i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −104.483 | −0.126493 | ||||||||
\(827\) | − 804.077i | − 0.972282i | −0.873880 | − | 0.486141i | \(-0.838404\pi\) | ||||
0.873880 | − | 0.486141i | \(-0.161596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 463.503 | 0.559111 | 0.279556 | − | 0.960129i | \(-0.409813\pi\) | ||||
0.279556 | + | 0.960129i | \(0.409813\pi\) | |||||||
\(830\) | 104.828i | 0.126299i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −581.465 | −0.698877 | ||||||||
\(833\) | 628.256i | 0.754209i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −191.078 | −0.228836 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 973.851 | 1.16211 | ||||||||
\(839\) | − 583.412i | − 0.695366i | −0.937612 | − | 0.347683i | \(-0.886969\pi\) | ||||
0.937612 | − | 0.347683i | \(-0.113031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 649.276 | 0.772029 | ||||||||
\(842\) | 304.975i | 0.362203i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −186.905 | −0.221451 | ||||||||
\(845\) | − 39.2424i | − 0.0464407i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 320.904i | − 0.378425i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 705.980 | 0.830565 | ||||||||
\(851\) | − 385.983i | − 0.453564i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 989.713 | 1.16027 | 0.580136 | − | 0.814519i | \(-0.302999\pi\) | ||||
0.580136 | + | 0.814519i | \(0.302999\pi\) | |||||||
\(854\) | − 1150.31i | − 1.34696i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −989.268 | −1.15569 | ||||||||
\(857\) | − 615.785i | − 0.718535i | −0.933235 | − | 0.359268i | \(-0.883027\pi\) | ||||
0.933235 | − | 0.359268i | \(-0.116973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 892.221 | 1.03867 | 0.519337 | − | 0.854569i | \(-0.326179\pi\) | ||||
0.519337 | + | 0.854569i | \(0.326179\pi\) | |||||||
\(860\) | − 119.433i | − 0.138875i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 337.897 | 0.391992 | ||||||||
\(863\) | 440.382i | 0.510292i | 0.966903 | + | 0.255146i | \(0.0821235\pi\) | ||||
−0.966903 | + | 0.255146i | \(0.917876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −127.741 | −0.147678 | ||||||||
\(866\) | − 313.789i | − 0.362343i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −350.379 | −0.403663 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 877.063 | 1.00696 | ||||||||
\(872\) | − 951.743i | − 1.09145i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −339.483 | −0.388425 | ||||||||
\(875\) | 336.440i | 0.384503i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1472.87 | 1.67944 | 0.839721 | − | 0.543018i | \(-0.182719\pi\) | ||||
0.839721 | + | 0.543018i | \(0.182719\pi\) | |||||||
\(878\) | − 266.043i | − 0.303010i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 581.242i | − 0.659752i | −0.944024 | − | 0.329876i | \(-0.892993\pi\) | ||||
0.944024 | − | 0.329876i | \(-0.107007\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 441.724 | 0.500253 | 0.250127 | − | 0.968213i | \(-0.419528\pi\) | ||||
0.250127 | + | 0.968213i | \(0.419528\pi\) | |||||||
\(884\) | 471.987i | 0.533921i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −741.611 | −0.837033 | ||||||||
\(887\) | − 336.440i | − 0.379301i | −0.981852 | − | 0.189650i | \(-0.939265\pi\) | ||||
0.981852 | − | 0.189650i | \(-0.0607355\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −800.255 | −0.900175 | ||||||||
\(890\) | − 120.560i | − 0.135460i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.4840 | 0.0409014 | ||||||||
\(893\) | − 660.571i | − 0.739721i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 152.207 | 0.170063 | ||||||||
\(896\) | − 374.498i | − 0.417967i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 115.060 | 0.128129 | ||||||||
\(899\) | − 261.936i | − 0.291364i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2011.93 | −2.23300 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1250.67 | −1.38349 | ||||||||
\(905\) | − 36.1851i | − 0.0399836i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1221.59 | 1.34684 | 0.673422 | − | 0.739259i | \(-0.264824\pi\) | ||||
0.673422 | + | 0.739259i | \(0.264824\pi\) | |||||||
\(908\) | 59.1097i | 0.0650988i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 102.298 | 0.112416 | ||||||||
\(911\) | 220.514i | 0.242058i | 0.992649 | + | 0.121029i | \(0.0386193\pi\) | ||||
−0.992649 | + | 0.121029i | \(0.961381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 596.018i | 0.652099i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 395.725 | 0.432014 | ||||||||
\(917\) | 559.200i | 0.609814i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −85.2485 | −0.0927623 | −0.0463811 | − | 0.998924i | \(-0.514769\pi\) | ||||
−0.0463811 | + | 0.998924i | \(0.514769\pi\) | |||||||
\(920\) | − 161.479i | − 0.175520i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 987.312 | 1.07084 | ||||||||
\(923\) | − 990.326i | − 1.07294i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 376.310 | 0.406822 | ||||||||
\(926\) | − 35.1891i | − 0.0380012i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 402.620 | 0.433858 | ||||||||
\(929\) | 908.218i | 0.977630i | 0.872388 | + | 0.488815i | \(0.162571\pi\) | ||||
−0.872388 | + | 0.488815i | \(0.837429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 294.538 | 0.316367 | ||||||||
\(932\) | 373.214i | 0.400445i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −336.132 | −0.359885 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −548.912 | −0.585819 | −0.292909 | − | 0.956140i | \(-0.594623\pi\) | ||||
−0.292909 | + | 0.956140i | \(0.594623\pi\) | |||||||
\(938\) | − 995.265i | − 1.06105i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 107.586 | 0.114453 | ||||||||
\(941\) | − 902.836i | − 0.959443i | −0.877421 | − | 0.479721i | \(-0.840738\pi\) | ||||
0.877421 | − | 0.479721i | \(-0.159262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1574.65 | 1.66983 | ||||||||
\(944\) | 28.2649i | 0.0299416i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 315.809i | 0.333483i | 0.986001 | + | 0.166742i | \(0.0533246\pi\) | ||||
−0.986001 | + | 0.166742i | \(0.946675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 173.503 | 0.182828 | ||||||||
\(950\) | − 330.976i | − 0.348396i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1564.22 | 1.64309 | ||||||||
\(953\) | 1332.76i | 1.39849i | 0.714881 | + | 0.699246i | \(0.246481\pi\) | ||||
−0.714881 | + | 0.699246i | \(0.753519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −72.4144 | −0.0758266 | ||||||||
\(956\) | − 827.874i | − 0.865977i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 222.862 | 0.232633 | ||||||||
\(959\) | − 256.732i | − 0.267708i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −603.138 | −0.627615 | ||||||||
\(962\) | − 231.590i | − 0.240738i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 514.867 | 0.534094 | ||||||||
\(965\) | − 48.2238i | − 0.0499729i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −244.523 | −0.252868 | −0.126434 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126434 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −155.034 | −0.159829 | ||||||||
\(971\) | 1014.99i | 1.04530i | 0.852547 | + | 0.522650i | \(0.175057\pi\) | ||||
−0.852547 | + | 0.522650i | \(0.824943\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2191.14 | −2.25194 | ||||||||
\(974\) | − 338.044i | − 0.347068i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −311.183 | −0.318835 | ||||||||
\(977\) | − 40.6707i | − 0.0416282i | −0.999783 | − | 0.0208141i | \(-0.993374\pi\) | ||||
0.999783 | − | 0.0208141i | \(-0.00662581\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 47.9707i | 0.0489497i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −287.586 | −0.292857 | ||||||||
\(983\) | − 1713.81i | − 1.74345i | −0.489999 | − | 0.871723i | \(-0.663003\pi\) | ||||
0.489999 | − | 0.871723i | \(-0.336997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.2927 | 0.0277083 | ||||||||
\(986\) | 400.401i | 0.406086i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 221.276 | 0.223963 | ||||||||
\(989\) | 1875.52i | 1.89638i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1465.15 | −1.47846 | −0.739229 | − | 0.673454i | \(-0.764810\pi\) | ||||
−0.739229 | + | 0.673454i | \(0.764810\pi\) | |||||||
\(992\) | 550.066i | 0.554502i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1123.79 | −1.13058 | ||||||||
\(995\) | − 217.544i | − 0.218637i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 639.090 | 0.641013 | 0.320506 | − | 0.947246i | \(-0.396147\pi\) | ||||
0.320506 | + | 0.947246i | \(0.396147\pi\) | |||||||
\(998\) | 758.785i | 0.760305i | ||||||||
\(999\) | 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.b.f.485.4 | yes | 8 | |
3.2 | odd | 2 | inner | 1089.3.b.f.485.5 | yes | 8 | |
11.10 | odd | 2 | inner | 1089.3.b.f.485.6 | yes | 8 | |
33.32 | even | 2 | inner | 1089.3.b.f.485.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1089.3.b.f.485.3 | ✓ | 8 | 33.32 | even | 2 | inner | |
1089.3.b.f.485.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1089.3.b.f.485.5 | yes | 8 | 3.2 | odd | 2 | inner | |
1089.3.b.f.485.6 | yes | 8 | 11.10 | odd | 2 | inner |