Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, 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("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.18 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.67 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.51986i | − 1.25993i | −0.776624 | − | 0.629965i | \(-0.783069\pi\) | ||||
0.776624 | − | 0.629965i | \(-0.216931\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.34969 | −0.587422 | ||||||||
\(5\) | 1.17863i | 0.235726i | 0.993030 | + | 0.117863i | \(0.0376043\pi\) | ||||
−0.993030 | + | 0.117863i | \(0.962396\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.92062 | 0.560089 | 0.280044 | − | 0.959987i | \(-0.409651\pi\) | ||||
0.280044 | + | 0.959987i | \(0.409651\pi\) | |||||||
\(8\) | − 4.15855i | − 0.519819i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.96998 | 0.296998 | ||||||||
\(11\) | 0.116151i | 0.0105592i | 0.999986 | + | 0.00527960i | \(0.00168056\pi\) | ||||
−0.999986 | + | 0.00527960i | \(0.998319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.8712 | −1.52855 | −0.764276 | − | 0.644889i | \(-0.776904\pi\) | ||||
−0.764276 | + | 0.644889i | \(0.776904\pi\) | |||||||
\(14\) | − 9.87941i | − 0.705672i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.8777 | −1.24236 | ||||||||
\(17\) | − 4.09340i | − 0.240788i | −0.992726 | − | 0.120394i | \(-0.961584\pi\) | ||||
0.992726 | − | 0.120394i | \(-0.0384158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.981142 | 0.0516391 | 0.0258195 | − | 0.999667i | \(-0.491780\pi\) | ||||
0.0258195 | + | 0.999667i | \(0.491780\pi\) | |||||||
\(20\) | − 2.76941i | − 0.138471i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.292685 | 0.0133038 | ||||||||
\(23\) | − 3.96962i | − 0.172592i | −0.996270 | − | 0.0862961i | \(-0.972497\pi\) | ||||
0.996270 | − | 0.0862961i | \(-0.0275031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.6108 | 0.944433 | ||||||||
\(26\) | 50.0726i | 1.92587i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.21224 | −0.329009 | ||||||||
\(29\) | − 1.24741i | − 0.0430140i | −0.999769 | − | 0.0215070i | \(-0.993154\pi\) | ||||
0.999769 | − | 0.0215070i | \(-0.00684642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50131 | −0.0484294 | −0.0242147 | − | 0.999707i | \(-0.507709\pi\) | ||||
−0.0242147 | + | 0.999707i | \(0.507709\pi\) | |||||||
\(32\) | 33.4548i | 1.04546i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.3148 | −0.303376 | ||||||||
\(35\) | 4.62096i | 0.132027i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −62.1179 | −1.67886 | −0.839430 | − | 0.543467i | \(-0.817111\pi\) | ||||
−0.839430 | + | 0.543467i | \(0.817111\pi\) | |||||||
\(38\) | − 2.47234i | − 0.0650616i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.90139 | 0.122535 | ||||||||
\(41\) | − 55.0004i | − 1.34147i | −0.741695 | − | 0.670737i | \(-0.765978\pi\) | ||||
0.741695 | − | 0.670737i | \(-0.234022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −48.4928 | −1.12774 | −0.563870 | − | 0.825863i | \(-0.690688\pi\) | ||||
−0.563870 | + | 0.825863i | \(0.690688\pi\) | |||||||
\(44\) | − 0.272919i | − 0.00620271i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0029 | −0.217454 | ||||||||
\(47\) | − 61.7325i | − 1.31346i | −0.754127 | − | 0.656729i | \(-0.771940\pi\) | ||||
0.754127 | − | 0.656729i | \(-0.228060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.6287 | −0.686301 | ||||||||
\(50\) | − 59.4960i | − 1.18992i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46.6911 | 0.897906 | ||||||||
\(53\) | − 27.1346i | − 0.511974i | −0.966680 | − | 0.255987i | \(-0.917600\pi\) | ||||
0.966680 | − | 0.255987i | \(-0.0824004\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.136899 | −0.00248907 | ||||||||
\(56\) | − 16.3041i | − 0.291145i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.14329 | −0.0541946 | ||||||||
\(59\) | 58.0100i | 0.983221i | 0.870815 | + | 0.491611i | \(0.163592\pi\) | ||||
−0.870815 | + | 0.491611i | \(0.836408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12498 | 0.116803 | 0.0584015 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0584015 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(62\) | 3.78310i | 0.0610177i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.79062 | 0.0748535 | ||||||||
\(65\) | − 23.4207i | − 0.360319i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −103.496 | −1.54472 | −0.772358 | − | 0.635188i | \(-0.780923\pi\) | ||||
−0.772358 | + | 0.635188i | \(0.780923\pi\) | |||||||
\(68\) | 9.61821i | 0.141444i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.6442 | 0.166345 | ||||||||
\(71\) | 31.8315i | 0.448331i | 0.974551 | + | 0.224166i | \(0.0719657\pi\) | ||||
−0.974551 | + | 0.224166i | \(0.928034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −47.2798 | −0.647668 | −0.323834 | − | 0.946114i | \(-0.604972\pi\) | ||||
−0.323834 | + | 0.946114i | \(0.604972\pi\) | |||||||
\(74\) | 156.528i | 2.11525i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.30538 | −0.0303339 | ||||||||
\(77\) | 0.455385i | 0.00591409i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.9794 | −0.518726 | −0.259363 | − | 0.965780i | \(-0.583513\pi\) | ||||
−0.259363 | + | 0.965780i | \(0.583513\pi\) | |||||||
\(80\) | − 23.4284i | − 0.292856i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −138.593 | −1.69016 | ||||||||
\(83\) | 93.8255i | 1.13043i | 0.824945 | + | 0.565214i | \(0.191206\pi\) | ||||
−0.824945 | + | 0.565214i | \(0.808794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82460 | 0.0567600 | ||||||||
\(86\) | 122.195i | 1.42087i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.483021 | 0.00548887 | ||||||||
\(89\) | − 92.6845i | − 1.04140i | −0.853740 | − | 0.520700i | \(-0.825671\pi\) | ||||
0.853740 | − | 0.520700i | \(-0.174329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −77.9074 | −0.856125 | ||||||||
\(92\) | 9.32737i | 0.101385i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −155.557 | −1.65486 | ||||||||
\(95\) | 1.15640i | 0.0121727i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 156.948 | 1.61802 | 0.809008 | − | 0.587797i | \(-0.200005\pi\) | ||||
0.809008 | + | 0.587797i | \(0.200005\pi\) | |||||||
\(98\) | 84.7396i | 0.864690i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −55.4781 | −0.554781 | ||||||||
\(101\) | 88.0834i | 0.872113i | 0.899919 | + | 0.436057i | \(0.143625\pi\) | ||||
−0.899919 | + | 0.436057i | \(0.856375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −24.6377 | −0.239201 | −0.119600 | − | 0.992822i | \(-0.538161\pi\) | ||||
−0.119600 | + | 0.992822i | \(0.538161\pi\) | |||||||
\(104\) | 82.6353i | 0.794570i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −68.3754 | −0.645051 | ||||||||
\(107\) | − 53.5903i | − 0.500844i | −0.968137 | − | 0.250422i | \(-0.919431\pi\) | ||||
0.968137 | − | 0.250422i | \(-0.0805693\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −110.122 | −1.01029 | −0.505147 | − | 0.863033i | \(-0.668562\pi\) | ||||
−0.505147 | + | 0.863033i | \(0.668562\pi\) | |||||||
\(110\) | 0.344966i | 0.00313606i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −77.9330 | −0.695830 | ||||||||
\(113\) | 117.149i | 1.03672i | 0.855164 | + | 0.518358i | \(0.173456\pi\) | ||||
−0.855164 | + | 0.518358i | \(0.826544\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.67871 | 0.0406844 | ||||||||
\(116\) | 2.93102i | 0.0252674i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 146.177 | 1.23879 | ||||||||
\(119\) | − 16.0487i | − 0.134863i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.987 | 0.999889 | ||||||||
\(122\) | − 17.9539i | − 0.147163i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.52762 | 0.0284485 | ||||||||
\(125\) | 57.2941i | 0.458353i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2694 | −0.0887357 | ||||||||
\(128\) | 121.748i | 0.951154i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −59.0170 | −0.453977 | ||||||||
\(131\) | − 213.224i | − 1.62766i | −0.581100 | − | 0.813832i | \(-0.697378\pi\) | ||||
0.581100 | − | 0.813832i | \(-0.302622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.84669 | 0.0289225 | ||||||||
\(134\) | 260.795i | 1.94623i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.0226 | −0.125166 | ||||||||
\(137\) | − 92.6280i | − 0.676117i | −0.941125 | − | 0.338058i | \(-0.890230\pi\) | ||||
0.941125 | − | 0.338058i | \(-0.109770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −46.4344 | −0.334060 | −0.167030 | − | 0.985952i | \(-0.553418\pi\) | ||||
−0.167030 | + | 0.985952i | \(0.553418\pi\) | |||||||
\(140\) | − 10.8578i | − 0.0775558i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 80.2109 | 0.564866 | ||||||||
\(143\) | − 2.30806i | − 0.0161403i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.47023 | 0.0101395 | ||||||||
\(146\) | 119.138i | 0.816016i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 145.958 | 0.986200 | ||||||||
\(149\) | − 139.438i | − 0.935824i | −0.883775 | − | 0.467912i | \(-0.845006\pi\) | ||||
0.883775 | − | 0.467912i | \(-0.154994\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 281.925 | 1.86705 | 0.933526 | − | 0.358510i | \(-0.116715\pi\) | ||||
0.933526 | + | 0.358510i | \(0.116715\pi\) | |||||||
\(152\) | − 4.08013i | − 0.0268430i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.14751 | 0.00745134 | ||||||||
\(155\) | − 1.76949i | − 0.0114161i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −89.4645 | −0.569837 | −0.284919 | − | 0.958552i | \(-0.591967\pi\) | ||||
−0.284919 | + | 0.958552i | \(0.591967\pi\) | |||||||
\(158\) | 103.262i | 0.653559i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −39.4308 | −0.246443 | ||||||||
\(161\) | − 15.5634i | − 0.0966669i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −89.8376 | −0.551151 | −0.275575 | − | 0.961279i | \(-0.588868\pi\) | ||||
−0.275575 | + | 0.961279i | \(0.588868\pi\) | |||||||
\(164\) | 129.234i | 0.788012i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 236.427 | 1.42426 | ||||||||
\(167\) | 216.719i | 1.29772i | 0.760908 | + | 0.648860i | \(0.224754\pi\) | ||||
−0.760908 | + | 0.648860i | \(0.775246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 225.864 | 1.33647 | ||||||||
\(170\) | − 12.1573i | − 0.0715135i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 113.943 | 0.662460 | ||||||||
\(173\) | − 147.874i | − 0.854763i | −0.904071 | − | 0.427382i | \(-0.859436\pi\) | ||||
0.904071 | − | 0.427382i | \(-0.140564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 92.5691 | 0.528967 | ||||||||
\(176\) | − 2.30882i | − 0.0131183i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −233.552 | −1.31209 | ||||||||
\(179\) | − 18.6836i | − 0.104378i | −0.998637 | − | 0.0521888i | \(-0.983380\pi\) | ||||
0.998637 | − | 0.0521888i | \(-0.0166198\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.48027 | −0.0302777 | −0.0151389 | − | 0.999885i | \(-0.504819\pi\) | ||||
−0.0151389 | + | 0.999885i | \(0.504819\pi\) | |||||||
\(182\) | 196.316i | 1.07866i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.5079 | −0.0897167 | ||||||||
\(185\) | − 73.2139i | − 0.395751i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.475453 | 0.00254253 | ||||||||
\(188\) | 145.052i | 0.771554i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.91397 | 0.0153367 | ||||||||
\(191\) | 230.705i | 1.20788i | 0.797029 | + | 0.603941i | \(0.206404\pi\) | ||||
−0.797029 | + | 0.603941i | \(0.793596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −232.264 | −1.20344 | −0.601721 | − | 0.798706i | \(-0.705518\pi\) | ||||
−0.601721 | + | 0.798706i | \(0.705518\pi\) | |||||||
\(194\) | − 395.486i | − 2.03859i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 79.0171 | 0.403148 | ||||||||
\(197\) | − 46.5025i | − 0.236053i | −0.993010 | − | 0.118027i | \(-0.962343\pi\) | ||||
0.993010 | − | 0.118027i | \(-0.0376568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 230.998 | 1.16079 | 0.580397 | − | 0.814334i | \(-0.302897\pi\) | ||||
0.580397 | + | 0.814334i | \(0.302897\pi\) | |||||||
\(200\) | − 98.1868i | − 0.490934i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 221.958 | 1.09880 | ||||||||
\(203\) | − 4.89061i | − 0.0240917i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 64.8251 | 0.316220 | ||||||||
\(206\) | 62.0835i | 0.301376i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 394.994 | 1.89901 | ||||||||
\(209\) | 0.113961i | 0 0.000545267i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −132.024 | −0.625704 | −0.312852 | − | 0.949802i | \(-0.601284\pi\) | ||||
−0.312852 | + | 0.949802i | \(0.601284\pi\) | |||||||
\(212\) | 63.7579i | 0.300745i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −135.040 | −0.631028 | ||||||||
\(215\) | − 57.1550i | − 0.265837i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.88608 | −0.0271248 | ||||||||
\(218\) | 277.492i | 1.27290i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.321670 | 0.00146214 | ||||||||
\(221\) | 81.3407i | 0.368057i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −268.297 | −1.20312 | −0.601562 | − | 0.798826i | \(-0.705455\pi\) | ||||
−0.601562 | + | 0.798826i | \(0.705455\pi\) | |||||||
\(224\) | 131.164i | 0.585553i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 295.199 | 1.30619 | ||||||||
\(227\) | 104.979i | 0.462461i | 0.972899 | + | 0.231231i | \(0.0742752\pi\) | ||||
−0.972899 | + | 0.231231i | \(0.925725\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −146.937 | −0.641647 | −0.320823 | − | 0.947139i | \(-0.603960\pi\) | ||||
−0.320823 | + | 0.947139i | \(0.603960\pi\) | |||||||
\(230\) | − 11.7897i | − 0.0512595i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.18740 | −0.0223595 | ||||||||
\(233\) | 96.9595i | 0.416135i | 0.978114 | + | 0.208068i | \(0.0667174\pi\) | ||||
−0.978114 | + | 0.208068i | \(0.933283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.7597 | 0.309616 | ||||||||
\(236\) | − 136.306i | − 0.577566i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −40.4404 | −0.169918 | ||||||||
\(239\) | − 198.906i | − 0.832244i | −0.909309 | − | 0.416122i | \(-0.863389\pi\) | ||||
0.909309 | − | 0.416122i | \(-0.136611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 264.284 | 1.09661 | 0.548307 | − | 0.836277i | \(-0.315273\pi\) | ||||
0.548307 | + | 0.836277i | \(0.315273\pi\) | |||||||
\(242\) | − 304.869i | − 1.25979i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.7415 | −0.0686126 | ||||||||
\(245\) | − 39.6358i | − 0.161779i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.4965 | −0.0789330 | ||||||||
\(248\) | 6.24328i | 0.0251745i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 144.373 | 0.577492 | ||||||||
\(251\) | − 31.6442i | − 0.126073i | −0.998011 | − | 0.0630363i | \(-0.979922\pi\) | ||||
0.998011 | − | 0.0630363i | \(-0.0200784\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.461076 | 0.00182244 | ||||||||
\(254\) | 28.3974i | 0.111801i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 325.949 | 1.27324 | ||||||||
\(257\) | − 345.962i | − 1.34615i | −0.739572 | − | 0.673077i | \(-0.764972\pi\) | ||||
0.739572 | − | 0.673077i | \(-0.235028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −243.541 | −0.940311 | ||||||||
\(260\) | 55.0315i | 0.211659i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −537.294 | −2.05074 | ||||||||
\(263\) | − 263.188i | − 1.00071i | −0.865819 | − | 0.500357i | \(-0.833202\pi\) | ||||
0.865819 | − | 0.500357i | \(-0.166798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.9816 | 0.120685 | ||||||||
\(266\) | − 9.69311i | − 0.0364403i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 243.183 | 0.907400 | ||||||||
\(269\) | 412.009i | 1.53163i | 0.643059 | + | 0.765816i | \(0.277665\pi\) | ||||
−0.643059 | + | 0.765816i | \(0.722335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −339.138 | −1.25143 | −0.625716 | − | 0.780051i | \(-0.715193\pi\) | ||||
−0.625716 | + | 0.780051i | \(0.715193\pi\) | |||||||
\(272\) | 81.3674i | 0.299145i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −233.410 | −0.851860 | ||||||||
\(275\) | 2.74243i | 0.00997246i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 345.943 | 1.24889 | 0.624447 | − | 0.781068i | \(-0.285325\pi\) | ||||
0.624447 | + | 0.781068i | \(0.285325\pi\) | |||||||
\(278\) | 117.008i | 0.420892i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.2165 | 0.0686303 | ||||||||
\(281\) | − 531.371i | − 1.89100i | −0.325621 | − | 0.945500i | \(-0.605573\pi\) | ||||
0.325621 | − | 0.945500i | \(-0.394427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 168.014 | 0.593689 | 0.296844 | − | 0.954926i | \(-0.404066\pi\) | ||||
0.296844 | + | 0.954926i | \(0.404066\pi\) | |||||||
\(284\) | − 74.7942i | − 0.263360i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.81599 | −0.0203356 | ||||||||
\(287\) | − 215.636i | − 0.751344i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 272.244 | 0.942021 | ||||||||
\(290\) | − 3.70477i | − 0.0127751i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 111.093 | 0.380455 | ||||||||
\(293\) | − 81.2495i | − 0.277302i | −0.990341 | − | 0.138651i | \(-0.955723\pi\) | ||||
0.990341 | − | 0.138651i | \(-0.0442766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −68.3723 | −0.231770 | ||||||||
\(296\) | 258.320i | 0.872703i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −351.363 | −1.17907 | ||||||||
\(299\) | 78.8810i | 0.263816i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −190.122 | −0.631635 | ||||||||
\(302\) | − 710.411i | − 2.35235i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.5029 | −0.0641542 | ||||||||
\(305\) | 8.39770i | 0.0275334i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 65.7639 | 0.214215 | 0.107107 | − | 0.994247i | \(-0.465841\pi\) | ||||
0.107107 | + | 0.994247i | \(0.465841\pi\) | |||||||
\(308\) | − 1.07001i | − 0.00347407i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.45886 | −0.0143834 | ||||||||
\(311\) | − 321.306i | − 1.03314i | −0.856245 | − | 0.516569i | \(-0.827209\pi\) | ||||
0.856245 | − | 0.516569i | \(-0.172791\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −175.188 | −0.559705 | −0.279852 | − | 0.960043i | \(-0.590286\pi\) | ||||
−0.279852 | + | 0.960043i | \(0.590286\pi\) | |||||||
\(314\) | 225.438i | 0.717955i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 96.2888 | 0.304711 | ||||||||
\(317\) | 335.093i | 1.05708i | 0.848909 | + | 0.528538i | \(0.177260\pi\) | ||||
−0.848909 | + | 0.528538i | \(0.822740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.144888 | 0.000454194 0 | ||||||||
\(320\) | 5.64636i | 0.0176449i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −39.2175 | −0.121794 | ||||||||
\(323\) | − 4.01621i | − 0.0124341i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −469.175 | −1.44362 | ||||||||
\(326\) | 226.378i | 0.694411i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −228.722 | −0.697323 | ||||||||
\(329\) | − 242.030i | − 0.735653i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 133.280 | 0.402659 | 0.201330 | − | 0.979524i | \(-0.435474\pi\) | ||||
0.201330 | + | 0.979524i | \(0.435474\pi\) | |||||||
\(332\) | − 220.461i | − 0.664038i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 546.102 | 1.63504 | ||||||||
\(335\) | − 121.983i | − 0.364129i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 303.240 | 0.899822 | 0.449911 | − | 0.893073i | \(-0.351456\pi\) | ||||
0.449911 | + | 0.893073i | \(0.351456\pi\) | |||||||
\(338\) | − 569.145i | − 1.68386i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.3363 | −0.0333421 | ||||||||
\(341\) | − 0.174379i | 0 0.000511376i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −323.956 | −0.944478 | ||||||||
\(344\) | 201.660i | 0.586221i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −372.622 | −1.07694 | ||||||||
\(347\) | 139.489i | 0.401985i | 0.979593 | + | 0.200992i | \(0.0644166\pi\) | ||||
−0.979593 | + | 0.200992i | \(0.935583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 412.489 | 1.18192 | 0.590958 | − | 0.806702i | \(-0.298750\pi\) | ||||
0.590958 | + | 0.806702i | \(0.298750\pi\) | |||||||
\(350\) | − 233.261i | − 0.666461i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.88582 | −0.0110393 | ||||||||
\(353\) | 4.08080i | 0.0115603i | 0.999983 | + | 0.00578016i | \(0.00183989\pi\) | ||||
−0.999983 | + | 0.00578016i | \(0.998160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.5175 | −0.105683 | ||||||||
\(356\) | 217.780i | 0.611741i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −47.0800 | −0.131508 | ||||||||
\(359\) | − 30.4463i | − 0.0848087i | −0.999101 | − | 0.0424044i | \(-0.986498\pi\) | ||||
0.999101 | − | 0.0424044i | \(-0.0135018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −360.037 | −0.997333 | ||||||||
\(362\) | 13.8095i | 0.0381478i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 183.058 | 0.502907 | ||||||||
\(365\) | − 55.7253i | − 0.152672i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 599.427 | 1.63332 | 0.816658 | − | 0.577122i | \(-0.195824\pi\) | ||||
0.816658 | + | 0.577122i | \(0.195824\pi\) | |||||||
\(368\) | 78.9070i | 0.214421i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −184.489 | −0.498618 | ||||||||
\(371\) | − 106.385i | − 0.286751i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 96.8953 | 0.259773 | 0.129886 | − | 0.991529i | \(-0.458539\pi\) | ||||
0.129886 | + | 0.991529i | \(0.458539\pi\) | |||||||
\(374\) | − 1.19807i | − 0.00320341i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −256.718 | −0.682760 | ||||||||
\(377\) | 24.7874i | 0.0657492i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 678.905 | 1.79131 | 0.895653 | − | 0.444753i | \(-0.146709\pi\) | ||||
0.895653 | + | 0.444753i | \(0.146709\pi\) | |||||||
\(380\) | − 2.71719i | − 0.00715049i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 581.345 | 1.52185 | ||||||||
\(383\) | 24.6072i | 0.0642486i | 0.999484 | + | 0.0321243i | \(0.0102272\pi\) | ||||
−0.999484 | + | 0.0321243i | \(0.989773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.536730 | −0.00139410 | ||||||||
\(386\) | 585.273i | 1.51625i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −368.778 | −0.950459 | ||||||||
\(389\) | − 105.592i | − 0.271444i | −0.990747 | − | 0.135722i | \(-0.956665\pi\) | ||||
0.990747 | − | 0.135722i | \(-0.0433353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2492 | −0.0415582 | ||||||||
\(392\) | 139.847i | 0.356752i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −117.180 | −0.297410 | ||||||||
\(395\) | − 48.2995i | − 0.122277i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −656.200 | −1.65290 | −0.826449 | − | 0.563012i | \(-0.809643\pi\) | ||||
−0.826449 | + | 0.563012i | \(0.809643\pi\) | |||||||
\(398\) | − 582.083i | − 1.46252i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −469.330 | −1.17332 | ||||||||
\(401\) | − 458.161i | − 1.14255i | −0.820760 | − | 0.571273i | \(-0.806450\pi\) | ||||
0.820760 | − | 0.571273i | \(-0.193550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.8329 | 0.0740269 | ||||||||
\(404\) | − 206.969i | − 0.512299i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.3236 | −0.0303538 | ||||||||
\(407\) | − 7.21506i | − 0.0177274i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 303.807 | 0.742803 | 0.371402 | − | 0.928472i | \(-0.378877\pi\) | ||||
0.371402 | + | 0.928472i | \(0.378877\pi\) | |||||||
\(410\) | − 163.350i | − 0.398415i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 57.8909 | 0.140512 | ||||||||
\(413\) | 227.435i | 0.550691i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −110.585 | −0.266471 | ||||||||
\(416\) | − 664.787i | − 1.59805i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.287165 | 0.000686998 0 | ||||||||
\(419\) | − 743.246i | − 1.77386i | −0.461906 | − | 0.886929i | \(-0.652834\pi\) | ||||
0.461906 | − | 0.886929i | \(-0.347166\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −487.274 | −1.15742 | −0.578710 | − | 0.815533i | \(-0.696444\pi\) | ||||
−0.578710 | + | 0.815533i | \(0.696444\pi\) | |||||||
\(422\) | 332.681i | 0.788343i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −112.841 | −0.266134 | ||||||||
\(425\) | − 96.6486i | − 0.227408i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.9343 | 0.0654200 | ||||||||
\(428\) | 125.921i | 0.294207i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −144.023 | −0.334936 | ||||||||
\(431\) | − 834.575i | − 1.93637i | −0.250237 | − | 0.968185i | \(-0.580509\pi\) | ||||
0.250237 | − | 0.968185i | \(-0.419491\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −454.402 | −1.04943 | −0.524713 | − | 0.851279i | \(-0.675828\pi\) | ||||
−0.524713 | + | 0.851279i | \(0.675828\pi\) | |||||||
\(434\) | 14.8321i | 0.0341753i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 258.753 | 0.593469 | ||||||||
\(437\) | − 3.89476i | − 0.00891250i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −69.1547 | −0.157528 | −0.0787639 | − | 0.996893i | \(-0.525097\pi\) | ||||
−0.0787639 | + | 0.996893i | \(0.525097\pi\) | |||||||
\(440\) | 0.569302i | 0.00129387i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 204.967 | 0.463726 | ||||||||
\(443\) | − 550.971i | − 1.24373i | −0.783126 | − | 0.621863i | \(-0.786376\pi\) | ||||
0.783126 | − | 0.621863i | \(-0.213624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 109.241 | 0.245485 | ||||||||
\(446\) | 676.070i | 1.51585i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.7822 | 0.0419246 | ||||||||
\(449\) | − 660.419i | − 1.47087i | −0.677597 | − | 0.735433i | \(-0.736979\pi\) | ||||
0.677597 | − | 0.735433i | \(-0.263021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.38837 | 0.0141649 | ||||||||
\(452\) | − 275.263i | − 0.608990i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 264.532 | 0.582669 | ||||||||
\(455\) | − 91.8239i | − 0.201811i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 332.594 | 0.727777 | 0.363888 | − | 0.931443i | \(-0.381449\pi\) | ||||
0.363888 | + | 0.931443i | \(0.381449\pi\) | |||||||
\(458\) | 370.261i | 0.808429i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.9935 | −0.0238989 | ||||||||
\(461\) | 129.547i | 0.281013i | 0.990080 | + | 0.140506i | \(0.0448730\pi\) | ||||
−0.990080 | + | 0.140506i | \(0.955127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.7590 | 0.0577949 | 0.0288975 | − | 0.999582i | \(-0.490800\pi\) | ||||
0.0288975 | + | 0.999582i | \(0.490800\pi\) | |||||||
\(464\) | 24.7956i | 0.0534388i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 244.324 | 0.524301 | ||||||||
\(467\) | − 300.066i | − 0.642540i | −0.946988 | − | 0.321270i | \(-0.895890\pi\) | ||||
0.946988 | − | 0.321270i | \(-0.104110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −405.768 | −0.865178 | ||||||||
\(470\) | − 183.344i | − 0.390094i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 241.238 | 0.511097 | ||||||||
\(473\) | − 5.63250i | − 0.0119080i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.1656 | 0.0487697 | ||||||||
\(476\) | 37.7094i | 0.0792214i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −501.216 | −1.04857 | ||||||||
\(479\) | 34.2241i | 0.0714491i | 0.999362 | + | 0.0357246i | \(0.0113739\pi\) | ||||
−0.999362 | + | 0.0357246i | \(0.988626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1234.36 | 2.56623 | ||||||||
\(482\) | − 665.958i | − 1.38166i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −284.281 | −0.587357 | ||||||||
\(485\) | 184.983i | 0.381408i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 241.028 | 0.494924 | 0.247462 | − | 0.968898i | \(-0.420404\pi\) | ||||
0.247462 | + | 0.968898i | \(0.420404\pi\) | |||||||
\(488\) | − 29.6296i | − 0.0607163i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −99.8766 | −0.203830 | ||||||||
\(491\) | − 221.985i | − 0.452107i | −0.974115 | − | 0.226054i | \(-0.927418\pi\) | ||||
0.974115 | − | 0.226054i | \(-0.0725825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.10613 | −0.0103573 | ||||||||
\(494\) | 49.1283i | 0.0994501i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.8427 | 0.0601667 | ||||||||
\(497\) | 124.799i | 0.251105i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 618.851 | 1.24018 | 0.620091 | − | 0.784530i | \(-0.287096\pi\) | ||||
0.620091 | + | 0.784530i | \(0.287096\pi\) | |||||||
\(500\) | − 134.623i | − 0.269247i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −79.7389 | −0.158843 | ||||||||
\(503\) | − 172.036i | − 0.342020i | −0.985269 | − | 0.171010i | \(-0.945297\pi\) | ||||
0.985269 | − | 0.171010i | \(-0.0547030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −103.818 | −0.205580 | ||||||||
\(506\) | − 1.16185i | − 0.00229614i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.4797 | 0.0521253 | ||||||||
\(509\) | − 592.690i | − 1.16442i | −0.813038 | − | 0.582211i | \(-0.802188\pi\) | ||||
0.813038 | − | 0.582211i | \(-0.197812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −185.366 | −0.362751 | ||||||||
\(512\) | − 334.356i | − 0.653039i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −871.774 | −1.69606 | ||||||||
\(515\) | − 29.0387i | − 0.0563858i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.17030 | 0.0138691 | ||||||||
\(518\) | 613.688i | 1.18473i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −97.3963 | −0.187301 | ||||||||
\(521\) | 622.280i | 1.19439i | 0.802094 | + | 0.597197i | \(0.203719\pi\) | ||||
−0.802094 | + | 0.597197i | \(0.796281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −357.150 | −0.682887 | −0.341443 | − | 0.939902i | \(-0.610916\pi\) | ||||
−0.341443 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(524\) | 501.010i | 0.956126i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −663.195 | −1.26083 | ||||||||
\(527\) | 6.14547i | 0.0116612i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 513.242 | 0.970212 | ||||||||
\(530\) | − 80.5892i | − 0.152055i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.03852 | −0.0169897 | ||||||||
\(533\) | 1092.92i | 2.05051i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 63.1630 | 0.118062 | ||||||||
\(536\) | 430.393i | 0.802972i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1038.21 | 1.92975 | ||||||||
\(539\) | − 3.90602i | − 0.00724678i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −277.130 | −0.512255 | −0.256128 | − | 0.966643i | \(-0.582447\pi\) | ||||
−0.256128 | + | 0.966643i | \(0.582447\pi\) | |||||||
\(542\) | 854.580i | 1.57672i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 136.944 | 0.251735 | ||||||||
\(545\) | − 129.793i | − 0.238152i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 629.328 | 1.15051 | 0.575254 | − | 0.817975i | \(-0.304903\pi\) | ||||
0.575254 | + | 0.817975i | \(0.304903\pi\) | |||||||
\(548\) | 217.647i | 0.397166i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.91053 | 0.0125646 | ||||||||
\(551\) | − 1.22388i | − 0.00222120i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −160.665 | −0.290533 | ||||||||
\(554\) | − 871.729i | − 1.57352i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 109.106 | 0.196234 | ||||||||
\(557\) | 92.7731i | 0.166559i | 0.996526 | + | 0.0832793i | \(0.0265394\pi\) | ||||
−0.996526 | + | 0.0832793i | \(0.973461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 963.610 | 1.72381 | ||||||||
\(560\) | − 91.8541i | − 0.164025i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1338.98 | −2.38253 | ||||||||
\(563\) | − 1037.13i | − 1.84214i | −0.389396 | − | 0.921071i | \(-0.627316\pi\) | ||||
0.389396 | − | 0.921071i | \(-0.372684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −138.075 | −0.244380 | ||||||||
\(566\) | − 423.371i | − 0.748006i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 132.373 | 0.233051 | ||||||||
\(569\) | − 192.618i | − 0.338521i | −0.985571 | − | 0.169260i | \(-0.945862\pi\) | ||||
0.985571 | − | 0.169260i | \(-0.0541379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 447.153 | 0.783105 | 0.391552 | − | 0.920156i | \(-0.371938\pi\) | ||||
0.391552 | + | 0.920156i | \(0.371938\pi\) | |||||||
\(572\) | 5.42323i | 0.00948117i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −543.372 | −0.946641 | ||||||||
\(575\) | − 93.7260i | − 0.163002i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −345.436 | −0.598675 | −0.299338 | − | 0.954147i | \(-0.596766\pi\) | ||||
−0.299338 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(578\) | − 686.017i | − 1.18688i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.45458 | −0.00595617 | ||||||||
\(581\) | 367.854i | 0.633140i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.15172 | 0.00540603 | ||||||||
\(584\) | 196.615i | 0.336670i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −204.737 | −0.349381 | ||||||||
\(587\) | − 459.636i | − 0.783026i | −0.920173 | − | 0.391513i | \(-0.871952\pi\) | ||||
0.920173 | − | 0.391513i | \(-0.128048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47300 | −0.00250085 | ||||||||
\(590\) | 172.289i | 0.292014i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1234.76 | 2.08575 | ||||||||
\(593\) | 782.439i | 1.31946i | 0.751504 | + | 0.659729i | \(0.229329\pi\) | ||||
−0.751504 | + | 0.659729i | \(0.770671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9154 | 0.0317906 | ||||||||
\(596\) | 327.635i | 0.549724i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 198.769 | 0.332390 | ||||||||
\(599\) | 162.105i | 0.270626i | 0.990803 | + | 0.135313i | \(0.0432040\pi\) | ||||
−0.990803 | + | 0.135313i | \(0.956796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −410.144 | −0.682436 | −0.341218 | − | 0.939984i | \(-0.610839\pi\) | ||||
−0.341218 | + | 0.939984i | \(0.610839\pi\) | |||||||
\(602\) | 479.081i | 0.795815i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −662.436 | −1.09675 | ||||||||
\(605\) | 142.598i | 0.235699i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −564.201 | −0.929490 | −0.464745 | − | 0.885444i | \(-0.653854\pi\) | ||||
−0.464745 | + | 0.885444i | \(0.653854\pi\) | |||||||
\(608\) | 32.8240i | 0.0539868i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.1610 | 0.0346902 | ||||||||
\(611\) | 1226.70i | 2.00769i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 842.376 | 1.37419 | 0.687093 | − | 0.726569i | \(-0.258886\pi\) | ||||
0.687093 | + | 0.726569i | \(0.258886\pi\) | |||||||
\(614\) | − 165.716i | − 0.269896i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.89374 | 0.00307425 | ||||||||
\(617\) | 298.792i | 0.484266i | 0.970243 | + | 0.242133i | \(0.0778470\pi\) | ||||
−0.970243 | + | 0.242133i | \(0.922153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 402.914 | 0.650910 | 0.325455 | − | 0.945557i | \(-0.394482\pi\) | ||||
0.325455 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(620\) | 4.15775i | 0.00670605i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −809.646 | −1.30168 | ||||||||
\(623\) | − 363.381i | − 0.583276i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 522.742 | 0.836388 | ||||||||
\(626\) | 441.448i | 0.705189i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 210.214 | 0.334735 | ||||||||
\(629\) | 254.273i | 0.404250i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 617.724 | 0.978960 | 0.489480 | − | 0.872015i | \(-0.337187\pi\) | ||||
0.489480 | + | 0.872015i | \(0.337187\pi\) | |||||||
\(632\) | 170.415i | 0.269644i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 844.388 | 1.33184 | ||||||||
\(635\) | − 13.2825i | − 0.0209173i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 668.243 | 1.04905 | ||||||||
\(638\) | − 0.365097i | 0 0.000572252i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −143.495 | −0.224211 | ||||||||
\(641\) | 871.699i | 1.35991i | 0.733256 | + | 0.679953i | \(0.238000\pi\) | ||||
−0.733256 | + | 0.679953i | \(0.762000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −915.020 | −1.42305 | −0.711524 | − | 0.702661i | \(-0.751995\pi\) | ||||
−0.711524 | + | 0.702661i | \(0.751995\pi\) | |||||||
\(644\) | 36.5691i | 0.0567843i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.1203 | −0.0156661 | ||||||||
\(647\) | − 99.8398i | − 0.154312i | −0.997019 | − | 0.0771559i | \(-0.975416\pi\) | ||||
0.997019 | − | 0.0771559i | \(-0.0245839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.73794 | −0.0103820 | ||||||||
\(650\) | 1182.26i | 1.81885i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 211.090 | 0.323758 | ||||||||
\(653\) | 322.455i | 0.493805i | 0.969040 | + | 0.246903i | \(0.0794128\pi\) | ||||
−0.969040 | + | 0.246903i | \(0.920587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 251.312 | 0.383682 | ||||||||
\(656\) | 1093.28i | 1.66659i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −609.881 | −0.926871 | ||||||||
\(659\) | 1044.59i | 1.58512i | 0.609796 | + | 0.792558i | \(0.291251\pi\) | ||||
−0.609796 | + | 0.792558i | \(0.708749\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −557.410 | −0.843282 | −0.421641 | − | 0.906763i | \(-0.638546\pi\) | ||||
−0.421641 | + | 0.906763i | \(0.638546\pi\) | |||||||
\(662\) | − 335.848i | − 0.507323i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 390.178 | 0.587617 | ||||||||
\(665\) | 4.53382i | 0.00681777i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.95173 | −0.00742388 | ||||||||
\(668\) | − 509.223i | − 0.762310i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −307.381 | −0.458777 | ||||||||
\(671\) | 0.827575i | 0.00123335i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1035.16 | −1.53812 | −0.769062 | − | 0.639174i | \(-0.779276\pi\) | ||||
−0.769062 | + | 0.639174i | \(0.779276\pi\) | |||||||
\(674\) | − 764.122i | − 1.13371i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −530.710 | −0.785074 | ||||||||
\(677\) | − 623.131i | − 0.920430i | −0.887807 | − | 0.460215i | \(-0.847772\pi\) | ||||
0.887807 | − | 0.460215i | \(-0.152228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 615.332 | 0.906233 | ||||||||
\(680\) | − 20.0633i | − 0.0295049i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.439411 | −0.000644298 0 | ||||||||
\(683\) | − 103.181i | − 0.151070i | −0.997143 | − | 0.0755351i | \(-0.975934\pi\) | ||||
0.997143 | − | 0.0755351i | \(-0.0240665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 109.174 | 0.159378 | ||||||||
\(686\) | 816.323i | 1.18998i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 963.927 | 1.40106 | ||||||||
\(689\) | 539.197i | 0.782579i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 326.699 | 0.472791 | 0.236396 | − | 0.971657i | \(-0.424034\pi\) | ||||
0.236396 | + | 0.971657i | \(0.424034\pi\) | |||||||
\(692\) | 347.458i | 0.502107i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 351.492 | 0.506472 | ||||||||
\(695\) | − 54.7289i | − 0.0787466i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −225.139 | −0.323011 | ||||||||
\(698\) | − 1039.41i | − 1.48913i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −217.509 | −0.310727 | ||||||||
\(701\) | 882.429i | 1.25881i | 0.777076 | + | 0.629407i | \(0.216702\pi\) | ||||
−0.777076 | + | 0.629407i | \(0.783298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.9465 | −0.0866948 | ||||||||
\(704\) | 0.556436i | 0 0.000790393i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.2830 | 0.0145652 | ||||||||
\(707\) | 345.342i | 0.488461i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3380 | 0.0413794 | 0.0206897 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206897 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(710\) | 94.5389i | 0.133153i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −385.433 | −0.541339 | ||||||||
\(713\) | 5.95964i | 0.00835854i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.72035 | 0.00380468 | ||||||||
\(716\) | 43.9006i | 0.0613138i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −76.7205 | −0.106853 | ||||||||
\(719\) | 112.619i | 0.156633i | 0.996929 | + | 0.0783163i | \(0.0249544\pi\) | ||||
−0.996929 | + | 0.0783163i | \(0.975046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −96.5950 | −0.133974 | ||||||||
\(722\) | 907.243i | 1.25657i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.8769 | 0.0177858 | ||||||||
\(725\) | − 29.4523i | − 0.0406239i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 60.0874 | 0.0826511 | 0.0413256 | − | 0.999146i | \(-0.486842\pi\) | ||||
0.0413256 | + | 0.999146i | \(0.486842\pi\) | |||||||
\(728\) | 323.982i | 0.445030i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −140.420 | −0.192356 | ||||||||
\(731\) | 198.500i | 0.271546i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 497.573 | 0.678817 | 0.339409 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339409 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(734\) | − 1510.47i | − 2.05786i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 132.803 | 0.180439 | ||||||||
\(737\) | − 12.0212i | − 0.0163110i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 216.118 | 0.292447 | 0.146223 | − | 0.989252i | \(-0.453288\pi\) | ||||
0.146223 | + | 0.989252i | \(0.453288\pi\) | |||||||
\(740\) | 172.030i | 0.232473i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −268.074 | −0.361286 | ||||||||
\(743\) | 1121.65i | 1.50962i | 0.655944 | + | 0.754810i | \(0.272271\pi\) | ||||
−0.655944 | + | 0.754810i | \(0.727729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 164.345 | 0.220598 | ||||||||
\(746\) | − 244.162i | − 0.327296i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.11717 | −0.00149354 | ||||||||
\(749\) | − 210.107i | − 0.280517i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 235.599 | 0.313714 | 0.156857 | − | 0.987621i | \(-0.449864\pi\) | ||||
0.156857 | + | 0.987621i | \(0.449864\pi\) | |||||||
\(752\) | 1227.10i | 1.63178i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 62.4609 | 0.0828393 | ||||||||
\(755\) | 332.285i | 0.440112i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.57579 | −0.00340263 | −0.00170132 | − | 0.999999i | \(-0.500542\pi\) | ||||
−0.00170132 | + | 0.999999i | \(0.500542\pi\) | |||||||
\(758\) | − 1710.75i | − 2.25692i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.80896 | 0.00632758 | ||||||||
\(761\) | 311.007i | 0.408682i | 0.978900 | + | 0.204341i | \(0.0655052\pi\) | ||||
−0.978900 | + | 0.204341i | \(0.934495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −431.747 | −0.565854 | ||||||||
\(764\) | − 542.086i | − 0.709537i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 62.0067 | 0.0809486 | ||||||||
\(767\) | − 1152.73i | − 1.50291i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −794.978 | −1.03378 | −0.516891 | − | 0.856051i | \(-0.672911\pi\) | ||||
−0.516891 | + | 0.856051i | \(0.672911\pi\) | |||||||
\(770\) | 1.35248i | 0.00175647i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 545.749 | 0.706929 | ||||||||
\(773\) | − 319.749i | − 0.413647i | −0.978378 | − | 0.206823i | \(-0.933687\pi\) | ||||
0.978378 | − | 0.206823i | \(-0.0663125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.4472 | −0.0457384 | ||||||||
\(776\) | − 652.675i | − 0.841075i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −266.076 | −0.342000 | ||||||||
\(779\) | − 53.9633i | − 0.0692725i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.69727 | −0.00473402 | ||||||||
\(782\) | 40.9458i | 0.0523603i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 668.462 | 0.852631 | ||||||||
\(785\) | − 105.445i | − 0.134325i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 548.874 | 0.697426 | 0.348713 | − | 0.937230i | \(-0.386619\pi\) | ||||
0.348713 | + | 0.937230i | \(0.386619\pi\) | |||||||
\(788\) | 109.266i | 0.138663i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −121.708 | −0.154061 | ||||||||
\(791\) | 459.296i | 0.580653i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −141.582 | −0.178539 | ||||||||
\(794\) | 1653.53i | 2.08253i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −542.774 | −0.681876 | ||||||||
\(797\) | 362.036i | 0.454249i | 0.973866 | + | 0.227124i | \(0.0729324\pi\) | ||||
−0.973866 | + | 0.227124i | \(0.927068\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −252.696 | −0.316265 | ||||||||
\(800\) | 789.897i | 0.987371i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1154.50 | −1.43953 | ||||||||
\(803\) | − 5.49160i | − 0.00683885i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.3434 | 0.0227869 | ||||||||
\(806\) | − 75.1746i | − 0.0932687i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 366.299 | 0.453341 | ||||||||
\(809\) | 1305.60i | 1.61385i | 0.590655 | + | 0.806924i | \(0.298869\pi\) | ||||
−0.590655 | + | 0.806924i | \(0.701131\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.45607 | 0.00796063 | 0.00398032 | − | 0.999992i | \(-0.498733\pi\) | ||||
0.00398032 | + | 0.999992i | \(0.498733\pi\) | |||||||
\(812\) | 11.4914i | 0.0141520i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.1809 | −0.0223353 | ||||||||
\(815\) | − 105.885i | − 0.129920i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.5784 | −0.0582355 | ||||||||
\(818\) | − 765.550i | − 0.935880i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −152.319 | −0.185755 | ||||||||
\(821\) | 240.575i | 0.293027i | 0.989209 | + | 0.146513i | \(0.0468051\pi\) | ||||
−0.989209 | + | 0.146513i | \(0.953195\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −226.340 | −0.275018 | −0.137509 | − | 0.990501i | \(-0.543910\pi\) | ||||
−0.137509 | + | 0.990501i | \(0.543910\pi\) | |||||||
\(824\) | 102.457i | 0.124341i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 573.105 | 0.693832 | ||||||||
\(827\) | 1086.04i | 1.31323i | 0.754228 | + | 0.656613i | \(0.228012\pi\) | ||||
−0.754228 | + | 0.656613i | \(0.771988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 458.391 | 0.552945 | 0.276473 | − | 0.961022i | \(-0.410835\pi\) | ||||
0.276473 | + | 0.961022i | \(0.410835\pi\) | |||||||
\(830\) | 278.660i | 0.335734i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −95.1953 | −0.114417 | ||||||||
\(833\) | 137.656i | 0.165253i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −255.432 | −0.305906 | ||||||||
\(836\) | − 0.267773i | 0 0.000320302i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1872.88 | −2.23494 | ||||||||
\(839\) | − 770.491i | − 0.918344i | −0.888347 | − | 0.459172i | \(-0.848146\pi\) | ||||
0.888347 | − | 0.459172i | \(-0.151854\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 839.444 | 0.998150 | ||||||||
\(842\) | 1227.86i | 1.45827i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 310.214 | 0.367553 | ||||||||
\(845\) | 266.210i | 0.315041i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 474.342 | 0.560026 | ||||||||
\(848\) | 539.374i | 0.636055i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −243.541 | −0.286519 | ||||||||
\(851\) | 246.584i | 0.289758i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −142.876 | −0.167498 | −0.0837489 | − | 0.996487i | \(-0.526689\pi\) | ||||
−0.0837489 | + | 0.996487i | \(0.526689\pi\) | |||||||
\(854\) | − 70.3906i | − 0.0824246i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −222.858 | −0.260348 | ||||||||
\(857\) | − 905.026i | − 1.05604i | −0.849232 | − | 0.528020i | \(-0.822935\pi\) | ||||
0.849232 | − | 0.528020i | \(-0.177065\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 143.642 | 0.167220 | 0.0836101 | − | 0.996499i | \(-0.473355\pi\) | ||||
0.0836101 | + | 0.996499i | \(0.473355\pi\) | |||||||
\(860\) | 134.297i | 0.156159i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2103.01 | −2.43969 | ||||||||
\(863\) | 915.923i | 1.06132i | 0.847583 | + | 0.530662i | \(0.178057\pi\) | ||||
−0.847583 | + | 0.530662i | \(0.821943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 174.289 | 0.201490 | ||||||||
\(866\) | 1145.03i | 1.32220i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.8305 | 0.0159337 | ||||||||
\(869\) | − 4.75980i | − 0.00547733i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2056.59 | 2.36118 | ||||||||
\(872\) | 457.948i | 0.525170i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.81425 | −0.0112291 | ||||||||
\(875\) | 224.629i | 0.256718i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −172.726 | −0.196951 | −0.0984753 | − | 0.995139i | \(-0.531397\pi\) | ||||
−0.0984753 | + | 0.995139i | \(0.531397\pi\) | |||||||
\(878\) | 174.260i | 0.198474i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.72124 | 0.00309232 | ||||||||
\(881\) | − 383.373i | − 0.435156i | −0.976043 | − | 0.217578i | \(-0.930184\pi\) | ||||
0.976043 | − | 0.217578i | \(-0.0698157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1187.34 | −1.34467 | −0.672334 | − | 0.740248i | \(-0.734708\pi\) | ||||
−0.672334 | + | 0.740248i | \(0.734708\pi\) | |||||||
\(884\) | − 191.125i | − 0.216205i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1388.37 | −1.56701 | ||||||||
\(887\) | − 1142.28i | − 1.28781i | −0.765107 | − | 0.643903i | \(-0.777314\pi\) | ||||
0.765107 | − | 0.643903i | \(-0.222686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.1832 | −0.0496998 | ||||||||
\(890\) | − 275.271i | − 0.309293i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 630.414 | 0.706742 | ||||||||
\(893\) | − 60.5684i | − 0.0678257i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.0210 | 0.0246045 | ||||||||
\(896\) | 477.327i | 0.532731i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1664.16 | −1.85319 | ||||||||
\(899\) | 1.87275i | 0.00208314i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −111.073 | −0.123277 | ||||||||
\(902\) | − 16.0978i | − 0.0178468i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 487.169 | 0.538904 | ||||||||
\(905\) | − 6.45920i | − 0.00713724i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −412.022 | −0.454269 | −0.227135 | − | 0.973863i | \(-0.572936\pi\) | ||||
−0.227135 | + | 0.973863i | \(0.572936\pi\) | |||||||
\(908\) | − 246.667i | − 0.271660i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −231.383 | −0.254267 | ||||||||
\(911\) | 1002.94i | 1.10093i | 0.834859 | + | 0.550464i | \(0.185549\pi\) | ||||
−0.834859 | + | 0.550464i | \(0.814451\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.8979 | −0.0119364 | ||||||||
\(914\) | − 838.090i | − 0.916947i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 345.256 | 0.376918 | ||||||||
\(917\) | − 835.970i | − 0.911636i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1339.72 | −1.45781 | −0.728903 | − | 0.684616i | \(-0.759970\pi\) | ||||
−0.728903 | + | 0.684616i | \(0.759970\pi\) | |||||||
\(920\) | − 19.4566i | − 0.0211485i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 326.440 | 0.354056 | ||||||||
\(923\) | − 632.530i | − 0.685298i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1466.65 | −1.58557 | ||||||||
\(926\) | − 67.4290i | − 0.0728175i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 41.7318 | 0.0449696 | ||||||||
\(929\) | 355.644i | 0.382824i | 0.981510 | + | 0.191412i | \(0.0613067\pi\) | ||||
−0.981510 | + | 0.191412i | \(0.938693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.9946 | −0.0354399 | ||||||||
\(932\) | − 227.825i | − 0.244447i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −756.125 | −0.809556 | ||||||||
\(935\) | 0.560383i | 0 0.000599340i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 548.887 | 0.585792 | 0.292896 | − | 0.956144i | \(-0.405381\pi\) | ||||
0.292896 | + | 0.956144i | \(0.405381\pi\) | |||||||
\(938\) | 1022.48i | 1.09006i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −170.963 | −0.181875 | ||||||||
\(941\) | − 648.277i | − 0.688924i | −0.938800 | − | 0.344462i | \(-0.888061\pi\) | ||||
0.938800 | − | 0.344462i | \(-0.111939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −218.331 | −0.231528 | ||||||||
\(944\) | − 1153.11i | − 1.22151i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.1931 | −0.0150033 | ||||||||
\(947\) | 284.695i | 0.300628i | 0.988638 | + | 0.150314i | \(0.0480285\pi\) | ||||
−0.988638 | + | 0.150314i | \(0.951971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 939.504 | 0.989994 | ||||||||
\(950\) | − 58.3740i | − 0.0614463i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −66.7392 | −0.0701042 | ||||||||
\(953\) | − 159.812i | − 0.167694i | −0.996479 | − | 0.0838468i | \(-0.973279\pi\) | ||||
0.996479 | − | 0.0838468i | \(-0.0267206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −271.916 | −0.284729 | ||||||||
\(956\) | 467.368i | 0.488879i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 86.2400 | 0.0900208 | ||||||||
\(959\) | − 363.159i | − 0.378686i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −958.746 | −0.997655 | ||||||||
\(962\) | − 3110.40i | − 3.23326i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −620.985 | −0.644176 | ||||||||
\(965\) | − 273.753i | − 0.283682i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 487.083 | 0.503705 | 0.251852 | − | 0.967766i | \(-0.418960\pi\) | ||||
0.251852 | + | 0.967766i | \(0.418960\pi\) | |||||||
\(968\) | − 503.128i | − 0.519761i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 466.131 | 0.480547 | ||||||||
\(971\) | − 126.842i | − 0.130630i | −0.997865 | − | 0.0653150i | \(-0.979195\pi\) | ||||
0.997865 | − | 0.0653150i | \(-0.0208052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −182.052 | −0.187103 | ||||||||
\(974\) | − 607.356i | − 0.623569i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −141.628 | −0.145111 | ||||||||
\(977\) | 1131.60i | 1.15824i | 0.815243 | + | 0.579119i | \(0.196604\pi\) | ||||
−0.815243 | + | 0.579119i | \(0.803396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7654 | 0.0109963 | ||||||||
\(980\) | 93.1318i | 0.0950324i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −559.370 | −0.569623 | ||||||||
\(983\) | 120.256i | 0.122336i | 0.998127 | + | 0.0611679i | \(0.0194825\pi\) | ||||
−0.998127 | + | 0.0611679i | \(0.980517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.8091 | 0.0556438 | ||||||||
\(986\) | 12.8667i | 0.0130494i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 45.8106 | 0.0463670 | ||||||||
\(989\) | 192.498i | 0.194639i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1347.36 | 1.35959 | 0.679796 | − | 0.733401i | \(-0.262068\pi\) | ||||
0.679796 | + | 0.733401i | \(0.262068\pi\) | |||||||
\(992\) | − 50.2262i | − 0.0506312i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 314.477 | 0.316375 | ||||||||
\(995\) | 272.261i | 0.273629i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −275.154 | −0.275982 | −0.137991 | − | 0.990433i | \(-0.544065\pi\) | ||||
−0.137991 | + | 0.990433i | \(0.544065\pi\) | |||||||
\(998\) | − 1559.42i | − 1.56254i | ||||||||
\(999\) | 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 | 1143.3.b.a.890.18 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.67 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.18 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.67 | yes | 84 | 3.2 | odd | 2 | inner |