Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (of order \(2\), degree \(1\), not 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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.6 | ||
Root | \(0.264658 + 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.ba.1849.1 |
$q$-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 \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 2.24914i | 1.29854i | 0.760557 | + | 0.649271i | \(0.224926\pi\) | ||||
−0.760557 | + | 0.649271i | \(0.775074\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.24914 | −0.918208 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −2.05863 | −0.686211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − 2.24914i | − 0.649271i | ||||||||
\(13\) | − 0.941367i | − 0.261088i | −0.991443 | − | 0.130544i | \(-0.958328\pi\) | ||||
0.991443 | − | 0.130544i | \(-0.0416724\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.49828i | 1.57606i | 0.615634 | + | 0.788032i | \(0.288900\pi\) | ||||
−0.615634 | + | 0.788032i | \(0.711100\pi\) | |||||||
\(18\) | − 2.05863i | − 0.485224i | ||||||||
\(19\) | 4.36641 | 1.00172 | 0.500861 | − | 0.865528i | \(-0.333017\pi\) | ||||
0.500861 | + | 0.865528i | \(0.333017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.24914 | 0.490803 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | − 6.24914i | − 1.30304i | −0.758633 | − | 0.651518i | \(-0.774133\pi\) | ||||
0.758633 | − | 0.651518i | \(-0.225867\pi\) | |||||||
\(24\) | 2.24914 | 0.459104 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.941367 | 0.184617 | ||||||||
\(27\) | 2.11727i | 0.407468i | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | −8.74742 | −1.62436 | −0.812178 | − | 0.583410i | \(-0.801718\pi\) | ||||
−0.812178 | + | 0.583410i | \(0.801718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.55691 | −1.71647 | −0.858236 | − | 0.513255i | \(-0.828440\pi\) | ||||
−0.858236 | + | 0.513255i | \(0.828440\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.24914i | 0.391525i | ||||||||
\(34\) | −6.49828 | −1.11445 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.05863 | 0.343106 | ||||||||
\(37\) | 4.24914i | 0.698554i | 0.937019 | + | 0.349277i | \(0.113573\pi\) | ||||
−0.937019 | + | 0.349277i | \(0.886427\pi\) | |||||||
\(38\) | 4.36641i | 0.708325i | ||||||||
\(39\) | 2.11727 | 0.339034 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.13187 | −0.332943 | −0.166471 | − | 0.986046i | \(-0.553237\pi\) | ||||
−0.166471 | + | 0.986046i | \(0.553237\pi\) | |||||||
\(42\) | 2.24914i | 0.347050i | ||||||||
\(43\) | − 7.67418i | − 1.17030i | −0.810925 | − | 0.585151i | \(-0.801035\pi\) | ||||
0.810925 | − | 0.585151i | \(-0.198965\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24914 | 0.921386 | ||||||||
\(47\) | 11.1138i | 1.62112i | 0.585657 | + | 0.810559i | \(0.300837\pi\) | ||||
−0.585657 | + | 0.810559i | \(0.699163\pi\) | |||||||
\(48\) | 2.24914i | 0.324635i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.6155 | −2.04659 | ||||||||
\(52\) | 0.941367i | 0.130544i | ||||||||
\(53\) | 4.74742i | 0.652109i | 0.945351 | + | 0.326054i | \(0.105719\pi\) | ||||
−0.945351 | + | 0.326054i | \(0.894281\pi\) | |||||||
\(54\) | −2.11727 | −0.288123 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 9.82066i | 1.30078i | ||||||||
\(58\) | − 8.74742i | − 1.14859i | ||||||||
\(59\) | 1.88273 | 0.245111 | 0.122556 | − | 0.992462i | \(-0.460891\pi\) | ||||
0.122556 | + | 0.992462i | \(0.460891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.11383 | 1.16691 | 0.583453 | − | 0.812147i | \(-0.301701\pi\) | ||||
0.583453 | + | 0.812147i | \(0.301701\pi\) | |||||||
\(62\) | − 9.55691i | − 1.21373i | ||||||||
\(63\) | 2.05863i | 0.259363i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.24914 | −0.276850 | ||||||||
\(67\) | 12.9966i | 1.58778i | 0.608060 | + | 0.793891i | \(0.291948\pi\) | ||||
−0.608060 | + | 0.793891i | \(0.708052\pi\) | |||||||
\(68\) | − 6.49828i | − 0.788032i | ||||||||
\(69\) | 14.0552 | 1.69205 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.6155 | −1.73455 | −0.867273 | − | 0.497833i | \(-0.834129\pi\) | ||||
−0.867273 | + | 0.497833i | \(0.834129\pi\) | |||||||
\(72\) | 2.05863i | 0.242612i | ||||||||
\(73\) | 10.4983i | 1.22873i | 0.789022 | + | 0.614365i | \(0.210588\pi\) | ||||
−0.789022 | + | 0.614365i | \(0.789412\pi\) | |||||||
\(74\) | −4.24914 | −0.493953 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.36641 | −0.500861 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | 2.11727i | 0.239733i | ||||||||
\(79\) | −8.36641 | −0.941294 | −0.470647 | − | 0.882322i | \(-0.655980\pi\) | ||||
−0.470647 | + | 0.882322i | \(0.655980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | − 2.13187i | − 0.235426i | ||||||||
\(83\) | 8.49828i | 0.932808i | 0.884572 | + | 0.466404i | \(0.154451\pi\) | ||||
−0.884572 | + | 0.466404i | \(0.845549\pi\) | |||||||
\(84\) | −2.24914 | −0.245401 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.67418 | 0.827528 | ||||||||
\(87\) | − 19.6742i | − 2.10929i | ||||||||
\(88\) | − 1.00000i | − 0.106600i | ||||||||
\(89\) | −12.3810 | −1.31238 | −0.656192 | − | 0.754594i | \(-0.727834\pi\) | ||||
−0.656192 | + | 0.754594i | \(0.727834\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.941367 | −0.0986821 | ||||||||
\(92\) | 6.24914i | 0.651518i | ||||||||
\(93\) | − 21.4948i | − 2.22891i | ||||||||
\(94\) | −11.1138 | −1.14630 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.24914 | −0.229552 | ||||||||
\(97\) | − 15.3630i | − 1.55987i | −0.625859 | − | 0.779937i | \(-0.715251\pi\) | ||||
0.625859 | − | 0.779937i | \(-0.284749\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | −2.05863 | −0.206900 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8793 | −1.67955 | −0.839776 | − | 0.542932i | \(-0.817314\pi\) | ||||
−0.839776 | + | 0.542932i | \(0.817314\pi\) | |||||||
\(102\) | − 14.6155i | − 1.44715i | ||||||||
\(103\) | 6.61555i | 0.651849i | 0.945396 | + | 0.325925i | \(0.105676\pi\) | ||||
−0.945396 | + | 0.325925i | \(0.894324\pi\) | |||||||
\(104\) | −0.941367 | −0.0923086 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.74742 | −0.461110 | ||||||||
\(107\) | − 14.5535i | − 1.40694i | −0.710726 | − | 0.703469i | \(-0.751633\pi\) | ||||
0.710726 | − | 0.703469i | \(-0.248367\pi\) | |||||||
\(108\) | − 2.11727i | − 0.203734i | ||||||||
\(109\) | 0.249141 | 0.0238633 | 0.0119317 | − | 0.999929i | \(-0.496202\pi\) | ||||
0.0119317 | + | 0.999929i | \(0.496202\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.55691 | −0.907102 | ||||||||
\(112\) | − 1.00000i | − 0.0944911i | ||||||||
\(113\) | − 10.9966i | − 1.03447i | −0.855844 | − | 0.517235i | \(-0.826961\pi\) | ||||
0.855844 | − | 0.517235i | \(-0.173039\pi\) | |||||||
\(114\) | −9.82066 | −0.919789 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.74742 | 0.812178 | ||||||||
\(117\) | 1.93793i | 0.179162i | ||||||||
\(118\) | 1.88273i | 0.173320i | ||||||||
\(119\) | 6.49828 | 0.595696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.11383i | 0.825127i | ||||||||
\(123\) | − 4.79488i | − 0.432340i | ||||||||
\(124\) | 9.55691 | 0.858236 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.05863 | −0.183398 | ||||||||
\(127\) | − 5.88273i | − 0.522008i | −0.965338 | − | 0.261004i | \(-0.915946\pi\) | ||||
0.965338 | − | 0.261004i | \(-0.0840536\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 17.2603 | 1.51969 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.25258 | −0.109438 | −0.0547191 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547191 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(132\) | − 2.24914i | − 0.195763i | ||||||||
\(133\) | − 4.36641i | − 0.378615i | ||||||||
\(134\) | −12.9966 | −1.12273 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.49828 | 0.557223 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | 14.0552i | 1.19646i | ||||||||
\(139\) | −10.9820 | −0.931477 | −0.465739 | − | 0.884922i | \(-0.654211\pi\) | ||||
−0.465739 | + | 0.884922i | \(0.654211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.9966 | −2.10509 | ||||||||
\(142\) | − 14.6155i | − 1.22651i | ||||||||
\(143\) | − 0.941367i | − 0.0787210i | ||||||||
\(144\) | −2.05863 | −0.171553 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.4983 | −0.868844 | ||||||||
\(147\) | − 2.24914i | − 0.185506i | ||||||||
\(148\) | − 4.24914i | − 0.349277i | ||||||||
\(149\) | −0.0146079 | −0.00119673 | −0.000598363 | − | 1.00000i | \(-0.500190\pi\) | ||||
−0.000598363 | 1.00000i | \(0.500190\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2457 | −1.24068 | −0.620339 | − | 0.784334i | \(-0.713005\pi\) | ||||
−0.620339 | + | 0.784334i | \(0.713005\pi\) | |||||||
\(152\) | − 4.36641i | − 0.354162i | ||||||||
\(153\) | − 13.3776i | − 1.08151i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.11727 | −0.169517 | ||||||||
\(157\) | − 5.50172i | − 0.439085i | −0.975603 | − | 0.219542i | \(-0.929544\pi\) | ||||
0.975603 | − | 0.219542i | \(-0.0704565\pi\) | |||||||
\(158\) | − 8.36641i | − 0.665596i | ||||||||
\(159\) | −10.6776 | −0.846790 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.24914 | −0.492501 | ||||||||
\(162\) | − 10.9379i | − 0.859365i | ||||||||
\(163\) | 18.2277i | 1.42770i | 0.700298 | + | 0.713850i | \(0.253050\pi\) | ||||
−0.700298 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(164\) | 2.13187 | 0.166471 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.49828 | −0.659595 | ||||||||
\(167\) | − 8.00000i | − 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | − 2.24914i | − 0.173525i | ||||||||
\(169\) | 12.1138 | 0.931833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.98883 | −0.687393 | ||||||||
\(172\) | 7.67418i | 0.585151i | ||||||||
\(173\) | − 0.117266i | − 0.00891559i | −0.999990 | − | 0.00445780i | \(-0.998581\pi\) | ||||
0.999990 | − | 0.00445780i | \(-0.00141897\pi\) | |||||||
\(174\) | 19.6742 | 1.49150 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 4.23453i | 0.318287i | ||||||||
\(178\) | − 12.3810i | − 0.927996i | ||||||||
\(179\) | 22.5535 | 1.68573 | 0.842863 | − | 0.538128i | \(-0.180868\pi\) | ||||
0.842863 | + | 0.538128i | \(0.180868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8793 | 1.55195 | 0.775973 | − | 0.630766i | \(-0.217259\pi\) | ||||
0.775973 | + | 0.630766i | \(0.217259\pi\) | |||||||
\(182\) | − 0.941367i | − 0.0697788i | ||||||||
\(183\) | 20.4983i | 1.51528i | ||||||||
\(184\) | −6.24914 | −0.460693 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 21.4948 | 1.57608 | ||||||||
\(187\) | 6.49828i | 0.475201i | ||||||||
\(188\) | − 11.1138i | − 0.810559i | ||||||||
\(189\) | 2.11727 | 0.154008 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.11383 | 0.225309 | 0.112654 | − | 0.993634i | \(-0.464065\pi\) | ||||
0.112654 | + | 0.993634i | \(0.464065\pi\) | |||||||
\(192\) | − 2.24914i | − 0.162318i | ||||||||
\(193\) | 6.17246i | 0.444304i | 0.975012 | + | 0.222152i | \(0.0713080\pi\) | ||||
−0.975012 | + | 0.222152i | \(0.928692\pi\) | |||||||
\(194\) | 15.3630 | 1.10300 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.73281i | 0.479693i | 0.970811 | + | 0.239847i | \(0.0770971\pi\) | ||||
−0.970811 | + | 0.239847i | \(0.922903\pi\) | |||||||
\(198\) | − 2.05863i | − 0.146301i | ||||||||
\(199\) | 13.2311 | 0.937927 | 0.468964 | − | 0.883217i | \(-0.344627\pi\) | ||||
0.468964 | + | 0.883217i | \(0.344627\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.2311 | −2.06180 | ||||||||
\(202\) | − 16.8793i | − 1.18762i | ||||||||
\(203\) | 8.74742i | 0.613949i | ||||||||
\(204\) | 14.6155 | 1.02329 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.61555 | −0.460927 | ||||||||
\(207\) | 12.8647i | 0.894158i | ||||||||
\(208\) | − 0.941367i | − 0.0652720i | ||||||||
\(209\) | 4.36641 | 0.302031 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.1138 | 1.59122 | 0.795611 | − | 0.605808i | \(-0.207150\pi\) | ||||
0.795611 | + | 0.605808i | \(0.207150\pi\) | |||||||
\(212\) | − 4.74742i | − 0.326054i | ||||||||
\(213\) | − 32.8724i | − 2.25238i | ||||||||
\(214\) | 14.5535 | 0.994855 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.11727 | 0.144062 | ||||||||
\(217\) | 9.55691i | 0.648766i | ||||||||
\(218\) | 0.249141i | 0.0168739i | ||||||||
\(219\) | −23.6121 | −1.59556 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.11727 | 0.411492 | ||||||||
\(222\) | − 9.55691i | − 0.641418i | ||||||||
\(223\) | − 10.3810i | − 0.695164i | −0.937650 | − | 0.347582i | \(-0.887003\pi\) | ||||
0.937650 | − | 0.347582i | \(-0.112997\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.9966 | 0.731480 | ||||||||
\(227\) | 16.1104i | 1.06928i | 0.845079 | + | 0.534642i | \(0.179554\pi\) | ||||
−0.845079 | + | 0.534642i | \(0.820446\pi\) | |||||||
\(228\) | − 9.82066i | − 0.650389i | ||||||||
\(229\) | −24.2897 | −1.60511 | −0.802555 | − | 0.596578i | \(-0.796527\pi\) | ||||
−0.802555 | + | 0.596578i | \(0.796527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.24914 | 0.147983 | ||||||||
\(232\) | 8.74742i | 0.574296i | ||||||||
\(233\) | − 6.88617i | − 0.451128i | −0.974228 | − | 0.225564i | \(-0.927578\pi\) | ||||
0.974228 | − | 0.225564i | \(-0.0724225\pi\) | |||||||
\(234\) | −1.93793 | −0.126686 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.88273 | −0.122556 | ||||||||
\(237\) | − 18.8172i | − 1.22231i | ||||||||
\(238\) | 6.49828i | 0.421221i | ||||||||
\(239\) | 11.1353 | 0.720283 | 0.360142 | − | 0.932898i | \(-0.382728\pi\) | ||||
0.360142 | + | 0.932898i | \(0.382728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.36641 | 0.152434 | 0.0762168 | − | 0.997091i | \(-0.475716\pi\) | ||||
0.0762168 | + | 0.997091i | \(0.475716\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | − 18.2491i | − 1.17068i | ||||||||
\(244\) | −9.11383 | −0.583453 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.79488 | 0.305711 | ||||||||
\(247\) | − 4.11039i | − 0.261538i | ||||||||
\(248\) | 9.55691i | 0.606865i | ||||||||
\(249\) | −19.1138 | −1.21129 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1070 | 1.58474 | 0.792368 | − | 0.610043i | \(-0.208848\pi\) | ||||
0.792368 | + | 0.610043i | \(0.208848\pi\) | |||||||
\(252\) | − 2.05863i | − 0.129682i | ||||||||
\(253\) | − 6.24914i | − 0.392880i | ||||||||
\(254\) | 5.88273 | 0.369116 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 2.86469i | − 0.178694i | −0.996001 | − | 0.0893472i | \(-0.971522\pi\) | ||||
0.996001 | − | 0.0893472i | \(-0.0284781\pi\) | |||||||
\(258\) | 17.2603i | 1.07458i | ||||||||
\(259\) | 4.24914 | 0.264029 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0077 | 1.11465 | ||||||||
\(262\) | − 1.25258i | − 0.0773846i | ||||||||
\(263\) | − 3.76547i | − 0.232189i | −0.993238 | − | 0.116094i | \(-0.962963\pi\) | ||||
0.993238 | − | 0.116094i | \(-0.0370375\pi\) | |||||||
\(264\) | 2.24914 | 0.138425 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.36641 | 0.267722 | ||||||||
\(267\) | − 27.8466i | − 1.70419i | ||||||||
\(268\) | − 12.9966i | − 0.793891i | ||||||||
\(269\) | −8.94137 | −0.545165 | −0.272582 | − | 0.962132i | \(-0.587878\pi\) | ||||
−0.272582 | + | 0.962132i | \(0.587878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4948 | 1.30572 | 0.652859 | − | 0.757479i | \(-0.273569\pi\) | ||||
0.652859 | + | 0.757479i | \(0.273569\pi\) | |||||||
\(272\) | 6.49828i | 0.394016i | ||||||||
\(273\) | − 2.11727i | − 0.128143i | ||||||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.0552 | −0.846023 | ||||||||
\(277\) | 7.64820i | 0.459536i | 0.973245 | + | 0.229768i | \(0.0737967\pi\) | ||||
−0.973245 | + | 0.229768i | \(0.926203\pi\) | |||||||
\(278\) | − 10.9820i | − 0.658654i | ||||||||
\(279\) | 19.6742 | 1.17786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.6155 | −1.70706 | −0.853530 | − | 0.521043i | \(-0.825543\pi\) | ||||
−0.853530 | + | 0.521043i | \(0.825543\pi\) | |||||||
\(282\) | − 24.9966i | − 1.48852i | ||||||||
\(283\) | 2.87930i | 0.171156i | 0.996331 | + | 0.0855782i | \(0.0272737\pi\) | ||||
−0.996331 | + | 0.0855782i | \(0.972726\pi\) | |||||||
\(284\) | 14.6155 | 0.867273 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.941367 | 0.0556642 | ||||||||
\(287\) | 2.13187i | 0.125841i | ||||||||
\(288\) | − 2.05863i | − 0.121306i | ||||||||
\(289\) | −25.2277 | −1.48398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.5535 | 2.02556 | ||||||||
\(292\) | − 10.4983i | − 0.614365i | ||||||||
\(293\) | 12.9414i | 0.756043i | 0.925797 | + | 0.378021i | \(0.123395\pi\) | ||||
−0.925797 | + | 0.378021i | \(0.876605\pi\) | |||||||
\(294\) | 2.24914 | 0.131173 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.24914 | 0.246976 | ||||||||
\(297\) | 2.11727i | 0.122856i | ||||||||
\(298\) | − 0.0146079i | 0 0.000846213i | ||||||||
\(299\) | −5.88273 | −0.340207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.67418 | −0.442332 | ||||||||
\(302\) | − 15.2457i | − 0.877292i | ||||||||
\(303\) | − 37.9639i | − 2.18097i | ||||||||
\(304\) | 4.36641 | 0.250431 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 13.3776 | 0.764745 | ||||||||
\(307\) | 0.498281i | 0.0284384i | 0.999899 | + | 0.0142192i | \(0.00452626\pi\) | ||||
−0.999899 | + | 0.0142192i | \(0.995474\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | −14.8793 | −0.846454 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.4396 | −1.32914 | −0.664570 | − | 0.747226i | \(-0.731385\pi\) | ||||
−0.664570 | + | 0.747226i | \(0.731385\pi\) | |||||||
\(312\) | − 2.11727i | − 0.119867i | ||||||||
\(313\) | − 9.36984i | − 0.529615i | −0.964301 | − | 0.264807i | \(-0.914692\pi\) | ||||
0.964301 | − | 0.264807i | \(-0.0853084\pi\) | |||||||
\(314\) | 5.50172 | 0.310480 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.36641 | 0.470647 | ||||||||
\(317\) | − 9.97852i | − 0.560449i | −0.959934 | − | 0.280225i | \(-0.909591\pi\) | ||||
0.959934 | − | 0.280225i | \(-0.0904090\pi\) | |||||||
\(318\) | − 10.6776i | − 0.598771i | ||||||||
\(319\) | −8.74742 | −0.489762 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 32.7328 | 1.82697 | ||||||||
\(322\) | − 6.24914i | − 0.348251i | ||||||||
\(323\) | 28.3741i | 1.57878i | ||||||||
\(324\) | 10.9379 | 0.607663 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.2277 | −1.00954 | ||||||||
\(327\) | 0.560352i | 0.0309875i | ||||||||
\(328\) | 2.13187i | 0.117713i | ||||||||
\(329\) | 11.1138 | 0.612725 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4362 | −1.12328 | −0.561638 | − | 0.827383i | \(-0.689829\pi\) | ||||
−0.561638 | + | 0.827383i | \(0.689829\pi\) | |||||||
\(332\) | − 8.49828i | − 0.466404i | ||||||||
\(333\) | − 8.74742i | − 0.479356i | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.24914 | 0.122701 | ||||||||
\(337\) | 7.88273i | 0.429400i | 0.976680 | + | 0.214700i | \(0.0688774\pi\) | ||||
−0.976680 | + | 0.214700i | \(0.931123\pi\) | |||||||
\(338\) | 12.1138i | 0.658905i | ||||||||
\(339\) | 24.7328 | 1.34330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.55691 | −0.517536 | ||||||||
\(342\) | − 8.98883i | − 0.486060i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −7.67418 | −0.413764 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.117266 | 0.00630428 | ||||||||
\(347\) | 13.5569i | 0.727773i | 0.931443 | + | 0.363887i | \(0.118550\pi\) | ||||
−0.931443 | + | 0.363887i | \(0.881450\pi\) | |||||||
\(348\) | 19.6742i | 1.05465i | ||||||||
\(349\) | 10.7328 | 0.574514 | 0.287257 | − | 0.957853i | \(-0.407257\pi\) | ||||
0.287257 | + | 0.957853i | \(0.407257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.99312 | 0.106385 | ||||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | 20.8578i | 1.11015i | 0.831801 | + | 0.555075i | \(0.187310\pi\) | ||||
−0.831801 | + | 0.555075i | \(0.812690\pi\) | |||||||
\(354\) | −4.23453 | −0.225063 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.3810 | 0.656192 | ||||||||
\(357\) | 14.6155i | 0.773537i | ||||||||
\(358\) | 22.5535i | 1.19199i | ||||||||
\(359\) | −0.366407 | −0.0193382 | −0.00966911 | − | 0.999953i | \(-0.503078\pi\) | ||||
−0.00966911 | + | 0.999953i | \(0.503078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0655089 | 0.00344783 | ||||||||
\(362\) | 20.8793i | 1.09739i | ||||||||
\(363\) | 2.24914i | 0.118049i | ||||||||
\(364\) | 0.941367 | 0.0493410 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.4983 | −1.07146 | ||||||||
\(367\) | 20.8432i | 1.08801i | 0.839083 | + | 0.544003i | \(0.183092\pi\) | ||||
−0.839083 | + | 0.544003i | \(0.816908\pi\) | |||||||
\(368\) | − 6.24914i | − 0.325759i | ||||||||
\(369\) | 4.38875 | 0.228469 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.74742 | 0.246474 | ||||||||
\(372\) | 21.4948i | 1.11446i | ||||||||
\(373\) | 5.37758i | 0.278440i | 0.990261 | + | 0.139220i | \(0.0444596\pi\) | ||||
−0.990261 | + | 0.139220i | \(0.955540\pi\) | |||||||
\(374\) | −6.49828 | −0.336018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1138 | 0.573152 | ||||||||
\(377\) | 8.23453i | 0.424100i | ||||||||
\(378\) | 2.11727i | 0.108900i | ||||||||
\(379\) | −3.53093 | −0.181372 | −0.0906860 | − | 0.995880i | \(-0.528906\pi\) | ||||
−0.0906860 | + | 0.995880i | \(0.528906\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.2311 | 0.677850 | ||||||||
\(382\) | 3.11383i | 0.159317i | ||||||||
\(383\) | − 1.38445i | − 0.0707422i | −0.999374 | − | 0.0353711i | \(-0.988739\pi\) | ||||
0.999374 | − | 0.0353711i | \(-0.0112613\pi\) | |||||||
\(384\) | 2.24914 | 0.114776 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.17246 | −0.314170 | ||||||||
\(387\) | 15.7983i | 0.803074i | ||||||||
\(388\) | 15.3630i | 0.779937i | ||||||||
\(389\) | −15.7294 | −0.797511 | −0.398756 | − | 0.917057i | \(-0.630558\pi\) | ||||
−0.398756 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.6087 | 2.05367 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | − 2.81722i | − 0.142110i | ||||||||
\(394\) | −6.73281 | −0.339194 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.05863 | 0.103450 | ||||||||
\(397\) | − 17.6121i | − 0.883926i | −0.897033 | − | 0.441963i | \(-0.854282\pi\) | ||||
0.897033 | − | 0.441963i | \(-0.145718\pi\) | |||||||
\(398\) | 13.2311i | 0.663215i | ||||||||
\(399\) | 9.82066 | 0.491648 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.8172 | −1.63881 | −0.819407 | − | 0.573212i | \(-0.805697\pi\) | ||||
−0.819407 | + | 0.573212i | \(0.805697\pi\) | |||||||
\(402\) | − 29.2311i | − 1.45791i | ||||||||
\(403\) | 8.99656i | 0.448151i | ||||||||
\(404\) | 16.8793 | 0.839776 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.74742 | −0.434127 | ||||||||
\(407\) | 4.24914i | 0.210622i | ||||||||
\(408\) | 14.6155i | 0.723577i | ||||||||
\(409\) | 33.3561 | 1.64935 | 0.824676 | − | 0.565605i | \(-0.191357\pi\) | ||||
0.824676 | + | 0.565605i | \(0.191357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.4914 | −1.10942 | ||||||||
\(412\) | − 6.61555i | − 0.325925i | ||||||||
\(413\) | − 1.88273i | − 0.0926433i | ||||||||
\(414\) | −12.8647 | −0.632265 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.941367 | 0.0461543 | ||||||||
\(417\) | − 24.7000i | − 1.20956i | ||||||||
\(418\) | 4.36641i | 0.213568i | ||||||||
\(419\) | −12.3449 | −0.603089 | −0.301544 | − | 0.953452i | \(-0.597502\pi\) | ||||
−0.301544 | + | 0.953452i | \(0.597502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.87930 | −0.432750 | −0.216375 | − | 0.976310i | \(-0.569423\pi\) | ||||
−0.216375 | + | 0.976310i | \(0.569423\pi\) | |||||||
\(422\) | 23.1138i | 1.12516i | ||||||||
\(423\) | − 22.8793i | − 1.11243i | ||||||||
\(424\) | 4.74742 | 0.230555 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 32.8724 | 1.59267 | ||||||||
\(427\) | − 9.11383i | − 0.441049i | ||||||||
\(428\) | 14.5535i | 0.703469i | ||||||||
\(429\) | 2.11727 | 0.102223 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2784 | 0.880437 | 0.440219 | − | 0.897891i | \(-0.354901\pi\) | ||||
0.440219 | + | 0.897891i | \(0.354901\pi\) | |||||||
\(432\) | 2.11727i | 0.101867i | ||||||||
\(433\) | − 6.86469i | − 0.329896i | −0.986302 | − | 0.164948i | \(-0.947254\pi\) | ||||
0.986302 | − | 0.164948i | \(-0.0527456\pi\) | |||||||
\(434\) | −9.55691 | −0.458747 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.249141 | −0.0119317 | ||||||||
\(437\) | − 27.2863i | − 1.30528i | ||||||||
\(438\) | − 23.6121i | − 1.12823i | ||||||||
\(439\) | 11.8466 | 0.565409 | 0.282705 | − | 0.959207i | \(-0.408768\pi\) | ||||
0.282705 | + | 0.959207i | \(0.408768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.05863 | 0.0980302 | ||||||||
\(442\) | 6.11727i | 0.290969i | ||||||||
\(443\) | − 17.8827i | − 0.849634i | −0.905279 | − | 0.424817i | \(-0.860338\pi\) | ||||
0.905279 | − | 0.424817i | \(-0.139662\pi\) | |||||||
\(444\) | 9.55691 | 0.453551 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.3810 | 0.491555 | ||||||||
\(447\) | − 0.0328552i | − 0.00155400i | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 16.8172 | 0.793654 | 0.396827 | − | 0.917893i | \(-0.370111\pi\) | ||||
0.396827 | + | 0.917893i | \(0.370111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.13187 | −0.100386 | ||||||||
\(452\) | 10.9966i | 0.517235i | ||||||||
\(453\) | − 34.2897i | − 1.61107i | ||||||||
\(454\) | −16.1104 | −0.756098 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.82066 | 0.459895 | ||||||||
\(457\) | − 12.2277i | − 0.571986i | −0.958232 | − | 0.285993i | \(-0.907677\pi\) | ||||
0.958232 | − | 0.285993i | \(-0.0923234\pi\) | |||||||
\(458\) | − 24.2897i | − 1.13498i | ||||||||
\(459\) | −13.7586 | −0.642196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6155 | −0.773863 | −0.386932 | − | 0.922108i | \(-0.626465\pi\) | ||||
−0.386932 | + | 0.922108i | \(0.626465\pi\) | |||||||
\(462\) | 2.24914i | 0.104639i | ||||||||
\(463\) | − 18.4837i | − 0.859009i | −0.903065 | − | 0.429505i | \(-0.858688\pi\) | ||||
0.903065 | − | 0.429505i | \(-0.141312\pi\) | |||||||
\(464\) | −8.74742 | −0.406089 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.88617 | 0.318996 | ||||||||
\(467\) | 24.3956i | 1.12889i | 0.825469 | + | 0.564447i | \(0.190911\pi\) | ||||
−0.825469 | + | 0.564447i | \(0.809089\pi\) | |||||||
\(468\) | − 1.93793i | − 0.0895808i | ||||||||
\(469\) | 12.9966 | 0.600125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.3741 | 0.570170 | ||||||||
\(472\) | − 1.88273i | − 0.0866598i | ||||||||
\(473\) | − 7.67418i | − 0.352859i | ||||||||
\(474\) | 18.8172 | 0.864304 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.49828 | −0.297848 | ||||||||
\(477\) | − 9.77320i | − 0.447484i | ||||||||
\(478\) | 11.1353i | 0.509317i | ||||||||
\(479\) | 27.7655 | 1.26864 | 0.634318 | − | 0.773072i | \(-0.281281\pi\) | ||||
0.634318 | + | 0.773072i | \(0.281281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 2.36641i | 0.107787i | ||||||||
\(483\) | − 14.0552i | − 0.639534i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.2491 | 0.827798 | ||||||||
\(487\) | 10.0958i | 0.457484i | 0.973487 | + | 0.228742i | \(0.0734612\pi\) | ||||
−0.973487 | + | 0.228742i | \(0.926539\pi\) | |||||||
\(488\) | − 9.11383i | − 0.412564i | ||||||||
\(489\) | −40.9966 | −1.85393 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.1104 | −1.44912 | −0.724561 | − | 0.689211i | \(-0.757957\pi\) | ||||
−0.724561 | + | 0.689211i | \(0.757957\pi\) | |||||||
\(492\) | 4.79488i | 0.216170i | ||||||||
\(493\) | − 56.8432i | − 2.56009i | ||||||||
\(494\) | 4.11039 | 0.184935 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.55691 | −0.429118 | ||||||||
\(497\) | 14.6155i | 0.655597i | ||||||||
\(498\) | − 19.1138i | − 0.856511i | ||||||||
\(499\) | 8.79488 | 0.393713 | 0.196857 | − | 0.980432i | \(-0.436927\pi\) | ||||
0.196857 | + | 0.980432i | \(0.436927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.9931 | 0.803874 | ||||||||
\(502\) | 25.1070i | 1.12058i | ||||||||
\(503\) | 15.0034i | 0.668970i | 0.942401 | + | 0.334485i | \(0.108562\pi\) | ||||
−0.942401 | + | 0.334485i | \(0.891438\pi\) | |||||||
\(504\) | 2.05863 | 0.0916988 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.24914 | 0.277808 | ||||||||
\(507\) | 27.2457i | 1.21002i | ||||||||
\(508\) | 5.88273i | 0.261004i | ||||||||
\(509\) | −21.8759 | −0.969630 | −0.484815 | − | 0.874617i | \(-0.661113\pi\) | ||||
−0.484815 | + | 0.874617i | \(0.661113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4983 | 0.464417 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 9.24485i | 0.408170i | ||||||||
\(514\) | 2.86469 | 0.126356 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17.2603 | −0.759843 | ||||||||
\(517\) | 11.1138i | 0.488786i | ||||||||
\(518\) | 4.24914i | 0.186697i | ||||||||
\(519\) | 0.263748 | 0.0115773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0292 | 0.614631 | 0.307316 | − | 0.951608i | \(-0.400569\pi\) | ||||
0.307316 | + | 0.951608i | \(0.400569\pi\) | |||||||
\(522\) | 18.0077i | 0.788177i | ||||||||
\(523\) | − 1.14992i | − 0.0502825i | −0.999684 | − | 0.0251412i | \(-0.991996\pi\) | ||||
0.999684 | − | 0.0251412i | \(-0.00800355\pi\) | |||||||
\(524\) | 1.25258 | 0.0547191 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.76547 | 0.164182 | ||||||||
\(527\) | − 62.1035i | − 2.70527i | ||||||||
\(528\) | 2.24914i | 0.0978813i | ||||||||
\(529\) | −16.0518 | −0.697902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.87586 | −0.168198 | ||||||||
\(532\) | 4.36641i | 0.189308i | ||||||||
\(533\) | 2.00688i | 0.0869274i | ||||||||
\(534\) | 27.8466 | 1.20504 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.9966 | 0.561366 | ||||||||
\(537\) | 50.7259i | 2.18899i | ||||||||
\(538\) | − 8.94137i | − 0.385490i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.47680 | −0.278459 | −0.139230 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139230 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(542\) | 21.4948i | 0.923283i | ||||||||
\(543\) | 46.9605i | 2.01527i | ||||||||
\(544\) | −6.49828 | −0.278612 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.11727 | 0.0906106 | ||||||||
\(547\) | 12.9966i | 0.555693i | 0.960626 | + | 0.277846i | \(0.0896206\pi\) | ||||
−0.960626 | + | 0.277846i | \(0.910379\pi\) | |||||||
\(548\) | − 10.0000i | − 0.427179i | ||||||||
\(549\) | −18.7620 | −0.800744 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.1948 | −1.62715 | ||||||||
\(552\) | − 14.0552i | − 0.598229i | ||||||||
\(553\) | 8.36641i | 0.355776i | ||||||||
\(554\) | −7.64820 | −0.324941 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.9820 | 0.465739 | ||||||||
\(557\) | − 16.4914i | − 0.698763i | −0.936981 | − | 0.349382i | \(-0.886392\pi\) | ||||
0.936981 | − | 0.349382i | \(-0.113608\pi\) | |||||||
\(558\) | 19.6742i | 0.832874i | ||||||||
\(559\) | −7.22422 | −0.305552 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.6155 | −0.617069 | ||||||||
\(562\) | − 28.6155i | − 1.20707i | ||||||||
\(563\) | 16.7620i | 0.706435i | 0.935541 | + | 0.353218i | \(0.114912\pi\) | ||||
−0.935541 | + | 0.353218i | \(0.885088\pi\) | |||||||
\(564\) | 24.9966 | 1.05255 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.87930 | −0.121026 | ||||||||
\(567\) | 10.9379i | 0.459350i | ||||||||
\(568\) | 14.6155i | 0.613255i | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7328 | 0.532852 | 0.266426 | − | 0.963855i | \(-0.414157\pi\) | ||||
0.266426 | + | 0.963855i | \(0.414157\pi\) | |||||||
\(572\) | 0.941367i | 0.0393605i | ||||||||
\(573\) | 7.00344i | 0.292573i | ||||||||
\(574\) | −2.13187 | −0.0889827 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.05863 | 0.0857764 | ||||||||
\(577\) | − 11.8613i | − 0.493790i | −0.969042 | − | 0.246895i | \(-0.920590\pi\) | ||||
0.969042 | − | 0.246895i | \(-0.0794103\pi\) | |||||||
\(578\) | − 25.2277i | − 1.04933i | ||||||||
\(579\) | −13.8827 | −0.576947 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.49828 | 0.352568 | ||||||||
\(582\) | 34.5535i | 1.43229i | ||||||||
\(583\) | 4.74742i | 0.196618i | ||||||||
\(584\) | 10.4983 | 0.434422 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.9414 | −0.534603 | ||||||||
\(587\) | − 8.60094i | − 0.354999i | −0.984121 | − | 0.177499i | \(-0.943199\pi\) | ||||
0.984121 | − | 0.177499i | \(-0.0568008\pi\) | |||||||
\(588\) | 2.24914i | 0.0927530i | ||||||||
\(589\) | −41.7294 | −1.71943 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.1430 | −0.622902 | ||||||||
\(592\) | 4.24914i | 0.174639i | ||||||||
\(593\) | − 10.7328i | − 0.440744i | −0.975416 | − | 0.220372i | \(-0.929273\pi\) | ||||
0.975416 | − | 0.220372i | \(-0.0707271\pi\) | |||||||
\(594\) | −2.11727 | −0.0868725 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0146079 | 0.000598363 0 | ||||||||
\(597\) | 29.7586i | 1.21794i | ||||||||
\(598\) | − 5.88273i | − 0.240563i | ||||||||
\(599\) | −16.0812 | −0.657059 | −0.328529 | − | 0.944494i | \(-0.606553\pi\) | ||||
−0.328529 | + | 0.944494i | \(0.606553\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.0889 | −1.39052 | −0.695258 | − | 0.718760i | \(-0.744710\pi\) | ||||
−0.695258 | + | 0.718760i | \(0.744710\pi\) | |||||||
\(602\) | − 7.67418i | − 0.312776i | ||||||||
\(603\) | − 26.7552i | − 1.08955i | ||||||||
\(604\) | 15.2457 | 0.620339 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 37.9639 | 1.54218 | ||||||||
\(607\) | 11.6742i | 0.473840i | 0.971529 | + | 0.236920i | \(0.0761380\pi\) | ||||
−0.971529 | + | 0.236920i | \(0.923862\pi\) | |||||||
\(608\) | 4.36641i | 0.177081i | ||||||||
\(609\) | −19.6742 | −0.797238 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4622 | 0.423255 | ||||||||
\(612\) | 13.3776i | 0.540756i | ||||||||
\(613\) | 34.2637i | 1.38390i | 0.721946 | + | 0.691950i | \(0.243248\pi\) | ||||
−0.721946 | + | 0.691950i | \(0.756752\pi\) | |||||||
\(614\) | −0.498281 | −0.0201090 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 39.3707i | 1.58500i | 0.609869 | + | 0.792502i | \(0.291222\pi\) | ||||
−0.609869 | + | 0.792502i | \(0.708778\pi\) | |||||||
\(618\) | − 14.8793i | − 0.598533i | ||||||||
\(619\) | −16.1104 | −0.647531 | −0.323766 | − | 0.946137i | \(-0.604949\pi\) | ||||
−0.323766 | + | 0.946137i | \(0.604949\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.2311 | 0.530946 | ||||||||
\(622\) | − 23.4396i | − 0.939844i | ||||||||
\(623\) | 12.3810i | 0.496035i | ||||||||
\(624\) | 2.11727 | 0.0847585 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.36984 | 0.374494 | ||||||||
\(627\) | 9.82066i | 0.392199i | ||||||||
\(628\) | 5.50172i | 0.219542i | ||||||||
\(629\) | −27.6121 | −1.10097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8827 | 0.552663 | 0.276331 | − | 0.961062i | \(-0.410881\pi\) | ||||
0.276331 | + | 0.961062i | \(0.410881\pi\) | |||||||
\(632\) | 8.36641i | 0.332798i | ||||||||
\(633\) | 51.9862i | 2.06627i | ||||||||
\(634\) | 9.97852 | 0.396298 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.6776 | 0.423395 | ||||||||
\(637\) | 0.941367i | 0.0372983i | ||||||||
\(638\) | − 8.74742i | − 0.346314i | ||||||||
\(639\) | 30.0881 | 1.19026 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3415 | −1.55390 | −0.776948 | − | 0.629565i | \(-0.783233\pi\) | ||||
−0.776948 | + | 0.629565i | \(0.783233\pi\) | |||||||
\(642\) | 32.7328i | 1.29186i | ||||||||
\(643\) | − 38.3595i | − 1.51275i | −0.654137 | − | 0.756376i | \(-0.726968\pi\) | ||||
0.654137 | − | 0.756376i | \(-0.273032\pi\) | |||||||
\(644\) | 6.24914 | 0.246251 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.3741 | −1.11637 | ||||||||
\(647\) | 25.7294i | 1.01153i | 0.862672 | + | 0.505763i | \(0.168789\pi\) | ||||
−0.862672 | + | 0.505763i | \(0.831211\pi\) | |||||||
\(648\) | 10.9379i | 0.429682i | ||||||||
\(649\) | 1.88273 | 0.0739038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.4948 | −0.842449 | ||||||||
\(652\) | − 18.2277i | − 0.713850i | ||||||||
\(653\) | − 18.4768i | − 0.723053i | −0.932362 | − | 0.361526i | \(-0.882256\pi\) | ||||
0.932362 | − | 0.361526i | \(-0.117744\pi\) | |||||||
\(654\) | −0.560352 | −0.0219115 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.13187 | −0.0832357 | ||||||||
\(657\) | − 21.6121i | − 0.843169i | ||||||||
\(658\) | 11.1138i | 0.433262i | ||||||||
\(659\) | 39.3776 | 1.53393 | 0.766966 | − | 0.641687i | \(-0.221765\pi\) | ||||
0.766966 | + | 0.641687i | \(0.221765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.2208 | −1.33103 | −0.665517 | − | 0.746383i | \(-0.731789\pi\) | ||||
−0.665517 | + | 0.746383i | \(0.731789\pi\) | |||||||
\(662\) | − 20.4362i | − 0.794276i | ||||||||
\(663\) | 13.7586i | 0.534339i | ||||||||
\(664\) | 8.49828 | 0.329797 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.74742 | 0.338956 | ||||||||
\(667\) | 54.6639i | 2.11659i | ||||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | 23.3484 | 0.902700 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.11383 | 0.351835 | ||||||||
\(672\) | 2.24914i | 0.0867625i | ||||||||
\(673\) | 24.4622i | 0.942948i | 0.881880 | + | 0.471474i | \(0.156278\pi\) | ||||
−0.881880 | + | 0.471474i | \(0.843722\pi\) | |||||||
\(674\) | −7.88273 | −0.303632 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1138 | −0.465916 | ||||||||
\(677\) | − 39.1070i | − 1.50300i | −0.659732 | − | 0.751501i | \(-0.729330\pi\) | ||||
0.659732 | − | 0.751501i | \(-0.270670\pi\) | |||||||
\(678\) | 24.7328i | 0.949858i | ||||||||
\(679\) | −15.3630 | −0.589577 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.2345 | −1.38851 | ||||||||
\(682\) | − 9.55691i | − 0.365953i | ||||||||
\(683\) | − 23.3776i | − 0.894518i | −0.894404 | − | 0.447259i | \(-0.852400\pi\) | ||||
0.894404 | − | 0.447259i | \(-0.147600\pi\) | |||||||
\(684\) | 8.98883 | 0.343697 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | − 54.6310i | − 2.08430i | ||||||||
\(688\) | − 7.67418i | − 0.292575i | ||||||||
\(689\) | 4.46907 | 0.170258 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.49828 | 0.323290 | 0.161645 | − | 0.986849i | \(-0.448320\pi\) | ||||
0.161645 | + | 0.986849i | \(0.448320\pi\) | |||||||
\(692\) | 0.117266i | 0.00445780i | ||||||||
\(693\) | 2.05863i | 0.0782010i | ||||||||
\(694\) | −13.5569 | −0.514613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −19.6742 | −0.745748 | ||||||||
\(697\) | − 13.8535i | − 0.524739i | ||||||||
\(698\) | 10.7328i | 0.406243i | ||||||||
\(699\) | 15.4880 | 0.585809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9751 | 0.565601 | 0.282800 | − | 0.959179i | \(-0.408737\pi\) | ||||
0.282800 | + | 0.959179i | \(0.408737\pi\) | |||||||
\(702\) | 1.99312i | 0.0752256i | ||||||||
\(703\) | 18.5535i | 0.699758i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.8578 | −0.784994 | ||||||||
\(707\) | 16.8793i | 0.634811i | ||||||||
\(708\) | − 4.23453i | − 0.159143i | ||||||||
\(709\) | −40.7259 | −1.52949 | −0.764747 | − | 0.644330i | \(-0.777136\pi\) | ||||
−0.764747 | + | 0.644330i | \(0.777136\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.2234 | 0.645927 | ||||||||
\(712\) | 12.3810i | 0.463998i | ||||||||
\(713\) | 59.7225i | 2.23663i | ||||||||
\(714\) | −14.6155 | −0.546973 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.5535 | −0.842863 | ||||||||
\(717\) | 25.0449i | 0.935318i | ||||||||
\(718\) | − 0.366407i | − 0.0136742i | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.61555 | 0.246376 | ||||||||
\(722\) | 0.0655089i | 0.00243799i | ||||||||
\(723\) | 5.32238i | 0.197942i | ||||||||
\(724\) | −20.8793 | −0.775973 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.24914 | −0.0834734 | ||||||||
\(727\) | − 51.6413i | − 1.91527i | −0.287984 | − | 0.957635i | \(-0.592985\pi\) | ||||
0.287984 | − | 0.957635i | \(-0.407015\pi\) | |||||||
\(728\) | 0.941367i | 0.0348894i | ||||||||
\(729\) | 8.23109 | 0.304855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.8690 | 1.84447 | ||||||||
\(732\) | − 20.4983i | − 0.757638i | ||||||||
\(733\) | 42.0000i | 1.55131i | 0.631160 | + | 0.775653i | \(0.282579\pi\) | ||||
−0.631160 | + | 0.775653i | \(0.717421\pi\) | |||||||
\(734\) | −20.8432 | −0.769337 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.24914 | 0.230346 | ||||||||
\(737\) | 12.9966i | 0.478735i | ||||||||
\(738\) | 4.38875i | 0.161552i | ||||||||
\(739\) | 49.1070 | 1.80643 | 0.903214 | − | 0.429190i | \(-0.141201\pi\) | ||||
0.903214 | + | 0.429190i | \(0.141201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.24485 | 0.339618 | ||||||||
\(742\) | 4.74742i | 0.174283i | ||||||||
\(743\) | 53.2311i | 1.95286i | 0.215836 | + | 0.976430i | \(0.430752\pi\) | ||||
−0.215836 | + | 0.976430i | \(0.569248\pi\) | |||||||
\(744\) | −21.4948 | −0.788039 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.37758 | −0.196887 | ||||||||
\(747\) | − 17.4948i | − 0.640103i | ||||||||
\(748\) | − 6.49828i | − 0.237601i | ||||||||
\(749\) | −14.5535 | −0.531772 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.6121 | −1.15354 | −0.576771 | − | 0.816906i | \(-0.695688\pi\) | ||||
−0.576771 | + | 0.816906i | \(0.695688\pi\) | |||||||
\(752\) | 11.1138i | 0.405280i | ||||||||
\(753\) | 56.4691i | 2.05785i | ||||||||
\(754\) | −8.23453 | −0.299884 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.11727 | −0.0770042 | ||||||||
\(757\) | − 1.24570i | − 0.0452758i | −0.999744 | − | 0.0226379i | \(-0.992794\pi\) | ||||
0.999744 | − | 0.0226379i | \(-0.00720649\pi\) | |||||||
\(758\) | − 3.53093i | − 0.128249i | ||||||||
\(759\) | 14.0552 | 0.510171 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6009 | −0.384284 | −0.192142 | − | 0.981367i | \(-0.561543\pi\) | ||||
−0.192142 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(762\) | 13.2311i | 0.479312i | ||||||||
\(763\) | − 0.249141i | − 0.00901949i | ||||||||
\(764\) | −3.11383 | −0.112654 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.38445 | 0.0500223 | ||||||||
\(767\) | − 1.77234i | − 0.0639956i | ||||||||
\(768\) | 2.24914i | 0.0811589i | ||||||||
\(769\) | 19.1284 | 0.689789 | 0.344895 | − | 0.938641i | \(-0.387915\pi\) | ||||
0.344895 | + | 0.938641i | \(0.387915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.44309 | 0.232042 | ||||||||
\(772\) | − 6.17246i | − 0.222152i | ||||||||
\(773\) | − 39.9931i | − 1.43845i | −0.694776 | − | 0.719226i | \(-0.744496\pi\) | ||||
0.694776 | − | 0.719226i | \(-0.255504\pi\) | |||||||
\(774\) | −15.7983 | −0.567859 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.3630 | −0.551498 | ||||||||
\(777\) | 9.55691i | 0.342852i | ||||||||
\(778\) | − 15.7294i | − 0.563925i | ||||||||
\(779\) | −9.30863 | −0.333516 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.6155 | −0.522985 | ||||||||
\(782\) | 40.6087i | 1.45216i | ||||||||
\(783\) | − 18.5206i | − 0.661873i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.81722 | 0.100487 | ||||||||
\(787\) | 37.9931i | 1.35431i | 0.735841 | + | 0.677154i | \(0.236787\pi\) | ||||
−0.735841 | + | 0.677154i | \(0.763213\pi\) | |||||||
\(788\) | − 6.73281i | − 0.239847i | ||||||||
\(789\) | 8.46907 | 0.301507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9966 | −0.390993 | ||||||||
\(792\) | 2.05863i | 0.0731503i | ||||||||
\(793\) | − 8.57946i | − 0.304665i | ||||||||
\(794\) | 17.6121 | 0.625030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.2311 | −0.468964 | ||||||||
\(797\) | − 20.3810i | − 0.721933i | −0.932579 | − | 0.360966i | \(-0.882447\pi\) | ||||
0.932579 | − | 0.360966i | \(-0.117553\pi\) | |||||||
\(798\) | 9.82066i | 0.347648i | ||||||||
\(799\) | −72.2208 | −2.55499 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4880 | 0.900573 | ||||||||
\(802\) | − 32.8172i | − 1.15882i | ||||||||
\(803\) | 10.4983i | 0.370476i | ||||||||
\(804\) | 29.2311 | 1.03090 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.99656 | −0.316890 | ||||||||
\(807\) | − 20.1104i | − 0.707919i | ||||||||
\(808\) | 16.8793i | 0.593812i | ||||||||
\(809\) | 31.7294 | 1.11555 | 0.557773 | − | 0.829994i | \(-0.311656\pi\) | ||||
0.557773 | + | 0.829994i | \(0.311656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.5095 | 1.52782 | 0.763912 | − | 0.645321i | \(-0.223276\pi\) | ||||
0.763912 | + | 0.645321i | \(0.223276\pi\) | |||||||
\(812\) | − 8.74742i | − 0.306974i | ||||||||
\(813\) | 48.3449i | 1.69553i | ||||||||
\(814\) | −4.24914 | −0.148932 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.6155 | −0.511646 | ||||||||
\(817\) | − 33.5086i | − 1.17232i | ||||||||
\(818\) | 33.3561i | 1.16627i | ||||||||
\(819\) | 1.93793 | 0.0677167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.7766 | −0.864711 | −0.432355 | − | 0.901703i | \(-0.642317\pi\) | ||||
−0.432355 | + | 0.901703i | \(0.642317\pi\) | |||||||
\(822\) | − 22.4914i | − 0.784478i | ||||||||
\(823\) | − 28.8647i | − 1.00616i | −0.864240 | − | 0.503080i | \(-0.832200\pi\) | ||||
0.864240 | − | 0.503080i | \(-0.167800\pi\) | |||||||
\(824\) | 6.61555 | 0.230464 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.88273 | 0.0655087 | ||||||||
\(827\) | 34.2277i | 1.19021i | 0.803647 | + | 0.595106i | \(0.202890\pi\) | ||||
−0.803647 | + | 0.595106i | \(0.797110\pi\) | |||||||
\(828\) | − 12.8647i | − 0.447079i | ||||||||
\(829\) | −23.6381 | −0.820985 | −0.410492 | − | 0.911864i | \(-0.634643\pi\) | ||||
−0.410492 | + | 0.911864i | \(0.634643\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2019 | −0.596727 | ||||||||
\(832\) | 0.941367i | 0.0326360i | ||||||||
\(833\) | − 6.49828i | − 0.225152i | ||||||||
\(834\) | 24.7000 | 0.855290 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.36641 | −0.151015 | ||||||||
\(837\) | − 20.2345i | − 0.699408i | ||||||||
\(838\) | − 12.3449i | − 0.426448i | ||||||||
\(839\) | 24.9053 | 0.859826 | 0.429913 | − | 0.902870i | \(-0.358544\pi\) | ||||
0.429913 | + | 0.902870i | \(0.358544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.5174 | 1.63853 | ||||||||
\(842\) | − 8.87930i | − 0.306001i | ||||||||
\(843\) | − 64.3604i | − 2.21669i | ||||||||
\(844\) | −23.1138 | −0.795611 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22.8793 | 0.786606 | ||||||||
\(847\) | − 1.00000i | − 0.0343604i | ||||||||
\(848\) | 4.74742i | 0.163027i | ||||||||
\(849\) | −6.47594 | −0.222254 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.5535 | 0.910241 | ||||||||
\(852\) | 32.8724i | 1.12619i | ||||||||
\(853\) | − 22.9966i | − 0.787387i | −0.919242 | − | 0.393694i | \(-0.871197\pi\) | ||||
0.919242 | − | 0.393694i | \(-0.128803\pi\) | |||||||
\(854\) | 9.11383 | 0.311869 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.5535 | −0.497428 | ||||||||
\(857\) | − 31.2603i | − 1.06783i | −0.845538 | − | 0.533916i | \(-0.820720\pi\) | ||||
0.845538 | − | 0.533916i | \(-0.179280\pi\) | |||||||
\(858\) | 2.11727i | 0.0722823i | ||||||||
\(859\) | −20.3449 | −0.694160 | −0.347080 | − | 0.937836i | \(-0.612827\pi\) | ||||
−0.347080 | + | 0.937836i | \(0.612827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.79488 | −0.163409 | ||||||||
\(862\) | 18.2784i | 0.622563i | ||||||||
\(863\) | 58.3595i | 1.98658i | 0.115644 | + | 0.993291i | \(0.463107\pi\) | ||||
−0.115644 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(864\) | −2.11727 | −0.0720309 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.86469 | 0.233272 | ||||||||
\(867\) | − 56.7405i | − 1.92701i | ||||||||
\(868\) | − 9.55691i | − 0.324383i | ||||||||
\(869\) | −8.36641 | −0.283811 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.2345 | 0.414551 | ||||||||
\(872\) | − 0.249141i | − 0.00843696i | ||||||||
\(873\) | 31.6267i | 1.07040i | ||||||||
\(874\) | 27.2863 | 0.922973 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.6121 | 0.797779 | ||||||||
\(877\) | 11.9639i | 0.403992i | 0.979386 | + | 0.201996i | \(0.0647429\pi\) | ||||
−0.979386 | + | 0.201996i | \(0.935257\pi\) | |||||||
\(878\) | 11.8466i | 0.399805i | ||||||||
\(879\) | −29.1070 | −0.981753 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.88961 | 0.198426 | 0.0992130 | − | 0.995066i | \(-0.468367\pi\) | ||||
0.0992130 | + | 0.995066i | \(0.468367\pi\) | |||||||
\(882\) | 2.05863i | 0.0693178i | ||||||||
\(883\) | 19.4880i | 0.655822i | 0.944709 | + | 0.327911i | \(0.106345\pi\) | ||||
−0.944709 | + | 0.327911i | \(0.893655\pi\) | |||||||
\(884\) | −6.11727 | −0.205746 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.8827 | 0.600782 | ||||||||
\(887\) | 50.4622i | 1.69435i | 0.531310 | + | 0.847177i | \(0.321700\pi\) | ||||
−0.531310 | + | 0.847177i | \(0.678300\pi\) | |||||||
\(888\) | 9.55691i | 0.320709i | ||||||||
\(889\) | −5.88273 | −0.197301 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9379 | −0.366434 | ||||||||
\(892\) | 10.3810i | 0.347582i | ||||||||
\(893\) | 48.5275i | 1.62391i | ||||||||
\(894\) | 0.0328552 | 0.00109884 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | − 13.2311i | − 0.441773i | ||||||||
\(898\) | 16.8172i | 0.561198i | ||||||||
\(899\) | 83.5984 | 2.78816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.8501 | −1.02777 | ||||||||
\(902\) | − 2.13187i | − 0.0709836i | ||||||||
\(903\) | − 17.2603i | − 0.574387i | ||||||||
\(904\) | −10.9966 | −0.365740 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.2897 | 1.13920 | ||||||||
\(907\) | − 16.8432i | − 0.559269i | −0.960106 | − | 0.279635i | \(-0.909787\pi\) | ||||
0.960106 | − | 0.279635i | \(-0.0902134\pi\) | |||||||
\(908\) | − 16.1104i | − 0.534642i | ||||||||
\(909\) | 34.7483 | 1.15253 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6155 | −1.27939 | −0.639695 | − | 0.768629i | \(-0.720939\pi\) | ||||
−0.639695 | + | 0.768629i | \(0.720939\pi\) | |||||||
\(912\) | 9.82066i | 0.325195i | ||||||||
\(913\) | 8.49828i | 0.281252i | ||||||||
\(914\) | 12.2277 | 0.404455 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.2897 | 0.802555 | ||||||||
\(917\) | 1.25258i | 0.0413638i | ||||||||
\(918\) | − 13.7586i | − 0.454101i | ||||||||
\(919\) | −17.2818 | −0.570074 | −0.285037 | − | 0.958517i | \(-0.592006\pi\) | ||||
−0.285037 | + | 0.958517i | \(0.592006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.12070 | −0.0369285 | ||||||||
\(922\) | − 16.6155i | − 0.547204i | ||||||||
\(923\) | 13.7586i | 0.452870i | ||||||||
\(924\) | −2.24914 | −0.0739913 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.4837 | 0.607411 | ||||||||
\(927\) | − 13.6190i | − 0.447306i | ||||||||
\(928\) | − 8.74742i | − 0.287148i | ||||||||
\(929\) | −2.91539 | −0.0956508 | −0.0478254 | − | 0.998856i | \(-0.515229\pi\) | ||||
−0.0478254 | + | 0.998856i | \(0.515229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.36641 | −0.143103 | ||||||||
\(932\) | 6.88617i | 0.225564i | ||||||||
\(933\) | − 52.7191i | − 1.72594i | ||||||||
\(934\) | −24.3956 | −0.798249 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.93793 | 0.0633432 | ||||||||
\(937\) | 22.5795i | 0.737639i | 0.929501 | + | 0.368819i | \(0.120238\pi\) | ||||
−0.929501 | + | 0.368819i | \(0.879762\pi\) | |||||||
\(938\) | 12.9966i | 0.424353i | ||||||||
\(939\) | 21.0741 | 0.687727 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.7655 | −0.709534 | −0.354767 | − | 0.934955i | \(-0.615440\pi\) | ||||
−0.354767 | + | 0.934955i | \(0.615440\pi\) | |||||||
\(942\) | 12.3741i | 0.403171i | ||||||||
\(943\) | 13.3224i | 0.433836i | ||||||||
\(944\) | 1.88273 | 0.0612778 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.67418 | 0.249509 | ||||||||
\(947\) | − 1.49484i | − 0.0485759i | −0.999705 | − | 0.0242879i | \(-0.992268\pi\) | ||||
0.999705 | − | 0.0242879i | \(-0.00773185\pi\) | |||||||
\(948\) | 18.8172i | 0.611155i | ||||||||
\(949\) | 9.88273 | 0.320807 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.4431 | 0.727767 | ||||||||
\(952\) | − 6.49828i | − 0.210610i | ||||||||
\(953\) | 4.83098i | 0.156491i | 0.996934 | + | 0.0782453i | \(0.0249317\pi\) | ||||
−0.996934 | + | 0.0782453i | \(0.975068\pi\) | |||||||
\(954\) | 9.77320 | 0.316419 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.1353 | −0.360142 | ||||||||
\(957\) | − 19.6742i | − 0.635976i | ||||||||
\(958\) | 27.7655i | 0.897062i | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.3346 | 1.94628 | ||||||||
\(962\) | 4.00000i | 0.128965i | ||||||||
\(963\) | 29.9603i | 0.965456i | ||||||||
\(964\) | −2.36641 | −0.0762168 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14.0552 | 0.452218 | ||||||||
\(967\) | − 51.9278i | − 1.66989i | −0.550336 | − | 0.834943i | \(-0.685501\pi\) | ||||
0.550336 | − | 0.834943i | \(-0.314499\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | −63.8174 | −2.05011 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.6933 | 1.91565 | 0.957824 | − | 0.287354i | \(-0.0927757\pi\) | ||||
0.957824 | + | 0.287354i | \(0.0927757\pi\) | |||||||
\(972\) | 18.2491i | 0.585341i | ||||||||
\(973\) | 10.9820i | 0.352065i | ||||||||
\(974\) | −10.0958 | −0.323490 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.11383 | 0.291727 | ||||||||
\(977\) | 31.2311i | 0.999171i | 0.866265 | + | 0.499586i | \(0.166514\pi\) | ||||
−0.866265 | + | 0.499586i | \(0.833486\pi\) | |||||||
\(978\) | − 40.9966i | − 1.31093i | ||||||||
\(979\) | −12.3810 | −0.395699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.512889 | −0.0163753 | ||||||||
\(982\) | − 32.1104i | − 1.02468i | ||||||||
\(983\) | 22.6155i | 0.721324i | 0.932697 | + | 0.360662i | \(0.117449\pi\) | ||||
−0.932697 | + | 0.360662i | \(0.882551\pi\) | |||||||
\(984\) | −4.79488 | −0.152855 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 56.8432 | 1.81026 | ||||||||
\(987\) | 24.9966i | 0.795649i | ||||||||
\(988\) | 4.11039i | 0.130769i | ||||||||
\(989\) | −47.9570 | −1.52494 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.4102 | 0.711884 | 0.355942 | − | 0.934508i | \(-0.384160\pi\) | ||||
0.355942 | + | 0.934508i | \(0.384160\pi\) | |||||||
\(992\) | − 9.55691i | − 0.303432i | ||||||||
\(993\) | − 45.9639i | − 1.45862i | ||||||||
\(994\) | −14.6155 | −0.463577 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 19.1138 | 0.605645 | ||||||||
\(997\) | − 27.3415i | − 0.865914i | −0.901415 | − | 0.432957i | \(-0.857470\pi\) | ||||
0.901415 | − | 0.432957i | \(-0.142530\pi\) | |||||||
\(998\) | 8.79488i | 0.278397i | ||||||||
\(999\) | −8.99656 | −0.284639 |
(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 | 3850.2.c.ba.1849.6 | 6 | ||
5.2 | odd | 4 | 3850.2.a.bt.1.3 | 3 | |||
5.3 | odd | 4 | 770.2.a.m.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 3850.2.c.ba.1849.1 | 6 | ||
15.8 | even | 4 | 6930.2.a.ce.1.2 | 3 | |||
20.3 | even | 4 | 6160.2.a.bf.1.3 | 3 | |||
35.13 | even | 4 | 5390.2.a.ca.1.3 | 3 | |||
55.43 | even | 4 | 8470.2.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.m.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
3850.2.a.bt.1.3 | 3 | 5.2 | odd | 4 | |||
3850.2.c.ba.1849.1 | 6 | 5.4 | even | 2 | inner | ||
3850.2.c.ba.1849.6 | 6 | 1.1 | even | 1 | trivial | ||
5390.2.a.ca.1.3 | 3 | 35.13 | even | 4 | |||
6160.2.a.bf.1.3 | 3 | 20.3 | even | 4 | |||
6930.2.a.ce.1.2 | 3 | 15.8 | even | 4 | |||
8470.2.a.ci.1.1 | 3 | 55.43 | even | 4 |