Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(307,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.e (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.2 | ||
Root | \(-0.437016 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.307 |
Dual form | 1386.2.e.d.307.7 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.12132 | + | 1.58114i | −0.801784 | + | 0.597614i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.41421 | −0.447214 | ||||||||
\(11\) | 3.16228 | + | 1.00000i | 0.953463 | + | 0.301511i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 1.58114 | + | 2.12132i | 0.422577 | + | 0.566947i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 1.41421i | 0.316228i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 3.16228i | 0.213201 | − | 0.674200i | ||||
\(23\) | −3.16228 | −0.659380 | −0.329690 | − | 0.944089i | \(-0.606944\pi\) | ||||
−0.329690 | + | 0.944089i | \(0.606944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 1.41421i | 0.277350i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.12132 | − | 1.58114i | 0.400892 | − | 0.298807i | ||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.94427i | − | 1.60644i | −0.595683 | − | 0.803219i | \(-0.703119\pi\) | ||
0.595683 | − | 0.803219i | \(-0.296881\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.47214i | − | 0.766965i | ||||||
\(35\) | 2.23607 | + | 3.00000i | 0.377964 | + | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | − | 2.82843i | − | 0.458831i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.41421 | 0.223607 | ||||||||
\(41\) | 8.94427 | 1.39686 | 0.698430 | − | 0.715678i | \(-0.253882\pi\) | ||||
0.698430 | + | 0.715678i | \(0.253882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.32456i | − | 0.964486i | −0.876038 | − | 0.482243i | \(-0.839822\pi\) | ||
0.876038 | − | 0.482243i | \(-0.160178\pi\) | |||||||
\(44\) | −3.16228 | − | 1.00000i | −0.476731 | − | 0.150756i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.16228i | 0.466252i | ||||||||
\(47\) | − | 7.07107i | − | 1.03142i | −0.856763 | − | 0.515711i | \(-0.827528\pi\) | ||
0.856763 | − | 0.515711i | \(-0.172472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | − | 6.70820i | 0.285714 | − | 0.958315i | ||||
\(50\) | − | 3.00000i | − | 0.424264i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41421 | 0.196116 | ||||||||
\(53\) | 3.16228 | 0.434372 | 0.217186 | − | 0.976130i | \(-0.430312\pi\) | ||||
0.217186 | + | 0.976130i | \(0.430312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | − | 4.47214i | 0.190693 | − | 0.603023i | ||||
\(56\) | −1.58114 | − | 2.12132i | −0.211289 | − | 0.283473i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | − | 2.82843i | − | 0.368230i | −0.982905 | − | 0.184115i | \(-0.941058\pi\) | ||
0.982905 | − | 0.184115i | \(-0.0589419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7279 | −1.62964 | −0.814822 | − | 0.579712i | \(-0.803165\pi\) | ||||
−0.814822 | + | 0.579712i | \(0.803165\pi\) | |||||||
\(62\) | −8.94427 | −1.13592 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000i | 0.248069i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | −4.47214 | −0.542326 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000 | − | 2.23607i | 0.358569 | − | 0.267261i | ||||
\(71\) | 3.16228 | 0.375293 | 0.187647 | − | 0.982237i | \(-0.439914\pi\) | ||||
0.187647 | + | 0.982237i | \(0.439914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | −8.28934 | + | 2.87868i | −0.944658 | + | 0.328056i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.16228i | 0.355784i | 0.984050 | + | 0.177892i | \(0.0569278\pi\) | ||||
−0.984050 | + | 0.177892i | \(0.943072\pi\) | |||||||
\(80\) | − | 1.41421i | − | 0.158114i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 8.94427i | − | 0.987730i | ||||||
\(83\) | 4.47214 | 0.490881 | 0.245440 | − | 0.969412i | \(-0.421067\pi\) | ||||
0.245440 | + | 0.969412i | \(0.421067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.32456i | − | 0.685994i | ||||||
\(86\) | −6.32456 | −0.681994 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | + | 3.16228i | −0.106600 | + | 0.337100i | ||||
\(89\) | 16.9706i | 1.79888i | 0.437048 | + | 0.899438i | \(0.356024\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | − | 2.23607i | 0.314485 | − | 0.234404i | ||||
\(92\) | 3.16228 | 0.329690 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.07107 | −0.729325 | ||||||||
\(95\) | − | 4.00000i | − | 0.410391i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.47214i | − | 0.454077i | −0.973886 | − | 0.227038i | \(-0.927096\pi\) | ||
0.973886 | − | 0.227038i | \(-0.0729043\pi\) | |||||||
\(98\) | −6.70820 | − | 2.00000i | −0.677631 | − | 0.202031i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | 13.4164 | 1.33498 | 0.667491 | − | 0.744618i | \(-0.267368\pi\) | ||||
0.667491 | + | 0.744618i | \(0.267368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.94427i | − | 0.881305i | −0.897678 | − | 0.440653i | \(-0.854747\pi\) | ||
0.897678 | − | 0.440653i | \(-0.145253\pi\) | |||||||
\(104\) | − | 1.41421i | − | 0.138675i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 3.16228i | − | 0.307148i | ||||||
\(107\) | − | 2.00000i | − | 0.193347i | −0.995316 | − | 0.0966736i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966736i | \(-0.0308203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.16228i | 0.302891i | 0.988466 | + | 0.151446i | \(0.0483928\pi\) | ||||
−0.988466 | + | 0.151446i | \(0.951607\pi\) | |||||||
\(110\) | −4.47214 | − | 1.41421i | −0.426401 | − | 0.134840i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.12132 | + | 1.58114i | −0.200446 | + | 0.149404i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.47214i | 0.417029i | ||||||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.82843 | −0.260378 | ||||||||
\(119\) | −9.48683 | + | 7.07107i | −0.869657 | + | 0.648204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | + | 6.32456i | 0.818182 | + | 0.574960i | ||||
\(122\) | 12.7279i | 1.15233i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.94427i | 0.803219i | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 22.1359i | − | 1.96425i | −0.188237 | − | 0.982124i | \(-0.560277\pi\) | ||
0.188237 | − | 0.982124i | \(-0.439723\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −4.47214 | −0.390732 | −0.195366 | − | 0.980730i | \(-0.562590\pi\) | ||||
−0.195366 | + | 0.980730i | \(0.562590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 4.47214i | −0.520266 | + | 0.387783i | ||||
\(134\) | − | 12.0000i | − | 1.03664i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.47214i | 0.383482i | ||||||||
\(137\) | 18.9737 | 1.62103 | 0.810515 | − | 0.585718i | \(-0.199187\pi\) | ||||
0.810515 | + | 0.585718i | \(0.199187\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82843 | 0.239904 | 0.119952 | − | 0.992780i | \(-0.461726\pi\) | ||||
0.119952 | + | 0.992780i | \(0.461726\pi\) | |||||||
\(140\) | −2.23607 | − | 3.00000i | −0.188982 | − | 0.253546i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 3.16228i | − | 0.265372i | ||||||
\(143\) | −4.47214 | − | 1.41421i | −0.373979 | − | 0.118262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.48528 | 0.704664 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 10.0000i | 0.819232i | 0.912258 | + | 0.409616i | \(0.134337\pi\) | ||||
−0.912258 | + | 0.409616i | \(0.865663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.8114i | 1.28671i | 0.765567 | + | 0.643356i | \(0.222459\pi\) | ||||
−0.765567 | + | 0.643356i | \(0.777541\pi\) | |||||||
\(152\) | 2.82843i | 0.229416i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.87868 | + | 8.28934i | 0.231971 | + | 0.667974i | ||||
\(155\) | −12.6491 | −1.01600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.4164i | − | 1.07075i | −0.844616 | − | 0.535373i | \(-0.820171\pi\) | ||
0.844616 | − | 0.535373i | \(-0.179829\pi\) | |||||||
\(158\) | 3.16228 | 0.251577 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.41421 | −0.111803 | ||||||||
\(161\) | 6.70820 | − | 5.00000i | 0.528681 | − | 0.394055i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0000 | −1.09656 | −0.548282 | − | 0.836293i | \(-0.684718\pi\) | ||||
−0.548282 | + | 0.836293i | \(0.684718\pi\) | |||||||
\(164\) | −8.94427 | −0.698430 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4.47214i | − | 0.347105i | ||||||
\(167\) | −17.8885 | −1.38426 | −0.692129 | − | 0.721774i | \(-0.743327\pi\) | ||||
−0.692129 | + | 0.721774i | \(0.743327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | −6.32456 | −0.485071 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.32456i | 0.482243i | ||||||||
\(173\) | 13.4164 | 1.02003 | 0.510015 | − | 0.860165i | \(-0.329640\pi\) | ||||
0.510015 | + | 0.860165i | \(0.329640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.36396 | + | 4.74342i | −0.481070 | + | 0.358569i | ||||
\(176\) | 3.16228 | + | 1.00000i | 0.238366 | + | 0.0753778i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.9706 | 1.27200 | ||||||||
\(179\) | 12.6491 | 0.945439 | 0.472719 | − | 0.881213i | \(-0.343272\pi\) | ||||
0.472719 | + | 0.881213i | \(0.343272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4164i | 0.997234i | 0.866822 | + | 0.498617i | \(0.166159\pi\) | ||||
−0.866822 | + | 0.498617i | \(0.833841\pi\) | |||||||
\(182\) | −2.23607 | − | 3.00000i | −0.165748 | − | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 3.16228i | − | 0.233126i | ||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.1421 | + | 4.47214i | 1.03418 | + | 0.327035i | ||||
\(188\) | 7.07107i | 0.515711i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 9.48683 | 0.686443 | 0.343222 | − | 0.939254i | \(-0.388482\pi\) | ||||
0.343222 | + | 0.939254i | \(0.388482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.32456i | 0.455251i | 0.973749 | + | 0.227626i | \(0.0730963\pi\) | ||||
−0.973749 | + | 0.227626i | \(0.926904\pi\) | |||||||
\(194\) | −4.47214 | −0.321081 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.00000 | + | 6.70820i | −0.142857 | + | 0.479157i | ||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.8885i | 1.26809i | 0.773298 | + | 0.634043i | \(0.218606\pi\) | ||||
−0.773298 | + | 0.634043i | \(0.781394\pi\) | |||||||
\(200\) | 3.00000i | 0.212132i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 13.4164i | − | 0.943975i | ||||||
\(203\) | −9.48683 | − | 12.7279i | −0.665845 | − | 0.893325i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 12.6491i | − | 0.883452i | ||||||
\(206\) | −8.94427 | −0.623177 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.41421 | −0.0980581 | ||||||||
\(209\) | 8.94427 | + | 2.82843i | 0.618688 | + | 0.195646i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.9737i | − | 1.30620i | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||
0.757271 | − | 0.653101i | \(-0.226532\pi\) | |||||||
\(212\) | −3.16228 | −0.217186 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.00000 | −0.136717 | ||||||||
\(215\) | −8.94427 | −0.609994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1421 | + | 18.9737i | 0.960031 | + | 1.28802i | ||||
\(218\) | 3.16228 | 0.214176 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.41421 | + | 4.47214i | −0.0953463 | + | 0.301511i | ||||
\(221\) | −6.32456 | −0.425436 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.8328i | 1.79686i | 0.439119 | + | 0.898429i | \(0.355291\pi\) | ||||
−0.439119 | + | 0.898429i | \(0.644709\pi\) | |||||||
\(224\) | 1.58114 | + | 2.12132i | 0.105644 | + | 0.141737i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.47214i | 0.295527i | 0.989023 | + | 0.147764i | \(0.0472075\pi\) | ||||
−0.989023 | + | 0.147764i | \(0.952793\pi\) | |||||||
\(230\) | 4.47214 | 0.294884 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0000 | −0.652328 | ||||||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.07107 | + | 9.48683i | 0.458349 | + | 0.614940i | ||||
\(239\) | − | 16.0000i | − | 1.03495i | −0.855697 | − | 0.517477i | \(-0.826871\pi\) | ||
0.855697 | − | 0.517477i | \(-0.173129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.48528 | −0.546585 | −0.273293 | − | 0.961931i | \(-0.588113\pi\) | ||||
−0.273293 | + | 0.961931i | \(0.588113\pi\) | |||||||
\(242\) | 6.32456 | − | 9.00000i | 0.406558 | − | 0.578542i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.7279 | 0.814822 | ||||||||
\(245\) | −9.48683 | − | 2.82843i | −0.606092 | − | 0.180702i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | −0.254514 | ||||||||
\(248\) | 8.94427 | 0.567962 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.3137 | −0.715542 | ||||||||
\(251\) | 19.7990i | 1.24970i | 0.780744 | + | 0.624851i | \(0.214840\pi\) | ||||
−0.780744 | + | 0.624851i | \(0.785160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.0000 | − | 3.16228i | −0.628695 | − | 0.198811i | ||||
\(254\) | −22.1359 | −1.38893 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 16.9706i | − | 1.05859i | −0.848436 | − | 0.529297i | \(-0.822456\pi\) | ||
0.848436 | − | 0.529297i | \(-0.177544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.24264 | + | 3.16228i | −0.263625 | + | 0.196494i | ||||
\(260\) | − | 2.00000i | − | 0.124035i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.47214i | 0.276289i | ||||||||
\(263\) | 4.00000i | 0.246651i | 0.992366 | + | 0.123325i | \(0.0393559\pi\) | ||||
−0.992366 | + | 0.123325i | \(0.960644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4.47214i | − | 0.274721i | ||||||
\(266\) | 4.47214 | + | 6.00000i | 0.274204 | + | 0.367884i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.0000 | −0.733017 | ||||||||
\(269\) | − | 18.3848i | − | 1.12094i | −0.828175 | − | 0.560470i | \(-0.810621\pi\) | ||
0.828175 | − | 0.560470i | \(-0.189379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7279 | −0.773166 | −0.386583 | − | 0.922255i | \(-0.626345\pi\) | ||||
−0.386583 | + | 0.922255i | \(0.626345\pi\) | |||||||
\(272\) | 4.47214 | 0.271163 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 18.9737i | − | 1.14624i | ||||||
\(275\) | 9.48683 | + | 3.00000i | 0.572078 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1359i | 1.33002i | 0.746834 | + | 0.665010i | \(0.231573\pi\) | ||||
−0.746834 | + | 0.665010i | \(0.768427\pi\) | |||||||
\(278\) | − | 2.82843i | − | 0.169638i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | + | 2.23607i | −0.179284 | + | 0.133631i | ||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −3.16228 | −0.187647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.41421 | + | 4.47214i | −0.0836242 | + | 0.264443i | ||||
\(287\) | −18.9737 | + | 14.1421i | −1.11998 | + | 0.834784i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | − | 8.48528i | − | 0.498273i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.47214 | 0.261265 | 0.130632 | − | 0.991431i | \(-0.458299\pi\) | ||||
0.130632 | + | 0.991431i | \(0.458299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.0000 | 0.579284 | ||||||||
\(299\) | 4.47214 | 0.258630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 13.4164i | 0.576390 | + | 0.773309i | ||||
\(302\) | 15.8114 | 0.909843 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.82843 | 0.162221 | ||||||||
\(305\) | 18.0000i | 1.03068i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.1421 | −0.807134 | −0.403567 | − | 0.914950i | \(-0.632230\pi\) | ||||
−0.403567 | + | 0.914950i | \(0.632230\pi\) | |||||||
\(308\) | 8.28934 | − | 2.87868i | 0.472329 | − | 0.164028i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.6491i | 0.718421i | ||||||||
\(311\) | 15.5563i | 0.882120i | 0.897478 | + | 0.441060i | \(0.145397\pi\) | ||||
−0.897478 | + | 0.441060i | \(0.854603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.8328i | 1.51668i | 0.651859 | + | 0.758340i | \(0.273989\pi\) | ||||
−0.651859 | + | 0.758340i | \(0.726011\pi\) | |||||||
\(314\) | −13.4164 | −0.757132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 3.16228i | − | 0.177892i | ||||||
\(317\) | −9.48683 | −0.532834 | −0.266417 | − | 0.963858i | \(-0.585840\pi\) | ||||
−0.266417 | + | 0.963858i | \(0.585840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | + | 18.9737i | −0.335936 | + | 1.06232i | ||||
\(320\) | 1.41421i | 0.0790569i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.00000 | − | 6.70820i | −0.278639 | − | 0.373834i | ||||
\(323\) | 12.6491 | 0.703815 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.24264 | −0.235339 | ||||||||
\(326\) | 14.0000i | 0.775388i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.94427i | 0.493865i | ||||||||
\(329\) | 11.1803 | + | 15.0000i | 0.616392 | + | 0.826977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(332\) | −4.47214 | −0.245440 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.8885i | 0.978818i | ||||||||
\(335\) | − | 16.9706i | − | 0.927201i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 25.2982i | − | 1.37808i | −0.724722 | − | 0.689041i | \(-0.758032\pi\) | ||
0.724722 | − | 0.689041i | \(-0.241968\pi\) | |||||||
\(338\) | 11.0000i | 0.598321i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.32456i | 0.342997i | ||||||||
\(341\) | 8.94427 | − | 28.2843i | 0.484359 | − | 1.53168i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.36396 | + | 17.3925i | 0.343622 | + | 0.939108i | ||||
\(344\) | 6.32456 | 0.340997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 13.4164i | − | 0.721271i | ||||||
\(347\) | − | 28.0000i | − | 1.50312i | −0.659665 | − | 0.751559i | \(-0.729302\pi\) | ||
0.659665 | − | 0.751559i | \(-0.270698\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.5269 | 1.74113 | 0.870563 | − | 0.492057i | \(-0.163755\pi\) | ||||
0.870563 | + | 0.492057i | \(0.163755\pi\) | |||||||
\(350\) | 4.74342 | + | 6.36396i | 0.253546 | + | 0.340168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | − | 3.16228i | 0.0533002 | − | 0.168550i | ||||
\(353\) | 28.2843i | 1.50542i | 0.658352 | + | 0.752710i | \(0.271254\pi\) | ||||
−0.658352 | + | 0.752710i | \(0.728746\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 4.47214i | − | 0.237356i | ||||||
\(356\) | − | 16.9706i | − | 0.899438i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12.6491i | − | 0.668526i | ||||||
\(359\) | − | 20.0000i | − | 1.05556i | −0.849381 | − | 0.527780i | \(-0.823025\pi\) | ||
0.849381 | − | 0.527780i | \(-0.176975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 13.4164 | 0.705151 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | + | 2.23607i | −0.157243 | + | 0.117202i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −3.16228 | −0.164845 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.82843 | −0.147043 | ||||||||
\(371\) | −6.70820 | + | 5.00000i | −0.348273 | + | 0.259587i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.8114i | − | 0.818683i | −0.912381 | − | 0.409341i | \(-0.865759\pi\) | ||
0.912381 | − | 0.409341i | \(-0.134241\pi\) | |||||||
\(374\) | 4.47214 | − | 14.1421i | 0.231249 | − | 0.731272i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.07107 | 0.364662 | ||||||||
\(377\) | − | 8.48528i | − | 0.437014i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 4.00000i | 0.205196i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 9.48683i | − | 0.485389i | ||||||
\(383\) | 15.5563i | 0.794892i | 0.917625 | + | 0.397446i | \(0.130103\pi\) | ||||
−0.917625 | + | 0.397446i | \(0.869897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.07107 | + | 11.7229i | 0.207481 | + | 0.597454i | ||||
\(386\) | 6.32456 | 0.321911 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.47214i | 0.227038i | ||||||||
\(389\) | 34.7851 | 1.76367 | 0.881836 | − | 0.471556i | \(-0.156307\pi\) | ||||
0.881836 | + | 0.471556i | \(0.156307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.1421 | −0.715199 | ||||||||
\(392\) | 6.70820 | + | 2.00000i | 0.338815 | + | 0.101015i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 4.47214 | 0.225018 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.47214i | − | 0.224450i | −0.993683 | − | 0.112225i | \(-0.964202\pi\) | ||
0.993683 | − | 0.112225i | \(-0.0357978\pi\) | |||||||
\(398\) | 17.8885 | 0.896672 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 18.9737 | 0.947500 | 0.473750 | − | 0.880659i | \(-0.342900\pi\) | ||||
0.473750 | + | 0.880659i | \(0.342900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6491i | 0.630097i | ||||||||
\(404\) | −13.4164 | −0.667491 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.7279 | + | 9.48683i | −0.631676 | + | 0.470824i | ||||
\(407\) | 6.32456 | + | 2.00000i | 0.313497 | + | 0.0991363i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.82843 | −0.139857 | −0.0699284 | − | 0.997552i | \(-0.522277\pi\) | ||||
−0.0699284 | + | 0.997552i | \(0.522277\pi\) | |||||||
\(410\) | −12.6491 | −0.624695 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.94427i | 0.440653i | ||||||||
\(413\) | 4.47214 | + | 6.00000i | 0.220059 | + | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.32456i | − | 0.310460i | ||||||
\(416\) | 1.41421i | 0.0693375i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.82843 | − | 8.94427i | 0.138343 | − | 0.437479i | ||||
\(419\) | 31.1127i | 1.51995i | 0.649950 | + | 0.759977i | \(0.274790\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.0000 | −1.46211 | −0.731055 | − | 0.682318i | \(-0.760972\pi\) | ||||
−0.731055 | + | 0.682318i | \(0.760972\pi\) | |||||||
\(422\) | −18.9737 | −0.923624 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.16228i | 0.153574i | ||||||||
\(425\) | 13.4164 | 0.650791 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.0000 | − | 20.1246i | 1.30662 | − | 0.973898i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.94427i | 0.431331i | ||||||||
\(431\) | − | 8.00000i | − | 0.385346i | −0.981263 | − | 0.192673i | \(-0.938284\pi\) | ||
0.981263 | − | 0.192673i | \(-0.0617157\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.94427i | 0.429834i | 0.976632 | + | 0.214917i | \(0.0689481\pi\) | ||||
−0.976632 | + | 0.214917i | \(0.931052\pi\) | |||||||
\(434\) | 18.9737 | − | 14.1421i | 0.910765 | − | 0.678844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 3.16228i | − | 0.151446i | ||||||
\(437\) | −8.94427 | −0.427863 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5269 | 1.55242 | 0.776212 | − | 0.630471i | \(-0.217138\pi\) | ||||
0.776212 | + | 0.630471i | \(0.217138\pi\) | |||||||
\(440\) | 4.47214 | + | 1.41421i | 0.213201 | + | 0.0674200i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.32456i | 0.300828i | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.0000 | 1.13771 | ||||||||
\(446\) | 26.8328 | 1.27057 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.12132 | − | 1.58114i | 0.100223 | − | 0.0747018i | ||||
\(449\) | −31.6228 | −1.49237 | −0.746186 | − | 0.665738i | \(-0.768117\pi\) | ||||
−0.746186 | + | 0.665738i | \(0.768117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.2843 | + | 8.94427i | 1.33185 | + | 0.421169i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.16228 | − | 4.24264i | −0.148250 | − | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 18.9737i | − | 0.887551i | −0.896138 | − | 0.443775i | \(-0.853639\pi\) | ||
0.896138 | − | 0.443775i | \(-0.146361\pi\) | |||||||
\(458\) | 4.47214 | 0.208969 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 4.47214i | − | 0.208514i | ||||||
\(461\) | 4.47214 | 0.208288 | 0.104144 | − | 0.994562i | \(-0.466790\pi\) | ||||
0.104144 | + | 0.994562i | \(0.466790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 6.00000i | 0.278543i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 16.9706i | 0.785304i | 0.919687 | + | 0.392652i | \(0.128442\pi\) | ||||
−0.919687 | + | 0.392652i | \(0.871558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.4558 | + | 18.9737i | −1.17544 | + | 0.876122i | ||||
\(470\) | 10.0000i | 0.461266i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.82843 | 0.130189 | ||||||||
\(473\) | 6.32456 | − | 20.0000i | 0.290803 | − | 0.919601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.48528 | 0.389331 | ||||||||
\(476\) | 9.48683 | − | 7.07107i | 0.434828 | − | 0.324102i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | −35.7771 | −1.63470 | −0.817348 | − | 0.576144i | \(-0.804557\pi\) | ||||
−0.817348 | + | 0.576144i | \(0.804557\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82843 | −0.128965 | ||||||||
\(482\) | 8.48528i | 0.386494i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.00000 | − | 6.32456i | −0.409091 | − | 0.287480i | ||||
\(485\) | −6.32456 | −0.287183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | − | 12.7279i | − | 0.576166i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.82843 | + | 9.48683i | −0.127775 | + | 0.428571i | ||||
\(491\) | 18.0000i | 0.812329i | 0.913800 | + | 0.406164i | \(0.133134\pi\) | ||||
−0.913800 | + | 0.406164i | \(0.866866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.8328i | 1.20849i | ||||||||
\(494\) | 4.00000i | 0.179969i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.94427i | − | 0.401610i | ||||||
\(497\) | −6.70820 | + | 5.00000i | −0.300904 | + | 0.224281i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.0000 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(500\) | 11.3137i | 0.505964i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.7990 | 0.883672 | ||||||||
\(503\) | −35.7771 | −1.59522 | −0.797611 | − | 0.603173i | \(-0.793903\pi\) | ||||
−0.797611 | + | 0.603173i | \(0.793903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.9737i | − | 0.844317i | ||||||
\(506\) | −3.16228 | + | 10.0000i | −0.140580 | + | 0.444554i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.1359i | 0.982124i | ||||||||
\(509\) | 9.89949i | 0.438787i | 0.975636 | + | 0.219394i | \(0.0704079\pi\) | ||||
−0.975636 | + | 0.219394i | \(0.929592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.9706 | −0.748539 | ||||||||
\(515\) | −12.6491 | −0.557386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.07107 | − | 22.3607i | 0.310985 | − | 0.983422i | ||||
\(518\) | 3.16228 | + | 4.24264i | 0.138943 | + | 0.186411i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | − | 19.7990i | − | 0.867409i | −0.901055 | − | 0.433705i | \(-0.857206\pi\) | ||
0.901055 | − | 0.433705i | \(-0.142794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.6274 | −0.989428 | −0.494714 | − | 0.869056i | \(-0.664727\pi\) | ||||
−0.494714 | + | 0.869056i | \(0.664727\pi\) | |||||||
\(524\) | 4.47214 | 0.195366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.00000 | 0.174408 | ||||||||
\(527\) | − | 40.0000i | − | 1.74243i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −4.47214 | −0.194257 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | − | 4.47214i | 0.260133 | − | 0.193892i | ||||
\(533\) | −12.6491 | −0.547894 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.82843 | −0.122284 | ||||||||
\(536\) | 12.0000i | 0.518321i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.3848 | −0.792624 | ||||||||
\(539\) | 13.0328 | − | 19.2132i | 0.561361 | − | 0.827571i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.1359i | − | 0.951699i | −0.879527 | − | 0.475849i | \(-0.842141\pi\) | ||
0.879527 | − | 0.475849i | \(-0.157859\pi\) | |||||||
\(542\) | 12.7279i | 0.546711i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 4.47214i | − | 0.191741i | ||||||
\(545\) | 4.47214 | 0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.6491i | − | 0.540837i | −0.962743 | − | 0.270418i | \(-0.912838\pi\) | ||
0.962743 | − | 0.270418i | \(-0.0871621\pi\) | |||||||
\(548\) | −18.9737 | −0.810515 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.00000 | − | 9.48683i | 0.127920 | − | 0.404520i | ||||
\(551\) | 16.9706i | 0.722970i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | − | 6.70820i | −0.212622 | − | 0.285262i | ||||
\(554\) | 22.1359 | 0.940466 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.82843 | −0.119952 | ||||||||
\(557\) | 2.00000i | 0.0847427i | 0.999102 | + | 0.0423714i | \(0.0134913\pi\) | ||||
−0.999102 | + | 0.0423714i | \(0.986509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.94427i | 0.378302i | ||||||||
\(560\) | 2.23607 | + | 3.00000i | 0.0944911 | + | 0.126773i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.0000 | 0.843649 | ||||||||
\(563\) | −35.7771 | −1.50782 | −0.753912 | − | 0.656975i | \(-0.771836\pi\) | ||||
−0.753912 | + | 0.656975i | \(0.771836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.16228i | 0.132686i | ||||||||
\(569\) | − | 24.0000i | − | 1.00613i | −0.864248 | − | 0.503066i | \(-0.832205\pi\) | ||
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6491i | 0.529349i | 0.964338 | + | 0.264674i | \(0.0852645\pi\) | ||||
−0.964338 | + | 0.264674i | \(0.914736\pi\) | |||||||
\(572\) | 4.47214 | + | 1.41421i | 0.186989 | + | 0.0591312i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.1421 | + | 18.9737i | 0.590281 | + | 0.791946i | ||||
\(575\) | −9.48683 | −0.395628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.3050i | − | 1.30324i | −0.758545 | − | 0.651621i | \(-0.774089\pi\) | ||
0.758545 | − | 0.651621i | \(-0.225911\pi\) | |||||||
\(578\) | − | 3.00000i | − | 0.124784i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.48528 | −0.352332 | ||||||||
\(581\) | −9.48683 | + | 7.07107i | −0.393580 | + | 0.293357i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0000 | + | 3.16228i | 0.414158 | + | 0.130968i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 4.47214i | − | 0.184742i | ||||||
\(587\) | − | 42.4264i | − | 1.75113i | −0.483105 | − | 0.875563i | \(-0.660491\pi\) | ||
0.483105 | − | 0.875563i | \(-0.339509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 25.2982i | − | 1.04240i | ||||||
\(590\) | 4.00000i | 0.164677i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −4.47214 | −0.183649 | −0.0918243 | − | 0.995775i | \(-0.529270\pi\) | ||||
−0.0918243 | + | 0.995775i | \(0.529270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | + | 13.4164i | 0.409960 | + | 0.550019i | ||||
\(596\) | − | 10.0000i | − | 0.409616i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 4.47214i | − | 0.182879i | ||||||
\(599\) | −9.48683 | −0.387621 | −0.193811 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193811 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.9411 | −1.38449 | −0.692244 | − | 0.721664i | \(-0.743378\pi\) | ||||
−0.692244 | + | 0.721664i | \(0.743378\pi\) | |||||||
\(602\) | 13.4164 | − | 10.0000i | 0.546812 | − | 0.407570i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 15.8114i | − | 0.643356i | ||||||
\(605\) | 8.94427 | − | 12.7279i | 0.363636 | − | 0.517464i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.1838 | −1.54983 | −0.774916 | − | 0.632065i | \(-0.782208\pi\) | ||||
−0.774916 | + | 0.632065i | \(0.782208\pi\) | |||||||
\(608\) | − | 2.82843i | − | 0.114708i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0000 | 0.728799 | ||||||||
\(611\) | 10.0000i | 0.404557i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4605i | 1.14951i | 0.818326 | + | 0.574754i | \(0.194902\pi\) | ||||
−0.818326 | + | 0.574754i | \(0.805098\pi\) | |||||||
\(614\) | 14.1421i | 0.570730i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.87868 | − | 8.28934i | −0.115985 | − | 0.333987i | ||||
\(617\) | −37.9473 | −1.52770 | −0.763851 | − | 0.645393i | \(-0.776694\pi\) | ||||
−0.763851 | + | 0.645393i | \(0.776694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.47214i | 0.179750i | 0.995953 | + | 0.0898752i | \(0.0286468\pi\) | ||||
−0.995953 | + | 0.0898752i | \(0.971353\pi\) | |||||||
\(620\) | 12.6491 | 0.508001 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.5563 | 0.623753 | ||||||||
\(623\) | −26.8328 | − | 36.0000i | −1.07503 | − | 1.44231i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 26.8328 | 1.07246 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.4164i | 0.535373i | ||||||||
\(629\) | 8.94427 | 0.356631 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | −3.16228 | −0.125789 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.48683i | 0.376770i | ||||||||
\(635\) | −31.3050 | −1.24230 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.82843 | + | 9.48683i | −0.112066 | + | 0.375882i | ||||
\(638\) | 18.9737 | + | 6.00000i | 0.751175 | + | 0.237542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.41421 | 0.0559017 | ||||||||
\(641\) | 6.32456 | 0.249805 | 0.124902 | − | 0.992169i | \(-0.460138\pi\) | ||||
0.124902 | + | 0.992169i | \(0.460138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.3050i | − | 1.23455i | −0.786749 | − | 0.617273i | \(-0.788237\pi\) | ||
0.786749 | − | 0.617273i | \(-0.211763\pi\) | |||||||
\(644\) | −6.70820 | + | 5.00000i | −0.264340 | + | 0.197028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 12.6491i | − | 0.497673i | ||||||
\(647\) | 32.5269i | 1.27876i | 0.768889 | + | 0.639382i | \(0.220810\pi\) | ||||
−0.768889 | + | 0.639382i | \(0.779190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.82843 | − | 8.94427i | 0.111025 | − | 0.351093i | ||||
\(650\) | 4.24264i | 0.166410i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.0000 | 0.548282 | ||||||||
\(653\) | 47.4342 | 1.85624 | 0.928121 | − | 0.372278i | \(-0.121423\pi\) | ||||
0.928121 | + | 0.372278i | \(0.121423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.32456i | 0.247121i | ||||||||
\(656\) | 8.94427 | 0.349215 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.0000 | − | 11.1803i | 0.584761 | − | 0.435855i | ||||
\(659\) | − | 30.0000i | − | 1.16863i | −0.811525 | − | 0.584317i | \(-0.801362\pi\) | ||
0.811525 | − | 0.584317i | \(-0.198638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 40.2492i | − | 1.56551i | −0.622328 | − | 0.782757i | \(-0.713813\pi\) | ||
0.622328 | − | 0.782757i | \(-0.286187\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.47214i | 0.173553i | ||||||||
\(665\) | 6.32456 | + | 8.48528i | 0.245256 | + | 0.329045i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.9737i | − | 0.734663i | ||||||
\(668\) | 17.8885 | 0.692129 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.9706 | −0.655630 | ||||||||
\(671\) | −40.2492 | − | 12.7279i | −1.55380 | − | 0.491356i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.9737i | − | 0.731381i | −0.930736 | − | 0.365691i | \(-0.880833\pi\) | ||
0.930736 | − | 0.365691i | \(-0.119167\pi\) | |||||||
\(674\) | −25.2982 | −0.974451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | −31.3050 | −1.20315 | −0.601574 | − | 0.798817i | \(-0.705459\pi\) | ||||
−0.601574 | + | 0.798817i | \(0.705459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.07107 | + | 9.48683i | 0.271363 | + | 0.364071i | ||||
\(680\) | 6.32456 | 0.242536 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.2843 | − | 8.94427i | −1.08306 | − | 0.342494i | ||||
\(683\) | −37.9473 | −1.45201 | −0.726007 | − | 0.687687i | \(-0.758626\pi\) | ||||
−0.726007 | + | 0.687687i | \(0.758626\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.8328i | − | 1.02523i | ||||||
\(686\) | 17.3925 | − | 6.36396i | 0.664050 | − | 0.242977i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 6.32456i | − | 0.241121i | ||||||
\(689\) | −4.47214 | −0.170375 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 13.4164i | − | 0.510384i | −0.966890 | − | 0.255192i | \(-0.917861\pi\) | ||
0.966890 | − | 0.255192i | \(-0.0821387\pi\) | |||||||
\(692\) | −13.4164 | −0.510015 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.0000 | −1.06287 | ||||||||
\(695\) | − | 4.00000i | − | 0.151729i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.0000 | 1.51511 | ||||||||
\(698\) | − | 32.5269i | − | 1.23116i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.36396 | − | 4.74342i | 0.240535 | − | 0.179284i | ||||
\(701\) | 18.0000i | 0.679851i | 0.940452 | + | 0.339925i | \(0.110402\pi\) | ||||
−0.940452 | + | 0.339925i | \(0.889598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.65685 | 0.213352 | ||||||||
\(704\) | −3.16228 | − | 1.00000i | −0.119183 | − | 0.0376889i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 28.2843 | 1.06449 | ||||||||
\(707\) | −28.4605 | + | 21.2132i | −1.07037 | + | 0.797805i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0000 | −0.525781 | −0.262891 | − | 0.964826i | \(-0.584676\pi\) | ||||
−0.262891 | + | 0.964826i | \(0.584676\pi\) | |||||||
\(710\) | −4.47214 | −0.167836 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.9706 | −0.635999 | ||||||||
\(713\) | 28.2843i | 1.05925i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00000 | + | 6.32456i | −0.0747958 | + | 0.236525i | ||||
\(716\) | −12.6491 | −0.472719 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.0000 | −0.746393 | ||||||||
\(719\) | − | 18.3848i | − | 0.685636i | −0.939402 | − | 0.342818i | \(-0.888619\pi\) | ||
0.939402 | − | 0.342818i | \(-0.111381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1421 | + | 18.9737i | 0.526681 | + | 0.706616i | ||||
\(722\) | 11.0000i | 0.409378i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 13.4164i | − | 0.498617i | ||||||
\(725\) | 18.0000i | 0.668503i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 26.8328i | − | 0.995174i | −0.867414 | − | 0.497587i | \(-0.834220\pi\) | ||
0.867414 | − | 0.497587i | \(-0.165780\pi\) | |||||||
\(728\) | 2.23607 | + | 3.00000i | 0.0828742 | + | 0.111187i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 28.2843i | − | 1.04613i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.2132 | 0.783528 | 0.391764 | − | 0.920066i | \(-0.371865\pi\) | ||||
0.391764 | + | 0.920066i | \(0.371865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.16228i | 0.116563i | ||||||||
\(737\) | 37.9473 | + | 12.0000i | 1.39781 | + | 0.442026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.9737i | − | 0.697958i | −0.937131 | − | 0.348979i | \(-0.886529\pi\) | ||
0.937131 | − | 0.348979i | \(-0.113471\pi\) | |||||||
\(740\) | 2.82843i | 0.103975i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.00000 | + | 6.70820i | 0.183556 | + | 0.246266i | ||||
\(743\) | − | 36.0000i | − | 1.32071i | −0.750953 | − | 0.660356i | \(-0.770405\pi\) | ||
0.750953 | − | 0.660356i | \(-0.229595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1421 | 0.518128 | ||||||||
\(746\) | −15.8114 | −0.578896 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.1421 | − | 4.47214i | −0.517088 | − | 0.163517i | ||||
\(749\) | 3.16228 | + | 4.24264i | 0.115547 | + | 0.155023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | − | 7.07107i | − | 0.257855i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.48528 | −0.309016 | ||||||||
\(755\) | 22.3607 | 0.813788 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 10.0000i | 0.363216i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.00000 | 0.145095 | ||||||||
\(761\) | 22.3607 | 0.810574 | 0.405287 | − | 0.914190i | \(-0.367172\pi\) | ||||
0.405287 | + | 0.914190i | \(0.367172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | − | 6.70820i | −0.181012 | − | 0.242853i | ||||
\(764\) | −9.48683 | −0.343222 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5563 | 0.562074 | ||||||||
\(767\) | 4.00000i | 0.144432i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.4558 | −0.917961 | −0.458981 | − | 0.888446i | \(-0.651785\pi\) | ||||
−0.458981 | + | 0.888446i | \(0.651785\pi\) | |||||||
\(770\) | 11.7229 | − | 4.07107i | 0.422464 | − | 0.146711i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 6.32456i | − | 0.227626i | ||||||
\(773\) | 15.5563i | 0.559523i | 0.960070 | + | 0.279761i | \(0.0902554\pi\) | ||||
−0.960070 | + | 0.279761i | \(0.909745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 26.8328i | − | 0.963863i | ||||||
\(776\) | 4.47214 | 0.160540 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 34.7851i | − | 1.24710i | ||||||
\(779\) | 25.2982 | 0.906403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 3.16228i | 0.357828 | + | 0.113155i | ||||
\(782\) | 14.1421i | 0.505722i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.00000 | − | 6.70820i | 0.0714286 | − | 0.239579i | ||||
\(785\) | −18.9737 | −0.677199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.2843 | −1.00823 | −0.504113 | − | 0.863638i | \(-0.668180\pi\) | ||||
−0.504113 | + | 0.863638i | \(0.668180\pi\) | |||||||
\(788\) | 2.00000i | 0.0712470i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 4.47214i | − | 0.159111i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | −4.47214 | −0.158710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 17.8885i | − | 0.634043i | ||||||
\(797\) | 21.2132i | 0.751410i | 0.926739 | + | 0.375705i | \(0.122599\pi\) | ||||
−0.926739 | + | 0.375705i | \(0.877401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 31.6228i | − | 1.11873i | ||||||
\(800\) | − | 3.00000i | − | 0.106066i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 18.9737i | − | 0.669983i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.07107 | − | 9.48683i | −0.249222 | − | 0.334367i | ||||
\(806\) | 12.6491 | 0.445546 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.4164i | 0.471988i | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.9411 | 1.19183 | 0.595917 | − | 0.803046i | \(-0.296789\pi\) | ||||
0.595917 | + | 0.803046i | \(0.296789\pi\) | |||||||
\(812\) | 9.48683 | + | 12.7279i | 0.332923 | + | 0.446663i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.00000 | − | 6.32456i | 0.0701000 | − | 0.221676i | ||||
\(815\) | 19.7990i | 0.693528i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 17.8885i | − | 0.625841i | ||||||
\(818\) | 2.82843i | 0.0988936i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.6491i | 0.441726i | ||||||||
\(821\) | − | 10.0000i | − | 0.349002i | −0.984657 | − | 0.174501i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174501i | \(-0.0558313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 8.94427 | 0.311588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | − | 4.47214i | 0.208767 | − | 0.155606i | ||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.47214i | 0.155324i | 0.996980 | + | 0.0776619i | \(0.0247455\pi\) | ||||
−0.996980 | + | 0.0776619i | \(0.975255\pi\) | |||||||
\(830\) | −6.32456 | −0.219529 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.41421 | 0.0490290 | ||||||||
\(833\) | 8.94427 | − | 30.0000i | 0.309901 | − | 1.03944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.2982i | 0.875481i | ||||||||
\(836\) | −8.94427 | − | 2.82843i | −0.309344 | − | 0.0978232i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.1127 | 1.07477 | ||||||||
\(839\) | 32.5269i | 1.12295i | 0.827492 | + | 0.561477i | \(0.189767\pi\) | ||||
−0.827492 | + | 0.561477i | \(0.810233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 30.0000i | 1.03387i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.9737i | 0.653101i | ||||||||
\(845\) | 15.5563i | 0.535155i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.0919 | + | 0.813842i | −0.999609 | + | 0.0279639i | ||||
\(848\) | 3.16228 | 0.108593 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 13.4164i | − | 0.460179i | ||||||
\(851\) | −6.32456 | −0.216803 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5563 | 0.532639 | 0.266320 | − | 0.963885i | \(-0.414192\pi\) | ||||
0.266320 | + | 0.963885i | \(0.414192\pi\) | |||||||
\(854\) | −20.1246 | − | 27.0000i | −0.688650 | − | 0.923921i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | −8.94427 | −0.305531 | −0.152765 | − | 0.988263i | \(-0.548818\pi\) | ||||
−0.152765 | + | 0.988263i | \(0.548818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 8.94427 | 0.304997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.00000 | −0.272481 | ||||||||
\(863\) | 28.4605 | 0.968807 | 0.484403 | − | 0.874845i | \(-0.339037\pi\) | ||||
0.484403 | + | 0.874845i | \(0.339037\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 18.9737i | − | 0.645124i | ||||||
\(866\) | 8.94427 | 0.303939 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.1421 | − | 18.9737i | −0.480015 | − | 0.644008i | ||||
\(869\) | −3.16228 | + | 10.0000i | −0.107273 | + | 0.339227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.9706 | −0.575026 | ||||||||
\(872\) | −3.16228 | −0.107088 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.94427i | 0.302545i | ||||||||
\(875\) | 17.8885 | + | 24.0000i | 0.604743 | + | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.1096i | 1.38817i | 0.719892 | + | 0.694086i | \(0.244191\pi\) | ||||
−0.719892 | + | 0.694086i | \(0.755809\pi\) | |||||||
\(878\) | − | 32.5269i | − | 1.09773i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.41421 | − | 4.47214i | 0.0476731 | − | 0.150756i | ||||
\(881\) | 5.65685i | 0.190584i | 0.995449 | + | 0.0952921i | \(0.0303785\pi\) | ||||
−0.995449 | + | 0.0952921i | \(0.969621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 6.32456 | 0.212718 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.7214 | −1.50160 | −0.750798 | − | 0.660532i | \(-0.770331\pi\) | ||||
−0.750798 | + | 0.660532i | \(0.770331\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.0000 | + | 46.9574i | 1.17386 | + | 1.57490i | ||||
\(890\) | − | 24.0000i | − | 0.804482i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 26.8328i | − | 0.898429i | ||||||
\(893\) | − | 20.0000i | − | 0.669274i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 17.8885i | − | 0.597948i | ||||||
\(896\) | −1.58114 | − | 2.12132i | −0.0528221 | − | 0.0708683i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.6228i | 1.05527i | ||||||||
\(899\) | 53.6656 | 1.78985 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.1421 | 0.471143 | ||||||||
\(902\) | 8.94427 | − | 28.2843i | 0.297812 | − | 0.941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.9737 | 0.630706 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.24264 | + | 3.16228i | −0.140642 | + | 0.104828i | ||||
\(911\) | −28.4605 | −0.942938 | −0.471469 | − | 0.881883i | \(-0.656276\pi\) | ||||
−0.471469 | + | 0.881883i | \(0.656276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1421 | + | 4.47214i | 0.468036 | + | 0.148006i | ||||
\(914\) | −18.9737 | −0.627593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 4.47214i | − | 0.147764i | ||||||
\(917\) | 9.48683 | − | 7.07107i | 0.313283 | − | 0.233507i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.1359i | − | 0.730197i | −0.930969 | − | 0.365099i | \(-0.881035\pi\) | ||
0.930969 | − | 0.365099i | \(-0.118965\pi\) | |||||||
\(920\) | −4.47214 | −0.147442 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 4.47214i | − | 0.147282i | ||||||
\(923\) | −4.47214 | −0.147202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 4.00000i | 0.131448i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | − | 31.1127i | − | 1.02077i | −0.859945 | − | 0.510387i | \(-0.829502\pi\) | ||
0.859945 | − | 0.510387i | \(-0.170498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.65685 | − | 18.9737i | 0.185396 | − | 0.621837i | ||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.9706 | 0.555294 | ||||||||
\(935\) | 6.32456 | − | 20.0000i | 0.206835 | − | 0.654070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.2548 | −1.47841 | −0.739205 | − | 0.673480i | \(-0.764799\pi\) | ||||
−0.739205 | + | 0.673480i | \(0.764799\pi\) | |||||||
\(938\) | 18.9737 | + | 25.4558i | 0.619512 | + | 0.831163i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.0000 | 0.326164 | ||||||||
\(941\) | 31.3050 | 1.02051 | 0.510256 | − | 0.860022i | \(-0.329551\pi\) | ||||
0.510256 | + | 0.860022i | \(0.329551\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.2843 | −0.921063 | ||||||||
\(944\) | − | 2.82843i | − | 0.0920575i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0000 | − | 6.32456i | −0.650256 | − | 0.205629i | ||||
\(947\) | 31.6228 | 1.02760 | 0.513801 | − | 0.857909i | \(-0.328237\pi\) | ||||
0.513801 | + | 0.857909i | \(0.328237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 8.48528i | − | 0.275299i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.07107 | − | 9.48683i | −0.229175 | − | 0.307470i | ||||
\(953\) | 54.0000i | 1.74923i | 0.484817 | + | 0.874616i | \(0.338886\pi\) | ||||
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13.4164i | − | 0.434145i | ||||||
\(956\) | 16.0000i | 0.517477i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.7771i | 1.15591i | ||||||||
\(959\) | −40.2492 | + | 30.0000i | −1.29972 | + | 0.968751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −49.0000 | −1.58065 | ||||||||
\(962\) | 2.82843i | 0.0911922i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.48528 | 0.273293 | ||||||||
\(965\) | 8.94427 | 0.287926 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.48683i | − | 0.305076i | −0.988298 | − | 0.152538i | \(-0.951255\pi\) | ||
0.988298 | − | 0.152538i | \(-0.0487446\pi\) | |||||||
\(968\) | −6.32456 | + | 9.00000i | −0.203279 | + | 0.289271i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.32456i | 0.203069i | ||||||||
\(971\) | − | 19.7990i | − | 0.635380i | −0.948195 | − | 0.317690i | \(-0.897093\pi\) | ||
0.948195 | − | 0.317690i | \(-0.102907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | + | 4.47214i | −0.192351 | + | 0.143370i | ||||
\(974\) | − | 12.0000i | − | 0.384505i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.7279 | −0.407411 | ||||||||
\(977\) | −18.9737 | −0.607021 | −0.303511 | − | 0.952828i | \(-0.598159\pi\) | ||||
−0.303511 | + | 0.952828i | \(0.598159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.9706 | + | 53.6656i | −0.542382 | + | 1.71516i | ||||
\(980\) | 9.48683 | + | 2.82843i | 0.303046 | + | 0.0903508i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.0000 | 0.574403 | ||||||||
\(983\) | − | 41.0122i | − | 1.30809i | −0.756457 | − | 0.654043i | \(-0.773072\pi\) | ||
0.756457 | − | 0.654043i | \(-0.226928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.82843 | −0.0901212 | ||||||||
\(986\) | 26.8328 | 0.854531 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 20.0000i | 0.635963i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | −8.94427 | −0.283981 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.00000 | + | 6.70820i | 0.158590 | + | 0.212771i | ||||
\(995\) | 25.2982 | 0.802008 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.2132 | −0.671829 | −0.335914 | − | 0.941893i | \(-0.609045\pi\) | ||||
−0.335914 | + | 0.941893i | \(0.609045\pi\) | |||||||
\(998\) | 10.0000i | 0.316544i | ||||||||
\(999\) | 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 | 1386.2.e.d.307.2 | yes | 8 | |
3.2 | odd | 2 | inner | 1386.2.e.d.307.8 | yes | 8 | |
7.6 | odd | 2 | inner | 1386.2.e.d.307.4 | yes | 8 | |
11.10 | odd | 2 | inner | 1386.2.e.d.307.5 | yes | 8 | |
21.20 | even | 2 | inner | 1386.2.e.d.307.6 | yes | 8 | |
33.32 | even | 2 | inner | 1386.2.e.d.307.3 | yes | 8 | |
77.76 | even | 2 | inner | 1386.2.e.d.307.7 | yes | 8 | |
231.230 | odd | 2 | inner | 1386.2.e.d.307.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.e.d.307.1 | ✓ | 8 | 231.230 | odd | 2 | inner | |
1386.2.e.d.307.2 | yes | 8 | 1.1 | even | 1 | trivial | |
1386.2.e.d.307.3 | yes | 8 | 33.32 | even | 2 | inner | |
1386.2.e.d.307.4 | yes | 8 | 7.6 | odd | 2 | inner | |
1386.2.e.d.307.5 | yes | 8 | 11.10 | odd | 2 | inner | |
1386.2.e.d.307.6 | yes | 8 | 21.20 | even | 2 | inner | |
1386.2.e.d.307.7 | yes | 8 | 77.76 | even | 2 | inner | |
1386.2.e.d.307.8 | yes | 8 | 3.2 | odd | 2 | inner |