Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(1471,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.i (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: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 44x^{12} + 162x^{10} + 404x^{8} - 84x^{6} - 79x^{4} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.2 | ||
Root | \(0.605201 + 2.04824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1471 |
Dual form | 1840.2.i.c.1471.15 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.94245i | − | 1.69883i | −0.527729 | − | 0.849413i | \(-0.676956\pi\) | ||
0.527729 | − | 0.849413i | \(-0.323044\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.89011 | 0.714393 | 0.357197 | − | 0.934029i | \(-0.383733\pi\) | ||||
0.357197 | + | 0.934029i | \(0.383733\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.65803 | −1.88601 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.17399 | 0.655483 | 0.327742 | − | 0.944767i | \(-0.393712\pi\) | ||||
0.327742 | + | 0.944767i | \(0.393712\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0572532 | −0.0158792 | −0.00793960 | − | 0.999968i | \(-0.502527\pi\) | ||||
−0.00793960 | + | 0.999968i | \(0.502527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.94245 | 0.759738 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.76546i | − | 0.428188i | −0.976813 | − | 0.214094i | \(-0.931320\pi\) | ||
0.976813 | − | 0.214094i | \(-0.0686798\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57399 | −0.361099 | −0.180550 | − | 0.983566i | \(-0.557788\pi\) | ||||
−0.180550 | + | 0.983566i | \(0.557788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.56155i | − | 1.21363i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.82081 | − | 4.43674i | 0.379665 | − | 0.925124i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.82113i | 1.50518i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.26116 | −0.791278 | −0.395639 | − | 0.918406i | \(-0.629477\pi\) | ||||
−0.395639 | + | 0.918406i | \(0.629477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.54245i | − | 0.636243i | −0.948050 | − | 0.318121i | \(-0.896948\pi\) | ||
0.948050 | − | 0.318121i | \(-0.103052\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.39687i | − | 1.11355i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.89011i | 0.319486i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.3161i | − | 1.86035i | −0.367117 | − | 0.930175i | \(-0.619655\pi\) | ||
0.367117 | − | 0.930175i | \(-0.380345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.168465i | 0.0269760i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.02663 | 0.316506 | 0.158253 | − | 0.987399i | \(-0.449414\pi\) | ||||
0.158253 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.72549 | 0.873129 | 0.436565 | − | 0.899673i | \(-0.356195\pi\) | ||||
0.436565 | + | 0.899673i | \(0.356195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 5.65803i | − | 0.843450i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.49395i | 0.947240i | 0.880729 | + | 0.473620i | \(0.157053\pi\) | ||||
−0.880729 | + | 0.473620i | \(0.842947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.42749 | −0.489642 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.19479 | −0.727417 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.7239i | − | 1.61040i | −0.593004 | − | 0.805200i | \(-0.702058\pi\) | ||
0.593004 | − | 0.805200i | \(-0.297942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.17399i | 0.293141i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.63140i | 0.613445i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3.46410i | − | 0.450988i | −0.974245 | − | 0.225494i | \(-0.927600\pi\) | ||
0.974245 | − | 0.225494i | \(-0.0723995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.00308i | − | 0.896652i | −0.893870 | − | 0.448326i | \(-0.852020\pi\) | ||
0.893870 | − | 0.448326i | \(-0.147980\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.6943 | −1.34735 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.0572532i | − | 0.00710139i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.96878 | −0.973542 | −0.486771 | − | 0.873530i | \(-0.661825\pi\) | ||||
−0.486771 | + | 0.873530i | \(0.661825\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.0549 | − | 5.35764i | −1.57163 | − | 0.644984i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.53373i | − | 1.13145i | −0.824596 | − | 0.565723i | \(-0.808597\pi\) | ||
0.824596 | − | 0.565723i | \(-0.191403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.21651 | 0.844628 | 0.422314 | − | 0.906449i | \(-0.361218\pi\) | ||||
0.422314 | + | 0.906449i | \(0.361218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.94245i | 0.339765i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.10908 | 0.468273 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.24329 | 0.252390 | 0.126195 | − | 0.992005i | \(-0.459724\pi\) | ||||
0.126195 | + | 0.992005i | \(0.459724\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.03923 | 0.671025 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.177514 | 0.0194847 | 0.00974236 | − | 0.999953i | \(-0.496899\pi\) | ||||
0.00974236 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.76546 | 0.191491 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.5383i | 1.34424i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1930i | 1.08045i | 0.841520 | + | 0.540226i | \(0.181661\pi\) | ||||
−0.841520 | + | 0.540226i | \(0.818339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.108215 | −0.0113440 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4235 | −1.08087 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.57399i | − | 0.161488i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.95842i | 0.808055i | 0.914747 | + | 0.404028i | \(0.132390\pi\) | ||||
−0.914747 | + | 0.404028i | \(0.867610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.3005 | −1.23625 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.53093 | 0.152333 | 0.0761664 | − | 0.997095i | \(-0.475732\pi\) | ||||
0.0761664 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.49949 | −0.541881 | −0.270941 | − | 0.962596i | \(-0.587335\pi\) | ||||
−0.270941 | + | 0.962596i | \(0.587335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.56155 | 0.542752 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0953 | 1.45932 | 0.729660 | − | 0.683811i | \(-0.239679\pi\) | ||||
0.729660 | + | 0.683811i | \(0.239679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.86594i | 0.849203i | 0.905380 | + | 0.424602i | \(0.139586\pi\) | ||||
−0.905380 | + | 0.424602i | \(0.860414\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33.2970 | −3.16041 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0785i | 0.948101i | 0.880498 | + | 0.474050i | \(0.157209\pi\) | ||||
−0.880498 | + | 0.474050i | \(0.842791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.43674 | + | 1.82081i | 0.413728 | + | 0.169791i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.323941 | 0.0299483 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.33692i | − | 0.305895i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.27376 | −0.570342 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.96326i | − | 0.537689i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0836i | 1.07224i | 0.844141 | + | 0.536121i | \(0.180111\pi\) | ||||
−0.844141 | + | 0.536121i | \(0.819889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 16.8470i | − | 1.48329i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2561i | 0.896077i | 0.894014 | + | 0.448038i | \(0.147877\pi\) | ||||
−0.894014 | + | 0.448038i | \(0.852123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.97502 | −0.257967 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.82113 | −0.673136 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.11215i | 0.0950176i | 0.998871 | + | 0.0475088i | \(0.0151282\pi\) | ||||
−0.998871 | + | 0.0475088i | \(0.984872\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.2638i | − | 1.54911i | −0.632505 | − | 0.774556i | \(-0.717973\pi\) | ||
0.632505 | − | 0.774556i | \(-0.282027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.1082 | 1.60920 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.124468 | −0.0104085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.26116i | − | 0.353870i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.0852i | 0.831817i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.84074i | 0.232723i | 0.993207 | + | 0.116361i | \(0.0371231\pi\) | ||||
−0.993207 | + | 0.116361i | \(0.962877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.60552i | − | 0.212034i | −0.994364 | − | 0.106017i | \(-0.966190\pi\) | ||
0.994364 | − | 0.106017i | \(-0.0338099\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.98905i | 0.807567i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.54245 | 0.284536 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.07845i | − | 0.644731i | −0.946615 | − | 0.322365i | \(-0.895522\pi\) | ||
0.946615 | − | 0.322365i | \(-0.104478\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −34.4970 | −2.73579 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.44152 | − | 8.38591i | 0.271230 | − | 0.660903i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.805532i | − | 0.0630941i | −0.999502 | − | 0.0315471i | \(-0.989957\pi\) | ||
0.999502 | − | 0.0315471i | \(-0.0100434\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.39687 | 0.497995 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7694i | 1.45242i | 0.687471 | + | 0.726211i | \(0.258721\pi\) | ||||
−0.687471 | + | 0.726211i | \(0.741279\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9967 | −0.999748 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.90571 | 0.681037 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6125 | −1.26302 | −0.631511 | − | 0.775367i | \(-0.717565\pi\) | ||||
−0.631511 | + | 0.775367i | \(0.717565\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.89011 | −0.142879 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1930 | −0.766150 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.69564i | 0.201482i | 0.994913 | + | 0.100741i | \(0.0321213\pi\) | ||||
−0.994913 | + | 0.100741i | \(0.967879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.4282i | − | 1.22110i | −0.791978 | − | 0.610550i | \(-0.790949\pi\) | ||
0.791978 | − | 0.610550i | \(-0.209051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.6062 | −1.52326 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.3161 | 0.831973 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.83810i | − | 0.280670i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.7828i | 1.07529i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.863064 | 0.0624491 | 0.0312246 | − | 0.999512i | \(-0.490059\pi\) | ||||
0.0312246 | + | 0.999512i | \(0.490059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.05490 | 0.0759333 | 0.0379667 | − | 0.999279i | \(-0.487912\pi\) | ||||
0.0379667 | + | 0.999279i | \(0.487912\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.168465 | −0.0120640 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.86502 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.8947 | 1.69385 | 0.846924 | − | 0.531715i | \(-0.178452\pi\) | ||||
0.846924 | + | 0.531715i | \(0.178452\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4478i | 1.65388i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.05406 | −0.565284 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.02663i | 0.141546i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.3022 | + | 25.1032i | −0.716052 | + | 1.74479i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.42185 | −0.236694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.75774i | − | 0.189850i | −0.995484 | − | 0.0949252i | \(-0.969739\pi\) | ||
0.995484 | − | 0.0949252i | \(-0.0302612\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.0525 | −1.92213 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.72549i | 0.390475i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.69561i | − | 0.454528i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 21.2342i | − | 1.43488i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.101079i | 0.00679928i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.10572i | 0.475834i | 0.971285 | + | 0.237917i | \(0.0764646\pi\) | ||||
−0.971285 | + | 0.237917i | \(0.923535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.65803 | 0.377202 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.0094 | 1.65993 | 0.829965 | − | 0.557815i | \(-0.188360\pi\) | ||||
0.829965 | + | 0.557815i | \(0.188360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.3413i | − | 1.41027i | −0.709073 | − | 0.705135i | \(-0.750886\pi\) | ||
0.709073 | − | 0.705135i | \(-0.249114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 12.0908i | − | 0.795514i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.615731 | −0.0403379 | −0.0201689 | − | 0.999797i | \(-0.506420\pi\) | ||||
−0.0201689 | + | 0.999797i | \(0.506420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.49395 | −0.423619 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.60078i | − | 0.428767i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.67754i | − | 0.173196i | −0.996243 | − | 0.0865979i | \(-0.972400\pi\) | ||
0.996243 | − | 0.0865979i | \(-0.0275995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.94675i | 0.511895i | 0.966691 | + | 0.255947i | \(0.0823874\pi\) | ||||
−0.966691 | + | 0.255947i | \(0.917613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.69326i | 0.365223i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.42749i | − | 0.218975i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0901163 | 0.00573396 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 0.522327i | − | 0.0331012i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9636 | 0.755135 | 0.377567 | − | 0.925982i | \(-0.376761\pi\) | ||||
0.377567 | + | 0.925982i | \(0.376761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.95842 | − | 9.64543i | 0.248864 | − | 0.606403i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 5.19479i | − | 0.325311i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.86994 | 0.179022 | 0.0895110 | − | 0.995986i | \(-0.471470\pi\) | ||||
0.0895110 | + | 0.995986i | \(0.471470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 21.3886i | − | 1.32902i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.1098 | 1.49236 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.5455 | 1.76019 | 0.880095 | − | 0.474797i | \(-0.157479\pi\) | ||||
0.880095 | + | 0.474797i | \(0.157479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.7239 | 0.720192 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.9923 | 1.83550 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7450 | 1.32582 | 0.662908 | − | 0.748701i | \(-0.269322\pi\) | ||||
0.662908 | + | 0.748701i | \(0.269322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.7626i | − | 1.32198i | −0.750394 | − | 0.660991i | \(-0.770136\pi\) | ||
0.750394 | − | 0.660991i | \(-0.229864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.318417i | 0.0192715i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.17399 | −0.131097 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3144 | −0.739902 | −0.369951 | − | 0.929051i | \(-0.620625\pi\) | ||||
−0.369951 | + | 0.929051i | \(0.620625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.0433i | 1.19996i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6094i | 1.05049i | 0.850952 | + | 0.525244i | \(0.176026\pi\) | ||||
−0.850952 | + | 0.525244i | \(0.823974\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9913 | 1.48558 | 0.742789 | − | 0.669526i | \(-0.233503\pi\) | ||||
0.742789 | + | 0.669526i | \(0.233503\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.63140 | −0.274341 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.83054 | 0.226110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.8831 | 0.816655 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.4173 | 1.37275 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.8697i | 1.86185i | 0.365210 | + | 0.930925i | \(0.380997\pi\) | ||||
−0.365210 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | 0.201688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.0031i | 0.986619i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.104247 | + | 0.254018i | −0.00602877 | + | 0.0146902i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8218 | 0.623758 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.50468i | − | 0.258787i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00308 | 0.400995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7297i | 0.897739i | 0.893597 | + | 0.448870i | \(0.148173\pi\) | ||||
−0.893597 | + | 0.448870i | \(0.851827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.1820i | 0.920562i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 15.1574i | − | 0.859498i | −0.902948 | − | 0.429749i | \(-0.858602\pi\) | ||
0.902948 | − | 0.429749i | \(-0.141398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.2519i | − | 1.31427i | −0.753772 | − | 0.657136i | \(-0.771768\pi\) | ||
0.753772 | − | 0.657136i | \(-0.228232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 10.6943i | − | 0.602555i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.5984 | −1.43775 | −0.718875 | − | 0.695139i | \(-0.755343\pi\) | ||||
−0.718875 | + | 0.695139i | \(0.755343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.26373 | −0.518669 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 44.4173i | − | 2.47913i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.77883i | 0.154618i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0572532 | 0.00317584 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.0876 | 1.44265 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.2743i | 0.676702i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.32314i | − | 0.182656i | −0.995821 | − | 0.0913281i | \(-0.970889\pi\) | ||
0.995821 | − | 0.0913281i | \(-0.0291112\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 64.0266i | 3.50864i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7.96878i | − | 0.435381i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2267i | 1.37418i | 0.726571 | + | 0.687092i | \(0.241113\pi\) | ||||
−0.726571 | + | 0.687092i | \(0.758887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.6554 | 1.61066 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7.70126i | − | 0.417046i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7091 | −1.06419 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.35764 | − | 13.0549i | 0.288446 | − | 0.702852i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 35.1015i | − | 1.88435i | −0.335122 | − | 0.942175i | \(-0.608778\pi\) | ||
0.335122 | − | 0.942175i | \(-0.391222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.95985 | −0.211966 | −0.105983 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105983 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.447785i | − | 0.0239010i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7702 | 1.05226 | 0.526130 | − | 0.850404i | \(-0.323642\pi\) | ||||
0.526130 | + | 0.850404i | \(0.323642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.53373 | 0.505998 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.81872 | −0.519662 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.1902 | 1.11838 | 0.559189 | − | 0.829040i | \(-0.311113\pi\) | ||||
0.559189 | + | 0.829040i | \(0.311113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5225 | −0.869607 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.4603i | 0.968912i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.21651i | 0.377729i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.94630 | −0.362594 | −0.181297 | − | 0.983428i | \(-0.558030\pi\) | ||||
−0.181297 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4667 | −0.596934 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 22.1594i | − | 1.15046i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.3466i | − | 0.742837i | −0.928466 | − | 0.371419i | \(-0.878871\pi\) | ||
0.928466 | − | 0.371419i | \(-0.121129\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.94245 | −0.151948 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.243965 | 0.0125649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4125 | 0.534856 | 0.267428 | − | 0.963578i | \(-0.413826\pi\) | ||||
0.267428 | + | 0.963578i | \(0.413826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.5553 | 1.82155 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.9853 | 1.73657 | 0.868283 | − | 0.496070i | \(-0.165224\pi\) | ||||
0.868283 | + | 0.496070i | \(0.165224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.10908i | 0.209418i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.3950 | −1.64673 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4422i | 0.580145i | 0.957005 | + | 0.290072i | \(0.0936794\pi\) | ||||
−0.957005 | + | 0.290072i | \(0.906321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.83290 | − | 3.21457i | −0.396127 | − | 0.162568i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.1780 | 1.52228 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.24329i | 0.112872i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4824 | 1.27892 | 0.639462 | − | 0.768822i | \(-0.279157\pi\) | ||||
0.639462 | + | 0.768822i | \(0.279157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.75385i | 0.438241i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 26.5789i | − | 1.32729i | −0.748050 | − | 0.663643i | \(-0.769010\pi\) | ||
0.748050 | − | 0.663643i | \(-0.230990\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.202817i | 0.0101030i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.03923i | 0.300092i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.6010i | − | 1.21943i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.8596 | −1.57536 | −0.787678 | − | 0.616088i | \(-0.788717\pi\) | ||||
−0.787678 | + | 0.616088i | \(0.788717\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.27246 | 0.161418 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.54752i | − | 0.322183i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.177514i | 0.00871383i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −53.7403 | −2.63167 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.34131 | 0.0655273 | 0.0327637 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327637 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 4.16481i | − | 0.202980i | −0.994837 | − | 0.101490i | \(-0.967639\pi\) | ||
0.994837 | − | 0.101490i | \(-0.0323610\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 36.7430i | − | 1.78651i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.76546i | 0.0856375i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 13.2366i | − | 0.640562i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.366241i | 0.0176823i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4329 | 0.550703 | 0.275351 | − | 0.961344i | \(-0.411206\pi\) | ||||
0.275351 | + | 0.961344i | \(0.411206\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.0755i | − | 1.15699i | −0.815684 | − | 0.578497i | \(-0.803639\pi\) | ||
0.815684 | − | 0.578497i | \(-0.196361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.5383 | −0.601164 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.86594 | + | 6.98340i | −0.137097 | + | 0.334061i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.1931i | 1.87058i | 0.353878 | + | 0.935291i | \(0.384863\pi\) | ||||
−0.353878 | + | 0.935291i | \(0.615137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3929 | 0.923470 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.46126i | 0.354495i | 0.984166 | + | 0.177248i | \(0.0567194\pi\) | ||||
−0.984166 | + | 0.177248i | \(0.943281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.1930 | −0.483193 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.35876 | 0.395356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.1122 | 0.524415 | 0.262207 | − | 0.965012i | \(-0.415550\pi\) | ||||
0.262207 | + | 0.965012i | \(0.415550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.40587 | 0.207464 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.66663 | −0.360210 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.108215i | − | 0.00507319i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2157i | 1.08598i | 0.839738 | + | 0.542992i | \(0.182709\pi\) | ||||
−0.839738 | + | 0.542992i | \(0.817291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.8079 | 0.644499 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.68313 | 0.311265 | 0.155632 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155632 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5078i | 0.906602i | 0.891357 | + | 0.453301i | \(0.149754\pi\) | ||||
−0.891357 | + | 0.453301i | \(0.850246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10.4235i | − | 0.483378i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.4054 | −1.12935 | −0.564674 | − | 0.825314i | \(-0.690998\pi\) | ||||
−0.564674 | + | 0.825314i | \(0.690998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0619 | −0.695492 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.7705 | −1.09529 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.4472 | 0.572321 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.57399 | 0.0722198 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66.3341i | 3.03723i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.95905 | −0.272276 | −0.136138 | − | 0.990690i | \(-0.543469\pi\) | ||||
−0.136138 | + | 0.990690i | \(0.543469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.647881i | 0.0295408i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.6752 | − | 10.1265i | −1.12276 | − | 0.460773i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.95842 | −0.361373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.21675i | 0.281708i | 0.990030 | + | 0.140854i | \(0.0449848\pi\) | ||||
−0.990030 | + | 0.140854i | \(0.955015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.37024 | −0.107186 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13.5325i | − | 0.610713i | −0.952238 | − | 0.305356i | \(-0.901224\pi\) | ||
0.952238 | − | 0.305356i | \(-0.0987756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.52293i | 0.338816i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 12.3005i | − | 0.552867i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 18.0198i | − | 0.808297i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2155i | 1.39740i | 0.715416 | + | 0.698698i | \(0.246237\pi\) | ||||
−0.715416 | + | 0.698698i | \(0.753763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 55.2282 | 2.46741 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.6976 | −0.744508 | −0.372254 | − | 0.928131i | \(-0.621415\pi\) | ||||
−0.372254 | + | 0.928131i | \(0.621415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.53093i | 0.0681253i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.2422i | 1.69840i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.16941 | 0.406427 | 0.203213 | − | 0.979134i | \(-0.434861\pi\) | ||||
0.203213 | + | 0.979134i | \(0.434861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.6400 | 0.603397 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 12.3104i | − | 0.543518i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.49949i | − | 0.242337i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1178i | 0.620900i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 48.8814i | 2.14565i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 44.9177i | 1.96788i | 0.178501 | + | 0.983940i | \(0.442875\pi\) | ||||
−0.178501 | + | 0.983940i | \(0.557125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.824149 | −0.0360375 | −0.0180188 | − | 0.999838i | \(-0.505736\pi\) | ||||
−0.0180188 | + | 0.999838i | \(0.505736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.56155i | 0.242726i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.25407 | −0.272431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3693 | − | 16.1569i | −0.711709 | − | 0.702474i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.6000i | 0.850567i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.116031 | −0.00502586 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0953i | 0.652627i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.93179 | 0.342282 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.45134 | −0.320952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.8572 | 1.06870 | 0.534348 | − | 0.845265i | \(-0.320557\pi\) | ||||
0.534348 | + | 0.845265i | \(0.320557\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −48.3393 | −2.07444 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.86594 | −0.379775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 29.8515i | − | 1.27636i | −0.769888 | − | 0.638179i | \(-0.779688\pi\) | ||
0.769888 | − | 0.638179i | \(-0.220312\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.6236i | 1.69109i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.70705 | 0.285730 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.24006 | 0.180306 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 33.2970i | − | 1.41338i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.4367i | 1.41676i | 0.705832 | + | 0.708380i | \(0.250574\pi\) | ||||
−0.705832 | + | 0.708380i | \(0.749426\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.327803 | −0.0138646 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2934 | −0.476809 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.7675 | 0.875245 | 0.437623 | − | 0.899159i | \(-0.355821\pi\) | ||||
0.437623 | + | 0.899159i | \(0.355821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0785 | −0.424004 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.4148 | 0.479376 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2880i | 1.31166i | 0.754908 | + | 0.655831i | \(0.227681\pi\) | ||||
−0.754908 | + | 0.655831i | \(0.772319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.8456 | −1.62564 | −0.812818 | − | 0.582518i | \(-0.802068\pi\) | ||||
−0.812818 | + | 0.582518i | \(0.802068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.53953i | − | 0.106090i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.82081 | + | 4.43674i | −0.0759329 | + | 0.185025i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.6172 | −1.69092 | −0.845458 | − | 0.534043i | \(-0.820672\pi\) | ||||
−0.845458 | + | 0.534043i | \(0.820672\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 3.10399i | − | 0.128997i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.335521 | 0.0139198 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 25.4876i | − | 1.05559i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.323941i | 0.0133933i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.6368i | 0.439026i | 0.975610 | + | 0.219513i | \(0.0704468\pi\) | ||||
−0.975610 | + | 0.219513i | \(0.929553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.57580i | 0.229747i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.3726i | 0.467808i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.3640 | 0.918380 | 0.459190 | − | 0.888338i | \(-0.348140\pi\) | ||||
0.459190 | + | 0.888338i | \(0.348140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.33692 | 0.136800 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 70.3089i | − | 2.87755i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.06196i | 0.288544i | 0.989538 | + | 0.144272i | \(0.0460840\pi\) | ||||
−0.989538 | + | 0.144272i | \(0.953916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7506 | 0.764854 | 0.382427 | − | 0.923986i | \(-0.375088\pi\) | ||||
0.382427 | + | 0.923986i | \(0.375088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.0876 | 1.83611 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 6.27376i | − | 0.255065i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.7967i | − | 1.45294i | −0.687197 | − | 0.726471i | \(-0.741159\pi\) | ||
0.687197 | − | 0.726471i | \(-0.258841\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.6987i | 0.960319i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.371800i | − | 0.0150414i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1735i | 0.855190i | 0.903971 | + | 0.427595i | \(0.140639\pi\) | ||||
−0.903971 | + | 0.427595i | \(0.859361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.96326 | 0.240462 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.76546i | 0.232109i | 0.993243 | + | 0.116054i | \(0.0370247\pi\) | ||||
−0.993243 | + | 0.116054i | \(0.962975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9390 | 0.921998 | 0.460999 | − | 0.887401i | \(-0.347491\pi\) | ||||
0.460999 | + | 0.887401i | \(0.347491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.7003 | + | 14.2408i | 1.39248 | + | 0.571463i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.2658i | 0.771867i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.0686i | 0.402102i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.9781 | −0.796579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.13384 | −0.244184 | −0.122092 | − | 0.992519i | \(-0.538960\pi\) | ||||
−0.122092 | + | 0.992519i | \(0.538960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.11451 | −0.322523 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0836 | −0.479522 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.196235 | 0.00777512 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 53.9421i | 2.13392i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.9316i | 1.61670i | 0.588702 | + | 0.808350i | \(0.299639\pi\) | ||||
−0.588702 | + | 0.808350i | \(0.700361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.24432 | 0.285688 | 0.142844 | − | 0.989745i | \(-0.454375\pi\) | ||||
0.142844 | + | 0.989745i | \(0.454375\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.8470 | 0.663350 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 36.5225i | − | 1.43585i | −0.696123 | − | 0.717923i | \(-0.745093\pi\) | ||
0.696123 | − | 0.717923i | \(-0.254907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.53093i | − | 0.295615i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.7015 | −0.772164 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1890 | 0.868321 | 0.434161 | − | 0.900836i | \(-0.357045\pi\) | ||||
0.434161 | + | 0.900836i | \(0.357045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2561 | −0.400738 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −40.8312 | −1.59298 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.47744 | −0.369189 | −0.184594 | − | 0.982815i | \(-0.559097\pi\) | ||||
−0.184594 | + | 0.982815i | \(0.559097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.151378i | − | 0.00588791i | −0.999996 | − | 0.00294396i | \(-0.999063\pi\) | ||
0.999996 | − | 0.00294396i | \(-0.000937092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.297419 | 0.0115508 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.97502i | − | 0.115366i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.75876 | + | 18.9057i | −0.300420 | + | 0.732031i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.9082 | 0.808359 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.2246i | − | 0.587740i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.6643 | 1.64459 | 0.822293 | − | 0.569064i | \(-0.192694\pi\) | ||||
0.822293 | + | 0.569064i | \(0.192694\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 7.82113i | − | 0.301036i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.9482i | 0.689805i | 0.938639 | + | 0.344902i | \(0.112088\pi\) | ||||
−0.938639 | + | 0.344902i | \(0.887912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.0423i | 0.577269i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 73.5889i | − | 2.81993i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 47.4418i | 1.81531i | 0.419719 | + | 0.907654i | \(0.362129\pi\) | ||||
−0.419719 | + | 0.907654i | \(0.637871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.11215 | −0.0424932 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −62.7957 | −2.39580 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.671230i | 0.0255718i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.9849i | − | 0.798305i | −0.916885 | − | 0.399153i | \(-0.869304\pi\) | ||
0.916885 | − | 0.399153i | \(-0.130696\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23.2493 | −0.883167 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.2638 | 0.692784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.57794i | − | 0.135524i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.81176i | 0.0685270i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1545i | 1.17669i | 0.808610 | + | 0.588346i | \(0.200220\pi\) | ||||
−0.808610 | + | 0.588346i | \(0.799780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8114i | 0.671770i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.1082i | 0.719655i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.89362 | 0.108826 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 17.2194i | − | 0.646687i | −0.946282 | − | 0.323344i | \(-0.895193\pi\) | ||
0.946282 | − | 0.323344i | \(-0.104807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.6926 | −0.476010 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.7169 | − | 6.45012i | −0.588604 | − | 0.241559i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.124468i | − | 0.00465484i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.87854 | −0.294229 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 36.8093i | − | 1.37276i | −0.727245 | − | 0.686378i | \(-0.759200\pi\) | ||
0.727245 | − | 0.686378i | \(-0.240800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3946 | −0.387116 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.3829 | 0.869620 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.26116 | 0.158256 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.1891 | −1.78724 | −0.893618 | − | 0.448828i | \(-0.851841\pi\) | ||||
−0.893618 | + | 0.448828i | \(0.851841\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.8698 | 1.29148 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.1081i | − | 0.373863i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.95064i | − | 0.256728i | −0.991727 | − | 0.128364i | \(-0.959027\pi\) | ||
0.991727 | − | 0.128364i | \(-0.0409725\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.0852 | −0.372000 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.3241 | −0.638140 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.3175i | 1.81417i | 0.420945 | + | 0.907086i | \(0.361698\pi\) | ||||
−0.420945 | + | 0.907086i | \(0.638302\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.265163i | − | 0.00974100i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.47597 | −0.0908347 | −0.0454173 | − | 0.998968i | \(-0.514462\pi\) | ||||
−0.0454173 | + | 0.998968i | \(0.514462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.84074 | −0.104077 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.00438 | −0.0367484 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.5318 | 1.04253 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.42441 | −0.234430 | −0.117215 | − | 0.993107i | \(-0.537397\pi\) | ||||
−0.117215 | + | 0.993107i | \(0.537397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 35.2023i | − | 1.28284i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.60552 | 0.0948247 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28.0485i | − | 1.01944i | −0.860340 | − | 0.509721i | \(-0.829749\pi\) | ||
0.860340 | − | 0.509721i | \(-0.170251\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.3812 | − | 11.6475i | −1.03017 | − | 0.422776i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.8815 | −1.01070 | −0.505352 | − | 0.862913i | \(-0.668637\pi\) | ||||
−0.505352 | + | 0.862913i | \(0.668637\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.7576i | 0.606665i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.98905 | −0.361155 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.198331i | 0.00716132i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 34.8642i | − | 1.25723i | −0.777715 | − | 0.628617i | \(-0.783621\pi\) | ||
0.777715 | − | 0.628617i | \(-0.216379\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 8.44467i | − | 0.304127i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.25666i | − | 0.0451988i | −0.999745 | − | 0.0225994i | \(-0.992806\pi\) | ||
0.999745 | − | 0.0225994i | \(-0.00719423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.54245i | 0.127249i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −62.9349 | −2.25778 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.18990 | −0.114290 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 20.7262i | − | 0.741643i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 33.3271i | − | 1.19101i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.07845 | 0.288332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.2400 | 1.18488 | 0.592439 | − | 0.805616i | \(-0.298165\pi\) | ||||
0.592439 | + | 0.805616i | \(0.298165\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 83.9938i | − | 2.99026i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.0494i | 0.677317i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.400949i | 0.0142381i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 34.4970i | − | 1.22348i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 0.675939i | − | 0.0239430i | −0.999928 | − | 0.0119715i | \(-0.996189\pi\) | ||
0.999928 | − | 0.0119715i | \(-0.00381073\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.4648 | 0.405597 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 57.6721i | − | 2.03774i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.6886 | 0.553640 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.38591 | + | 3.44152i | 0.295565 | + | 0.121298i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 63.9836i | − | 2.25233i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.86911 | −0.136031 | −0.0680153 | − | 0.997684i | \(-0.521667\pi\) | ||||
−0.0680153 | + | 0.997684i | \(0.521667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.51005i | − | 0.0530252i | −0.999648 | − | 0.0265126i | \(-0.991560\pi\) | ||
0.999648 | − | 0.0265126i | \(-0.00844020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −64.0354 | −2.24582 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.805532 | 0.0282166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.01189 | −0.315286 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.612283 | 0.0213949 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.7380 | −0.898264 | −0.449132 | − | 0.893466i | \(-0.648267\pi\) | ||||
−0.449132 | + | 0.893466i | \(0.648267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.67020i | 0.337082i | 0.985695 | + | 0.168541i | \(0.0539056\pi\) | ||||
−0.985695 | + | 0.168541i | \(0.946094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.39687i | 0.222710i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.2044 | 1.18940 | 0.594702 | − | 0.803946i | \(-0.297270\pi\) | ||||
0.594702 | + | 0.803946i | \(0.297270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9058 | −0.760820 | −0.380410 | − | 0.924818i | \(-0.624217\pi\) | ||||
−0.380410 | + | 0.924818i | \(0.624217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.2346i | 1.25696i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.05111i | 0.209659i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.7694 | −0.649543 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7060 | 0.957659 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.46985 | −0.292412 | −0.146206 | − | 0.989254i | \(-0.546706\pi\) | ||||
−0.146206 | + | 0.989254i | \(0.546706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8425 | −0.373879 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.8148 | 1.78460 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 12.9967i | − | 0.447101i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.8581 | −0.407449 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 73.5357i | − | 2.52374i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.2064 | − | 20.6044i | −1.72105 | − | 0.706309i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2525 | 0.419516 | 0.209758 | − | 0.977753i | \(-0.432732\pi\) | ||||
0.209758 | + | 0.977753i | \(0.432732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.90571i | 0.304569i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.4746 | 1.04099 | 0.520496 | − | 0.853864i | \(-0.325747\pi\) | ||||
0.520496 | + | 0.853864i | \(0.325747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.3587i | − | 1.37702i | −0.725226 | − | 0.688511i | \(-0.758265\pi\) | ||
0.725226 | − | 0.688511i | \(-0.241735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 11.2712i | − | 0.384121i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.1628i | 0.720391i | 0.932877 | + | 0.360195i | \(0.117290\pi\) | ||||
−0.932877 | + | 0.360195i | \(0.882710\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 16.6125i | − | 0.564840i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 40.8505i | − | 1.38736i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.87689 | 0.165437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.456239 | 0.0154591 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 45.0290i | − | 1.52400i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.89011i | − | 0.0638973i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.4236 | −1.93906 | −0.969529 | − | 0.244976i | \(-0.921220\pi\) | ||||
−0.969529 | + | 0.244976i | \(0.921220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 93.7752 | 3.16296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.2714i | 1.35678i | 0.734703 | + | 0.678389i | \(0.237322\pi\) | ||||
−0.734703 | + | 0.678389i | \(0.762678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.6562i | 0.829747i | 0.909879 | + | 0.414873i | \(0.136174\pi\) | ||||
−0.909879 | + | 0.414873i | \(0.863826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 10.1930i | − | 0.342633i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 51.5560i | − | 1.73108i | −0.500838 | − | 0.865541i | \(-0.666975\pi\) | ||
0.500838 | − | 0.865541i | \(-0.333025\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.8392i | 0.766003i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.1292 | 0.439846 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.2214i | − | 0.342048i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.69564 | −0.0901053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.747435 | + | 0.306742i | 0.0249561 | + | 0.0102418i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0950i | 0.503445i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.6981 | −0.689553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 31.8426i | − | 1.05966i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.4282 | 0.546092 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9567 | −0.695855 | −0.347928 | − | 0.937521i | \(-0.613115\pi\) | ||||
−0.347928 | + | 0.937521i | \(0.613115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.66203 | −0.287301 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.8181 | −1.21984 | −0.609919 | − | 0.792464i | \(-0.708798\pi\) | ||||
−0.609919 | + | 0.792464i | \(0.708798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.385914 | 0.0127719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 20.6062i | − | 0.681221i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.3851i | 0.640151i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2312 | −0.502431 | −0.251215 | − | 0.967931i | \(-0.580830\pi\) | ||||
−0.251215 | + | 0.967931i | \(0.580830\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.2838 | 1.52510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.545837i | 0.0179664i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3161i | 0.372070i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.1163 | 1.02199 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.2878 | 1.51865 | 0.759327 | − | 0.650709i | \(-0.225528\pi\) | ||||
0.759327 | + | 0.650709i | \(0.225528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.39486 | 0.176809 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.6000 | −1.46014 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.83810 | 0.125519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.9505i | − | 1.01111i | −0.862794 | − | 0.505555i | \(-0.831288\pi\) | ||
0.862794 | − | 0.505555i | \(-0.168712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.4175 | −2.23272 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 40.4680i | − | 1.31922i | −0.751608 | − | 0.659610i | \(-0.770721\pi\) | ||
0.751608 | − | 0.659610i | \(-0.229279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.69010 | − | 8.99162i | 0.120166 | − | 0.292807i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.7828 | −0.480884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.85793i | 0.255348i | 0.991816 | + | 0.127674i | \(0.0407512\pi\) | ||||
−0.991816 | + | 0.127674i | \(0.959249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.413169 | −0.0134120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 75.3222i | 2.44249i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.97973i | − | 0.161309i | −0.996742 | − | 0.0806546i | \(-0.974299\pi\) | ||
0.996742 | − | 0.0806546i | \(-0.0257011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.863064i | 0.0279281i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.2581i | 0.881129i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.10209i | 0.0678799i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.4510 | 0.595195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −85.4098 | −2.75229 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.05490i | 0.0339584i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.4682i | 1.17274i | 0.810045 | + | 0.586368i | \(0.199443\pi\) | ||||
−0.810045 | + | 0.586368i | \(0.800557\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.17657 | 0.262669 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.3022 | 1.55009 | 0.775045 | − | 0.631905i | \(-0.217727\pi\) | ||||
0.775045 | + | 0.631905i | \(0.217727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 34.5205i | − | 1.10668i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.168465i | − | 0.00539520i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.2738i | 1.25648i | 0.778020 | + | 0.628239i | \(0.216224\pi\) | ||||
−0.778020 | + | 0.628239i | \(0.783776\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.1594i | 0.708217i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 50.1638i | − | 1.60161i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.9582 | 0.796042 | 0.398021 | − | 0.917376i | \(-0.369697\pi\) | ||||
0.398021 | + | 0.917376i | \(0.369697\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.86502i | − | 0.123150i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.1165 | 1.14960 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.4250 | − | 25.4025i | 0.331496 | − | 0.807753i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.7770i | − | 0.787066i | −0.919310 | − | 0.393533i | \(-0.871253\pi\) | ||
0.919310 | − | 0.393533i | \(-0.128747\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.77818 | −0.310301 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.8947i | 0.757511i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.0627 | 1.45882 | 0.729410 | − | 0.684077i | \(-0.239795\pi\) | ||||
0.729410 | + | 0.684077i | \(0.239795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 88.5044 | 2.80016 |
(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 | 1840.2.i.c.1471.2 | yes | 16 | |
4.3 | odd | 2 | inner | 1840.2.i.c.1471.16 | yes | 16 | |
23.22 | odd | 2 | inner | 1840.2.i.c.1471.1 | ✓ | 16 | |
92.91 | even | 2 | inner | 1840.2.i.c.1471.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1840.2.i.c.1471.1 | ✓ | 16 | 23.22 | odd | 2 | inner | |
1840.2.i.c.1471.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1840.2.i.c.1471.15 | yes | 16 | 92.91 | even | 2 | inner | |
1840.2.i.c.1471.16 | yes | 16 | 4.3 | odd | 2 | inner |