Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,3,Mod(1101,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1101");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(51.7712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1101.9 | ||
Root | \(1.84332i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1101 |
Dual form | 1900.3.e.g.1101.6 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.84332i | 0.614441i | 0.951638 | + | 0.307220i | \(0.0993989\pi\) | ||||
−0.951638 | + | 0.307220i | \(0.900601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.5375 | −1.50535 | −0.752676 | − | 0.658391i | \(-0.771237\pi\) | ||||
−0.752676 | + | 0.658391i | \(0.771237\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.60216 | 0.622462 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.7272 | 1.15702 | 0.578509 | − | 0.815676i | \(-0.303635\pi\) | ||||
0.578509 | + | 0.815676i | \(0.303635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.0282i | 1.77140i | 0.464258 | + | 0.885700i | \(0.346321\pi\) | ||||
−0.464258 | + | 0.885700i | \(0.653679\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.77411 | 0.280830 | 0.140415 | − | 0.990093i | \(-0.455156\pi\) | ||||
0.140415 | + | 0.990093i | \(0.455156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.66986 | − | 18.9265i | 0.0878871 | − | 0.996130i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 19.4239i | − | 0.924950i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.7018 | 1.55225 | 0.776127 | − | 0.630576i | \(-0.217181\pi\) | ||||
0.776127 | + | 0.630576i | \(0.217181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.9165i | 0.996907i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 13.7704i | − | 0.474842i | −0.971407 | − | 0.237421i | \(-0.923698\pi\) | ||
0.971407 | − | 0.237421i | \(-0.0763020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 30.5166i | − | 0.984405i | −0.870481 | − | 0.492203i | \(-0.836192\pi\) | ||
0.870481 | − | 0.492203i | \(-0.163808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 23.4603i | 0.710919i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 54.8524i | − | 1.48250i | −0.671230 | − | 0.741249i | \(-0.734234\pi\) | ||
0.671230 | − | 0.741249i | \(-0.265766\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −42.4484 | −1.08842 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.6001i | 0.453660i | 0.973934 | + | 0.226830i | \(0.0728362\pi\) | ||||
−0.973934 | + | 0.226830i | \(0.927164\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.0112 | −0.674679 | −0.337340 | − | 0.941383i | \(-0.609527\pi\) | ||||
−0.337340 | + | 0.941383i | \(0.609527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3148 | −0.240740 | −0.120370 | − | 0.992729i | \(-0.538408\pi\) | ||||
−0.120370 | + | 0.992729i | \(0.538408\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 62.0382 | 1.26609 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.80023i | 0.172553i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7760i | 0.203321i | 0.994819 | + | 0.101660i | \(0.0324155\pi\) | ||||
−0.994819 | + | 0.101660i | \(0.967585\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34.8876 | + | 3.07808i | 0.612063 | + | 0.0540014i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.5728i | 0.924963i | 0.886629 | + | 0.462482i | \(0.153041\pi\) | ||||
−0.886629 | + | 0.462482i | \(0.846959\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17.7698 | 0.291308 | 0.145654 | − | 0.989336i | \(-0.453471\pi\) | ||||
0.145654 | + | 0.989336i | \(0.453471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −59.0326 | −0.937025 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.2136i | 0.898710i | 0.893353 | + | 0.449355i | \(0.148346\pi\) | ||||
−0.893353 | + | 0.449355i | \(0.851654\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 65.8100i | 0.953768i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.9041i | 0.562030i | 0.959703 | + | 0.281015i | \(0.0906710\pi\) | ||||
−0.959703 | + | 0.281015i | \(0.909329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.6243 | 0.337319 | 0.168660 | − | 0.985674i | \(-0.446056\pi\) | ||||
0.168660 | + | 0.985674i | \(0.446056\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −134.112 | −1.74172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.95992i | − | 0.0881003i | −0.999029 | − | 0.0440502i | \(-0.985974\pi\) | ||
0.999029 | − | 0.0440502i | \(-0.0140261\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.803679 | 0.00992196 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 130.188 | 1.56853 | 0.784263 | − | 0.620429i | \(-0.213041\pi\) | ||||
0.784263 | + | 0.620429i | \(0.213041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 25.3833 | 0.291762 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 160.576i | 1.80423i | 0.431498 | + | 0.902114i | \(0.357985\pi\) | ||||
−0.431498 | + | 0.902114i | \(0.642015\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 242.659i | − | 2.66658i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 56.2519 | 0.604859 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 71.2997i | 0.735049i | 0.930014 | + | 0.367524i | \(0.119795\pi\) | ||||
−0.930014 | + | 0.367524i | \(0.880205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 71.2998 | 0.720200 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.366 | 1.06303 | 0.531514 | − | 0.847049i | \(-0.321623\pi\) | ||||
0.531514 | + | 0.847049i | \(0.321623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.6106i | − | 0.161268i | −0.996744 | − | 0.0806341i | \(-0.974305\pi\) | ||
0.996744 | − | 0.0806341i | \(-0.0256945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 133.725i | 1.24977i | 0.780718 | + | 0.624884i | \(0.214854\pi\) | ||||
−0.780718 | + | 0.624884i | \(0.785146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 176.340i | 1.61780i | 0.587947 | + | 0.808899i | \(0.299936\pi\) | ||||
−0.587947 | + | 0.808899i | \(0.700064\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 101.111 | 0.910908 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 224.945i | 1.99066i | 0.0965339 | + | 0.995330i | \(0.469224\pi\) | ||||
−0.0965339 | + | 0.995330i | \(0.530776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 129.008i | 1.10263i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −50.3070 | −0.422748 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 40.9815 | 0.338690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −34.2859 | −0.278747 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 125.867i | − | 0.991076i | −0.868586 | − | 0.495538i | \(-0.834971\pi\) | ||
0.868586 | − | 0.495538i | \(-0.165029\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 53.4770i | − | 0.414551i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −169.986 | −1.29760 | −0.648800 | − | 0.760959i | \(-0.724729\pi\) | ||||
−0.648800 | + | 0.760959i | \(0.724729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.5960 | + | 199.437i | −0.132301 | + | 1.49953i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 169.636 | 1.23822 | 0.619109 | − | 0.785305i | \(-0.287494\pi\) | ||||
0.619109 | + | 0.785305i | \(0.287494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 250.882 | 1.80491 | 0.902455 | − | 0.430784i | \(-0.141763\pi\) | ||||
0.902455 | + | 0.430784i | \(0.141763\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.8568i | − | 0.147920i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 293.084i | 2.04954i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 114.356i | 0.777935i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −156.146 | −1.04796 | −0.523979 | − | 0.851731i | \(-0.675553\pi\) | ||||
−0.523979 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 86.4696i | − | 0.572646i | −0.958133 | − | 0.286323i | \(-0.907567\pi\) | ||
0.958133 | − | 0.286323i | \(-0.0924331\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.7453 | 0.174806 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 59.9932 | 0.382122 | 0.191061 | − | 0.981578i | \(-0.438807\pi\) | ||||
0.191061 | + | 0.981578i | \(0.438807\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.8636 | −0.124929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −376.207 | −2.33669 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −206.566 | −1.26727 | −0.633637 | − | 0.773630i | \(-0.718439\pi\) | ||||
−0.633637 | + | 0.773630i | \(0.718439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 175.728i | − | 1.05227i | −0.850403 | − | 0.526133i | \(-0.823642\pi\) | ||
0.850403 | − | 0.526133i | \(-0.176358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −361.298 | −2.13786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.35480 | − | 106.029i | 0.0547064 | − | 0.620054i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 36.0672i | 0.208481i | 0.994552 | + | 0.104241i | \(0.0332412\pi\) | ||||
−0.994552 | + | 0.104241i | \(0.966759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −100.595 | −0.568335 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 219.282i | 1.22504i | 0.790456 | + | 0.612518i | \(0.209843\pi\) | ||||
−0.790456 | + | 0.612518i | \(0.790157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 40.5089i | − | 0.223806i | −0.993719 | − | 0.111903i | \(-0.964305\pi\) | ||
0.993719 | − | 0.111903i | \(-0.0356946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.7555i | 0.178992i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 60.7611 | 0.324925 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 283.632i | − | 1.50070i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −83.0565 | −0.434851 | −0.217425 | − | 0.976077i | \(-0.569766\pi\) | ||||
−0.217425 | + | 0.976077i | \(0.569766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 187.911i | 0.973630i | 0.873505 | + | 0.486815i | \(0.161841\pi\) | ||||
−0.873505 | + | 0.486815i | \(0.838159\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −170.319 | −0.864562 | −0.432281 | − | 0.901739i | \(-0.642291\pi\) | ||||
−0.432281 | + | 0.901739i | \(0.642291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 121.271 | 0.609400 | 0.304700 | − | 0.952448i | \(-0.401444\pi\) | ||||
0.304700 | + | 0.952448i | \(0.401444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −110.993 | −0.552204 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 145.105i | 0.714804i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 200.008 | 0.966220 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.2526 | − | 240.881i | 0.101687 | − | 1.15254i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 182.151i | − | 0.863276i | −0.902047 | − | 0.431638i | \(-0.857936\pi\) | ||
0.902047 | − | 0.431638i | \(-0.142064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −73.5561 | −0.345334 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 321.567i | 1.48188i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.3906i | 0.207263i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 109.939i | 0.497462i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 215.134i | − | 0.964727i | −0.875971 | − | 0.482363i | \(-0.839778\pi\) | ||
0.875971 | − | 0.482363i | \(-0.160222\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 265.837i | − | 1.17109i | −0.810640 | − | 0.585545i | \(-0.800881\pi\) | ||
0.810640 | − | 0.585545i | \(-0.199119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 115.365 | 0.503777 | 0.251889 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251889 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 247.212i | − | 1.07018i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −189.784 | −0.814524 | −0.407262 | − | 0.913311i | \(-0.633516\pi\) | ||||
−0.407262 | + | 0.913311i | \(0.633516\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8294 | 0.0541324 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 99.3829 | 0.415828 | 0.207914 | − | 0.978147i | \(-0.433333\pi\) | ||||
0.207914 | + | 0.978147i | \(0.433333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 130.340i | − | 0.540829i | −0.962744 | − | 0.270414i | \(-0.912839\pi\) | ||
0.962744 | − | 0.270414i | \(-0.0871607\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.730i | 1.00300i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 435.843 | + | 38.4538i | 1.76455 | + | 0.155683i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 239.978i | 0.963766i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 501.184 | 1.99675 | 0.998374 | − | 0.0569953i | \(-0.0181520\pi\) | ||||
0.998374 | + | 0.0569953i | \(0.0181520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 454.384 | 1.79599 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 162.791i | − | 0.633428i | −0.948521 | − | 0.316714i | \(-0.897420\pi\) | ||
0.948521 | − | 0.316714i | \(-0.102580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 578.006i | 2.23168i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 77.1440i | − | 0.295571i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −50.4816 | −0.191945 | −0.0959727 | − | 0.995384i | \(-0.530596\pi\) | ||||
−0.0959727 | + | 0.995384i | \(0.530596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −295.994 | −1.10859 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 28.7859i | − | 0.107011i | −0.998568 | − | 0.0535053i | \(-0.982961\pi\) | ||
0.998568 | − | 0.0535053i | \(-0.0170394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −400.882 | −1.47927 | −0.739634 | − | 0.673009i | \(-0.765001\pi\) | ||||
−0.739634 | + | 0.673009i | \(0.765001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 447.299 | 1.63846 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −213.844 | −0.772001 | −0.386000 | − | 0.922499i | \(-0.626144\pi\) | ||||
−0.386000 | + | 0.922499i | \(0.626144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 170.959i | − | 0.612755i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 229.607i | 0.817108i | 0.912734 | + | 0.408554i | \(0.133967\pi\) | ||||
−0.912734 | + | 0.408554i | \(0.866033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −201.356 | −0.711506 | −0.355753 | − | 0.934580i | \(-0.615776\pi\) | ||||
−0.355753 | + | 0.934580i | \(0.615776\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 195.998i | − | 0.682919i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −266.208 | −0.921134 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −131.428 | −0.451644 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 285.899i | 0.975765i | 0.872909 | + | 0.487883i | \(0.162231\pi\) | ||||
−0.872909 | + | 0.487883i | \(0.837769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 342.572i | 1.15344i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 822.149i | 2.74966i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 305.705 | 1.01563 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 197.910i | 0.653168i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 38.7426i | − | 0.126197i | −0.998007 | − | 0.0630986i | \(-0.979902\pi\) | ||
0.998007 | − | 0.0630986i | \(-0.0200983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.6187 | 0.0990898 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 607.655 | 1.95387 | 0.976937 | − | 0.213526i | \(-0.0684949\pi\) | ||||
0.976937 | + | 0.213526i | \(0.0684949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −293.775 | −0.938577 | −0.469289 | − | 0.883045i | \(-0.655490\pi\) | ||||
−0.469289 | + | 0.883045i | \(0.655490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 558.422i | 1.76158i | 0.473503 | + | 0.880792i | \(0.342989\pi\) | ||||
−0.473503 | + | 0.880792i | \(0.657011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 175.259i | − | 0.549400i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −246.498 | −0.767908 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.97208 | − | 90.3571i | 0.0246814 | − | 0.279743i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −325.052 | −0.994041 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 119.229 | 0.362398 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 366.890i | 1.10843i | 0.832374 | + | 0.554214i | \(0.186981\pi\) | ||||
−0.832374 | + | 0.554214i | \(0.813019\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 307.292i | − | 0.922800i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 466.486i | 1.38423i | 0.721787 | + | 0.692115i | \(0.243321\pi\) | ||||
−0.721787 | + | 0.692115i | \(0.756679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −414.645 | −1.22314 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 388.390i | − | 1.13897i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −137.389 | −0.400552 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 490.615 | 1.41388 | 0.706938 | − | 0.707275i | \(-0.250076\pi\) | ||||
0.706938 | + | 0.707275i | \(0.250076\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 503.588 | 1.44295 | 0.721473 | − | 0.692443i | \(-0.243465\pi\) | ||||
0.721473 | + | 0.692443i | \(0.243465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −619.838 | −1.76592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −353.912 | −1.00258 | −0.501292 | − | 0.865278i | \(-0.667142\pi\) | ||||
−0.501292 | + | 0.865278i | \(0.667142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 92.7321i | − | 0.259754i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 226.398 | 0.630634 | 0.315317 | − | 0.948986i | \(-0.397889\pi\) | ||||
0.315317 | + | 0.948986i | \(0.397889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −355.423 | − | 63.2090i | −0.984552 | − | 0.175094i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 75.5422i | 0.208105i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −427.998 | −1.16621 | −0.583104 | − | 0.812398i | \(-0.698162\pi\) | ||||
−0.583104 | + | 0.812398i | \(0.698162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 104.201i | 0.282387i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 113.552i | − | 0.306069i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 275.474i | − | 0.738537i | −0.929323 | − | 0.369268i | \(-0.879608\pi\) | ||
0.929323 | − | 0.369268i | \(-0.120392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 317.108 | 0.841134 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 250.621i | − | 0.661268i | −0.943759 | − | 0.330634i | \(-0.892737\pi\) | ||
0.943759 | − | 0.330634i | \(-0.107263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 232.013 | 0.608957 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 148.912i | − | 0.388805i | −0.980922 | − | 0.194403i | \(-0.937723\pi\) | ||
0.980922 | − | 0.194403i | \(-0.0622768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −162.526 | −0.419963 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 57.2486 | 0.147169 | 0.0735843 | − | 0.997289i | \(-0.476556\pi\) | ||||
0.0735843 | + | 0.997289i | \(0.476556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 170.445 | 0.435920 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 313.338i | − | 0.797298i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 597.128 | 1.50410 | 0.752050 | − | 0.659106i | \(-0.229065\pi\) | ||||
0.752050 | + | 0.659106i | \(0.229065\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −367.627 | − | 32.4352i | −0.921371 | − | 0.0812912i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 422.141i | 1.05272i | 0.850262 | + | 0.526360i | \(0.176444\pi\) | ||||
−0.850262 | + | 0.526360i | \(0.823556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 702.741 | 1.74378 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 698.118i | − | 1.71528i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 244.086i | − | 0.596786i | −0.954443 | − | 0.298393i | \(-0.903549\pi\) | ||
0.954443 | − | 0.298393i | \(-0.0964506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 312.693i | 0.760811i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 575.059i | − | 1.39240i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 462.457i | 1.10901i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 499.432 | 1.19196 | 0.595980 | − | 0.802999i | \(-0.296764\pi\) | ||||
0.595980 | + | 0.802999i | \(0.296764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 521.240i | 1.23810i | 0.785351 | + | 0.619050i | \(0.212482\pi\) | ||||
−0.785351 | + | 0.619050i | \(0.787518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −63.3872 | −0.149851 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −187.249 | −0.438522 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −540.249 | −1.25932 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 252.375i | − | 0.585557i | −0.956180 | − | 0.292778i | \(-0.905420\pi\) | ||
0.956180 | − | 0.292778i | \(-0.0945798\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 516.782i | 1.19349i | 0.802430 | + | 0.596746i | \(0.203540\pi\) | ||||
−0.802430 | + | 0.596746i | \(0.796460\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 59.6169 | − | 675.710i | 0.136423 | − | 1.54625i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 706.635i | − | 1.60965i | −0.593514 | − | 0.804823i | \(-0.702260\pi\) | ||
0.593514 | − | 0.804823i | \(-0.297740\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 347.548 | 0.788091 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 405.631 | 0.915645 | 0.457823 | − | 0.889044i | \(-0.348630\pi\) | ||||
0.457823 | + | 0.889044i | \(0.348630\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 287.827i | − | 0.643908i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 585.708i | − | 1.30447i | −0.758015 | − | 0.652237i | \(-0.773831\pi\) | ||
0.758015 | − | 0.652237i | \(-0.226169\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 236.727i | 0.524893i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 159.391 | 0.351857 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −445.652 | −0.975169 | −0.487585 | − | 0.873076i | \(-0.662122\pi\) | ||||
−0.487585 | + | 0.873076i | \(0.662122\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 128.502i | 0.279962i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 334.203 | 0.724953 | 0.362476 | − | 0.931993i | \(-0.381931\pi\) | ||||
0.362476 | + | 0.931993i | \(0.381931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 180.792 | 0.390479 | 0.195240 | − | 0.980756i | \(-0.437452\pi\) | ||||
0.195240 | + | 0.980756i | \(0.437452\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −629.520 | −1.34801 | −0.674004 | − | 0.738727i | \(-0.735427\pi\) | ||||
−0.674004 | + | 0.738727i | \(0.735427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 634.498i | − | 1.35287i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 110.587i | 0.234792i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −369.231 | −0.780616 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 60.3689i | 0.126559i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 304.093 | 0.634849 | 0.317425 | − | 0.948284i | \(-0.397182\pi\) | ||||
0.317425 | + | 0.948284i | \(0.397182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1263.15 | 2.62610 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 693.471i | − | 1.43576i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 235.191i | − | 0.482938i | −0.970409 | − | 0.241469i | \(-0.922371\pi\) | ||
0.970409 | − | 0.241469i | \(-0.0776291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 380.767i | − | 0.778665i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 289.350 | 0.589308 | 0.294654 | − | 0.955604i | \(-0.404796\pi\) | ||||
0.294654 | + | 0.955604i | \(0.404796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 65.7415i | − | 0.133350i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 420.488i | − | 0.846053i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −754.978 | −1.51298 | −0.756491 | − | 0.654004i | \(-0.773088\pi\) | ||||
−0.756491 | + | 0.654004i | \(0.773088\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 323.924 | 0.646555 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −347.663 | −0.691180 | −0.345590 | − | 0.938386i | \(-0.612321\pi\) | ||||
−0.345590 | + | 0.938386i | \(0.612321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 665.989i | − | 1.31359i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 117.878i | 0.231587i | 0.993273 | + | 0.115794i | \(0.0369411\pi\) | ||||
−0.993273 | + | 0.115794i | \(0.963059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −259.478 | −0.507784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 509.434 | + | 44.9467i | 0.993050 | + | 0.0876153i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −144.005 | −0.278540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −66.4836 | −0.128099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 844.507i | − | 1.62093i | −0.585784 | − | 0.810467i | \(-0.699213\pi\) | ||
0.585784 | − | 0.810467i | \(-0.300787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 482.142i | − | 0.921879i | −0.887432 | − | 0.460939i | \(-0.847513\pi\) | ||
0.887432 | − | 0.460939i | \(-0.152487\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 145.689i | − | 0.276451i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 745.622 | 1.40949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 305.726i | 0.575755i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −428.326 | −0.803614 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −404.207 | −0.752713 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 789.572 | 1.46488 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −973.284 | −1.79905 | −0.899524 | − | 0.436872i | \(-0.856086\pi\) | ||||
−0.899524 | + | 0.436872i | \(0.856086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 74.6709 | 0.137516 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 425.904i | 0.778618i | 0.921107 | + | 0.389309i | \(0.127286\pi\) | ||||
−0.921107 | + | 0.389309i | \(0.872714\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 99.5493 | 0.181328 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −260.625 | − | 22.9946i | −0.473004 | − | 0.0417325i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.3400i | 0.132622i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −401.955 | −0.721643 | −0.360822 | − | 0.932635i | \(-0.617504\pi\) | ||||
−0.360822 | + | 0.932635i | \(0.617504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 668.076i | − | 1.19513i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 112.002i | 0.199647i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 655.640i | − | 1.16455i | −0.812993 | − | 0.582274i | \(-0.802163\pi\) | ||
0.812993 | − | 0.582274i | \(-0.197837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.46874 | −0.0149361 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 485.171i | − | 0.852674i | −0.904564 | − | 0.426337i | \(-0.859804\pi\) | ||
0.904564 | − | 0.426337i | \(-0.140196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1001.50 | 1.75395 | 0.876974 | − | 0.480537i | \(-0.159558\pi\) | ||||
0.876974 | + | 0.480537i | \(0.159558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 153.100i | − | 0.267190i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.1105 | 0.0573838 | 0.0286919 | − | 0.999588i | \(-0.490866\pi\) | ||||
0.0286919 | + | 0.999588i | \(0.490866\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −346.380 | −0.598238 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1371.85 | −2.36118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 137.148i | 0.235246i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 635.756 | 1.08306 | 0.541530 | − | 0.840681i | \(-0.317845\pi\) | ||||
0.541530 | + | 0.840681i | \(0.317845\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −577.571 | − | 50.9582i | −0.980596 | − | 0.0865165i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 313.952i | − | 0.531222i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 59.1677 | 0.0997770 | 0.0498885 | − | 0.998755i | \(-0.484113\pi\) | ||||
0.0498885 | + | 0.998755i | \(0.484113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 223.541i | 0.374440i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 941.332i | 1.57151i | 0.618540 | + | 0.785753i | \(0.287724\pi\) | ||||
−0.618540 | + | 0.785753i | \(0.712276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 333.283i | 0.554547i | 0.960791 | + | 0.277274i | \(0.0894308\pi\) | ||||
−0.960791 | + | 0.277274i | \(0.910569\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 337.326i | 0.559413i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 747.914i | − | 1.23215i | −0.787688 | − | 0.616074i | \(-0.788722\pi\) | ||
0.787688 | − | 0.616074i | \(-0.211278\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −267.476 | −0.439205 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 260.559i | − | 0.426446i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −226.642 | −0.369726 | −0.184863 | − | 0.982764i | \(-0.559184\pi\) | ||||
−0.184863 | + | 0.982764i | \(0.559184\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 796.334 | 1.29065 | 0.645327 | − | 0.763906i | \(-0.276721\pi\) | ||||
0.645327 | + | 0.763906i | \(0.276721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.3780 | −0.0506914 | −0.0253457 | − | 0.999679i | \(-0.508069\pi\) | ||||
−0.0253457 | + | 0.999679i | \(0.508069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 960.969i | 1.54745i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1692.07i | − | 2.71600i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 444.021 | + | 39.1754i | 0.708168 | + | 0.0624806i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 261.872i | − | 0.416330i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −493.470 | −0.782045 | −0.391022 | − | 0.920381i | \(-0.627878\pi\) | ||||
−0.391022 | + | 0.920381i | \(0.627878\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 335.763 | 0.530432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1428.63i | 2.24274i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 223.549i | 0.349842i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 946.351i | 1.47637i | 0.674600 | + | 0.738183i | \(0.264316\pi\) | ||||
−0.674600 | + | 0.738183i | \(0.735684\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −816.065 | −1.26915 | −0.634576 | − | 0.772860i | \(-0.718825\pi\) | ||||
−0.634576 | + | 0.772860i | \(0.718825\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 573.382 | 0.886217 | 0.443108 | − | 0.896468i | \(-0.353876\pi\) | ||||
0.443108 | + | 0.896468i | \(0.353876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 694.559i | 1.07020i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −592.752 | −0.910525 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 443.988 | 0.679920 | 0.339960 | − | 0.940440i | \(-0.389586\pi\) | ||||
0.339960 | + | 0.940440i | \(0.389586\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 137.949 | 0.209969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 571.755i | 0.867609i | 0.901007 | + | 0.433805i | \(0.142829\pi\) | ||||
−0.901007 | + | 0.433805i | \(0.857171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1244.42i | 1.88264i | 0.337519 | + | 0.941319i | \(0.390412\pi\) | ||||
−0.337519 | + | 0.941319i | \(0.609588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −202.653 | −0.305661 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 491.629i | − | 0.737075i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 396.562 | 0.592768 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 226.160 | 0.337049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 236.320i | 0.351144i | 0.984467 | + | 0.175572i | \(0.0561775\pi\) | ||||
−0.984467 | + | 0.175572i | \(0.943823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1066.35i | − | 1.57512i | −0.616239 | − | 0.787559i | \(-0.711345\pi\) | ||
0.616239 | − | 0.787559i | \(-0.288655\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 751.318i | − | 1.10651i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 490.024 | 0.719566 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1176.02i | − | 1.72184i | −0.508739 | − | 0.860921i | \(-0.669888\pi\) | ||
0.508739 | − | 0.860921i | \(-0.330112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 212.655i | 0.309541i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −248.152 | −0.360162 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.1811 | 0.0263113 | 0.0131557 | − | 0.999913i | \(-0.495812\pi\) | ||||
0.0131557 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −751.319 | −1.08415 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 88.7988i | 0.127401i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 349.833i | − | 0.500477i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −438.306 | −0.625258 | −0.312629 | − | 0.949875i | \(-0.601210\pi\) | ||||
−0.312629 | + | 0.949875i | \(0.601210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1038.16 | − | 91.5957i | −1.47676 | − | 0.130293i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1131.36 | −1.60023 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −629.057 | −0.887245 | −0.443622 | − | 0.896214i | \(-0.646307\pi\) | ||||
−0.443622 | + | 0.896214i | \(0.646307\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 38.9906i | − | 0.0548391i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1089.50i | − | 1.52805i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 183.195i | 0.255502i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1112.31 | −1.54702 | −0.773509 | − | 0.633786i | \(-0.781500\pi\) | ||||
−0.773509 | + | 0.633786i | \(0.781500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 175.034i | 0.242765i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 240.258 | 0.332307 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 684.037 | 0.940904 | 0.470452 | − | 0.882426i | \(-0.344091\pi\) | ||||
0.470452 | + | 0.882426i | \(0.344091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −442.040 | −0.606364 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −138.503 | −0.189470 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 171.268 | 0.233653 | 0.116826 | − | 0.993152i | \(-0.462728\pi\) | ||||
0.116826 | + | 0.993152i | \(0.462728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 766.350i | 1.03982i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 317.424 | 0.429532 | 0.214766 | − | 0.976665i | \(-0.431101\pi\) | ||||
0.214766 | + | 0.976665i | \(0.431101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −70.8827 | + | 803.399i | −0.0956582 | + | 1.08421i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 140.619i | − | 0.189258i | −0.995513 | − | 0.0946289i | \(-0.969834\pi\) | ||
0.995513 | − | 0.0946289i | \(-0.0301664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 729.332 | 0.976348 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1409.12i | − | 1.88134i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 825.612i | 1.09935i | 0.835378 | + | 0.549675i | \(0.185249\pi\) | ||||
−0.835378 | + | 0.549675i | \(0.814751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 923.844i | 1.22688i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 693.756 | 0.916454 | 0.458227 | − | 0.888835i | \(-0.348485\pi\) | ||||
0.458227 | + | 0.888835i | \(0.348485\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 837.577i | 1.10353i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −148.006 | −0.194489 | −0.0972447 | − | 0.995261i | \(-0.531003\pi\) | ||||
−0.0972447 | + | 0.995261i | \(0.531003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1858.18i | − | 2.43536i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1256.71 | −1.63848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1090.86 | 1.41854 | 0.709270 | − | 0.704937i | \(-0.249025\pi\) | ||||
0.709270 | + | 0.704937i | \(0.249025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 300.076 | 0.389204 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 498.925i | − | 0.645440i | −0.946494 | − | 0.322720i | \(-0.895403\pi\) | ||
0.946494 | − | 0.322720i | \(-0.104597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1065.45 | −1.37124 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 352.034 | + | 31.0594i | 0.451905 | + | 0.0398709i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 507.867i | 0.650278i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 370.651 | 0.473373 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 703.635i | − | 0.894072i | −0.894516 | − | 0.447036i | \(-0.852480\pi\) | ||
0.894516 | − | 0.447036i | \(-0.147520\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 93.0539i | − | 0.117939i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2370.35i | − | 2.99664i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 409.207i | 0.516023i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.1611i | 0.0353339i | 0.999844 | + | 0.0176669i | \(0.00562385\pi\) | ||||
−0.999844 | + | 0.0176669i | \(0.994376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.0180 | −0.0676070 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 899.574i | 1.12306i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 313.399 | 0.390285 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53.0616 | 0.0657517 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 666.095 | 0.823356 | 0.411678 | − | 0.911329i | \(-0.364943\pi\) | ||||
0.411678 | + | 0.911329i | \(0.364943\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 803.237i | 0.990428i | 0.868771 | + | 0.495214i | \(0.164910\pi\) | ||||
−0.868771 | + | 0.495214i | \(0.835090\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 738.954i | − | 0.908923i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.4445 | + | 549.080i | −0.0592956 | + | 0.672069i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1359.41i | − | 1.65985i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 433.616 | 0.528157 | 0.264078 | − | 0.964501i | \(-0.414932\pi\) | ||||
0.264078 | + | 0.964501i | \(0.414932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 69.2993 | 0.0842033 | 0.0421016 | − | 0.999113i | \(-0.486595\pi\) | ||||
0.0421016 | + | 0.999113i | \(0.486595\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 282.525i | − | 0.341626i | −0.985303 | − | 0.170813i | \(-0.945361\pi\) | ||
0.985303 | − | 0.170813i | \(-0.0546394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1136.04i | − | 1.37037i | −0.728369 | − | 0.685185i | \(-0.759722\pi\) | ||
0.728369 | − | 0.685185i | \(-0.240278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 394.184i | − | 0.474349i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 296.177 | 0.355555 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 821.399 | 0.981361 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 474.238i | 0.565242i | 0.959232 | + | 0.282621i | \(0.0912039\pi\) | ||||
−0.959232 | + | 0.282621i | \(0.908796\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 651.376 | 0.774526 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −423.240 | −0.502065 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −431.842 | −0.509848 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 371.164i | − | 0.437178i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1958.33i | − | 2.30121i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −843.815 | −0.989232 | −0.494616 | − | 0.869112i | \(-0.664691\pi\) | ||||
−0.494616 | + | 0.869112i | \(0.664691\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 435.275i | − | 0.507906i | −0.967217 | − | 0.253953i | \(-0.918269\pi\) | ||
0.967217 | − | 0.253953i | \(-0.0817308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 715.550 | 0.833003 | 0.416502 | − | 0.909135i | \(-0.363256\pi\) | ||||
0.416502 | + | 0.909135i | \(0.363256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 361.287 | 0.419613 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1083.60i | 1.25562i | 0.778366 | + | 0.627811i | \(0.216049\pi\) | ||||
−0.778366 | + | 0.627811i | \(0.783951\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 490.707i | − | 0.565983i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 88.5803i | − | 0.101934i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1386.61 | −1.59197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 399.433i | 0.457540i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 737.245i | 0.840644i | 0.907375 | + | 0.420322i | \(0.138083\pi\) | ||||
−0.907375 | + | 0.420322i | \(0.861917\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −527.005 | −0.599550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −64.9086 | −0.0736761 | −0.0368380 | − | 0.999321i | \(-0.511729\pi\) | ||||
−0.0368380 | + | 0.999321i | \(0.511729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1325.97 | 1.50166 | 0.750830 | − | 0.660495i | \(-0.229654\pi\) | ||||
0.750830 | + | 0.660495i | \(0.229654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 842.262i | − | 0.949563i | −0.880104 | − | 0.474781i | \(-0.842527\pi\) | ||
0.880104 | − | 0.474781i | \(-0.157473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1326.32i | 1.49192i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2286 | 0.0114799 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8940 | + | 214.149i | −0.0211579 | + | 0.239808i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1515.49 | −1.68951 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −420.225 | −0.467436 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.4458i | 0.0570986i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 563.512i | 0.624045i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1212.41i | − | 1.33673i | −0.743834 | − | 0.668364i | \(-0.766995\pi\) | ||
0.743834 | − | 0.668364i | \(-0.233005\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 601.481 | 0.661695 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1204.26i | 1.32191i | 0.750427 | + | 0.660954i | \(0.229848\pi\) | ||||
−0.750427 | + | 0.660954i | \(0.770152\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1656.92 | 1.81481 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1791.22 | 1.95334 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −117.855 | −0.128243 | −0.0641214 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641214 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 71.4150 | 0.0775408 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −918.920 | −0.995579 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 93.0554i | − | 0.100383i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1171.59 | −1.26113 | −0.630566 | − | 0.776136i | \(-0.717177\pi\) | ||||
−0.630566 | + | 0.776136i | \(0.717177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 103.595 | − | 1174.16i | 0.111273 | − | 1.26119i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1120.10i | 1.20054i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1657.08 | 1.76849 | 0.884247 | − | 0.467020i | \(-0.154672\pi\) | ||||
0.884247 | + | 0.467020i | \(0.154672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 541.522i | − | 0.576700i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 897.326i | 0.953588i | 0.879015 | + | 0.476794i | \(0.158201\pi\) | ||||
−0.879015 | + | 0.476794i | \(0.841799\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 664.057i | 0.704196i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1458.19 | −1.53980 | −0.769901 | − | 0.638163i | \(-0.779695\pi\) | ||||
−0.769901 | + | 0.638163i | \(0.779695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 567.054i | 0.597528i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1029.35 | −1.08239 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1049.86i | 1.10164i | 0.834624 | + | 0.550820i | \(0.185685\pi\) | ||||
−0.834624 | + | 0.550820i | \(0.814315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 323.058 | 0.337574 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1787.53 | −1.86395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7397 | 0.0309466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 749.150i | 0.777933i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 236.232 | 0.244293 | 0.122147 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122147 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 166.557 | + | 14.6951i | 0.171886 | + | 0.0151652i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1281.82i | − | 1.32010i | −0.751220 | − | 0.660052i | \(-0.770534\pi\) | ||
0.751220 | − | 0.660052i | \(-0.229466\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2643.67 | −2.71702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1475.99i | − | 1.51074i | −0.655300 | − | 0.755369i | \(-0.727458\pi\) | ||
0.655300 | − | 0.755369i | \(-0.272542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2043.69i | 2.08752i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 987.885i | 1.00702i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 574.909i | − | 0.584851i | −0.956288 | − | 0.292426i | \(-0.905538\pi\) | ||
0.956288 | − | 0.292426i | \(-0.0944624\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 219.777i | 0.222672i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1035.75 | −1.04727 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.2482i | − | 0.0476773i | −0.999716 | − | 0.0238387i | \(-0.992411\pi\) | ||
0.999716 | − | 0.0238387i | \(-0.00758880\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −676.296 | −0.681064 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −671.475 | −0.673495 | −0.336748 | − | 0.941595i | \(-0.609327\pi\) | ||||
−0.336748 | + | 0.941595i | \(0.609327\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1476.44 | 1.47791 |
(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 | 1900.3.e.g.1101.9 | yes | 14 | |
5.2 | odd | 4 | 1900.3.g.d.949.18 | 28 | |||
5.3 | odd | 4 | 1900.3.g.d.949.11 | 28 | |||
5.4 | even | 2 | 1900.3.e.h.1101.6 | yes | 14 | ||
19.18 | odd | 2 | inner | 1900.3.e.g.1101.6 | ✓ | 14 | |
95.18 | even | 4 | 1900.3.g.d.949.17 | 28 | |||
95.37 | even | 4 | 1900.3.g.d.949.12 | 28 | |||
95.94 | odd | 2 | 1900.3.e.h.1101.9 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.3.e.g.1101.6 | ✓ | 14 | 19.18 | odd | 2 | inner | |
1900.3.e.g.1101.9 | yes | 14 | 1.1 | even | 1 | trivial | |
1900.3.e.h.1101.6 | yes | 14 | 5.4 | even | 2 | ||
1900.3.e.h.1101.9 | yes | 14 | 95.94 | odd | 2 | ||
1900.3.g.d.949.11 | 28 | 5.3 | odd | 4 | |||
1900.3.g.d.949.12 | 28 | 95.37 | even | 4 | |||
1900.3.g.d.949.17 | 28 | 95.18 | even | 4 | |||
1900.3.g.d.949.18 | 28 | 5.2 | odd | 4 |