Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(49,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0767639626\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.49 |
Dual form | 200.6.c.d.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.00000i | 0.128300i | 0.997940 | + | 0.0641500i | \(0.0204336\pi\) | ||||
−0.997940 | + | 0.0641500i | \(0.979566\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 62.0000i | − 0.478241i | −0.970990 | − | 0.239120i | \(-0.923141\pi\) | ||||
0.970990 | − | 0.239120i | \(-0.0768591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 239.000 | 0.983539 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −144.000 | −0.358823 | −0.179412 | − | 0.983774i | \(-0.557419\pi\) | ||||
−0.179412 | + | 0.983774i | \(0.557419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 654.000i | 1.07330i | 0.843806 | + | 0.536648i | \(0.180310\pi\) | ||||
−0.843806 | + | 0.536648i | \(0.819690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1190.00i | − 0.998676i | −0.866407 | − | 0.499338i | \(-0.833577\pi\) | ||||
0.866407 | − | 0.499338i | \(-0.166423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −556.000 | −0.353338 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 124.000 | 0.0613583 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2182.00i | − 0.860073i | −0.902812 | − | 0.430036i | \(-0.858501\pi\) | ||||
0.902812 | − | 0.430036i | \(-0.141499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 964.000i | 0.254488i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1578.00 | 0.348427 | 0.174214 | − | 0.984708i | \(-0.444262\pi\) | ||||
0.174214 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9660.00 | 1.80540 | 0.902699 | − | 0.430273i | \(-0.141583\pi\) | ||||
0.902699 | + | 0.430273i | \(0.141583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 288.000i | − 0.0460371i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3534.00i | − 0.424387i | −0.977228 | − | 0.212194i | \(-0.931939\pi\) | ||||
0.977228 | − | 0.212194i | \(-0.0680607\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1308.00 | −0.137704 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7462.00 | 0.693259 | 0.346630 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346630 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7114.00i | 0.586736i | 0.956000 | + | 0.293368i | \(0.0947761\pi\) | ||||
−0.956000 | + | 0.293368i | \(0.905224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 28294.0i | − 1.86831i | −0.356863 | − | 0.934157i | \(-0.616154\pi\) | ||||
0.356863 | − | 0.934157i | \(-0.383846\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12963.0 | 0.771286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2380.00 | 0.128130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13046.0i | 0.637952i | 0.947763 | + | 0.318976i | \(0.103339\pi\) | ||||
−0.947763 | + | 0.318976i | \(0.896661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1112.00i | − 0.0453333i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37092.0 | 1.38724 | 0.693618 | − | 0.720343i | \(-0.256016\pi\) | ||||
0.693618 | + | 0.720343i | \(0.256016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39570.0 | 1.36157 | 0.680787 | − | 0.732481i | \(-0.261638\pi\) | ||||
0.680787 | + | 0.732481i | \(0.261638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 14818.0i | − 0.470368i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 56734.0i | − 1.54403i | −0.635603 | − | 0.772016i | \(-0.719248\pi\) | ||||
0.635603 | − | 0.772016i | \(-0.280752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4364.00 | 0.110347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45588.0 | 1.07326 | 0.536630 | − | 0.843818i | \(-0.319697\pi\) | ||||
0.536630 | + | 0.843818i | \(0.319697\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11842.0i | − 0.260087i | −0.991508 | − | 0.130043i | \(-0.958488\pi\) | ||||
0.991508 | − | 0.130043i | \(-0.0415116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8928.00i | 0.171604i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94216.0 | −1.69847 | −0.849233 | − | 0.528018i | \(-0.822935\pi\) | ||||
−0.849233 | + | 0.528018i | \(0.822935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 56149.0 | 0.950888 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31482.0i | 0.501611i | 0.968037 | + | 0.250806i | \(0.0806955\pi\) | ||||
−0.968037 | + | 0.250806i | \(0.919305\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3156.00i | 0.0447032i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 94054.0 | 1.25864 | 0.629321 | − | 0.777145i | \(-0.283333\pi\) | ||||
0.629321 | + | 0.777145i | \(0.283333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 40548.0 | 0.513294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19320.0i | 0.231633i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23714.0i | 0.255903i | 0.991780 | + | 0.127952i | \(0.0408402\pi\) | ||||
−0.991780 | + | 0.127952i | \(0.959160\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34416.0 | −0.352917 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −129674. | −1.26488 | −0.632440 | − | 0.774609i | \(-0.717947\pi\) | ||||
−0.632440 | + | 0.774609i | \(0.717947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 136846.i | − 1.27098i | −0.772109 | − | 0.635490i | \(-0.780798\pi\) | ||||
0.772109 | − | 0.635490i | \(-0.219202\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 193190.i | − 1.63127i | −0.578569 | − | 0.815634i | \(-0.696388\pi\) | ||||
0.578569 | − | 0.815634i | \(-0.303612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 120046. | 0.967791 | 0.483895 | − | 0.875126i | \(-0.339222\pi\) | ||||
0.483895 | + | 0.875126i | \(0.339222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7068.00 | 0.0544489 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 152646.i | 1.12458i | 0.826941 | + | 0.562289i | \(0.190079\pi\) | ||||
−0.826941 | + | 0.562289i | \(0.809921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 156306.i | 1.05563i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −73780.0 | −0.477608 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140315. | −0.871246 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14924.0i | 0.0889452i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 107906.i | 0.593658i | 0.954931 | + | 0.296829i | \(0.0959291\pi\) | ||||
−0.954931 | + | 0.296829i | \(0.904071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14228.0 | −0.0752783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −233072. | −1.18662 | −0.593310 | − | 0.804974i | \(-0.702179\pi\) | ||||
−0.593310 | + | 0.804974i | \(0.702179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34472.0i | 0.168981i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 356082.i | 1.62087i | 0.585827 | + | 0.810436i | \(0.300770\pi\) | ||||
−0.585827 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −312204. | −1.37057 | −0.685285 | − | 0.728275i | \(-0.740323\pi\) | ||||
−0.685285 | + | 0.728275i | \(0.740323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56588.0 | 0.239705 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 94176.0i | − 0.385124i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25926.0i | 0.0989560i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −27498.0 | −0.101469 | −0.0507347 | − | 0.998712i | \(-0.516156\pi\) | ||||
−0.0507347 | + | 0.998712i | \(0.516156\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −136908. | −0.488637 | −0.244319 | − | 0.969695i | \(-0.578564\pi\) | ||||
−0.244319 | + | 0.969695i | \(0.578564\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 284410.i | − 0.982237i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 406714.i | 1.31686i | 0.752641 | + | 0.658431i | \(0.228779\pi\) | ||||
−0.752641 | + | 0.658431i | \(0.771221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −26092.0 | −0.0818492 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −135284. | −0.411322 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13642.0i | 0.0402169i | 0.999798 | + | 0.0201085i | \(0.00640116\pi\) | ||||
−0.999798 | + | 0.0201085i | \(0.993599\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 203438.i | − 0.564470i | −0.959345 | − | 0.282235i | \(-0.908924\pi\) | ||||
0.959345 | − | 0.282235i | \(-0.0910758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −56423.0 | −0.151964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −132884. | −0.347522 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 127242.i | − 0.323233i | −0.986854 | − | 0.161616i | \(-0.948329\pi\) | ||||
0.986854 | − | 0.161616i | \(-0.0516707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 74184.0i | 0.177982i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 94684.0 | 0.220874 | 0.110437 | − | 0.993883i | \(-0.464775\pi\) | ||||
0.110437 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −517018. | −1.17303 | −0.586515 | − | 0.809938i | \(-0.699501\pi\) | ||||
−0.586515 | + | 0.809938i | \(0.699501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 79140.0i | 0.174690i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 171360.i | 0.358348i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 59768.0 | 0.121707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −412300. | −0.817768 | −0.408884 | − | 0.912586i | \(-0.634082\pi\) | ||||
−0.408884 | + | 0.912586i | \(0.634082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 771654.i | 1.49118i | 0.666406 | + | 0.745589i | \(0.267832\pi\) | ||||
−0.666406 | + | 0.745589i | \(0.732168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 190238.i | − 0.349246i | −0.984635 | − | 0.174623i | \(-0.944129\pi\) | ||||
0.984635 | − | 0.174623i | \(-0.0558707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −132072. | −0.236417 | −0.118208 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118208 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 113468. | 0.198099 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 97836.0i | − 0.166632i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 521498.i | − 0.845915i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 80064.0 | 0.126786 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 928704. | 1.43606 | 0.718028 | − | 0.696015i | \(-0.245045\pi\) | ||||
0.718028 | + | 0.696015i | \(0.245045\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 91176.0i | 0.137699i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 598920.i | − 0.863415i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23684.0 | 0.0333691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 778260. | 1.07187 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 421494.i | − 0.567583i | −0.958886 | − | 0.283791i | \(-0.908408\pi\) | ||||
0.958886 | − | 0.283791i | \(-0.0915923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 991962.i | 1.27770i | 0.769329 | + | 0.638852i | \(0.220590\pi\) | ||||
−0.769329 | + | 0.638852i | \(0.779410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 266946. | 0.336384 | 0.168192 | − | 0.985754i | \(-0.446207\pi\) | ||||
0.168192 | + | 0.985754i | \(0.446207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17856.0 | −0.0220168 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 960314.i | − 1.15884i | −0.815029 | − | 0.579420i | \(-0.803279\pi\) | ||||
0.815029 | − | 0.579420i | \(-0.196721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 188432.i | − 0.217913i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 492696. | 0.557936 | 0.278968 | − | 0.960300i | \(-0.410008\pi\) | ||||
0.278968 | + | 0.960300i | \(0.410008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 56078.0 | 0.0621942 | 0.0310971 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310971 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 346550.i | 0.376487i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 363624.i | − 0.379237i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −62964.0 | −0.0643567 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.96792e6 | 1.97162 | 0.985810 | − | 0.167866i | \(-0.0536876\pi\) | ||||
0.985810 | + | 0.167866i | \(0.0536876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 314208.i | 0.308614i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 971910.i | − 0.917896i | −0.888463 | − | 0.458948i | \(-0.848227\pi\) | ||||
0.888463 | − | 0.458948i | \(-0.151773\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −219108. | −0.202959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 377142. | 0.342692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 154770.i | 0.137974i | 0.997618 | + | 0.0689870i | \(0.0219767\pi\) | ||||
−0.997618 | + | 0.0689870i | \(0.978023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 188108.i | 0.161484i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.02371e6 | −0.862577 | −0.431289 | − | 0.902214i | \(-0.641941\pi\) | ||||
−0.431289 | + | 0.902214i | \(0.641941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.14776e6 | −0.949350 | −0.474675 | − | 0.880161i | \(-0.657434\pi\) | ||||
−0.474675 | + | 0.880161i | \(0.657434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 81096.0i | 0.0658556i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.49676e6i | − 1.95514i | −0.210619 | − | 0.977568i | \(-0.567548\pi\) | ||||
0.210619 | − | 0.977568i | \(-0.432452\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.30874e6 | 1.77568 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.69540e6 | 1.28087 | 0.640436 | − | 0.768011i | \(-0.278754\pi\) | ||||
0.640436 | + | 0.768011i | \(0.278754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.12395e6i | 1.57645i | 0.615390 | + | 0.788223i | \(0.288999\pi\) | ||||
−0.615390 | + | 0.788223i | \(0.711001\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 462644.i | − 0.331545i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3757.00 | 0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −47428.0 | −0.0328324 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 992722.i | − 0.675552i | −0.941227 | − | 0.337776i | \(-0.890325\pi\) | ||||
0.941227 | − | 0.337776i | \(-0.109675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 138816.i | − 0.0913163i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.42703e6 | 0.923112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 441068. | 0.280601 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 259348.i | − 0.162284i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 487522.i | 0.295222i | 0.989046 | + | 0.147611i | \(0.0471583\pi\) | ||||
−0.989046 | + | 0.147611i | \(0.952842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 273692. | 0.163067 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −444116. | −0.260373 | −0.130186 | − | 0.991490i | \(-0.541558\pi\) | ||||
−0.130186 | + | 0.991490i | \(0.541558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 47242.0i | − 0.0272563i | −0.999907 | − | 0.0136282i | \(-0.995662\pi\) | ||||
0.999907 | − | 0.0136282i | \(-0.00433811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 694058.i | 0.387925i | 0.981009 | + | 0.193962i | \(0.0621340\pi\) | ||||
−0.981009 | + | 0.193962i | \(0.937866\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −227232. | −0.125024 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 386380. | 0.209292 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 661640.i | 0.352871i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 240092.i | 0.124168i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.75423e6 | −0.893504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 82168.0 | 0.0412223 | 0.0206112 | − | 0.999788i | \(-0.493439\pi\) | ||||
0.0206112 | + | 0.999788i | \(0.493439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 844626.i | − 0.417401i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 727934.i | − 0.349154i | −0.984644 | − | 0.174577i | \(-0.944144\pi\) | ||||
0.984644 | − | 0.174577i | \(-0.0558558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −305292. | −0.144283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.39104e6 | −0.647819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.84574e6i | − 0.847101i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.02298e6i | 0.901919i | 0.892544 | + | 0.450959i | \(0.148918\pi\) | ||||
−0.892544 | + | 0.450959i | \(0.851082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.40858e6 | −1.93747 | −0.968736 | − | 0.248095i | \(-0.920196\pi\) | ||||
−0.968736 | + | 0.248095i | \(0.920196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −630456. | −0.273141 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 1.06965e6i | − 0.456883i | −0.973558 | − | 0.228441i | \(-0.926637\pi\) | ||||
0.973558 | − | 0.228441i | \(-0.0733630\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 147560.i | − 0.0612771i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32968.0 | 0.0135007 | 0.00675035 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675035 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.16696e6 | −0.875152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 280630.i | − 0.111781i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.64081e6i | 1.41102i | 0.708700 | + | 0.705509i | \(0.249282\pi\) | ||||
−0.708700 | + | 0.705509i | \(0.750718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.78342e6 | 0.681847 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 808852. | 0.305094 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17311e6i | 1.18090i | 0.807074 | + | 0.590450i | \(0.201050\pi\) | ||||
−0.807074 | + | 0.590450i | \(0.798950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.03201e6i | 0.373965i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.60498e6 | −0.573947 | −0.286973 | − | 0.957939i | \(-0.592649\pi\) | ||||
−0.286973 | + | 0.957939i | \(0.592649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −215812. | −0.0761664 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.98925e6i | − 0.692936i | −0.938062 | − | 0.346468i | \(-0.887381\pi\) | ||||
0.938062 | − | 0.346468i | \(-0.112619\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.70025e6i | 0.577078i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.16495e6 | 1.73058 | 0.865291 | − | 0.501270i | \(-0.167134\pi\) | ||||
0.865291 | + | 0.501270i | \(0.167134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.59658e6 | −0.858934 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 466144.i | − 0.152243i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 937586.i | 0.298562i | 0.988795 | + | 0.149281i | \(0.0476959\pi\) | ||||
−0.988795 | + | 0.149281i | \(0.952304\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −68944.0 | −0.0216802 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.63657e6 | −1.75047 | −0.875234 | − | 0.483699i | \(-0.839293\pi\) | ||||
−0.875234 | + | 0.483699i | \(0.839293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.31764e6i | 1.93773i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 508896.i | 0.152280i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.06137e6 | −1.20051 | −0.600254 | − | 0.799810i | \(-0.704934\pi\) | ||||
−0.600254 | + | 0.799810i | \(0.704934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −712164. | −0.207958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.29970e6i | − 0.663433i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 624408.i | − 0.175844i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 976108. | 0.271621 | 0.135810 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135810 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.62706e6 | −0.447403 | −0.223701 | − | 0.974658i | \(-0.571814\pi\) | ||||
−0.223701 | + | 0.974658i | \(0.571814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 6.76227e6i | − 1.83756i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.45334e6i | − 0.651161i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 188352. | 0.0494114 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.27900e6 | −1.10956 | −0.554778 | − | 0.831998i | \(-0.687197\pi\) | ||||
−0.554778 | + | 0.831998i | \(0.687197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.20195e6i | 0.820720i | 0.911924 | + | 0.410360i | \(0.134597\pi\) | ||||
−0.911924 | + | 0.410360i | \(0.865403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.21319e6i | 0.303897i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.09246e6 | −1.26115 | −0.630574 | − | 0.776129i | \(-0.717180\pi\) | ||||
−0.630574 | + | 0.776129i | \(0.717180\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.09816e6 | 0.758590 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.43551e6i | 1.31593i | 0.753050 | + | 0.657963i | \(0.228582\pi\) | ||||
−0.753050 | + | 0.657963i | \(0.771418\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 54996.0i | − 0.0130185i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.99007e6 | 0.699948 | 0.349974 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349974 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07453e6 | −0.248758 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 273816.i | − 0.0626922i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.01759e6i | 1.79578i | 0.440218 | + | 0.897891i | \(0.354901\pi\) | ||||
−0.440218 | + | 0.897891i | \(0.645099\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.14716e6 | 0.254151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.58462e6 | 0.566428 | 0.283214 | − | 0.959057i | \(-0.408599\pi\) | ||||
0.283214 | + | 0.959057i | \(0.408599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.14261e6i | − 1.33168i | −0.746094 | − | 0.665840i | \(-0.768073\pi\) | ||||
0.746094 | − | 0.665840i | \(-0.231927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.59270e6i | − 0.337942i | −0.985621 | − | 0.168971i | \(-0.945956\pi\) | ||||
0.985621 | − | 0.168971i | \(-0.0540444\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.51751e6 | −0.738419 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −813428. | −0.168953 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.02442e6i | − 0.210535i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.11799e6i | 0.627450i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −863592. | −0.171977 | −0.0859884 | − | 0.996296i | \(-0.527405\pi\) | ||||
−0.0859884 | + | 0.996296i | \(0.527405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31124e6 | 0.455493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 270568.i | − 0.0527726i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.20714e6i | − 1.56808i | −0.620707 | − | 0.784042i | \(-0.713154\pi\) | ||||
0.620707 | − | 0.784042i | \(-0.286846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27284.0 | −0.00515984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.93394e6 | 1.67240 | 0.836198 | − | 0.548428i | \(-0.184773\pi\) | ||||
0.836198 | + | 0.548428i | \(0.184773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.87782e6i | − 0.347966i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.82646e6i | − 0.513276i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.11960e6 | −0.201284 | −0.100642 | − | 0.994923i | \(-0.532090\pi\) | ||||
−0.100642 | + | 0.994923i | \(0.532090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 406876. | 0.0724215 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.68177e6i | − 0.648839i | −0.945913 | − | 0.324420i | \(-0.894831\pi\) | ||||
0.945913 | − | 0.324420i | \(-0.105169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 112846.i | − 0.0194969i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.73483e6 | 1.15221 | 0.576105 | − | 0.817375i | \(-0.304572\pi\) | ||||
0.576105 | + | 0.817375i | \(0.304572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −734204. | −0.124384 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 535984.i | − 0.0899204i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.07434e6i | 0.670395i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 254484. | 0.0414708 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 441370. | 0.0712375 | 0.0356187 | − | 0.999365i | \(-0.488660\pi\) | ||||
0.0356187 | + | 0.999365i | \(0.488660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.17300e7i | 1.87518i | 0.347744 | + | 0.937589i | \(0.386948\pi\) | ||||
−0.347744 | + | 0.937589i | \(0.613052\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.14954e7i | − 1.80301i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.67522e6 | 0.260275 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.86499e6 | 1.36440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.88015e6i | 0.744072i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 189368.i | 0.0283381i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.86667e6 | −0.276755 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 744158. | 0.109313 | 0.0546565 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546565 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.03404e6i | − 0.150500i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.24801e6i | − 0.464139i | −0.972699 | − | 0.232070i | \(-0.925450\pi\) | ||||
0.972699 | − | 0.232070i | \(-0.0745498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.45723e6 | 1.33916 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −877368. | −0.123113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.84139e6i | 0.812276i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.94446e6i | − 1.35814i | −0.734075 | − | 0.679068i | \(-0.762384\pi\) | ||||
0.734075 | − | 0.679068i | \(-0.237616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.65256e6 | −0.629741 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −342720. | −0.0459761 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3.89374e6i | − 0.517721i | −0.965915 | − | 0.258861i | \(-0.916653\pi\) | ||||
0.965915 | − | 0.258861i | \(-0.0833471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 3.48124e6i | − 0.454754i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.11951e7 | 1.44960 | 0.724801 | − | 0.688958i | \(-0.241932\pi\) | ||||
0.724801 | + | 0.688958i | \(0.241932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −844040. | −0.108336 | −0.0541680 | − | 0.998532i | \(-0.517251\pi\) | ||||
−0.0541680 | + | 0.998532i | \(0.517251\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 824600.i | − 0.104920i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 5.13378e6i | − 0.641945i | −0.947088 | − | 0.320973i | \(-0.895990\pi\) | ||||
0.947088 | − | 0.320973i | \(-0.104010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.54331e6 | −0.191318 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.95188e6 | 0.239891 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.87862e6i | − 0.228912i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.76156e6i | 1.16929i | 0.811287 | + | 0.584647i | \(0.198767\pi\) | ||||
−0.811287 | + | 0.584647i | \(0.801233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.37096e6 | −0.637916 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 380476. | 0.0448083 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 966226.i | − 0.112835i | −0.998407 | − | 0.0564173i | \(-0.982032\pi\) | ||||
0.998407 | − | 0.0564173i | \(-0.0179677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 264144.i | − 0.0303323i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.90000e6 | 0.899622 | 0.449811 | − | 0.893124i | \(-0.351491\pi\) | ||||
0.449811 | + | 0.893124i | \(0.351491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.03126e7 | 1.16461 | 0.582307 | − | 0.812969i | \(-0.302150\pi\) | ||||
0.582307 | + | 0.812969i | \(0.302150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.35594e7i | − 1.51862i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 9.70767e6i | − 1.06941i | −0.845040 | − | 0.534704i | \(-0.820423\pi\) | ||||
0.845040 | − | 0.534704i | \(-0.179577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 195672. | 0.0213789 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.85043e7 | 2.00525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.10568e7i | 1.18844i | 0.804304 | + | 0.594219i | \(0.202539\pi\) | ||||
−0.804304 | + | 0.594219i | \(0.797461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.31174e6i | 0.878980i | 0.898248 | + | 0.439490i | \(0.144841\pi\) | ||||
−0.898248 | + | 0.439490i | \(0.855159\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.15451e7 | −1.21108 | −0.605539 | − | 0.795816i | \(-0.707042\pi\) | ||||
−0.605539 | + | 0.795816i | \(0.707042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.10345e6 | 0.218878 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 5.83135e6i | − 0.601934i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 160128.i | 0.0162667i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.20546e6 | −0.423825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.20262e6 | −0.820123 | −0.410062 | − | 0.912058i | \(-0.634493\pi\) | ||||
−0.410062 | + | 0.912058i | \(0.634493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.85741e6i | 0.184246i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.47780e6i | 0.827818i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.08955e7 | 1.05559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.39695e6 | −0.518804 | −0.259402 | − | 0.965769i | \(-0.583525\pi\) | ||||
−0.259402 | + | 0.965769i | \(0.583525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.33896e7i | 1.27715i | 0.769561 | + | 0.638573i | \(0.220475\pi\) | ||||
−0.769561 | + | 0.638573i | \(0.779525\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.48254e6i | 0.608814i | 0.952542 | + | 0.304407i | \(0.0984582\pi\) | ||||
−0.952542 | + | 0.304407i | \(0.901542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.34125e6 | −0.497773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.19784e6 | 0.110776 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.44907e7i | − 1.32986i | −0.746904 | − | 0.664931i | \(-0.768461\pi\) | ||||
0.746904 | − | 0.664931i | \(-0.231539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.83024e6i | − 0.255805i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.59080e6 | −0.591187 | −0.295593 | − | 0.955314i | \(-0.595517\pi\) | ||||
−0.295593 | + | 0.955314i | \(0.595517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.25233e6 | −0.289528 | −0.144764 | − | 0.989466i | \(-0.546242\pi\) | ||||
−0.144764 | + | 0.989466i | \(0.546242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.55652e6i | 0.137522i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.44320e6i | − 0.299673i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 842988. | 0.0728209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.69808e6 | −0.488565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 3.86655e6i | − 0.329068i | −0.986371 | − | 0.164534i | \(-0.947388\pi\) | ||||
0.986371 | − | 0.164534i | \(-0.0526120\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.23856e6i | 0.103859i | 0.998651 | + | 0.0519297i | \(0.0165372\pi\) | ||||
−0.998651 | + | 0.0519297i | \(0.983463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.47027e6 | 0.122383 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.98392e6 | −0.163930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.31376e7i | 1.07762i | 0.842427 | + | 0.538810i | \(0.181126\pi\) | ||||
−0.842427 | + | 0.538810i | \(0.818874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 533892.i | 0.0431580i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.53208e6 | −0.684711 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.23841e7 | −0.986664 | −0.493332 | − | 0.869841i | \(-0.664221\pi\) | ||||
−0.493332 | + | 0.869841i | \(0.664221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.13379e6i | 0.168779i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 8.87978e6i | − 0.692341i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.92063e6 | 0.148679 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.78952e6 | −0.752430 | −0.376215 | − | 0.926532i | \(-0.622775\pi\) | ||||
−0.376215 | + | 0.926532i | \(0.622775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.96490e6i | 0.149952i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.03979e6i | 0.604917i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.22257e7 | −0.913397 | −0.456699 | − | 0.889622i | \(-0.650968\pi\) | ||||
−0.456699 | + | 0.889622i | \(0.650968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.25176e7 | −1.67051 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.10781e7i | − 1.55277i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 985392.i | 0.0715832i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.35053e7 | 0.974276 | 0.487138 | − | 0.873325i | \(-0.338041\pi\) | ||||
0.487138 | + | 0.873325i | \(0.338041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.48445e6 | −0.607835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 112156.i | 0.00797952i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17271e7i | 0.822916i | 0.911429 | + | 0.411458i | \(0.134980\pi\) | ||||
−0.911429 | + | 0.411458i | \(0.865020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.29511e7 | 0.902585 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.46566e6 | 0.585959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.16512e7i | 0.800960i | 0.916305 | + | 0.400480i | \(0.131157\pi\) | ||||
−0.916305 | + | 0.400480i | \(0.868843\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.16970e6i | 0.554035i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26808e7 | 0.854155 | 0.427077 | − | 0.904215i | \(-0.359543\pi\) | ||||
0.427077 | + | 0.904215i | \(0.359543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 727248. | 0.0486561 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 197370.i | 0.0131162i | 0.999978 | + | 0.00655812i | \(0.00208753\pi\) | ||||
−0.999978 | + | 0.00655812i | \(0.997912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.52420e6i | 0.493354i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.19778e7 | −0.780139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.33282e7 | −0.862326 | −0.431163 | − | 0.902274i | \(-0.641897\pi\) | ||||
−0.431163 | + | 0.902274i | \(0.641897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.93584e6i | 0.252959i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.86122e6i | − 0.244898i | −0.992475 | − | 0.122449i | \(-0.960925\pi\) | ||||
0.992475 | − | 0.122449i | \(-0.0390748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −628416. | −0.0395952 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.31756e6 | −0.520636 | −0.260318 | − | 0.965523i | \(-0.583827\pi\) | ||||
−0.260318 | + | 0.965523i | \(0.583827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 7.44285e6i | − 0.462837i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.42582e7i | 1.48891i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.76358e7 | −1.68522 | −0.842609 | − | 0.538527i | \(-0.818981\pi\) | ||||
−0.842609 | + | 0.538527i | \(0.818981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.94382e6 | 0.117766 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.78842e7i | − 1.07652i | −0.842780 | − | 0.538259i | \(-0.819082\pi\) | ||||
0.842780 | − | 0.538259i | \(-0.180918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 438216.i | − 0.0260397i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.14887e6 | −0.244955 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.56467e6 | −0.385111 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.52119e6i | 0.0886706i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.15691e7i | 1.24135i | 0.784067 | + | 0.620676i | \(0.213142\pi\) | ||||
−0.784067 | + | 0.620676i | \(0.786858\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −309540. | −0.0177021 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.46405e6 | 0.537819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.58788e7i | 1.46137i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.03060e7i | − 0.574705i | −0.957825 | − | 0.287353i | \(-0.907225\pi\) | ||||
0.957825 | − | 0.287353i | \(-0.0927752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.36699e7 | −1.86584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.24789e7 | 1.23792 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.70525e6i | 0.0933251i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.04743e6i | − 0.110669i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −372378. | −0.0200038 | −0.0100019 | − | 0.999950i | \(-0.503184\pi\) | ||||
−0.0100019 | + | 0.999950i | \(0.503184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.94795e7 | −1.03998 | −0.519990 | − | 0.854173i | \(-0.674064\pi\) | ||||
−0.519990 | + | 0.854173i | \(0.674064\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.29551e6i | − 0.121802i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.95538e6i | − 0.207316i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.69097e6 | 0.504844 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −469318. | −0.0243002 | −0.0121501 | − | 0.999926i | \(-0.503868\pi\) | ||||
−0.0121501 | + | 0.999926i | \(0.503868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.78622e7i | − 0.919253i | −0.888112 | − | 0.459626i | \(-0.847983\pi\) | ||||
0.888112 | − | 0.459626i | \(-0.152017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.42560e6i | 0.479231i | 0.970868 | + | 0.239616i | \(0.0770215\pi\) | ||||
−0.970868 | + | 0.239616i | \(0.922979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.48622e7 | 0.751098 | 0.375549 | − | 0.926803i | \(-0.377454\pi\) | ||||
0.375549 | + | 0.926803i | \(0.377454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.99352e6 | 0.250844 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.54260e7i | − 0.770265i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.31224e6i | 0.459452i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.71170e6 | 0.231085 | 0.115543 | − | 0.993303i | \(-0.463139\pi\) | ||||
0.115543 | + | 0.993303i | \(0.463139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80211e7 | −0.878599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.39080e6i | 0.164336i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.69953e6i | 0.416665i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.24791e6 | −0.202258 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.71119e6 | −0.365004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.62685e7i | − 0.765552i | −0.923841 | − | 0.382776i | \(-0.874968\pi\) | ||||
0.923841 | − | 0.382776i | \(-0.125032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.92667e7i | − 1.36120i | −0.732656 | − | 0.680600i | \(-0.761719\pi\) | ||||
0.732656 | − | 0.680600i | \(-0.238281\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.31062e7 | 1.53083 | 0.765413 | − | 0.643539i | \(-0.222535\pi\) | ||||
0.765413 | + | 0.643539i | \(0.222535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 925288. | 0.0425372 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.58052e7i | 0.722391i | 0.932490 | + | 0.361196i | \(0.117631\pi\) | ||||
−0.932490 | + | 0.361196i | \(0.882369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7514.00i | 0 0.000339487i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.35671e7 | 0.609449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.71040e7 | 1.65720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.66765e6i | 0.251691i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 4.26834e7i | − 1.87396i | −0.349384 | − | 0.936980i | \(-0.613609\pi\) | ||||
0.349384 | − | 0.936980i | \(-0.386391\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.98544e6 | 0.0866733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.57397e6 | −0.155135 | −0.0775677 | − | 0.996987i | \(-0.524715\pi\) | ||||
−0.0775677 | + | 0.996987i | \(0.524715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.68471e7i | 0.727149i | 0.931565 | + | 0.363574i | \(0.118444\pi\) | ||||
−0.931565 | + | 0.363574i | \(0.881556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 8.36792e6i | − 0.357115i | −0.983929 | − | 0.178558i | \(-0.942857\pi\) | ||||
0.983929 | − | 0.178558i | \(-0.0571431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.69017e6 | 0.283911 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.08546e6 | −0.341201 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57315e7i | 0.660147i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.85406e6i | 0.118435i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.52435e7 | 0.629050 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.55247e7 | 0.637107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 882136.i | 0.0360011i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 2.57230e7i | − 1.03825i | −0.854697 | − | 0.519127i | \(-0.826257\pi\) | ||||
0.854697 | − | 0.519127i | \(-0.173743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.09921e7 | −1.24406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.42108e7 | 1.36574 | 0.682869 | − | 0.730540i | \(-0.260732\pi\) | ||||
0.682869 | + | 0.730540i | \(0.260732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.53341e6i | − 0.179990i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.44505e7i | 0.567490i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.44034e6 | −0.0953149 | −0.0476575 | − | 0.998864i | \(-0.515176\pi\) | ||||
−0.0476575 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −975044. | −0.0378770 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.98146e7i | 1.15192i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.27062e7i | − 1.25006i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.34361e7 | −0.510781 | −0.255390 | − | 0.966838i | \(-0.582204\pi\) | ||||
−0.255390 | + | 0.966838i | \(0.582204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.20743e6 | −0.272525 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 888232.i | − 0.0334058i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.96529e6i | 0.296383i | 0.988959 | + | 0.148191i | \(0.0473451\pi\) | ||||
−0.988959 | + | 0.148191i | \(0.952655\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 94484.0 | 0.00349699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.08025e6 | 0.334290 | 0.167145 | − | 0.985932i | \(-0.446545\pi\) | ||||
0.167145 | + | 0.985932i | \(0.446545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.62821e7i | − 0.596253i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3.21769e7i | − 1.16592i | −0.812500 | − | 0.582961i | \(-0.801894\pi\) | ||||
0.812500 | − | 0.582961i | \(-0.198106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.74467e6 | 0.279150 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.38812e6 | −0.0497708 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 5.33807e6i | − 0.190394i | −0.995458 | − | 0.0951968i | \(-0.969652\pi\) | ||||
0.995458 | − | 0.0951968i | \(-0.0303480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 454464.i | − 0.0160406i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.20771e7 | 0.775167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.46864e7 | 2.25946 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 4.61724e7i | − 1.60442i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.71522e7i | 1.27767i | 0.769345 | + | 0.638834i | \(0.220583\pi\) | ||||
−0.769345 | + | 0.638834i | \(0.779417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.32328e6 | −0.0452733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.09865e7 | −0.373949 | −0.186975 | − | 0.982365i | \(-0.559868\pi\) | ||||
−0.186975 | + | 0.982365i | \(0.559868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.93566e7i | 0.655463i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 2.65054e7i | − 0.888379i | −0.895933 | − | 0.444190i | \(-0.853492\pi\) | ||||
0.895933 | − | 0.444190i | \(-0.146508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.35438e7 | −0.451630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.86910e7 | 0.951860 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.75726e7i | 1.57027i | 0.619327 | + | 0.785133i | \(0.287406\pi\) | ||||
−0.619327 | + | 0.785133i | \(0.712594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.50846e6i | − 0.114637i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55227e7 | 0.504636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.22149e7 | 1.04201 | 0.521006 | − | 0.853553i | \(-0.325557\pi\) | ||||
0.521006 | + | 0.853553i | \(0.325557\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 164336.i | 0.00528883i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.87072e7i | 1.23326i | 0.787253 | + | 0.616630i | \(0.211502\pi\) | ||||
−0.787253 | + | 0.616630i | \(0.788498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.40678e6 | 0.108002 |
(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 | 200.6.c.d.49.2 | 2 | ||
4.3 | odd | 2 | 400.6.c.k.49.1 | 2 | |||
5.2 | odd | 4 | 200.6.a.b.1.1 | 1 | |||
5.3 | odd | 4 | 40.6.a.c.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 200.6.c.d.49.1 | 2 | ||
15.8 | even | 4 | 360.6.a.f.1.1 | 1 | |||
20.3 | even | 4 | 80.6.a.d.1.1 | 1 | |||
20.7 | even | 4 | 400.6.a.h.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.k.49.2 | 2 | |||
40.3 | even | 4 | 320.6.a.h.1.1 | 1 | |||
40.13 | odd | 4 | 320.6.a.i.1.1 | 1 | |||
60.23 | odd | 4 | 720.6.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.c.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
80.6.a.d.1.1 | 1 | 20.3 | even | 4 | |||
200.6.a.b.1.1 | 1 | 5.2 | odd | 4 | |||
200.6.c.d.49.1 | 2 | 5.4 | even | 2 | inner | ||
200.6.c.d.49.2 | 2 | 1.1 | even | 1 | trivial | ||
320.6.a.h.1.1 | 1 | 40.3 | even | 4 | |||
320.6.a.i.1.1 | 1 | 40.13 | odd | 4 | |||
360.6.a.f.1.1 | 1 | 15.8 | even | 4 | |||
400.6.a.h.1.1 | 1 | 20.7 | even | 4 | |||
400.6.c.k.49.1 | 2 | 4.3 | odd | 2 | |||
400.6.c.k.49.2 | 2 | 20.19 | odd | 2 | |||
720.6.a.t.1.1 | 1 | 60.23 | odd | 4 |