Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,6,Mod(1,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.a (trivial) |
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: | yes |
Analytic conductor: | \(144.345437832\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 900.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 244.000 | 1.88211 | 0.941054 | − | 0.338255i | \(-0.109837\pi\) | ||||
0.941054 | + | 0.338255i | \(0.109837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 144.000 | 0.358823 | 0.179412 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179412 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.0000 | −0.0820562 | −0.0410281 | − | 0.999158i | \(-0.513063\pi\) | ||||
−0.0410281 | + | 0.999158i | \(0.513063\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1914.00 | −1.60627 | −0.803137 | − | 0.595794i | \(-0.796837\pi\) | ||||
−0.803137 | + | 0.595794i | \(0.796837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 140.000 | 0.0889701 | 0.0444850 | − | 0.999010i | \(-0.485835\pi\) | ||||
0.0444850 | + | 0.999010i | \(0.485835\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −624.000 | −0.245960 | −0.122980 | − | 0.992409i | \(-0.539245\pi\) | ||||
−0.122980 | + | 0.992409i | \(0.539245\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3126.00 | 0.690230 | 0.345115 | − | 0.938560i | \(-0.387840\pi\) | ||||
0.345115 | + | 0.938560i | \(0.387840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5176.00 | −0.967364 | −0.483682 | − | 0.875244i | \(-0.660701\pi\) | ||||
−0.483682 | + | 0.875244i | \(0.660701\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15698.0 | −1.88512 | −0.942562 | − | 0.334031i | \(-0.891591\pi\) | ||||
−0.942562 | + | 0.334031i | \(0.891591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12570.0 | −1.16782 | −0.583910 | − | 0.811819i | \(-0.698478\pi\) | ||||
−0.583910 | + | 0.811819i | \(0.698478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11516.0 | −0.949796 | −0.474898 | − | 0.880041i | \(-0.657515\pi\) | ||||
−0.474898 | + | 0.880041i | \(0.657515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −26736.0 | −1.76544 | −0.882718 | − | 0.469904i | \(-0.844289\pi\) | ||||
−0.882718 | + | 0.469904i | \(0.844289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 42729.0 | 2.54233 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −19158.0 | −0.936829 | −0.468415 | − | 0.883509i | \(-0.655175\pi\) | ||||
−0.468415 | + | 0.883509i | \(0.655175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −27984.0 | −1.04660 | −0.523299 | − | 0.852149i | \(-0.675299\pi\) | ||||
−0.523299 | + | 0.852149i | \(0.675299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22022.0 | 0.757761 | 0.378880 | − | 0.925446i | \(-0.376309\pi\) | ||||
0.378880 | + | 0.925446i | \(0.376309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12676.0 | 0.344981 | 0.172491 | − | 0.985011i | \(-0.444819\pi\) | ||||
0.172491 | + | 0.985011i | \(0.444819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59520.0 | 1.40125 | 0.700627 | − | 0.713527i | \(-0.252904\pi\) | ||||
0.700627 | + | 0.713527i | \(0.252904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 67102.0 | 1.47377 | 0.736883 | − | 0.676021i | \(-0.236297\pi\) | ||||
0.736883 | + | 0.676021i | \(0.236297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 35136.0 | 0.675345 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11048.0 | 0.199166 | 0.0995832 | − | 0.995029i | \(-0.468249\pi\) | ||||
0.0995832 | + | 0.995029i | \(0.468249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −115284. | −1.83685 | −0.918425 | − | 0.395595i | \(-0.870539\pi\) | ||||
−0.918425 | + | 0.395595i | \(0.870539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −73650.0 | −0.985593 | −0.492797 | − | 0.870145i | \(-0.664025\pi\) | ||||
−0.492797 | + | 0.870145i | \(0.664025\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12200.0 | −0.154439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −35522.0 | −0.383326 | −0.191663 | − | 0.981461i | \(-0.561388\pi\) | ||||
−0.191663 | + | 0.981461i | \(0.561388\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112062. | 1.09309 | 0.546544 | − | 0.837431i | \(-0.315943\pi\) | ||||
0.546544 | + | 0.837431i | \(0.315943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 106516. | 0.989286 | 0.494643 | − | 0.869096i | \(-0.335299\pi\) | ||||
0.494643 | + | 0.869096i | \(0.335299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −29292.0 | −0.247337 | −0.123669 | − | 0.992324i | \(-0.539466\pi\) | ||||
−0.123669 | + | 0.992324i | \(0.539466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 125318. | 1.01029 | 0.505146 | − | 0.863034i | \(-0.331439\pi\) | ||||
0.505146 | + | 0.863034i | \(0.331439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 166638. | 1.22766 | 0.613830 | − | 0.789438i | \(-0.289628\pi\) | ||||
0.613830 | + | 0.789438i | \(0.289628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −467016. | −3.02318 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140315. | −0.871246 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 201724. | 1.10981 | 0.554905 | − | 0.831914i | \(-0.312755\pi\) | ||||
0.554905 | + | 0.831914i | \(0.312755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −131472. | −0.669353 | −0.334676 | − | 0.942333i | \(-0.608627\pi\) | ||||
−0.334676 | + | 0.942333i | \(0.608627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34160.0 | 0.167451 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −102042. | −0.464491 | −0.232246 | − | 0.972657i | \(-0.574607\pi\) | ||||
−0.232246 | + | 0.972657i | \(0.574607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −243604. | −1.06942 | −0.534709 | − | 0.845036i | \(-0.679579\pi\) | ||||
−0.534709 | + | 0.845036i | \(0.679579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7200.00 | −0.0294437 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 309462. | 1.14194 | 0.570968 | − | 0.820972i | \(-0.306568\pi\) | ||||
0.570968 | + | 0.820972i | \(0.306568\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −147160. | −0.525227 | −0.262614 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262614 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −268082. | −0.867998 | −0.433999 | − | 0.900913i | \(-0.642898\pi\) | ||||
−0.433999 | + | 0.900913i | \(0.642898\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −152256. | −0.462924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 276580. | 0.815364 | 0.407682 | − | 0.913124i | \(-0.366337\pi\) | ||||
0.407682 | + | 0.913124i | \(0.366337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −592272. | −1.64335 | −0.821675 | − | 0.569956i | \(-0.806960\pi\) | ||||
−0.821675 | + | 0.569956i | \(0.806960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −368793. | −0.993267 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 29154.0 | 0.0740599 | 0.0370299 | − | 0.999314i | \(-0.488210\pi\) | ||||
0.0370299 | + | 0.999314i | \(0.488210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −131784. | −0.307419 | −0.153709 | − | 0.988116i | \(-0.549122\pi\) | ||||
−0.153709 | + | 0.988116i | \(0.549122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −297730. | −0.675501 | −0.337751 | − | 0.941236i | \(-0.609666\pi\) | ||||
−0.337751 | + | 0.941236i | \(0.609666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −275616. | −0.576369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −851784. | −1.68945 | −0.844726 | − | 0.535198i | \(-0.820237\pi\) | ||||
−0.844726 | + | 0.535198i | \(0.820237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −292394. | −0.565035 | −0.282517 | − | 0.959262i | \(-0.591169\pi\) | ||||
−0.282517 | + | 0.959262i | \(0.591169\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −869526. | −1.59631 | −0.798155 | − | 0.602453i | \(-0.794190\pi\) | ||||
−0.798155 | + | 0.602453i | \(0.794190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −143992. | −0.257754 | −0.128877 | − | 0.991661i | \(-0.541137\pi\) | ||||
−0.128877 | + | 0.991661i | \(0.541137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 762744. | 1.29909 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20160.0 | 0.0319246 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 836420. | 1.29336 | 0.646678 | − | 0.762763i | \(-0.276158\pi\) | ||||
0.646678 | + | 0.762763i | \(0.276158\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.26294e6 | −1.82068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 95700.0 | 0.131805 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.22090e6 | −1.64406 | −0.822031 | − | 0.569443i | \(-0.807159\pi\) | ||||
−0.822031 | + | 0.569443i | \(0.807159\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −173580. | −0.223581 | −0.111791 | − | 0.993732i | \(-0.535659\pi\) | ||||
−0.111791 | + | 0.993732i | \(0.535659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 120806. | 0.152230 | 0.0761149 | − | 0.997099i | \(-0.475748\pi\) | ||||
0.0761149 | + | 0.997099i | \(0.475748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 592590. | 0.715096 | 0.357548 | − | 0.933895i | \(-0.383613\pi\) | ||||
0.357548 | + | 0.933895i | \(0.383613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −706008. | −0.799493 | −0.399747 | − | 0.916626i | \(-0.630902\pi\) | ||||
−0.399747 | + | 0.916626i | \(0.630902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.56154e6 | 1.73185 | 0.865924 | − | 0.500175i | \(-0.166731\pi\) | ||||
0.865924 | + | 0.500175i | \(0.166731\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7000.00 | −0.00730055 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.48471e6 | 1.48750 | 0.743752 | − | 0.668456i | \(-0.233045\pi\) | ||||
0.743752 | + | 0.668456i | \(0.233045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −89856.0 | −0.0882563 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 624558. | 0.589848 | 0.294924 | − | 0.955521i | \(-0.404706\pi\) | ||||
0.294924 | + | 0.955521i | \(0.404706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.83031e6 | −3.54801 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 778896. | 0.694369 | 0.347184 | − | 0.937797i | \(-0.387138\pi\) | ||||
0.347184 | + | 0.937797i | \(0.387138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11574.0 | 0.00975220 | 0.00487610 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487610 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 118064. | 0.0976550 | 0.0488275 | − | 0.998807i | \(-0.484452\pi\) | ||||
0.0488275 | + | 0.998807i | \(0.484452\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −659282. | −0.516264 | −0.258132 | − | 0.966110i | \(-0.583107\pi\) | ||||
−0.258132 | + | 0.966110i | \(0.583107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.49057e6 | 1.12613 | 0.563064 | − | 0.826413i | \(-0.309622\pi\) | ||||
0.563064 | + | 0.826413i | \(0.309622\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.13129e6 | 0.839670 | 0.419835 | − | 0.907600i | \(-0.362088\pi\) | ||||
0.419835 | + | 0.907600i | \(0.362088\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.06708e6 | −2.19796 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.24354e6 | 1.58012 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 896298. | 0.609935 | 0.304967 | − | 0.952363i | \(-0.401354\pi\) | ||||
0.304967 | + | 0.952363i | \(0.401354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31200.0 | 0.0201826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.80990e6 | −1.78762 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.38641e6 | 0.839550 | 0.419775 | − | 0.907628i | \(-0.362109\pi\) | ||||
0.419775 | + | 0.907628i | \(0.362109\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.19238e6 | −1.87160 | −0.935802 | − | 0.352525i | \(-0.885323\pi\) | ||||
−0.935802 | + | 0.352525i | \(0.885323\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.51683e6 | −1.45209 | −0.726045 | − | 0.687647i | \(-0.758644\pi\) | ||||
−0.726045 | + | 0.687647i | \(0.758644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.21897e6 | −1.24024 | −0.620118 | − | 0.784509i | \(-0.712915\pi\) | ||||
−0.620118 | + | 0.784509i | \(0.712915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 450144. | 0.247671 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −267960. | −0.142910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.52358e6 | −3.32274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27148.0 | −0.0136197 | −0.00680985 | − | 0.999977i | \(-0.502168\pi\) | ||||
−0.00680985 | + | 0.999977i | \(0.502168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.19670e6 | −1.05365 | −0.526824 | − | 0.849974i | \(-0.676617\pi\) | ||||
−0.526824 | + | 0.849974i | \(0.676617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −745344. | −0.347113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.32497e6 | 2.90284 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −989652. | −0.441224 | −0.220612 | − | 0.975362i | \(-0.570805\pi\) | ||||
−0.220612 | + | 0.975362i | \(0.570805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.05055e6 | −1.34065 | −0.670325 | − | 0.742068i | \(-0.733845\pi\) | ||||
−0.670325 | + | 0.742068i | \(0.733845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −339642. | −0.145072 | −0.0725362 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725362 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.20678e6 | 0.903696 | 0.451848 | − | 0.892095i | \(-0.350765\pi\) | ||||
0.451848 | + | 0.892095i | \(0.350765\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.45650e6 | −0.992084 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.07132e6 | −0.802752 | −0.401376 | − | 0.915913i | \(-0.631468\pi\) | ||||
−0.401376 | + | 0.915913i | \(0.631468\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.67455e6 | −1.76321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.94997e6 | 0.725699 | 0.362850 | − | 0.931848i | \(-0.381804\pi\) | ||||
0.362850 | + | 0.931848i | \(0.381804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −156300. | −0.0566377 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85003e6 | 1.37678 | 0.688392 | − | 0.725339i | \(-0.258317\pi\) | ||||
0.688392 | + | 0.725339i | \(0.258317\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −67152.0 | −0.0233917 | −0.0116959 | − | 0.999932i | \(-0.503723\pi\) | ||||
−0.0116959 | + | 0.999932i | \(0.503723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.32331e6 | −1.44858 | −0.724289 | − | 0.689496i | \(-0.757832\pi\) | ||||
−0.724289 | + | 0.689496i | \(0.757832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19434e6 | 0.395080 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −118298. | −0.0376705 | −0.0188352 | − | 0.999823i | \(-0.505996\pi\) | ||||
−0.0188352 | + | 0.999823i | \(0.505996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.13901e6 | 0.974838 | 0.487419 | − | 0.873168i | \(-0.337938\pi\) | ||||
0.487419 | + | 0.873168i | \(0.337938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 258800. | 0.0793783 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26051e6 | −0.676427 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −452614. | −0.133789 | −0.0668944 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668944 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.82810e6 | −1.96981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.73579e6 | −1.03956 | −0.519778 | − | 0.854302i | \(-0.673985\pi\) | ||||
−0.519778 | + | 0.854302i | \(0.673985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.87465e6 | −0.515484 | −0.257742 | − | 0.966214i | \(-0.582978\pi\) | ||||
−0.257742 | + | 0.966214i | \(0.582978\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.37337e6 | 1.42619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.74019e6 | 1.22914 | 0.614572 | − | 0.788861i | \(-0.289329\pi\) | ||||
0.614572 | + | 0.788861i | \(0.289329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.35377e6 | 1.11595 | 0.557976 | − | 0.829857i | \(-0.311578\pi\) | ||||
0.557976 | + | 0.829857i | \(0.311578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −87360.0 | −0.0218831 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.04929e6 | 0.259856 | 0.129928 | − | 0.991523i | \(-0.458525\pi\) | ||||
0.129928 | + | 0.991523i | \(0.458525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00788e6 | 1.45449 | 0.727247 | − | 0.686375i | \(-0.240799\pi\) | ||||
0.727247 | + | 0.686375i | \(0.240799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.37222e6 | −0.321223 | −0.160612 | − | 0.987018i | \(-0.551347\pi\) | ||||
−0.160612 | + | 0.987018i | \(0.551347\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81008e6 | −0.419041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 389830. | 0.0873142 | 0.0436571 | − | 0.999047i | \(-0.486099\pi\) | ||||
0.0436571 | + | 0.999047i | \(0.486099\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.15137e6 | 0.690633 | 0.345317 | − | 0.938486i | \(-0.387771\pi\) | ||||
0.345317 | + | 0.938486i | \(0.387771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.66939e6 | −1.01230 | −0.506148 | − | 0.862447i | \(-0.668931\pi\) | ||||
−0.506148 | + | 0.862447i | \(0.668931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.92445e6 | −1.04488 | −0.522439 | − | 0.852677i | \(-0.674978\pi\) | ||||
−0.522439 | + | 0.852677i | \(0.674978\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.09294e6 | 0.649292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.65830e6 | −0.340809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.03030e6 | 0.802598 | 0.401299 | − | 0.915947i | \(-0.368559\pi\) | ||||
0.401299 | + | 0.915947i | \(0.368559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 784900. | 0.154686 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.14213e6 | −0.791410 | −0.395705 | − | 0.918378i | \(-0.629500\pi\) | ||||
−0.395705 | + | 0.918378i | \(0.629500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.22854e6 | 0.229977 | 0.114988 | − | 0.993367i | \(-0.463317\pi\) | ||||
0.114988 | + | 0.993367i | \(0.463317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.98316e6 | −1.10870 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.45229e7 | 2.63731 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.64756e6 | 0.655770 | 0.327885 | − | 0.944718i | \(-0.393664\pi\) | ||||
0.327885 | + | 0.944718i | \(0.393664\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.98454e6 | −0.349735 | −0.174867 | − | 0.984592i | \(-0.555950\pi\) | ||||
−0.174867 | + | 0.984592i | \(0.555950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.75852e6 | 0.985182 | 0.492591 | − | 0.870261i | \(-0.336050\pi\) | ||||
0.492591 | + | 0.870261i | \(0.336050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63729e7 | 2.77379 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.84998e6 | −0.633480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.84008e6 | 1.10399 | 0.551997 | − | 0.833846i | \(-0.313866\pi\) | ||||
0.551997 | + | 0.833846i | \(0.313866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.26991e6 | −1.16218 | −0.581092 | − | 0.813838i | \(-0.697374\pi\) | ||||
−0.581092 | + | 0.813838i | \(0.697374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.90686e6 | 1.55385 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.04697e6 | −0.939504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 628500. | 0.0958269 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.15298e6 | 0.912249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.88876e6 | −0.277450 | −0.138725 | − | 0.990331i | \(-0.544300\pi\) | ||||
−0.138725 | + | 0.990331i | \(0.544300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.64867e6 | 0.378494 | 0.189247 | − | 0.981929i | \(-0.439395\pi\) | ||||
0.189247 | + | 0.981929i | \(0.439395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 437640. | 0.0614098 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.69571e6 | 0.374853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.82704e6 | −0.386095 | −0.193047 | − | 0.981189i | \(-0.561837\pi\) | ||||
−0.193047 | + | 0.981189i | \(0.561837\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 575800. | 0.0779367 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.22050e6 | 1.22598 | 0.612990 | − | 0.790091i | \(-0.289967\pi\) | ||||
0.612990 | + | 0.790091i | \(0.289967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.96705e6 | 0.384189 | 0.192094 | − | 0.981376i | \(-0.438472\pi\) | ||||
0.192094 | + | 0.981376i | \(0.438472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.56746e6 | 0.201190 | 0.100595 | − | 0.994927i | \(-0.467925\pi\) | ||||
0.100595 | + | 0.994927i | \(0.467925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.07923e7 | 1.34951 | 0.674754 | − | 0.738043i | \(-0.264250\pi\) | ||||
0.674754 | + | 0.738043i | \(0.264250\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.81293e7 | −3.45715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.75875e6 | −0.336156 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.34368e7 | −1.60954 | −0.804770 | − | 0.593586i | \(-0.797712\pi\) | ||||
−0.804770 | + | 0.593586i | \(0.797712\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −724640. | −0.0860665 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.53507e6 | −0.412821 | −0.206410 | − | 0.978465i | \(-0.566178\pi\) | ||||
−0.206410 | + | 0.978465i | \(0.566178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.56850e6 | 0.975749 | 0.487874 | − | 0.872914i | \(-0.337772\pi\) | ||||
0.487874 | + | 0.872914i | \(0.337772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.15733e7 | −1.30699 | −0.653493 | − | 0.756932i | \(-0.726697\pi\) | ||||
−0.653493 | + | 0.756932i | \(0.726697\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.76651e6 | −0.414923 | −0.207461 | − | 0.978243i | \(-0.566520\pi\) | ||||
−0.207461 | + | 0.978243i | \(0.566520\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33680e6 | 0.144865 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.55106e6 | −0.596657 | −0.298328 | − | 0.954463i | \(-0.596429\pi\) | ||||
−0.298328 | + | 0.954463i | \(0.596429\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.66393e6 | 0.916225 | 0.458113 | − | 0.888894i | \(-0.348526\pi\) | ||||
0.458113 | + | 0.888894i | \(0.348526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.11780e6 | −0.641754 | −0.320877 | − | 0.947121i | \(-0.603978\pi\) | ||||
−0.320877 | + | 0.947121i | \(0.603978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.79706e7 | −1.85499 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.00460e7 | 3.02803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.11315e6 | 0.411246 | 0.205623 | − | 0.978631i | \(-0.434078\pi\) | ||||
0.205623 | + | 0.978631i | \(0.434078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.13645e6 | −0.208614 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −64674.0 | −0.00621705 | −0.00310853 | − | 0.999995i | \(-0.500989\pi\) | ||||
−0.00310853 | + | 0.999995i | \(0.500989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.42852e6 | 0.231640 | 0.115820 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115820 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.43777e6 | 0.698525 | 0.349262 | − | 0.937025i | \(-0.386432\pi\) | ||||
0.349262 | + | 0.937025i | \(0.386432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.02970e6 | −0.375544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.99762e7 | 1.83329 | 0.916644 | − | 0.399706i | \(-0.130888\pi\) | ||||
0.916644 | + | 0.399706i | \(0.130888\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 742752. | 0.0666239 | 0.0333120 | − | 0.999445i | \(-0.489395\pi\) | ||||
0.0333120 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.20838e7 | −1.07573 | −0.537863 | − | 0.843032i | \(-0.680768\pi\) | ||||
−0.537863 | + | 0.843032i | \(0.680768\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.95062e6 | −0.169769 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.17117e6 | 0.271902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.14487e6 | 0.608074 | 0.304037 | − | 0.952660i | \(-0.401665\pi\) | ||||
0.304037 | + | 0.952660i | \(0.401665\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.03255e7 | 1.70440 | 0.852198 | − | 0.523219i | \(-0.175269\pi\) | ||||
0.852198 | + | 0.523219i | \(0.175269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.66737e6 | −0.721461 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.65416e6 | −0.545810 | −0.272905 | − | 0.962041i | \(-0.587984\pi\) | ||||
−0.272905 | + | 0.962041i | \(0.587984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 957900. | 0.0768727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.11430e7 | −0.887784 | −0.443892 | − | 0.896080i | \(-0.646403\pi\) | ||||
−0.443892 | + | 0.896080i | \(0.646403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.40590e7 | 1.87584 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.47407e7 | −1.13299 | −0.566493 | − | 0.824067i | \(-0.691700\pi\) | ||||
−0.566493 | + | 0.824067i | \(0.691700\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.19772e6 | −0.167720 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.73431e7 | 2.05731 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.01119e7 | 1.50258 | 0.751290 | − | 0.659973i | \(-0.229432\pi\) | ||||
0.751290 | + | 0.659973i | \(0.229432\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.22982e6 | 0.237933 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.17933e6 | −0.662199 | −0.331100 | − | 0.943596i | \(-0.607420\pi\) | ||||
−0.331100 | + | 0.943596i | \(0.607420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.59899e7 | 1.86194 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.72524e7 | 1.21064 | 0.605319 | − | 0.795983i | \(-0.293046\pi\) | ||||
0.605319 | + | 0.795983i | \(0.293046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.20416e7 | 1.52563 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.79936e7 | −1.92442 | −0.962209 | − | 0.272314i | \(-0.912211\pi\) | ||||
−0.962209 | + | 0.272314i | \(0.912211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.82534e6 | 0.123787 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.96778e6 | −0.469335 | −0.234668 | − | 0.972076i | \(-0.575400\pi\) | ||||
−0.234668 | + | 0.972076i | \(0.575400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.35720e7 | 0.901929 | 0.450965 | − | 0.892542i | \(-0.351080\pi\) | ||||
0.450965 | + | 0.892542i | \(0.351080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.14725e6 | −0.465516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.17647e6 | 0.529013 | 0.264506 | − | 0.964384i | \(-0.414791\pi\) | ||||
0.264506 | + | 0.964384i | \(0.414791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.60741e6 | 0.545925 | 0.272962 | − | 0.962025i | \(-0.411997\pi\) | ||||
0.272962 | + | 0.962025i | \(0.411997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.28596e7 | 1.43089 | 0.715446 | − | 0.698668i | \(-0.246223\pi\) | ||||
0.715446 | + | 0.698668i | \(0.246223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.05776e7 | 1.90148 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.39920e6 | 0.0858799 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.54790e7 | 0.943905 | 0.471952 | − | 0.881624i | \(-0.343549\pi\) | ||||
0.471952 | + | 0.881624i | \(0.343549\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.99671e7 | −1.80383 | −0.901915 | − | 0.431913i | \(-0.857839\pi\) | ||||
−0.901915 | + | 0.431913i | \(0.857839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.75980e6 | −0.103901 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.57088e6 | 0.502803 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.06695e6 | 0.0614054 | 0.0307027 | − | 0.999529i | \(-0.490225\pi\) | ||||
0.0307027 | + | 0.999529i | \(0.490225\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.06597e7 | 2.31059 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.10110e6 | −0.0621790 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.28008e6 | −0.294438 | −0.147219 | − | 0.989104i | \(-0.547032\pi\) | ||||
−0.147219 | + | 0.989104i | \(0.547032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.11727e7 | 2.83577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.66269e6 | 0.528821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.68555e6 | −0.305422 | −0.152711 | − | 0.988271i | \(-0.548800\pi\) | ||||
−0.152711 | + | 0.988271i | \(0.548800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.71746e7 | −1.45081 | −0.725405 | − | 0.688322i | \(-0.758348\pi\) | ||||
−0.725405 | + | 0.688322i | \(0.758348\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.61224e6 | −0.0845035 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.30951e7 | −1.71359 | −0.856793 | − | 0.515661i | \(-0.827547\pi\) | ||||
−0.856793 | + | 0.515661i | \(0.827547\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.90631e6 | −0.355424 | −0.177712 | − | 0.984083i | \(-0.556869\pi\) | ||||
−0.177712 | + | 0.984083i | \(0.556869\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.37490e7 | 1.20748 | 0.603742 | − | 0.797180i | \(-0.293676\pi\) | ||||
0.603742 | + | 0.797180i | \(0.293676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.22011e7 | −1.62736 | −0.813681 | − | 0.581311i | \(-0.802540\pi\) | ||||
−0.813681 | + | 0.581311i | \(0.802540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.17833e7 | −4.08368 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.62821e7 | 0.798554 | 0.399277 | − | 0.916830i | \(-0.369261\pi\) | ||||
0.399277 | + | 0.916830i | \(0.369261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.07393e7 | −0.523582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.42369e7 | −1.63978 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.79555e6 | 0.463666 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.06728e7 | 1.91395 | 0.956977 | − | 0.290164i | \(-0.0937098\pi\) | ||||
0.956977 | + | 0.290164i | \(0.0937098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.99154e6 | −0.0926268 | −0.0463134 | − | 0.998927i | \(-0.514747\pi\) | ||||
−0.0463134 | + | 0.998927i | \(0.514747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.62242e6 | −0.167500 | −0.0837502 | − | 0.996487i | \(-0.526690\pi\) | ||||
−0.0837502 | + | 0.996487i | \(0.526690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.38014e7 | 1.08786 | 0.543932 | − | 0.839129i | \(-0.316935\pi\) | ||||
0.543932 | + | 0.839129i | \(0.316935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.59091e6 | 0.0714655 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −633800. | −0.0283078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.08955e7 | −0.478352 | −0.239176 | − | 0.970976i | \(-0.576877\pi\) | ||||
−0.239176 | + | 0.970976i | \(0.576877\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.79389e7 | −0.778674 | −0.389337 | − | 0.921095i | \(-0.627296\pi\) | ||||
−0.389337 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.70601e6 | −0.332604 | −0.166302 | − | 0.986075i | \(-0.553183\pi\) | ||||
−0.166302 | + | 0.986075i | \(0.553183\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.56776e7 | −1.52260 | −0.761301 | − | 0.648399i | \(-0.775439\pi\) | ||||
−0.761301 | + | 0.648399i | \(0.775439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.92207e7 | 2.08878 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.74304e6 | −0.157071 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.61802e7 | −0.667704 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.66684e7 | 1.50480 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.90905e7 | −0.770547 | −0.385274 | − | 0.922802i | \(-0.625893\pi\) | ||||
−0.385274 | + | 0.922802i | \(0.625893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.40453e6 | −0.295598 | −0.147799 | − | 0.989017i | \(-0.547219\pi\) | ||||
−0.147799 | + | 0.989017i | \(0.547219\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.66009e7 | −0.659105 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.20792e7 | −1.25979 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.47415e7 | 0.966356 | 0.483178 | − | 0.875522i | \(-0.339482\pi\) | ||||
0.483178 | + | 0.875522i | \(0.339482\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.97600e6 | −0.114982 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.85830e6 | −0.336753 | −0.168376 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168376 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.98206e6 | 0.226192 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.06569e7 | 1.14072 | 0.570360 | − | 0.821395i | \(-0.306804\pi\) | ||||
0.570360 | + | 0.821395i | \(0.306804\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.29302e7 | −0.476027 | −0.238013 | − | 0.971262i | \(-0.576496\pi\) | ||||
−0.238013 | + | 0.971262i | \(0.576496\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.84368e6 | 0.287237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.05701e7 | 0.745354 | 0.372677 | − | 0.927961i | \(-0.378440\pi\) | ||||
0.372677 | + | 0.927961i | \(0.378440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.35510e6 | −0.120932 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00489e7 | 0.715087 | 0.357544 | − | 0.933896i | \(-0.383614\pi\) | ||||
0.357544 | + | 0.933896i | \(0.383614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.48982e7 | −0.874223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.83818e6 | −0.0642064 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.37266e6 | 0.150376 | 0.0751882 | − | 0.997169i | \(-0.476044\pi\) | ||||
0.0751882 | + | 0.997169i | \(0.476044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.61184e7 | −0.888994 | −0.444497 | − | 0.895780i | \(-0.646617\pi\) | ||||
−0.444497 | + | 0.895780i | \(0.646617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.94394e7 | −2.01276 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.61443e7 | −0.876275 | −0.438138 | − | 0.898908i | \(-0.644362\pi\) | ||||
−0.438138 | + | 0.898908i | \(0.644362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.06056e7 | −0.353654 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.52466e7 | 0.503258 | 0.251629 | − | 0.967824i | \(-0.419034\pi\) | ||||
0.251629 | + | 0.967824i | \(0.419034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.18598e6 | 0.233612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.90665e7 | −0.940175 | −0.470088 | − | 0.882620i | \(-0.655778\pi\) | ||||
−0.470088 | + | 0.882620i | \(0.655778\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.92663e6 | −0.0932461 | −0.0466230 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466230 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 900.6.a.k.1.1 | 1 | ||
3.2 | odd | 2 | 300.6.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 900.6.d.f.649.2 | 2 | |||
5.3 | odd | 4 | 900.6.d.f.649.1 | 2 | |||
5.4 | even | 2 | 180.6.a.c.1.1 | 1 | |||
15.2 | even | 4 | 300.6.d.c.49.2 | 2 | |||
15.8 | even | 4 | 300.6.d.c.49.1 | 2 | |||
15.14 | odd | 2 | 60.6.a.c.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 720.6.a.x.1.1 | 1 | |||
60.59 | even | 2 | 240.6.a.d.1.1 | 1 | |||
120.29 | odd | 2 | 960.6.a.g.1.1 | 1 | |||
120.59 | even | 2 | 960.6.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.a.c.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
180.6.a.c.1.1 | 1 | 5.4 | even | 2 | |||
240.6.a.d.1.1 | 1 | 60.59 | even | 2 | |||
300.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
300.6.d.c.49.1 | 2 | 15.8 | even | 4 | |||
300.6.d.c.49.2 | 2 | 15.2 | even | 4 | |||
720.6.a.x.1.1 | 1 | 20.19 | odd | 2 | |||
900.6.a.k.1.1 | 1 | 1.1 | even | 1 | trivial | ||
900.6.d.f.649.1 | 2 | 5.3 | odd | 4 | |||
900.6.d.f.649.2 | 2 | 5.2 | odd | 4 | |||
960.6.a.g.1.1 | 1 | 120.29 | odd | 2 | |||
960.6.a.bb.1.1 | 1 | 120.59 | even | 2 |