Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,6,Mod(1,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, 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("980.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.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: | \(157.176143417\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 499x - 210 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 140) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.420991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.1 |
$q$-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 | ||||||||
\(3\) | −1.57901 | −0.101293 | −0.0506467 | − | 0.998717i | \(-0.516128\pi\) | ||||
−0.0506467 | + | 0.998717i | \(0.516128\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −240.507 | −0.989740 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 322.771 | 0.804290 | 0.402145 | − | 0.915576i | \(-0.368265\pi\) | ||||
0.402145 | + | 0.915576i | \(0.368265\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −657.331 | −1.07876 | −0.539381 | − | 0.842062i | \(-0.681342\pi\) | ||||
−0.539381 | + | 0.842062i | \(0.681342\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 39.4752 | 0.0452998 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −665.753 | −0.558715 | −0.279358 | − | 0.960187i | \(-0.590122\pi\) | ||||
−0.279358 | + | 0.960187i | \(0.590122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2215.14 | 1.40772 | 0.703862 | − | 0.710337i | \(-0.251457\pi\) | ||||
0.703862 | + | 0.710337i | \(0.251457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1586.87 | 0.625492 | 0.312746 | − | 0.949837i | \(-0.398751\pi\) | ||||
0.312746 | + | 0.949837i | \(0.398751\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 763.461 | 0.201548 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6386.70 | 1.41020 | 0.705102 | − | 0.709106i | \(-0.250901\pi\) | ||||
0.705102 | + | 0.709106i | \(0.250901\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7712.24 | −1.44137 | −0.720686 | − | 0.693262i | \(-0.756173\pi\) | ||||
−0.720686 | + | 0.693262i | \(0.756173\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −509.658 | −0.0814693 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3433.65 | 0.412337 | 0.206169 | − | 0.978517i | \(-0.433900\pi\) | ||||
0.206169 | + | 0.978517i | \(0.433900\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1037.93 | 0.109272 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6537.24 | 0.607344 | 0.303672 | − | 0.952777i | \(-0.401787\pi\) | ||||
0.303672 | + | 0.952777i | \(0.401787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16611.0 | 1.37001 | 0.685007 | − | 0.728536i | \(-0.259799\pi\) | ||||
0.685007 | + | 0.728536i | \(0.259799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6012.67 | 0.442625 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12516.9 | −0.826515 | −0.413257 | − | 0.910614i | \(-0.635609\pi\) | ||||
−0.413257 | + | 0.910614i | \(0.635609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1051.23 | 0.0565942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4240.34 | 0.207353 | 0.103677 | − | 0.994611i | \(-0.466939\pi\) | ||||
0.103677 | + | 0.994611i | \(0.466939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8069.27 | −0.359689 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3497.73 | −0.142593 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −26156.3 | −0.978243 | −0.489122 | − | 0.872216i | \(-0.662683\pi\) | ||||
−0.489122 | + | 0.872216i | \(0.662683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32683.8 | −1.12463 | −0.562313 | − | 0.826924i | \(-0.690089\pi\) | ||||
−0.562313 | + | 0.826924i | \(0.690089\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16433.3 | 0.482437 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6153.18 | −0.167461 | −0.0837303 | − | 0.996488i | \(-0.526683\pi\) | ||||
−0.0837303 | + | 0.996488i | \(0.526683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2505.68 | −0.0633583 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33827.2 | −0.796379 | −0.398190 | − | 0.917303i | \(-0.630361\pi\) | ||||
−0.398190 | + | 0.917303i | \(0.630361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 82194.4 | 1.80524 | 0.902621 | − | 0.430437i | \(-0.141640\pi\) | ||||
0.902621 | + | 0.430437i | \(0.141640\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −986.880 | −0.0202587 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35205.3 | −0.634659 | −0.317329 | − | 0.948315i | \(-0.602786\pi\) | ||||
−0.317329 | + | 0.948315i | \(0.602786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 57237.6 | 0.969324 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17529.6 | −0.279304 | −0.139652 | − | 0.990201i | \(-0.544598\pi\) | ||||
−0.139652 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16643.8 | 0.249865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10084.7 | −0.142844 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 72867.8 | 0.975126 | 0.487563 | − | 0.873088i | \(-0.337886\pi\) | ||||
0.487563 | + | 0.873088i | \(0.337886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12177.7 | 0.146002 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −55378.5 | −0.629553 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 166047. | 1.79185 | 0.895927 | − | 0.444202i | \(-0.146513\pi\) | ||||
0.895927 | + | 0.444202i | \(0.146513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −77628.6 | −0.796038 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19577.2 | −0.190963 | −0.0954813 | − | 0.995431i | \(-0.530439\pi\) | ||||
−0.0954813 | + | 0.995431i | \(0.530439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −83864.5 | −0.778906 | −0.389453 | − | 0.921046i | \(-0.627336\pi\) | ||||
−0.389453 | + | 0.921046i | \(0.627336\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −105704. | −0.892547 | −0.446273 | − | 0.894897i | \(-0.647249\pi\) | ||||
−0.446273 | + | 0.894897i | \(0.647249\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −114386. | −0.922160 | −0.461080 | − | 0.887359i | \(-0.652538\pi\) | ||||
−0.461080 | + | 0.887359i | \(0.652538\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5421.77 | −0.0417670 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −95123.1 | −0.700793 | −0.350396 | − | 0.936601i | \(-0.613953\pi\) | ||||
−0.350396 | + | 0.936601i | \(0.613953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −39671.8 | −0.279729 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 158092. | 1.06769 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −56870.0 | −0.353118 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10322.4 | −0.0615199 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 97854.5 | 0.538358 | 0.269179 | − | 0.963090i | \(-0.413248\pi\) | ||||
0.269179 | + | 0.963090i | \(0.413248\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26228.9 | −0.138773 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 31926.2 | 0.162543 | 0.0812715 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812715 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −19086.5 | −0.0901348 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22595.8 | 0.102855 | 0.0514276 | − | 0.998677i | \(-0.483623\pi\) | ||||
0.0514276 | + | 0.998677i | \(0.483623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −287232. | −1.26094 | −0.630472 | − | 0.776212i | \(-0.717139\pi\) | ||||
−0.630472 | + | 0.776212i | \(0.717139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19764.2 | 0.0837205 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −212167. | −0.867637 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −159668. | −0.630662 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −437546. | −1.61458 | −0.807288 | − | 0.590158i | \(-0.799065\pi\) | ||||
−0.807288 | + | 0.590158i | \(0.799065\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 505868. | 1.80549 | 0.902744 | − | 0.430179i | \(-0.141550\pi\) | ||||
0.902744 | + | 0.430179i | \(0.141550\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 160118. | 0.552983 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 192806. | 0.644601 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 214333. | 0.693967 | 0.346984 | − | 0.937871i | \(-0.387206\pi\) | ||||
0.346984 | + | 0.937871i | \(0.387206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6695.54 | −0.0210035 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −587081. | −1.73073 | −0.865364 | − | 0.501143i | \(-0.832913\pi\) | ||||
−0.865364 | + | 0.501143i | \(0.832913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12741.5 | 0.0364342 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 387234. | 1.07444 | 0.537220 | − | 0.843442i | \(-0.319475\pi\) | ||||
0.537220 | + | 0.843442i | \(0.319475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 60790.6 | 0.163727 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −532757. | −1.39328 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −610438. | −1.55069 | −0.775347 | − | 0.631535i | \(-0.782425\pi\) | ||||
−0.775347 | + | 0.631535i | \(0.782425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41301.1 | 0.0990897 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 169505. | 0.395412 | 0.197706 | − | 0.980261i | \(-0.436651\pi\) | ||||
0.197706 | + | 0.980261i | \(0.436651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −305167. | −0.692374 | −0.346187 | − | 0.938166i | \(-0.612524\pi\) | ||||
−0.346187 | + | 0.938166i | \(0.612524\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 51608.1 | 0.113917 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −85841.4 | −0.184403 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −214886. | −0.449369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 941471. | 1.86734 | 0.933670 | − | 0.358134i | \(-0.116587\pi\) | ||||
0.933670 | + | 0.358134i | \(0.116587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 385057. | 0.744101 | 0.372051 | − | 0.928212i | \(-0.378655\pi\) | ||||
0.372051 | + | 0.928212i | \(0.378655\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −25948.3 | −0.0488677 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.03718e6 | −1.90410 | −0.952048 | − | 0.305948i | \(-0.901026\pi\) | ||||
−0.952048 | + | 0.305948i | \(0.901026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −410855. | −0.735455 | −0.367727 | − | 0.929934i | \(-0.619864\pi\) | ||||
−0.367727 | + | 0.929934i | \(0.619864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9715.93 | 0.0169627 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −163431. | −0.271612 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −381653. | −0.619075 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 714983. | 1.13222 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 442714. | 0.684568 | 0.342284 | − | 0.939597i | \(-0.388799\pi\) | ||||
0.342284 | + | 0.939597i | \(0.388799\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 53413.4 | 0.0806680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −415275. | −0.612689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −129786. | −0.182859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 437620. | 0.602721 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −93933.5 | −0.126491 | −0.0632453 | − | 0.997998i | \(-0.520145\pi\) | ||||
−0.0632453 | + | 0.997998i | \(0.520145\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −150317. | −0.197948 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −234538. | −0.302099 | −0.151049 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151049 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −239032. | −0.301208 | −0.150604 | − | 0.988594i | \(-0.548122\pi\) | ||||
−0.150604 | + | 0.988594i | \(0.548122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.47330e6 | −1.77788 | −0.888939 | − | 0.458025i | \(-0.848557\pi\) | ||||
−0.888939 | + | 0.458025i | \(0.848557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 312921. | 0.369629 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 55589.5 | 0.0642868 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.31478e6 | −1.48887 | −0.744436 | − | 0.667694i | \(-0.767282\pi\) | ||||
−0.744436 | + | 0.667694i | \(0.767282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20810e6 | −1.33986 | −0.669932 | − | 0.742423i | \(-0.733677\pi\) | ||||
−0.669932 | + | 0.742423i | \(0.733677\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −275900. | −0.299734 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.45608e6 | −1.51860 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27679.4 | 0.0282916 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 518940. | 0.519916 | 0.259958 | − | 0.965620i | \(-0.416291\pi\) | ||||
0.259958 | + | 0.965620i | \(0.416291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 512196. | 0.503077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26280.7 | −0.0253097 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 566825. | 0.535324 | 0.267662 | − | 0.963513i | \(-0.413749\pi\) | ||||
0.267662 | + | 0.963513i | \(0.413749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.53605e6 | −1.39573 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.27389e6 | −1.13564 | −0.567822 | − | 0.823151i | \(-0.692214\pi\) | ||||
−0.567822 | + | 0.823151i | \(0.692214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −106009. | −0.0927313 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −115059. | −0.0987738 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 445770. | 0.375604 | 0.187802 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187802 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.26776e6 | −1.04861 | −0.524306 | − | 0.851530i | \(-0.675675\pi\) | ||||
−0.524306 | + | 0.851530i | \(0.675675\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 201732. | 0.160858 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −309948. | −0.242711 | −0.121355 | − | 0.992609i | \(-0.538724\pi\) | ||||
−0.121355 | + | 0.992609i | \(0.538724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.85484e6 | 1.42658 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 291247. | 0.220037 | 0.110018 | − | 0.993930i | \(-0.464909\pi\) | ||||
0.110018 | + | 0.993930i | \(0.464909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −723026. | −0.536646 | −0.268323 | − | 0.963329i | \(-0.586469\pi\) | ||||
−0.268323 | + | 0.963329i | \(0.586469\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 87443.2 | 0.0637696 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −976630. | −0.687837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −262190. | −0.181503 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.19632e6 | 0.814098 | 0.407049 | − | 0.913406i | \(-0.366558\pi\) | ||||
0.407049 | + | 0.913406i | \(0.366558\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 653908. | 0.437484 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 246423. | 0.162103 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.04310e6 | −0.674757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30912.6 | 0.0193433 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 817096. | 0.502948 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.95349e6 | 1.18295 | 0.591475 | − | 0.806324i | \(-0.298546\pi\) | ||||
0.591475 | + | 0.806324i | \(0.298546\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 132423. | 0.0788981 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −794401. | −0.465735 | −0.232868 | − | 0.972508i | \(-0.574811\pi\) | ||||
−0.232868 | + | 0.972508i | \(0.574811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 118598. | 0.0684255 | 0.0342127 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342127 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.78228e6 | −1.55508 | −0.777540 | − | 0.628833i | \(-0.783533\pi\) | ||||
−0.777540 | + | 0.628833i | \(0.783533\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.06144e6 | 1.13421 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 166907. | 0.0904092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.47474e6 | −0.786517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −410832. | −0.215752 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 180616. | 0.0934088 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.38160e6 | −1.19481 | −0.597404 | − | 0.801940i | \(-0.703801\pi\) | ||||
−0.597404 | + | 0.801940i | \(0.703801\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −825817. | −0.408106 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 153830. | 0.0748907 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 270123. | 0.129565 | 0.0647823 | − | 0.997899i | \(-0.479365\pi\) | ||||
0.0647823 | + | 0.997899i | \(0.479365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 150200. | 0.0709857 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.48929e6 | −1.15928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 62642.1 | 0.0283347 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.58739e6 | 1.59939 | 0.799696 | − | 0.600405i | \(-0.204994\pi\) | ||||
0.799696 | + | 0.600405i | \(0.204994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.13696e6 | 0.499666 | 0.249833 | − | 0.968289i | \(-0.419624\pi\) | ||||
0.249833 | + | 0.968289i | \(0.419624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −501847. | −0.217422 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.49344e6 | −1.49216 | −0.746081 | − | 0.665855i | \(-0.768067\pi\) | ||||
−0.746081 | + | 0.665855i | \(0.768067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 845680. | 0.356152 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −986571. | −0.404010 | −0.202005 | − | 0.979384i | \(-0.564746\pi\) | ||||
−0.202005 | + | 0.979384i | \(0.564746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.43075e6 | 0.981687 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 89798.2 | 0.0357685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.05486e6 | −0.807329 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.28626e6 | −1.27361 | −0.636805 | − | 0.771025i | \(-0.719745\pi\) | ||||
−0.636805 | + | 0.771025i | \(0.719745\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.57225e6 | −0.601112 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.67518e6 | 1.36775 | 0.683874 | − | 0.729600i | \(-0.260294\pi\) | ||||
0.683874 | + | 0.729600i | \(0.260294\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24672.0 | 0.00905996 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.19818e6 | −1.52127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.18583e6 | −0.424059 | −0.212029 | − | 0.977263i | \(-0.568007\pi\) | ||||
−0.212029 | + | 0.977263i | \(0.568007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −154513. | −0.0545322 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.67224e6 | 0.930846 | 0.465423 | − | 0.885088i | \(-0.345902\pi\) | ||||
0.465423 | + | 0.885088i | \(0.345902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.99506e6 | −1.35596 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.60515e6 | −0.872890 | −0.436445 | − | 0.899731i | \(-0.643763\pi\) | ||||
−0.436445 | + | 0.899731i | \(0.643763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.05646e6 | −0.349472 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −50411.7 | −0.0164646 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 880133. | 0.283828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.59840e6 | −1.46430 | −0.732151 | − | 0.681142i | \(-0.761483\pi\) | ||||
−0.732151 | + | 0.681142i | \(0.761483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.14418e6 | −0.665887 | −0.332943 | − | 0.942947i | \(-0.608042\pi\) | ||||
−0.332943 | + | 0.942947i | \(0.608042\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.06949e6 | 1.55490 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.43094e6 | −0.433495 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.10828e6 | 0.331639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.01508e6 | −1.18682 | −0.593411 | − | 0.804900i | \(-0.702219\pi\) | ||||
−0.593411 | + | 0.804900i | \(0.702219\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35679.0 | −0.0104186 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 438240. | 0.124908 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 453542. | 0.127725 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.05677e6 | −0.572335 | −0.286168 | − | 0.958180i | \(-0.592381\pi\) | ||||
−0.286168 | + | 0.958180i | \(0.592381\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −536575. | −0.147545 | −0.0737726 | − | 0.997275i | \(-0.523504\pi\) | ||||
−0.0737726 | + | 0.997275i | \(0.523504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.01039e6 | 0.818034 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −416096. | −0.111743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 335014. | 0.0878860 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.57365e6 | −1.44526 | −0.722631 | − | 0.691234i | \(-0.757067\pi\) | ||||
−0.722631 | + | 0.691234i | \(0.757067\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 600292. | 0.153866 | 0.0769331 | − | 0.997036i | \(-0.475487\pi\) | ||||
0.0769331 | + | 0.997036i | \(0.475487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 252117. | 0.0638820 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.51514e6 | 0.880521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.08074e6 | −1.01060 | −0.505298 | − | 0.862945i | \(-0.668617\pi\) | ||||
−0.505298 | + | 0.862945i | \(0.668617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.45140e6 | −1.56187 | −0.780935 | − | 0.624612i | \(-0.785257\pi\) | ||||
−0.780935 | + | 0.624612i | \(0.785257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.82169e6 | −0.436089 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 690889. | 0.163546 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.62778e6 | 0.849230 | 0.424615 | − | 0.905374i | \(-0.360409\pi\) | ||||
0.424615 | + | 0.905374i | \(0.360409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.11003e6 | 0.488480 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −798769. | −0.182884 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.12392e6 | 1.14766 | 0.573828 | − | 0.818976i | \(-0.305458\pi\) | ||||
0.573828 | + | 0.818976i | \(0.305458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −508277. | −0.112608 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.96610e6 | 0.869184 | 0.434592 | − | 0.900627i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 310011. | 0.0672085 | 0.0336043 | − | 0.999435i | \(-0.489301\pi\) | ||||
0.0336043 | + | 0.999435i | \(0.489301\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −304442. | −0.0652939 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.07130e6 | 0.227311 | 0.113655 | − | 0.993520i | \(-0.463744\pi\) | ||||
0.113655 | + | 0.993520i | \(0.463744\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −338433. | −0.0702943 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.36155e6 | 1.10189 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.38446e6 | 0.281545 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.01983e6 | −0.205226 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.62151e6 | −1.11947 | −0.559737 | − | 0.828670i | \(-0.689098\pi\) | ||||
−0.559737 | + | 0.828670i | \(0.689098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.25705e6 | −0.444813 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.15118e6 | −0.801341 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.04558e6 | −0.772962 | −0.386481 | − | 0.922297i | \(-0.626309\pi\) | ||||
−0.386481 | + | 0.922297i | \(0.626309\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 927006. | 0.175312 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.15461e6 | −0.777727 | −0.388863 | − | 0.921295i | \(-0.627132\pi\) | ||||
−0.388863 | + | 0.921295i | \(0.627132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.25197e6 | −0.787903 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.94071e6 | 0.355999 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.79365e6 | −0.502251 | −0.251125 | − | 0.967955i | \(-0.580801\pi\) | ||||
−0.251125 | + | 0.967955i | \(0.580801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −611445. | −0.108834 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.95171e6 | 1.22510 | 0.612551 | − | 0.790431i | \(-0.290144\pi\) | ||||
0.612551 | + | 0.790431i | \(0.290144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 489431. | 0.0854010 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −95988.9 | −0.0165845 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.84503e6 | 1.34215 | 0.671073 | − | 0.741391i | \(-0.265834\pi\) | ||||
0.671073 | + | 0.741391i | \(0.265834\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.69118e6 | 0.283723 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.09661e6 | 0.348337 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.04008e6 | −0.664758 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 963887. | 0.157075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.03460e6 | 0.973989 | 0.486995 | − | 0.873405i | \(-0.338093\pi\) | ||||
0.486995 | + | 0.873405i | \(0.338093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.59256e6 | 0.254590 | 0.127295 | − | 0.991865i | \(-0.459371\pi\) | ||||
0.127295 | + | 0.991865i | \(0.459371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.13444e6 | 0.805317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.91818e6 | −0.608759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.29078e6 | 0.968206 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.29713e6 | −0.655179 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.64259e6 | 0.399159 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −267650. | −0.0400526 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.73741e6 | −0.255217 | −0.127608 | − | 0.991825i | \(-0.540730\pi\) | ||||
−0.127608 | + | 0.991825i | \(0.540730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 481861. | 0.0701330 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.85965e6 | 0.412402 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.14309e7 | 1.63348 | 0.816738 | − | 0.577009i | \(-0.195780\pi\) | ||||
0.816738 | + | 0.577009i | \(0.195780\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.86068e6 | 1.11309 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41475e7 | 1.98518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 135544. | 0.0186788 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.08461e7 | 1.48127 | 0.740635 | − | 0.671908i | \(-0.234525\pi\) | ||||
0.740635 | + | 0.671908i | \(0.234525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.09189e7 | −1.47792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 339306. | 0.0455182 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −203287. | −0.0270295 | −0.0135148 | − | 0.999909i | \(-0.504302\pi\) | ||||
−0.0135148 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.37808e6 | 0.313404 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.04184e7 | 1.34903 | 0.674514 | − | 0.738262i | \(-0.264353\pi\) | ||||
0.674514 | + | 0.738262i | \(0.264353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.44964e6 | −0.571129 | −0.285565 | − | 0.958359i | \(-0.592181\pi\) | ||||
−0.285565 | + | 0.958359i | \(0.592181\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.48659e6 | −0.189149 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 991794. | 0.125098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.10826e6 | 0.513711 | 0.256855 | − | 0.966450i | \(-0.417314\pi\) | ||||
0.256855 | + | 0.966450i | \(0.417314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −608009. | −0.0753726 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.36866e6 | 0.166772 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.95231e6 | −0.477487 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.10539e7 | 1.32409 | 0.662047 | − | 0.749463i | \(-0.269688\pi\) | ||||
0.662047 | + | 0.749463i | \(0.269688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.70837e7 | −2.02905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.63772e6 | 0.192872 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.01113e7 | −1.18078 | −0.590390 | − | 0.807118i | \(-0.701026\pi\) | ||||
−0.590390 | + | 0.807118i | \(0.701026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 648744. | 0.0744968 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.10092e6 | −0.125369 | −0.0626845 | − | 0.998033i | \(-0.519966\pi\) | ||||
−0.0626845 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.03055e6 | −0.229312 | −0.114656 | − | 0.993405i | \(-0.536577\pi\) | ||||
−0.114656 | + | 0.993405i | \(0.536577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.47988e6 | 0.165742 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.42175e6 | 0.157919 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.20572e6 | −0.463307 | −0.231654 | − | 0.972798i | \(-0.574414\pi\) | ||||
−0.231654 | + | 0.972798i | \(0.574414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.22771e6 | 0.891612 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.34913e7 | −1.45012 | −0.725060 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725060 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 258059. | 0.0275126 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.26037e6 | 0.979299 | 0.489650 | − | 0.871919i | \(-0.337125\pi\) | ||||
0.489650 | + | 0.871919i | \(0.337125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.11560e7 | −1.17026 | −0.585131 | − | 0.810939i | \(-0.698957\pi\) | ||||
−0.585131 | + | 0.810939i | \(0.698957\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.21151e6 | 0.126067 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.12896e6 | −0.114686 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.28597e6 | −0.230379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.72868e6 | 0.872721 | 0.436360 | − | 0.899772i | \(-0.356267\pi\) | ||||
0.436360 | + | 0.899772i | \(0.356267\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −699049. | −0.0693423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.44636e6 | −0.240761 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.13566e6 | 0.788208 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 646402. | 0.0621380 | 0.0310690 | − | 0.999517i | \(-0.490109\pi\) | ||||
0.0310690 | + | 0.999517i | \(0.490109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.36895e7 | −1.30575 | −0.652873 | − | 0.757468i | \(-0.726436\pi\) | ||||
−0.652873 | + | 0.757468i | \(0.726436\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 655723. | 0.0620614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.12743e7 | 1.05884 | 0.529418 | − | 0.848361i | \(-0.322410\pi\) | ||||
0.529418 | + | 0.848361i | \(0.322410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.44250e6 | −0.786791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.23867e7 | 1.13677 | 0.568384 | − | 0.822763i | \(-0.307569\pi\) | ||||
0.568384 | + | 0.822763i | \(0.307569\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −798154. | −0.0726915 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.97683e7 | −1.78672 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.93495e6 | 0.891153 | 0.445576 | − | 0.895244i | \(-0.352999\pi\) | ||||
0.445576 | + | 0.895244i | \(0.352999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.30434e6 | 0.383181 | 0.191590 | − | 0.981475i | \(-0.438636\pi\) | ||||
0.191590 | + | 0.981475i | \(0.438636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −691005. | −0.0610517 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.01349e7 | 0.882072 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 148322. | 0.0128127 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05494e7 | −0.904526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −252232. | −0.0214665 | −0.0107333 | − | 0.999942i | \(-0.503417\pi\) | ||||
−0.0107333 | + | 0.999942i | \(0.503417\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 477163. | 0.0403095 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.06012e7 | 0.888960 | 0.444480 | − | 0.895789i | \(-0.353388\pi\) | ||||
0.444480 | + | 0.895789i | \(0.353388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 370338. | 0.0306006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.30105e7 | −1.06719 | −0.533594 | − | 0.845741i | \(-0.679159\pi\) | ||||
−0.533594 | + | 0.845741i | \(0.679159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −564895. | −0.0459983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 377433. | 0.0305104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.78731e6 | −0.223685 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.67711e6 | 0.770993 | 0.385496 | − | 0.922709i | \(-0.374030\pi\) | ||||
0.385496 | + | 0.922709i | \(0.374030\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.18080e6 | 0.563911 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.35218e6 | −0.339332 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.32636e6 | 0.180087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.63711e7 | −1.25829 | −0.629147 | − | 0.777286i | \(-0.716596\pi\) | ||||
−0.629147 | + | 0.777286i | \(0.716596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.60603e6 | 0.580457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −494106. | −0.0374410 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.10343e6 | 0.530704 | 0.265352 | − | 0.964152i | \(-0.414512\pi\) | ||||
0.265352 | + | 0.964152i | \(0.414512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.46711e6 | 0.628147 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.22383e7 | −0.901567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.30418e6 | 0.388019 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.07604e6 | 0.150813 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.87623e6 | 0.496053 | 0.248027 | − | 0.968753i | \(-0.420218\pi\) | ||||
0.248027 | + | 0.968753i | \(0.420218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.90760e6 | 0.135719 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.99169e6 | 0.282041 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.71330e6 | −0.681602 | −0.340801 | − | 0.940136i | \(-0.610698\pi\) | ||||
−0.340801 | + | 0.940136i | \(0.610698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.34731e7 | −0.938963 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.10588e7 | −0.765448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.14783e7 | 0.789070 | 0.394535 | − | 0.918881i | \(-0.370906\pi\) | ||||
0.394535 | + | 0.918881i | \(0.370906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.98607e6 | −0.134687 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.55073e7 | 1.04454 | 0.522270 | − | 0.852780i | \(-0.325085\pi\) | ||||
0.522270 | + | 0.852780i | \(0.325085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.29916e6 | 0.153824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.49648e7 | 1.65904 | 0.829520 | − | 0.558477i | \(-0.188614\pi\) | ||||
0.829520 | + | 0.558477i | \(0.188614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.09387e7 | 0.722060 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.21599e6 | 0.276438 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.59690e6 | 0.103319 | 0.0516593 | − | 0.998665i | \(-0.483549\pi\) | ||||
0.0516593 | + | 0.998665i | \(0.483549\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −819411. | −0.0526641 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.26467e7 | −0.807438 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.30133e6 | −0.526512 | −0.263256 | − | 0.964726i | \(-0.584796\pi\) | ||||
−0.263256 | + | 0.964726i | \(0.584796\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −808762. | −0.0509584 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −911464. | −0.0570529 | −0.0285265 | − | 0.999593i | \(-0.509081\pi\) | ||||
−0.0285265 | + | 0.999593i | \(0.509081\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00295e6 | −0.247301 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.71934e7 | 1.05529 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.51616e7 | 1.53434 | 0.767171 | − | 0.641442i | \(-0.221664\pi\) | ||||
0.767171 | + | 0.641442i | \(0.221664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −895022. | −0.0542248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.10309e6 | 0.246980 | 0.123490 | − | 0.992346i | \(-0.460591\pi\) | ||||
0.123490 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.82015e6 | −0.288274 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.44809e7 | 0.854972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.09184e7 | −0.640520 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.87600e6 | 0.284223 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.35831e6 | −0.310352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.32406e7 | 1.33755 | 0.668777 | − | 0.743463i | \(-0.266818\pi\) | ||||
0.668777 | + | 0.743463i | \(0.266818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.01148e6 | 0.115033 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.14841e7 | 1.21320 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 167388. | 0.00939307 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.23259e6 | 0.514846 | 0.257423 | − | 0.966299i | \(-0.417127\pi\) | ||||
0.257423 | + | 0.966299i | \(0.417127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.33313e6 | 0.461787 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.75252e7 | −0.965120 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.65300e7 | 1.45194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −703874. | −0.0380462 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.27151e7 | −1.75743 | −0.878714 | − | 0.477349i | \(-0.841598\pi\) | ||||
−0.878714 | + | 0.477349i | \(0.841598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.01835e7 | 0.543681 | 0.271840 | − | 0.962342i | \(-0.412368\pi\) | ||||
0.271840 | + | 0.962342i | \(0.412368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00181e6 | 0.106218 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.46770e7 | 0.774005 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.67958e7 | 1.92860 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.37256e7 | 1.74623 | 0.873116 | − | 0.487512i | \(-0.162096\pi\) | ||||
0.873116 | + | 0.487512i | \(0.162096\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.33753e7 | −0.688343 | −0.344171 | − | 0.938907i | \(-0.611840\pi\) | ||||
−0.344171 | + | 0.938907i | \(0.611840\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −318536. | −0.0162939 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.05590e7 | 0.536856 | 0.268428 | − | 0.963300i | \(-0.413496\pi\) | ||||
0.268428 | + | 0.963300i | \(0.413496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.01166e7 | 1.52202 | 0.761009 | − | 0.648741i | \(-0.224704\pi\) | ||||
0.761009 | + | 0.648741i | \(0.224704\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 489410. | 0.0245850 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.68084e6 | −0.480504 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.88799e6 | −0.290505 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.47935e6 | −0.121600 | −0.0607998 | − | 0.998150i | \(-0.519365\pi\) | ||||
−0.0607998 | + | 0.998150i | \(0.519365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.02788e7 | 0.988674 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −459881. | −0.0222883 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.51977e6 | −0.0732208 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14166e6 | 0.0543587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.44877e6 | 0.257914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.23084e6 | 0.0579199 | 0.0289600 | − | 0.999581i | \(-0.490780\pi\) | ||||
0.0289600 | + | 0.999581i | \(0.490780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.33189e7 | 0.623094 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.75099e7 | 1.27949 | 0.639746 | − | 0.768586i | \(-0.279039\pi\) | ||||
0.639746 | + | 0.768586i | \(0.279039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.28833e7 | 0.595722 | 0.297861 | − | 0.954609i | \(-0.403727\pi\) | ||||
0.297861 | + | 0.954609i | \(0.403727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.57981e7 | −0.722067 | −0.361033 | − | 0.932553i | \(-0.617576\pi\) | ||||
−0.361033 | + | 0.932553i | \(0.617576\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.52610e7 | 0.693492 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.54211e6 | 0.0696734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.13632e7 | −0.510450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.04468e6 | 0.180650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.99355e7 | −1.77347 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.99471e7 | −1.75383 | −0.876913 | − | 0.480649i | \(-0.840401\pi\) | ||||
−0.876913 | + | 0.480649i | \(0.840401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.88899e6 | −0.0824628 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.20714e7 | −1.82620 | −0.913098 | − | 0.407740i | \(-0.866317\pi\) | ||||
−0.913098 | + | 0.407740i | \(0.866317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.82226e7 | −1.21813 | −0.609067 | − | 0.793118i | \(-0.708456\pi\) | ||||
−0.609067 | + | 0.793118i | \(0.708456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.03253e6 | −0.0443142 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.26687e7 | 0.540658 | 0.270329 | − | 0.962768i | \(-0.412868\pi\) | ||||
0.270329 | + | 0.962768i | \(0.412868\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.84746e7 | 0.779618 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.77266e7 | −1.16350 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.23762e6 | −0.176833 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.64706e6 | 0.0683485 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.92558e7 | −2.03263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.82302e6 | −0.115852 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.62917e6 | 0.309639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50368e7 | −0.606928 | −0.303464 | − | 0.952843i | \(-0.598143\pi\) | ||||
−0.303464 | + | 0.952843i | \(0.598143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.70846e6 | 0.189003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.13882e7 | −0.454630 | −0.227315 | − | 0.973821i | \(-0.572995\pi\) | ||||
−0.227315 | + | 0.973821i | \(0.572995\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.65804e6 | −0.224641 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.29020e6 | −0.0509454 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.66749e7 | 0.651292 | 0.325646 | − | 0.945492i | \(-0.394418\pi\) | ||||
0.325646 | + | 0.945492i | \(0.394418\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.08458e6 | −0.119825 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.22356e7 | 0.859103 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.14603e6 | 0.0824674 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.01700e7 | 0.770914 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.13311e7 | −1.19107 | −0.595534 | − | 0.803330i | \(-0.703059\pi\) | ||||
−0.595534 | + | 0.803330i | \(0.703059\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.25437e6 | 0.0471759 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.37214e6 | 0.200964 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.22607e7 | −1.57249 | −0.786245 | − | 0.617914i | \(-0.787978\pi\) | ||||
−0.786245 | + | 0.617914i | \(0.787978\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −187268. | −0.00693105 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.46633e7 | 0.907980 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.03738e7 | 0.379889 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.33679e7 | −0.484383 | −0.242191 | − | 0.970229i | \(-0.577866\pi\) | ||||
−0.242191 | + | 0.970229i | \(0.577866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.40289e7 | −1.94743 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.39325e6 | 0.157519 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.17678e7 | −0.776395 | −0.388198 | − | 0.921576i | \(-0.626902\pi\) | ||||
−0.388198 | + | 0.921576i | \(0.626902\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.35368e7 | −0.835100 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.25504e6 | −0.114888 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.08494e7 | 1.07755 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.54225e7 | 0.883389 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.62643e6 | −0.332772 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.58647e7 | 0.889491 | 0.444746 | − | 0.895657i | \(-0.353294\pi\) | ||||
0.444746 | + | 0.895657i | \(0.353294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.32862e6 | 0.0796691 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.76225e7 | −1.28056 | −0.640280 | − | 0.768142i | \(-0.721181\pi\) | ||||
−0.640280 | + | 0.768142i | \(0.721181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 648707. | 0.0218543 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.22400e7 | 1.41575 | 0.707876 | − | 0.706336i | \(-0.249653\pi\) | ||||
0.707876 | + | 0.706336i | \(0.249653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.35196e7 | 0.784284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.75106e7 | 0.912698 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.18464e7 | −0.721100 | −0.360550 | − | 0.932740i | \(-0.617411\pi\) | ||||
−0.360550 | + | 0.932740i | \(0.617411\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.59295e7 | 0.851538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.63595e7 | 0.856933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.62904e6 | 0.149729 | 0.0748646 | − | 0.997194i | \(-0.476148\pi\) | ||||
0.0748646 | + | 0.997194i | \(0.476148\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.76056e6 | 0.121026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.02714e7 | 0.328905 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.99110e7 | 1.59023 | 0.795113 | − | 0.606462i | \(-0.207412\pi\) | ||||
0.795113 | + | 0.606462i | \(0.207412\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.62146e6 | 0.0831055 |
(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 | 980.6.a.h.1.2 | 3 | ||
7.6 | odd | 2 | 140.6.a.d.1.2 | ✓ | 3 | ||
28.27 | even | 2 | 560.6.a.t.1.2 | 3 | |||
35.13 | even | 4 | 700.6.e.g.449.4 | 6 | |||
35.27 | even | 4 | 700.6.e.g.449.3 | 6 | |||
35.34 | odd | 2 | 700.6.a.i.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.6.a.d.1.2 | ✓ | 3 | 7.6 | odd | 2 | ||
560.6.a.t.1.2 | 3 | 28.27 | even | 2 | |||
700.6.a.i.1.2 | 3 | 35.34 | odd | 2 | |||
700.6.e.g.449.3 | 6 | 35.27 | even | 4 | |||
700.6.e.g.449.4 | 6 | 35.13 | even | 4 | |||
980.6.a.h.1.2 | 3 | 1.1 | even | 1 | trivial |