Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,6,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1104.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(177.063737074\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4608x^{6} - 3161x^{5} + 6284039x^{4} - 8279002x^{3} - 2677454576x^{2} + 13573192447x + 77901299860 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 552) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(9.78333\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.5667 | 0.385796 | 0.192898 | − | 0.981219i | \(-0.438211\pi\) | ||||
0.192898 | + | 0.981219i | \(0.438211\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 125.104 | 0.964994 | 0.482497 | − | 0.875898i | \(-0.339730\pi\) | ||||
0.482497 | + | 0.875898i | \(0.339730\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 251.622 | 0.626999 | 0.313500 | − | 0.949588i | \(-0.398499\pi\) | ||||
0.313500 | + | 0.949588i | \(0.398499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1049.36 | −1.72214 | −0.861068 | − | 0.508489i | \(-0.830204\pi\) | ||||
−0.861068 | + | 0.508489i | \(0.830204\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −194.100 | −0.222739 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1732.72 | 1.45414 | 0.727069 | − | 0.686564i | \(-0.240882\pi\) | ||||
0.727069 | + | 0.686564i | \(0.240882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 952.726 | 0.605458 | 0.302729 | − | 0.953077i | \(-0.402102\pi\) | ||||
0.302729 | + | 0.953077i | \(0.402102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1125.93 | −0.557140 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2659.88 | −0.851161 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8873.99 | 1.95940 | 0.979702 | − | 0.200459i | \(-0.0642435\pi\) | ||||
0.979702 | + | 0.200459i | \(0.0642435\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5017.18 | −0.937681 | −0.468841 | − | 0.883283i | \(-0.655328\pi\) | ||||
−0.468841 | + | 0.883283i | \(0.655328\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2264.60 | −0.361998 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2698.07 | 0.372291 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3179.77 | −0.381849 | −0.190924 | − | 0.981605i | \(-0.561149\pi\) | ||||
−0.190924 | + | 0.981605i | \(0.561149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9444.27 | 0.994276 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20516.0 | 1.90604 | 0.953020 | − | 0.302906i | \(-0.0979569\pi\) | ||||
0.953020 | + | 0.302906i | \(0.0979569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8597.82 | −0.709116 | −0.354558 | − | 0.935034i | \(-0.615369\pi\) | ||||
−0.354558 | + | 0.935034i | \(0.615369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1746.90 | 0.128599 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5687.90 | −0.375584 | −0.187792 | − | 0.982209i | \(-0.560133\pi\) | ||||
−0.187792 | + | 0.982209i | \(0.560133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1156.09 | −0.0687860 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15594.5 | −0.839547 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22168.2 | 1.08403 | 0.542013 | − | 0.840370i | \(-0.317662\pi\) | ||||
0.542013 | + | 0.840370i | \(0.317662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5426.65 | 0.241894 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8574.54 | −0.349561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 541.135 | 0.0202384 | 0.0101192 | − | 0.999949i | \(-0.496779\pi\) | ||||
0.0101192 | + | 0.999949i | \(0.496779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18613.6 | 0.640481 | 0.320241 | − | 0.947336i | \(-0.396236\pi\) | ||||
0.320241 | + | 0.947336i | \(0.396236\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10133.4 | 0.321665 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22631.3 | −0.664394 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3031.98 | −0.0825163 | −0.0412581 | − | 0.999149i | \(-0.513137\pi\) | ||||
−0.0412581 | + | 0.999149i | \(0.513137\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 34389.7 | 0.809622 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 23801.1 | 0.522744 | 0.261372 | − | 0.965238i | \(-0.415825\pi\) | ||||
0.261372 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 23938.9 | 0.491418 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31478.8 | 0.605051 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25487.8 | 0.459478 | 0.229739 | − | 0.973252i | \(-0.426213\pi\) | ||||
0.229739 | + | 0.973252i | \(0.426213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79525.8 | −1.26711 | −0.633553 | − | 0.773699i | \(-0.718404\pi\) | ||||
−0.633553 | + | 0.773699i | \(0.718404\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37368.9 | 0.561001 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −79865.9 | −1.13126 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 91114.9 | 1.21931 | 0.609655 | − | 0.792667i | \(-0.291308\pi\) | ||||
0.609655 | + | 0.792667i | \(0.291308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −131279. | −1.66185 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 45154.6 | 0.541371 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20547.1 | 0.233583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −66083.7 | −0.713124 | −0.356562 | − | 0.934272i | \(-0.616051\pi\) | ||||
−0.356562 | + | 0.934272i | \(0.616051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20381.4 | 0.209000 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47843.2 | −0.466677 | −0.233339 | − | 0.972396i | \(-0.574965\pi\) | ||||
−0.233339 | + | 0.972396i | \(0.574965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26932.5 | 0.250140 | 0.125070 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125070 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −24282.6 | −0.214942 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −137140. | −1.15799 | −0.578993 | − | 0.815332i | \(-0.696554\pi\) | ||||
−0.578993 | + | 0.815332i | \(0.696554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −151536. | −1.22165 | −0.610827 | − | 0.791764i | \(-0.709163\pi\) | ||||
−0.610827 | + | 0.791764i | \(0.709163\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28617.9 | 0.220460 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −84239.3 | −0.620610 | −0.310305 | − | 0.950637i | \(-0.600431\pi\) | ||||
−0.310305 | + | 0.950637i | \(0.600431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11408.8 | 0.0804440 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −84998.5 | −0.574046 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 216769. | 1.40324 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −97737.3 | −0.606872 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −184644. | −1.10045 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124761. | −0.714171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7734.17 | 0.0425505 | 0.0212752 | − | 0.999774i | \(-0.493227\pi\) | ||||
0.0212752 | + | 0.999774i | \(0.493227\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 77380.4 | 0.409408 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −158784. | −0.808403 | −0.404201 | − | 0.914670i | \(-0.632450\pi\) | ||||
−0.404201 | + | 0.914670i | \(0.632450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 119189. | 0.584264 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15722.1 | −0.0742465 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 152990. | 0.696405 | 0.348203 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348203 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −270171. | −1.18605 | −0.593023 | − | 0.805185i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805185i | \(0.702066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 51191.1 | 0.216844 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −264043. | −1.07978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 191382. | 0.755930 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10404.8 | 0.0397136 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 220050. | 0.812000 | 0.406000 | − | 0.913873i | \(-0.366923\pi\) | ||||
0.406000 | + | 0.913873i | \(0.366923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 432844. | 1.54486 | 0.772430 | − | 0.635099i | \(-0.219041\pi\) | ||||
0.772430 | + | 0.635099i | \(0.219041\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 140350. | 0.484713 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −108204. | −0.361754 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8947.45 | 0.0289701 | 0.0144851 | − | 0.999895i | \(-0.495389\pi\) | ||||
0.0144851 | + | 0.999895i | \(0.495389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −199513. | −0.625863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 66179.8 | 0.201215 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −128349. | −0.378375 | −0.189187 | − | 0.981941i | \(-0.560585\pi\) | ||||
−0.189187 | + | 0.981941i | \(0.560585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −48839.8 | −0.139657 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −84294.9 | −0.233889 | −0.116945 | − | 0.993138i | \(-0.537310\pi\) | ||||
−0.116945 | + | 0.993138i | \(0.537310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 729871. | 1.96575 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 77170.8 | 0.201819 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 303801. | 0.771744 | 0.385872 | − | 0.922552i | \(-0.373901\pi\) | ||||
0.385872 | + | 0.922552i | \(0.373901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −332761. | −0.821366 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4870.22 | −0.0116846 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 365012. | 0.851481 | 0.425740 | − | 0.904845i | \(-0.360014\pi\) | ||||
0.425740 | + | 0.904845i | \(0.360014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 561526. | 1.27401 | 0.637006 | − | 0.770859i | \(-0.280173\pi\) | ||||
0.637006 | + | 0.770859i | \(0.280173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −167523. | −0.369782 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −68577.0 | −0.147316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 435990. | 0.911744 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −91200.5 | −0.185713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −337877. | −0.670156 | −0.335078 | − | 0.942190i | \(-0.608763\pi\) | ||||
−0.335078 | + | 0.942190i | \(0.608763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 795781. | 1.53780 | 0.768900 | − | 0.639369i | \(-0.220804\pi\) | ||||
0.768900 | + | 0.639369i | \(0.220804\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 203681. | 0.383588 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23009.5 | 0.0422417 | 0.0211208 | − | 0.999777i | \(-0.493277\pi\) | ||||
0.0211208 | + | 0.999777i | \(0.493277\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 70554.9 | 0.126297 | 0.0631487 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631487 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27287.8 | 0.0476408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.11017e6 | 1.89081 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 442461. | 0.735343 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 239727. | 0.379622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07231e6 | 1.65812 | 0.829060 | − | 0.559159i | \(-0.188876\pi\) | ||||
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −309507. | −0.467436 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −185426. | −0.273574 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −627667. | −0.904857 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −214210. | −0.301806 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.81825e6 | −2.50423 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.43797e6 | −1.93636 | −0.968182 | − | 0.250246i | \(-0.919489\pi\) | ||||
−0.968182 | + | 0.250246i | \(0.919489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −215450. | −0.283720 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −156122. | −0.201095 | −0.100547 | − | 0.994932i | \(-0.532059\pi\) | ||||
−0.100547 | + | 0.994932i | \(0.532059\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 957388. | 1.20642 | 0.603211 | − | 0.797582i | \(-0.293888\pi\) | ||||
0.603211 | + | 0.797582i | \(0.293888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −283309. | −0.349326 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 395600. | 0.477382 | 0.238691 | − | 0.971096i | \(-0.423282\pi\) | ||||
0.238691 | + | 0.971096i | \(0.423282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −122669. | −0.144899 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −229390. | −0.265280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.10437e6 | −1.25060 | −0.625301 | − | 0.780384i | \(-0.715024\pi\) | ||||
−0.625301 | + | 0.780384i | \(0.715024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.10391e6 | 1.22431 | 0.612153 | − | 0.790739i | \(-0.290304\pi\) | ||||
0.612153 | + | 0.790739i | \(0.290304\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24932.9 | −0.0265374 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −999756. | −1.04268 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 715732. | 0.731564 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.40907e6 | 1.41172 | 0.705858 | − | 0.708354i | \(-0.250562\pi\) | ||||
0.705858 | + | 0.708354i | \(0.250562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 133108. | 0.130738 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −336321. | −0.323894 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 251097. | 0.237142 | 0.118571 | − | 0.992946i | \(-0.462169\pi\) | ||||
0.118571 | + | 0.992946i | \(0.462169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −397801. | −0.368482 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 718793. | 0.653135 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.46040e6 | 1.30191 | 0.650956 | − | 0.759115i | \(-0.274368\pi\) | ||||
0.650956 | + | 0.759115i | \(0.274368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 478093. | 0.418213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −820034. | −0.703969 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.02652e6 | 0.864942 | 0.432471 | − | 0.901648i | \(-0.357642\pi\) | ||||
0.432471 | + | 0.901648i | \(0.357642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.34412e6 | 1.93891 | 0.969454 | − | 0.245273i | \(-0.0788777\pi\) | ||||
0.969454 | + | 0.245273i | \(0.0788777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.18151e6 | 0.959471 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −669284. | −0.533678 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −858672. | −0.672400 | −0.336200 | − | 0.941791i | \(-0.609142\pi\) | ||||
−0.336200 | + | 0.941791i | \(0.609142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −406391. | −0.312560 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.25896e6 | 1.70664 | 0.853322 | − | 0.521384i | \(-0.174584\pi\) | ||||
0.853322 | + | 0.521384i | \(0.174584\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.35838e6 | 1.00822 | 0.504108 | − | 0.863640i | \(-0.331821\pi\) | ||||
0.504108 | + | 0.863640i | \(0.331821\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −184924. | −0.134859 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.56662e6 | 1.83932 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.58246e6 | 1.11452 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 594753. | 0.411722 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.05384e6 | 0.717143 | 0.358571 | − | 0.933502i | \(-0.383264\pi\) | ||||
0.358571 | + | 0.933502i | \(0.383264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11670.5 | 0.00780789 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −183433. | −0.120666 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −555113. | −0.359090 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07562e6 | −0.684293 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 430589. | 0.269436 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 401434. | 0.247095 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 144724. | 0.0876385 | 0.0438193 | − | 0.999039i | \(-0.486047\pi\) | ||||
0.0438193 | + | 0.999039i | \(0.486047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −242392. | −0.144418 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.10152e6 | 0.645791 | 0.322895 | − | 0.946435i | \(-0.395344\pi\) | ||||
0.322895 | + | 0.946435i | \(0.395344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.01260e6 | −0.584218 | −0.292109 | − | 0.956385i | \(-0.594357\pi\) | ||||
−0.292109 | + | 0.956385i | \(0.594357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 218543. | 0.124097 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 597212. | 0.333796 | 0.166898 | − | 0.985974i | \(-0.446625\pi\) | ||||
0.166898 | + | 0.985974i | \(0.446625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.23289e6 | 1.22854 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.23426e6 | 0.668564 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.65081e6 | 0.880420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.79118e6 | 1.46582 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.36382e6 | 0.705323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −711577. | −0.362437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.42336e6 | −1.71744 | −0.858722 | − | 0.512442i | \(-0.828741\pi\) | ||||
−0.858722 | + | 0.512442i | \(0.828741\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −257561. | −0.127283 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −65389.7 | −0.0318345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.22913e6 | −1.06921 | −0.534603 | − | 0.845103i | \(-0.679539\pi\) | ||||
−0.534603 | + | 0.845103i | \(0.679539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 758154. | 0.358309 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.26243e6 | −0.587926 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.24725e6 | −1.03137 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −102679. | −0.0464444 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −919683. | −0.410029 | −0.205014 | − | 0.978759i | \(-0.565724\pi\) | ||||
−0.205014 | + | 0.978759i | \(0.565724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −939403. | −0.412846 | −0.206423 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206423 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 764986. | 0.331425 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.95083e6 | 1.68753 | 0.843765 | − | 0.536712i | \(-0.180334\pi\) | ||||
0.843765 | + | 0.536712i | \(0.180334\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 741671. | 0.312349 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.95092e6 | −0.810158 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.11247e6 | 1.68410 | 0.842048 | − | 0.539402i | \(-0.181350\pi\) | ||||
0.842048 | + | 0.539402i | \(0.181350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.56841e6 | −0.633420 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 879636. | 0.350378 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 513309. | 0.201673 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.03521e6 | −1.17631 | −0.588157 | − | 0.808747i | \(-0.700146\pi\) | ||||
−0.588157 | + | 0.808747i | \(0.700146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.66179e6 | 0.635347 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.77332e6 | 1.04608 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −263081. | −0.0979077 | −0.0489538 | − | 0.998801i | \(-0.515589\pi\) | ||||
−0.0489538 | + | 0.998801i | \(0.515589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.12284e6 | 0.412327 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.31204e6 | −3.37436 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.23360e6 | 1.51395 | 0.756976 | − | 0.653443i | \(-0.226676\pi\) | ||||
0.756976 | + | 0.653443i | \(0.226676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −69607.5 | −0.0245665 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.88943e6 | 1.70318 | 0.851592 | − | 0.524206i | \(-0.175638\pi\) | ||||
0.851592 | + | 0.524206i | \(0.175638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 678893. | 0.233426 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −696423. | −0.236372 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.42103e6 | −1.14626 | −0.573130 | − | 0.819464i | \(-0.694271\pi\) | ||||
−0.573130 | + | 0.819464i | \(0.694271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 916608. | 0.303209 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.42905e6 | 0.466732 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 549687. | 0.177265 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 563878. | 0.179560 | 0.0897798 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897798 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.07271e6 | −0.337325 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 590550. | 0.183398 | 0.0916992 | − | 0.995787i | \(-0.470770\pi\) | ||||
0.0916992 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.26484e6 | 1.61482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 141499. | 0.0428662 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −800100. | −0.239419 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.88465e6 | −1.44386 | −0.721929 | − | 0.691967i | \(-0.756744\pi\) | ||||
−0.721929 | + | 0.691967i | \(0.756744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.37691e6 | −0.402070 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 67698.0 | 0.0195299 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.71511e6 | −0.488844 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.43154e6 | 0.684764 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.32253e6 | −0.924558 | −0.462279 | − | 0.886735i | \(-0.652968\pi\) | ||||
−0.462279 | + | 0.886735i | \(0.652968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 338104. | 0.0929706 | 0.0464853 | − | 0.998919i | \(-0.485198\pi\) | ||||
0.0464853 | + | 0.998919i | \(0.485198\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −460720. | −0.125195 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.60882e6 | −1.23771 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.32863e6 | 0.618061 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.37639e6 | 0.623410 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.86095e6 | 1.00115 | 0.500577 | − | 0.865692i | \(-0.333121\pi\) | ||||
0.500577 | + | 0.865692i | \(0.333121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.91822e6 | 0.747995 | 0.373998 | − | 0.927430i | \(-0.377987\pi\) | ||||
0.373998 | + | 0.927430i | \(0.377987\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.72244e6 | −0.436437 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 503992. | 0.126247 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5405.96 | 0.00133879 | 0.000669394 | − | 1.00000i | \(-0.499787\pi\) | ||||
0.000669394 | 1.00000i | \(0.499787\pi\) | ||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −93642.9 | −0.0229287 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 625169. | 0.151352 | 0.0756760 | − | 0.997132i | \(-0.475889\pi\) | ||||
0.0756760 | + | 0.997132i | \(0.475889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.96504e6 | 0.470405 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.98045e6 | −0.468808 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.52906e6 | −0.826121 | −0.413060 | − | 0.910704i | \(-0.635540\pi\) | ||||
−0.413060 | + | 0.910704i | \(0.635540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.16227e6 | 1.19509 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.89560e6 | −0.891926 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.83125e6 | −0.641136 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.99355e6 | 1.34244 | 0.671218 | − | 0.741260i | \(-0.265771\pi\) | ||||
0.671218 | + | 0.741260i | \(0.265771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.26315e6 | −0.279849 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.60655e6 | −0.352080 | −0.176040 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176040 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 803811. | 0.174262 | 0.0871308 | − | 0.996197i | \(-0.472230\pi\) | ||||
0.0871308 | + | 0.996197i | \(0.472230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 973834. | 0.208859 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.51941e6 | 0.322391 | 0.161195 | − | 0.986923i | \(-0.448465\pi\) | ||||
0.161195 | + | 0.986923i | \(0.448465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −379312. | −0.0796277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −80527.1 | −0.0167259 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.16340e6 | −0.444615 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.53414e6 | −0.515343 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.79562e6 | 0.361342 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.26116e6 | 1.44600 | 0.722998 | − | 0.690850i | \(-0.242764\pi\) | ||||
0.722998 | + | 0.690850i | \(0.242764\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.33673e6 | 0.657596 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −595618. | −0.116172 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.42520e6 | −0.275120 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.94840e6 | 0.563331 | 0.281666 | − | 0.959513i | \(-0.409113\pi\) | ||||
0.281666 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.15514e6 | 0.218455 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.80951e6 | 0.713125 | 0.356563 | − | 0.934271i | \(-0.383949\pi\) | ||||
0.356563 | + | 0.934271i | \(0.383949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.53761e7 | 2.84924 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 439558. | 0.0806313 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.30227e6 | 0.781281 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.41466e6 | −0.613898 | −0.306949 | − | 0.951726i | \(-0.599308\pi\) | ||||
−0.306949 | + | 0.951726i | \(0.599308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 758655. | 0.135036 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.54455e6 | 1.50581 | 0.752903 | − | 0.658132i | \(-0.228653\pi\) | ||||
0.752903 | + | 0.658132i | \(0.228653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.03182e6 | −0.180042 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.56884e6 | −1.13493 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.29142e6 | −1.58960 | −0.794800 | − | 0.606871i | \(-0.792424\pi\) | ||||
−0.794800 | + | 0.606871i | \(0.792424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.97760e6 | 0.504445 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −694537. | −0.116520 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 580843. | 0.0965030 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.43120e6 | −0.235491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.73421e6 | −0.445567 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.43542e6 | 1.52288 | 0.761442 | − | 0.648233i | \(-0.224492\pi\) | ||||
0.761442 | + | 0.648233i | \(0.224492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.97282e6 | −0.475241 | −0.237620 | − | 0.971358i | \(-0.576367\pi\) | ||||
−0.237620 | + | 0.971358i | \(0.576367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.99484e6 | 0.474216 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.69336e6 | −1.36352 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 43832.0 | 0.00674613 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.15287e7 | −3.28246 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.95764e6 | −0.446747 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.28511e6 | −0.491603 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −290897. | −0.0431288 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.75824e6 | 0.992751 | 0.496375 | − | 0.868108i | \(-0.334664\pi\) | ||||
0.496375 | + | 0.868108i | \(0.334664\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.05373e6 | −0.735551 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.26812e6 | −0.471309 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.23996e6 | 0.891690 | 0.445845 | − | 0.895110i | \(-0.352903\pi\) | ||||
0.445845 | + | 0.895110i | \(0.352903\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50770e6 | 0.213494 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.45448e6 | 1.18634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.18862e6 | 0.443394 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 617193. | 0.0850528 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.06303e7 | 1.45180 | 0.725901 | − | 0.687799i | \(-0.241423\pi\) | ||||
0.725901 | + | 0.687799i | \(0.241423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.02224e6 | 1.22119 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.92391e6 | −0.526396 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.89621e6 | −1.31582 | −0.657912 | − | 0.753095i | \(-0.728560\pi\) | ||||
−0.657912 | + | 0.753095i | \(0.728560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.81676e6 | −0.239429 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 820805. | 0.107222 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.02669e7 | −1.32940 | −0.664702 | − | 0.747108i | \(-0.731442\pi\) | ||||
−0.664702 | + | 0.747108i | \(0.731442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.72214e6 | −0.862814 | −0.431407 | − | 0.902157i | \(-0.641983\pi\) | ||||
−0.431407 | + | 0.902157i | \(0.641983\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.04090e6 | 0.386915 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.40708e6 | −0.177479 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.82589e6 | −0.728489 | −0.364244 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364244 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.16203e6 | −0.887850 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94896e6 | −1.22275 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.57800e6 | 0.679684 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.83313e6 | −0.221465 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.28402e6 | −0.752735 | −0.376367 | − | 0.926471i | \(-0.622827\pi\) | ||||
−0.376367 | + | 0.926471i | \(0.622827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.78000e6 | −0.567727 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −207085. | −0.0243883 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.46432e6 | 0.754894 | 0.377447 | − | 0.926031i | \(-0.376802\pi\) | ||||
0.377447 | + | 0.926031i | \(0.376802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.67499e6 | 0.541363 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −634994. | −0.0729179 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.39101e6 | −1.06941 | −0.534706 | − | 0.845038i | \(-0.679578\pi\) | ||||
−0.534706 | + | 0.845038i | \(0.679578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.92451e6 | −0.669062 | −0.334531 | − | 0.942385i | \(-0.608578\pi\) | ||||
−0.334531 | + | 0.942385i | \(0.608578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −245591. | −0.0275054 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.10787e6 | −0.234129 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.27590e7 | −1.40555 | −0.702774 | − | 0.711414i | \(-0.748055\pi\) | ||||
−0.702774 | + | 0.711414i | \(0.748055\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.99152e6 | −1.09166 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.96868e6 | 0.646807 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.84906e6 | 1.05863 | 0.529314 | − | 0.848426i | \(-0.322449\pi\) | ||||
0.529314 | + | 0.848426i | \(0.322449\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.98215e6 | −0.424550 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.75963e7 | 1.86084 | 0.930419 | − | 0.366498i | \(-0.119443\pi\) | ||||
0.930419 | + | 0.366498i | \(0.119443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.79122e7 | −1.87898 | −0.939491 | − | 0.342573i | \(-0.888702\pi\) | ||||
−0.939491 | + | 0.342573i | \(0.888702\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.13988e7 | 1.17663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.62146e6 | 0.575637 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.15754e6 | −0.219175 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.50965e6 | −0.555261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.76600e6 | 0.276553 | 0.138277 | − | 0.990394i | \(-0.455844\pi\) | ||||
0.138277 | + | 0.990394i | \(0.455844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.65083e6 | −0.957317 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 166800. | 0.0164158 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.21315e6 | 0.118459 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.78556e6 | 0.269874 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 741083. | 0.0712396 | 0.0356198 | − | 0.999365i | \(-0.488659\pi\) | ||||
0.0356198 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.91735e6 | 0.850567 | 0.425283 | − | 0.905060i | \(-0.360174\pi\) | ||||
0.425283 | + | 0.905060i | \(0.360174\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.66884e6 | 0.157948 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.34913e7 | −1.26705 | −0.633523 | − | 0.773724i | \(-0.718392\pi\) | ||||
−0.633523 | + | 0.773724i | \(0.718392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 136162. | 0.0126895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.64900e6 | 0.522420 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.38594e6 | −0.402513 | −0.201256 | − | 0.979539i | \(-0.564502\pi\) | ||||
−0.201256 | + | 0.979539i | \(0.564502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.42443e6 | −0.311879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.92789e6 | 0.174248 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.23076e6 | −0.827988 | −0.413994 | − | 0.910280i | \(-0.635866\pi\) | ||||
−0.413994 | + | 0.910280i | \(0.635866\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 880035. | 0.0783423 | 0.0391711 | − | 0.999233i | \(-0.487528\pi\) | ||||
0.0391711 | + | 0.999233i | \(0.487528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.63643e7 | 1.44582 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.57052e6 | 0.225407 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.69434e6 | 0.408564 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.29417e7 | 1.11796 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.68360e6 | 0.401581 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.80265e6 | 0.238524 | 0.119262 | − | 0.992863i | \(-0.461947\pi\) | ||||
0.119262 | + | 0.992863i | \(0.461947\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.93905e6 | 0.163806 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.05399e7 | 0.883822 | 0.441911 | − | 0.897059i | \(-0.354301\pi\) | ||||
0.441911 | + | 0.897059i | \(0.354301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.26731e6 | −0.688161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.40510e6 | 0.116102 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.50195e7 | −1.23198 | −0.615989 | − | 0.787755i | \(-0.711243\pi\) | ||||
−0.615989 | + | 0.787755i | \(0.711243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.29949e6 | 0.268670 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.61649e6 | −0.696528 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.32625e7 | −1.86684 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.82611e7 | 1.45489 | 0.727446 | − | 0.686165i | \(-0.240707\pi\) | ||||
0.727446 | + | 0.686165i | \(0.240707\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.54979e6 | 0.201684 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.82669e6 | −0.457572 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.55484e7 | 2.77165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.56040e6 | −0.275617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.06422e6 | 0.542961 | 0.271481 | − | 0.962444i | \(-0.412487\pi\) | ||||
0.271481 | + | 0.962444i | \(0.412487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.02945e6 | −0.231193 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.10402e6 | 0.0836574 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.98536e6 | −0.450341 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.59888e7 | 1.19454 | 0.597269 | − | 0.802041i | \(-0.296252\pi\) | ||||
0.597269 | + | 0.802041i | \(0.296252\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.06451e6 | 0.153159 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.65409e6 | −0.195520 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.69453e6 | −0.416574 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.93931e6 | 0.722035 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.77395e7 | 1.27974 | 0.639868 | − | 0.768485i | \(-0.278989\pi\) | ||||
0.639868 | + | 0.768485i | \(0.278989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.36935e6 | 0.241384 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.93517e6 | −0.706854 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.36037e7 | −1.66777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.80420e7 | 1.26604 | 0.633020 | − | 0.774135i | \(-0.281815\pi\) | ||||
0.633020 | + | 0.774135i | \(0.281815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.48976e7 | −1.03115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.81120e7 | −1.24511 | −0.622555 | − | 0.782576i | \(-0.713905\pi\) | ||||
−0.622555 | + | 0.782576i | \(0.713905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 224396. | 0.0153213 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −762914. | −0.0517376 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.22649e7 | 0.826142 | 0.413071 | − | 0.910699i | \(-0.364456\pi\) | ||||
0.413071 | + | 0.910699i | \(0.364456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.99781e6 | 0.601993 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.15977e6 | 0.0770727 | 0.0385363 | − | 0.999257i | \(-0.487730\pi\) | ||||
0.0385363 | + | 0.999257i | \(0.487730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.74575e6 | 0.313266 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.44159e6 | −0.422369 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71567e7 | −1.11745 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.28675e7 | −1.47952 | −0.739758 | − | 0.672873i | \(-0.765060\pi\) | ||||
−0.739758 | + | 0.672873i | \(0.765060\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.26816e7 | −0.815054 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.33500e6 | 0.596001 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.04495e7 | −1.29701 | −0.648505 | − | 0.761210i | \(-0.724606\pi\) | ||||
−0.648505 | + | 0.761210i | \(0.724606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.19797e6 | −0.0754818 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.13704e6 | 0.258957 | 0.129479 | − | 0.991582i | \(-0.458670\pi\) | ||||
0.129479 | + | 0.991582i | \(0.458670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.89576e7 | −1.17889 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.02688e6 | 0.187000 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −567848. | −0.0348533 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.34189e7 | 1.42807 | 0.714037 | − | 0.700108i | \(-0.246865\pi\) | ||||
0.714037 | + | 0.700108i | \(0.246865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.25987e6 | −0.136914 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.26269e6 | 0.136200 | 0.0681000 | − | 0.997678i | \(-0.478306\pi\) | ||||
0.0681000 | + | 0.997678i | \(0.478306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.33451e7 | 0.798118 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.58021e6 | 0.212743 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.95461e7 | 1.15403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.65320e6 | 0.507632 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.46914e6 | −0.377087 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 192967. | 0.0111766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.10877e7 | −1.78917 | −0.894586 | − | 0.446896i | \(-0.852529\pi\) | ||||
−0.894586 | + | 0.446896i | \(0.852529\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.31436e7 | −0.751659 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.05386e7 | −0.598885 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.95325e7 | −1.10300 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.30284e6 | −0.241456 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.36116e6 | 0.243196 | 0.121598 | − | 0.992579i | \(-0.461198\pi\) | ||||
0.121598 | + | 0.992579i | \(0.461198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.85553e6 | −0.546152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.38031e6 | 0.406437 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.98887e6 | 0.327760 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.42728e6 | 0.0776280 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.23869e6 | −0.499375 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.01001e7 | 0.542568 | 0.271284 | − | 0.962499i | \(-0.412552\pi\) | ||||
0.271284 | + | 0.962499i | \(0.412552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.25188e7 | −0.668360 | −0.334180 | − | 0.942509i | \(-0.608459\pi\) | ||||
−0.334180 | + | 0.942509i | \(0.608459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.10971e7 | −1.11943 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.76805e6 | −0.145975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.19137e6 | −0.429340 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.06336e7 | −0.553951 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.44647e6 | 0.385560 | 0.192780 | − | 0.981242i | \(-0.438250\pi\) | ||||
0.192780 | + | 0.981242i | \(0.438250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.59841e7 | 1.33724 | 0.668619 | − | 0.743605i | \(-0.266886\pi\) | ||||
0.668619 | + | 0.743605i | \(0.266886\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.02356e6 | 0.308119 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.71328e6 | −0.137953 | −0.0689765 | − | 0.997618i | \(-0.521973\pi\) | ||||
−0.0689765 | + | 0.997618i | \(0.521973\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.59063e7 | −0.803867 | −0.401933 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401933 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.72805e6 | 0.388210 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00317e6 | −0.100024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.81796e6 | −0.0902336 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.65752e6 | 0.180457 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.05208e7 | −0.515991 | −0.257996 | − | 0.966146i | \(-0.583062\pi\) | ||||
−0.257996 | + | 0.966146i | \(0.583062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.82366e7 | 2.83926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.03306e7 | −0.985331 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.57409e7 | 0.758380 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.22273e7 | −0.585628 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.22254e7 | −0.582094 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.68210e6 | −0.0796210 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.04557e6 | −0.143316 | −0.0716582 | − | 0.997429i | \(-0.522829\pi\) | ||||
−0.0716582 | + | 0.997429i | \(0.522829\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.66432e6 | 0.0778611 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.54022e7 | −1.18146 | −0.590731 | − | 0.806868i | \(-0.701161\pi\) | ||||
−0.590731 | + | 0.806868i | \(0.701161\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.29634e7 | −1.52423 | −0.762114 | − | 0.647443i | \(-0.775838\pi\) | ||||
−0.762114 | + | 0.647443i | \(0.775838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.30996e7 | −1.06193 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.82024e7 | 1.28902 | 0.644510 | − | 0.764596i | \(-0.277061\pi\) | ||||
0.644510 | + | 0.764596i | \(0.277061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.55196e6 | 0.297736 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.42421e7 | −0.643468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.41329e6 | 0.288092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.18165e6 | 0.142104 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.35278e6 | −0.237708 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.56080e7 | −0.689171 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.55923e7 | −1.56263 | −0.781316 | − | 0.624136i | \(-0.785451\pi\) | ||||
−0.781316 | + | 0.624136i | \(0.785451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.48456e6 | −0.414042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.51982e7 | 1.09378 | 0.546889 | − | 0.837205i | \(-0.315812\pi\) | ||||
0.546889 | + | 0.837205i | \(0.315812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.18247e6 | 0.396331 | 0.198165 | − | 0.980169i | \(-0.436502\pi\) | ||||
0.198165 | + | 0.980169i | \(0.436502\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −105034. | −0.00450789 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.18530e7 | −0.932612 | −0.466306 | − | 0.884623i | \(-0.654415\pi\) | ||||
−0.466306 | + | 0.884623i | \(0.654415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 967573. | 0.0410610 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.65089e6 | 0.0696666 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.41901e6 | −0.227401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.87209e6 | 0.328498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.99602e6 | 0.207321 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.45224e7 | −1.83730 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84112e7 | 1.57633 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.68056e6 | 0.395077 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.21102e7 | 0.491509 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.65912e7 | 1.47692 | 0.738462 | − | 0.674295i | \(-0.235552\pi\) | ||||
0.738462 | + | 0.674295i | \(0.235552\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.87530e6 | −0.155559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.17284e6 | −0.166585 | −0.0832925 | − | 0.996525i | \(-0.526544\pi\) | ||||
−0.0832925 | + | 0.996525i | \(0.526544\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00104e7 | −0.794474 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.61290e6 | −0.142660 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.98644e7 | −0.780104 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.44852e6 | −0.329983 | −0.164992 | − | 0.986295i | \(-0.552760\pi\) | ||||
−0.164992 | + | 0.986295i | \(0.552760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.30252e6 | −0.0505981 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.60873e7 | −1.39428 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.45780e6 | 0.325015 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.18153e6 | 0.0833800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.57958e7 | −1.74095 | −0.870476 | − | 0.492211i | \(-0.836189\pi\) | ||||
−0.870476 | + | 0.492211i | \(0.836189\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.10143e6 | −0.0416470 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.91369e6 | −0.372847 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.40285e6 | 0.351747 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.99626e7 | −1.85907 | −0.929536 | − | 0.368732i | \(-0.879792\pi\) | ||||
−0.929536 | + | 0.368732i | \(0.879792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.11336e6 | 0.337298 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.50119e6 | 0.0920814 | 0.0460407 | − | 0.998940i | \(-0.485340\pi\) | ||||
0.0460407 | + | 0.998940i | \(0.485340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.08529e7 | 0.397437 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.96689e6 | −0.0716474 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.59210e6 | −0.0576893 | −0.0288446 | − | 0.999584i | \(-0.509183\pi\) | ||||
−0.0288446 | + | 0.999584i | \(0.509183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.49760e7 | −0.900237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.37491e6 | −0.192717 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.66688e7 | −0.594528 | −0.297264 | − | 0.954795i | \(-0.596074\pi\) | ||||
−0.297264 | + | 0.954795i | \(0.596074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.28689e6 | −0.258544 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.00960e7 | −0.709301 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.91396e7 | 0.672027 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.45707e6 | −0.120753 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.11083e7 | −0.385996 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.71623e7 | 0.593278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.17727e7 | 1.09267 | 0.546334 | − | 0.837567i | \(-0.316023\pi\) | ||||
0.546334 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.48573e7 | −0.508311 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.25778e7 | −0.428112 | −0.214056 | − | 0.976821i | \(-0.568668\pi\) | ||||
−0.214056 | + | 0.976821i | \(0.568668\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.37994e7 | −1.14453 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.51206e7 | −0.846289 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.21153e7 | −0.406066 | −0.203033 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203033 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.29265e7 | 0.764507 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22744e7 | −0.407218 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.70328e7 | −1.88253 | −0.941263 | − | 0.337675i | \(-0.890360\pi\) | ||||
−0.941263 | + | 0.337675i | \(0.890360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 496238. | 0.0162967 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.40419e6 | 0.209253 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.54825e6 | −0.147861 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.45826e6 | −0.241242 | −0.120621 | − | 0.992699i | \(-0.538489\pi\) | ||||
−0.120621 | + | 0.992699i | \(0.538489\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.08102e7 | 0.991567 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.52163e6 | 0.0487251 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.46400e7 | −0.466447 | −0.233224 | − | 0.972423i | \(-0.574927\pi\) | ||||
−0.233224 | + | 0.972423i | \(0.574927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.31805e6 | 0.0734868 |
(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 | 1104.6.a.ba.1.5 | 8 | ||
4.3 | odd | 2 | 552.6.a.i.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.6.a.i.1.5 | ✓ | 8 | 4.3 | odd | 2 | ||
1104.6.a.ba.1.5 | 8 | 1.1 | even | 1 | trivial |