Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 198x^{2} + 43x + 5999 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 224) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.08658\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −8.17317 | −0.524309 | −0.262154 | − | 0.965026i | \(-0.584433\pi\) | ||||
−0.262154 | + | 0.965026i | \(0.584433\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.6340 | 0.369111 | 0.184556 | − | 0.982822i | \(-0.440915\pi\) | ||||
0.184556 | + | 0.982822i | \(0.440915\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −176.199 | −0.725100 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −506.585 | −1.26232 | −0.631162 | − | 0.775651i | \(-0.717422\pi\) | ||||
−0.631162 | + | 0.775651i | \(0.717422\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −635.256 | −1.04253 | −0.521267 | − | 0.853394i | \(-0.674540\pi\) | ||||
−0.521267 | + | 0.853394i | \(0.674540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −168.645 | −0.193528 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −716.795 | −0.601551 | −0.300775 | − | 0.953695i | \(-0.597245\pi\) | ||||
−0.300775 | + | 0.953695i | \(0.597245\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1380.65 | 0.877405 | 0.438702 | − | 0.898632i | \(-0.355438\pi\) | ||||
0.438702 | + | 0.898632i | \(0.355438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 400.485 | 0.198170 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 354.448 | 0.139712 | 0.0698558 | − | 0.997557i | \(-0.477746\pi\) | ||||
0.0698558 | + | 0.997557i | \(0.477746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2699.24 | −0.863757 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3426.19 | 0.904485 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6242.07 | 1.37827 | 0.689134 | − | 0.724634i | \(-0.257991\pi\) | ||||
0.689134 | + | 0.724634i | \(0.257991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1377.52 | −0.257450 | −0.128725 | − | 0.991680i | \(-0.541088\pi\) | ||||
−0.128725 | + | 0.991680i | \(0.541088\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4140.41 | 0.661848 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1011.06 | −0.139511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11674.8 | −1.40199 | −0.700993 | − | 0.713168i | \(-0.747260\pi\) | ||||
−0.700993 | + | 0.713168i | \(0.747260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5192.05 | 0.546610 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4460.60 | −0.414413 | −0.207206 | − | 0.978297i | \(-0.566437\pi\) | ||||
−0.207206 | + | 0.978297i | \(0.566437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21996.6 | 1.81419 | 0.907097 | − | 0.420922i | \(-0.138293\pi\) | ||||
0.907097 | + | 0.420922i | \(0.138293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3635.69 | −0.267643 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −25906.3 | −1.71065 | −0.855325 | − | 0.518092i | \(-0.826643\pi\) | ||||
−0.855325 | + | 0.518092i | \(0.826643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5858.48 | 0.315399 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5048.64 | −0.246879 | −0.123440 | − | 0.992352i | \(-0.539393\pi\) | ||||
−0.123440 | + | 0.992352i | \(0.539393\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10452.9 | −0.465938 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11284.3 | −0.460031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2119.87 | −0.0792828 | −0.0396414 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396414 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8844.91 | −0.304347 | −0.152173 | − | 0.988354i | \(-0.548627\pi\) | ||||
−0.152173 | + | 0.988354i | \(0.548627\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8633.77 | 0.274062 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13107.8 | −0.384811 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50339.9 | 1.37002 | 0.685008 | − | 0.728535i | \(-0.259799\pi\) | ||||
0.685008 | + | 0.728535i | \(0.259799\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2896.96 | −0.0732520 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13753.2 | 0.323786 | 0.161893 | − | 0.986808i | \(-0.448240\pi\) | ||||
0.161893 | + | 0.986808i | \(0.448240\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39915.1 | 0.876658 | 0.438329 | − | 0.898815i | \(-0.355570\pi\) | ||||
0.438329 | + | 0.898815i | \(0.355570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22061.3 | 0.452875 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24822.7 | 0.477114 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −66614.9 | −1.20089 | −0.600445 | − | 0.799666i | \(-0.705010\pi\) | ||||
−0.600445 | + | 0.799666i | \(0.705010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14813.6 | 0.250870 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 80813.7 | 1.28763 | 0.643813 | − | 0.765183i | \(-0.277352\pi\) | ||||
0.643813 | + | 0.765183i | \(0.277352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14790.3 | −0.222039 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −51017.5 | −0.722638 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17914.3 | 0.239731 | 0.119866 | − | 0.992790i | \(-0.461754\pi\) | ||||
0.119866 | + | 0.992790i | \(0.461754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 31127.5 | 0.394041 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11258.7 | 0.134983 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28488.3 | 0.323860 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −154822. | −1.67072 | −0.835360 | − | 0.549704i | \(-0.814741\pi\) | ||||
−0.835360 | + | 0.549704i | \(0.814741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 89260.0 | 0.915311 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 98993.4 | 0.965612 | 0.482806 | − | 0.875727i | \(-0.339618\pi\) | ||||
0.482806 | + | 0.875727i | \(0.339618\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 167746. | 1.55797 | 0.778983 | − | 0.627045i | \(-0.215736\pi\) | ||||
0.778983 | + | 0.627045i | \(0.215736\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8263.59 | 0.0731468 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 131142. | 1.10734 | 0.553671 | − | 0.832735i | \(-0.313226\pi\) | ||||
0.553671 | + | 0.832735i | \(0.313226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49878.7 | −0.402114 | −0.201057 | − | 0.979580i | \(-0.564438\pi\) | ||||
−0.201057 | + | 0.979580i | \(0.564438\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 95419.7 | 0.735074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 155443. | 1.14519 | 0.572593 | − | 0.819839i | \(-0.305937\pi\) | ||||
0.572593 | + | 0.819839i | \(0.305937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7313.66 | 0.0515691 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 111932. | 0.755941 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 35122.9 | 0.227365 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 95577.5 | 0.593461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 36457.2 | 0.217280 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −120177. | −0.687934 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 141092. | 0.776234 | 0.388117 | − | 0.921610i | \(-0.373126\pi\) | ||||
0.388117 | + | 0.921610i | \(0.373126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −179782. | −0.951198 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −133498. | −0.679669 | −0.339834 | − | 0.940485i | \(-0.610371\pi\) | ||||
−0.339834 | + | 0.940485i | \(0.610371\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −67651.9 | −0.331628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 70695.8 | 0.333856 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 66087.7 | 0.300829 | 0.150414 | − | 0.988623i | \(-0.451939\pi\) | ||||
0.150414 | + | 0.988623i | \(0.451939\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 131816. | 0.578670 | 0.289335 | − | 0.957228i | \(-0.406566\pi\) | ||||
0.289335 | + | 0.957228i | \(0.406566\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 211737. | 0.896909 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 321811. | 1.31602 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 128799. | 0.508734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −19623.8 | −0.0749013 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −25250.6 | −0.0931764 | −0.0465882 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465882 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 207999. | 0.742369 | 0.371184 | − | 0.928559i | \(-0.378952\pi\) | ||||
0.371184 | + | 0.928559i | \(0.378952\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 126299. | 0.436185 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28423.6 | −0.0950276 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −129188. | −0.418287 | −0.209143 | − | 0.977885i | \(-0.567068\pi\) | ||||
−0.209143 | + | 0.977885i | \(0.567068\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 41263.3 | 0.129441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17367.9 | −0.0528060 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 190635. | 0.561996 | 0.280998 | − | 0.959708i | \(-0.409335\pi\) | ||||
0.280998 | + | 0.959708i | \(0.409335\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 85432.9 | 0.244295 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 314255. | 0.871949 | 0.435975 | − | 0.899959i | \(-0.356404\pi\) | ||||
0.435975 | + | 0.899959i | \(0.356404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32256.6 | 0.0868765 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −243270. | −0.636206 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −533441. | −1.35510 | −0.677550 | − | 0.735477i | \(-0.736958\pi\) | ||||
−0.677550 | + | 0.735477i | \(0.736958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 132263. | 0.326469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17326.0 | 0.0415687 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −532404. | −1.24196 | −0.620982 | − | 0.783825i | \(-0.713266\pi\) | ||||
−0.620982 | + | 0.783825i | \(0.713266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 439799. | 0.997834 | 0.498917 | − | 0.866650i | \(-0.333731\pi\) | ||||
0.498917 | + | 0.866650i | \(0.333731\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 72290.9 | 0.159572 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −240896. | −0.517489 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 363118. | 0.759352 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −167883. | −0.341863 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 253509. | 0.502817 | 0.251408 | − | 0.967881i | \(-0.419106\pi\) | ||||
0.251408 | + | 0.967881i | \(0.419106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −456826. | −0.882791 | −0.441396 | − | 0.897313i | \(-0.645516\pi\) | ||||
−0.441396 | + | 0.897313i | \(0.645516\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 107132. | 0.201760 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −281017. | −0.515902 | −0.257951 | − | 0.966158i | \(-0.583047\pi\) | ||||
−0.257951 | + | 0.966158i | \(0.583047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 889110. | 1.59156 | 0.795780 | − | 0.605586i | \(-0.207061\pi\) | ||||
0.795780 | + | 0.605586i | \(0.207061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −411437. | −0.718312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −305861. | −0.520936 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −92039.7 | −0.152964 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −62453.4 | −0.101305 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −699417. | −1.10757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 265521. | 0.410575 | 0.205288 | − | 0.978702i | \(-0.434187\pi\) | ||||
0.205288 | + | 0.978702i | \(0.434187\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −112407. | −0.169764 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 453876. | 0.669639 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 67498.3 | 0.0973068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −326233. | −0.459640 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 455348. | 0.627137 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −737166. | −0.992666 | −0.496333 | − | 0.868132i | \(-0.665320\pi\) | ||||
−0.496333 | + | 0.868132i | \(0.665320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 475604. | 0.626310 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.36368e6 | 1.75650 | 0.878250 | − | 0.478202i | \(-0.158711\pi\) | ||||
0.878250 | + | 0.478202i | \(0.158711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 204640. | 0.257871 | 0.128936 | − | 0.991653i | \(-0.458844\pi\) | ||||
0.128936 | + | 0.991653i | \(0.458844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −202880. | −0.250155 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 617695. | 0.745391 | 0.372696 | − | 0.927954i | \(-0.378434\pi\) | ||||
0.372696 | + | 0.927954i | \(0.378434\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −534550. | −0.631420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 544455. | 0.629638 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −288474. | −0.326672 | −0.163336 | − | 0.986571i | \(-0.552225\pi\) | ||||
−0.163336 | + | 0.986571i | \(0.552225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.52454e6 | 1.69082 | 0.845408 | − | 0.534121i | \(-0.179358\pi\) | ||||
0.845408 | + | 0.534121i | \(0.179358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −953638. | −1.03602 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 49542.1 | 0.0527302 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −877066. | −0.914724 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −660504. | −0.675113 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −263840. | −0.264336 | −0.132168 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132168 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −179558. | −0.176361 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 120884. | 0.116417 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −38044.1 | −0.0359298 | −0.0179649 | − | 0.999839i | \(-0.505719\pi\) | ||||
−0.0179649 | + | 0.999839i | \(0.505719\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 572063. | 0.529901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.09985e6 | −0.999382 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.17804e6 | −1.05019 | −0.525097 | − | 0.851042i | \(-0.675971\pi\) | ||||
−0.525097 | + | 0.851042i | \(0.675971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −104173. | −0.0911259 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −146416. | −0.125693 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 530015. | 0.446588 | 0.223294 | − | 0.974751i | \(-0.428319\pi\) | ||||
0.223294 | + | 0.974751i | \(0.428319\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.69277e6 | −1.40015 | −0.700075 | − | 0.714069i | \(-0.746850\pi\) | ||||
−0.700075 | + | 0.714069i | \(0.746850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −254410. | −0.206599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.36740e6 | 1.09034 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 267761. | 0.209676 | 0.104838 | − | 0.994489i | \(-0.466568\pi\) | ||||
0.104838 | + | 0.994489i | \(0.466568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 242717. | 0.186677 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21948e6 | 0.921319 | 0.460659 | − | 0.887577i | \(-0.347613\pi\) | ||||
0.460659 | + | 0.887577i | \(0.347613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −234277. | −0.173886 | −0.0869429 | − | 0.996213i | \(-0.527710\pi\) | ||||
−0.0869429 | + | 0.996213i | \(0.527710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −232839. | −0.169803 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 218569. | 0.156633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −906063. | −0.638136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.26539e6 | 0.875973 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.75507e6 | 1.19434 | 0.597168 | − | 0.802116i | \(-0.296293\pi\) | ||||
0.597168 | + | 0.802116i | \(0.296293\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −43741.3 | −0.0292642 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.73566e6 | −1.14175 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −225165. | −0.145654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07783e6 | −0.685701 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −809089. | −0.506279 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −182505. | −0.112338 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.11032e6 | 0.672360 | 0.336180 | − | 0.941798i | \(-0.390865\pi\) | ||||
0.336180 | + | 0.941798i | \(0.390865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.37101e6 | −0.816856 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.69745e6 | −1.58144 | −0.790719 | − | 0.612179i | \(-0.790293\pi\) | ||||
−0.790719 | + | 0.612179i | \(0.790293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.33517e6 | 1.92423 | 0.962114 | − | 0.272646i | \(-0.0878988\pi\) | ||||
0.962114 | + | 0.272646i | \(0.0878988\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 178149. | 0.101159 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.01830e6 | −1.68700 | −0.843498 | − | 0.537133i | \(-0.819507\pi\) | ||||
−0.843498 | + | 0.537133i | \(0.819507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.16214e6 | −1.73982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.07184e6 | −0.580590 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −989643. | −0.527804 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.71471e6 | 0.900496 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 407667. | 0.210832 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.26941e6 | 0.646565 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.26736e6 | −1.13750 | −0.568748 | − | 0.822512i | \(-0.692572\pi\) | ||||
−0.568748 | + | 0.822512i | \(0.692572\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.05708e6 | 1.01658 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.03871e6 | 0.505689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28130.5 | −0.0134928 | −0.00674641 | − | 0.999977i | \(-0.502147\pi\) | ||||
−0.00674641 | + | 0.999977i | \(0.502147\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.27047e6 | −0.600432 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 697829. | 0.324985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −59775.7 | −0.0270382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.55790e6 | −1.58624 | −0.793122 | − | 0.609063i | \(-0.791546\pi\) | ||||
−0.793122 | + | 0.609063i | \(0.791546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.81954e6 | 1.23913 | 0.619563 | − | 0.784947i | \(-0.287310\pi\) | ||||
0.619563 | + | 0.784947i | \(0.287310\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.17650e6 | −0.942956 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.19876e6 | −0.512030 | −0.256015 | − | 0.966673i | \(-0.582410\pi\) | ||||
−0.256015 | + | 0.966673i | \(0.582410\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 283783. | 0.119513 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −287066. | −0.119209 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 224779. | 0.0920492 | 0.0460246 | − | 0.998940i | \(-0.485345\pi\) | ||||
0.0460246 | + | 0.998940i | \(0.485345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −569902. | −0.230161 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −781171. | −0.311157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 823607. | 0.323584 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.39774e6 | −0.929261 | −0.464631 | − | 0.885505i | \(-0.653813\pi\) | ||||
−0.464631 | + | 0.885505i | \(0.653813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 785954. | 0.300491 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 247383. | 0.0933115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 295184. | 0.109855 | 0.0549277 | − | 0.998490i | \(-0.482507\pi\) | ||||
0.0549277 | + | 0.998490i | \(0.482507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 982227. | 0.360690 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.96531e6 | −1.43689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.15015e6 | 0.768900 | 0.384450 | − | 0.923146i | \(-0.374391\pi\) | ||||
0.384450 | + | 0.923146i | \(0.374391\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.15317e6 | −0.406987 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.11282e6 | −1.78100 | −0.890499 | − | 0.454986i | \(-0.849644\pi\) | ||||
−0.890499 | + | 0.454986i | \(0.849644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 512190. | 0.176108 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.87578e6 | −1.31547 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.99434e6 | −0.668230 | −0.334115 | − | 0.942532i | \(-0.608437\pi\) | ||||
−0.334115 | + | 0.942532i | \(0.608437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −254066. | −0.0840436 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.09110e6 | 0.356356 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.37453e6 | −0.443262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −191644. | −0.0610267 | −0.0305133 | − | 0.999534i | \(-0.509714\pi\) | ||||
−0.0305133 | + | 0.999534i | \(0.509714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 552930. | 0.173875 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.69084e6 | 1.45677 | 0.728383 | − | 0.685170i | \(-0.240272\pi\) | ||||
0.728383 | + | 0.685170i | \(0.240272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 875074. | 0.268400 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 305664. | 0.0925991 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.91426e6 | 1.76976 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.85501e6 | −1.13951 | −0.569754 | − | 0.821815i | \(-0.692962\pi\) | ||||
−0.569754 | + | 0.821815i | \(0.692962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −540146. | −0.157727 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 103874. | 0.0299661 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.66751e6 | 0.475277 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.07735e6 | −0.303402 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 107560. | 0.0299307 | 0.0149654 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149654 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.61644e6 | −1.54439 | −0.772193 | − | 0.635388i | \(-0.780840\pi\) | ||||
−0.772193 | + | 0.635388i | \(0.780840\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.56468e6 | 1.24039 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.93480e6 | 0.519594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 433401. | 0.115032 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.63022e6 | −0.689998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.57448e6 | 1.18617 | 0.593087 | − | 0.805138i | \(-0.297909\pi\) | ||||
0.593087 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.44508e6 | −1.90831 | −0.954157 | − | 0.299307i | \(-0.903244\pi\) | ||||
−0.954157 | + | 0.299307i | \(0.903244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.05269e6 | −0.266734 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 489368. | 0.122584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.16275e6 | 0.535605 | 0.267803 | − | 0.963474i | \(-0.413702\pi\) | ||||
0.267803 | + | 0.963474i | \(0.413702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −423055. | −0.103586 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.75516e6 | −1.39331 | −0.696655 | − | 0.717406i | \(-0.745329\pi\) | ||||
−0.696655 | + | 0.717406i | \(0.745329\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 369642. | 0.0884875 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 206377. | 0.0488532 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.25653e6 | 1.69869 | 0.849343 | − | 0.527841i | \(-0.176998\pi\) | ||||
0.849343 | + | 0.527841i | \(0.176998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.25967e6 | 0.523123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.70001e6 | −0.389231 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 642284. | 0.145445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.83702e6 | 0.859417 | 0.429709 | − | 0.902968i | \(-0.358616\pi\) | ||||
0.429709 | + | 0.902968i | \(0.358616\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.45587e6 | −0.544094 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.45089e6 | 1.85204 | 0.926020 | − | 0.377475i | \(-0.123208\pi\) | ||||
0.926020 | + | 0.377475i | \(0.123208\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.84019e6 | −0.398943 | −0.199471 | − | 0.979904i | \(-0.563923\pi\) | ||||
−0.199471 | + | 0.979904i | \(0.563923\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 232311. | 0.0498238 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.94986e6 | −0.413725 | −0.206862 | − | 0.978370i | \(-0.566325\pi\) | ||||
−0.206862 | + | 0.978370i | \(0.566325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.46666e6 | −0.517818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.05588e6 | 0.219311 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.11431e7 | −2.29010 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.72671e6 | −0.757864 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 889566. | 0.179012 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −399165. | −0.0794901 | −0.0397451 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397451 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.41646e6 | 1.46162 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 141951. | 0.0276867 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.19459e6 | −0.616681 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.33763e6 | −1.21089 | −0.605444 | − | 0.795888i | \(-0.707005\pi\) | ||||
−0.605444 | + | 0.795888i | \(0.707005\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.55809e6 | −0.294659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.67112e6 | −0.687218 | −0.343609 | − | 0.939113i | \(-0.611650\pi\) | ||||
−0.343609 | + | 0.939113i | \(0.611650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.47428e6 | −0.829098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.84179e6 | 0.337852 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −673906. | −0.122379 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.03184e6 | 1.62377 | 0.811886 | − | 0.583816i | \(-0.198441\pi\) | ||||
0.811886 | + | 0.583816i | \(0.198441\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.56846e6 | −0.457171 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.08465e7 | 1.91148 | 0.955739 | − | 0.294217i | \(-0.0950588\pi\) | ||||
0.955739 | + | 0.294217i | \(0.0950588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.04262e6 | 0.356418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −263639. | −0.0455501 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.09958e6 | 0.872449 | 0.436224 | − | 0.899838i | \(-0.356315\pi\) | ||||
0.436224 | + | 0.899838i | \(0.356315\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.95584e6 | −0.331346 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.73037e6 | 0.793600 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.46125e6 | 0.575063 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.31238e7 | 2.15939 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.35991e6 | 0.710491 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 282838. | 0.0456503 | 0.0228252 | − | 0.999739i | \(-0.492734\pi\) | ||||
0.0228252 | + | 0.999739i | \(0.492734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 814044. | 0.130135 | 0.0650674 | − | 0.997881i | \(-0.479274\pi\) | ||||
0.0650674 | + | 0.997881i | \(0.479274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.08101e6 | −0.171171 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 987396. | 0.154869 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.31071e6 | −0.980481 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 373519. | 0.0574880 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.83362e6 | 0.432039 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.70598e6 | 0.408733 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.35143e6 | 0.651172 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.21631e6 | −0.180332 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20661e6 | −0.617930 | −0.308965 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308965 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.59455e6 | −0.523173 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.02919e6 | −0.148425 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.24593e6 | 1.17834 | 0.589171 | − | 0.808009i | \(-0.299455\pi\) | ||||
0.589171 | + | 0.808009i | \(0.299455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.55847e6 | 0.220682 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.61812e6 | 1.20930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.26413e6 | 0.453894 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.96889e6 | 0.271324 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 969510. | 0.132408 | 0.0662040 | − | 0.997806i | \(-0.478911\pi\) | ||||
0.0662040 | + | 0.997806i | \(0.478911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.39734e7 | −1.89136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.96782e6 | −0.398135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.58996e6 | 1.27510 | 0.637552 | − | 0.770407i | \(-0.279947\pi\) | ||||
0.637552 | + | 0.770407i | \(0.279947\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.20741e6 | 0.422701 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −725869. | −0.0948201 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.56904e6 | −0.850592 | −0.425296 | − | 0.905054i | \(-0.639830\pi\) | ||||
−0.425296 | + | 0.905054i | \(0.639830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 51314.1 | 0.00658638 | 0.00329319 | − | 0.999995i | \(-0.498952\pi\) | ||||
0.00329319 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.07197e6 | −0.263631 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −956739. | −0.120677 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.11070e7 | −1.38886 | −0.694430 | − | 0.719560i | \(-0.744343\pi\) | ||||
−0.694430 | + | 0.719560i | \(0.744343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.73372e6 | 0.462855 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.95987e6 | −0.486677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.55756e6 | 0.311641 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.30959e6 | 0.279027 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.36125e6 | 1.12134 | 0.560672 | − | 0.828038i | \(-0.310543\pi\) | ||||
0.560672 | + | 0.828038i | \(0.310543\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.90187e6 | −0.225887 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.29680e6 | 0.270492 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.35675e7 | 1.58440 | 0.792198 | − | 0.610264i | \(-0.208937\pi\) | ||||
0.792198 | + | 0.610264i | \(0.208937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 724725. | 0.0839230 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.26684e6 | −0.834469 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.24270e7 | 1.41514 | 0.707569 | − | 0.706644i | \(-0.249792\pi\) | ||||
0.707569 | + | 0.706644i | \(0.249792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.31586e6 | −0.261532 | −0.130766 | − | 0.991413i | \(-0.541744\pi\) | ||||
−0.130766 | + | 0.991413i | \(0.541744\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.86987e6 | −0.993399 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.97214e6 | 0.219053 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.12911e6 | −0.344706 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.49986e6 | 0.273131 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.64571e7 | 1.78341 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.56901e6 | 0.706071 | 0.353036 | − | 0.935610i | \(-0.385149\pi\) | ||||
0.353036 | + | 0.935610i | \(0.385149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 752256. | 0.0802006 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.77884e7 | 1.88115 | 0.940576 | − | 0.339583i | \(-0.110286\pi\) | ||||
0.940576 | + | 0.339583i | \(0.110286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.09519e6 | 0.639382 | 0.319691 | − | 0.947522i | \(-0.396421\pi\) | ||||
0.319691 | + | 0.947522i | \(0.396421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.21440e6 | 0.126367 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −877800. | −0.0906098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.95540e6 | 0.609833 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.71645e6 | 0.580708 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.36840e6 | 0.843366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.65385e7 | −1.65357 | −0.826783 | − | 0.562521i | \(-0.809832\pi\) | ||||
−0.826783 | + | 0.562521i | \(0.809832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.17015e6 | −0.215268 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.91128e6 | 0.286517 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52525e6 | −0.148933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.42330e6 | −0.234777 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.32064e7 | −1.26952 | −0.634761 | − | 0.772708i | \(-0.718902\pi\) | ||||
−0.634761 | + | 0.772708i | \(0.718902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.94568e6 | 0.567119 | 0.283560 | − | 0.958955i | \(-0.408485\pi\) | ||||
0.283560 | + | 0.958955i | \(0.408485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.70960e6 | −0.351098 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.93647e6 | 0.933193 | 0.466597 | − | 0.884470i | \(-0.345480\pi\) | ||||
0.466597 | + | 0.884470i | \(0.345480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.07389e6 | 0.100081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −551675. | −0.0510188 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.45044e6 | −0.867300 | −0.433650 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433650 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.75460e6 | −0.250873 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.03302e6 | −0.635665 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.78565e6 | 0.788062 | 0.394031 | − | 0.919097i | \(-0.371080\pi\) | ||||
0.394031 | + | 0.919097i | \(0.371080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 313228. | 0.0278841 | 0.0139421 | − | 0.999903i | \(-0.495562\pi\) | ||||
0.0139421 | + | 0.999903i | \(0.495562\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.72163e6 | −0.328814 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.39593e6 | −0.122408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.21249e6 | 0.192560 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.02498e6 | 0.520464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.48070e6 | 0.384184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.95224e6 | 0.251254 | 0.125627 | − | 0.992078i | \(-0.459906\pi\) | ||||
0.125627 | + | 0.992078i | \(0.459906\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.24810e6 | −0.781255 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.36433e6 | 0.365970 | 0.182985 | − | 0.983116i | \(-0.441424\pi\) | ||||
0.182985 | + | 0.983116i | \(0.441424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.58628e6 | 0.631472 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11456e7 | −0.920949 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.14494e6 | 0.422015 | 0.211008 | − | 0.977484i | \(-0.432326\pi\) | ||||
0.211008 | + | 0.977484i | \(0.432326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.36365e6 | 0.111039 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.67256e6 | −0.135204 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.20717e6 | 0.257380 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.02588e7 | 1.61405 | 0.807027 | − | 0.590514i | \(-0.201075\pi\) | ||||
0.807027 | + | 0.590514i | \(0.201075\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.37374e6 | −0.345955 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.71988e6 | 0.213593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.19733e6 | 0.249290 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.04852e6 | −0.390815 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.99355e7 | −1.53226 | −0.766128 | − | 0.642688i | \(-0.777819\pi\) | ||||
−0.766128 | + | 0.642688i | \(0.777819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.61188e7 | −1.23011 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.36897e6 | 0.331059 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.85068e6 | −0.364967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.08928e7 | −1.56092 | −0.780461 | − | 0.625204i | \(-0.785016\pi\) | ||||
−0.780461 | + | 0.625204i | \(0.785016\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17375e7 | 0.870766 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −488257. | −0.0359687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.64023e6 | 0.485756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.35775e6 | 0.171277 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.70208e6 | 0.483490 | 0.241745 | − | 0.970340i | \(-0.422280\pi\) | ||||
0.241745 | + | 0.970340i | \(0.422280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.21953e6 | −0.588856 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.24603e7 | −0.886510 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.68488e7 | −1.19049 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.01375e7 | −1.41309 | −0.706546 | − | 0.707668i | \(-0.749747\pi\) | ||||
−0.706546 | + | 0.707668i | \(0.749747\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.19452e6 | 0.292324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.57670e7 | −1.09133 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.39391e7 | 1.64569 | 0.822845 | − | 0.568266i | \(-0.192385\pi\) | ||||
0.822845 | + | 0.568266i | \(0.192385\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −404916. | −0.0276469 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.55015e7 | −1.72940 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.87678e6 | −0.126416 | −0.0632081 | − | 0.998000i | \(-0.520133\pi\) | ||||
−0.0632081 | + | 0.998000i | \(0.520133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.16841e6 | 0.479598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.28689e7 | 0.855202 | 0.427601 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427601 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −521019. | −0.0343925 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.42393e7 | −0.933657 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.42595e6 | −0.418536 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.28520e7 | −1.47851 | −0.739255 | − | 0.673425i | \(-0.764822\pi\) | ||||
−0.739255 | + | 0.673425i | \(0.764822\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.15641e6 | 0.138594 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.29185e6 | 0.274017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.57978e7 | 1.63622 | 0.818112 | − | 0.575059i | \(-0.195021\pi\) | ||||
0.818112 | + | 0.575059i | \(0.195021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.46756e6 | 0.0924678 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00550e7 | 0.629391 | 0.314696 | − | 0.949193i | \(-0.398098\pi\) | ||||
0.314696 | + | 0.949193i | \(0.398098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.44406e6 | 0.151985 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.60604e6 | 0.161001 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.34666e6 | 0.0826550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.06616e7 | 0.650139 | 0.325069 | − | 0.945690i | \(-0.394612\pi\) | ||||
0.325069 | + | 0.945690i | \(0.394612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 310941. | 0.0188383 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.29622e6 | −0.0780245 | −0.0390123 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390123 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.71825e6 | 0.222374 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.67557e6 | −0.277832 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.15853e6 | −0.363608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.96716e6 | −0.408722 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.13865e7 | 1.24662 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.66567e6 | −0.154394 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.29627e7 | −0.746036 | −0.373018 | − | 0.927824i | \(-0.621677\pi\) | ||||
−0.373018 | + | 0.927824i | \(0.621677\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.62829e6 | 0.550626 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.61673e6 | −0.432840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.61878e6 | 0.317292 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 851426. | 0.0477781 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.11336e7 | 1.17849 | 0.589247 | − | 0.807953i | \(-0.299425\pi\) | ||||
0.589247 | + | 0.807953i | \(0.299425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.85695e7 | 1.02904 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.15648e6 | −0.173829 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.02204e7 | −1.10663 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −358369. | −0.0194913 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.33190e6 | −0.234150 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.74328e7 | −1.47367 | −0.736834 | − | 0.676074i | \(-0.763680\pi\) | ||||
−0.736834 | + | 0.676074i | \(0.763680\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.45319e7 | −1.84360 | −0.921802 | − | 0.387660i | \(-0.873283\pi\) | ||||
−0.921802 | + | 0.387660i | \(0.873283\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.38353e7 | 0.734112 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.93355e6 | 0.207439 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.03696e7 | 1.59178 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.48465e6 | −0.285719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.22242e6 | −0.373960 | −0.186980 | − | 0.982364i | \(-0.559870\pi\) | ||||
−0.186980 | + | 0.982364i | \(0.559870\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.80242e7 | 0.927589 | 0.463795 | − | 0.885943i | \(-0.346488\pi\) | ||||
0.463795 | + | 0.885943i | \(0.346488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.11759e7 | −0.571675 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.17107e7 | −0.595412 | −0.297706 | − | 0.954658i | \(-0.596221\pi\) | ||||
−0.297706 | + | 0.954658i | \(0.596221\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.82504e7 | −1.42771 | −0.713853 | − | 0.700295i | \(-0.753052\pi\) | ||||
−0.713853 | + | 0.700295i | \(0.753052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.18846e6 | −0.109935 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.72102e6 | −0.0859358 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.48432e6 | 0.321846 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.71962e6 | −0.232859 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.56383e7 | −0.766979 | −0.383489 | − | 0.923545i | \(-0.625278\pi\) | ||||
−0.383489 | + | 0.923545i | \(0.625278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.84523e7 | 0.899622 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.96704e6 | −0.483056 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 665582. | 0.0320671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.68330e6 | −0.224307 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.91479e6 | 0.0911699 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.13809e6 | −0.195874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.63205e7 | −0.767997 | −0.383999 | − | 0.923334i | \(-0.625453\pi\) | ||||
−0.383999 | + | 0.923334i | \(0.625453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.01962e6 | −0.234831 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.75860e6 | 0.174813 | 0.0874065 | − | 0.996173i | \(-0.472142\pi\) | ||||
0.0874065 | + | 0.996173i | \(0.472142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.09131e7 | −1.42942 | −0.714709 | − | 0.699422i | \(-0.753441\pi\) | ||||
−0.714709 | + | 0.699422i | \(0.753441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.78640e6 | −0.0821243 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.71516e7 | 1.24099 | 0.620494 | − | 0.784211i | \(-0.286932\pi\) | ||||
0.620494 | + | 0.784211i | \(0.286932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.10070e7 | −0.500183 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.40540e6 | 0.334581 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.37461e7 | 1.51591 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.19787e7 | −1.42829 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.72795e7 | 1.21144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.88868e6 | 0.260015 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.17865e6 | −0.271265 | −0.135633 | − | 0.990759i | \(-0.543307\pi\) | ||||
−0.135633 | + | 0.990759i | \(0.543307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.43445e7 | −0.626201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26917e7 | 0.984979 | 0.492490 | − | 0.870318i | \(-0.336087\pi\) | ||||
0.492490 | + | 0.870318i | \(0.336087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.63213e7 | −0.704456 | −0.352228 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352228 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 357505. | 0.0153435 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.07946e7 | 0.460677 | 0.230339 | − | 0.973111i | \(-0.426017\pi\) | ||||
0.230339 | + | 0.973111i | \(0.426017\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.91351e6 | −0.293389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.50438e6 | −0.316680 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.57676e7 | −1.50093 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09856e7 | −0.458423 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.84031e6 | 0.0763677 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.59855e6 | −0.354834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.61883e6 | 0.148510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.80930e6 | 0.359519 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.07480e6 | 0.368312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.68130e7 | 0.678622 | 0.339311 | − | 0.940674i | \(-0.389806\pi\) | ||||
0.339311 | + | 0.940674i | \(0.389806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.74426e7 | −0.700165 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.84236e7 | −1.13471 | −0.567353 | − | 0.823475i | \(-0.692032\pi\) | ||||
−0.567353 | + | 0.823475i | \(0.692032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.09390e7 | −1.62540 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.49165e6 | 0.0588998 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.54141e6 | 0.256891 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.80746e6 | −0.0705960 | −0.0352980 | − | 0.999377i | \(-0.511238\pi\) | ||||
−0.0352980 | + | 0.999377i | \(0.511238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.07482e6 | −0.352524 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.73679e6 | −0.337557 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.15130e7 | 1.21097 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.95567e7 | −1.12968 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.32726e7 | −0.884719 | −0.442359 | − | 0.896838i | \(-0.645858\pi\) | ||||
−0.442359 | + | 0.896838i | \(0.645858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.31494e6 | 0.125344 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.20467e7 | 0.829162 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.49255e6 | 0.280285 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.81529e7 | 1.04755 | 0.523775 | − | 0.851857i | \(-0.324523\pi\) | ||||
0.523775 | + | 0.851857i | \(0.324523\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.72589e7 | −1.00889 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.52770e6 | −0.203503 | −0.101751 | − | 0.994810i | \(-0.532445\pi\) | ||||
−0.101751 | + | 0.994810i | \(0.532445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.58105e6 | −0.0578983 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.46409e6 | −0.126186 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.47822e7 | −0.897977 | −0.448988 | − | 0.893538i | \(-0.648216\pi\) | ||||
−0.448988 | + | 0.893538i | \(0.648216\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.53563e7 | −0.913946 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.46691e7 | 0.884507 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.86371e6 | 0.137807 | 0.0689036 | − | 0.997623i | \(-0.478050\pi\) | ||||
0.0689036 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.23089e6 | 0.185595 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.58447e7 | 0.912203 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.23830e6 | −0.113703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.67316e7 | −0.933720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.31071e7 | −0.802935 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.42613e6 | −0.325848 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.82182e6 | −0.0626527 | −0.0313263 | − | 0.999509i | \(-0.509973\pi\) | ||||
−0.0313263 | + | 0.999509i | \(0.509973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.08852e6 | 0.276732 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00199e7 | 1.70253 | 0.851265 | − | 0.524737i | \(-0.175836\pi\) | ||||
0.851265 | + | 0.524737i | \(0.175836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.45898e6 | −0.218717 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.40146e7 | −0.472138 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.28871e7 | 1.77261 | 0.886306 | − | 0.463101i | \(-0.153263\pi\) | ||||
0.886306 | + | 0.463101i | \(0.153263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.07511e6 | −0.302618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.78859e6 | 0.291573 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.94239e7 | 1.63137 | 0.815687 | − | 0.578494i | \(-0.196359\pi\) | ||||
0.815687 | + | 0.578494i | \(0.196359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.79849e6 | −0.190425 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.03751e7 | −0.339000 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.79663e6 | 0.253464 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.07021e7 | −0.993078 | −0.496539 | − | 0.868014i | \(-0.665396\pi\) | ||||
−0.496539 | + | 0.868014i | \(0.665396\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.85315e7 | 0.596399 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.83458e7 | 0.587462 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.47688e6 | −0.142639 | −0.0713194 | − | 0.997454i | \(-0.522721\pi\) | ||||
−0.0713194 | + | 0.997454i | \(0.522721\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.99999e7 | −1.26808 |
(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 | 448.6.a.bd.1.2 | 4 | ||
4.3 | odd | 2 | 448.6.a.bc.1.3 | 4 | |||
8.3 | odd | 2 | 224.6.a.h.1.2 | yes | 4 | ||
8.5 | even | 2 | 224.6.a.g.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.g.1.3 | ✓ | 4 | 8.5 | even | 2 | ||
224.6.a.h.1.2 | yes | 4 | 8.3 | odd | 2 | ||
448.6.a.bc.1.3 | 4 | 4.3 | odd | 2 | |||
448.6.a.bd.1.2 | 4 | 1.1 | even | 1 | trivial |