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: | \(3\) |
Coefficient field: | 3.3.5333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.20733\) 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 | ||||||||
\(5\) | −59.5955 | −1.06608 | −0.533038 | − | 0.846091i | \(-0.678950\pi\) | ||||
−0.533038 | + | 0.846091i | \(0.678950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −96.8268 | −0.746879 | −0.373440 | − | 0.927654i | \(-0.621822\pi\) | ||||
−0.373440 | + | 0.927654i | \(0.621822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 731.078 | 1.82172 | 0.910861 | − | 0.412713i | \(-0.135419\pi\) | ||||
0.910861 | + | 0.412713i | \(0.135419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −631.879 | −1.03699 | −0.518496 | − | 0.855080i | \(-0.673508\pi\) | ||||
−0.518496 | + | 0.855080i | \(0.673508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 536.360 | 0.615500 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 75.7854 | 0.0636009 | 0.0318005 | − | 0.999494i | \(-0.489876\pi\) | ||||
0.0318005 | + | 0.999494i | \(0.489876\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.35318 | −0.00149545 | −0.000747725 | − | 1.00000i | \(-0.500238\pi\) | ||||
−0.000747725 | 1.00000i | \(0.500238\pi\) | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 871.441 | 0.431211 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 426.625 | 0.136520 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2425.82 | −0.535628 | −0.267814 | − | 0.963471i | \(-0.586301\pi\) | ||||
−0.267814 | + | 0.963471i | \(0.586301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 349.683 | 0.0653537 | 0.0326769 | − | 0.999466i | \(-0.489597\pi\) | ||||
0.0326769 | + | 0.999466i | \(0.489597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6579.70 | −1.05177 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5770.44 | 0.796231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8314.43 | 0.998454 | 0.499227 | − | 0.866471i | \(-0.333617\pi\) | ||||
0.499227 | + | 0.866471i | \(0.333617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5686.91 | 0.598707 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4198.56 | 0.390068 | 0.195034 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195034 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9372.62 | −0.773019 | −0.386509 | − | 0.922285i | \(-0.626319\pi\) | ||||
−0.386509 | + | 0.922285i | \(0.626319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4827.24 | −0.355359 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2436.94 | 0.160916 | 0.0804581 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804581 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7431.57 | −0.442171 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −682.069 | −0.0367200 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −34979.0 | −1.71048 | −0.855241 | − | 0.518231i | \(-0.826591\pi\) | ||||
−0.855241 | + | 0.518231i | \(0.826591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −43569.0 | −1.94210 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21.1787 | 0.000863399 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15086.9 | −0.564249 | −0.282125 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282125 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 987.986 | 0.0339959 | 0.0169979 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169979 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7842.97 | −0.248960 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 37657.1 | 1.10551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44337.8 | −1.20667 | −0.603333 | − | 0.797490i | \(-0.706161\pi\) | ||||
−0.603333 | + | 0.797490i | \(0.706161\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 33934.4 | 0.798904 | 0.399452 | − | 0.916754i | \(-0.369200\pi\) | ||||
0.399452 | + | 0.916754i | \(0.369200\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −42483.0 | −0.933058 | −0.466529 | − | 0.884506i | \(-0.654496\pi\) | ||||
−0.466529 | + | 0.884506i | \(0.654496\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3839.62 | −0.0788198 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −70788.0 | −1.36061 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51187.8 | −0.922782 | −0.461391 | − | 0.887197i | \(-0.652649\pi\) | ||||
−0.461391 | + | 0.887197i | \(0.652649\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 88496.5 | 1.41004 | 0.705019 | − | 0.709188i | \(-0.250938\pi\) | ||||
0.705019 | + | 0.709188i | \(0.250938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4516.47 | −0.0678035 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21832.4 | 0.309245 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −34083.9 | −0.456115 | −0.228058 | − | 0.973648i | \(-0.573237\pi\) | ||||
−0.228058 | + | 0.973648i | \(0.573237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 61182.8 | 0.774508 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3147.15 | −0.0377320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 140.239 | 0.00159427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −156803. | −1.69209 | −0.846047 | − | 0.533108i | \(-0.821024\pi\) | ||||
−0.846047 | + | 0.533108i | \(0.821024\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 59217.3 | 0.607241 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −148400. | −1.44754 | −0.723772 | − | 0.690039i | \(-0.757593\pi\) | ||||
−0.723772 | + | 0.690039i | \(0.757593\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −155116. | −1.44067 | −0.720335 | − | 0.693626i | \(-0.756012\pi\) | ||||
−0.720335 | + | 0.693626i | \(0.756012\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −51934.0 | −0.459704 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 177527. | 1.49901 | 0.749504 | − | 0.662000i | \(-0.230292\pi\) | ||||
0.749504 | + | 0.662000i | \(0.230292\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −169314. | −1.36498 | −0.682492 | − | 0.730893i | \(-0.739104\pi\) | ||||
−0.682492 | + | 0.730893i | \(0.739104\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74829.8 | −0.576458 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 81710.2 | 0.601977 | 0.300989 | − | 0.953628i | \(-0.402683\pi\) | ||||
0.300989 | + | 0.953628i | \(0.402683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31526.0 | 0.222292 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −51182.2 | −0.345664 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7338.06 | −0.0475022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 373424. | 2.31867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −37787.0 | −0.225206 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 160811. | 0.920536 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 317307. | 1.74570 | 0.872851 | − | 0.487986i | \(-0.162268\pi\) | ||||
0.872851 | + | 0.487986i | \(0.162268\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 84353.6 | 0.446303 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 154610. | 0.787151 | 0.393576 | − | 0.919292i | \(-0.371238\pi\) | ||||
0.393576 | + | 0.919292i | \(0.371238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 227.851 | 0.00111692 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 43445.1 | 0.205167 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 217676. | 0.990852 | 0.495426 | − | 0.868650i | \(-0.335012\pi\) | ||||
0.495426 | + | 0.868650i | \(0.335012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −236914. | −1.04005 | −0.520023 | − | 0.854152i | \(-0.674077\pi\) | ||||
−0.520023 | + | 0.854152i | \(0.674077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21932.4 | −0.0929050 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −461953. | −1.88911 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 144568. | 0.571021 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 66884.1 | 0.255288 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 434197. | 1.60221 | 0.801107 | − | 0.598521i | \(-0.204245\pi\) | ||||
0.801107 | + | 0.598521i | \(0.204245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 135760. | 0.484541 | 0.242270 | − | 0.970209i | \(-0.422108\pi\) | ||||
0.242270 | + | 0.970209i | \(0.422108\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6138.62 | 0.0212003 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20839.5 | −0.0696721 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −355399. | −1.15071 | −0.575356 | − | 0.817903i | \(-0.695136\pi\) | ||||
−0.575356 | + | 0.817903i | \(0.695136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 314811. | 0.987547 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 51221.4 | 0.155735 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 514344. | 1.51630 | 0.758148 | − | 0.652082i | \(-0.226104\pi\) | ||||
0.758148 | + | 0.652082i | \(0.226104\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 392121. | 1.12127 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −178285. | −0.494680 | −0.247340 | − | 0.968929i | \(-0.579556\pi\) | ||||
−0.247340 | + | 0.968929i | \(0.579556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27977.5 | 0.0753515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −190.608 | −0.000498483 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −535921. | −1.36140 | −0.680699 | − | 0.732563i | \(-0.738324\pi\) | ||||
−0.680699 | + | 0.732563i | \(0.738324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −41308.7 | −0.101964 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 135782. | 0.325769 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 58891.2 | 0.137378 | 0.0686891 | − | 0.997638i | \(-0.478118\pi\) | ||||
0.0686891 | + | 0.997638i | \(0.478118\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 829741. | 1.88255 | 0.941274 | − | 0.337644i | \(-0.109630\pi\) | ||||
0.941274 | + | 0.337644i | \(0.109630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8891.88 | −0.0196275 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −495502. | −1.06443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55405.1 | 0.115863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 70586.7 | 0.143737 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −149335. | −0.296195 | −0.148097 | − | 0.988973i | \(-0.547315\pi\) | ||||
−0.148097 | + | 0.988973i | \(0.547315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 913030. | 1.76438 | 0.882189 | − | 0.470895i | \(-0.156069\pi\) | ||||
0.882189 | + | 0.470895i | \(0.156069\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −338914. | −0.638268 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −919205. | −1.68751 | −0.843756 | − | 0.536727i | \(-0.819661\pi\) | ||||
−0.843756 | + | 0.536727i | \(0.819661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −493730. | −0.883806 | −0.441903 | − | 0.897063i | \(-0.645696\pi\) | ||||
−0.441903 | + | 0.897063i | \(0.645696\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 399040. | 0.696669 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 234884. | 0.400050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −250215. | −0.415843 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −42849.0 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1720.36 | −0.00272430 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 133387. | 0.206257 | 0.103129 | − | 0.994668i | \(-0.467115\pi\) | ||||
0.103129 | + | 0.994668i | \(0.467115\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −305410. | −0.461247 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 558566. | 0.824098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33858.7 | −0.0488114 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 382347. | 0.538701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −47887.2 | −0.0659536 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −362735. | −0.488457 | −0.244229 | − | 0.969718i | \(-0.578535\pi\) | ||||
−0.244229 | + | 0.969718i | \(0.578535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 34556.6 | 0.0455067 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 190962. | 0.245970 | 0.122985 | − | 0.992409i | \(-0.460753\pi\) | ||||
0.122985 | + | 0.992409i | \(0.460753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 745968. | 0.940008 | 0.470004 | − | 0.882664i | \(-0.344252\pi\) | ||||
0.470004 | + | 0.882664i | \(0.344252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 637092. | 0.785547 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 636804. | 0.768450 | 0.384225 | − | 0.923239i | \(-0.374469\pi\) | ||||
0.384225 | + | 0.923239i | \(0.374469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −145231. | −0.171549 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 460691. | 0.532768 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.44028e6 | −1.63099 | −0.815494 | − | 0.578765i | \(-0.803535\pi\) | ||||
−0.815494 | + | 0.578765i | \(0.803535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.13226e6 | 1.25575 | 0.627876 | − | 0.778313i | \(-0.283924\pi\) | ||||
0.627876 | + | 0.778313i | \(0.283924\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 442888. | 0.471388 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1486.93 | 0.00155077 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −796469. | −0.814086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 622529. | 0.623700 | 0.311850 | − | 0.950131i | \(-0.399051\pi\) | ||||
0.311850 | + | 0.950131i | \(0.399051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −386740. | −0.379855 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 40648.2 | 0.0391463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.10304e6 | −1.98616 | −0.993082 | − | 0.117419i | \(-0.962538\pi\) | ||||
−0.993082 | + | 0.117419i | \(0.962538\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −805059. | −0.745725 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −196491. | −0.178543 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −838283. | −0.747310 | −0.373655 | − | 0.927568i | \(-0.621896\pi\) | ||||
−0.373655 | + | 0.927568i | \(0.621896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.08459e6 | 1.82350 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 306755. | 0.263338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 897532. | 0.756257 | 0.378128 | − | 0.925753i | \(-0.376568\pi\) | ||||
0.378128 | + | 0.925753i | \(0.376568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.00088e6 | 0.827864 | 0.413932 | − | 0.910308i | \(-0.364155\pi\) | ||||
0.413932 | + | 0.910308i | \(0.364155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −550645. | −0.447162 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 311896. | 0.248701 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.09974e6 | 1.64424 | 0.822120 | − | 0.569314i | \(-0.192791\pi\) | ||||
0.822120 | + | 0.569314i | \(0.192791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28324.3 | 0.0217846 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 503227. | 0.380188 | 0.190094 | − | 0.981766i | \(-0.439121\pi\) | ||||
0.190094 | + | 0.981766i | \(0.439121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.61771e6 | 1.20070 | 0.600349 | − | 0.799738i | \(-0.295028\pi\) | ||||
0.600349 | + | 0.799738i | \(0.295028\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1262.15 | −0.000920449 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −406533. | −0.291334 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41411e6 | −0.995955 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.41123e6 | 0.976932 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.04521e6 | 0.711270 | 0.355635 | − | 0.934625i | \(-0.384265\pi\) | ||||
0.355635 | + | 0.934625i | \(0.384265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 899113. | 0.601533 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −532956. | −0.350591 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 334264. | 0.216228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 907521. | 0.577352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.33560e6 | 0.835740 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −58879.6 | −0.0362422 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 697539. | 0.422399 | 0.211199 | − | 0.977443i | \(-0.432263\pi\) | ||||
0.211199 | + | 0.977443i | \(0.432263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.39605e6 | 0.831771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.68619e6 | 1.57484 | 0.787419 | − | 0.616419i | \(-0.211417\pi\) | ||||
0.787419 | + | 0.616419i | \(0.211417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.62222e6 | 0.935944 | 0.467972 | − | 0.883743i | \(-0.344985\pi\) | ||||
0.467972 | + | 0.883743i | \(0.344985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 467406. | 0.265410 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 648171. | 0.362277 | 0.181139 | − | 0.983458i | \(-0.442022\pi\) | ||||
0.181139 | + | 0.983458i | \(0.442022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.77346e6 | −0.975766 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.59774e6 | −0.865452 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −178.337 | −9.51120e−5 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −269575. | −0.141570 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52383e6 | 0.788074 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −235961. | −0.120185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66550e6 | 0.835552 | 0.417776 | − | 0.908550i | \(-0.362810\pi\) | ||||
0.417776 | + | 0.908550i | \(0.362810\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 673468. | 0.332818 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.64233e6 | 1.28640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.11943e6 | −1.01659 | −0.508294 | − | 0.861184i | \(-0.669724\pi\) | ||||
−0.508294 | + | 0.861184i | \(0.669724\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −735392. | −0.347552 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 255646. | 0.119056 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.34694e6 | 1.07713 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −283734. | −0.128341 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 791717. | 0.352977 | 0.176488 | − | 0.984303i | \(-0.443526\pi\) | ||||
0.176488 | + | 0.984303i | \(0.443526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 743781. | 0.326875 | 0.163437 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163437 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 460639. | 0.199569 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −646287. | −0.276051 | −0.138025 | − | 0.990429i | \(-0.544076\pi\) | ||||
−0.138025 | + | 0.990429i | \(0.544076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.02234e6 | −0.851693 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 66042.5 | 0.0274254 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.89862e6 | −0.777503 | −0.388752 | − | 0.921343i | \(-0.627094\pi\) | ||||
−0.388752 | + | 0.921343i | \(0.627094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47609e6 | −0.999998 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.36082e6 | −1.33869 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.53180e6 | 0.994711 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.19082e6 | −0.461509 | −0.230754 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230754 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 340083. | 0.130023 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.38691e6 | 1.27752 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −254301. | −0.0946402 | −0.0473201 | − | 0.998880i | \(-0.515068\pi\) | ||||
−0.0473201 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.44730e6 | −0.531472 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.53282e6 | 0.555442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.16696e6 | 1.84772 | 0.923861 | − | 0.382728i | \(-0.125015\pi\) | ||||
0.923861 | + | 0.382728i | \(0.125015\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.85576e6 | −1.00788 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.10331e6 | −1.77769 | −0.888843 | − | 0.458212i | \(-0.848490\pi\) | ||||
−0.888843 | + | 0.458212i | \(0.848490\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.21865e6 | 1.45051 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −759183. | −0.257673 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.00400e6 | −0.336403 | −0.168201 | − | 0.985753i | \(-0.553796\pi\) | ||||
−0.168201 | + | 0.985753i | \(0.553796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −40090.5 | −0.0132617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.39149e6 | −0.454462 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.05057e6 | 0.983757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.62003e6 | 1.15275 | 0.576377 | − | 0.817184i | \(-0.304466\pi\) | ||||
0.576377 | + | 0.817184i | \(0.304466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2050.66 | −0.000644855 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.18825e6 | 0.369016 | 0.184508 | − | 0.982831i | \(-0.440931\pi\) | ||||
0.184508 | + | 0.982831i | \(0.440931\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −220957. | −0.0677713 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −391006. | −0.118453 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.07850e6 | 1.81891 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −64602.3 | −0.0190959 | −0.00954794 | − | 0.999954i | \(-0.503039\pi\) | ||||
−0.00954794 | + | 0.999954i | \(0.503039\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.95908e6 | −0.572068 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.46082e6 | 0.421426 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.27399e6 | −1.50321 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.13222e6 | 0.600471 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.92057e6 | 0.812704 | 0.406352 | − | 0.913717i | \(-0.366801\pi\) | ||||
0.406352 | + | 0.913717i | \(0.366801\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.99592e6 | −0.823807 | −0.411904 | − | 0.911227i | \(-0.635136\pi\) | ||||
−0.411904 | + | 0.911227i | \(0.635136\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 197392. | 0.0536387 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32331.9 | 0.00868280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −95663.6 | −0.0253908 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.15757e6 | 1.09068 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.82982e6 | −1.51169 | −0.755844 | − | 0.654752i | \(-0.772773\pi\) | ||||
−0.755844 | + | 0.654752i | \(0.772773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.98624e6 | −0.765429 | −0.382714 | − | 0.923867i | \(-0.625011\pi\) | ||||
−0.382714 | + | 0.923867i | \(0.625011\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.30111e6 | −0.329679 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1244.83 | 0.000311823 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.68591e6 | 1.40812 | 0.704058 | − | 0.710142i | \(-0.251369\pi\) | ||||
0.704058 | + | 0.710142i | \(0.251369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −601957. | −0.147390 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 68926.8 | 0.0166870 | 0.00834352 | − | 0.999965i | \(-0.497344\pi\) | ||||
0.00834352 | + | 0.999965i | \(0.497344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.03125e6 | 0.486254 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.90777e6 | −0.925039 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.63362e6 | 1.08469 | 0.542343 | − | 0.840157i | \(-0.317537\pi\) | ||||
0.542343 | + | 0.840157i | \(0.317537\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.06948e6 | 0.710596 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.22184e6 | −0.279750 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.64622e6 | −0.825685 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.33421e6 | −0.970777 | −0.485388 | − | 0.874299i | \(-0.661322\pi\) | ||||
−0.485388 | + | 0.874299i | \(0.661322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −55247.6 | −0.0122400 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.08958e6 | 0.457938 | 0.228969 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228969 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.24932e6 | 0.270846 | 0.135423 | − | 0.990788i | \(-0.456761\pi\) | ||||
0.135423 | + | 0.990788i | \(0.456761\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 187556. | 0.0402252 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 157302. | 0.0333765 | 0.0166883 | − | 0.999861i | \(-0.494688\pi\) | ||||
0.0166883 | + | 0.999861i | \(0.494688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.29309e6 | 0.901234 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.19859e6 | 0.664364 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.85212e6 | −1.40823 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1003.93 | −0.000204159 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.83330e6 | −0.570160 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.74855e6 | −0.547350 | −0.273675 | − | 0.961822i | \(-0.588239\pi\) | ||||
−0.273675 | + | 0.961822i | \(0.588239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.25371e6 | −1.03539 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −460992. | −0.0899137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.34475e6 | 1.80390 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.01838e7 | 1.94576 | 0.972878 | − | 0.231319i | \(-0.0743041\pi\) | ||||
0.972878 | + | 0.231319i | \(0.0743041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.62909e6 | −0.875434 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.81893e6 | 1.65087 | 0.825434 | − | 0.564499i | \(-0.190931\pi\) | ||||
0.825434 | + | 0.564499i | \(0.190931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −183842. | −0.0340664 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.52909e6 | −0.647365 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.28576e6 | −0.596685 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.27705e6 | 1.30829 | 0.654145 | − | 0.756369i | \(-0.273029\pi\) | ||||
0.654145 | + | 0.756369i | \(0.273029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.60457e6 | 0.285604 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.82184e6 | 0.497293 | 0.248646 | − | 0.968594i | \(-0.420014\pi\) | ||||
0.248646 | + | 0.968594i | \(0.420014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.84400e6 | 1.54319 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −251797. | −0.0435042 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.78063e6 | −0.817881 | −0.408941 | − | 0.912561i | \(-0.634102\pi\) | ||||
−0.408941 | + | 0.912561i | \(0.634102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.11350e6 | 0.696882 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1715.47 | 0.000287800 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.24424e6 | 1.53587 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.78159e6 | 0.293145 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.82329e6 | 0.786004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.11976e6 | 1.14914 | 0.574568 | − | 0.818457i | \(-0.305170\pi\) | ||||
0.574568 | + | 0.818457i | \(0.305170\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.97980e6 | −0.796082 | −0.398041 | − | 0.917368i | \(-0.630310\pi\) | ||||
−0.398041 | + | 0.917368i | \(0.630310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 371779. | 0.0588689 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26500.9 | 0.00415656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.22204e6 | −0.188083 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.65298e6 | −0.404498 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.05798e7 | −1.59806 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −530021. | −0.0793153 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.43306e6 | −0.805513 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.34995e6 | 0.345196 | 0.172598 | − | 0.984992i | \(-0.444784\pi\) | ||||
0.172598 | + | 0.984992i | \(0.444784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.46767e6 | −1.08689 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.00904e7 | 1.45518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27753e7 | −1.82559 | −0.912795 | − | 0.408419i | \(-0.866080\pi\) | ||||
−0.912795 | + | 0.408419i | \(0.866080\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 80026.9 | 0.0113320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5708.40 | 0.000801005 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.95636e6 | 0.689207 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.45952e6 | 0.614548 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.13111e6 | −0.837339 | −0.418670 | − | 0.908139i | \(-0.637503\pi\) | ||||
−0.418670 | + | 0.908139i | \(0.637503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.92236e6 | 0.801614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −498646. | −0.0668937 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.30613e7 | −1.73667 | −0.868334 | − | 0.495979i | \(-0.834809\pi\) | ||||
−0.868334 | + | 0.495979i | \(0.834809\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.86956e6 | −0.641754 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −635281. | −0.0829866 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.03952e6 | −0.652542 | −0.326271 | − | 0.945276i | \(-0.605792\pi\) | ||||
−0.326271 | + | 0.945276i | \(0.605792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.67025e6 | 0.984508 | 0.492254 | − | 0.870452i | \(-0.336173\pi\) | ||||
0.492254 | + | 0.870452i | \(0.336173\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.34401e6 | 0.171008 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −225685. | −0.0284664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.25985e7 | 1.57536 | 0.787681 | − | 0.616083i | \(-0.211281\pi\) | ||||
0.787681 | + | 0.616083i | \(0.211281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.21727e6 | −1.01866 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.56883e6 | −1.05313 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.55724e7 | −3.11602 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.05023e6 | 0.368504 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.11295e6 | −0.612457 | −0.306229 | − | 0.951958i | \(-0.599067\pi\) | ||||
−0.306229 | + | 0.951958i | \(0.599067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −822.869 | −9.77333e−5 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.27285e6 | 0.974286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.45932e6 | 0.637532 | 0.318766 | − | 0.947833i | \(-0.396732\pi\) | ||||
0.318766 | + | 0.947833i | \(0.396732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 437315. | 0.0506410 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.44357e6 | 0.510265 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22496.6 | 0.00256183 | 0.00128091 | − | 0.999999i | \(-0.499592\pi\) | ||||
0.00128091 | + | 0.999999i | \(0.499592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00912e6 | 0.113962 | 0.0569808 | − | 0.998375i | \(-0.481853\pi\) | ||||
0.0569808 | + | 0.998375i | \(0.481853\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.59136e6 | −0.402222 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.22544e7 | −2.47188 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 68503.9 | 0.00754646 | 0.00377323 | − | 0.999993i | \(-0.498799\pi\) | ||||
0.00377323 | + | 0.999993i | \(0.498799\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.11396e6 | −0.230969 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.53985e6 | −0.166869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.67884e6 | 0.825362 | 0.412681 | − | 0.910876i | \(-0.364593\pi\) | ||||
0.412681 | + | 0.910876i | \(0.364593\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.25194e6 | 0.240087 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.85528e6 | −0.196199 | −0.0980995 | − | 0.995177i | \(-0.531276\pi\) | ||||
−0.0980995 | + | 0.995177i | \(0.531276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.88941e6 | 0.303098 | 0.151549 | − | 0.988450i | \(-0.451574\pi\) | ||||
0.151549 | + | 0.988450i | \(0.451574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.30024e6 | 0.340663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.09168e7 | −1.11788 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15483.3 | 0.00157287 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 630112. | 0.0635026 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.22946e7 | 1.22925 | 0.614625 | − | 0.788819i | \(-0.289307\pi\) | ||||
0.614625 | + | 0.788819i | \(0.289307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.20049e6 | −0.119083 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.89101e7 | −1.86105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.69585e6 | 0.458528 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.74869e6 | 0.266301 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.87250e6 | −0.756776 | −0.378388 | − | 0.925647i | \(-0.623522\pi\) | ||||
−0.378388 | + | 0.925647i | \(0.623522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.14575e6 | −0.300052 | −0.150026 | − | 0.988682i | \(-0.547936\pi\) | ||||
−0.150026 | + | 0.988682i | \(0.547936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.02710e6 | −0.475793 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.14059e6 | −0.388867 | −0.194434 | − | 0.980916i | \(-0.562287\pi\) | ||||
−0.194434 | + | 0.980916i | \(0.562287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.10297e7 | −1.02791 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 304728. | 0.0281813 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.09894e7 | 1.00854 | 0.504268 | − | 0.863547i | \(-0.331762\pi\) | ||||
0.504268 | + | 0.863547i | \(0.331762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.21404e6 | −0.839164 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.44113e6 | −0.311019 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.78286e7 | −1.59920 | −0.799602 | − | 0.600530i | \(-0.794956\pi\) | ||||
−0.799602 | + | 0.600530i | \(0.794956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.39680e6 | 0.391411 | 0.195705 | − | 0.980663i | \(-0.437300\pi\) | ||||
0.195705 | + | 0.980663i | \(0.437300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 430985. | 0.0380783 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13578.9 | −0.00119072 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28326e6 | 0.111686 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.26461e6 | 0.282011 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 722295. | 0.0619311 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.98954e7 | −1.69322 | −0.846612 | − | 0.532210i | \(-0.821362\pi\) | ||||
−0.846612 | + | 0.532210i | \(0.821362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −311010. | −0.0262733 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −796059. | −0.0667535 | −0.0333767 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333767 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51827e7 | 1.26379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.71865e6 | −0.142011 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.97449e6 | 0.818162 | 0.409081 | − | 0.912498i | \(-0.365849\pi\) | ||||
0.409081 | + | 0.912498i | \(0.365849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.29725e7 | −1.05632 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.71371e6 | −0.542714 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.21025e7 | 1.77375 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.67183e6 | 0.531557 | 0.265779 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265779 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.73383e6 | −0.453536 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41190e7 | 1.10877 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 318190. | 0.0248087 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.73123e6 | −0.443665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.64132e6 | 0.433597 | 0.216798 | − | 0.976216i | \(-0.430439\pi\) | ||||
0.216798 | + | 0.976216i | \(0.430439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19565.4 | −0.00149314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.30708e6 | 0.0990439 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.43691e7 | 1.08114 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.86950e6 | −0.139672 | −0.0698361 | − | 0.997558i | \(-0.522248\pi\) | ||||
−0.0698361 | + | 0.997558i | \(0.522248\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.14622e6 | −0.307594 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −184982. | −0.0136272 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.75303e7 | 2.01394 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.29625e7 | 0.941652 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.87348e7 | −1.35153 | −0.675766 | − | 0.737116i | \(-0.736187\pi\) | ||||
−0.675766 | + | 0.737116i | \(0.736187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50194e7 | 1.07601 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.01904e7 | −0.725009 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.03492e6 | −0.0731240 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.88165e6 | −0.553071 | −0.276536 | − | 0.961004i | \(-0.589186\pi\) | ||||
−0.276536 | + | 0.961004i | \(0.589186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −710308. | −0.0491647 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 196627. | 0.0135171 | 0.00675854 | − | 0.999977i | \(-0.497849\pi\) | ||||
0.00675854 | + | 0.999977i | \(0.497849\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.98599e6 | −0.272156 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.24144e7 | −2.19821 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.89161e7 | 1.27415 | 0.637074 | − | 0.770803i | \(-0.280145\pi\) | ||||
0.637074 | + | 0.770803i | \(0.280145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13382.3 | −0.000895337 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.29482e6 | 0.351867 | 0.175934 | − | 0.984402i | \(-0.443706\pi\) | ||||
0.175934 | + | 0.984402i | \(0.443706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.58762e7 | −1.70808 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.16822e6 | 0.470013 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.71893e7 | −1.11958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.23104e7 | 0.796478 | 0.398239 | − | 0.917282i | \(-0.369621\pi\) | ||||
0.398239 | + | 0.917282i | \(0.369621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.60276e6 | −0.360093 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.09070e6 | −0.516558 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.33051e6 | −0.464938 | −0.232469 | − | 0.972604i | \(-0.574680\pi\) | ||||
−0.232469 | + | 0.972604i | \(0.574680\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.48066e6 | 0.219310 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.11913e6 | 0.195242 | 0.0976208 | − | 0.995224i | \(-0.468877\pi\) | ||||
0.0976208 | + | 0.995224i | \(0.468877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.63942e7 | 1.01948 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −365834. | −0.0226012 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.53311e6 | 0.585122 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.07903e6 | −0.431676 | −0.215838 | − | 0.976429i | \(-0.569248\pi\) | ||||
−0.215838 | + | 0.976429i | \(0.569248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.89274e7 | 1.14671 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.91702e7 | 1.15393 | 0.576964 | − | 0.816770i | \(-0.304237\pi\) | ||||
0.576964 | + | 0.816770i | \(0.304237\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 149184. | 0.00892209 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.24553e6 | 0.430544 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9879.99 | −0.000583328 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.48087e7 | 1.45538 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.76842e6 | 0.103082 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.11802e7 | 1.22675 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.38766e6 | −0.482730 | −0.241365 | − | 0.970434i | \(-0.577595\pi\) | ||||
−0.241365 | + | 0.970434i | \(0.577595\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.54454e6 | 0.431460 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.91173e6 | −0.449604 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −624287. | −0.0352534 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.87613e7 | −1.05280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.36638e7 | −0.761950 | −0.380975 | − | 0.924585i | \(-0.624412\pi\) | ||||
−0.380975 | + | 0.924585i | \(0.624412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 184684. | 0.0102344 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.76080e6 | −0.152038 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.10584e7 | −1.69977 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.05256e6 | −0.166026 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.07779e6 | −0.436625 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.16198e6 | 0.277297 | 0.138648 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138648 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.20275e7 | −0.642131 | −0.321065 | − | 0.947057i | \(-0.604041\pi\) | ||||
−0.321065 | + | 0.947057i | \(0.604041\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.00793e6 | −0.477968 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.06526e7 | −1.61649 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22055.5 | 0.00115601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.95580e6 | 0.258169 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.25894e6 | −0.220518 | −0.110259 | − | 0.993903i | \(-0.535168\pi\) | ||||
−0.110259 | + | 0.993903i | \(0.535168\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.63473e7 | −0.841290 | −0.420645 | − | 0.907225i | \(-0.638196\pi\) | ||||
−0.420645 | + | 0.907225i | \(0.638196\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.80707e6 | −0.143588 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.62566e7 | 0.826542 | 0.413271 | − | 0.910608i | \(-0.364386\pi\) | ||||
0.413271 | + | 0.910608i | \(0.364386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.87989e7 | 1.96080 | 0.980400 | − | 0.197018i | \(-0.0631256\pi\) | ||||
0.980400 | + | 0.197018i | \(0.0631256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.88976e7 | −0.949302 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −563205. | −0.0281225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.06250e7 | 0.527367 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −254919. | −0.0125773 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.96779e7 | 1.45555 | 0.727776 | − | 0.685815i | \(-0.240554\pi\) | ||||
0.727776 | + | 0.685815i | \(0.240554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46265e7 | −0.713102 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.52904e6 | −0.219502 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.66733e6 | −0.0803305 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.61575e7 | −1.73177 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.45594e7 | −0.693224 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.39833e6 | −0.208192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.20704e7 | −1.50915 | −0.754573 | − | 0.656216i | \(-0.772156\pi\) | ||||
−0.754573 | + | 0.656216i | \(0.772156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11359.4 | 0.000531422 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.10540e7 | −0.514123 | −0.257061 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257061 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.49699e6 | −0.0692206 | −0.0346103 | − | 0.999401i | \(-0.511019\pi\) | ||||
−0.0346103 | + | 0.999401i | \(0.511019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.65880e6 | 0.168202 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.26672e6 | −0.332132 | −0.166066 | − | 0.986115i | \(-0.553107\pi\) | ||||
−0.166066 | + | 0.986115i | \(0.553107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.19385e7 | 1.45136 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.27270e7 | 0.575015 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.74223e7 | −1.68105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.80161e7 | 1.25130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.27010e7 | −0.564032 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.55708e7 | −0.687529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.36708e6 | −0.147827 | −0.0739137 | − | 0.997265i | \(-0.523549\pi\) | ||||
−0.0739137 | + | 0.997265i | \(0.523549\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.40688e6 | −0.410652 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.40164e7 | −0.608409 | −0.304204 | − | 0.952607i | \(-0.598391\pi\) | ||||
−0.304204 | + | 0.952607i | \(0.598391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00921e7 | 1.73044 | 0.865220 | − | 0.501392i | \(-0.167179\pi\) | ||||
0.865220 | + | 0.501392i | \(0.167179\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.09202e6 | −0.347295 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.57779e7 | −1.52688 | −0.763442 | − | 0.645877i | \(-0.776492\pi\) | ||||
−0.763442 | + | 0.645877i | \(0.776492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.07238e7 | −1.30383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.79660e6 | 0.202414 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5734.56 | −0.000240642 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.50965e6 | −0.146456 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.00837e6 | −0.124839 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −848268. | −0.0350053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.65090e6 | −0.108788 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.16769e6 | −0.333334 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.94488e7 | −2.00694 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.64880e6 | −0.106913 | −0.0534565 | − | 0.998570i | \(-0.517024\pi\) | ||||
−0.0534565 | + | 0.998570i | \(0.517024\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.20204e7 | −0.482515 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.49769e7 | 1.39632 | 0.698161 | − | 0.715941i | \(-0.254002\pi\) | ||||
0.698161 | + | 0.715941i | \(0.254002\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.46979e7 | 2.56870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 529916. | 0.0209245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.49704e7 | −0.587907 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.60166e7 | 1.01616 | 0.508079 | − | 0.861310i | \(-0.330356\pi\) | ||||
0.508079 | + | 0.861310i | \(0.330356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.27785e6 | −0.243872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.14424e7 | −0.828457 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.54714e6 | 0.136309 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.25644e7 | −0.480223 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.76233e7 | 1.81042 | 0.905212 | − | 0.424960i | \(-0.139712\pi\) | ||||
0.905212 | + | 0.424960i | \(0.139712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17487.9 | 0.000661245 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.41757e7 | −0.909233 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.30189e6 | −0.123519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.81079e6 | −0.216215 | −0.108108 | − | 0.994139i | \(-0.534479\pi\) | ||||
−0.108108 | + | 0.994139i | \(0.534479\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.46000e7 | −0.540367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.47870e6 | −0.238514 | −0.119257 | − | 0.992863i | \(-0.538051\pi\) | ||||
−0.119257 | + | 0.992863i | \(0.538051\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.22104e6 | −0.0813349 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.20665e6 | −0.153235 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.16257e6 | 0.150830 | 0.0754149 | − | 0.997152i | \(-0.475972\pi\) | ||||
0.0754149 | + | 0.997152i | \(0.475972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.68441e7 | 0.967573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.83354e6 | −0.209161 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.93375e7 | −1.04638 | −0.523191 | − | 0.852216i | \(-0.675259\pi\) | ||||
−0.523191 | + | 0.852216i | \(0.675259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.89968e6 | 0.315766 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.59612e7 | 0.563359 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.10768e7 | −0.740047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.85069e7 | −0.995729 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.43796e7 | 0.499669 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.44125e7 | −1.88096 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.34493e6 | −0.149423 | −0.0747113 | − | 0.997205i | \(-0.523804\pi\) | ||||
−0.0747113 | + | 0.997205i | \(0.523804\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1605.03 | 5.49129e−5 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.84656e7 | 0.628514 | 0.314257 | − | 0.949338i | \(-0.398245\pi\) | ||||
0.314257 | + | 0.949338i | \(0.398245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.29396e7 | 0.776790 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.42618e6 | 0.0817355 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.05887e7 | 1.36041 | 0.680203 | − | 0.733023i | \(-0.261891\pi\) | ||||
0.680203 | + | 0.733023i | \(0.261891\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.49180e7 | −0.830915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.37145e7 | −0.454995 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.29637e7 | −1.74822 | −0.874108 | − | 0.485732i | \(-0.838553\pi\) | ||||
−0.874108 | + | 0.485732i | \(0.838553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.47805e7 | 1.79902 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.12365e6 | 0.0693888 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.95812e6 | 0.161186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26953e7 | −0.410636 | −0.205318 | − | 0.978695i | \(-0.565823\pi\) | ||||
−0.205318 | + | 0.978695i | \(0.565823\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.49895e7 | −0.482406 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.94241e7 | 0.942205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.65074e7 | 1.48178 | 0.740890 | − | 0.671626i | \(-0.234404\pi\) | ||||
0.740890 | + | 0.671626i | \(0.234404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.06122e6 | −0.192153 |
(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.i.1.1 | 3 | ||
4.3 | odd | 2 | 69.6.a.b.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 207.6.a.c.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.b.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
207.6.a.c.1.1 | 3 | 12.11 | even | 2 | |||
1104.6.a.i.1.1 | 3 | 1.1 | even | 1 | trivial |