Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.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: | \(16.0020205651\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.161121.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.261082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.38924 | −0.621285 | −0.310643 | − | 0.950527i | \(-0.600544\pi\) | ||||
−0.310643 | + | 0.950527i | \(0.600544\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.871845 | −0.329527 | −0.164763 | − | 0.986333i | \(-0.552686\pi\) | ||||
−0.164763 | + | 0.986333i | \(0.552686\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.74903 | −1.73340 | −0.866698 | − | 0.498833i | \(-0.833762\pi\) | ||||
−0.866698 | + | 0.498833i | \(0.833762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.90849 | 1.08402 | 0.542009 | − | 0.840372i | \(-0.317664\pi\) | ||||
0.542009 | + | 0.840372i | \(0.317664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.38924 | −0.358699 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.477836 | −0.115892 | −0.0579461 | − | 0.998320i | \(-0.518455\pi\) | ||||
−0.0579461 | + | 0.998320i | \(0.518455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16161 | 0.495908 | 0.247954 | − | 0.968772i | \(-0.420242\pi\) | ||||
0.247954 | + | 0.968772i | \(0.420242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.871845 | −0.190252 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.53227 | 0.736530 | 0.368265 | − | 0.929721i | \(-0.379952\pi\) | ||||
0.368265 | + | 0.929721i | \(0.379952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.07002 | −0.614004 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.05174 | −0.938085 | −0.469042 | − | 0.883176i | \(-0.655401\pi\) | ||||
−0.469042 | + | 0.883176i | \(0.655401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.41763 | 0.613824 | 0.306912 | − | 0.951738i | \(-0.400704\pi\) | ||||
0.306912 | + | 0.951738i | \(0.400704\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.74903 | −1.00078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.21120 | 0.204730 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.98967 | −0.820297 | −0.410149 | − | 0.912019i | \(-0.634523\pi\) | ||||
−0.410149 | + | 0.912019i | \(0.634523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.90849 | 0.625859 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.50706 | −0.860059 | −0.430029 | − | 0.902815i | \(-0.641497\pi\) | ||||
−0.430029 | + | 0.902815i | \(0.641497\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.83237 | −0.584431 | −0.292215 | − | 0.956353i | \(-0.594392\pi\) | ||||
−0.292215 | + | 0.956353i | \(0.594392\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.38924 | −0.207095 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.6631 | −1.99297 | −0.996486 | − | 0.0837634i | \(-0.973306\pi\) | ||||
−0.996486 | + | 0.0837634i | \(0.973306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.23989 | −0.891412 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.477836 | −0.0669104 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6543 | −1.60085 | −0.800423 | − | 0.599436i | \(-0.795392\pi\) | ||||
−0.800423 | + | 0.599436i | \(0.795392\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.98676 | 1.07693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16161 | 0.286313 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.528261 | −0.0687737 | −0.0343868 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343868 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.27251 | 0.162929 | 0.0814643 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814643 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.871845 | −0.109842 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.42981 | −0.673485 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.13778 | 0.994188 | 0.497094 | − | 0.867697i | \(-0.334400\pi\) | ||||
0.497094 | + | 0.867697i | \(0.334400\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.53227 | 0.425236 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17968 | 0.496036 | 0.248018 | − | 0.968755i | \(-0.420221\pi\) | ||||
0.248018 | + | 0.968755i | \(0.420221\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12260 | −0.716596 | −0.358298 | − | 0.933607i | \(-0.616643\pi\) | ||||
−0.358298 | + | 0.933607i | \(0.616643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.07002 | −0.354496 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.01226 | 0.571200 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4461 | −1.73782 | −0.868911 | − | 0.494969i | \(-0.835179\pi\) | ||||
−0.868911 | + | 0.494969i | \(0.835179\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.01912 | −0.111863 | −0.0559315 | − | 0.998435i | \(-0.517813\pi\) | ||||
−0.0559315 | + | 0.998435i | \(0.517813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.663827 | 0.0720022 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.05174 | −0.541603 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.40919 | −0.997372 | −0.498686 | − | 0.866783i | \(-0.666184\pi\) | ||||
−0.498686 | + | 0.866783i | \(0.666184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.40760 | −0.357213 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.41763 | 0.354391 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00299 | −0.308101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.321073 | −0.0326000 | −0.0163000 | − | 0.999867i | \(-0.505189\pi\) | ||||
−0.0163000 | + | 0.999867i | \(0.505189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.74903 | −0.577799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5077 | 1.44357 | 0.721784 | − | 0.692119i | \(-0.243322\pi\) | ||||
0.721784 | + | 0.692119i | \(0.243322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.14201 | 0.605190 | 0.302595 | − | 0.953119i | \(-0.402147\pi\) | ||||
0.302595 | + | 0.953119i | \(0.402147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.21120 | 0.118201 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.05659 | 0.392165 | 0.196083 | − | 0.980587i | \(-0.437178\pi\) | ||||
0.196083 | + | 0.980587i | \(0.437178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8310 | −1.70790 | −0.853951 | − | 0.520353i | \(-0.825800\pi\) | ||||
−0.853951 | + | 0.520353i | \(0.825800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.98967 | −0.473599 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.27411 | 0.119858 | 0.0599289 | − | 0.998203i | \(-0.480913\pi\) | ||||
0.0599289 | + | 0.998203i | \(0.480913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.90716 | −0.457595 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.90849 | 0.361340 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.416599 | 0.0381896 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.0513 | 2.00466 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.50706 | −0.496555 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2112 | 1.00276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.67900 | −0.237723 | −0.118862 | − | 0.992911i | \(-0.537924\pi\) | ||||
−0.118862 | + | 0.992911i | \(0.537924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.83237 | −0.337421 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43675 | 0.475011 | 0.237505 | − | 0.971386i | \(-0.423670\pi\) | ||||
0.237505 | + | 0.971386i | \(0.423670\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.88459 | −0.163415 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.38924 | −0.119566 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.68828 | 0.400547 | 0.200273 | − | 0.979740i | \(-0.435817\pi\) | ||||
0.200273 | + | 0.979740i | \(0.435817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4563 | 1.22617 | 0.613086 | − | 0.790017i | \(-0.289928\pi\) | ||||
0.613086 | + | 0.790017i | \(0.289928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.6631 | −1.15064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.4700 | −1.87903 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.01806 | 0.582818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.23989 | −0.514657 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.97719 | 0.325824 | 0.162912 | − | 0.986641i | \(-0.447911\pi\) | ||||
0.162912 | + | 0.986641i | \(0.447911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.552927 | 0.0449965 | 0.0224983 | − | 0.999747i | \(-0.492838\pi\) | ||||
0.0224983 | + | 0.999747i | \(0.492838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.477836 | −0.0386307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.74789 | −0.381360 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.90396 | −0.710613 | −0.355307 | − | 0.934750i | \(-0.615624\pi\) | ||||
−0.355307 | + | 0.934750i | \(0.615624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6543 | −0.924249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.07960 | −0.242706 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32106 | −0.181800 | −0.0908999 | − | 0.995860i | \(-0.528974\pi\) | ||||
−0.0908999 | + | 0.995860i | \(0.528974\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.98676 | 0.621768 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.27626 | 0.175097 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.16161 | 0.165303 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.53893 | −0.497146 | −0.248573 | − | 0.968613i | \(-0.579962\pi\) | ||||
−0.248573 | + | 0.968613i | \(0.579962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.67658 | 0.202331 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.528261 | −0.0397065 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.03006 | −0.450708 | −0.225354 | − | 0.974277i | \(-0.572354\pi\) | ||||
−0.225354 | + | 0.974277i | \(0.572354\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.9128 | 1.77743 | 0.888713 | − | 0.458464i | \(-0.151600\pi\) | ||||
0.888713 | + | 0.458464i | \(0.151600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.27251 | 0.0940669 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.93184 | 0.509639 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.74709 | 0.200887 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.871845 | −0.0634174 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.15759 | −0.373190 | −0.186595 | − | 0.982437i | \(-0.559745\pi\) | ||||
−0.186595 | + | 0.982437i | \(0.559745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.38508 | −0.171682 | −0.0858410 | − | 0.996309i | \(-0.527358\pi\) | ||||
−0.0858410 | + | 0.996309i | \(0.527358\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.42981 | −0.388837 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.00129542 | −9.22949e−5 0 | −4.61475e−5 | − | 1.00000i | \(-0.500015\pi\) | ||||
−4.61475e−5 | 1.00000i | \(0.500015\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7180 | 1.18511 | 0.592555 | − | 0.805530i | \(-0.298119\pi\) | ||||
0.592555 | + | 0.805530i | \(0.298119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.13778 | 0.573995 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.40434 | 0.309124 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.65061 | 0.534342 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.53227 | 0.245510 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.4272 | −0.859605 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.08873 | −0.212637 | −0.106319 | − | 0.994332i | \(-0.533906\pi\) | ||||
−0.106319 | + | 0.994332i | \(0.533906\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.17968 | 0.286387 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.32407 | 0.363098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.97964 | −0.202271 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.12260 | −0.413727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.86761 | −0.125629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.4949 | 0.970648 | 0.485324 | − | 0.874334i | \(-0.338702\pi\) | ||||
0.485324 | + | 0.874334i | \(0.338702\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.07002 | −0.204668 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.04675 | −0.600454 | −0.300227 | − | 0.953868i | \(-0.597062\pi\) | ||||
−0.300227 | + | 0.953868i | \(0.597062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9796 | −1.05596 | −0.527982 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527982 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.01226 | 0.329783 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.78880 | 0.117188 | 0.0585941 | − | 0.998282i | \(-0.481338\pi\) | ||||
0.0585941 | + | 0.998282i | \(0.481338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.9813 | 1.23820 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.4461 | −1.00333 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.43119 | 0.286630 | 0.143315 | − | 0.989677i | \(-0.454224\pi\) | ||||
0.143315 | + | 0.989677i | \(0.454224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3349 | 0.987808 | 0.493904 | − | 0.869517i | \(-0.335570\pi\) | ||||
0.493904 | + | 0.869517i | \(0.335570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.66868 | 0.553821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.44863 | 0.537574 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.01912 | −0.0645841 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.6393 | 1.61834 | 0.809168 | − | 0.587577i | \(-0.199918\pi\) | ||||
0.809168 | + | 0.587577i | \(0.199918\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.3071 | −1.27670 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.663827 | 0.0415705 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.6727 | −1.41429 | −0.707143 | − | 0.707070i | \(-0.750016\pi\) | ||||
−0.707143 | + | 0.707070i | \(0.750016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.35022 | 0.270310 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.05174 | −0.312695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.4884 | −1.75667 | −0.878335 | − | 0.478045i | \(-0.841346\pi\) | ||||
−0.878335 | + | 0.478045i | \(0.841346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.1906 | 0.994582 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.40919 | −0.575833 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0734 | 0.797100 | 0.398550 | − | 0.917147i | \(-0.369514\pi\) | ||||
0.398550 | + | 0.917147i | \(0.369514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.04487 | −0.184963 | −0.0924814 | − | 0.995714i | \(-0.529480\pi\) | ||||
−0.0924814 | + | 0.995714i | \(0.529480\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.40760 | −0.206237 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.6496 | 1.06431 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.04405 | 0.242984 | 0.121492 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121492 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.41763 | 0.204608 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2904 | −1.03146 | −0.515728 | − | 0.856752i | \(-0.672479\pi\) | ||||
−0.515728 | + | 0.856752i | \(0.672479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.1428 | 1.37570 | 0.687849 | − | 0.725853i | \(-0.258555\pi\) | ||||
0.687849 | + | 0.725853i | \(0.258555\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00299 | −0.177882 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.80131 | 0.283412 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7717 | −0.986569 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.321073 | −0.0188216 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.4973 | −1.66483 | −0.832416 | − | 0.554152i | \(-0.813043\pi\) | ||||
−0.832416 | + | 0.554152i | \(0.813043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.733879 | 0.0427281 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.74903 | −0.333592 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8058 | 0.798412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.34123 | 0.192585 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.5077 | 0.833444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.76782 | −0.101225 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4381 | 1.33768 | 0.668842 | − | 0.743405i | \(-0.266790\pi\) | ||||
0.668842 | + | 0.743405i | \(0.266790\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.14201 | 0.349407 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.33992 | 0.529618 | 0.264809 | − | 0.964301i | \(-0.414691\pi\) | ||||
0.264809 | + | 0.964301i | \(0.414691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9683 | 1.01563 | 0.507815 | − | 0.861466i | \(-0.330453\pi\) | ||||
0.507815 | + | 0.861466i | \(0.330453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.21120 | 0.0682434 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.1619 | −1.35706 | −0.678532 | − | 0.734570i | \(-0.737384\pi\) | ||||
−0.678532 | + | 0.734570i | \(0.737384\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.0426 | 1.62607 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.05659 | 0.226417 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.03290 | −0.0574719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9991 | −0.665592 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.8310 | −0.986058 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.9121 | 0.656737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6022 | 0.967505 | 0.483753 | − | 0.875205i | \(-0.339273\pi\) | ||||
0.483753 | + | 0.875205i | \(0.339273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.98967 | −0.273432 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3053 | −0.617674 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.14881 | −0.117053 | −0.0585265 | − | 0.998286i | \(-0.518640\pi\) | ||||
−0.0585265 | + | 0.998286i | \(0.518640\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.27411 | 0.0691999 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.6480 | −1.06400 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5431 | 0.623271 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.90716 | −0.264193 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0393 | 0.592622 | 0.296311 | − | 0.955091i | \(-0.404243\pi\) | ||||
0.296311 | + | 0.955091i | \(0.404243\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.603266 | −0.0322921 | −0.0161460 | − | 0.999870i | \(-0.505140\pi\) | ||||
−0.0161460 | + | 0.999870i | \(0.505140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.90849 | 0.208620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6385 | 1.52427 | 0.762137 | − | 0.647416i | \(-0.224150\pi\) | ||||
0.762137 | + | 0.647416i | \(0.224150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.80656 | −0.308180 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.416599 | 0.0220488 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.2365 | −1.49026 | −0.745132 | − | 0.666918i | \(-0.767613\pi\) | ||||
−0.745132 | + | 0.666918i | \(0.767613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3274 | −0.754075 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.0513 | 1.15739 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.50574 | 0.445211 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.9271 | −1.04019 | −0.520093 | − | 0.854110i | \(-0.674103\pi\) | ||||
−0.520093 | + | 0.854110i | \(0.674103\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.50706 | −0.286686 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1608 | 0.527521 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.4724 | −1.21535 | −0.607677 | − | 0.794184i | \(-0.707899\pi\) | ||||
−0.607677 | + | 0.794184i | \(0.707899\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.2112 | 0.578942 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.7447 | −1.01690 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2367 | −0.577192 | −0.288596 | − | 0.957451i | \(-0.593188\pi\) | ||||
−0.288596 | + | 0.957451i | \(0.593188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.67900 | −0.137250 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.1612 | −1.74555 | −0.872777 | − | 0.488119i | \(-0.837683\pi\) | ||||
−0.872777 | + | 0.488119i | \(0.837683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.96322 | −0.354878 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.83237 | −0.194810 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6706 | 0.845233 | 0.422617 | − | 0.906309i | \(-0.361112\pi\) | ||||
0.422617 | + | 0.906309i | \(0.361112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.68785 | −0.0853581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.43675 | 0.274248 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.4583 | 1.07968 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3298 | 0.669006 | 0.334503 | − | 0.942395i | \(-0.391432\pi\) | ||||
0.334503 | + | 0.942395i | \(0.391432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.88459 | −0.0943476 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9727 | 1.24708 | 0.623539 | − | 0.781792i | \(-0.285694\pi\) | ||||
0.623539 | + | 0.781792i | \(0.285694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.3577 | 0.665397 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.38924 | −0.0690317 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.6858 | 1.42190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3474 | −1.10501 | −0.552504 | − | 0.833510i | \(-0.686328\pi\) | ||||
−0.552504 | + | 0.833510i | \(0.686328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.68828 | 0.231256 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.460562 | 0.0226628 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41580 | 0.0694988 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.4563 | 0.707930 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.6024 | 1.29961 | 0.649805 | − | 0.760101i | \(-0.274850\pi\) | ||||
0.649805 | + | 0.760101i | \(0.274850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3727 | −1.13911 | −0.569557 | − | 0.821952i | \(-0.692885\pi\) | ||||
−0.569557 | + | 0.821952i | \(0.692885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.6631 | −0.664324 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.46697 | 0.0711583 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.10944 | −0.0536893 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.4700 | −1.08486 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.7703 | −1.67483 | −0.837414 | − | 0.546570i | \(-0.815933\pi\) | ||||
−0.837414 | + | 0.546570i | \(0.815933\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.3677 | −1.02687 | −0.513433 | − | 0.858130i | \(-0.671626\pi\) | ||||
−0.513433 | + | 0.858130i | \(0.671626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.01806 | 0.336490 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.63541 | 0.365251 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2625 | 0.489802 | 0.244901 | − | 0.969548i | \(-0.421245\pi\) | ||||
0.244901 | + | 0.969548i | \(0.421245\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.23989 | −0.297137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.69185 | 0.222917 | 0.111458 | − | 0.993769i | \(-0.464448\pi\) | ||||
0.111458 | + | 0.993769i | \(0.464448\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0716 | 0.619653 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.97719 | 0.188115 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2687 | −0.578998 | −0.289499 | − | 0.957178i | \(-0.593489\pi\) | ||||
−0.289499 | + | 0.957178i | \(0.593489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.6603 | 1.49082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.552927 | 0.0259788 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.73396 | 0.221931 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1775 | 0.522862 | 0.261431 | − | 0.965222i | \(-0.415806\pi\) | ||||
0.261431 | + | 0.965222i | \(0.415806\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.477836 | −0.0223035 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.2919 | 0.898516 | 0.449258 | − | 0.893402i | \(-0.351688\pi\) | ||||
0.449258 | + | 0.893402i | \(0.351688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1247 | 0.563481 | 0.281741 | − | 0.959491i | \(-0.409088\pi\) | ||||
0.281741 | + | 0.959491i | \(0.409088\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.74789 | −0.220178 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.6560 | −0.585650 | −0.292825 | − | 0.956166i | \(-0.594595\pi\) | ||||
−0.292825 | + | 0.956166i | \(0.594595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.09488 | −0.327611 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.90396 | −0.410273 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0324 | 1.01305 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.63620 | −0.304490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.6543 | −0.533615 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.3944 | 1.48014 | 0.740068 | − | 0.672532i | \(-0.234793\pi\) | ||||
0.740068 | + | 0.672532i | \(0.234793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5021 | −0.889218 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.07960 | −0.140126 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.446046 | 0.0202539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.5332 | 1.74610 | 0.873052 | − | 0.487627i | \(-0.162138\pi\) | ||||
0.873052 | + | 0.487627i | \(0.162138\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.32106 | −0.104962 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3207 | 0.781672 | 0.390836 | − | 0.920460i | \(-0.372186\pi\) | ||||
0.390836 | + | 0.920460i | \(0.372186\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.41390 | 0.108717 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.98676 | 0.358978 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.64403 | −0.163457 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7924 | −0.751729 | −0.375865 | − | 0.926675i | \(-0.622654\pi\) | ||||
−0.375865 | + | 0.926675i | \(0.622654\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.45950 | −0.154252 | −0.0771258 | − | 0.997021i | \(-0.524574\pi\) | ||||
−0.0771258 | + | 0.997021i | \(0.524574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.1546 | −0.896868 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.27626 | 0.101092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8751 | −0.659326 | −0.329663 | − | 0.944099i | \(-0.606935\pi\) | ||||
−0.329663 | + | 0.944099i | \(0.606935\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.33796 | 0.236138 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.16161 | 0.0954376 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.53270 | −0.375996 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 78.5497 | 3.45461 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.53893 | −0.287027 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.52656 | −0.285934 | −0.142967 | − | 0.989727i | \(-0.545664\pi\) | ||||
−0.142967 | + | 0.989727i | \(0.545664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.7225 | 1.43086 | 0.715428 | − | 0.698686i | \(-0.246232\pi\) | ||||
0.715428 | + | 0.698686i | \(0.246232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.67658 | 0.116816 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.63306 | −0.0711374 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5231 | −0.457524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.528261 | −0.0229246 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.5243 | −0.932320 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.63556 | −0.243647 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.03006 | −0.260216 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.8733 | 1.54517 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.3810 | −1.52115 | −0.760573 | − | 0.649252i | \(-0.775082\pi\) | ||||
−0.760573 | + | 0.649252i | \(0.775082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.9128 | 1.02620 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.7715 | 1.06109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.10909 | 0.132935 | 0.0664676 | − | 0.997789i | \(-0.478827\pi\) | ||||
0.0664676 | + | 0.997789i | \(0.478827\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.27251 | 0.0543096 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9199 | −0.465204 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.4666 | 0.572658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.93184 | 0.294240 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.3530 | 0.904757 | 0.452379 | − | 0.891826i | \(-0.350576\pi\) | ||||
0.452379 | + | 0.891826i | \(0.350576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.9788 | −0.633534 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.74709 | 0.115982 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8320 | 0.625093 | 0.312546 | − | 0.949903i | \(-0.398818\pi\) | ||||
0.312546 | + | 0.949903i | \(0.398818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.77003 | −0.0744659 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.871845 | −0.0366141 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.6942 | 1.24485 | 0.622423 | − | 0.782681i | \(-0.286148\pi\) | ||||
0.622423 | + | 0.782681i | \(0.286148\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.20664 | −0.343437 | −0.171719 | − | 0.985146i | \(-0.554932\pi\) | ||||
−0.171719 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.15759 | −0.215462 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8442 | −0.452232 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.6609 | 1.44295 | 0.721477 | − | 0.692438i | \(-0.243464\pi\) | ||||
0.721477 | + | 0.692438i | \(0.243464\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.38508 | −0.0991207 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.888515 | 0.0368618 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 67.0011 | 2.77490 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.42981 | −0.224495 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3087 | 0.920780 | 0.460390 | − | 0.887717i | \(-0.347710\pi\) | ||||
0.460390 | + | 0.887717i | \(0.347710\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.38759 | 0.304400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.00129542 | −5.32865e−5 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.3835 | 1.98687 | 0.993435 | − | 0.114394i | \(-0.0364926\pi\) | ||||
0.993435 | + | 0.114394i | \(0.0364926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.578755 | −0.0237266 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.7180 | 0.684224 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.7439 | −1.01101 | −0.505503 | − | 0.862825i | \(-0.668693\pi\) | ||||
−0.505503 | + | 0.862825i | \(0.668693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.4466 | 1.69064 | 0.845320 | − | 0.534260i | \(-0.179410\pi\) | ||||
0.845320 | + | 0.534260i | \(0.179410\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.13778 | 0.331396 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.6345 | −1.24547 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.13247 | 0.330087 | 0.165043 | − | 0.986286i | \(-0.447224\pi\) | ||||
0.165043 | + | 0.986286i | \(0.447224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.40434 | 0.178473 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −53.4021 | −2.16042 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6117 | −0.549771 | −0.274886 | − | 0.961477i | \(-0.588640\pi\) | ||||
−0.274886 | + | 0.961477i | \(0.588640\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65061 | 0.308503 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.02573 | −0.0815528 | −0.0407764 | − | 0.999168i | \(-0.512983\pi\) | ||||
−0.0407764 | + | 0.999168i | \(0.512983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.8882 | −0.558213 | −0.279106 | − | 0.960260i | \(-0.590038\pi\) | ||||
−0.279106 | + | 0.960260i | \(0.590038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.53227 | 0.141745 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.20336 | 0.328661 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.224859 | −0.00899436 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.4272 | −0.496293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.38424 | 0.0950661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.724370 | 0.0288367 | 0.0144184 | − | 0.999896i | \(-0.495410\pi\) | ||||
0.0144184 | + | 0.999896i | \(0.495410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.08873 | −0.122766 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.72177 | 0.147694 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.3885 | −0.966308 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.17968 | 0.165345 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.4957 | 0.730537 | 0.365269 | − | 0.930902i | \(-0.380977\pi\) | ||||
0.365269 | + | 0.930902i | \(0.380977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.03941 | −0.277607 | −0.138804 | − | 0.990320i | \(-0.544326\pi\) | ||||
−0.138804 | + | 0.990320i | \(0.544326\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.32407 | 0.209635 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.7368 | −1.83741 | −0.918706 | − | 0.394942i | \(-0.870765\pi\) | ||||
−0.918706 | + | 0.394942i | \(0.870765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.03698 | 0.119212 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.97964 | −0.116781 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.06283 | 0.0807247 | 0.0403624 | − | 0.999185i | \(-0.487149\pi\) | ||||
0.0403624 | + | 0.999185i | \(0.487149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.55293 | −0.295117 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.12260 | −0.238865 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.3610 | 1.02688 | 0.513440 | − | 0.858126i | \(-0.328371\pi\) | ||||
0.513440 | + | 0.858126i | \(0.328371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.1696 | −0.978982 | −0.489491 | − | 0.872008i | \(-0.662817\pi\) | ||||
−0.489491 | + | 0.872008i | \(0.662817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.86761 | −0.0725321 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.61815 | 0.101527 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.8441 | −0.690927 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.4949 | 0.560404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.31572 | −0.282420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.4885 | 0.558491 | 0.279245 | − | 0.960220i | \(-0.409916\pi\) | ||||
0.279245 | + | 0.960220i | \(0.409916\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.07002 | −0.118165 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.9862 | −1.69053 | −0.845263 | − | 0.534350i | \(-0.820556\pi\) | ||||
−0.845263 | + | 0.534350i | \(0.820556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.279926 | 0.0107426 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.04675 | −0.346672 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.4959 | 0.439878 | 0.219939 | − | 0.975514i | \(-0.429414\pi\) | ||||
0.219939 | + | 0.975514i | \(0.429414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.51313 | −0.248854 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9796 | −0.609661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45.5508 | −1.73535 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.9678 | 1.82478 | 0.912390 | − | 0.409323i | \(-0.134235\pi\) | ||||
0.912390 | + | 0.409323i | \(0.134235\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.01226 | 0.190400 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.0833 | −0.761802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.63147 | 0.0996741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.78880 | 0.0676586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4427 | 0.696571 | 0.348285 | − | 0.937389i | \(-0.386764\pi\) | ||||
0.348285 | + | 0.937389i | \(0.386764\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7857 | −0.406792 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.9813 | 0.714878 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.6485 | −0.475694 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.1171 | 1.39396 | 0.696981 | − | 0.717090i | \(-0.254526\pi\) | ||||
0.696981 | + | 0.717090i | \(0.254526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.4461 | −0.579274 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0720 | 0.452099 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.2161 | 1.16742 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.43119 | 0.165486 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.72522 | −0.325396 | −0.162698 | − | 0.986676i | \(-0.552020\pi\) | ||||
−0.162698 | + | 0.986676i | \(0.552020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.35488 | −0.199426 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.3349 | 0.570311 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5090 | 0.575988 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.9456 | −1.44441 | −0.722206 | − | 0.691678i | \(-0.756872\pi\) | ||||
−0.722206 | + | 0.691678i | \(0.756872\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.83124 | 0.0677310 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0832 | −0.409367 | −0.204684 | − | 0.978828i | \(-0.565617\pi\) | ||||
−0.204684 | + | 0.978828i | \(0.565617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.66868 | 0.319749 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.7843 | −1.72332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.0330 | −1.43585 | −0.717927 | − | 0.696119i | \(-0.754909\pi\) | ||||
−0.717927 | + | 0.696119i | \(0.754909\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.44863 | 0.310368 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.69917 | 0.319142 | 0.159571 | − | 0.987186i | \(-0.448989\pi\) | ||||
0.159571 | + | 0.987186i | \(0.448989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.52526 | −0.202430 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.01912 | −0.0372876 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.53672 | −0.129229 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.1732 | −1.10104 | −0.550518 | − | 0.834823i | \(-0.685570\pi\) | ||||
−0.550518 | + | 0.834823i | \(0.685570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.6393 | 0.934347 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.768146 | −0.0279557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.93772 | −0.0704277 | −0.0352138 | − | 0.999380i | \(-0.511211\pi\) | ||||
−0.0352138 | + | 0.999380i | \(0.511211\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.3071 | −0.737102 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.4526 | −1.17641 | −0.588203 | − | 0.808713i | \(-0.700164\pi\) | ||||
−0.588203 | + | 0.808713i | \(0.700164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.5459 | 0.562799 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.663827 | 0.0240007 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.06470 | −0.0745519 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5848 | −0.489882 | −0.244941 | − | 0.969538i | \(-0.578769\pi\) | ||||
−0.244941 | + | 0.969538i | \(0.578769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.6727 | −0.816539 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.72819 | −0.206029 | −0.103014 | − | 0.994680i | \(-0.532849\pi\) | ||||
−0.103014 | + | 0.994680i | \(0.532849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4922 | −0.376890 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.35022 | 0.156063 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.9041 | −0.426510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.0291 | −0.859828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.05174 | −0.180534 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.3697 | 0.441494 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.9123 | −1.77918 | −0.889591 | − | 0.456758i | \(-0.849010\pi\) | ||||
−0.889591 | + | 0.456758i | \(0.849010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.4884 | −1.01421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.11082 | −0.0394963 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.97360 | 0.176618 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.1906 | 0.574222 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.1371 | 1.13836 | 0.569178 | − | 0.822214i | \(-0.307262\pi\) | ||||
0.569178 | + | 0.822214i | \(0.307262\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.52873 | 0.230970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.40919 | −0.332457 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.1990 | 1.24215 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.27829 | 0.150790 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.0734 | 0.460206 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.77641 | 0.238246 | 0.119123 | − | 0.992880i | \(-0.461992\pi\) | ||||
0.119123 | + | 0.992880i | \(0.461992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4544 | 1.13963 | 0.569814 | − | 0.821774i | \(-0.307015\pi\) | ||||
0.569814 | + | 0.821774i | \(0.307015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.04487 | −0.106788 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.22451 | 0.112950 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.28410 | −0.289824 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.40760 | −0.119071 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.8054 | −0.865716 | −0.432858 | − | 0.901462i | \(-0.642495\pi\) | ||||
−0.432858 | + | 0.901462i | \(0.642495\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.2673 | −0.532184 | −0.266092 | − | 0.963948i | \(-0.585732\pi\) | ||||
−0.266092 | + | 0.963948i | \(0.585732\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.6496 | 0.614481 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.3232 | −0.463292 | −0.231646 | − | 0.972800i | \(-0.574411\pi\) | ||||
−0.231646 | + | 0.972800i | \(0.574411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.9301 | −1.73414 | −0.867072 | − | 0.498183i | \(-0.834001\pi\) | ||||
−0.867072 | + | 0.498183i | \(0.834001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.04405 | 0.140287 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.98164 | 0.103308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.38924 | 0.0480765 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.41763 | 0.118130 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8275 | 0.684520 | 0.342260 | − | 0.939605i | \(-0.388808\pi\) | ||||
0.342260 | + | 0.939605i | \(0.388808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.47992 | −0.119997 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2904 | −0.595512 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.16226 | −0.108785 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.2253 | −0.660590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.1428 | 0.794260 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.6249 | −0.604173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1965 | −0.588798 | −0.294399 | − | 0.955683i | \(-0.595119\pi\) | ||||
−0.294399 | + | 0.955683i | \(0.595119\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00299 | −0.102700 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.21284 | −0.0414299 | −0.0207149 | − | 0.999785i | \(-0.506594\pi\) | ||||
−0.0207149 | + | 0.999785i | \(0.506594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6809 | 0.773863 | 0.386932 | − | 0.922108i | \(-0.373535\pi\) | ||||
0.386932 | + | 0.922108i | \(0.373535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.80131 | 0.163628 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.21615 | 0.313721 | 0.156861 | − | 0.987621i | \(-0.449863\pi\) | ||||
0.156861 | + | 0.987621i | \(0.449863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.08412 | 0.308869 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7717 | −0.569596 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 88.8000 | 3.01233 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.8064 | 1.07772 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.321073 | −0.0108667 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.77441 | −0.330435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5985 | −1.13454 | −0.567270 | − | 0.823532i | \(-0.692000\pi\) | ||||
−0.567270 | + | 0.823532i | \(0.692000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.4973 | −0.961191 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.4124 | −1.66475 | −0.832373 | − | 0.554216i | \(-0.813018\pi\) | ||||
−0.832373 | + | 0.554216i | \(0.813018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.9558 | 0.940786 | 0.470393 | − | 0.882457i | \(-0.344112\pi\) | ||||
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.733879 | 0.0246691 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.31976 | −0.0778899 | −0.0389449 | − | 0.999241i | \(-0.512400\pi\) | ||||
−0.0389449 | + | 0.999241i | \(0.512400\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.33568 | 0.0783361 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.74903 | −0.192600 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.5344 | −0.988331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.37718 | 0.280018 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.8058 | 0.460963 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.2650 | −0.575819 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.56886 | 0.185526 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.34123 | 0.111189 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.2206 | −1.10429 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.0556 | −0.665936 | −0.332968 | − | 0.942938i | \(-0.608050\pi\) | ||||
−0.332968 | + | 0.942938i | \(0.608050\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.5077 | 0.481189 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8720 | −0.625258 | −0.312629 | − | 0.949875i | \(-0.601210\pi\) | ||||
−0.312629 | + | 0.949875i | \(0.601210\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.85895 | 0.193903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.76782 | −0.0584424 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.74000 | −0.156529 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.4602 | 1.76349 | 0.881745 | − | 0.471727i | \(-0.156369\pi\) | ||||
0.881745 | + | 0.471727i | \(0.156369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.4381 | 0.772312 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.3362 | 0.537713 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.3184 | 0.503666 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.14201 | 0.201730 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.7913 | −1.01023 | −0.505114 | − | 0.863052i | \(-0.668550\pi\) | ||||
−0.505114 | + | 0.863052i | \(0.668550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.4882 | −0.442059 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.33992 | 0.305775 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.81636 | −0.124808 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.5516 | −0.867405 | −0.433702 | − | 0.901056i | \(-0.642793\pi\) | ||||
−0.433702 | + | 0.901056i | \(0.642793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.9683 | 0.586374 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.2200 | −1.50673 | −0.753364 | − | 0.657603i | \(-0.771570\pi\) | ||||
−0.753364 | + | 0.657603i | \(0.771570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.4525 | −0.633459 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.21120 | 0.0394003 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.8101 | 1.26116 | 0.630579 | − | 0.776125i | \(-0.282817\pi\) | ||||
0.630579 | + | 0.776125i | \(0.282817\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.9301 | −0.776804 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.1619 | −0.783502 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1074 | 0.456982 | 0.228491 | − | 0.973546i | \(-0.426621\pi\) | ||||
0.228491 | + | 0.973546i | \(0.426621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.16512 | 0.231858 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29.0426 | 0.938814 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.08746 | −0.131991 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3198 | −0.623220 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.05659 | 0.130722 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.31344 | 0.106664 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.47705 | −0.304761 | −0.152381 | − | 0.988322i | \(-0.548694\pi\) | ||||
−0.152381 | + | 0.988322i | \(0.548694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.03290 | −0.0331814 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.76536 | −0.217111 | −0.108555 | − | 0.994090i | \(-0.534622\pi\) | ||||
−0.108555 | + | 0.994090i | \(0.534622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6037 | −0.404056 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.9991 | −0.384280 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.48932 | 0.143626 | 0.0718131 | − | 0.997418i | \(-0.477121\pi\) | ||||
0.0718131 | + | 0.997418i | \(0.477121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0937 | 1.72884 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8310 | −0.569301 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.64779 | 0.212032 | 0.106016 | − | 0.994364i | \(-0.466191\pi\) | ||||
0.106016 | + | 0.994364i | \(0.466191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.00179965 | 5.73415e−5 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.9121 | 0.379167 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.5370 | −0.430450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9862 | −0.889011 | −0.444505 | − | 0.895776i | \(-0.646621\pi\) | ||||
−0.444505 | + | 0.895776i | \(0.646621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6022 | 0.558589 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.2253 | −0.736292 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.59766 | 0.303961 | 0.151981 | − | 0.988383i | \(-0.451435\pi\) | ||||
0.151981 | + | 0.988383i | \(0.451435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.98967 | −0.157866 |
(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 | 2004.2.a.b.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 6012.2.a.f.1.3 | 5 | |||
4.3 | odd | 2 | 8016.2.a.q.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.b.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6012.2.a.f.1.3 | 5 | 3.2 | odd | 2 | |||
8016.2.a.q.1.3 | 5 | 4.3 | odd | 2 |