Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(703,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.703");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.56070144.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(0.500000 + 1.19293i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.703 |
Dual form | 1728.3.g.m.703.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.59655 | −1.31931 | −0.659655 | − | 0.751569i | \(-0.729297\pi\) | ||||
−0.659655 | + | 0.751569i | \(0.729297\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.56106i | − 0.651580i | −0.945442 | − | 0.325790i | \(-0.894370\pi\) | ||||
0.945442 | − | 0.325790i | \(-0.105630\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.16066i | 0.105515i | 0.998607 | + | 0.0527575i | \(0.0168010\pi\) | ||||
−0.998607 | + | 0.0527575i | \(0.983199\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.5580 | −1.04292 | −0.521461 | − | 0.853275i | \(-0.674613\pi\) | ||||
−0.521461 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.32636 | −0.313315 | −0.156658 | − | 0.987653i | \(-0.550072\pi\) | ||||
−0.156658 | + | 0.987653i | \(0.550072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.1900i | 1.32579i | 0.748712 | + | 0.662896i | \(0.230673\pi\) | ||||
−0.748712 | + | 0.662896i | \(0.769327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 10.4309i | − 0.453515i | −0.973951 | − | 0.226758i | \(-0.927187\pi\) | ||||
0.973951 | − | 0.226758i | \(-0.0728125\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.5144 | 0.740577 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −47.0288 | −1.62168 | −0.810842 | − | 0.585265i | \(-0.800990\pi\) | ||||
−0.810842 | + | 0.585265i | \(0.800990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.3862i | 0.722135i | 0.932540 | + | 0.361067i | \(0.117588\pi\) | ||||
−0.932540 | + | 0.361067i | \(0.882412\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.0872i | 0.859635i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 60.7288 | 1.64132 | 0.820659 | − | 0.571418i | \(-0.193606\pi\) | ||||
0.820659 | + | 0.571418i | \(0.193606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.81696 | −0.215048 | −0.107524 | − | 0.994202i | \(-0.534292\pi\) | ||||
−0.107524 | + | 0.994202i | \(0.534292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 29.1160i | − 0.677116i | −0.940945 | − | 0.338558i | \(-0.890061\pi\) | ||||
0.940945 | − | 0.338558i | \(-0.109939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 78.2321i | − 1.66451i | −0.554392 | − | 0.832256i | \(-0.687049\pi\) | ||||
0.554392 | − | 0.832256i | \(-0.312951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.1968 | 0.575444 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −62.7623 | −1.18419 | −0.592097 | − | 0.805866i | \(-0.701700\pi\) | ||||
−0.592097 | + | 0.805866i | \(0.701700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.65637i | − 0.139207i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 109.116i | 1.84942i | 0.380666 | + | 0.924712i | \(0.375695\pi\) | ||||
−0.380666 | + | 0.924712i | \(0.624305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 66.4997 | 1.09016 | 0.545079 | − | 0.838384i | \(-0.316500\pi\) | ||||
0.545079 | + | 0.838384i | \(0.316500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 89.4360 | 1.37594 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 81.9685i | − 1.22341i | −0.791086 | − | 0.611705i | \(-0.790484\pi\) | ||||
0.791086 | − | 0.611705i | \(-0.209516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.7276i | 0.573629i | 0.957986 | + | 0.286814i | \(0.0925963\pi\) | ||||
−0.957986 | + | 0.286814i | \(0.907404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.29030 | −0.0587713 | −0.0293856 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293856 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.29386 | 0.0687514 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.20371i | 0.0658698i | 0.999457 | + | 0.0329349i | \(0.0104854\pi\) | ||||
−0.999457 | + | 0.0329349i | \(0.989515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 115.114i | − 1.38691i | −0.720498 | − | 0.693457i | \(-0.756087\pi\) | ||||
0.720498 | − | 0.693457i | \(-0.243913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.1356 | 0.413359 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 141.504 | 1.58993 | 0.794965 | − | 0.606656i | \(-0.207489\pi\) | ||||
0.794965 | + | 0.606656i | \(0.207489\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 61.8388i | 0.679547i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 166.167i | − 1.74913i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 136.769 | 1.40999 | 0.704994 | − | 0.709213i | \(-0.250950\pi\) | ||||
0.704994 | + | 0.709213i | \(0.250950\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −45.2350 | −0.447871 | −0.223935 | − | 0.974604i | \(-0.571890\pi\) | ||||
−0.223935 | + | 0.974604i | \(0.571890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 114.604i | − 1.11266i | −0.830963 | − | 0.556328i | \(-0.812210\pi\) | ||||
0.830963 | − | 0.556328i | \(-0.187790\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 194.930i | 1.82178i | 0.412652 | + | 0.910889i | \(0.364603\pi\) | ||||
−0.412652 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.35150 | −0.0582706 | −0.0291353 | − | 0.999575i | \(-0.509275\pi\) | ||||
−0.0291353 | + | 0.999575i | \(0.509275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 48.7068 | 0.431034 | 0.215517 | − | 0.976500i | \(-0.430856\pi\) | ||||
0.215517 | + | 0.976500i | \(0.430856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 68.8076i | 0.598327i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.2938i | 0.204150i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.653 | 0.988867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 42.7824 | 0.342259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 86.3509i | 0.679929i | 0.940438 | + | 0.339964i | \(0.110415\pi\) | ||||
−0.940438 | + | 0.339964i | \(0.889585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 90.6946i | 0.692325i | 0.938175 | + | 0.346162i | \(0.112515\pi\) | ||||
−0.938175 | + | 0.346162i | \(0.887485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 114.893 | 0.863859 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 148.355 | 1.08288 | 0.541442 | − | 0.840738i | \(-0.317878\pi\) | ||||
0.541442 | + | 0.840738i | \(0.317878\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 101.426i | 0.729684i | 0.931069 | + | 0.364842i | \(0.118877\pi\) | ||||
−0.931069 | + | 0.364842i | \(0.881123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 15.7363i | − 0.110044i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 310.228 | 2.13950 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 219.221 | 1.47128 | 0.735639 | − | 0.677373i | \(-0.236882\pi\) | ||||
0.735639 | + | 0.677373i | \(0.236882\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 26.1638i | − 0.173270i | −0.996240 | − | 0.0866350i | \(-0.972389\pi\) | ||||
0.996240 | − | 0.0866350i | \(-0.0276114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 147.671i | − 0.952719i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 257.715 | 1.64150 | 0.820748 | − | 0.571290i | \(-0.193557\pi\) | ||||
0.820748 | + | 0.571290i | \(0.193557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.5757 | −0.295501 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 140.310i | − 0.860796i | −0.902639 | − | 0.430398i | \(-0.858373\pi\) | ||||
0.902639 | − | 0.430398i | \(-0.141627\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 28.2435i | − 0.169123i | −0.996418 | − | 0.0845613i | \(-0.973051\pi\) | ||||
0.996418 | − | 0.0845613i | \(-0.0269489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8193 | 0.0876881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −127.532 | −0.737177 | −0.368589 | − | 0.929593i | \(-0.620159\pi\) | ||||
−0.368589 | + | 0.929593i | \(0.620159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 84.4453i | − 0.482545i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 167.254i | − 0.934378i | −0.884157 | − | 0.467189i | \(-0.845267\pi\) | ||||
0.884157 | − | 0.467189i | \(-0.154733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.841 | 0.921775 | 0.460887 | − | 0.887459i | \(-0.347531\pi\) | ||||
0.460887 | + | 0.887459i | \(0.347531\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −400.600 | −2.16541 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.18211i | − 0.0330594i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 163.153i | 0.854203i | 0.904204 | + | 0.427102i | \(0.140465\pi\) | ||||
−0.904204 | + | 0.427102i | \(0.859535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −137.611 | −0.713010 | −0.356505 | − | 0.934293i | \(-0.616032\pi\) | ||||
−0.356505 | + | 0.934293i | \(0.616032\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −132.978 | −0.675017 | −0.337509 | − | 0.941322i | \(-0.609584\pi\) | ||||
−0.337509 | + | 0.941322i | \(0.609584\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 371.097i | 1.86481i | 0.361418 | + | 0.932404i | \(0.382293\pi\) | ||||
−0.361418 | + | 0.932404i | \(0.617707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 214.501i | 1.05666i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 58.1615 | 0.283715 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.2372 | −0.139891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 239.571i | − 1.13541i | −0.823233 | − | 0.567704i | \(-0.807832\pi\) | ||||
0.823233 | − | 0.567704i | \(-0.192168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 192.065i | 0.893326i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 102.105 | 0.470528 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.2147 | 0.326763 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 121.555i | 0.545089i | 0.962143 | + | 0.272545i | \(0.0878652\pi\) | ||||
−0.962143 | + | 0.272545i | \(0.912135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 223.023i | − 0.982481i | −0.871024 | − | 0.491241i | \(-0.836544\pi\) | ||||
0.871024 | − | 0.491241i | \(-0.163456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 139.599 | 0.609605 | 0.304802 | − | 0.952416i | \(-0.401410\pi\) | ||||
0.304802 | + | 0.952416i | \(0.401410\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −103.682 | −0.444986 | −0.222493 | − | 0.974934i | \(-0.571419\pi\) | ||||
−0.222493 | + | 0.974934i | \(0.571419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 516.061i | 2.19601i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 110.844i | − 0.463783i | −0.972742 | − | 0.231892i | \(-0.925508\pi\) | ||||
0.972742 | − | 0.231892i | \(-0.0744915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −80.6426 | −0.334616 | −0.167308 | − | 0.985905i | \(-0.553508\pi\) | ||||
−0.167308 | + | 0.985905i | \(0.553508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −186.001 | −0.759188 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 341.526i | − 1.38270i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 471.180i | − 1.87721i | −0.344990 | − | 0.938606i | \(-0.612118\pi\) | ||||
0.344990 | − | 0.938606i | \(-0.387882\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.1067 | 0.0478526 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −330.588 | −1.28633 | −0.643167 | − | 0.765726i | \(-0.722380\pi\) | ||||
−0.643167 | + | 0.765726i | \(0.722380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 276.988i | − 1.06945i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 494.228i | 1.87919i | 0.342283 | + | 0.939597i | \(0.388800\pi\) | ||||
−0.342283 | + | 0.939597i | \(0.611200\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 414.014 | 1.56232 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 214.548 | 0.797576 | 0.398788 | − | 0.917043i | \(-0.369431\pi\) | ||||
0.398788 | + | 0.917043i | \(0.369431\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 283.519i | 1.04620i | 0.852272 | + | 0.523099i | \(0.175224\pi\) | ||||
−0.852272 | + | 0.523099i | \(0.824776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.4890i | 0.0781419i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −107.432 | −0.387842 | −0.193921 | − | 0.981017i | \(-0.562121\pi\) | ||||
−0.193921 | + | 0.981017i | \(0.562121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.7120 | −0.0986193 | −0.0493096 | − | 0.998784i | \(-0.515702\pi\) | ||||
−0.0493096 | + | 0.998784i | \(0.515702\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 311.956i | − 1.10232i | −0.834400 | − | 0.551159i | \(-0.814186\pi\) | ||||
0.834400 | − | 0.551159i | \(-0.185814\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.2147i | 0.140121i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −260.630 | −0.901834 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 536.810 | 1.83212 | 0.916058 | − | 0.401045i | \(-0.131353\pi\) | ||||
0.916058 | + | 0.401045i | \(0.131353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 719.789i | − 2.43996i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 141.421i | 0.472982i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −132.800 | −0.441195 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −438.668 | −1.43826 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 296.075i | 0.964415i | 0.876057 | + | 0.482208i | \(0.160165\pi\) | ||||
−0.876057 | + | 0.482208i | \(0.839835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 274.720i | − 0.883345i | −0.897176 | − | 0.441673i | \(-0.854385\pi\) | ||||
0.897176 | − | 0.441673i | \(-0.145615\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 204.294 | 0.652697 | 0.326348 | − | 0.945250i | \(-0.394182\pi\) | ||||
0.326348 | + | 0.945250i | \(0.394182\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.6889 | 0.0873466 | 0.0436733 | − | 0.999046i | \(-0.486094\pi\) | ||||
0.0436733 | + | 0.999046i | \(0.486094\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 54.5847i | − 0.171112i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 134.171i | − 0.415390i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −251.018 | −0.772364 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −356.821 | −1.08456 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 77.6640i | 0.234634i | 0.993094 | + | 0.117317i | \(0.0374294\pi\) | ||||
−0.993094 | + | 0.117317i | \(0.962571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 540.709i | 1.61406i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 314.619 | 0.933588 | 0.466794 | − | 0.884366i | \(-0.345409\pi\) | ||||
0.466794 | + | 0.884366i | \(0.345409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.9828 | −0.0761960 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 352.099i | − 1.02653i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 485.244i | − 1.39840i | −0.714928 | − | 0.699198i | \(-0.753540\pi\) | ||||
0.714928 | − | 0.699198i | \(-0.246460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 61.2165 | 0.175405 | 0.0877027 | − | 0.996147i | \(-0.472047\pi\) | ||||
0.0877027 | + | 0.996147i | \(0.472047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 274.644 | 0.778028 | 0.389014 | − | 0.921232i | \(-0.372816\pi\) | ||||
0.389014 | + | 0.921232i | \(0.372816\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 268.662i | − 0.756793i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 406.229i | − 1.13156i | −0.824557 | − | 0.565779i | \(-0.808576\pi\) | ||||
0.824557 | − | 0.565779i | \(-0.191424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −273.538 | −0.757722 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.3012 | 0.0775375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 678.650i | 1.84918i | 0.380959 | + | 0.924592i | \(0.375594\pi\) | ||||
−0.380959 | + | 0.924592i | \(0.624406\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 286.263i | 0.771597i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1447 | −0.0459645 | −0.0229822 | − | 0.999736i | \(-0.507316\pi\) | ||||
−0.0229822 | + | 0.999736i | \(0.507316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 637.617 | 1.69129 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 669.773i | 1.76721i | 0.468231 | + | 0.883606i | \(0.344891\pi\) | ||||
−0.468231 | + | 0.883606i | \(0.655109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 282.840i | 0.738486i | 0.929333 | + | 0.369243i | \(0.120383\pi\) | ||||
−0.929333 | + | 0.369243i | \(0.879617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34.9212 | −0.0907043 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 197.725 | 0.508290 | 0.254145 | − | 0.967166i | \(-0.418206\pi\) | ||||
0.254145 | + | 0.967166i | \(0.418206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 55.5584i | 0.142093i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 34.3265i | − 0.0869026i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 546.375 | 1.37626 | 0.688129 | − | 0.725588i | \(-0.258432\pi\) | ||||
0.688129 | + | 0.725588i | \(0.258432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 586.152 | 1.46173 | 0.730863 | − | 0.682525i | \(-0.239118\pi\) | ||||
0.730863 | + | 0.682525i | \(0.239118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 303.512i | − 0.753131i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 70.4857i | 0.173184i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −614.056 | −1.50136 | −0.750679 | − | 0.660667i | \(-0.770274\pi\) | ||||
−0.750679 | + | 0.660667i | \(0.770274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 497.685 | 1.20505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 759.354i | 1.82977i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 509.128i | 1.21510i | 0.794281 | + | 0.607551i | \(0.207848\pi\) | ||||
−0.794281 | + | 0.607551i | \(0.792152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −478.025 | −1.13545 | −0.567725 | − | 0.823218i | \(-0.692176\pi\) | ||||
−0.567725 | + | 0.823218i | \(0.692176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −98.6144 | −0.232034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 303.309i | − 0.710325i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 158.810i | 0.368468i | 0.982882 | + | 0.184234i | \(0.0589804\pi\) | ||||
−0.982882 | + | 0.184234i | \(0.941020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −367.803 | −0.849429 | −0.424715 | − | 0.905327i | \(-0.639626\pi\) | ||||
−0.424715 | + | 0.905327i | \(0.639626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 262.754 | 0.601267 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 145.096i | − 0.330514i | −0.986251 | − | 0.165257i | \(-0.947155\pi\) | ||||
0.986251 | − | 0.165257i | \(-0.0528453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 771.496i | − 1.74153i | −0.491703 | − | 0.870763i | \(-0.663626\pi\) | ||||
0.491703 | − | 0.870763i | \(-0.336374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −933.436 | −2.09761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −56.2630 | −0.125307 | −0.0626536 | − | 0.998035i | \(-0.519956\pi\) | ||||
−0.0626536 | + | 0.998035i | \(0.519956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 10.2335i | − 0.0226908i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 407.923i | − 0.896533i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −804.889 | −1.76125 | −0.880623 | − | 0.473817i | \(-0.842876\pi\) | ||||
−0.880623 | + | 0.473817i | \(0.842876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −46.1301 | −0.100065 | −0.0500327 | − | 0.998748i | \(-0.515933\pi\) | ||||
−0.0500327 | + | 0.998748i | \(0.515933\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 273.418i | − 0.590536i | −0.955414 | − | 0.295268i | \(-0.904591\pi\) | ||||
0.955414 | − | 0.295268i | \(-0.0954090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 109.131i | 0.233684i | 0.993150 | + | 0.116842i | \(0.0372772\pi\) | ||||
−0.993150 | + | 0.116842i | \(0.962723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −373.863 | −0.797150 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.7939 | 0.0714459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 466.379i | 0.981850i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.5978i | 0.0889306i | 0.999011 | + | 0.0444653i | \(0.0141584\pi\) | ||||
−0.999011 | + | 0.0444653i | \(0.985842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −823.361 | −1.71177 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −902.202 | −1.86021 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 445.984i | 0.915779i | 0.889009 | + | 0.457889i | \(0.151394\pi\) | ||||
−0.889009 | + | 0.457889i | \(0.848606\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 565.533i | 1.15180i | 0.817521 | + | 0.575899i | \(0.195348\pi\) | ||||
−0.817521 | + | 0.575899i | \(0.804652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 250.492 | 0.508098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 185.761 | 0.373765 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 923.261i | − 1.85022i | −0.379696 | − | 0.925111i | \(-0.623971\pi\) | ||||
0.379696 | − | 0.925111i | \(-0.376029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 406.646i | − 0.808441i | −0.914662 | − | 0.404220i | \(-0.867543\pi\) | ||||
0.914662 | − | 0.404220i | \(-0.132457\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 298.394 | 0.590880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −674.031 | −1.32423 | −0.662113 | − | 0.749404i | \(-0.730340\pi\) | ||||
−0.662113 | + | 0.749404i | \(0.730340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.5683i | 0.0382942i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 755.988i | 1.46794i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 90.8011 | 0.175631 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 513.618 | 0.985831 | 0.492916 | − | 0.870077i | \(-0.335931\pi\) | ||||
0.492916 | + | 0.870077i | \(0.335931\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 381.030i | 0.728547i | 0.931292 | + | 0.364274i | \(0.118683\pi\) | ||||
−0.931292 | + | 0.364274i | \(0.881317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 119.237i | − 0.226256i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 420.197 | 0.794324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 119.540 | 0.224278 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1285.87i | − 2.40349i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.7270i | 0.0607179i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −626.913 | −1.15880 | −0.579402 | − | 0.815042i | \(-0.696714\pi\) | ||||
−0.579402 | + | 0.815042i | \(0.696714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.8980 | 0.0768770 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 18.9275i | − 0.0346023i | −0.999850 | − | 0.0173012i | \(-0.994493\pi\) | ||||
0.999850 | − | 0.0173012i | \(-0.00550740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1184.66i | − 2.15001i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.7344 | 0.0429194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.9003 | 0.0482949 | 0.0241475 | − | 0.999708i | \(-0.492313\pi\) | ||||
0.0241475 | + | 0.999708i | \(0.492313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 394.755i | 0.706180i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 488.414i | − 0.867520i | −0.901029 | − | 0.433760i | \(-0.857187\pi\) | ||||
0.901029 | − | 0.433760i | \(-0.142813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −321.297 | −0.568667 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −266.712 | −0.468739 | −0.234369 | − | 0.972148i | \(-0.575302\pi\) | ||||
−0.234369 | + | 0.972148i | \(0.575302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 880.359i | 1.54178i | 0.636966 | + | 0.770892i | \(0.280189\pi\) | ||||
−0.636966 | + | 0.770892i | \(0.719811\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 193.121i | − 0.335863i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 82.9805 | 0.143814 | 0.0719069 | − | 0.997411i | \(-0.477092\pi\) | ||||
0.0719069 | + | 0.997411i | \(0.477092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −525.041 | −0.903685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 72.8460i | − 0.124950i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 965.562i | 1.64491i | 0.568831 | + | 0.822455i | \(0.307396\pi\) | ||||
−0.568831 | + | 0.822455i | \(0.692604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −563.909 | −0.957400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −289.460 | −0.488128 | −0.244064 | − | 0.969759i | \(-0.578481\pi\) | ||||
−0.244064 | + | 0.969759i | \(0.578481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 160.255i | − 0.269337i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 448.245i | 0.748322i | 0.927364 | + | 0.374161i | \(0.122069\pi\) | ||||
−0.927364 | + | 0.374161i | \(0.877931\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −229.348 | −0.381610 | −0.190805 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190805 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −789.296 | −1.30462 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 85.4214i | 0.140727i | 0.997521 | + | 0.0703636i | \(0.0224160\pi\) | ||||
−0.997521 | + | 0.0703636i | \(0.977584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1060.67i | 1.73596i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −534.037 | −0.871187 | −0.435593 | − | 0.900144i | \(-0.643461\pi\) | ||||
−0.435593 | + | 0.900144i | \(0.643461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 151.146 | 0.244970 | 0.122485 | − | 0.992470i | \(-0.460914\pi\) | ||||
0.122485 | + | 0.992470i | \(0.460914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 59.2078i | 0.0956507i | 0.998856 | + | 0.0478253i | \(0.0152291\pi\) | ||||
−0.998856 | + | 0.0478253i | \(0.984771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 645.407i | − 1.03597i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −745.077 | −1.19212 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −323.463 | −0.514250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 70.0390i | − 0.110997i | −0.998459 | − | 0.0554984i | \(-0.982325\pi\) | ||||
0.998459 | − | 0.0554984i | \(-0.0176748\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 569.618i | − 0.897036i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −382.292 | −0.600144 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 195.338 | 0.304739 | 0.152370 | − | 0.988324i | \(-0.451310\pi\) | ||||
0.152370 | + | 0.988324i | \(0.451310\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 346.902i | − 0.539505i | −0.962930 | − | 0.269753i | \(-0.913058\pi\) | ||||
0.962930 | − | 0.269753i | \(-0.0869419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 746.221i | 1.15335i | 0.816972 | + | 0.576677i | \(0.195651\pi\) | ||||
−0.816972 | + | 0.576677i | \(0.804349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −126.647 | −0.195142 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −850.046 | −1.30176 | −0.650878 | − | 0.759183i | \(-0.725599\pi\) | ||||
−0.650878 | + | 0.759183i | \(0.725599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 598.271i | − 0.913391i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 817.574i | − 1.24063i | −0.784354 | − | 0.620314i | \(-0.787005\pi\) | ||||
0.784354 | − | 0.620314i | \(-0.212995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 670.001 | 1.01362 | 0.506809 | − | 0.862058i | \(-0.330825\pi\) | ||||
0.506809 | + | 0.862058i | \(0.330825\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −757.898 | −1.13970 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 490.551i | 0.735459i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 77.1838i | 0.115028i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.6868 | −0.0619418 | −0.0309709 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309709 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −71.8534 | −0.106135 | −0.0530675 | − | 0.998591i | \(-0.516900\pi\) | ||||
−0.0530675 | + | 0.998591i | \(0.516900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 623.811i | − 0.918720i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 486.468i | 0.712252i | 0.934438 | + | 0.356126i | \(0.115903\pi\) | ||||
−0.934438 | + | 0.356126i | \(0.884097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −978.632 | −1.42866 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 850.931 | 1.23502 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1153.88i | − 1.66988i | −0.550344 | − | 0.834938i | \(-0.685503\pi\) | ||||
0.550344 | − | 0.834938i | \(-0.314497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 669.062i | − 0.962679i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.9623 | 0.0673778 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −278.673 | −0.397537 | −0.198768 | − | 0.980047i | \(-0.563694\pi\) | ||||
−0.198768 | + | 0.980047i | \(0.563694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1529.76i | 2.17605i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 206.319i | 0.291824i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 128.606 | 0.181390 | 0.0906950 | − | 0.995879i | \(-0.471091\pi\) | ||||
0.0906950 | + | 0.995879i | \(0.471091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 233.507 | 0.327499 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 103.805i | 0.145182i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 99.8703i | − 0.138902i | −0.997585 | − | 0.0694508i | \(-0.977875\pi\) | ||||
0.997585 | − | 0.0694508i | \(-0.0221247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −522.714 | −0.724984 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −870.712 | −1.20098 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 605.619i | − 0.833039i | −0.909127 | − | 0.416519i | \(-0.863250\pi\) | ||||
0.909127 | − | 0.416519i | \(-0.136750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 155.082i | 0.212151i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.5244 | −0.0157223 | −0.00786113 | − | 0.999969i | \(-0.502502\pi\) | ||||
−0.00786113 | + | 0.999969i | \(0.502502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 95.1379 | 0.129088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 241.471i | − 0.326753i | −0.986564 | − | 0.163377i | \(-0.947761\pi\) | ||||
0.986564 | − | 0.163377i | \(-0.0522386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 660.096i | 0.888420i | 0.895923 | + | 0.444210i | \(0.146516\pi\) | ||||
−0.895923 | + | 0.444210i | \(0.853484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1446.10 | −1.94107 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 889.088 | 1.18703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 624.342i | 0.831347i | 0.909514 | + | 0.415674i | \(0.136454\pi\) | ||||
−0.909514 | + | 0.415674i | \(0.863546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 172.590i | 0.228597i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 291.603 | 0.385209 | 0.192604 | − | 0.981276i | \(-0.438307\pi\) | ||||
0.192604 | + | 0.981276i | \(0.438307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1333.83 | 1.75274 | 0.876369 | − | 0.481640i | \(-0.159959\pi\) | ||||
0.876369 | + | 0.481640i | \(0.159959\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9696i | 0.0379680i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1479.40i | − 1.92881i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −75.3889 | −0.0980349 | −0.0490175 | − | 0.998798i | \(-0.515609\pi\) | ||||
−0.0490175 | + | 0.998798i | \(0.515609\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1331.18 | 1.72210 | 0.861049 | − | 0.508521i | \(-0.169808\pi\) | ||||
0.861049 | + | 0.508521i | \(0.169808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 414.467i | 0.534796i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 222.100i | − 0.285109i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.2711 | −0.0605264 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1700.03 | −2.16564 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1099.10i | − 1.39657i | −0.715820 | − | 0.698285i | \(-0.753947\pi\) | ||||
0.715820 | − | 0.698285i | \(-0.246053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 222.155i | − 0.280853i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −901.603 | −1.13695 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 640.713 | 0.803906 | 0.401953 | − | 0.915660i | \(-0.368332\pi\) | ||||
0.401953 | + | 0.915660i | \(0.368332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 416.692i | 0.521517i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.97960i | − 0.00620125i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 313.835 | 0.389858 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 733.593 | 0.906790 | 0.453395 | − | 0.891310i | \(-0.350213\pi\) | ||||
0.453395 | + | 0.891310i | \(0.350213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1149.16i | 1.41697i | 0.705728 | + | 0.708483i | \(0.250620\pi\) | ||||
−0.705728 | + | 0.708483i | \(0.749380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 925.560i | 1.13566i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 733.433 | 0.897715 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 293.112 | 0.357019 | 0.178509 | − | 0.983938i | \(-0.442873\pi\) | ||||
0.178509 | + | 0.983938i | \(0.442873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 466.668i | − 0.567033i | −0.958967 | − | 0.283517i | \(-0.908499\pi\) | ||||
0.958967 | − | 0.283517i | \(-0.0915011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 340.554i | 0.411794i | 0.978574 | + | 0.205897i | \(0.0660112\pi\) | ||||
−0.978574 | + | 0.205897i | \(0.933989\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1368.33 | 1.65058 | 0.825289 | − | 0.564710i | \(-0.191012\pi\) | ||||
0.825289 | + | 0.564710i | \(0.191012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −150.186 | −0.180295 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 186.309i | 0.223125i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 297.555i | 0.354654i | 0.984152 | + | 0.177327i | \(0.0567450\pi\) | ||||
−0.984152 | + | 0.177327i | \(0.943255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1370.71 | 1.62986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −97.7562 | −0.115688 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 545.744i | − 0.644325i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 633.453i | − 0.744363i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −941.528 | −1.10378 | −0.551892 | − | 0.833916i | \(-0.686094\pi\) | ||||
−0.551892 | + | 0.833916i | \(0.686094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −458.626 | −0.535153 | −0.267576 | − | 0.963537i | \(-0.586223\pi\) | ||||
−0.267576 | + | 0.963537i | \(0.586223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 40.4325i | − 0.0470693i | −0.999723 | − | 0.0235346i | \(-0.992508\pi\) | ||||
0.999723 | − | 0.0235346i | \(-0.00749200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1233.37i | 1.42917i | 0.699548 | + | 0.714585i | \(0.253385\pi\) | ||||
−0.699548 | + | 0.714585i | \(0.746615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 841.268 | 0.972565 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.03976 | −0.00695025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1111.33i | 1.27592i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 195.133i | − 0.223009i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −584.678 | −0.666680 | −0.333340 | − | 0.942807i | \(-0.608176\pi\) | ||||
−0.333340 | + | 0.942807i | \(0.608176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 733.997 | 0.833140 | 0.416570 | − | 0.909104i | \(-0.363232\pi\) | ||||
0.416570 | + | 0.909104i | \(0.363232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 855.769i | 0.969161i | 0.874747 | + | 0.484580i | \(0.161028\pi\) | ||||
−0.874747 | + | 0.484580i | \(0.838972\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 767.876i | 0.865700i | 0.901466 | + | 0.432850i | \(0.142492\pi\) | ||||
−0.901466 | + | 0.432850i | \(0.857508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 393.852 | 0.443028 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1970.67 | 2.20680 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1103.30i | 1.23273i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1052.80i | − 1.17107i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 334.294 | 0.371026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1100.58 | −1.21611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 957.563i | 1.05575i | 0.849323 | + | 0.527874i | \(0.177011\pi\) | ||||
−0.849323 | + | 0.527874i | \(0.822989\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 413.981i | − 0.454425i | −0.973845 | − | 0.227212i | \(-0.927039\pi\) | ||||
0.973845 | − | 0.227212i | \(-0.0729611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 133.608 | 0.146340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 413.663 | 0.451105 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1703.44i | − 1.85358i | −0.375579 | − | 0.926790i | \(-0.622556\pi\) | ||||
0.375579 | − | 0.926790i | \(-0.377444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 552.185i | − 0.598250i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1124.36 | 1.21552 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 645.209 | 0.694520 | 0.347260 | − | 0.937769i | \(-0.387112\pi\) | ||||
0.347260 | + | 0.937769i | \(0.387112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 710.277i | 0.762918i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 40.7806i | 0.0436156i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 360.662 | 0.384911 | 0.192456 | − | 0.981306i | \(-0.438355\pi\) | ||||
0.192456 | + | 0.981306i | \(0.438355\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 111.816 | 0.118827 | 0.0594134 | − | 0.998233i | \(-0.481077\pi\) | ||||
0.0594134 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 91.9685i | 0.0975275i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.7456i | 0.0261306i | 0.999915 | + | 0.0130653i | \(0.00415893\pi\) | ||||
−0.999915 | + | 0.0130653i | \(0.995841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 58.1679 | 0.0612939 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1569.10 | −1.64649 | −0.823245 | − | 0.567686i | \(-0.807839\pi\) | ||||
−0.823245 | + | 0.567686i | \(0.807839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1076.25i | − 1.12696i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 676.657i | − 0.705586i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 459.859 | 0.478521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 907.757 | 0.940681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 129.015i | − 0.133418i | −0.997772 | − | 0.0667090i | \(-0.978750\pi\) | ||||
0.997772 | − | 0.0667090i | \(-0.0212499\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 595.591i | 0.613379i | 0.951810 | + | 0.306689i | \(0.0992212\pi\) | ||||
−0.951810 | + | 0.306689i | \(0.900779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 462.610 | 0.475447 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1232.40 | 1.26141 | 0.630706 | − | 0.776022i | \(-0.282765\pi\) | ||||
0.630706 | + | 0.776022i | \(0.282765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 164.238i | 0.167761i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1335.14i | 1.35823i | 0.734031 | + | 0.679115i | \(0.237636\pi\) | ||||
−0.734031 | + | 0.679115i | \(0.762364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 877.198 | 0.890556 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −303.705 | −0.307083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 617.773i | − 0.623384i | −0.950183 | − | 0.311692i | \(-0.899104\pi\) | ||||
0.950183 | − | 0.311692i | \(-0.100896\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2447.96i | − 2.46026i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −622.311 | −0.624183 | −0.312092 | − | 0.950052i | \(-0.601030\pi\) | ||||
−0.312092 | + | 0.950052i | \(0.601030\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1728.3.g.m.703.1 | 8 | ||
3.2 | odd | 2 | 1728.3.g.j.703.7 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.g.m.703.2 | 8 | ||
8.3 | odd | 2 | 864.3.g.b.703.8 | yes | 8 | ||
8.5 | even | 2 | 864.3.g.b.703.7 | ✓ | 8 | ||
12.11 | even | 2 | 1728.3.g.j.703.8 | 8 | |||
24.5 | odd | 2 | 864.3.g.d.703.1 | yes | 8 | ||
24.11 | even | 2 | 864.3.g.d.703.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.3.g.b.703.7 | ✓ | 8 | 8.5 | even | 2 | ||
864.3.g.b.703.8 | yes | 8 | 8.3 | odd | 2 | ||
864.3.g.d.703.1 | yes | 8 | 24.5 | odd | 2 | ||
864.3.g.d.703.2 | yes | 8 | 24.11 | even | 2 | ||
1728.3.g.j.703.7 | 8 | 3.2 | odd | 2 | |||
1728.3.g.j.703.8 | 8 | 12.11 | even | 2 | |||
1728.3.g.m.703.1 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.g.m.703.2 | 8 | 4.3 | odd | 2 | inner |