Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\), degree \(1\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + \cdots + 2924100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.13 | ||
Root | \(0.252484 + 1.95155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.a.55.14 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.36416 | − | 2.16389i | 0.841040 | − | 0.540973i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.63513 | − | 14.5594i | 0.414696 | − | 0.909960i | ||||
\(5\) | −43.0579 | −1.72231 | −0.861157 | − | 0.508339i | \(-0.830260\pi\) | ||||
−0.861157 | + | 0.508339i | \(0.830260\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 14.1139i | − | 0.288038i | −0.989575 | − | 0.144019i | \(-0.953997\pi\) | ||
0.989575 | − | 0.144019i | \(-0.0460027\pi\) | |||||||
\(8\) | −9.18328 | − | 63.3377i | −0.143489 | − | 0.989652i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −144.853 | + | 93.1726i | −1.44853 | + | 0.931726i | ||||
\(11\) | 209.481i | 1.73125i | 0.500691 | + | 0.865626i | \(0.333079\pi\) | ||||
−0.500691 | + | 0.865626i | \(0.666921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −195.703 | −1.15801 | −0.579003 | − | 0.815326i | \(-0.696558\pi\) | ||||
−0.579003 | + | 0.815326i | \(0.696558\pi\) | |||||||
\(14\) | −30.5409 | − | 47.4813i | −0.155821 | − | 0.242252i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −167.950 | − | 193.207i | −0.656055 | − | 0.754713i | ||||
\(17\) | −303.688 | −1.05082 | −0.525412 | − | 0.850848i | \(-0.676089\pi\) | ||||
−0.525412 | + | 0.850848i | \(0.676089\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 274.792i | − | 0.761196i | −0.924741 | − | 0.380598i | \(-0.875718\pi\) | ||
0.924741 | − | 0.380598i | \(-0.124282\pi\) | |||||||
\(20\) | −285.694 | + | 626.895i | −0.714236 | + | 1.56724i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 453.296 | + | 704.729i | 0.936561 | + | 1.45605i | ||||
\(23\) | − | 466.347i | − | 0.881563i | −0.897614 | − | 0.440782i | \(-0.854701\pi\) | ||
0.897614 | − | 0.440782i | \(-0.145299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1228.98 | 1.96637 | ||||||||
\(26\) | −658.376 | + | 423.480i | −0.973928 | + | 0.626450i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −205.489 | − | 93.6473i | −0.262103 | − | 0.119448i | ||||
\(29\) | −439.835 | −0.522990 | −0.261495 | − | 0.965205i | \(-0.584216\pi\) | ||||
−0.261495 | + | 0.965205i | \(0.584216\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1220.96i | − | 1.27051i | −0.772304 | − | 0.635253i | \(-0.780896\pi\) | ||
0.772304 | − | 0.635253i | \(-0.219104\pi\) | |||||||
\(32\) | −983.089 | − | 286.551i | −0.960048 | − | 0.279835i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1021.65 | + | 657.148i | −0.883784 | + | 0.568467i | ||||
\(35\) | 607.713i | 0.496092i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 624.147 | 0.455914 | 0.227957 | − | 0.973671i | \(-0.426795\pi\) | ||||
0.227957 | + | 0.973671i | \(0.426795\pi\) | |||||||
\(38\) | −594.620 | − | 924.443i | −0.411787 | − | 0.640196i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 395.412 | + | 2727.19i | 0.247133 | + | 1.70449i | ||||
\(41\) | −203.592 | −0.121114 | −0.0605568 | − | 0.998165i | \(-0.519288\pi\) | ||||
−0.0605568 | + | 0.998165i | \(0.519288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 419.418i | − | 0.226835i | −0.993547 | − | 0.113418i | \(-0.963820\pi\) | ||
0.993547 | − | 0.113418i | \(-0.0361798\pi\) | |||||||
\(44\) | 3049.92 | + | 1389.94i | 1.57537 | + | 0.717943i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1009.12 | − | 1568.86i | −0.476902 | − | 0.741430i | ||||
\(47\) | 1995.53i | 0.903364i | 0.892179 | + | 0.451682i | \(0.149176\pi\) | ||||
−0.892179 | + | 0.451682i | \(0.850824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2201.80 | 0.917034 | ||||||||
\(50\) | 4134.48 | − | 2659.38i | 1.65379 | − | 1.06375i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1298.51 | + | 2849.31i | −0.480220 | + | 1.05374i | ||||
\(53\) | −206.451 | −0.0734962 | −0.0367481 | − | 0.999325i | \(-0.511700\pi\) | ||||
−0.0367481 | + | 0.999325i | \(0.511700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9019.82i | − | 2.98176i | ||||||
\(56\) | −893.940 | + | 129.612i | −0.285057 | + | 0.0413302i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1479.67 | + | 951.756i | −0.439856 | + | 0.282924i | ||||
\(59\) | − | 2321.87i | − | 0.667011i | −0.942748 | − | 0.333505i | \(-0.891768\pi\) | ||
0.942748 | − | 0.333505i | \(-0.108232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1392.10 | −0.374120 | −0.187060 | − | 0.982349i | \(-0.559896\pi\) | ||||
−0.187060 | + | 0.982349i | \(0.559896\pi\) | |||||||
\(62\) | −2642.02 | − | 4107.49i | −0.687310 | − | 1.06855i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3927.33 | + | 1163.30i | −0.958822 | + | 0.284008i | ||||
\(65\) | 8426.55 | 1.99445 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7348.27i | 1.63695i | 0.574542 | + | 0.818475i | \(0.305180\pi\) | ||||
−0.574542 | + | 0.818475i | \(0.694820\pi\) | |||||||
\(68\) | −2015.01 | + | 4421.50i | −0.435772 | + | 0.956207i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1315.03 | + | 2044.44i | 0.268373 | + | 0.417233i | ||||
\(71\) | − | 8546.65i | − | 1.69543i | −0.530453 | − | 0.847714i | \(-0.677978\pi\) | ||
0.530453 | − | 0.847714i | \(-0.322022\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3245.43 | −0.609012 | −0.304506 | − | 0.952510i | \(-0.598491\pi\) | ||||
−0.304506 | + | 0.952510i | \(0.598491\pi\) | |||||||
\(74\) | 2099.73 | − | 1350.59i | 0.383442 | − | 0.246638i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4000.79 | − | 1823.28i | −0.692658 | − | 0.315665i | ||||
\(77\) | 2956.59 | 0.498667 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6157.41i | − | 0.986606i | −0.869858 | − | 0.493303i | \(-0.835789\pi\) | ||
0.869858 | − | 0.493303i | \(-0.164211\pi\) | |||||||
\(80\) | 7231.57 | + | 8319.06i | 1.12993 | + | 1.29985i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −684.915 | + | 440.551i | −0.101861 | + | 0.0655192i | ||||
\(83\) | 213.990i | 0.0310626i | 0.999879 | + | 0.0155313i | \(0.00494397\pi\) | ||||
−0.999879 | + | 0.0155313i | \(0.995056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13076.2 | 1.80985 | ||||||||
\(86\) | −907.576 | − | 1410.99i | −0.122712 | − | 0.190777i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13268.1 | − | 1923.73i | 1.71334 | − | 0.248415i | ||||
\(89\) | −8439.35 | −1.06544 | −0.532720 | − | 0.846292i | \(-0.678830\pi\) | ||||
−0.532720 | + | 0.846292i | \(0.678830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2762.12i | 0.333550i | ||||||||
\(92\) | −6789.71 | − | 3094.27i | −0.802187 | − | 0.365580i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4318.11 | + | 6713.28i | 0.488696 | + | 0.759765i | ||||
\(95\) | 11831.9i | 1.31102i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1022.49 | −0.108672 | −0.0543358 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543358 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(98\) | 7407.20 | − | 4764.46i | 0.771262 | − | 0.496091i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8154.44 | − | 17893.2i | 0.815444 | − | 1.78932i | ||||
\(101\) | 2374.52 | 0.232773 | 0.116387 | − | 0.993204i | \(-0.462869\pi\) | ||||
0.116387 | + | 0.993204i | \(0.462869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8481.02i | 0.799418i | 0.916642 | + | 0.399709i | \(0.130889\pi\) | ||||
−0.916642 | + | 0.399709i | \(0.869111\pi\) | |||||||
\(104\) | 1797.19 | + | 12395.4i | 0.166161 | + | 1.14602i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −694.533 | + | 446.738i | −0.0618132 | + | 0.0397595i | ||||
\(107\) | 9579.93i | 0.836748i | 0.908275 | + | 0.418374i | \(0.137400\pi\) | ||||
−0.908275 | + | 0.418374i | \(0.862600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11549.9 | −0.972130 | −0.486065 | − | 0.873923i | \(-0.661568\pi\) | ||||
−0.486065 | + | 0.873923i | \(0.661568\pi\) | |||||||
\(110\) | −19517.9 | − | 30344.1i | −1.61305 | − | 2.50778i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2726.89 | + | 2370.43i | −0.217386 | + | 0.188969i | ||||
\(113\) | −21853.8 | −1.71147 | −0.855735 | − | 0.517414i | \(-0.826895\pi\) | ||||
−0.855735 | + | 0.517414i | \(0.826895\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20079.9i | 1.51833i | ||||||||
\(116\) | −2918.36 | + | 6403.71i | −0.216882 | + | 0.475900i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5024.27 | − | 7811.12i | −0.360835 | − | 0.560983i | ||||
\(119\) | 4286.21i | 0.302677i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29241.5 | −1.99723 | ||||||||
\(122\) | −4683.25 | + | 3012.36i | −0.314650 | + | 0.202389i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17776.4 | − | 8101.21i | −1.15611 | − | 0.526874i | ||||
\(125\) | −26006.0 | −1.66439 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7358.63i | 0.456236i | 0.973634 | + | 0.228118i | \(0.0732572\pi\) | ||||
−0.973634 | + | 0.228118i | \(0.926743\pi\) | |||||||
\(128\) | −10694.9 | + | 12411.8i | −0.652767 | + | 0.757559i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28348.2 | − | 18234.2i | 1.67741 | − | 1.07894i | ||||
\(131\) | − | 8567.97i | − | 0.499270i | −0.968340 | − | 0.249635i | \(-0.919689\pi\) | ||
0.968340 | − | 0.249635i | \(-0.0803106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3878.37 | −0.219253 | ||||||||
\(134\) | 15900.9 | + | 24720.7i | 0.885546 | + | 1.37674i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2788.85 | + | 19234.9i | 0.150781 | + | 1.03995i | ||||
\(137\) | 33585.2 | 1.78940 | 0.894699 | − | 0.446669i | \(-0.147390\pi\) | ||||
0.894699 | + | 0.446669i | \(0.147390\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8638.51i | − | 0.447104i | −0.974692 | − | 0.223552i | \(-0.928235\pi\) | ||
0.974692 | − | 0.223552i | \(-0.0717653\pi\) | |||||||
\(140\) | 8847.91 | + | 4032.25i | 0.451424 | + | 0.205727i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18494.1 | − | 28752.3i | −0.917182 | − | 1.42592i | ||||
\(143\) | − | 40996.1i | − | 2.00480i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18938.3 | 0.900754 | ||||||||
\(146\) | −10918.1 | + | 7022.75i | −0.512203 | + | 0.329459i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4141.29 | − | 9087.18i | 0.189066 | − | 0.414864i | ||||
\(149\) | 24096.5 | 1.08538 | 0.542689 | − | 0.839934i | \(-0.317406\pi\) | ||||
0.542689 | + | 0.839934i | \(0.317406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 26512.7i | 1.16279i | 0.813623 | + | 0.581393i | \(0.197492\pi\) | ||||
−0.813623 | + | 0.581393i | \(0.802508\pi\) | |||||||
\(152\) | −17404.7 | + | 2523.49i | −0.753319 | + | 0.109223i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9946.45 | − | 6397.75i | 0.419398 | − | 0.269765i | ||||
\(155\) | 52571.8i | 2.18821i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −33191.1 | −1.34655 | −0.673274 | − | 0.739393i | \(-0.735113\pi\) | ||||
−0.673274 | + | 0.739393i | \(0.735113\pi\) | |||||||
\(158\) | −13324.0 | − | 20714.5i | −0.533727 | − | 0.829775i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 42329.7 | + | 12338.3i | 1.65350 | + | 0.481964i | ||||
\(161\) | −6581.96 | −0.253924 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22135.9i | 0.833146i | 0.909102 | + | 0.416573i | \(0.136769\pi\) | ||||
−0.909102 | + | 0.416573i | \(0.863231\pi\) | |||||||
\(164\) | −1350.86 | + | 2964.17i | −0.0502252 | + | 0.110208i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 463.052 | + | 719.897i | 0.0168040 | + | 0.0261249i | ||||
\(167\) | − | 31233.9i | − | 1.11993i | −0.828515 | − | 0.559967i | \(-0.810814\pi\) | ||
0.828515 | − | 0.559967i | \(-0.189186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9738.62 | 0.340976 | ||||||||
\(170\) | 43990.3 | − | 28295.4i | 1.52215 | − | 0.979080i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6106.46 | − | 2782.89i | −0.206411 | − | 0.0940675i | ||||
\(173\) | 19702.2 | 0.658298 | 0.329149 | − | 0.944278i | \(-0.393238\pi\) | ||||
0.329149 | + | 0.944278i | \(0.393238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 17345.6i | − | 0.566388i | ||||||
\(176\) | 40473.2 | − | 35182.4i | 1.30660 | − | 1.13580i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −28391.3 | + | 18261.9i | −0.896077 | + | 0.576375i | ||||
\(179\) | 931.868i | 0.0290836i | 0.999894 | + | 0.0145418i | \(0.00462896\pi\) | ||||
−0.999894 | + | 0.0145418i | \(0.995371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8201.99 | 0.250358 | 0.125179 | − | 0.992134i | \(-0.460049\pi\) | ||||
0.125179 | + | 0.992134i | \(0.460049\pi\) | |||||||
\(182\) | 5976.94 | + | 9292.23i | 0.180441 | + | 0.280529i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −29537.3 | + | 4282.59i | −0.872441 | + | 0.126494i | ||||
\(185\) | −26874.4 | −0.785228 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 63617.0i | − | 1.81924i | ||||||
\(188\) | 29053.6 | + | 13240.6i | 0.822025 | + | 0.374621i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25603.1 | + | 39804.5i | 0.709226 | + | 1.10262i | ||||
\(191\) | 3283.65i | 0.0900099i | 0.998987 | + | 0.0450049i | \(0.0143304\pi\) | ||||
−0.998987 | + | 0.0450049i | \(0.985670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70666.2 | 1.89713 | 0.948565 | − | 0.316583i | \(-0.102536\pi\) | ||||
0.948565 | + | 0.316583i | \(0.102536\pi\) | |||||||
\(194\) | −3439.82 | + | 2212.56i | −0.0913971 | + | 0.0587884i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14609.2 | − | 32056.8i | 0.380290 | − | 0.834464i | ||||
\(197\) | −14865.2 | −0.383034 | −0.191517 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191517 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63878.1i | 1.61304i | 0.591205 | + | 0.806521i | \(0.298652\pi\) | ||||
−0.591205 | + | 0.806521i | \(0.701348\pi\) | |||||||
\(200\) | −11286.1 | − | 77840.7i | −0.282151 | − | 1.94602i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7988.26 | − | 5138.21i | 0.195771 | − | 0.125924i | ||||
\(203\) | 6207.77i | 0.150641i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8766.23 | 0.208596 | ||||||||
\(206\) | 18352.0 | + | 28531.5i | 0.432464 | + | 0.672342i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 32868.3 | + | 37811.1i | 0.759715 | + | 0.873962i | ||||
\(209\) | 57563.8 | 1.31782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 66608.9i | − | 1.49612i | −0.663629 | − | 0.748062i | \(-0.730985\pi\) | ||
0.663629 | − | 0.748062i | \(-0.269015\pi\) | |||||||
\(212\) | −1369.83 | + | 3005.79i | −0.0304786 | + | 0.0668786i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20729.9 | + | 32228.4i | 0.452658 | + | 0.703738i | ||||
\(215\) | 18059.2i | 0.390681i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17232.4 | −0.365954 | ||||||||
\(218\) | −38855.6 | + | 24992.7i | −0.817600 | + | 0.525896i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −131323. | − | 59847.7i | −2.71328 | − | 1.23652i | ||||
\(221\) | 59432.6 | 1.21686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 48074.2i | − | 0.966723i | −0.875421 | − | 0.483361i | \(-0.839416\pi\) | ||
0.875421 | − | 0.483361i | \(-0.160584\pi\) | |||||||
\(224\) | −4044.35 | + | 13875.2i | −0.0806032 | + | 0.276530i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −73519.5 | + | 47289.2i | −1.43941 | + | 0.925860i | ||||
\(227\) | − | 18940.2i | − | 0.367564i | −0.982967 | − | 0.183782i | \(-0.941166\pi\) | ||
0.982967 | − | 0.183782i | \(-0.0588341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 349.738 | 0.00666917 | 0.00333458 | − | 0.999994i | \(-0.498939\pi\) | ||||
0.00333458 | + | 0.999994i | \(0.498939\pi\) | |||||||
\(230\) | 43450.8 | + | 67552.0i | 0.821375 | + | 1.27697i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4039.13 | + | 27858.1i | 0.0750432 | + | 0.517578i | ||||
\(233\) | 7529.14 | 0.138686 | 0.0693432 | − | 0.997593i | \(-0.477910\pi\) | ||||
0.0693432 | + | 0.997593i | \(0.477910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 85923.3i | − | 1.55588i | ||||||
\(236\) | −33804.9 | − | 15405.9i | −0.606953 | − | 0.276607i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9274.91 | + | 14419.5i | 0.163740 | + | 0.254564i | ||||
\(239\) | − | 53394.8i | − | 0.934766i | −0.884055 | − | 0.467383i | \(-0.845197\pi\) | ||
0.884055 | − | 0.467383i | \(-0.154803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −88157.7 | −1.51784 | −0.758920 | − | 0.651184i | \(-0.774273\pi\) | ||||
−0.758920 | + | 0.651184i | \(0.774273\pi\) | |||||||
\(242\) | −98373.0 | + | 63275.5i | −1.67975 | + | 1.08045i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9236.76 | + | 20268.1i | −0.155146 | + | 0.340434i | ||||
\(245\) | −94804.7 | −1.57942 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 53777.5i | 0.881469i | ||||||||
\(248\) | −77332.6 | + | 11212.4i | −1.25736 | + | 0.182303i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −87488.4 | + | 56274.3i | −1.39982 | + | 0.900389i | ||||
\(251\) | − | 23284.3i | − | 0.369587i | −0.982777 | − | 0.184793i | \(-0.940838\pi\) | ||
0.982777 | − | 0.184793i | \(-0.0591616\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 97691.0 | 1.52621 | ||||||||
\(254\) | 15923.3 | + | 24755.6i | 0.246811 | + | 0.383712i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9121.53 | + | 64898.1i | −0.139183 | + | 0.990267i | ||||
\(257\) | −118409. | −1.79274 | −0.896369 | − | 0.443308i | \(-0.853805\pi\) | ||||
−0.896369 | + | 0.443308i | \(0.853805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8809.12i | − | 0.131321i | ||||||
\(260\) | 55911.2 | − | 122685.i | 0.827089 | − | 1.81487i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18540.2 | − | 28824.0i | −0.270092 | − | 0.419906i | ||||
\(263\) | − | 44424.6i | − | 0.642262i | −0.947035 | − | 0.321131i | \(-0.895937\pi\) | ||
0.947035 | − | 0.321131i | \(-0.104063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8889.33 | 0.126584 | ||||||||
\(266\) | −13047.5 | + | 8392.39i | −0.184401 | + | 0.118610i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 106986. | + | 48756.7i | 1.48956 | + | 0.678836i | ||||
\(269\) | −55818.5 | −0.771390 | −0.385695 | − | 0.922626i | \(-0.626038\pi\) | ||||
−0.385695 | + | 0.922626i | \(0.626038\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 98301.7i | − | 1.33851i | −0.743032 | − | 0.669256i | \(-0.766613\pi\) | ||
0.743032 | − | 0.669256i | \(-0.233387\pi\) | |||||||
\(272\) | 51004.4 | + | 58674.5i | 0.689398 | + | 0.793070i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 112986. | − | 72674.8i | 1.50496 | − | 0.968017i | ||||
\(275\) | 257448.i | 3.40428i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 111306. | 1.45063 | 0.725317 | − | 0.688415i | \(-0.241693\pi\) | ||||
0.725317 | + | 0.688415i | \(0.241693\pi\) | |||||||
\(278\) | −18692.8 | − | 29061.3i | −0.241872 | − | 0.376033i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 38491.2 | − | 5580.80i | 0.490959 | − | 0.0711836i | ||||
\(281\) | 24996.7 | 0.316571 | 0.158285 | − | 0.987393i | \(-0.449403\pi\) | ||||
0.158285 | + | 0.987393i | \(0.449403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30559.7i | − | 0.381571i | −0.981632 | − | 0.190786i | \(-0.938896\pi\) | ||
0.981632 | − | 0.190786i | \(-0.0611035\pi\) | |||||||
\(284\) | −124434. | − | 56708.2i | −1.54277 | − | 0.703087i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −88711.3 | − | 137917.i | −1.08454 | − | 1.68612i | ||||
\(287\) | 2873.47i | 0.0348853i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8705.37 | 0.104230 | ||||||||
\(290\) | 63711.6 | − | 40980.6i | 0.757570 | − | 0.487284i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −21533.8 | + | 47251.3i | −0.252555 | + | 0.554177i | ||||
\(293\) | 49225.1 | 0.573392 | 0.286696 | − | 0.958022i | \(-0.407443\pi\) | ||||
0.286696 | + | 0.958022i | \(0.407443\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 99974.5i | 1.14880i | ||||||||
\(296\) | −5731.71 | − | 39532.0i | −0.0654186 | − | 0.451197i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 81064.4 | − | 52142.2i | 0.912846 | − | 0.587160i | ||||
\(299\) | 91265.4i | 1.02085i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5919.61 | −0.0653372 | ||||||||
\(302\) | 57370.7 | + | 89192.9i | 0.629037 | + | 0.977950i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −53091.5 | + | 46151.3i | −0.574484 | + | 0.499386i | ||||
\(305\) | 59940.8 | 0.644352 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 143871.i | 1.52650i | 0.646105 | + | 0.763249i | \(0.276397\pi\) | ||||
−0.646105 | + | 0.763249i | \(0.723603\pi\) | |||||||
\(308\) | 19617.4 | − | 43046.1i | 0.206795 | − | 0.453767i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 113760. | + | 176860.i | 1.18376 | + | 1.84037i | ||||
\(311\) | − | 144670.i | − | 1.49575i | −0.663842 | − | 0.747873i | \(-0.731075\pi\) | ||
0.663842 | − | 0.747873i | \(-0.268925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 80345.4 | 0.820111 | 0.410055 | − | 0.912061i | \(-0.365509\pi\) | ||||
0.410055 | + | 0.912061i | \(0.365509\pi\) | |||||||
\(314\) | −111660. | + | 71821.9i | −1.13250 | + | 0.728447i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −89647.9 | − | 40855.2i | −0.897772 | − | 0.409141i | ||||
\(317\) | −144593. | −1.43889 | −0.719445 | − | 0.694549i | \(-0.755604\pi\) | ||||
−0.719445 | + | 0.694549i | \(0.755604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 92137.2i | − | 0.905428i | ||||||
\(320\) | 169103. | − | 50089.0i | 1.65139 | − | 0.489151i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22142.8 | + | 14242.7i | −0.213560 | + | 0.137366i | ||||
\(323\) | 83450.9i | 0.799882i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −240515. | −2.27706 | ||||||||
\(326\) | 47899.6 | + | 74468.5i | 0.450710 | + | 0.700709i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1869.64 | + | 12895.0i | 0.0173784 | + | 0.119860i | ||||
\(329\) | 28164.7 | 0.260203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 89506.7i | 0.816957i | 0.912768 | + | 0.408479i | \(0.133941\pi\) | ||||
−0.912768 | + | 0.408479i | \(0.866059\pi\) | |||||||
\(332\) | 3115.56 | + | 1419.85i | 0.0282657 | + | 0.0128815i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −67586.8 | − | 105076.i | −0.605855 | − | 0.941910i | ||||
\(335\) | − | 316401.i | − | 2.81934i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −134427. | −1.18366 | −0.591830 | − | 0.806062i | \(-0.701595\pi\) | ||||
−0.591830 | + | 0.806062i | \(0.701595\pi\) | |||||||
\(338\) | 32762.3 | − | 21073.3i | 0.286775 | − | 0.184459i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 86762.0 | − | 190380.i | 0.750536 | − | 1.64689i | ||||
\(341\) | 255768. | 2.19957 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 64963.3i | − | 0.552179i | ||||||
\(344\) | −26565.0 | + | 3851.63i | −0.224488 | + | 0.0325483i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 66281.3 | − | 42633.4i | 0.553654 | − | 0.356121i | ||||
\(347\) | − | 73087.9i | − | 0.606997i | −0.952832 | − | 0.303499i | \(-0.901845\pi\) | ||
0.952832 | − | 0.303499i | \(-0.0981547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −54237.0 | −0.445292 | −0.222646 | − | 0.974899i | \(-0.571469\pi\) | ||||
−0.222646 | + | 0.974899i | \(0.571469\pi\) | |||||||
\(350\) | −37534.1 | − | 58353.5i | −0.306401 | − | 0.476355i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 60027.2 | − | 205939.i | 0.484465 | − | 1.66208i | ||||
\(353\) | 29031.6 | 0.232982 | 0.116491 | − | 0.993192i | \(-0.462835\pi\) | ||||
0.116491 | + | 0.993192i | \(0.462835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 368001.i | 2.92006i | ||||||||
\(356\) | −55996.2 | + | 122872.i | −0.441833 | + | 0.969508i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2016.46 | + | 3134.95i | 0.0157335 | + | 0.0244605i | ||||
\(359\) | − | 9197.54i | − | 0.0713646i | −0.999363 | − | 0.0356823i | \(-0.988640\pi\) | ||
0.999363 | − | 0.0356823i | \(-0.0113604\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54810.5 | 0.420581 | ||||||||
\(362\) | 27592.8 | − | 17748.2i | 0.210561 | − | 0.135437i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 40214.8 | + | 18327.1i | 0.303517 | + | 0.138322i | ||||
\(365\) | 139741. | 1.04891 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 96131.3i | − | 0.713728i | −0.934156 | − | 0.356864i | \(-0.883846\pi\) | ||
0.934156 | − | 0.356864i | \(-0.116154\pi\) | |||||||
\(368\) | −90101.3 | + | 78323.0i | −0.665327 | + | 0.578354i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −90409.8 | + | 58153.4i | −0.660408 | + | 0.424787i | ||||
\(371\) | 2913.82i | 0.0211697i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27728.8 | −0.199303 | −0.0996513 | − | 0.995022i | \(-0.531773\pi\) | ||||
−0.0996513 | + | 0.995022i | \(0.531773\pi\) | |||||||
\(374\) | −137660. | − | 214018.i | −0.984160 | − | 1.53005i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 126392. | − | 18325.5i | 0.894016 | − | 0.129623i | ||||
\(377\) | 86076.9 | 0.605626 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 101903.i | − | 0.709432i | −0.934974 | − | 0.354716i | \(-0.884578\pi\) | ||
0.934974 | − | 0.354716i | \(-0.115422\pi\) | |||||||
\(380\) | 172266. | + | 78506.5i | 1.19297 | + | 0.543674i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7105.47 | + | 11046.7i | 0.0486930 | + | 0.0757019i | ||||
\(383\) | 6261.76i | 0.0426873i | 0.999772 | + | 0.0213437i | \(0.00679442\pi\) | ||||
−0.999772 | + | 0.0213437i | \(0.993206\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −127305. | −0.858860 | ||||||||
\(386\) | 237732. | − | 152914.i | 1.59556 | − | 1.02630i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6784.36 | + | 14886.8i | −0.0450656 | + | 0.0988867i | ||||
\(389\) | −147789. | −0.976658 | −0.488329 | − | 0.872660i | \(-0.662393\pi\) | ||||
−0.488329 | + | 0.872660i | \(0.662393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 141624.i | 0.926367i | ||||||||
\(392\) | −20219.7 | − | 139457.i | −0.131584 | − | 0.907545i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −50008.8 | + | 32166.6i | −0.322147 | + | 0.207211i | ||||
\(395\) | 265125.i | 1.69924i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −142937. | −0.906912 | −0.453456 | − | 0.891279i | \(-0.649809\pi\) | ||||
−0.453456 | + | 0.891279i | \(0.649809\pi\) | |||||||
\(398\) | 138225. | + | 214896.i | 0.872613 | + | 1.35663i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −206407. | − | 237447.i | −1.29004 | − | 1.48404i | ||||
\(401\) | 18071.6 | 0.112385 | 0.0561923 | − | 0.998420i | \(-0.482104\pi\) | ||||
0.0561923 | + | 0.998420i | \(0.482104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 238945.i | 1.47125i | ||||||||
\(404\) | 15755.2 | − | 34571.5i | 0.0965300 | − | 0.211814i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13433.0 | + | 20883.9i | 0.0814928 | + | 0.126695i | ||||
\(407\) | 130747.i | 0.789303i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 166751. | 0.996831 | 0.498416 | − | 0.866938i | \(-0.333915\pi\) | ||||
0.498416 | + | 0.866938i | \(0.333915\pi\) | |||||||
\(410\) | 29491.0 | − | 18969.2i | 0.175437 | − | 0.112845i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 123478. | + | 56272.7i | 0.727438 | + | 0.331515i | ||||
\(413\) | −32770.5 | −0.192125 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 9213.96i | − | 0.0534996i | ||||||
\(416\) | 192393. | + | 56078.9i | 1.11174 | + | 0.324051i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 193654. | − | 124562.i | 1.10834 | − | 0.712906i | ||||
\(419\) | − | 24068.3i | − | 0.137094i | −0.997648 | − | 0.0685469i | \(-0.978164\pi\) | ||
0.997648 | − | 0.0685469i | \(-0.0218363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −113463. | −0.640162 | −0.320081 | − | 0.947390i | \(-0.603710\pi\) | ||||
−0.320081 | + | 0.947390i | \(0.603710\pi\) | |||||||
\(422\) | −144135. | − | 224083.i | −0.809363 | − | 1.25830i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1895.90 | + | 13076.1i | 0.0105459 | + | 0.0727357i | ||||
\(425\) | −373226. | −2.06630 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19647.9i | 0.107761i | ||||||||
\(428\) | 139478. | + | 63564.1i | 0.761407 | + | 0.346996i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39078.3 | + | 60754.2i | 0.211348 | + | 0.328579i | ||||
\(431\) | − | 154439.i | − | 0.831388i | −0.909505 | − | 0.415694i | \(-0.863539\pi\) | ||
0.909505 | − | 0.415694i | \(-0.136461\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 124462. | 0.663836 | 0.331918 | − | 0.943308i | \(-0.392304\pi\) | ||||
0.331918 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(434\) | −57972.6 | + | 37289.1i | −0.307782 | + | 0.197972i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −76634.9 | + | 168159.i | −0.403138 | + | 0.884600i | ||||
\(437\) | −128148. | −0.671042 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 100585.i | − | 0.521921i | −0.965349 | − | 0.260960i | \(-0.915961\pi\) | ||
0.965349 | − | 0.260960i | \(-0.0840392\pi\) | |||||||
\(440\) | −571295. | + | 82831.5i | −2.95090 | + | 0.427849i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 199941. | − | 128606.i | 1.02343 | − | 0.658288i | ||||
\(443\) | 195614.i | 0.996764i | 0.866957 | + | 0.498382i | \(0.166072\pi\) | ||||
−0.866957 | + | 0.498382i | \(0.833928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 363380. | 1.83502 | ||||||||
\(446\) | −104027. | − | 161729.i | −0.522971 | − | 0.813052i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16418.6 | + | 55429.9i | 0.0818051 | + | 0.276177i | ||||
\(449\) | −47139.5 | −0.233826 | −0.116913 | − | 0.993142i | \(-0.537300\pi\) | ||||
−0.116913 | + | 0.993142i | \(0.537300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 42648.7i | − | 0.209678i | ||||||
\(452\) | −145003. | + | 318177.i | −0.709739 | + | 1.55737i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −40984.6 | − | 63717.9i | −0.198842 | − | 0.309136i | ||||
\(455\) | − | 118931.i | − | 0.574477i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −44420.0 | −0.212690 | −0.106345 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106345 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(458\) | 1176.57 | − | 756.796i | 0.00560904 | − | 0.00360784i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 292350. | + | 133233.i | 1.38162 | + | 0.629644i | ||||
\(461\) | 189396. | 0.891187 | 0.445594 | − | 0.895235i | \(-0.352993\pi\) | ||||
0.445594 | + | 0.895235i | \(0.352993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 146188.i | − | 0.681944i | −0.940073 | − | 0.340972i | \(-0.889244\pi\) | ||
0.940073 | − | 0.340972i | \(-0.110756\pi\) | |||||||
\(464\) | 73870.3 | + | 84979.0i | 0.343110 | + | 0.394708i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25329.2 | − | 16292.3i | 0.116641 | − | 0.0750256i | ||||
\(467\) | 145806.i | 0.668563i | 0.942473 | + | 0.334281i | \(0.108494\pi\) | ||||
−0.942473 | + | 0.334281i | \(0.891506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 103712. | 0.471504 | ||||||||
\(470\) | −185929. | − | 289059.i | −0.841687 | − | 1.30855i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −147062. | + | 21322.3i | −0.660109 | + | 0.0957086i | ||||
\(473\) | 87860.3 | 0.392709 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 337713.i | − | 1.49679i | ||||||
\(476\) | 62404.5 | + | 28439.6i | 0.275424 | + | 0.125519i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −115541. | − | 179629.i | −0.505684 | − | 0.786175i | ||||
\(479\) | − | 366733.i | − | 1.59838i | −0.601081 | − | 0.799188i | \(-0.705263\pi\) | ||
0.601081 | − | 0.799188i | \(-0.294737\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −122147. | −0.527951 | ||||||||
\(482\) | −296576. | + | 190764.i | −1.27656 | + | 0.821111i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −194021. | + | 425737.i | −0.828244 | + | 1.81740i | ||||
\(485\) | 44026.2 | 0.187166 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 202033.i | 0.851851i | 0.904758 | + | 0.425926i | \(0.140051\pi\) | ||||
−0.904758 | + | 0.425926i | \(0.859949\pi\) | |||||||
\(488\) | 12784.0 | + | 88172.4i | 0.0536820 | + | 0.370248i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −318938. | + | 205147.i | −1.32836 | + | 0.854425i | ||||
\(491\) | 229449.i | 0.951750i | 0.879513 | + | 0.475875i | \(0.157869\pi\) | ||||
−0.879513 | + | 0.475875i | \(0.842131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 133573. | 0.549570 | ||||||||
\(494\) | 116369. | + | 180916.i | 0.476851 | + | 0.741350i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −235897. | + | 205060.i | −0.958868 | + | 0.833523i | ||||
\(497\) | −120626. | −0.488348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 353378.i | − | 1.41918i | −0.704613 | − | 0.709592i | \(-0.748879\pi\) | ||
0.704613 | − | 0.709592i | \(-0.251121\pi\) | |||||||
\(500\) | −172553. | + | 378631.i | −0.690214 | + | 1.51453i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −50384.8 | − | 78332.2i | −0.199937 | − | 0.310837i | ||||
\(503\) | − | 173765.i | − | 0.686793i | −0.939190 | − | 0.343397i | \(-0.888422\pi\) | ||
0.939190 | − | 0.343397i | \(-0.111578\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −102242. | −0.400908 | ||||||||
\(506\) | 328648. | − | 211393.i | 1.28360 | − | 0.825638i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 107137. | + | 48825.4i | 0.415156 | + | 0.189199i | ||||
\(509\) | −427247. | −1.64909 | −0.824543 | − | 0.565800i | \(-0.808568\pi\) | ||||
−0.824543 | + | 0.565800i | \(0.808568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45805.5i | 0.175419i | ||||||||
\(512\) | 109746. | + | 238066.i | 0.418649 | + | 0.908148i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −398345. | + | 256224.i | −1.50776 | + | 0.969824i | ||||
\(515\) | − | 365175.i | − | 1.37685i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −418027. | −1.56395 | ||||||||
\(518\) | −19062.0 | − | 29635.3i | −0.0710410 | − | 0.110446i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −77383.3 | − | 533718.i | −0.286181 | − | 1.97381i | ||||
\(521\) | 238355. | 0.878111 | 0.439056 | − | 0.898460i | \(-0.355313\pi\) | ||||
0.439056 | + | 0.898460i | \(0.355313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 65331.4i | 0.238846i | 0.992843 | + | 0.119423i | \(0.0381045\pi\) | ||||
−0.992843 | + | 0.119423i | \(0.961895\pi\) | |||||||
\(524\) | −124744. | − | 56849.6i | −0.454315 | − | 0.207045i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −96130.1 | − | 149451.i | −0.347446 | − | 0.540168i | ||||
\(527\) | 370790.i | 1.33508i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62361.6 | 0.222847 | ||||||||
\(530\) | 29905.1 | − | 19235.6i | 0.106462 | − | 0.0684783i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25733.5 | + | 56466.6i | −0.0909234 | + | 0.199512i | ||||
\(533\) | 39843.5 | 0.140250 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 412491.i | − | 1.44114i | ||||||
\(536\) | 465423. | − | 67481.2i | 1.62001 | − | 0.234884i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −187782. | + | 120785.i | −0.648769 | + | 0.417301i | ||||
\(539\) | 461236.i | 1.58762i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 343182. | 1.17255 | 0.586273 | − | 0.810113i | \(-0.300595\pi\) | ||||
0.586273 | + | 0.810113i | \(0.300595\pi\) | |||||||
\(542\) | −212714. | − | 330703.i | −0.724100 | − | 1.12574i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 298552. | + | 87022.2i | 1.00884 | + | 0.294057i | ||||
\(545\) | 497313. | 1.67431 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 135514.i | − | 0.452908i | −0.974022 | − | 0.226454i | \(-0.927287\pi\) | ||
0.974022 | − | 0.226454i | \(-0.0727133\pi\) | |||||||
\(548\) | 222842. | − | 488979.i | 0.742056 | − | 1.62828i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 557091. | + | 866097.i | 1.84162 | + | 2.86313i | ||||
\(551\) | 120863.i | 0.398098i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −86904.8 | −0.284180 | ||||||||
\(554\) | 374450. | − | 240854.i | 1.22004 | − | 0.784755i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −125771. | − | 57317.6i | −0.406847 | − | 0.185412i | ||||
\(557\) | −64031.9 | −0.206389 | −0.103194 | − | 0.994661i | \(-0.532906\pi\) | ||||
−0.103194 | + | 0.994661i | \(0.532906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 82081.3i | 0.262676i | ||||||||
\(560\) | 117414. | − | 102065.i | 0.374407 | − | 0.325464i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 84093.0 | − | 54090.3i | 0.266248 | − | 0.171256i | ||||
\(563\) | 53438.7i | 0.168593i | 0.996441 | + | 0.0842964i | \(0.0268643\pi\) | ||||
−0.996441 | + | 0.0842964i | \(0.973136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 940976. | 2.94769 | ||||||||
\(566\) | −66127.9 | − | 102808.i | −0.206420 | − | 0.320917i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −541326. | + | 78486.3i | −1.67788 | + | 0.243275i | ||||
\(569\) | −225959. | −0.697919 | −0.348960 | − | 0.937138i | \(-0.613465\pi\) | ||||
−0.348960 | + | 0.937138i | \(0.613465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 472292.i | − | 1.44857i | −0.689502 | − | 0.724284i | \(-0.742171\pi\) | ||
0.689502 | − | 0.724284i | \(-0.257829\pi\) | |||||||
\(572\) | −596878. | − | 272015.i | −1.82429 | − | 0.831381i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6217.88 | + | 9666.80i | 0.0188720 | + | 0.0293399i | ||||
\(575\) | − | 573130.i | − | 1.73348i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 376338. | 1.13038 | 0.565192 | − | 0.824959i | \(-0.308802\pi\) | ||||
0.565192 | + | 0.824959i | \(0.308802\pi\) | |||||||
\(578\) | 29286.2 | − | 18837.5i | 0.0876613 | − | 0.0563855i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 125658. | − | 275730.i | 0.373539 | − | 0.819650i | ||||
\(581\) | 3020.23 | 0.00894722 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 43247.6i | − | 0.127240i | ||||||
\(584\) | 29803.6 | + | 205558.i | 0.0873864 | + | 0.602710i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 165601. | − | 106518.i | 0.482245 | − | 0.310190i | ||||
\(587\) | 282756.i | 0.820608i | 0.911949 | + | 0.410304i | \(0.134577\pi\) | ||||
−0.911949 | + | 0.410304i | \(0.865423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −335509. | −0.967104 | ||||||||
\(590\) | 216334. | + | 336330.i | 0.621472 | + | 0.966189i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −104826. | − | 120589.i | −0.299105 | − | 0.344085i | ||||
\(593\) | −439919. | −1.25102 | −0.625508 | − | 0.780217i | \(-0.715108\pi\) | ||||
−0.625508 | + | 0.780217i | \(0.715108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 184555.i | − | 0.521305i | ||||||
\(596\) | 159883. | − | 350829.i | 0.450101 | − | 0.987651i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 197489. | + | 307031.i | 0.552255 | + | 0.858579i | ||||
\(599\) | − | 384400.i | − | 1.07135i | −0.844425 | − | 0.535673i | \(-0.820058\pi\) | ||
0.844425 | − | 0.535673i | \(-0.179942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −495470. | −1.37173 | −0.685864 | − | 0.727730i | \(-0.740576\pi\) | ||||
−0.685864 | + | 0.727730i | \(0.740576\pi\) | |||||||
\(602\) | −19914.5 | + | 12809.4i | −0.0549512 | + | 0.0353457i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 386008. | + | 175915.i | 1.05809 | + | 0.482203i | ||||
\(605\) | 1.25908e6 | 3.43986 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 630975.i | 1.71252i | 0.516549 | + | 0.856258i | \(0.327216\pi\) | ||||
−0.516549 | + | 0.856258i | \(0.672784\pi\) | |||||||
\(608\) | −78741.9 | + | 270145.i | −0.213009 | + | 0.730784i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 201651. | − | 129706.i | 0.541926 | − | 0.348577i | ||||
\(611\) | − | 390531.i | − | 1.04610i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −256888. | −0.683634 | −0.341817 | − | 0.939767i | \(-0.611042\pi\) | ||||
−0.341817 | + | 0.939767i | \(0.611042\pi\) | |||||||
\(614\) | 311321. | + | 484004.i | 0.825794 | + | 1.28384i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27151.2 | − | 187264.i | −0.0715530 | − | 0.493506i | ||||
\(617\) | 115496. | 0.303387 | 0.151694 | − | 0.988428i | \(-0.451527\pi\) | ||||
0.151694 | + | 0.988428i | \(0.451527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 229059.i | 0.597814i | 0.954282 | + | 0.298907i | \(0.0966221\pi\) | ||||
−0.954282 | + | 0.298907i | \(0.903378\pi\) | |||||||
\(620\) | 765412. | + | 348821.i | 1.99119 | + | 0.907442i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −313051. | − | 486693.i | −0.809159 | − | 1.25798i | ||||
\(623\) | 119112.i | 0.306887i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 351652. | 0.900230 | ||||||||
\(626\) | 270295. | − | 173859.i | 0.689746 | − | 0.443658i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −220227. | + | 483241.i | −0.558408 | + | 1.22531i | ||||
\(629\) | −189546. | −0.479085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 481121.i | 1.20836i | 0.796849 | + | 0.604178i | \(0.206499\pi\) | ||||
−0.796849 | + | 0.604178i | \(0.793501\pi\) | |||||||
\(632\) | −389996. | + | 56545.2i | −0.976396 | + | 0.141567i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −486433. | + | 312883.i | −1.21016 | + | 0.778402i | ||||
\(635\) | − | 316847.i | − | 0.785781i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −430898. | −1.06193 | ||||||||
\(638\) | −199375. | − | 309964.i | −0.489812 | − | 0.761501i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 460501. | − | 534428.i | 1.12427 | − | 1.30475i | ||||
\(641\) | 476453. | 1.15959 | 0.579794 | − | 0.814763i | \(-0.303133\pi\) | ||||
0.579794 | + | 0.814763i | \(0.303133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 416293.i | − | 1.00688i | −0.864030 | − | 0.503440i | \(-0.832068\pi\) | ||
0.864030 | − | 0.503440i | \(-0.167932\pi\) | |||||||
\(644\) | −43672.1 | + | 95829.1i | −0.105301 | + | 0.231061i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 180579. | + | 280742.i | 0.432715 | + | 0.672733i | ||||
\(647\) | − | 18567.6i | − | 0.0443554i | −0.999754 | − | 0.0221777i | \(-0.992940\pi\) | ||
0.999754 | − | 0.0221777i | \(-0.00705996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 486388. | 1.15476 | ||||||||
\(650\) | −809130. | + | 520448.i | −1.91510 | + | 1.23183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 322284. | + | 146874.i | 0.758130 | + | 0.345502i | ||||
\(653\) | −462788. | −1.08531 | −0.542657 | − | 0.839954i | \(-0.682582\pi\) | ||||
−0.542657 | + | 0.839954i | \(0.682582\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 368918.i | 0.859899i | ||||||||
\(656\) | 34193.3 | + | 39335.3i | 0.0794571 | + | 0.0914059i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 94750.4 | − | 60945.3i | 0.218841 | − | 0.140763i | ||||
\(659\) | 602985.i | 1.38847i | 0.719749 | + | 0.694234i | \(0.244257\pi\) | ||||
−0.719749 | + | 0.694234i | \(0.755743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 412862. | 0.944935 | 0.472468 | − | 0.881348i | \(-0.343363\pi\) | ||||
0.472468 | + | 0.881348i | \(0.343363\pi\) | |||||||
\(662\) | 193683. | + | 301115.i | 0.441952 | + | 0.687094i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13553.7 | − | 1965.13i | 0.0307412 | − | 0.00445713i | ||||
\(665\) | 166994. | 0.377623 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 205116.i | 0.461049i | ||||||||
\(668\) | −454745. | − | 207241.i | −1.01910 | − | 0.464432i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −684657. | − | 1.06442e6i | −1.52519 | − | 2.37118i | ||||
\(671\) | − | 291619.i | − | 0.647696i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −372998. | −0.823525 | −0.411763 | − | 0.911291i | \(-0.635087\pi\) | ||||
−0.411763 | + | 0.911291i | \(0.635087\pi\) | |||||||
\(674\) | −452234. | + | 290886.i | −0.995506 | + | 0.640329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64617.0 | − | 141788.i | 0.141401 | − | 0.310275i | ||||
\(677\) | −359783. | −0.784989 | −0.392494 | − | 0.919754i | \(-0.628388\pi\) | ||||
−0.392494 | + | 0.919754i | \(0.628388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14431.3i | 0.0313015i | ||||||||
\(680\) | −120082. | − | 828214.i | −0.259693 | − | 1.79112i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 860444. | − | 553454.i | 1.84992 | − | 1.18991i | ||||
\(683\) | − | 107389.i | − | 0.230206i | −0.993354 | − | 0.115103i | \(-0.963280\pi\) | ||
0.993354 | − | 0.115103i | \(-0.0367199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.44611e6 | −3.08191 | ||||||||
\(686\) | −140574. | − | 218547.i | −0.298714 | − | 0.464404i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −81034.3 | + | 70441.3i | −0.171195 | + | 0.148816i | ||||
\(689\) | 40403.0 | 0.0851090 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 617454.i | − | 1.29315i | −0.762851 | − | 0.646574i | \(-0.776201\pi\) | ||
0.762851 | − | 0.646574i | \(-0.223799\pi\) | |||||||
\(692\) | 130727. | − | 286851.i | 0.272993 | − | 0.599025i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −158154. | − | 245879.i | −0.328369 | − | 0.510509i | ||||
\(695\) | 371956.i | 0.770054i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61828.4 | 0.127269 | ||||||||
\(698\) | −182462. | + | 117363.i | −0.374508 | + | 0.240891i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −252542. | − | 115091.i | −0.515391 | − | 0.234879i | ||||
\(701\) | −486515. | −0.990057 | −0.495028 | − | 0.868877i | \(-0.664842\pi\) | ||||
−0.495028 | + | 0.868877i | \(0.664842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 171510.i | − | 0.347040i | ||||||
\(704\) | −243689. | − | 822704.i | −0.491689 | − | 1.65996i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 97667.0 | − | 62821.3i | 0.195947 | − | 0.126037i | ||||
\(707\) | − | 33513.6i | − | 0.0670475i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −144205. | −0.286872 | −0.143436 | − | 0.989660i | \(-0.545815\pi\) | ||||
−0.143436 | + | 0.989660i | \(0.545815\pi\) | |||||||
\(710\) | 796314. | + | 1.23801e6i | 1.57967 | + | 2.45589i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 77500.9 | + | 534529.i | 0.152879 | + | 1.05441i | ||||
\(713\) | −569390. | −1.12003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.76521e6i | 3.45289i | ||||||||
\(716\) | 13567.4 | + | 6183.06i | 0.0264649 | + | 0.0120608i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19902.5 | − | 30942.0i | −0.0386063 | − | 0.0600204i | ||||
\(719\) | 978439.i | 1.89268i | 0.323179 | + | 0.946338i | \(0.395248\pi\) | ||||
−0.323179 | + | 0.946338i | \(0.604752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 119700. | 0.230263 | ||||||||
\(722\) | 184391. | − | 118604.i | 0.353725 | − | 0.227523i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 54421.3 | − | 119416.i | 0.103822 | − | 0.227816i | ||||
\(725\) | −540548. | −1.02839 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 650971.i | 1.23166i | 0.787877 | + | 0.615832i | \(0.211180\pi\) | ||||
−0.787877 | + | 0.615832i | \(0.788820\pi\) | |||||||
\(728\) | 174947. | − | 25365.4i | 0.330098 | − | 0.0478606i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 470111. | − | 302385.i | 0.882175 | − | 0.567432i | ||||
\(731\) | 127372.i | 0.238364i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −502166. | −0.934629 | −0.467315 | − | 0.884091i | \(-0.654778\pi\) | ||||
−0.467315 | + | 0.884091i | \(0.654778\pi\) | |||||||
\(734\) | −208018. | − | 323401.i | −0.386108 | − | 0.600274i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −133632. | + | 458461.i | −0.246692 | + | 0.846343i | ||||
\(737\) | −1.53933e6 | −2.83397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 143898.i | − | 0.263491i | −0.991284 | − | 0.131745i | \(-0.957942\pi\) | ||
0.991284 | − | 0.131745i | \(-0.0420581\pi\) | |||||||
\(740\) | −178315. | + | 391274.i | −0.325631 | + | 0.714526i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6305.20 | + | 9802.55i | 0.0114522 | + | 0.0178046i | ||||
\(743\) | 639135.i | 1.15775i | 0.815416 | + | 0.578876i | \(0.196508\pi\) | ||||
−0.815416 | + | 0.578876i | \(0.803492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.03754e6 | −1.86936 | ||||||||
\(746\) | −93284.0 | + | 60002.1i | −0.167621 | + | 0.107817i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −926223. | − | 422107.i | −1.65544 | − | 0.754431i | ||||
\(749\) | 135210. | 0.241015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 494004.i | 0.875892i | 0.899001 | + | 0.437946i | \(0.144294\pi\) | ||||
−0.899001 | + | 0.437946i | \(0.855706\pi\) | |||||||
\(752\) | 385549. | − | 335150.i | 0.681780 | − | 0.592656i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 289577. | − | 186261.i | 0.509355 | − | 0.327627i | ||||
\(755\) | − | 1.14158e6i | − | 2.00268i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −207090. | −0.361382 | −0.180691 | − | 0.983540i | \(-0.557833\pi\) | ||||
−0.180691 | + | 0.983540i | \(0.557833\pi\) | |||||||
\(758\) | −220508. | − | 342819.i | −0.383784 | − | 0.596660i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 749408. | − | 108656.i | 1.29745 | − | 0.188116i | ||||
\(761\) | 584487. | 1.00927 | 0.504633 | − | 0.863334i | \(-0.331628\pi\) | ||||
0.504633 | + | 0.863334i | \(0.331628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 163013.i | 0.280011i | ||||||||
\(764\) | 47807.9 | + | 21787.4i | 0.0819054 | + | 0.0373267i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13549.8 | + | 21065.6i | 0.0230927 | + | 0.0359017i | ||||
\(767\) | 454396.i | 0.772402i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 521698. | 0.882200 | 0.441100 | − | 0.897458i | \(-0.354588\pi\) | ||||
0.441100 | + | 0.897458i | \(0.354588\pi\) | |||||||
\(770\) | −428273. | + | 275474.i | −0.722336 | + | 0.464621i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 468879. | − | 1.02885e6i | 0.786731 | − | 1.72631i | ||||
\(773\) | 810366. | 1.35620 | 0.678098 | − | 0.734971i | \(-0.262804\pi\) | ||||
0.678098 | + | 0.734971i | \(0.262804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.50053e6i | − | 2.49828i | ||||||
\(776\) | 9389.81 | + | 64762.2i | 0.0155931 | + | 0.107547i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −497185. | + | 319799.i | −0.821408 | + | 0.528346i | ||||
\(779\) | 55945.3i | 0.0921911i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.79037e6 | 2.93521 | ||||||||
\(782\) | 306459. | + | 476445.i | 0.501140 | + | 0.779111i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −369792. | − | 425402.i | −0.601625 | − | 0.692098i | ||||
\(785\) | 1.42914e6 | 2.31918 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 380693.i | 0.614646i | 0.951605 | + | 0.307323i | \(0.0994332\pi\) | ||||
−0.951605 | + | 0.307323i | \(0.900567\pi\) | |||||||
\(788\) | −98632.3 | + | 216427.i | −0.158842 | + | 0.348546i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 573702. | + | 891922.i | 0.919246 | + | 1.42913i | ||||
\(791\) | 308441.i | 0.492969i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 272438. | 0.433233 | ||||||||
\(794\) | −480864. | + | 309301.i | −0.762749 | + | 0.490615i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 930024. | + | 423839.i | 1.46780 | + | 0.668921i | ||||
\(797\) | −174404. | −0.274562 | −0.137281 | − | 0.990532i | \(-0.543836\pi\) | ||||
−0.137281 | + | 0.990532i | \(0.543836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 606018.i | − | 0.949276i | ||||||
\(800\) | −1.20820e6 | − | 352166.i | −1.88781 | − | 0.550259i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 60795.6 | − | 39104.9i | 0.0945199 | − | 0.0607971i | ||||
\(803\) | − | 679856.i | − | 1.05435i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 283405. | 0.437337 | ||||||||
\(806\) | 517051. | + | 803848.i | 0.795909 | + | 1.23738i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21805.9 | − | 150397.i | −0.0334003 | − | 0.230364i | ||||
\(809\) | 334685. | 0.511375 | 0.255688 | − | 0.966759i | \(-0.417698\pi\) | ||||
0.255688 | + | 0.966759i | \(0.417698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.01253e6i | 1.53946i | 0.638372 | + | 0.769728i | \(0.279608\pi\) | ||||
−0.638372 | + | 0.769728i | \(0.720392\pi\) | |||||||
\(812\) | 90381.2 | + | 41189.4i | 0.137077 | + | 0.0624702i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 282923. | + | 439854.i | 0.426992 | + | 0.663835i | ||||
\(815\) | − | 953122.i | − | 1.43494i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −115253. | −0.172666 | ||||||||
\(818\) | 560977. | − | 360831.i | 0.838375 | − | 0.539259i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 58165.1 | − | 127631.i | 0.0865037 | − | 0.189814i | ||||
\(821\) | 672538. | 0.997770 | 0.498885 | − | 0.866668i | \(-0.333743\pi\) | ||||
0.498885 | + | 0.866668i | \(0.333743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 790727.i | − | 1.16742i | −0.811962 | − | 0.583710i | \(-0.801601\pi\) | ||
0.811962 | − | 0.583710i | \(-0.198399\pi\) | |||||||
\(824\) | 537169. | − | 77883.6i | 0.791145 | − | 0.114707i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −110245. | + | 70911.9i | −0.161584 | + | 0.103934i | ||||
\(827\) | − | 688532.i | − | 1.00673i | −0.864074 | − | 0.503365i | \(-0.832095\pi\) | ||
0.864074 | − | 0.503365i | \(-0.167905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 301250. | 0.438348 | 0.219174 | − | 0.975686i | \(-0.429664\pi\) | ||||
0.219174 | + | 0.975686i | \(0.429664\pi\) | |||||||
\(830\) | −19938.0 | − | 30997.2i | −0.0289418 | − | 0.0449953i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 768591. | − | 227660.i | 1.11032 | − | 0.328883i | ||||
\(833\) | −668660. | −0.963641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.34486e6i | 1.92888i | ||||||||
\(836\) | 381943. | − | 838092.i | 0.546495 | − | 1.19917i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52081.3 | − | 80969.7i | −0.0741641 | − | 0.115301i | ||||
\(839\) | 269219.i | 0.382456i | 0.981546 | + | 0.191228i | \(0.0612470\pi\) | ||||
−0.981546 | + | 0.191228i | \(0.938753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −513826. | −0.726481 | ||||||||
\(842\) | −381707. | + | 245522.i | −0.538401 | + | 0.346310i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −969783. | − | 441959.i | −1.36141 | − | 0.620436i | ||||
\(845\) | −419324. | −0.587268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 412710.i | 0.575279i | ||||||||
\(848\) | 34673.4 | + | 39887.7i | 0.0482176 | + | 0.0554685i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.25559e6 | + | 807621.i | −1.73784 | + | 1.11782i | ||||
\(851\) | − | 291069.i | − | 0.401917i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 379053. | 0.520957 | 0.260478 | − | 0.965480i | \(-0.416120\pi\) | ||||
0.260478 | + | 0.965480i | \(0.416120\pi\) | |||||||
\(854\) | 42516.0 | + | 66098.7i | 0.0582957 | + | 0.0906311i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 606771. | − | 87975.1i | 0.828089 | − | 0.120064i | ||||
\(857\) | −818271. | −1.11413 | −0.557064 | − | 0.830469i | \(-0.688072\pi\) | ||||
−0.557064 | + | 0.830469i | \(0.688072\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.16384e6i | − | 1.57727i | −0.614862 | − | 0.788635i | \(-0.710788\pi\) | ||
0.614862 | − | 0.788635i | \(-0.289212\pi\) | |||||||
\(860\) | 262931. | + | 119825.i | 0.355504 | + | 0.162014i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −334191. | − | 519559.i | −0.449759 | − | 0.699230i | ||||
\(863\) | − | 1.11517e6i | − | 1.49734i | −0.662945 | − | 0.748668i | \(-0.730694\pi\) | ||
0.662945 | − | 0.748668i | \(-0.269306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −848334. | −1.13380 | ||||||||
\(866\) | 418710. | − | 269322.i | 0.558313 | − | 0.359118i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −114339. | + | 250893.i | −0.151760 | + | 0.333004i | ||||
\(869\) | 1.28986e6 | 1.70806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.43808e6i | − | 1.89560i | ||||||
\(872\) | 106066. | + | 731543.i | 0.139490 | + | 0.962070i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −431111. | + | 277299.i | −0.564373 | + | 0.363016i | ||||
\(875\) | 367046.i | 0.479407i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −573209. | −0.745270 | −0.372635 | − | 0.927978i | \(-0.621546\pi\) | ||||
−0.372635 | + | 0.927978i | \(0.621546\pi\) | |||||||
\(878\) | −217655. | − | 338384.i | −0.282345 | − | 0.438956i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.74269e6 | + | 1.51488e6i | −2.25037 | + | 1.95620i | ||||
\(881\) | 517273. | 0.666451 | 0.333226 | − | 0.942847i | \(-0.391863\pi\) | ||||
0.333226 | + | 0.942847i | \(0.391863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.38647e6i | − | 1.77824i | −0.457678 | − | 0.889118i | \(-0.651319\pi\) | ||
0.457678 | − | 0.889118i | \(-0.348681\pi\) | |||||||
\(884\) | 394343. | − | 865301.i | 0.504626 | − | 1.10729i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 423288. | + | 658077.i | 0.539223 | + | 0.838318i | ||||
\(887\) | 1.30999e6i | 1.66503i | 0.554005 | + | 0.832513i | \(0.313099\pi\) | ||||
−0.554005 | + | 0.832513i | \(0.686901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 103859. | 0.131413 | ||||||||
\(890\) | 1.22247e6 | − | 786316.i | 1.54333 | − | 0.992698i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −699929. | − | 318978.i | −0.879679 | − | 0.400896i | ||||
\(893\) | 548355. | 0.687637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 40124.2i | − | 0.0500911i | ||||||
\(896\) | 175179. | + | 150947.i | 0.218206 | + | 0.188022i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −158585. | + | 102005.i | −0.196657 | + | 0.126494i | ||||
\(899\) | 537019.i | 0.664463i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62696.6 | 0.0772315 | ||||||||
\(902\) | −92287.3 | − | 143477.i | −0.113430 | − | 0.176348i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 200689. | + | 1.38417e6i | 0.245577 | + | 1.69376i | ||||
\(905\) | −353160. | −0.431196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 947897.i | 1.15225i | 0.817362 | + | 0.576125i | \(0.195436\pi\) | ||||
−0.817362 | + | 0.576125i | \(0.804564\pi\) | |||||||
\(908\) | −275758. | − | 125671.i | −0.334469 | − | 0.152427i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −257354. | − | 400103.i | −0.310777 | − | 0.483158i | ||||
\(911\) | − | 1.17071e6i | − | 1.41062i | −0.708898 | − | 0.705311i | \(-0.750807\pi\) | ||
0.708898 | − | 0.705311i | \(-0.249193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44827.0 | −0.0537772 | ||||||||
\(914\) | −149436. | + | 96120.2i | −0.178880 | + | 0.115059i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2320.56 | − | 5091.96i | 0.00276568 | − | 0.00606868i | ||||
\(917\) | −120927. | −0.143809 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 949625.i | − | 1.12440i | −0.827001 | − | 0.562200i | \(-0.809955\pi\) | ||
0.827001 | − | 0.562200i | \(-0.190045\pi\) | |||||||
\(920\) | 1.27181e6 | − | 184399.i | 1.50262 | − | 0.217863i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 637158. | − | 409833.i | 0.749524 | − | 0.482108i | ||||
\(923\) | 1.67261e6i | 1.96332i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 767063. | 0.896495 | ||||||||
\(926\) | −316334. | − | 491798.i | −0.368913 | − | 0.573542i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 432397. | + | 126035.i | 0.502096 | + | 0.146351i | ||||
\(929\) | 314076. | 0.363918 | 0.181959 | − | 0.983306i | \(-0.441756\pi\) | ||||
0.181959 | + | 0.983306i | \(0.441756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 605036.i | − | 0.698042i | ||||||
\(932\) | 49956.8 | − | 109620.i | 0.0575126 | − | 0.126199i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 315509. | + | 490515.i | 0.361675 | + | 0.562288i | ||||
\(935\) | 2.73921e6i | 3.13330i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.50272e6 | 1.71159 | 0.855795 | − | 0.517315i | \(-0.173069\pi\) | ||||
0.855795 | + | 0.517315i | \(0.173069\pi\) | |||||||
\(938\) | 348905. | − | 224423.i | 0.396554 | − | 0.255071i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.25099e6 | − | 570112.i | −1.41579 | − | 0.645215i | ||||
\(941\) | −71086.4 | −0.0802800 | −0.0401400 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401400 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 94944.4i | 0.106769i | ||||||||
\(944\) | −448600. | + | 389957.i | −0.503402 | + | 0.437596i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 295576. | − | 190120.i | 0.330284 | − | 0.212445i | ||||
\(947\) | − | 1.58311e6i | − | 1.76527i | −0.470058 | − | 0.882636i | \(-0.655767\pi\) | ||
0.470058 | − | 0.882636i | \(-0.344233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 635139. | 0.705239 | ||||||||
\(950\) | −730775. | − | 1.13612e6i | −0.809723 | − | 1.25886i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 271479. | − | 39361.5i | 0.299545 | − | 0.0434308i | ||||
\(953\) | 1.05600e6 | 1.16273 | 0.581367 | − | 0.813642i | \(-0.302518\pi\) | ||||
0.581367 | + | 0.813642i | \(0.302518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 141387.i | − | 0.155025i | ||||||
\(956\) | −777394. | − | 354281.i | −0.850600 | − | 0.387643i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −793571. | − | 1.23375e6i | −0.864679 | − | 1.34430i | ||||
\(959\) | − | 474017.i | − | 0.515415i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −567215. | −0.614188 | ||||||||
\(962\) | −410923. | + | 264314.i | −0.444028 | + | 0.285608i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −584938. | + | 1.28352e6i | −0.629442 | + | 1.38117i | ||||
\(965\) | −3.04273e6 | −3.26745 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 104102.i | − | 0.111328i | −0.998450 | − | 0.0556642i | \(-0.982272\pi\) | ||
0.998450 | − | 0.0556642i | \(-0.0177276\pi\) | |||||||
\(968\) | 268533. | + | 1.85209e6i | 0.286580 | + | 1.97657i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 148111. | − | 95268.1i | 0.157414 | − | 0.101252i | ||||
\(971\) | − | 865558.i | − | 0.918032i | −0.888428 | − | 0.459016i | \(-0.848202\pi\) | ||
0.888428 | − | 0.459016i | \(-0.151798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −121923. | −0.128783 | ||||||||
\(974\) | 437177. | + | 679670.i | 0.460829 | + | 0.716441i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 233803. | + | 268963.i | 0.245443 | + | 0.282353i | ||||
\(977\) | 303107. | 0.317546 | 0.158773 | − | 0.987315i | \(-0.449246\pi\) | ||||
0.158773 | + | 0.987315i | \(0.449246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.76789e6i | − | 1.84454i | ||||||
\(980\) | −629042. | + | 1.38030e6i | −0.654979 | + | 1.43721i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 496503. | + | 771903.i | 0.514872 | + | 0.800460i | ||||
\(983\) | 769392.i | 0.796234i | 0.917335 | + | 0.398117i | \(0.130336\pi\) | ||||
−0.917335 | + | 0.398117i | \(0.869664\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 640062. | 0.659705 | ||||||||
\(986\) | 449359. | − | 289037.i | 0.462211 | − | 0.297303i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 782967. | + | 356821.i | 0.802101 | + | 0.365541i | ||||
\(989\) | −195594. | −0.199969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 885320.i | 0.901473i | 0.892657 | + | 0.450737i | \(0.148839\pi\) | ||||
−0.892657 | + | 0.450737i | \(0.851161\pi\) | |||||||
\(992\) | −349867. | + | 1.20031e6i | −0.355533 | + | 1.21975i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −405806. | + | 261023.i | −0.410720 | + | 0.264183i | ||||
\(995\) | − | 2.75045e6i | − | 2.77817i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.24546e6 | −1.25297 | −0.626483 | − | 0.779435i | \(-0.715506\pi\) | ||||
−0.626483 | + | 0.779435i | \(0.715506\pi\) | |||||||
\(998\) | −764673. | − | 1.18882e6i | −0.767741 | − | 1.19359i | ||||
\(999\) | 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 | 108.5.d.a.55.13 | yes | 16 | |
3.2 | odd | 2 | inner | 108.5.d.a.55.4 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.a.55.14 | yes | 16 | |
12.11 | even | 2 | inner | 108.5.d.a.55.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.a.55.3 | ✓ | 16 | 12.11 | even | 2 | inner | |
108.5.d.a.55.4 | yes | 16 | 3.2 | odd | 2 | inner | |
108.5.d.a.55.13 | yes | 16 | 1.1 | even | 1 | trivial | |
108.5.d.a.55.14 | yes | 16 | 4.3 | odd | 2 | inner |