Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(89,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.89");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.y (of order \(10\), degree \(4\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 89.16 | ||
Character | \(\chi\) | \(=\) | 900.89 |
Dual form | 900.3.y.a.809.16 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 | ||||||||
\(5\) | 3.94179 | − | 3.07609i | 0.788357 | − | 0.615218i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.41454i | 1.05922i | 0.848241 | + | 0.529610i | \(0.177662\pi\) | ||||
−0.848241 | + | 0.529610i | \(0.822338\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.4971 | − | 15.8244i | −1.04519 | − | 1.43858i | −0.892905 | − | 0.450246i | \(-0.851336\pi\) |
−0.152286 | − | 0.988336i | \(-0.548664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.29536 | + | 5.91205i | −0.330412 | + | 0.454773i | −0.941610 | − | 0.336704i | \(-0.890688\pi\) |
0.611198 | + | 0.791477i | \(0.290688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.99059 | + | 27.6702i | 0.528858 | + | 1.62766i | 0.756558 | + | 0.653927i | \(0.226880\pi\) |
−0.227700 | + | 0.973731i | \(0.573120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.64430 | + | 29.6821i | 0.507595 | + | 1.56222i | 0.796364 | + | 0.604817i | \(0.206754\pi\) |
−0.288769 | + | 0.957399i | \(0.593246\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −13.1297 | + | 9.53925i | −0.570855 | + | 0.414750i | −0.835416 | − | 0.549619i | \(-0.814773\pi\) |
0.264561 | + | 0.964369i | \(0.414773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.07535 | − | 24.2506i | 0.243014 | − | 0.970023i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 43.8931 | + | 14.2617i | 1.51356 | + | 0.491784i | 0.943937 | − | 0.330125i | \(-0.107091\pi\) |
0.569619 | + | 0.821909i | \(0.307091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.23512 | − | 3.80131i | −0.0398426 | − | 0.122623i | 0.929157 | − | 0.369686i | \(-0.120535\pi\) |
−0.968999 | + | 0.247063i | \(0.920535\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.8078 | + | 29.2265i | 0.651651 | + | 0.835044i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.5940 | + | 15.9578i | −0.313351 | + | 0.431291i | −0.936423 | − | 0.350874i | \(-0.885885\pi\) |
0.623071 | + | 0.782165i | \(0.285885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 23.4213 | − | 32.2366i | 0.571251 | − | 0.786259i | −0.421451 | − | 0.906851i | \(-0.638479\pi\) |
0.992702 | + | 0.120592i | \(0.0384792\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.31409i | 0.216607i | 0.994118 | + | 0.108303i | \(0.0345418\pi\) | ||||
−0.994118 | + | 0.108303i | \(0.965458\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.13800 | + | 18.8908i | −0.130596 | + | 0.401932i | −0.994879 | − | 0.101073i | \(-0.967772\pi\) |
0.864283 | + | 0.503005i | \(0.167772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.97546 | −0.121948 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −17.5851 | + | 54.1214i | −0.331795 | + | 1.02116i | 0.636485 | + | 0.771289i | \(0.280388\pi\) |
−0.968280 | + | 0.249870i | \(0.919612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −93.9964 | − | 27.0103i | −1.70903 | − | 0.491096i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 41.9182 | − | 57.6954i | 0.710477 | − | 0.977888i | −0.289309 | − | 0.957236i | \(-0.593426\pi\) |
0.999787 | − | 0.0206524i | \(-0.00657435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.9280 | + | 39.1810i | −0.884065 | + | 0.642311i | −0.934324 | − | 0.356425i | \(-0.883995\pi\) |
0.0502585 | + | 0.998736i | \(0.483995\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.25462 | + | 36.5170i | 0.0193018 | + | 0.561799i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −100.605 | + | 32.6887i | −1.50157 | + | 0.487891i | −0.940476 | − | 0.339859i | \(-0.889621\pi\) |
−0.561097 | + | 0.827750i | \(0.689621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 79.5907 | + | 25.8606i | 1.12100 | + | 0.364233i | 0.810147 | − | 0.586226i | \(-0.199387\pi\) |
0.310848 | + | 0.950460i | \(0.399387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50.2620 | + | 69.1797i | 0.688520 | + | 0.947667i | 0.999997 | − | 0.00258691i | \(-0.000823440\pi\) |
−0.311476 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 117.331 | − | 85.2458i | 1.52378 | − | 1.10709i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.4848 | − | 69.2010i | 0.284617 | − | 0.875962i | −0.701896 | − | 0.712280i | \(-0.747663\pi\) |
0.986513 | − | 0.163682i | \(-0.0523372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.0766 | − | 46.4011i | −0.181646 | − | 0.559049i | 0.818228 | − | 0.574893i | \(-0.194956\pi\) |
−0.999874 | + | 0.0158440i | \(0.994956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 120.555 | + | 81.4141i | 1.41829 | + | 0.957813i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 74.8317 | + | 102.997i | 0.840805 | + | 1.15727i | 0.985814 | + | 0.167839i | \(0.0536789\pi\) |
−0.145009 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −43.8352 | − | 31.8481i | −0.481705 | − | 0.349979i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 129.321 | + | 87.3338i | 1.36127 | + | 0.919303i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 141.583 | + | 46.0030i | 1.45962 | + | 0.474258i | 0.927953 | − | 0.372698i | \(-0.121567\pi\) |
0.531663 | + | 0.846956i | \(0.321567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.9546i | 0.563907i | 0.959428 | + | 0.281954i | \(0.0909824\pi\) | ||||
−0.959428 | + | 0.281954i | \(0.909018\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 166.959 | + | 54.2484i | 1.62096 | + | 0.526683i | 0.972169 | − | 0.234280i | \(-0.0752732\pi\) |
0.648795 | + | 0.760963i | \(0.275273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27.6818 | −0.258708 | −0.129354 | − | 0.991598i | \(-0.541290\pi\) | ||||
−0.129354 | + | 0.991598i | \(0.541290\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −119.820 | − | 87.0542i | −1.09926 | − | 0.798663i | −0.118325 | − | 0.992975i | \(-0.537752\pi\) |
−0.980940 | + | 0.194312i | \(0.937752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 75.5907 | + | 54.9198i | 0.668944 | + | 0.486016i | 0.869672 | − | 0.493631i | \(-0.164331\pi\) |
−0.200728 | + | 0.979647i | \(0.564331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.4107 | + | 77.9897i | −0.194876 | + | 0.678171i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −205.162 | + | 66.6611i | −1.72405 | + | 0.560177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −80.8373 | + | 248.792i | −0.668077 | + | 2.05613i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −50.6492 | − | 114.279i | −0.405193 | − | 0.914231i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −81.9260 | − | 112.762i | −0.645087 | − | 0.887886i | 0.353787 | − | 0.935326i | \(-0.384894\pi\) |
−0.998874 | + | 0.0474399i | \(0.984894\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −87.3442 | + | 28.3798i | −0.666749 | + | 0.216640i | −0.622785 | − | 0.782393i | \(-0.713999\pi\) |
−0.0439645 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −220.079 | + | 71.5081i | −1.65473 | + | 0.537655i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.43646 | − | 3.94982i | −0.0396822 | − | 0.0288308i | 0.567767 | − | 0.823189i | \(-0.307807\pi\) |
−0.607450 | + | 0.794358i | \(0.707807\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −93.1731 | + | 67.6942i | −0.670310 | + | 0.487009i | −0.870129 | − | 0.492824i | \(-0.835965\pi\) |
0.199819 | + | 0.979833i | \(0.435965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 142.939 | 0.999573 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 216.888 | − | 78.8024i | 1.49578 | − | 0.543465i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 91.4528i | − | 0.613777i | −0.951745 | − | 0.306889i | \(-0.900712\pi\) | ||
0.951745 | − | 0.306889i | \(-0.0992879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −83.0238 | −0.549827 | −0.274913 | − | 0.961469i | \(-0.588649\pi\) | ||||
−0.274913 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5618 | − | 11.1846i | −0.106850 | − | 0.0721588i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 105.588i | − | 0.672535i | −0.941766 | − | 0.336268i | \(-0.890835\pi\) | ||
0.941766 | − | 0.336268i | \(-0.109165\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −70.7292 | − | 97.3504i | −0.439312 | − | 0.604661i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −148.647 | + | 204.594i | −0.911942 | + | 1.25518i | 0.0545570 | + | 0.998511i | \(0.482625\pi\) |
−0.966499 | + | 0.256670i | \(0.917375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 68.8019 | + | 211.750i | 0.411987 | + | 1.26797i | 0.914918 | + | 0.403640i | \(0.132255\pi\) |
−0.502930 | + | 0.864327i | \(0.667745\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.7216 | + | 109.940i | 0.211370 | + | 0.650531i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −50.1311 | + | 36.4224i | −0.289775 | + | 0.210534i | −0.723170 | − | 0.690670i | \(-0.757316\pi\) |
0.433395 | + | 0.901204i | \(0.357316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 179.807 | + | 45.0460i | 1.02747 | + | 0.257406i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7014 | + | 6.72629i | 0.115650 | + | 0.0375770i | 0.366270 | − | 0.930508i | \(-0.380635\pi\) |
−0.250620 | + | 0.968085i | \(0.580635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.60737 | − | 20.3354i | −0.0365048 | − | 0.112350i | 0.931144 | − | 0.364653i | \(-0.118812\pi\) |
−0.967648 | + | 0.252302i | \(0.918812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.38646 | + | 98.5663i | 0.0183052 | + | 0.532791i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 334.499 | − | 460.398i | 1.78876 | − | 2.46202i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −59.5744 | + | 81.9971i | −0.311908 | + | 0.429304i | −0.935975 | − | 0.352066i | \(-0.885479\pi\) |
0.624067 | + | 0.781371i | \(0.285479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 300.637i | − | 1.55770i | −0.627208 | − | 0.778852i | \(-0.715802\pi\) | ||
0.627208 | − | 0.778852i | \(-0.284198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 53.3613 | − | 164.229i | 0.270870 | − | 0.833651i | −0.719413 | − | 0.694582i | \(-0.755589\pi\) |
0.990283 | − | 0.139069i | \(-0.0444109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −294.792 | −1.48137 | −0.740684 | − | 0.671854i | \(-0.765498\pi\) | ||||
−0.740684 | + | 0.671854i | \(0.765498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −105.744 | + | 325.447i | −0.520908 | + | 1.60319i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.84106 | − | 199.116i | −0.0333710 | − | 0.971297i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 358.820 | − | 493.874i | 1.71684 | − | 2.36303i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 50.9872 | − | 37.0443i | 0.241645 | − | 0.175566i | −0.460371 | − | 0.887727i | \(-0.652284\pi\) |
0.702016 | + | 0.712161i | \(0.252284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.6510 | + | 36.7142i | 0.133260 | + | 0.170764i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.1850 | − | 9.15786i | 0.129885 | − | 0.0422021i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −202.205 | − | 65.7005i | −0.914957 | − | 0.297287i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 109.047 | + | 150.091i | 0.489002 | + | 0.673053i | 0.980204 | − | 0.197993i | \(-0.0634422\pi\) |
−0.491202 | + | 0.871046i | \(0.663442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −164.163 | + | 119.271i | −0.723183 | + | 0.525423i | −0.887400 | − | 0.461001i | \(-0.847490\pi\) |
0.164217 | + | 0.986424i | \(0.447490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 74.7205 | − | 229.966i | 0.326291 | − | 1.00422i | −0.644564 | − | 0.764550i | \(-0.722961\pi\) |
0.970855 | − | 0.239669i | \(-0.0770389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −133.667 | − | 411.386i | −0.573680 | − | 1.76560i | −0.640632 | − | 0.767848i | \(-0.721328\pi\) |
0.0669527 | − | 0.997756i | \(-0.478672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.9152 | + | 93.3446i | 0.144320 | + | 0.397211i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −131.387 | − | 180.839i | −0.549736 | − | 0.756647i | 0.440240 | − | 0.897880i | \(-0.354893\pi\) |
−0.989976 | + | 0.141233i | \(0.954893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 154.774 | + | 112.450i | 0.642217 | + | 0.466598i | 0.860611 | − | 0.509262i | \(-0.170082\pi\) |
−0.218394 | + | 0.975861i | \(0.570082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.5540 | + | 18.3811i | −0.0961387 | + | 0.0750247i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −216.908 | − | 70.4777i | −0.878170 | − | 0.285335i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 381.283i | − | 1.51906i | −0.650475 | − | 0.759528i | \(-0.725430\pi\) | ||
0.650475 | − | 0.759528i | \(-0.274570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 301.906 | + | 98.0952i | 1.19330 | + | 0.387728i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 461.439 | 1.79548 | 0.897742 | − | 0.440522i | \(-0.145207\pi\) | ||||
0.897742 | + | 0.440522i | \(0.145207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −118.320 | − | 85.9642i | −0.456833 | − | 0.331908i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −369.060 | − | 268.138i | −1.40327 | − | 1.01954i | −0.994258 | − | 0.107008i | \(-0.965873\pi\) |
−0.409013 | − | 0.912528i | \(-0.634127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 97.1655 | + | 267.428i | 0.366662 | + | 1.00916i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −93.6036 | + | 30.4137i | −0.347969 | + | 0.113062i | −0.477787 | − | 0.878476i | \(-0.658561\pi\) |
0.129818 | + | 0.991538i | \(0.458561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 60.5821 | − | 186.453i | 0.223550 | − | 0.688017i | −0.774885 | − | 0.632102i | \(-0.782192\pi\) |
0.998436 | − | 0.0559149i | \(-0.0178075\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −453.600 | + | 182.672i | −1.64945 | + | 0.664263i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −104.438 | − | 143.746i | −0.377032 | − | 0.518940i | 0.577763 | − | 0.816204i | \(-0.303926\pi\) |
−0.954795 | + | 0.297264i | \(0.903926\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −59.9546 | + | 19.4804i | −0.213362 | + | 0.0693254i | −0.413748 | − | 0.910392i | \(-0.635780\pi\) |
0.200386 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 316.388 | − | 102.801i | 1.11798 | − | 0.363254i | 0.308983 | − | 0.951067i | \(-0.400011\pi\) |
0.808996 | + | 0.587814i | \(0.200011\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 239.020 | + | 173.658i | 0.832822 | + | 0.605081i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −451.003 | + | 327.673i | −1.56056 | + | 1.13382i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −307.520 | −1.04956 | −0.524778 | − | 0.851239i | \(-0.675852\pi\) | ||||
−0.524778 | + | 0.851239i | \(0.675852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2438 | − | 356.367i | −0.0415043 | − | 1.20802i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 118.598i | − | 0.396648i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −69.0597 | −0.229434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −92.0484 | + | 320.330i | −0.301798 | + | 1.05026i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.6987i | − | 0.0869666i | −0.999054 | − | 0.0434833i | \(-0.986154\pi\) | ||
0.999054 | − | 0.0434833i | \(-0.0138455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −127.356 | − | 175.290i | −0.409504 | − | 0.563634i | 0.553594 | − | 0.832787i | \(-0.313256\pi\) |
−0.963097 | + | 0.269153i | \(0.913256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9638 | − | 27.4777i | 0.0637819 | − | 0.0877883i | −0.775934 | − | 0.630814i | \(-0.782721\pi\) |
0.839716 | + | 0.543025i | \(0.182721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −39.3540 | − | 121.119i | −0.124145 | − | 0.382079i | 0.869599 | − | 0.493758i | \(-0.164377\pi\) |
−0.993744 | + | 0.111679i | \(0.964377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −278.960 | − | 858.551i | −0.874483 | − | 2.69138i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −734.602 | + | 533.719i | −2.27431 | + | 1.65238i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 117.275 | + | 140.083i | 0.360846 | + | 0.431024i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −140.067 | − | 45.5105i | −0.425735 | − | 0.138330i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 125.378 | + | 385.875i | 0.378786 | + | 1.16578i | 0.940888 | + | 0.338717i | \(0.109993\pi\) |
−0.562102 | + | 0.827068i | \(0.690007\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −296.012 | + | 438.323i | −0.883617 | + | 1.30843i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.2691 | − | 40.2855i | 0.0868520 | − | 0.119542i | −0.763380 | − | 0.645950i | \(-0.776462\pi\) |
0.850232 | + | 0.526408i | \(0.176462\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −45.9532 | + | 63.2492i | −0.134760 | + | 0.185481i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 319.007i | 0.930051i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 115.083 | − | 354.189i | 0.331651 | − | 1.02072i | −0.636697 | − | 0.771114i | \(-0.719700\pi\) |
0.968348 | − | 0.249603i | \(-0.0803002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 513.030 | 1.47000 | 0.735000 | − | 0.678067i | \(-0.237182\pi\) | ||||
0.735000 | + | 0.678067i | \(0.237182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 114.892 | − | 353.603i | 0.325474 | − | 1.00171i | −0.645752 | − | 0.763548i | \(-0.723456\pi\) |
0.971226 | − | 0.238160i | \(-0.0765441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 393.279 | − | 142.891i | 1.10783 | − | 0.402510i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 143.229 | − | 197.138i | 0.398968 | − | 0.549132i | −0.561517 | − | 0.827465i | \(-0.689782\pi\) |
0.960485 | + | 0.278333i | \(0.0897820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −495.960 | + | 360.336i | −1.37385 | + | 0.998160i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 410.925 | + | 118.081i | 1.12582 | + | 0.323510i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 527.034 | − | 171.244i | 1.43606 | − | 0.466604i | 0.515393 | − | 0.856954i | \(-0.327646\pi\) |
0.920667 | + | 0.390350i | \(0.127646\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −401.286 | − | 130.386i | −1.08163 | − | 0.351444i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 192.939 | + | 265.558i | 0.517263 | + | 0.711952i | 0.985123 | − | 0.171851i | \(-0.0549748\pi\) |
−0.467860 | + | 0.883803i | \(0.654975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −272.853 | + | 198.239i | −0.723748 | + | 0.525833i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1823 | + | 52.8816i | −0.0453358 | + | 0.139529i | −0.971162 | − | 0.238420i | \(-0.923371\pi\) |
0.925826 | + | 0.377949i | \(0.123371\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 89.5142 | + | 275.496i | 0.233719 | + | 0.719312i | 0.997289 | + | 0.0735870i | \(0.0234446\pi\) |
−0.763570 | + | 0.645725i | \(0.776555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 200.269 | − | 696.940i | 0.520179 | − | 1.81023i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.8740 | − | 36.9888i | −0.0690847 | − | 0.0950869i | 0.773076 | − | 0.634313i | \(-0.218717\pi\) |
−0.842161 | + | 0.539226i | \(0.818717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −381.996 | − | 277.537i | −0.976972 | − | 0.709812i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −124.238 | − | 341.941i | −0.314527 | − | 0.865673i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7843 | + | 6.75323i | 0.0523534 | + | 0.0170107i | 0.335077 | − | 0.942191i | \(-0.391238\pi\) |
−0.282723 | + | 0.959202i | \(0.591238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 693.977i | − | 1.73062i | −0.501240 | − | 0.865308i | \(-0.667123\pi\) | ||
0.501240 | − | 0.865308i | \(-0.332877\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.7789 | + | 9.02590i | 0.0689302 | + | 0.0223968i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 385.820 | 0.947960 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 155.964 | + | 113.315i | 0.381331 | + | 0.277053i | 0.761894 | − | 0.647702i | \(-0.224270\pi\) |
−0.380563 | + | 0.924755i | \(0.624270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 427.785 | + | 310.804i | 1.03580 | + | 0.752552i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −202.163 | − | 136.526i | −0.487139 | − | 0.328979i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 78.4830 | − | 25.5007i | 0.187310 | − | 0.0608608i | −0.213860 | − | 0.976864i | \(-0.568604\pi\) |
0.401170 | + | 0.916004i | \(0.368604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −199.344 | + | 613.519i | −0.473502 | + | 1.45729i | 0.374466 | + | 0.927241i | \(0.377826\pi\) |
−0.847967 | + | 0.530048i | \(0.822174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 725.639 | − | 49.9207i | 1.70739 | − | 0.117460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −290.509 | − | 399.851i | −0.680349 | − | 0.936420i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −55.8508 | + | 18.1470i | −0.129584 | + | 0.0421045i | −0.373091 | − | 0.927795i | \(-0.621702\pi\) |
0.243507 | + | 0.969899i | \(0.421702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.0577 | + | 7.49189i | −0.0532510 | + | 0.0173023i | −0.335521 | − | 0.942033i | \(-0.608912\pi\) |
0.282270 | + | 0.959335i | \(0.408912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −409.771 | − | 297.716i | −0.937692 | − | 0.681273i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −89.7741 | + | 65.2247i | −0.204497 | + | 0.148576i | −0.685320 | − | 0.728242i | \(-0.740338\pi\) |
0.480823 | + | 0.876817i | \(0.340338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −100.429 | −0.226701 | −0.113351 | − | 0.993555i | \(-0.536158\pi\) | ||||
−0.113351 | + | 0.993555i | \(0.536158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 611.798 | + | 175.803i | 1.37483 | + | 0.395063i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 114.908i | 0.255920i | 0.991779 | + | 0.127960i | \(0.0408428\pi\) | ||||
−0.991779 | + | 0.127960i | \(0.959157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −779.402 | −1.72817 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −270.757 | + | 9.30243i | −0.595069 | + | 0.0204449i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 816.492i | − | 1.78663i | −0.449427 | − | 0.893317i | \(-0.648372\pi\) | ||
0.449427 | − | 0.893317i | \(-0.351628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.5319 | + | 48.9055i | 0.0770758 | + | 0.106086i | 0.845814 | − | 0.533478i | \(-0.179115\pi\) |
−0.768738 | + | 0.639563i | \(0.779115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −234.495 | + | 322.755i | −0.506469 | + | 0.697094i | −0.983319 | − | 0.181890i | \(-0.941778\pi\) |
0.476850 | + | 0.878985i | \(0.341778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.9533 | − | 126.041i | −0.0876944 | − | 0.269895i | 0.897587 | − | 0.440838i | \(-0.145319\pi\) |
−0.985281 | + | 0.170943i | \(0.945319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −242.372 | − | 745.943i | −0.516784 | − | 1.59050i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 147.390 | − | 107.085i | 0.311607 | − | 0.226395i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 778.401 | − | 53.5505i | 1.63874 | − | 0.112738i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 445.196 | + | 144.653i | 0.929427 | + | 0.301989i | 0.734328 | − | 0.678794i | \(-0.237497\pi\) |
0.195099 | + | 0.980784i | \(0.437497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −44.5428 | − | 137.089i | −0.0926046 | − | 0.285008i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 699.598 | − | 254.187i | 1.44247 | − | 0.524097i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −233.802 | + | 321.801i | −0.480087 | + | 0.660783i | −0.978522 | − | 0.206144i | \(-0.933908\pi\) |
0.498435 | + | 0.866927i | \(0.333908\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 70.8954 | − | 97.5791i | 0.144390 | − | 0.198735i | −0.730697 | − | 0.682702i | \(-0.760805\pi\) |
0.875086 | + | 0.483967i | \(0.160805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1342.75i | 2.72364i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −191.744 | + | 590.129i | −0.385804 | + | 1.18738i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −713.310 | −1.42948 | −0.714739 | − | 0.699391i | \(-0.753455\pi\) | ||||
−0.714739 | + | 0.699391i | \(0.753455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −72.9299 | + | 224.455i | −0.144990 | + | 0.446233i | −0.997010 | − | 0.0772767i | \(-0.975378\pi\) |
0.852020 | + | 0.523509i | \(0.175378\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 175.197 | + | 224.503i | 0.346926 | + | 0.444560i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −50.1595 | + | 69.0386i | −0.0985452 | + | 0.135636i | −0.855442 | − | 0.517898i | \(-0.826714\pi\) |
0.756897 | + | 0.653534i | \(0.226714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −512.936 | + | 372.670i | −1.00379 | + | 0.729295i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 824.991 | − | 299.746i | 1.60192 | − | 0.582032i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 369.505 | − | 120.059i | 0.714710 | − | 0.232223i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −563.754 | − | 183.175i | −1.08206 | − | 0.351583i | −0.286888 | − | 0.957964i | \(-0.592621\pi\) |
−0.795174 | + | 0.606381i | \(0.792621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −46.6987 | − | 64.2752i | −0.0892900 | − | 0.122897i | 0.762035 | − | 0.647536i | \(-0.224200\pi\) |
−0.851325 | + | 0.524639i | \(0.824200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 94.0786 | − | 68.3521i | 0.178517 | − | 0.129700i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −82.0795 | + | 252.615i | −0.155160 | + | 0.477533i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 89.9819 | + | 276.936i | 0.168822 | + | 0.519579i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −109.116 | + | 85.1515i | −0.203954 | + | 0.159162i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 68.7005 | + | 94.5581i | 0.127459 | + | 0.175433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −146.918 | − | 106.742i | −0.271567 | − | 0.197305i | 0.443664 | − | 0.896193i | \(-0.353678\pi\) |
−0.715231 | + | 0.698888i | \(0.753678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −740.091 | + | 25.4274i | −1.35796 | + | 0.0466558i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −252.310 | − | 81.9804i | −0.461261 | − | 0.149873i | 0.0691628 | − | 0.997605i | \(-0.477967\pi\) |
−0.530424 | + | 0.847733i | \(0.677967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1440.38i | 2.61413i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 513.094 | + | 166.714i | 0.927837 | + | 0.301473i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 779.122 | 1.39878 | 0.699392 | − | 0.714739i | \(-0.253454\pi\) | ||||
0.699392 | + | 0.714739i | \(0.253454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.0654 | − | 40.0074i | −0.0985070 | − | 0.0715695i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 379.921 | + | 276.029i | 0.674816 | + | 0.490282i | 0.871634 | − | 0.490158i | \(-0.163061\pi\) |
−0.196818 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 466.901 | − | 16.0414i | 0.826373 | − | 0.0283918i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 498.674 | − | 162.029i | 0.876404 | − | 0.284761i | 0.163941 | − | 0.986470i | \(-0.447579\pi\) |
0.712463 | + | 0.701709i | \(0.247579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 162.539 | − | 500.242i | 0.284656 | − | 0.876081i | −0.701846 | − | 0.712329i | \(-0.747640\pi\) |
0.986502 | − | 0.163752i | \(-0.0523596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 151.565 | + | 376.356i | 0.263591 | + | 0.654532i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.9051 | − | 63.1830i | −0.0795583 | − | 0.109503i | 0.767383 | − | 0.641189i | \(-0.221559\pi\) |
−0.846941 | + | 0.531686i | \(0.821559\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 344.043 | − | 111.786i | 0.592157 | − | 0.192403i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1058.62 | − | 343.965i | 1.81581 | − | 0.589992i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.15368 | + | 6.65053i | 0.0155940 | + | 0.0113297i | 0.595555 | − | 0.803315i | \(-0.296932\pi\) |
−0.579961 | + | 0.814644i | \(0.696932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 100.919 | − | 73.3220i | 0.171340 | − | 0.124486i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −390.250 | −0.658094 | −0.329047 | − | 0.944313i | \(-0.606728\pi\) | ||||
−0.329047 | + | 0.944313i | \(0.606728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −603.649 | + | 893.860i | −1.01454 | + | 1.50229i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.7243i | 0.0763343i | 0.999271 | + | 0.0381672i | \(0.0121519\pi\) | ||||
−0.999271 | + | 0.0381672i | \(0.987848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 408.687 | 0.680012 | 0.340006 | − | 0.940423i | \(-0.389571\pi\) | ||||
0.340006 | + | 0.940423i | \(0.389571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 446.662 | + | 1229.35i | 0.738284 | + | 2.03198i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 401.268i | 0.661068i | 0.943794 | + | 0.330534i | \(0.107229\pi\) | ||||
−0.943794 | + | 0.330534i | \(0.892771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −85.3186 | − | 117.431i | −0.139638 | − | 0.192195i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −465.247 | + | 640.358i | −0.758968 | + | 1.04463i | 0.238331 | + | 0.971184i | \(0.423400\pi\) |
−0.997299 | + | 0.0734459i | \(0.976600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 287.494 | + | 884.816i | 0.465955 | + | 1.43406i | 0.857778 | + | 0.514021i | \(0.171845\pi\) |
−0.391823 | + | 0.920041i | \(0.628155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −140.385 | − | 432.061i | −0.226793 | − | 0.697998i | −0.998105 | − | 0.0615399i | \(-0.980399\pi\) |
0.771311 | − | 0.636458i | \(-0.219601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −763.676 | + | 554.843i | −1.22580 | + | 0.890598i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −551.180 | − | 294.662i | −0.881888 | − | 0.471459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −545.792 | − | 177.338i | −0.867713 | − | 0.281937i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 368.588 | + | 1134.40i | 0.584133 | + | 1.79778i | 0.602725 | + | 0.797949i | \(0.294081\pi\) |
−0.0185925 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −669.799 | − | 192.470i | −1.05480 | − | 0.303102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.6668 | − | 35.3273i | 0.0402932 | − | 0.0554588i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 559.013 | − | 769.415i | 0.872095 | − | 1.20034i | −0.106453 | − | 0.994318i | \(-0.533949\pi\) |
0.978548 | − | 0.206018i | \(-0.0660506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 983.678i | 1.52983i | 0.644134 | + | 0.764913i | \(0.277218\pi\) | ||||
−0.644134 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 283.311 | − | 871.942i | 0.437885 | − | 1.34767i | −0.452217 | − | 0.891908i | \(-0.649367\pi\) |
0.890102 | − | 0.455762i | \(-0.150633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1394.93 | −2.14936 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 74.2283 | − | 228.451i | 0.113673 | − | 0.349849i | −0.877995 | − | 0.478670i | \(-0.841119\pi\) |
0.991668 | + | 0.128821i | \(0.0411192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −256.993 | + | 380.546i | −0.392356 | + | 0.580986i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 419.142 | − | 576.900i | 0.636028 | − | 0.875417i | −0.362368 | − | 0.932035i | \(-0.618032\pi\) |
0.998396 | + | 0.0566182i | \(0.0180318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −142.102 | + | 103.243i | −0.214980 | + | 0.156192i | −0.690064 | − | 0.723748i | \(-0.742418\pi\) |
0.475084 | + | 0.879940i | \(0.342418\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −647.540 | + | 958.853i | −0.973745 | + | 1.44188i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −712.348 | + | 231.456i | −1.06799 | + | 0.347010i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1240.03 | + | 402.911i | 1.84803 | + | 0.600463i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −639.821 | − | 880.639i | −0.950700 | − | 1.30853i | −0.951216 | − | 0.308527i | \(-0.900164\pi\) |
0.000515262 | − | 1.00000i | \(-0.499836\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 967.184 | − | 702.700i | 1.42863 | − | 1.03796i | 0.438363 | − | 0.898798i | \(-0.355558\pi\) |
0.990269 | − | 0.139164i | \(-0.0444416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −341.092 | + | 1049.77i | −0.502344 | + | 1.54606i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −163.918 | − | 504.488i | −0.239997 | − | 0.738635i | −0.996419 | − | 0.0845514i | \(-0.973054\pi\) |
0.756422 | − | 0.654084i | \(-0.226946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.5793 | + | 1.15369i | −0.0490209 | + | 0.00168422i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −244.434 | − | 336.435i | −0.354767 | − | 0.488295i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 331.197 | + | 240.629i | 0.479301 | + | 0.348233i | 0.801055 | − | 0.598591i | \(-0.204272\pi\) |
−0.321754 | + | 0.946823i | \(0.604272\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −159.035 | + | 553.445i | −0.228827 | + | 0.796324i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1102.56 | + | 358.245i | 1.58187 | + | 0.513981i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 446.906i | − | 0.637527i | −0.947834 | − | 0.318763i | \(-0.896732\pi\) | ||
0.947834 | − | 0.318763i | \(-0.103268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −585.476 | − | 190.233i | −0.832826 | − | 0.270601i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −422.293 | −0.597302 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 426.777 | + | 310.072i | 0.601942 | + | 0.437337i | 0.846568 | − | 0.532281i | \(-0.178665\pi\) |
−0.244625 | + | 0.969618i | \(0.578665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.4784 | + | 38.1278i | 0.0736023 | + | 0.0534752i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 563.435 | − | 439.693i | 0.788020 | − | 0.614955i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 595.734 | − | 193.566i | 0.828558 | − | 0.269215i | 0.136120 | − | 0.990692i | \(-0.456537\pi\) |
0.692438 | + | 0.721477i | \(0.256537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −402.227 | + | 1237.93i | −0.557874 | + | 1.71696i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 612.522 | − | 977.788i | 0.844857 | − | 1.34867i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 108.843 | + | 149.809i | 0.149715 | + | 0.206065i | 0.877287 | − | 0.479966i | \(-0.159351\pi\) |
−0.727572 | + | 0.686032i | \(0.759351\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −257.723 | + | 83.7392i | −0.352562 | + | 0.114554i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 249.865 | − | 81.1861i | 0.340880 | − | 0.110759i | −0.133574 | − | 0.991039i | \(-0.542645\pi\) |
0.474454 | + | 0.880280i | \(0.342645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1673.95 | + | 1216.20i | 2.27130 | + | 1.65020i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 932.258 | − | 677.325i | 1.26151 | − | 0.916543i | 0.262683 | − | 0.964882i | \(-0.415393\pi\) |
0.998831 | + | 0.0483391i | \(0.0153928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 239.970 | 0.322974 | 0.161487 | − | 0.986875i | \(-0.448371\pi\) | ||||
0.161487 | + | 0.986875i | \(0.448371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −281.317 | − | 360.488i | −0.377607 | − | 0.483876i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 205.248i | − | 0.274029i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 526.348 | 0.700863 | 0.350432 | − | 0.936588i | \(-0.386035\pi\) | ||||
0.350432 | + | 0.936588i | \(0.386035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −327.262 | + | 255.389i | −0.433460 | + | 0.338263i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 643.956i | − | 0.850669i | −0.905036 | − | 0.425334i | \(-0.860157\pi\) | ||
0.905036 | − | 0.425334i | \(-0.139843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −260.104 | − | 358.003i | −0.341792 | − | 0.470437i | 0.603171 | − | 0.797612i | \(-0.293903\pi\) |
−0.944964 | + | 0.327175i | \(0.893903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 645.467 | − | 888.410i | 0.845960 | − | 1.16436i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 161.045 | + | 495.645i | 0.209967 | + | 0.646212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 154.778 | + | 476.357i | 0.201271 | + | 0.619450i | 0.999846 | + | 0.0175537i | \(0.00558780\pi\) |
−0.798575 | + | 0.601896i | \(0.794412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −92.1756 | + | 66.9695i | −0.119244 | + | 0.0866358i | −0.645809 | − | 0.763499i | \(-0.723480\pi\) |
0.526565 | + | 0.850135i | \(0.323480\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −99.6878 | + | 6.85808i | −0.128629 | + | 0.00884913i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1182.73 | + | 384.293i | 1.51827 | + | 0.493316i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −505.834 | − | 1556.80i | −0.647675 | − | 1.99334i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −324.798 | − | 416.205i | −0.413756 | − | 0.530198i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 739.560 | − | 1017.92i | 0.939720 | − | 1.29341i | −0.0162253 | − | 0.999868i | \(-0.505165\pi\) |
0.955945 | − | 0.293545i | \(-0.0948351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −407.206 | + | 560.470i | −0.514798 | + | 0.708559i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 487.121i | − | 0.614277i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −370.640 | + | 1140.71i | −0.465043 | + | 1.43126i | 0.393885 | + | 0.919160i | \(0.371131\pi\) |
−0.858928 | + | 0.512096i | \(0.828869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −577.897 | −0.723275 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 516.860 | − | 1590.73i | 0.643661 | − | 1.98099i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −578.258 | − | 166.165i | −0.718333 | − | 0.206416i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −234.795 | + | 323.168i | −0.290229 | + | 0.399466i | −0.929088 | − | 0.369858i | \(-0.879406\pi\) |
0.638860 | + | 0.769323i | \(0.279406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 585.320 | − | 425.260i | 0.721727 | − | 0.524365i | −0.165209 | − | 0.986259i | \(-0.552830\pi\) |
0.886935 | + | 0.461894i | \(0.152830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.4177 | + | 1263.72i | 0.0532733 | + | 1.55057i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −276.462 | + | 89.8279i | −0.338387 | + | 0.109948i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −893.252 | − | 290.235i | −1.08800 | − | 0.353514i | −0.290529 | − | 0.956866i | \(-0.593831\pi\) |
−0.797475 | + | 0.603352i | \(0.793831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −502.715 | − | 691.928i | −0.610832 | − | 0.840738i | 0.385813 | − | 0.922577i | \(-0.373921\pi\) |
−0.996646 | + | 0.0818385i | \(0.973921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 331.899 | − | 241.139i | 0.401329 | − | 0.291583i | −0.368753 | − | 0.929527i | \(-0.620215\pi\) |
0.770082 | + | 0.637945i | \(0.220215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −422.256 | + | 1299.57i | −0.509356 | + | 1.56764i | 0.283967 | + | 0.958834i | \(0.408349\pi\) |
−0.793323 | + | 0.608801i | \(0.791651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.7229 | − | 165.342i | −0.0644933 | − | 0.198490i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 922.566 | + | 623.034i | 1.10487 | + | 0.746149i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −239.913 | − | 330.212i | −0.285951 | − | 0.393578i | 0.641743 | − | 0.766920i | \(-0.278212\pi\) |
−0.927694 | + | 0.373342i | \(0.878212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1042.83 | + | 757.657i | 1.23998 | + | 0.900900i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 478.991 | + | 323.476i | 0.566854 | + | 0.382812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1844.68 | − | 599.372i | −2.17790 | − | 0.707641i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 320.118i | − | 0.376167i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1289.30 | − | 418.919i | −1.51149 | − | 0.491113i | −0.568145 | − | 0.822928i | \(-0.692339\pi\) |
−0.943344 | + | 0.331816i | \(0.892339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1412.12 | −1.64775 | −0.823876 | − | 0.566770i | \(-0.808193\pi\) | ||||
−0.823876 | + | 0.566770i | \(0.808193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9579 | + | 37.0231i | 0.0593223 | + | 0.0431002i | 0.617051 | − | 0.786923i | \(-0.288327\pi\) |
−0.557729 | + | 0.830023i | \(0.688327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 788.212 | + | 572.669i | 0.913339 | + | 0.663580i | 0.941857 | − | 0.336013i | \(-0.109079\pi\) |
−0.0285178 | + | 0.999593i | \(0.509079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −85.5676 | + | 297.777i | −0.0989221 | + | 0.344251i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1353.57 | + | 439.803i | −1.55762 | + | 0.506102i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 238.879 | − | 735.194i | 0.274258 | − | 0.844081i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 847.326 | − | 375.540i | 0.968372 | − | 0.429189i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 423.700 | + | 583.173i | 0.483125 | + | 0.664964i | 0.979102 | − | 0.203372i | \(-0.0651900\pi\) |
−0.495977 | + | 0.868336i | \(0.665190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −595.534 | + | 193.501i | −0.675975 | + | 0.219637i | −0.626832 | − | 0.779154i | \(-0.715649\pi\) |
−0.0491424 | + | 0.998792i | \(0.515649\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 217.128 | − | 70.5493i | 0.245899 | − | 0.0798973i | −0.183475 | − | 0.983024i | \(-0.558735\pi\) |
0.429373 | + | 0.903127i | \(0.358735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −552.382 | − | 401.329i | −0.622754 | − | 0.452457i | 0.231129 | − | 0.972923i | \(-0.425758\pi\) |
−0.853882 | + | 0.520466i | \(0.825758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 836.075 | − | 607.444i | 0.940467 | − | 0.683289i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −619.916 | −0.694195 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 102.291 | − | 37.1657i | 0.114292 | − | 0.0415260i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 184.467i | − | 0.205191i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1655.65 | −1.83757 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −88.5984 | − | 59.8329i | −0.0978987 | − | 0.0661137i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 359.601i | 0.396473i | 0.980154 | + | 0.198236i | \(0.0635214\pi\) | ||||
−0.980154 | + | 0.198236i | \(0.936479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −152.344 | − | 209.683i | −0.167227 | − | 0.230168i | 0.717176 | − | 0.696892i | \(-0.245434\pi\) |
−0.884403 | + | 0.466724i | \(0.845434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −560.932 | + | 772.057i | −0.614383 | + | 0.845626i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −210.424 | − | 647.617i | −0.229470 | − | 0.706235i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 222.003 | + | 683.256i | 0.241571 | + | 0.743478i | 0.996182 | + | 0.0873053i | \(0.0278256\pi\) |
−0.754611 | + | 0.656172i | \(0.772174\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −494.760 | + | 359.464i | −0.536034 | + | 0.389452i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 316.547 | + | 378.110i | 0.342213 | + | 0.408768i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 268.545 | + | 87.2554i | 0.289068 | + | 0.0939240i | 0.449962 | − | 0.893048i | \(-0.351438\pi\) |
−0.160893 | + | 0.986972i | \(0.551438\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.6292 | − | 177.364i | −0.0619003 | − | 0.190509i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −97.7027 | − | 2843.74i | −0.104495 | − | 3.04143i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 235.993 | − | 324.816i | 0.251860 | − | 0.346656i | −0.664302 | − | 0.747465i | \(-0.731271\pi\) |
0.916162 | + | 0.400809i | \(0.131271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −299.227 | + | 411.850i | −0.317988 | + | 0.437673i | −0.937852 | − | 0.347037i | \(-0.887188\pi\) |
0.619864 | + | 0.784710i | \(0.287188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 646.677i | 0.685766i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.77217 | − | 20.8426i | 0.00715118 | − | 0.0220091i | −0.947417 | − | 0.320001i | \(-0.896317\pi\) |
0.954568 | + | 0.297992i | \(0.0963168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −624.887 | −0.658469 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6943 | + | 63.6905i | −0.0217149 | + | 0.0668316i | −0.961327 | − | 0.275410i | \(-0.911186\pi\) |
0.939612 | + | 0.342242i | \(0.111186\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.4009 | + | 506.471i | 0.0182208 | + | 0.530336i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.2861 | − | 40.3089i | 0.0305382 | − | 0.0420322i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 764.541 | − | 555.471i | 0.795568 | − | 0.578014i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −924.785 | − | 1185.05i | −0.958327 | − | 1.22803i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −405.451 | + | 131.739i | −0.419287 | + | 0.136235i | −0.511059 | − | 0.859545i | \(-0.670747\pi\) |
0.0917723 | + | 0.995780i | \(0.470747\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −310.284 | − | 100.818i | −0.319551 | − | 0.103829i | 0.144849 | − | 0.989454i | \(-0.453730\pi\) |
−0.464401 | + | 0.885625i | \(0.653730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −501.922 | − | 690.836i | −0.515850 | − | 0.710006i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.2546 | + | 28.5201i | −0.0401787 | + | 0.0291915i | −0.607693 | − | 0.794172i | \(-0.707905\pi\) |
0.567515 | + | 0.823363i | \(0.307905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 769.518 | − | 2368.33i | 0.786025 | − | 2.41914i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.61928 | + | 14.2167i | 0.00469916 | + | 0.0144625i | 0.953379 | − | 0.301777i | \(-0.0975797\pi\) |
−0.948679 | + | 0.316239i | \(0.897580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −294.845 | − | 811.501i | −0.299335 | − | 0.823859i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −88.8495 | − | 122.291i | −0.0898377 | − | 0.123651i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −307.992 | − | 223.769i | −0.310789 | − | 0.225801i | 0.421446 | − | 0.906853i | \(-0.361523\pi\) |
−0.732235 | + | 0.681052i | \(0.761523\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1162.01 | + | 906.807i | −1.16785 | + | 0.911364i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1099.82 | + | 357.353i | 1.10313 | + | 0.358428i | 0.803306 | − | 0.595567i | \(-0.203073\pi\) |
0.299822 | + | 0.953995i | \(0.403073\pi\) | |||||||
\(998\) | 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 | 900.3.y.a.89.16 | yes | 80 | |
3.2 | odd | 2 | inner | 900.3.y.a.89.5 | ✓ | 80 | |
25.9 | even | 10 | inner | 900.3.y.a.809.5 | yes | 80 | |
75.59 | odd | 10 | inner | 900.3.y.a.809.16 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.y.a.89.5 | ✓ | 80 | 3.2 | odd | 2 | inner | |
900.3.y.a.89.16 | yes | 80 | 1.1 | even | 1 | trivial | |
900.3.y.a.809.5 | yes | 80 | 25.9 | even | 10 | inner | |
900.3.y.a.809.16 | yes | 80 | 75.59 | odd | 10 | inner |