Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(353,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.353");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.c (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: | \(20.8866761420\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 353.14 | ||
Character | \(\chi\) | \(=\) | 354.353 |
Dual form | 354.4.c.a.353.13 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −1.46648 | + | 4.98492i | −0.282225 | + | 0.959348i | ||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 18.9931i | 1.69879i | 0.527757 | + | 0.849395i | \(0.323033\pi\) | ||||
−0.527757 | + | 0.849395i | \(0.676967\pi\) | |||||||
\(6\) | 2.93296 | − | 9.96984i | 0.199563 | − | 0.678362i | ||||
\(7\) | −10.1890 | −0.550154 | −0.275077 | − | 0.961422i | \(-0.588703\pi\) | ||||
−0.275077 | + | 0.961422i | \(0.588703\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −22.6989 | − | 14.6206i | −0.840699 | − | 0.541503i | ||||
\(10\) | − | 37.9861i | − | 1.20123i | ||||||
\(11\) | −10.1714 | −0.278798 | −0.139399 | − | 0.990236i | \(-0.544517\pi\) | ||||
−0.139399 | + | 0.990236i | \(0.544517\pi\) | |||||||
\(12\) | −5.86593 | + | 19.9397i | −0.141112 | + | 0.479674i | ||||
\(13\) | − | 82.2827i | − | 1.75547i | −0.479146 | − | 0.877735i | \(-0.659054\pi\) | ||
0.479146 | − | 0.877735i | \(-0.340946\pi\) | |||||||
\(14\) | 20.3780 | 0.389018 | ||||||||
\(15\) | −94.6789 | − | 27.8530i | −1.62973 | − | 0.479441i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 92.4725i | − | 1.31929i | −0.751579 | − | 0.659644i | \(-0.770707\pi\) | ||
0.751579 | − | 0.659644i | \(-0.229293\pi\) | |||||||
\(18\) | 45.3977 | + | 29.2412i | 0.594464 | + | 0.382901i | ||||
\(19\) | 23.3309 | 0.281710 | 0.140855 | − | 0.990030i | \(-0.455015\pi\) | ||||
0.140855 | + | 0.990030i | \(0.455015\pi\) | |||||||
\(20\) | 75.9722i | 0.849395i | ||||||||
\(21\) | 14.9420 | − | 50.7914i | 0.155267 | − | 0.527790i | ||||
\(22\) | 20.3427 | 0.197140 | ||||||||
\(23\) | 39.6956 | 0.359874 | 0.179937 | − | 0.983678i | \(-0.442411\pi\) | ||||
0.179937 | + | 0.983678i | \(0.442411\pi\) | |||||||
\(24\) | 11.7319 | − | 39.8794i | 0.0997815 | − | 0.339181i | ||||
\(25\) | −235.736 | −1.88589 | ||||||||
\(26\) | 164.565i | 1.24131i | ||||||||
\(27\) | 106.170 | − | 91.7112i | 0.756756 | − | 0.653697i | ||||
\(28\) | −40.7560 | −0.275077 | ||||||||
\(29\) | 118.325i | 0.757672i | 0.925464 | + | 0.378836i | \(0.123675\pi\) | ||||
−0.925464 | + | 0.378836i | \(0.876325\pi\) | |||||||
\(30\) | 189.358 | + | 55.7060i | 1.15239 | + | 0.339016i | ||||
\(31\) | 30.7291i | 0.178036i | 0.996030 | + | 0.0890179i | \(0.0283728\pi\) | ||||
−0.996030 | + | 0.0890179i | \(0.971627\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 14.9161 | − | 50.7034i | 0.0786837 | − | 0.267465i | ||||
\(34\) | 184.945i | 0.932877i | ||||||||
\(35\) | − | 193.520i | − | 0.934597i | ||||||
\(36\) | −90.7954 | − | 58.4824i | −0.420349 | − | 0.270752i | ||||
\(37\) | 221.478i | 0.984073i | 0.870575 | + | 0.492036i | \(0.163747\pi\) | ||||
−0.870575 | + | 0.492036i | \(0.836253\pi\) | |||||||
\(38\) | −46.6619 | −0.199199 | ||||||||
\(39\) | 410.173 | + | 120.666i | 1.68411 | + | 0.495437i | ||||
\(40\) | − | 151.944i | − | 0.600613i | ||||||
\(41\) | − | 63.0445i | − | 0.240144i | −0.992765 | − | 0.120072i | \(-0.961687\pi\) | ||
0.992765 | − | 0.120072i | \(-0.0383125\pi\) | |||||||
\(42\) | −29.8840 | + | 101.583i | −0.109790 | + | 0.373204i | ||||
\(43\) | 147.338i | 0.522532i | 0.965267 | + | 0.261266i | \(0.0841400\pi\) | ||||
−0.965267 | + | 0.261266i | \(0.915860\pi\) | |||||||
\(44\) | −40.6854 | −0.139399 | ||||||||
\(45\) | 277.690 | − | 431.121i | 0.919901 | − | 1.42817i | ||||
\(46\) | −79.3912 | −0.254470 | ||||||||
\(47\) | −37.8072 | −0.117335 | −0.0586675 | − | 0.998278i | \(-0.518685\pi\) | ||||
−0.0586675 | + | 0.998278i | \(0.518685\pi\) | |||||||
\(48\) | −23.4637 | + | 79.7587i | −0.0705562 | + | 0.239837i | ||||
\(49\) | −239.184 | −0.697330 | ||||||||
\(50\) | 471.472 | 1.33353 | ||||||||
\(51\) | 460.968 | + | 135.609i | 1.26566 | + | 0.372335i | ||||
\(52\) | − | 329.131i | − | 0.877735i | ||||||
\(53\) | 409.038i | 1.06011i | 0.847964 | + | 0.530054i | \(0.177828\pi\) | ||||
−0.847964 | + | 0.530054i | \(0.822172\pi\) | |||||||
\(54\) | −212.340 | + | 183.422i | −0.535108 | + | 0.462234i | ||||
\(55\) | − | 193.185i | − | 0.473620i | ||||||
\(56\) | 81.5120 | 0.194509 | ||||||||
\(57\) | −34.2144 | + | 116.303i | −0.0795054 | + | 0.270258i | ||||
\(58\) | − | 236.651i | − | 0.535755i | ||||||
\(59\) | 170.128 | − | 420.042i | 0.375403 | − | 0.926862i | ||||
\(60\) | −378.715 | − | 111.412i | −0.814866 | − | 0.239720i | ||||
\(61\) | − | 709.628i | − | 1.48949i | −0.667352 | − | 0.744743i | \(-0.732572\pi\) | ||
0.667352 | − | 0.744743i | \(-0.267428\pi\) | |||||||
\(62\) | − | 61.4582i | − | 0.125890i | ||||||
\(63\) | 231.279 | + | 148.969i | 0.462514 | + | 0.297911i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 1562.80 | 2.98218 | ||||||||
\(66\) | −29.8322 | + | 101.407i | −0.0556378 | + | 0.189126i | ||||
\(67\) | − | 1044.75i | − | 1.90502i | −0.304513 | − | 0.952508i | \(-0.598494\pi\) | ||
0.304513 | − | 0.952508i | \(-0.401506\pi\) | |||||||
\(68\) | − | 369.890i | − | 0.659644i | ||||||
\(69\) | −58.2129 | + | 197.880i | −0.101565 | + | 0.345245i | ||||
\(70\) | 387.041i | 0.660860i | ||||||||
\(71\) | 361.984i | 0.605064i | 0.953139 | + | 0.302532i | \(0.0978319\pi\) | ||||
−0.953139 | + | 0.302532i | \(0.902168\pi\) | |||||||
\(72\) | 181.591 | + | 116.965i | 0.297232 | + | 0.191450i | ||||
\(73\) | − | 327.686i | − | 0.525380i | −0.964880 | − | 0.262690i | \(-0.915390\pi\) | ||
0.964880 | − | 0.262690i | \(-0.0846097\pi\) | |||||||
\(74\) | − | 442.955i | − | 0.695844i | ||||||
\(75\) | 345.703 | − | 1175.13i | 0.532244 | − | 1.80922i | ||||
\(76\) | 93.3238 | 0.140855 | ||||||||
\(77\) | 103.636 | 0.153382 | ||||||||
\(78\) | −820.345 | − | 241.332i | −1.19084 | − | 0.350327i | ||||
\(79\) | −238.712 | −0.339964 | −0.169982 | − | 0.985447i | \(-0.554371\pi\) | ||||
−0.169982 | + | 0.985447i | \(0.554371\pi\) | |||||||
\(80\) | 303.889i | 0.424698i | ||||||||
\(81\) | 301.476 | + | 663.742i | 0.413548 | + | 0.910482i | ||||
\(82\) | 126.089i | 0.169807i | ||||||||
\(83\) | −156.436 | −0.206880 | −0.103440 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103440 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(84\) | 59.7680 | − | 203.165i | 0.0776336 | − | 0.263895i | ||||
\(85\) | 1756.34 | 2.24119 | ||||||||
\(86\) | − | 294.677i | − | 0.369486i | ||||||
\(87\) | −589.843 | − | 173.522i | −0.726871 | − | 0.213834i | ||||
\(88\) | 81.3709 | 0.0985701 | ||||||||
\(89\) | −1097.96 | −1.30768 | −0.653838 | − | 0.756634i | \(-0.726842\pi\) | ||||
−0.653838 | + | 0.756634i | \(0.726842\pi\) | |||||||
\(90\) | −555.379 | + | 862.241i | −0.650468 | + | 1.00987i | ||||
\(91\) | 838.379i | 0.965780i | ||||||||
\(92\) | 158.782 | 0.179937 | ||||||||
\(93\) | −153.182 | − | 45.0637i | −0.170798 | − | 0.0502461i | ||||
\(94\) | 75.6143 | 0.0829683 | ||||||||
\(95\) | 443.126i | 0.478566i | ||||||||
\(96\) | 46.9274 | − | 159.517i | 0.0498907 | − | 0.169590i | ||||
\(97\) | 1334.04i | 1.39640i | 0.715902 | + | 0.698201i | \(0.246016\pi\) | ||||
−0.715902 | + | 0.698201i | \(0.753984\pi\) | |||||||
\(98\) | 478.368 | 0.493087 | ||||||||
\(99\) | 230.878 | + | 148.711i | 0.234385 | + | 0.150970i | ||||
\(100\) | −942.945 | −0.942945 | ||||||||
\(101\) | 807.886 | 0.795917 | 0.397958 | − | 0.917403i | \(-0.369719\pi\) | ||||
0.397958 | + | 0.917403i | \(0.369719\pi\) | |||||||
\(102\) | −921.936 | − | 271.219i | −0.894954 | − | 0.263281i | ||||
\(103\) | − | 1915.68i | − | 1.83260i | −0.400492 | − | 0.916300i | \(-0.631161\pi\) | ||
0.400492 | − | 0.916300i | \(-0.368839\pi\) | |||||||
\(104\) | 658.262i | 0.620653i | ||||||||
\(105\) | 964.683 | + | 283.794i | 0.896604 | + | 0.263766i | ||||
\(106\) | − | 818.076i | − | 0.749609i | ||||||
\(107\) | − | 1003.68i | − | 0.906815i | −0.891303 | − | 0.453407i | \(-0.850208\pi\) | ||
0.891303 | − | 0.453407i | \(-0.149792\pi\) | |||||||
\(108\) | 424.680 | − | 366.845i | 0.378378 | − | 0.326849i | ||||
\(109\) | − | 1972.94i | − | 1.73370i | −0.498567 | − | 0.866851i | \(-0.666140\pi\) | ||
0.498567 | − | 0.866851i | \(-0.333860\pi\) | |||||||
\(110\) | 386.370i | 0.334900i | ||||||||
\(111\) | −1104.05 | − | 324.793i | −0.944069 | − | 0.277730i | ||||
\(112\) | −163.024 | −0.137539 | ||||||||
\(113\) | 524.671 | 0.436787 | 0.218393 | − | 0.975861i | \(-0.429918\pi\) | ||||
0.218393 | + | 0.975861i | \(0.429918\pi\) | |||||||
\(114\) | 68.4288 | − | 232.606i | 0.0562188 | − | 0.191101i | ||||
\(115\) | 753.941i | 0.611351i | ||||||||
\(116\) | 473.302i | 0.378836i | ||||||||
\(117\) | −1203.02 | + | 1867.72i | −0.950593 | + | 1.47582i | ||||
\(118\) | −340.256 | + | 840.084i | −0.265450 | + | 0.655390i | ||||
\(119\) | 942.203i | 0.725812i | ||||||||
\(120\) | 757.431 | + | 222.824i | 0.576197 | + | 0.169508i | ||||
\(121\) | −1227.54 | −0.922272 | ||||||||
\(122\) | 1419.26i | 1.05322i | ||||||||
\(123\) | 314.272 | + | 92.4537i | 0.230382 | + | 0.0677745i | ||||
\(124\) | 122.916i | 0.0890179i | ||||||||
\(125\) | − | 2103.22i | − | 1.50494i | ||||||
\(126\) | −462.558 | − | 297.939i | −0.327047 | − | 0.210655i | ||||
\(127\) | 1399.78 | 0.978037 | 0.489018 | − | 0.872273i | \(-0.337355\pi\) | ||||
0.489018 | + | 0.872273i | \(0.337355\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −734.470 | − | 216.069i | −0.501291 | − | 0.147472i | ||||
\(130\) | −3125.60 | −2.10872 | ||||||||
\(131\) | −2065.19 | −1.37738 | −0.688689 | − | 0.725057i | \(-0.741813\pi\) | ||||
−0.688689 | + | 0.725057i | \(0.741813\pi\) | |||||||
\(132\) | 59.6645 | − | 202.814i | 0.0393419 | − | 0.133732i | ||||
\(133\) | −237.719 | −0.154984 | ||||||||
\(134\) | 2089.49i | 1.34705i | ||||||||
\(135\) | 1741.88 | + | 2016.49i | 1.11049 | + | 1.28557i | ||||
\(136\) | 739.780i | 0.466438i | ||||||||
\(137\) | − | 438.983i | − | 0.273758i | −0.990588 | − | 0.136879i | \(-0.956293\pi\) | ||
0.990588 | − | 0.136879i | \(-0.0437071\pi\) | |||||||
\(138\) | 116.426 | − | 395.759i | 0.0718176 | − | 0.244125i | ||||
\(139\) | 2717.07 | 1.65798 | 0.828989 | − | 0.559266i | \(-0.188917\pi\) | ||||
0.828989 | + | 0.559266i | \(0.188917\pi\) | |||||||
\(140\) | − | 774.081i | − | 0.467299i | ||||||
\(141\) | 55.4435 | − | 188.466i | 0.0331148 | − | 0.112565i | ||||
\(142\) | − | 723.967i | − | 0.427845i | ||||||
\(143\) | 836.927i | 0.489422i | ||||||||
\(144\) | −363.182 | − | 233.929i | −0.210175 | − | 0.135376i | ||||
\(145\) | −2247.36 | −1.28713 | ||||||||
\(146\) | 655.372i | 0.371500i | ||||||||
\(147\) | 350.759 | − | 1192.31i | 0.196804 | − | 0.668982i | ||||
\(148\) | 885.910i | 0.492036i | ||||||||
\(149\) | −2675.78 | −1.47120 | −0.735600 | − | 0.677417i | \(-0.763099\pi\) | ||||
−0.735600 | + | 0.677417i | \(0.763099\pi\) | |||||||
\(150\) | −691.406 | + | 2350.25i | −0.376354 | + | 1.27932i | ||||
\(151\) | − | 2596.05i | − | 1.39910i | −0.714585 | − | 0.699548i | \(-0.753385\pi\) | ||
0.714585 | − | 0.699548i | \(-0.246615\pi\) | |||||||
\(152\) | −186.648 | −0.0995995 | ||||||||
\(153\) | −1352.00 | + | 2099.02i | −0.714399 | + | 1.10912i | ||||
\(154\) | −207.272 | −0.108458 | ||||||||
\(155\) | −583.639 | −0.302445 | ||||||||
\(156\) | 1640.69 | + | 482.664i | 0.842054 | + | 0.247719i | ||||
\(157\) | 1973.10i | 1.00300i | 0.865158 | + | 0.501499i | \(0.167218\pi\) | ||||
−0.865158 | + | 0.501499i | \(0.832782\pi\) | |||||||
\(158\) | 477.423 | 0.240391 | ||||||||
\(159\) | −2039.02 | − | 599.847i | −1.01701 | − | 0.299189i | ||||
\(160\) | − | 607.778i | − | 0.300307i | ||||||
\(161\) | −404.459 | −0.197986 | ||||||||
\(162\) | −602.953 | − | 1327.48i | −0.292423 | − | 0.643808i | ||||
\(163\) | 1338.42 | 0.643150 | 0.321575 | − | 0.946884i | \(-0.395788\pi\) | ||||
0.321575 | + | 0.946884i | \(0.395788\pi\) | |||||||
\(164\) | − | 252.178i | − | 0.120072i | ||||||
\(165\) | 963.013 | + | 283.303i | 0.454366 | + | 0.133667i | ||||
\(166\) | 312.872 | 0.146286 | ||||||||
\(167\) | 916.784i | 0.424808i | 0.977182 | + | 0.212404i | \(0.0681292\pi\) | ||||
−0.977182 | + | 0.212404i | \(0.931871\pi\) | |||||||
\(168\) | −119.536 | + | 406.331i | −0.0548952 | + | 0.186602i | ||||
\(169\) | −4573.44 | −2.08168 | ||||||||
\(170\) | −3512.67 | −1.58476 | ||||||||
\(171\) | −529.586 | − | 341.112i | −0.236833 | − | 0.152547i | ||||
\(172\) | 589.354i | 0.261266i | ||||||||
\(173\) | 1781.69 | 0.783004 | 0.391502 | − | 0.920177i | \(-0.371956\pi\) | ||||
0.391502 | + | 0.920177i | \(0.371956\pi\) | |||||||
\(174\) | 1179.69 | + | 347.044i | 0.513975 | + | 0.151203i | ||||
\(175\) | 2401.92 | 1.03753 | ||||||||
\(176\) | −162.742 | −0.0696996 | ||||||||
\(177\) | 1844.39 | + | 1464.06i | 0.783235 | + | 0.621725i | ||||
\(178\) | 2195.91 | 0.924667 | ||||||||
\(179\) | −870.852 | −0.363634 | −0.181817 | − | 0.983332i | \(-0.558198\pi\) | ||||
−0.181817 | + | 0.983332i | \(0.558198\pi\) | |||||||
\(180\) | 1110.76 | − | 1724.48i | 0.459950 | − | 0.714085i | ||||
\(181\) | −3247.54 | −1.33364 | −0.666818 | − | 0.745221i | \(-0.732344\pi\) | ||||
−0.666818 | + | 0.745221i | \(0.732344\pi\) | |||||||
\(182\) | − | 1676.76i | − | 0.682910i | ||||||
\(183\) | 3537.44 | + | 1040.66i | 1.42894 | + | 0.420369i | ||||
\(184\) | −317.565 | −0.127235 | ||||||||
\(185\) | −4206.54 | −1.67173 | ||||||||
\(186\) | 306.364 | + | 90.1273i | 0.120773 | + | 0.0355293i | ||||
\(187\) | 940.572i | 0.367815i | ||||||||
\(188\) | −151.229 | −0.0586675 | ||||||||
\(189\) | −1081.77 | + | 934.445i | −0.416333 | + | 0.359634i | ||||
\(190\) | − | 886.252i | − | 0.338397i | ||||||
\(191\) | 1580.55 | 0.598766 | 0.299383 | − | 0.954133i | \(-0.403219\pi\) | ||||
0.299383 | + | 0.954133i | \(0.403219\pi\) | |||||||
\(192\) | −93.8549 | + | 319.035i | −0.0352781 | + | 0.119919i | ||||
\(193\) | 1657.33 | 0.618120 | 0.309060 | − | 0.951043i | \(-0.399986\pi\) | ||||
0.309060 | + | 0.951043i | \(0.399986\pi\) | |||||||
\(194\) | − | 2668.08i | − | 0.987405i | ||||||
\(195\) | −2291.82 | + | 7790.43i | −0.841644 | + | 2.86095i | ||||
\(196\) | −956.737 | −0.348665 | ||||||||
\(197\) | − | 1740.87i | − | 0.629602i | −0.949158 | − | 0.314801i | \(-0.898062\pi\) | ||
0.949158 | − | 0.314801i | \(-0.101938\pi\) | |||||||
\(198\) | −461.757 | − | 297.423i | −0.165735 | − | 0.106752i | ||||
\(199\) | 614.923 | 0.219049 | 0.109524 | − | 0.993984i | \(-0.465067\pi\) | ||||
0.109524 | + | 0.993984i | \(0.465067\pi\) | |||||||
\(200\) | 1885.89 | 0.666763 | ||||||||
\(201\) | 5207.98 | + | 1532.10i | 1.82757 | + | 0.537643i | ||||
\(202\) | −1615.77 | −0.562798 | ||||||||
\(203\) | − | 1205.62i | − | 0.416836i | ||||||
\(204\) | 1843.87 | + | 542.437i | 0.632828 | + | 0.186168i | ||||
\(205\) | 1197.41 | 0.407954 | ||||||||
\(206\) | 3831.37i | 1.29584i | ||||||||
\(207\) | −901.045 | − | 580.374i | −0.302546 | − | 0.194873i | ||||
\(208\) | − | 1316.52i | − | 0.438868i | ||||||
\(209\) | −237.308 | −0.0785402 | ||||||||
\(210\) | −1929.37 | − | 567.588i | −0.633995 | − | 0.186511i | ||||
\(211\) | − | 3523.30i | − | 1.14954i | −0.818313 | − | 0.574772i | \(-0.805091\pi\) | ||
0.818313 | − | 0.574772i | \(-0.194909\pi\) | |||||||
\(212\) | 1636.15i | 0.530054i | ||||||||
\(213\) | −1804.46 | − | 530.842i | −0.580467 | − | 0.170764i | ||||
\(214\) | 2007.36i | 0.641215i | ||||||||
\(215\) | −2798.41 | −0.887673 | ||||||||
\(216\) | −849.360 | + | 733.689i | −0.267554 | + | 0.231117i | ||||
\(217\) | − | 313.099i | − | 0.0979471i | ||||||
\(218\) | 3945.88i | 1.22591i | ||||||||
\(219\) | 1633.49 | + | 480.546i | 0.504022 | + | 0.148275i | ||||
\(220\) | − | 772.741i | − | 0.236810i | ||||||
\(221\) | −7608.89 | −2.31597 | ||||||||
\(222\) | 2208.10 | + | 649.586i | 0.667557 | + | 0.196384i | ||||
\(223\) | 4805.24 | 1.44297 | 0.721485 | − | 0.692430i | \(-0.243460\pi\) | ||||
0.721485 | + | 0.692430i | \(0.243460\pi\) | |||||||
\(224\) | 326.048 | 0.0972545 | ||||||||
\(225\) | 5350.94 | + | 3446.60i | 1.58546 | + | 1.02122i | ||||
\(226\) | −1049.34 | −0.308855 | ||||||||
\(227\) | 4618.27 | 1.35033 | 0.675166 | − | 0.737665i | \(-0.264072\pi\) | ||||
0.675166 | + | 0.737665i | \(0.264072\pi\) | |||||||
\(228\) | −136.858 | + | 465.212i | −0.0397527 | + | 0.135129i | ||||
\(229\) | − | 3653.07i | − | 1.05415i | −0.849817 | − | 0.527077i | \(-0.823288\pi\) | ||
0.849817 | − | 0.527077i | \(-0.176712\pi\) | |||||||
\(230\) | − | 1507.88i | − | 0.432291i | ||||||
\(231\) | −151.980 | + | 516.617i | −0.0432882 | + | 0.147147i | ||||
\(232\) | − | 946.603i | − | 0.267877i | ||||||
\(233\) | 1303.90 | 0.366615 | 0.183307 | − | 0.983056i | \(-0.441320\pi\) | ||||
0.183307 | + | 0.983056i | \(0.441320\pi\) | |||||||
\(234\) | 2406.04 | − | 3735.45i | 0.672171 | − | 1.04356i | ||||
\(235\) | − | 718.074i | − | 0.199327i | ||||||
\(236\) | 680.512 | − | 1680.17i | 0.187702 | − | 0.463431i | ||||
\(237\) | 350.066 | − | 1189.96i | 0.0959462 | − | 0.326144i | ||||
\(238\) | − | 1884.41i | − | 0.513226i | ||||||
\(239\) | 6935.79i | 1.87715i | 0.345073 | + | 0.938576i | \(0.387854\pi\) | ||||
−0.345073 | + | 0.938576i | \(0.612146\pi\) | |||||||
\(240\) | −1514.86 | − | 445.648i | −0.407433 | − | 0.119860i | ||||
\(241\) | 974.319 | 0.260421 | 0.130210 | − | 0.991486i | \(-0.458435\pi\) | ||||
0.130210 | + | 0.991486i | \(0.458435\pi\) | |||||||
\(242\) | 2455.09 | 0.652144 | ||||||||
\(243\) | −3750.81 | + | 529.471i | −0.990183 | + | 0.139776i | ||||
\(244\) | − | 2838.51i | − | 0.744743i | ||||||
\(245\) | − | 4542.84i | − | 1.18462i | ||||||
\(246\) | −628.544 | − | 184.907i | −0.162904 | − | 0.0479238i | ||||
\(247\) | − | 1919.73i | − | 0.494533i | ||||||
\(248\) | − | 245.833i | − | 0.0629451i | ||||||
\(249\) | 229.410 | − | 779.820i | 0.0583867 | − | 0.198470i | ||||
\(250\) | 4206.44i | 1.06415i | ||||||||
\(251\) | − | 2287.55i | − | 0.575254i | −0.957742 | − | 0.287627i | \(-0.907134\pi\) | ||
0.957742 | − | 0.287627i | \(-0.0928664\pi\) | |||||||
\(252\) | 925.115 | + | 595.877i | 0.231257 | + | 0.148955i | ||||
\(253\) | −403.759 | −0.100332 | ||||||||
\(254\) | −2799.57 | −0.691577 | ||||||||
\(255\) | −2575.64 | + | 8755.19i | −0.632520 | + | 2.15008i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 6990.89i | − | 1.69681i | −0.529349 | − | 0.848404i | \(-0.677564\pi\) | ||
0.529349 | − | 0.848404i | \(-0.322436\pi\) | |||||||
\(258\) | 1468.94 | + | 432.138i | 0.354466 | + | 0.104278i | ||||
\(259\) | − | 2256.64i | − | 0.541392i | ||||||
\(260\) | 6251.20 | 1.49109 | ||||||||
\(261\) | 1729.99 | − | 2685.85i | 0.410282 | − | 0.636973i | ||||
\(262\) | 4130.38 | 0.973953 | ||||||||
\(263\) | − | 2946.13i | − | 0.690747i | −0.938465 | − | 0.345373i | \(-0.887752\pi\) | ||
0.938465 | − | 0.345373i | \(-0.112248\pi\) | |||||||
\(264\) | −119.329 | + | 405.627i | −0.0278189 | + | 0.0945630i | ||||
\(265\) | −7768.89 | −1.80090 | ||||||||
\(266\) | 475.438 | 0.109590 | ||||||||
\(267\) | 1610.13 | − | 5473.23i | 0.369059 | − | 1.25452i | ||||
\(268\) | − | 4178.99i | − | 0.952508i | ||||||
\(269\) | −1274.53 | −0.288882 | −0.144441 | − | 0.989513i | \(-0.546138\pi\) | ||||
−0.144441 | + | 0.989513i | \(0.546138\pi\) | |||||||
\(270\) | −3483.75 | − | 4032.98i | −0.785238 | − | 0.909036i | ||||
\(271\) | −4929.25 | −1.10491 | −0.552455 | − | 0.833543i | \(-0.686309\pi\) | ||||
−0.552455 | + | 0.833543i | \(0.686309\pi\) | |||||||
\(272\) | − | 1479.56i | − | 0.329822i | ||||||
\(273\) | −4179.25 | − | 1229.47i | −0.926519 | − | 0.272567i | ||||
\(274\) | 877.966i | 0.193576i | ||||||||
\(275\) | 2397.76 | 0.525783 | ||||||||
\(276\) | −232.852 | + | 791.518i | −0.0507827 | + | 0.172622i | ||||
\(277\) | −6811.99 | −1.47759 | −0.738796 | − | 0.673929i | \(-0.764605\pi\) | ||||
−0.738796 | + | 0.673929i | \(0.764605\pi\) | |||||||
\(278\) | −5434.14 | −1.17237 | ||||||||
\(279\) | 449.278 | − | 697.515i | 0.0964070 | − | 0.149674i | ||||
\(280\) | 1548.16i | 0.330430i | ||||||||
\(281\) | − | 4763.12i | − | 1.01119i | −0.862771 | − | 0.505594i | \(-0.831273\pi\) | ||
0.862771 | − | 0.505594i | \(-0.168727\pi\) | |||||||
\(282\) | −110.887 | + | 376.931i | −0.0234157 | + | 0.0795955i | ||||
\(283\) | − | 6042.10i | − | 1.26914i | −0.772867 | − | 0.634568i | \(-0.781178\pi\) | ||
0.772867 | − | 0.634568i | \(-0.218822\pi\) | |||||||
\(284\) | 1447.93i | 0.302532i | ||||||||
\(285\) | −2208.95 | − | 649.836i | −0.459111 | − | 0.135063i | ||||
\(286\) | − | 1673.85i | − | 0.346074i | ||||||
\(287\) | 642.361i | 0.132116i | ||||||||
\(288\) | 726.364 | + | 467.859i | 0.148616 | + | 0.0957252i | ||||
\(289\) | −3638.17 | −0.740519 | ||||||||
\(290\) | 4494.72 | 0.910135 | ||||||||
\(291\) | −6650.07 | − | 1956.34i | −1.33964 | − | 0.394099i | ||||
\(292\) | − | 1310.74i | − | 0.262690i | ||||||
\(293\) | 1472.96i | 0.293691i | 0.989159 | + | 0.146845i | \(0.0469120\pi\) | ||||
−0.989159 | + | 0.146845i | \(0.953088\pi\) | |||||||
\(294\) | −701.519 | + | 2384.63i | −0.139161 | + | 0.473042i | ||||
\(295\) | 7977.89 | + | 3231.25i | 1.57454 | + | 0.637731i | ||||
\(296\) | − | 1771.82i | − | 0.347922i | ||||||
\(297\) | −1079.89 | + | 932.827i | −0.210982 | + | 0.182250i | ||||
\(298\) | 5351.57 | 1.04029 | ||||||||
\(299\) | − | 3266.26i | − | 0.631749i | ||||||
\(300\) | 1382.81 | − | 4700.50i | 0.266122 | − | 0.904612i | ||||
\(301\) | − | 1501.23i | − | 0.287474i | ||||||
\(302\) | 5192.10i | 0.989311i | ||||||||
\(303\) | −1184.75 | + | 4027.24i | −0.224627 | + | 0.763562i | ||||
\(304\) | 373.295 | 0.0704275 | ||||||||
\(305\) | 13478.0 | 2.53032 | ||||||||
\(306\) | 2704.01 | − | 4198.04i | 0.505156 | − | 0.784268i | ||||
\(307\) | 2075.53 | 0.385852 | 0.192926 | − | 0.981213i | \(-0.438202\pi\) | ||||
0.192926 | + | 0.981213i | \(0.438202\pi\) | |||||||
\(308\) | 414.544 | 0.0766911 | ||||||||
\(309\) | 9549.53 | + | 2809.31i | 1.75810 | + | 0.517205i | ||||
\(310\) | 1167.28 | 0.213861 | ||||||||
\(311\) | − | 5120.23i | − | 0.933575i | −0.884370 | − | 0.466787i | \(-0.845411\pi\) | ||
0.884370 | − | 0.466787i | \(-0.154589\pi\) | |||||||
\(312\) | −3281.38 | − | 965.329i | −0.595422 | − | 0.175163i | ||||
\(313\) | − | 4181.55i | − | 0.755128i | −0.925984 | − | 0.377564i | \(-0.876762\pi\) | ||
0.925984 | − | 0.377564i | \(-0.123238\pi\) | |||||||
\(314\) | − | 3946.21i | − | 0.709227i | ||||||
\(315\) | −2829.38 | + | 4392.69i | −0.506088 | + | 0.785714i | ||||
\(316\) | −954.846 | −0.169982 | ||||||||
\(317\) | 5414.77i | 0.959380i | 0.877438 | + | 0.479690i | \(0.159251\pi\) | ||||
−0.877438 | + | 0.479690i | \(0.840749\pi\) | |||||||
\(318\) | 4078.05 | + | 1199.69i | 0.719137 | + | 0.211558i | ||||
\(319\) | − | 1203.53i | − | 0.211238i | ||||||
\(320\) | 1215.56i | 0.212349i | ||||||||
\(321\) | 5003.25 | + | 1471.88i | 0.869951 | + | 0.255925i | ||||
\(322\) | 808.918 | 0.139998 | ||||||||
\(323\) | − | 2157.47i | − | 0.371656i | ||||||
\(324\) | 1205.91 | + | 2654.97i | 0.206774 | + | 0.455241i | ||||
\(325\) | 19397.0i | 3.31062i | ||||||||
\(326\) | −2676.85 | −0.454776 | ||||||||
\(327\) | 9834.96 | + | 2893.28i | 1.66322 | + | 0.489293i | ||||
\(328\) | 504.356i | 0.0849037i | ||||||||
\(329\) | 385.217 | 0.0645523 | ||||||||
\(330\) | −1926.03 | − | 566.605i | −0.321286 | − | 0.0945170i | ||||
\(331\) | 1106.67 | 0.183770 | 0.0918852 | − | 0.995770i | \(-0.470711\pi\) | ||||
0.0918852 | + | 0.995770i | \(0.470711\pi\) | |||||||
\(332\) | −625.743 | −0.103440 | ||||||||
\(333\) | 3238.13 | − | 5027.29i | 0.532879 | − | 0.827308i | ||||
\(334\) | − | 1833.57i | − | 0.300384i | ||||||
\(335\) | 19842.9 | 3.23622 | ||||||||
\(336\) | 239.072 | − | 812.662i | 0.0388168 | − | 0.131947i | ||||
\(337\) | 8283.09i | 1.33890i | 0.742858 | + | 0.669449i | \(0.233470\pi\) | ||||
−0.742858 | + | 0.669449i | \(0.766530\pi\) | |||||||
\(338\) | 9146.89 | 1.47197 | ||||||||
\(339\) | −769.421 | + | 2615.44i | −0.123272 | + | 0.419031i | ||||
\(340\) | 7025.34 | 1.12060 | ||||||||
\(341\) | − | 312.557i | − | 0.0496360i | ||||||
\(342\) | 1059.17 | + | 682.225i | 0.167466 | + | 0.107867i | ||||
\(343\) | 5931.88 | 0.933794 | ||||||||
\(344\) | − | 1178.71i | − | 0.184743i | ||||||
\(345\) | −3758.34 | − | 1105.64i | −0.586499 | − | 0.172538i | ||||
\(346\) | −3563.39 | −0.553668 | ||||||||
\(347\) | −3871.50 | −0.598943 | −0.299471 | − | 0.954105i | \(-0.596810\pi\) | ||||
−0.299471 | + | 0.954105i | \(0.596810\pi\) | |||||||
\(348\) | −2359.37 | − | 694.088i | −0.363435 | − | 0.106917i | ||||
\(349\) | 10305.7i | 1.58067i | 0.612678 | + | 0.790333i | \(0.290092\pi\) | ||||
−0.612678 | + | 0.790333i | \(0.709908\pi\) | |||||||
\(350\) | −4803.83 | −0.733645 | ||||||||
\(351\) | −7546.24 | − | 8735.95i | −1.14755 | − | 1.32846i | ||||
\(352\) | 325.484 | 0.0492850 | ||||||||
\(353\) | −5062.97 | −0.763385 | −0.381692 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381692 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(354\) | −3688.77 | − | 2928.12i | −0.553831 | − | 0.439626i | ||||
\(355\) | −6875.17 | −1.02788 | ||||||||
\(356\) | −4391.83 | −0.653838 | ||||||||
\(357\) | −4696.81 | − | 1381.72i | −0.696306 | − | 0.204842i | ||||
\(358\) | 1741.70 | 0.257128 | ||||||||
\(359\) | 7093.69i | 1.04287i | 0.853291 | + | 0.521435i | \(0.174603\pi\) | ||||
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(360\) | −2221.52 | + | 3448.97i | −0.325234 | + | 0.504935i | ||||
\(361\) | −6314.67 | −0.920640 | ||||||||
\(362\) | 6495.09 | 0.943022 | ||||||||
\(363\) | 1800.17 | − | 6119.21i | 0.260288 | − | 0.884780i | ||||
\(364\) | 3353.52i | 0.482890i | ||||||||
\(365\) | 6223.76 | 0.892511 | ||||||||
\(366\) | −7074.88 | − | 2081.31i | −1.01041 | − | 0.297246i | ||||
\(367\) | 7928.64i | 1.12772i | 0.825872 | + | 0.563858i | \(0.190683\pi\) | ||||
−0.825872 | + | 0.563858i | \(0.809317\pi\) | |||||||
\(368\) | 635.130 | 0.0899686 | ||||||||
\(369\) | −921.749 | + | 1431.04i | −0.130039 | + | 0.201889i | ||||
\(370\) | 8413.07 | 1.18209 | ||||||||
\(371\) | − | 4167.69i | − | 0.583223i | ||||||
\(372\) | −612.728 | − | 180.255i | −0.0853991 | − | 0.0251230i | ||||
\(373\) | −8719.31 | −1.21037 | −0.605186 | − | 0.796084i | \(-0.706901\pi\) | ||||
−0.605186 | + | 0.796084i | \(0.706901\pi\) | |||||||
\(374\) | − | 1881.14i | − | 0.260084i | ||||||
\(375\) | 10484.4 | + | 3084.33i | 1.44376 | + | 0.424731i | ||||
\(376\) | 302.457 | 0.0414842 | ||||||||
\(377\) | 9736.13 | 1.33007 | ||||||||
\(378\) | 2163.53 | − | 1868.89i | 0.294392 | − | 0.254300i | ||||
\(379\) | −789.446 | −0.106995 | −0.0534975 | − | 0.998568i | \(-0.517037\pi\) | ||||
−0.0534975 | + | 0.998568i | \(0.517037\pi\) | |||||||
\(380\) | 1772.50i | 0.239283i | ||||||||
\(381\) | −2052.76 | + | 6977.81i | −0.276026 | + | 0.938278i | ||||
\(382\) | −3161.09 | −0.423392 | ||||||||
\(383\) | − | 4907.40i | − | 0.654717i | −0.944900 | − | 0.327359i | \(-0.893842\pi\) | ||
0.944900 | − | 0.327359i | \(-0.106158\pi\) | |||||||
\(384\) | 187.710 | − | 638.070i | 0.0249454 | − | 0.0847952i | ||||
\(385\) | 1968.37i | 0.260564i | ||||||||
\(386\) | −3314.66 | −0.437077 | ||||||||
\(387\) | 2154.17 | − | 3344.41i | 0.282953 | − | 0.439292i | ||||
\(388\) | 5336.15i | 0.698201i | ||||||||
\(389\) | 2497.38i | 0.325507i | 0.986667 | + | 0.162754i | \(0.0520376\pi\) | ||||
−0.986667 | + | 0.162754i | \(0.947962\pi\) | |||||||
\(390\) | 4583.64 | − | 15580.9i | 0.595132 | − | 2.02299i | ||||
\(391\) | − | 3670.75i | − | 0.474778i | ||||||
\(392\) | 1913.47 | 0.246543 | ||||||||
\(393\) | 3028.56 | − | 10294.8i | 0.388730 | − | 1.32139i | ||||
\(394\) | 3481.73i | 0.445196i | ||||||||
\(395\) | − | 4533.86i | − | 0.577527i | ||||||
\(396\) | 923.513 | + | 594.845i | 0.117193 | + | 0.0754851i | ||||
\(397\) | − | 6068.25i | − | 0.767145i | −0.923511 | − | 0.383573i | \(-0.874694\pi\) | ||
0.923511 | − | 0.383573i | \(-0.125306\pi\) | |||||||
\(398\) | −1229.85 | −0.154891 | ||||||||
\(399\) | 348.611 | − | 1185.01i | 0.0437403 | − | 0.148684i | ||||
\(400\) | −3771.78 | −0.471472 | ||||||||
\(401\) | −9709.46 | −1.20915 | −0.604573 | − | 0.796550i | \(-0.706656\pi\) | ||||
−0.604573 | + | 0.796550i | \(0.706656\pi\) | |||||||
\(402\) | −10416.0 | − | 3064.20i | −1.29229 | − | 0.380171i | ||||
\(403\) | 2528.47 | 0.312536 | ||||||||
\(404\) | 3231.54 | 0.397958 | ||||||||
\(405\) | −12606.5 | + | 5725.96i | −1.54672 | + | 0.702531i | ||||
\(406\) | 2411.24i | 0.294748i | ||||||||
\(407\) | − | 2252.73i | − | 0.274358i | ||||||
\(408\) | −3687.75 | − | 1084.87i | −0.447477 | − | 0.131640i | ||||
\(409\) | 5832.59i | 0.705142i | 0.935785 | + | 0.352571i | \(0.114693\pi\) | ||||
−0.935785 | + | 0.352571i | \(0.885307\pi\) | |||||||
\(410\) | −2394.82 | −0.288467 | ||||||||
\(411\) | 2188.29 | + | 643.761i | 0.262629 | + | 0.0772612i | ||||
\(412\) | − | 7662.73i | − | 0.916300i | ||||||
\(413\) | −1733.43 | + | 4279.81i | −0.206530 | + | 0.509917i | ||||
\(414\) | 1802.09 | + | 1160.75i | 0.213932 | + | 0.137796i | ||||
\(415\) | − | 2971.19i | − | 0.351446i | ||||||
\(416\) | 2633.05i | 0.310326i | ||||||||
\(417\) | −3984.53 | + | 13544.4i | −0.467922 | + | 1.59058i | ||||
\(418\) | 474.615 | 0.0555363 | ||||||||
\(419\) | −6572.59 | −0.766330 | −0.383165 | − | 0.923680i | \(-0.625166\pi\) | ||||
−0.383165 | + | 0.923680i | \(0.625166\pi\) | |||||||
\(420\) | 3858.73 | + | 1135.18i | 0.448302 | + | 0.131883i | ||||
\(421\) | − | 8822.88i | − | 1.02138i | −0.859765 | − | 0.510690i | \(-0.829390\pi\) | ||
0.859765 | − | 0.510690i | \(-0.170610\pi\) | |||||||
\(422\) | 7046.60i | 0.812851i | ||||||||
\(423\) | 858.179 | + | 552.763i | 0.0986433 | + | 0.0635373i | ||||
\(424\) | − | 3272.31i | − | 0.374805i | ||||||
\(425\) | 21799.1i | 2.48803i | ||||||||
\(426\) | 3608.92 | + | 1061.68i | 0.410452 | + | 0.120748i | ||||
\(427\) | 7230.40i | 0.819447i | ||||||||
\(428\) | − | 4014.71i | − | 0.453407i | ||||||
\(429\) | −4172.02 | − | 1227.34i | −0.469526 | − | 0.138127i | ||||
\(430\) | 5596.81 | 0.627680 | ||||||||
\(431\) | −9519.82 | −1.06393 | −0.531965 | − | 0.846767i | \(-0.678546\pi\) | ||||
−0.531965 | + | 0.846767i | \(0.678546\pi\) | |||||||
\(432\) | 1698.72 | − | 1467.38i | 0.189189 | − | 0.163424i | ||||
\(433\) | −4618.05 | −0.512539 | −0.256269 | − | 0.966605i | \(-0.582493\pi\) | ||||
−0.256269 | + | 0.966605i | \(0.582493\pi\) | |||||||
\(434\) | 626.198i | 0.0692591i | ||||||||
\(435\) | 3295.71 | − | 11202.9i | 0.363258 | − | 1.23480i | ||||
\(436\) | − | 7891.77i | − | 0.866851i | ||||||
\(437\) | 926.136 | 0.101380 | ||||||||
\(438\) | −3266.98 | − | 961.091i | −0.356398 | − | 0.104846i | ||||
\(439\) | −6509.93 | −0.707749 | −0.353875 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353875 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(440\) | 1545.48i | 0.167450i | ||||||||
\(441\) | 5429.21 | + | 3497.02i | 0.586244 | + | 0.377607i | ||||
\(442\) | 15217.8 | 1.63764 | ||||||||
\(443\) | −13277.5 | −1.42401 | −0.712003 | − | 0.702176i | \(-0.752212\pi\) | ||||
−0.712003 | + | 0.702176i | \(0.752212\pi\) | |||||||
\(444\) | −4416.19 | − | 1299.17i | −0.472034 | − | 0.138865i | ||||
\(445\) | − | 20853.6i | − | 2.22147i | ||||||
\(446\) | −9610.47 | −1.02033 | ||||||||
\(447\) | 3923.99 | − | 13338.6i | 0.415209 | − | 1.41139i | ||||
\(448\) | −652.096 | −0.0687693 | ||||||||
\(449\) | 12397.8i | 1.30310i | 0.758607 | + | 0.651548i | \(0.225880\pi\) | ||||
−0.758607 | + | 0.651548i | \(0.774120\pi\) | |||||||
\(450\) | −10701.9 | − | 6893.21i | −1.12109 | − | 0.722108i | ||||
\(451\) | 641.249i | 0.0669517i | ||||||||
\(452\) | 2098.69 | 0.218393 | ||||||||
\(453\) | 12941.1 | + | 3807.06i | 1.34222 | + | 0.394860i | ||||
\(454\) | −9236.55 | −0.954829 | ||||||||
\(455\) | −15923.4 | −1.64066 | ||||||||
\(456\) | 273.715 | − | 930.423i | 0.0281094 | − | 0.0955506i | ||||
\(457\) | 2877.48i | 0.294536i | 0.989097 | + | 0.147268i | \(0.0470479\pi\) | ||||
−0.989097 | + | 0.147268i | \(0.952952\pi\) | |||||||
\(458\) | 7306.13i | 0.745400i | ||||||||
\(459\) | −8480.76 | − | 9817.81i | −0.862414 | − | 0.998379i | ||||
\(460\) | 3015.76i | 0.305676i | ||||||||
\(461\) | − | 5221.95i | − | 0.527571i | −0.964581 | − | 0.263786i | \(-0.915029\pi\) | ||
0.964581 | − | 0.263786i | \(-0.0849712\pi\) | |||||||
\(462\) | 303.961 | − | 1033.23i | 0.0306094 | − | 0.104049i | ||||
\(463\) | 16063.6i | 1.61240i | 0.591645 | + | 0.806198i | \(0.298479\pi\) | ||||
−0.591645 | + | 0.806198i | \(0.701521\pi\) | |||||||
\(464\) | 1893.21i | 0.189418i | ||||||||
\(465\) | 855.897 | − | 2909.40i | 0.0853575 | − | 0.290150i | ||||
\(466\) | −2607.80 | −0.259236 | ||||||||
\(467\) | −19210.6 | −1.90356 | −0.951778 | − | 0.306787i | \(-0.900746\pi\) | ||||
−0.951778 | + | 0.306787i | \(0.900746\pi\) | |||||||
\(468\) | −4812.09 | + | 7470.89i | −0.475297 | + | 0.737911i | ||||
\(469\) | 10644.9i | 1.04805i | ||||||||
\(470\) | 1436.15i | 0.140946i | ||||||||
\(471\) | −9835.76 | − | 2893.52i | −0.962225 | − | 0.283071i | ||||
\(472\) | −1361.02 | + | 3360.34i | −0.132725 | + | 0.327695i | ||||
\(473\) | − | 1498.63i | − | 0.145681i | ||||||
\(474\) | −700.132 | + | 2379.92i | −0.0678442 | + | 0.230618i | ||||
\(475\) | −5499.95 | −0.531273 | ||||||||
\(476\) | 3768.81i | 0.362906i | ||||||||
\(477\) | 5980.38 | − | 9284.70i | 0.574052 | − | 0.891231i | ||||
\(478\) | − | 13871.6i | − | 1.32735i | ||||||
\(479\) | − | 11153.0i | − | 1.06387i | −0.846786 | − | 0.531934i | \(-0.821466\pi\) | ||
0.846786 | − | 0.531934i | \(-0.178534\pi\) | |||||||
\(480\) | 3029.72 | + | 891.295i | 0.288099 | + | 0.0847539i | ||||
\(481\) | 18223.8 | 1.72751 | ||||||||
\(482\) | −1948.64 | −0.184145 | ||||||||
\(483\) | 593.132 | − | 2016.20i | 0.0558767 | − | 0.189938i | ||||
\(484\) | −4910.17 | −0.461136 | ||||||||
\(485\) | −25337.4 | −2.37219 | ||||||||
\(486\) | 7501.62 | − | 1058.94i | 0.700165 | − | 0.0988366i | ||||
\(487\) | 7355.98 | 0.684459 | 0.342229 | − | 0.939616i | \(-0.388818\pi\) | ||||
0.342229 | + | 0.939616i | \(0.388818\pi\) | |||||||
\(488\) | 5677.03i | 0.526612i | ||||||||
\(489\) | −1962.77 | + | 6671.94i | −0.181513 | + | 0.617005i | ||||
\(490\) | 9085.68i | 0.837651i | ||||||||
\(491\) | − | 2400.04i | − | 0.220596i | −0.993899 | − | 0.110298i | \(-0.964820\pi\) | ||
0.993899 | − | 0.110298i | \(-0.0351805\pi\) | |||||||
\(492\) | 1257.09 | + | 369.815i | 0.115191 | + | 0.0338873i | ||||
\(493\) | 10941.8 | 0.999586 | ||||||||
\(494\) | 3839.47i | 0.349688i | ||||||||
\(495\) | −2824.48 | + | 4385.08i | −0.256467 | + | 0.398172i | ||||
\(496\) | 491.665i | 0.0445089i | ||||||||
\(497\) | − | 3688.25i | − | 0.332879i | ||||||
\(498\) | −458.821 | + | 1559.64i | −0.0412856 | + | 0.140340i | ||||
\(499\) | 18219.5 | 1.63450 | 0.817252 | − | 0.576280i | \(-0.195496\pi\) | ||||
0.817252 | + | 0.576280i | \(0.195496\pi\) | |||||||
\(500\) | − | 8412.87i | − | 0.752470i | ||||||
\(501\) | −4570.09 | − | 1344.45i | −0.407538 | − | 0.119891i | ||||
\(502\) | 4575.10i | 0.406766i | ||||||||
\(503\) | −812.931 | −0.0720612 | −0.0360306 | − | 0.999351i | \(-0.511471\pi\) | ||||
−0.0360306 | + | 0.999351i | \(0.511471\pi\) | |||||||
\(504\) | −1850.23 | − | 1191.75i | −0.163523 | − | 0.105327i | ||||
\(505\) | 15344.2i | 1.35210i | ||||||||
\(506\) | 807.517 | 0.0709457 | ||||||||
\(507\) | 6706.87 | − | 22798.3i | 0.587500 | − | 1.99705i | ||||
\(508\) | 5599.13 | 0.489018 | ||||||||
\(509\) | −7475.46 | −0.650971 | −0.325485 | − | 0.945547i | \(-0.605528\pi\) | ||||
−0.325485 | + | 0.945547i | \(0.605528\pi\) | |||||||
\(510\) | 5151.27 | − | 17510.4i | 0.447259 | − | 1.52034i | ||||
\(511\) | 3338.79i | 0.289040i | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 2477.05 | − | 2139.71i | 0.213186 | − | 0.184153i | ||||
\(514\) | 13981.8i | 1.19983i | ||||||||
\(515\) | 36384.7 | 3.11320 | ||||||||
\(516\) | −2937.88 | − | 864.277i | −0.250645 | − | 0.0737358i | ||||
\(517\) | 384.550 | 0.0327128 | ||||||||
\(518\) | 4513.27i | 0.382822i | ||||||||
\(519\) | −2612.82 | + | 8881.61i | −0.220983 | + | 0.751174i | ||||
\(520\) | −12502.4 | −1.05436 | ||||||||
\(521\) | 13918.5i | 1.17041i | 0.810886 | + | 0.585204i | \(0.198986\pi\) | ||||
−0.810886 | + | 0.585204i | \(0.801014\pi\) | |||||||
\(522\) | −3459.98 | + | 5371.70i | −0.290113 | + | 0.450408i | ||||
\(523\) | 10698.0 | 0.894438 | 0.447219 | − | 0.894425i | \(-0.352415\pi\) | ||||
0.447219 | + | 0.894425i | \(0.352415\pi\) | |||||||
\(524\) | −8260.76 | −0.688689 | ||||||||
\(525\) | −3522.37 | + | 11973.4i | −0.292817 | + | 0.995353i | ||||
\(526\) | 5892.27i | 0.488432i | ||||||||
\(527\) | 2841.60 | 0.234880 | ||||||||
\(528\) | 238.658 | − | 811.255i | 0.0196709 | − | 0.0668662i | ||||
\(529\) | −10591.3 | −0.870490 | ||||||||
\(530\) | 15537.8 | 1.27343 | ||||||||
\(531\) | −10003.0 | + | 7047.11i | −0.817500 | + | 0.575929i | ||||
\(532\) | −950.876 | −0.0774920 | ||||||||
\(533\) | −5187.48 | −0.421566 | ||||||||
\(534\) | −3220.27 | + | 10946.5i | −0.260964 | + | 0.887078i | ||||
\(535\) | 19062.9 | 1.54049 | ||||||||
\(536\) | 8357.97i | 0.673525i | ||||||||
\(537\) | 1277.09 | − | 4341.13i | 0.102627 | − | 0.348852i | ||||
\(538\) | 2549.06 | 0.204271 | ||||||||
\(539\) | 2432.83 | 0.194414 | ||||||||
\(540\) | 6967.50 | + | 8065.97i | 0.555247 | + | 0.642785i | ||||
\(541\) | − | 11634.8i | − | 0.924616i | −0.886720 | − | 0.462308i | \(-0.847022\pi\) | ||
0.886720 | − | 0.462308i | \(-0.152978\pi\) | |||||||
\(542\) | 9858.49 | 0.781289 | ||||||||
\(543\) | 4762.46 | − | 16188.7i | 0.376385 | − | 1.27942i | ||||
\(544\) | 2959.12i | 0.233219i | ||||||||
\(545\) | 37472.2 | 2.94520 | ||||||||
\(546\) | 8358.50 | + | 2458.94i | 0.655148 | + | 0.192734i | ||||
\(547\) | −19199.4 | −1.50074 | −0.750371 | − | 0.661016i | \(-0.770125\pi\) | ||||
−0.750371 | + | 0.661016i | \(0.770125\pi\) | |||||||
\(548\) | − | 1755.93i | − | 0.136879i | ||||||
\(549\) | −10375.2 | + | 16107.8i | −0.806561 | + | 1.25221i | ||||
\(550\) | −4795.52 | −0.371784 | ||||||||
\(551\) | 2760.64i | 0.213444i | ||||||||
\(552\) | 465.703 | − | 1583.04i | 0.0359088 | − | 0.122062i | ||||
\(553\) | 2432.23 | 0.187033 | ||||||||
\(554\) | 13624.0 | 1.04482 | ||||||||
\(555\) | 6168.81 | − | 20969.2i | 0.471804 | − | 1.60377i | ||||
\(556\) | 10868.3 | 0.828989 | ||||||||
\(557\) | − | 12237.1i | − | 0.930883i | −0.885079 | − | 0.465442i | \(-0.845896\pi\) | ||
0.885079 | − | 0.465442i | \(-0.154104\pi\) | |||||||
\(558\) | −898.555 | + | 1395.03i | −0.0681700 | + | 0.105836i | ||||
\(559\) | 12123.4 | 0.917290 | ||||||||
\(560\) | − | 3096.32i | − | 0.233649i | ||||||
\(561\) | −4688.67 | − | 1379.33i | −0.352863 | − | 0.103806i | ||||
\(562\) | 9526.24i | 0.715018i | ||||||||
\(563\) | −1826.20 | −0.136705 | −0.0683527 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683527 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(564\) | 221.774 | − | 753.863i | 0.0165574 | − | 0.0562825i | ||||
\(565\) | 9965.11i | 0.742010i | ||||||||
\(566\) | 12084.2i | 0.897415i | ||||||||
\(567\) | −3071.74 | − | 6762.87i | −0.227515 | − | 0.500906i | ||||
\(568\) | − | 2895.87i | − | 0.213922i | ||||||
\(569\) | −4352.74 | −0.320696 | −0.160348 | − | 0.987061i | \(-0.551262\pi\) | ||||
−0.160348 | + | 0.987061i | \(0.551262\pi\) | |||||||
\(570\) | 4417.90 | + | 1299.67i | 0.324641 | + | 0.0955040i | ||||
\(571\) | 5189.16i | 0.380315i | 0.981754 | + | 0.190157i | \(0.0608998\pi\) | ||||
−0.981754 | + | 0.190157i | \(0.939100\pi\) | |||||||
\(572\) | 3347.71i | 0.244711i | ||||||||
\(573\) | −2317.84 | + | 7878.90i | −0.168987 | + | 0.574426i | ||||
\(574\) | − | 1284.72i | − | 0.0934203i | ||||||
\(575\) | −9357.69 | −0.678683 | ||||||||
\(576\) | −1452.73 | − | 935.718i | −0.105087 | − | 0.0676879i | ||||
\(577\) | 9056.33 | 0.653414 | 0.326707 | − | 0.945126i | \(-0.394061\pi\) | ||||
0.326707 | + | 0.945126i | \(0.394061\pi\) | |||||||
\(578\) | 7276.34 | 0.523626 | ||||||||
\(579\) | −2430.44 | + | 8261.66i | −0.174449 | + | 0.592993i | ||||
\(580\) | −8989.44 | −0.643563 | ||||||||
\(581\) | 1593.93 | 0.113816 | ||||||||
\(582\) | 13300.1 | + | 3912.68i | 0.947266 | + | 0.278670i | ||||
\(583\) | − | 4160.48i | − | 0.295556i | ||||||
\(584\) | 2621.49i | 0.185750i | ||||||||
\(585\) | −35473.8 | − | 22849.1i | −2.50711 | − | 1.61486i | ||||
\(586\) | − | 2945.93i | − | 0.207671i | ||||||
\(587\) | −25369.7 | −1.78385 | −0.891925 | − | 0.452183i | \(-0.850645\pi\) | ||||
−0.891925 | + | 0.452183i | \(0.850645\pi\) | |||||||
\(588\) | 1403.04 | − | 4769.26i | 0.0984019 | − | 0.334491i | ||||
\(589\) | 716.939i | 0.0501544i | ||||||||
\(590\) | −15955.8 | − | 6462.50i | −1.11337 | − | 0.450944i | ||||
\(591\) | 8678.08 | + | 2552.95i | 0.604008 | + | 0.177689i | ||||
\(592\) | 3543.64i | 0.246018i | ||||||||
\(593\) | 556.620i | 0.0385457i | 0.999814 | + | 0.0192729i | \(0.00613512\pi\) | ||||
−0.999814 | + | 0.0192729i | \(0.993865\pi\) | |||||||
\(594\) | 2159.79 | − | 1865.65i | 0.149187 | − | 0.128870i | ||||
\(595\) | −17895.3 | −1.23300 | ||||||||
\(596\) | −10703.1 | −0.735600 | ||||||||
\(597\) | −901.773 | + | 3065.34i | −0.0618210 | + | 0.210144i | ||||
\(598\) | 6532.53i | 0.446714i | ||||||||
\(599\) | − | 15541.0i | − | 1.06008i | −0.847973 | − | 0.530039i | \(-0.822177\pi\) | ||
0.847973 | − | 0.530039i | \(-0.177823\pi\) | |||||||
\(600\) | −2765.62 | + | 9401.01i | −0.188177 | + | 0.639658i | ||||
\(601\) | − | 3882.45i | − | 0.263508i | −0.991282 | − | 0.131754i | \(-0.957939\pi\) | ||
0.991282 | − | 0.131754i | \(-0.0420609\pi\) | |||||||
\(602\) | 3002.46i | 0.203275i | ||||||||
\(603\) | −15274.8 | + | 23714.6i | −1.03157 | + | 1.60154i | ||||
\(604\) | − | 10384.2i | − | 0.699548i | ||||||
\(605\) | − | 23314.8i | − | 1.56675i | ||||||
\(606\) | 2369.50 | − | 8054.49i | 0.158836 | − | 0.539920i | ||||
\(607\) | −2132.51 | −0.142596 | −0.0712982 | − | 0.997455i | \(-0.522714\pi\) | ||||
−0.0712982 | + | 0.997455i | \(0.522714\pi\) | |||||||
\(608\) | −746.590 | −0.0497997 | ||||||||
\(609\) | 6009.91 | + | 1768.02i | 0.399891 | + | 0.117642i | ||||
\(610\) | −26956.0 | −1.78921 | ||||||||
\(611\) | 3110.88i | 0.205978i | ||||||||
\(612\) | −5408.01 | + | 8396.08i | −0.357199 | + | 0.554561i | ||||
\(613\) | − | 842.437i | − | 0.0555069i | −0.999615 | − | 0.0277534i | \(-0.991165\pi\) | ||
0.999615 | − | 0.0277534i | \(-0.00883533\pi\) | |||||||
\(614\) | −4151.05 | −0.272838 | ||||||||
\(615\) | −1755.98 | + | 5968.99i | −0.115135 | + | 0.391370i | ||||
\(616\) | −829.088 | −0.0542288 | ||||||||
\(617\) | − | 22352.9i | − | 1.45850i | −0.684250 | − | 0.729248i | \(-0.739870\pi\) | ||
0.684250 | − | 0.729248i | \(-0.260130\pi\) | |||||||
\(618\) | −19099.1 | − | 5618.63i | −1.24317 | − | 0.365719i | ||||
\(619\) | −12127.3 | −0.787458 | −0.393729 | − | 0.919227i | \(-0.628815\pi\) | ||||
−0.393729 | + | 0.919227i | \(0.628815\pi\) | |||||||
\(620\) | −2334.56 | −0.151223 | ||||||||
\(621\) | 4214.48 | − | 3640.53i | 0.272337 | − | 0.235249i | ||||
\(622\) | 10240.5i | 0.660137i | ||||||||
\(623\) | 11187.1 | 0.719424 | ||||||||
\(624\) | 6562.76 | + | 1930.66i | 0.421027 | + | 0.123859i | ||||
\(625\) | 10479.5 | 0.670689 | ||||||||
\(626\) | 8363.09i | 0.533956i | ||||||||
\(627\) | 348.007 | − | 1182.96i | 0.0221660 | − | 0.0753474i | ||||
\(628\) | 7892.41i | 0.501499i | ||||||||
\(629\) | 20480.6 | 1.29827 | ||||||||
\(630\) | 5658.76 | − | 8785.38i | 0.357858 | − | 0.555584i | ||||
\(631\) | 18241.3 | 1.15083 | 0.575414 | − | 0.817862i | \(-0.304841\pi\) | ||||
0.575414 | + | 0.817862i | \(0.304841\pi\) | |||||||
\(632\) | 1909.69 | 0.120195 | ||||||||
\(633\) | 17563.4 | + | 5166.86i | 1.10281 | + | 0.324430i | ||||
\(634\) | − | 10829.5i | − | 0.678384i | ||||||
\(635\) | 26586.2i | 1.66148i | ||||||||
\(636\) | −8156.09 | − | 2399.39i | −0.508506 | − | 0.149594i | ||||
\(637\) | 19680.7i | 1.22414i | ||||||||
\(638\) | 2407.06i | 0.149367i | ||||||||
\(639\) | 5292.41 | − | 8216.61i | 0.327644 | − | 0.508676i | ||||
\(640\) | − | 2431.11i | − | 0.150153i | ||||||
\(641\) | 27962.8i | 1.72303i | 0.507728 | + | 0.861517i | \(0.330485\pi\) | ||||
−0.507728 | + | 0.861517i | \(0.669515\pi\) | |||||||
\(642\) | −10006.5 | − | 2943.75i | −0.615148 | − | 0.180967i | ||||
\(643\) | 2162.12 | 0.132606 | 0.0663031 | − | 0.997800i | \(-0.478880\pi\) | ||||
0.0663031 | + | 0.997800i | \(0.478880\pi\) | |||||||
\(644\) | −1617.84 | −0.0989932 | ||||||||
\(645\) | 4103.81 | − | 13949.8i | 0.250523 | − | 0.851588i | ||||
\(646\) | 4314.94i | 0.262801i | ||||||||
\(647\) | − | 1584.19i | − | 0.0962614i | −0.998841 | − | 0.0481307i | \(-0.984674\pi\) | ||
0.998841 | − | 0.0481307i | \(-0.0153264\pi\) | |||||||
\(648\) | −2411.81 | − | 5309.93i | −0.146211 | − | 0.321904i | ||||
\(649\) | −1730.43 | + | 4272.40i | −0.104662 | + | 0.258407i | ||||
\(650\) | − | 38794.0i | − | 2.34096i | ||||||
\(651\) | 1560.77 | + | 459.154i | 0.0939654 | + | 0.0276431i | ||||
\(652\) | 5353.69 | 0.321575 | ||||||||
\(653\) | − | 31720.4i | − | 1.90094i | −0.310814 | − | 0.950471i | \(-0.600602\pi\) | ||
0.310814 | − | 0.950471i | \(-0.399398\pi\) | |||||||
\(654\) | −19669.9 | − | 5786.57i | −1.17608 | − | 0.345983i | ||||
\(655\) | − | 39224.3i | − | 2.33988i | ||||||
\(656\) | − | 1008.71i | − | 0.0600360i | ||||||
\(657\) | −4790.96 | + | 7438.10i | −0.284495 | + | 0.441686i | ||||
\(658\) | −770.435 | −0.0456454 | ||||||||
\(659\) | −1761.47 | −0.104123 | −0.0520615 | − | 0.998644i | \(-0.516579\pi\) | ||||
−0.0520615 | + | 0.998644i | \(0.516579\pi\) | |||||||
\(660\) | 3852.05 | + | 1133.21i | 0.227183 | + | 0.0668336i | ||||
\(661\) | 22221.3 | 1.30758 | 0.653788 | − | 0.756677i | \(-0.273179\pi\) | ||||
0.653788 | + | 0.756677i | \(0.273179\pi\) | |||||||
\(662\) | −2213.34 | −0.129945 | ||||||||
\(663\) | 11158.3 | − | 37929.7i | 0.653624 | − | 2.22182i | ||||
\(664\) | 1251.49 | 0.0731432 | ||||||||
\(665\) | − | 4515.01i | − | 0.263285i | ||||||
\(666\) | −6476.27 | + | 10054.6i | −0.376802 | + | 0.584995i | ||||
\(667\) | 4697.00i | 0.272667i | ||||||||
\(668\) | 3667.13i | 0.212404i | ||||||||
\(669\) | −7046.79 | + | 23953.7i | −0.407242 | + | 1.38431i | ||||
\(670\) | −39685.9 | −2.28836 | ||||||||
\(671\) | 7217.89i | 0.415266i | ||||||||
\(672\) | −478.144 | + | 1625.32i | −0.0274476 | + | 0.0933009i | ||||
\(673\) | − | 18991.3i | − | 1.08776i | −0.839163 | − | 0.543880i | \(-0.816955\pi\) | ||
0.839163 | − | 0.543880i | \(-0.183045\pi\) | |||||||
\(674\) | − | 16566.2i | − | 0.946744i | ||||||
\(675\) | −25028.1 | + | 21619.6i | −1.42716 | + | 1.23280i | ||||
\(676\) | −18293.8 | −1.04084 | ||||||||
\(677\) | 26193.0i | 1.48697i | 0.668754 | + | 0.743484i | \(0.266828\pi\) | ||||
−0.668754 | + | 0.743484i | \(0.733172\pi\) | |||||||
\(678\) | 1538.84 | − | 5230.89i | 0.0871665 | − | 0.296300i | ||||
\(679\) | − | 13592.5i | − | 0.768237i | ||||||
\(680\) | −14050.7 | −0.792381 | ||||||||
\(681\) | −6772.61 | + | 23021.7i | −0.381097 | + | 1.29544i | ||||
\(682\) | 625.113i | 0.0350980i | ||||||||
\(683\) | 29944.8 | 1.67761 | 0.838803 | − | 0.544435i | \(-0.183256\pi\) | ||||
0.838803 | + | 0.544435i | \(0.183256\pi\) | |||||||
\(684\) | −2118.34 | − | 1364.45i | −0.118417 | − | 0.0762734i | ||||
\(685\) | 8337.63 | 0.465057 | ||||||||
\(686\) | −11863.8 | −0.660292 | ||||||||
\(687\) | 18210.2 | + | 5357.16i | 1.01130 | + | 0.297508i | ||||
\(688\) | 2357.41i | 0.130633i | ||||||||
\(689\) | 33656.8 | 1.86099 | ||||||||
\(690\) | 7516.67 | + | 2211.28i | 0.414717 | + | 0.122003i | ||||
\(691\) | 4559.60i | 0.251021i | 0.992092 | + | 0.125510i | \(0.0400568\pi\) | ||||
−0.992092 | + | 0.125510i | \(0.959943\pi\) | |||||||
\(692\) | 7126.78 | 0.391502 | ||||||||
\(693\) | −2352.42 | − | 1515.22i | −0.128948 | − | 0.0830569i | ||||
\(694\) | 7743.00 | 0.423516 | ||||||||
\(695\) | 51605.5i | 2.81656i | ||||||||
\(696\) | 4718.74 | + | 1388.18i | 0.256988 | + | 0.0756016i | ||||
\(697\) | −5829.89 | −0.316819 | ||||||||
\(698\) | − | 20611.4i | − | 1.11770i | ||||||
\(699\) | −1912.14 | + | 6499.83i | −0.103468 | + | 0.351711i | ||||
\(700\) | 9607.67 | 0.518765 | ||||||||
\(701\) | −23909.3 | −1.28822 | −0.644109 | − | 0.764934i | \(-0.722772\pi\) | ||||
−0.644109 | + | 0.764934i | \(0.722772\pi\) | |||||||
\(702\) | 15092.5 | + | 17471.9i | 0.811438 | + | 0.939365i | ||||
\(703\) | 5167.28i | 0.277223i | ||||||||
\(704\) | −650.967 | −0.0348498 | ||||||||
\(705\) | 3579.54 | + | 1053.04i | 0.191224 | + | 0.0562551i | ||||
\(706\) | 10125.9 | 0.539794 | ||||||||
\(707\) | −8231.55 | −0.437877 | ||||||||
\(708\) | 7377.55 | + | 5856.24i | 0.391618 | + | 0.310863i | ||||
\(709\) | 7047.67 | 0.373316 | 0.186658 | − | 0.982425i | \(-0.440234\pi\) | ||||
0.186658 | + | 0.982425i | \(0.440234\pi\) | |||||||
\(710\) | 13750.3 | 0.726819 | ||||||||
\(711\) | 5418.48 | + | 3490.10i | 0.285807 | + | 0.184092i | ||||
\(712\) | 8783.66 | 0.462334 | ||||||||
\(713\) | 1219.81i | 0.0640705i | ||||||||
\(714\) | 9393.61 | + | 2763.45i | 0.492363 | + | 0.144845i | ||||
\(715\) | −15895.8 | −0.831426 | ||||||||
\(716\) | −3483.41 | −0.181817 | ||||||||
\(717\) | −34574.4 | − | 10171.2i | −1.80084 | − | 0.529778i | ||||
\(718\) | − | 14187.4i | − | 0.737421i | ||||||
\(719\) | 11771.4 | 0.610567 | 0.305283 | − | 0.952262i | \(-0.401249\pi\) | ||||
0.305283 | + | 0.952262i | \(0.401249\pi\) | |||||||
\(720\) | 4443.04 | − | 6897.93i | 0.229975 | − | 0.357043i | ||||
\(721\) | 19518.9i | 1.00821i | ||||||||
\(722\) | 12629.3 | 0.650990 | ||||||||
\(723\) | −1428.82 | + | 4856.90i | −0.0734972 | + | 0.249834i | ||||
\(724\) | −12990.2 | −0.666818 | ||||||||
\(725\) | − | 27893.6i | − | 1.42888i | ||||||
\(726\) | −3600.34 | + | 12238.4i | −0.184051 | + | 0.625634i | ||||
\(727\) | 29044.3 | 1.48170 | 0.740848 | − | 0.671673i | \(-0.234424\pi\) | ||||
0.740848 | + | 0.671673i | \(0.234424\pi\) | |||||||
\(728\) | − | 6707.03i | − | 0.341455i | ||||||
\(729\) | 2861.12 | − | 19473.9i | 0.145360 | − | 0.989379i | ||||
\(730\) | −12447.5 | −0.631100 | ||||||||
\(731\) | 13624.8 | 0.689370 | ||||||||
\(732\) | 14149.8 | + | 4162.63i | 0.714468 | + | 0.210185i | ||||
\(733\) | −2188.98 | −0.110303 | −0.0551514 | − | 0.998478i | \(-0.517564\pi\) | ||||
−0.0551514 | + | 0.998478i | \(0.517564\pi\) | |||||||
\(734\) | − | 15857.3i | − | 0.797416i | ||||||
\(735\) | 22645.7 | + | 6661.99i | 1.13646 | + | 0.334328i | ||||
\(736\) | −1270.26 | −0.0636174 | ||||||||
\(737\) | 10626.5i | 0.531115i | ||||||||
\(738\) | 1843.50 | − | 2862.08i | 0.0919513 | − | 0.142757i | ||||
\(739\) | 21285.6i | 1.05955i | 0.848140 | + | 0.529773i | \(0.177723\pi\) | ||||
−0.848140 | + | 0.529773i | \(0.822277\pi\) | |||||||
\(740\) | −16826.1 | −0.835867 | ||||||||
\(741\) | 9569.72 | + | 2815.25i | 0.474430 | + | 0.139569i | ||||
\(742\) | 8335.38i | 0.412401i | ||||||||
\(743\) | − | 28955.4i | − | 1.42971i | −0.699275 | − | 0.714853i | \(-0.746494\pi\) | ||
0.699275 | − | 0.714853i | \(-0.253506\pi\) | |||||||
\(744\) | 1225.46 | + | 360.509i | 0.0603863 | + | 0.0177647i | ||||
\(745\) | − | 50821.3i | − | 2.49926i | ||||||
\(746\) | 17438.6 | 0.855862 | ||||||||
\(747\) | 3550.92 | + | 2287.19i | 0.173924 | + | 0.112026i | ||||
\(748\) | 3762.29i | 0.183907i | ||||||||
\(749\) | 10226.5i | 0.498888i | ||||||||
\(750\) | −20968.7 | − | 6168.66i | −1.02089 | − | 0.300330i | ||||
\(751\) | − | 31748.3i | − | 1.54263i | −0.636456 | − | 0.771313i | \(-0.719600\pi\) | ||
0.636456 | − | 0.771313i | \(-0.280400\pi\) | |||||||
\(752\) | −604.915 | −0.0293337 | ||||||||
\(753\) | 11403.3 | + | 3354.65i | 0.551869 | + | 0.162351i | ||||
\(754\) | −19472.3 | −0.940502 | ||||||||
\(755\) | 49306.9 | 2.37677 | ||||||||
\(756\) | −4327.06 | + | 3737.78i | −0.208166 | + | 0.179817i | ||||
\(757\) | −16734.2 | −0.803453 | −0.401727 | − | 0.915760i | \(-0.631590\pi\) | ||||
−0.401727 | + | 0.915760i | \(0.631590\pi\) | |||||||
\(758\) | 1578.89 | 0.0756569 | ||||||||
\(759\) | 592.105 | − | 2012.70i | 0.0283163 | − | 0.0962537i | ||||
\(760\) | − | 3545.01i | − | 0.169199i | ||||||
\(761\) | − | 25291.3i | − | 1.20474i | −0.798216 | − | 0.602371i | \(-0.794223\pi\) | ||
0.798216 | − | 0.602371i | \(-0.205777\pi\) | |||||||
\(762\) | 4105.51 | − | 13955.6i | 0.195180 | − | 0.663463i | ||||
\(763\) | 20102.3i | 0.953804i | ||||||||
\(764\) | 6322.19 | 0.299383 | ||||||||
\(765\) | −39866.8 | − | 25678.7i | −1.88417 | − | 1.21361i | ||||
\(766\) | 9814.81i | 0.462955i | ||||||||
\(767\) | −34562.2 | − | 13998.6i | −1.62708 | − | 0.659009i | ||||
\(768\) | −375.419 | + | 1276.14i | −0.0176390 | + | 0.0599593i | ||||
\(769\) | − | 18921.8i | − | 0.887307i | −0.896198 | − | 0.443653i | \(-0.853682\pi\) | ||
0.896198 | − | 0.443653i | \(-0.146318\pi\) | |||||||
\(770\) | − | 3936.73i | − | 0.184247i | ||||||
\(771\) | 34849.0 | + | 10252.0i | 1.62783 | + | 0.478881i | ||||
\(772\) | 6629.32 | 0.309060 | ||||||||
\(773\) | 29323.8 | 1.36443 | 0.682215 | − | 0.731152i | \(-0.261017\pi\) | ||||
0.682215 | + | 0.731152i | \(0.261017\pi\) | |||||||
\(774\) | −4308.35 | + | 6688.83i | −0.200078 | + | 0.310627i | ||||
\(775\) | − | 7243.96i | − | 0.335756i | ||||||
\(776\) | − | 10672.3i | − | 0.493703i | ||||||
\(777\) | 11249.1 | + | 3309.32i | 0.519384 | + | 0.152794i | ||||
\(778\) | − | 4994.77i | − | 0.230169i | ||||||
\(779\) | − | 1470.89i | − | 0.0676509i | ||||||
\(780\) | −9167.27 | + | 31161.7i | −0.420822 | + | 1.43047i | ||||
\(781\) | − | 3681.87i | − | 0.168691i | ||||||
\(782\) | 7341.51i | 0.335718i | ||||||||
\(783\) | 10851.8 | + | 12562.6i | 0.495288 | + | 0.573373i | ||||
\(784\) | −3826.95 | −0.174333 | ||||||||
\(785\) | −37475.3 | −1.70388 | ||||||||
\(786\) | −6057.13 | + | 20589.6i | −0.274874 | + | 0.934360i | ||||
\(787\) | 29548.3 | 1.33835 | 0.669177 | − | 0.743103i | \(-0.266647\pi\) | ||||
0.669177 | + | 0.743103i | \(0.266647\pi\) | |||||||
\(788\) | − | 6963.47i | − | 0.314801i | ||||||
\(789\) | 14686.2 | + | 4320.45i | 0.662667 | + | 0.194946i | ||||
\(790\) | 9067.72i | 0.408374i | ||||||||
\(791\) | −5345.88 | −0.240300 | ||||||||
\(792\) | −1847.03 | − | 1189.69i | −0.0828677 | − | 0.0533760i | ||||
\(793\) | −58390.1 | −2.61475 | ||||||||
\(794\) | 12136.5i | 0.542454i | ||||||||
\(795\) | 11392.9 | − | 38727.3i | 0.508259 | − | 1.72769i | ||||
\(796\) | 2459.69 | 0.109524 | ||||||||
\(797\) | −22579.7 | −1.00353 | −0.501765 | − | 0.865004i | \(-0.667316\pi\) | ||||
−0.501765 | + | 0.865004i | \(0.667316\pi\) | |||||||
\(798\) | −697.222 | + | 2370.02i | −0.0309290 | + | 0.105135i | ||||
\(799\) | 3496.12i | 0.154798i | ||||||||
\(800\) | 7543.56 | 0.333381 | ||||||||
\(801\) | 24922.4 | + | 16052.8i | 1.09936 | + | 0.708111i | ||||
\(802\) | 19418.9 | 0.854995 | ||||||||
\(803\) | 3333.01i | 0.146475i | ||||||||
\(804\) | 20831.9 | + | 6128.41i | 0.913787 | + | 0.268821i | ||||
\(805\) | − | 7681.91i | − | 0.336338i | ||||||
\(806\) | −5056.95 | −0.220997 | ||||||||
\(807\) | 1869.07 | − | 6353.42i | 0.0815297 | − | 0.277139i | ||||
\(808\) | −6463.08 | −0.281399 | ||||||||
\(809\) | −11940.1 | −0.518902 | −0.259451 | − | 0.965756i | \(-0.583542\pi\) | ||||
−0.259451 | + | 0.965756i | \(0.583542\pi\) | |||||||
\(810\) | 25213.0 | − | 11451.9i | 1.09370 | − | 0.496765i | ||||
\(811\) | − | 3871.63i | − | 0.167634i | −0.996481 | − | 0.0838171i | \(-0.973289\pi\) | ||
0.996481 | − | 0.0838171i | \(-0.0267111\pi\) | |||||||
\(812\) | − | 4822.47i | − | 0.208418i | ||||||
\(813\) | 7228.65 | − | 24571.9i | 0.311833 | − | 1.05999i | ||||
\(814\) | 4505.46i | 0.194000i | ||||||||
\(815\) | 25420.8i | 1.09258i | ||||||||
\(816\) | 7375.49 | + | 2169.75i | 0.316414 | + | 0.0930838i | ||||
\(817\) | 3437.54i | 0.147203i | ||||||||
\(818\) | − | 11665.2i | − | 0.498611i | ||||||
\(819\) | 12257.6 | − | 19030.2i | 0.522973 | − | 0.811930i | ||||
\(820\) | 4789.63 | 0.203977 | ||||||||
\(821\) | −1641.98 | −0.0697996 | −0.0348998 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0348998 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(822\) | −4376.59 | − | 1287.52i | −0.185707 | − | 0.0546319i | ||||
\(823\) | 34300.1i | 1.45277i | 0.687289 | + | 0.726384i | \(0.258801\pi\) | ||||
−0.687289 | + | 0.726384i | \(0.741199\pi\) | |||||||
\(824\) | 15325.5i | 0.647922i | ||||||||
\(825\) | −3516.27 | + | 11952.6i | −0.148389 | + | 0.504409i | ||||
\(826\) | 3466.87 | − | 8559.62i | 0.146039 | − | 0.360566i | ||||
\(827\) | 33600.0i | 1.41280i | 0.707812 | + | 0.706401i | \(0.249682\pi\) | ||||
−0.707812 | + | 0.706401i | \(0.750318\pi\) | |||||||
\(828\) | −3604.18 | − | 2321.49i | −0.151273 | − | 0.0974366i | ||||
\(829\) | −27672.8 | −1.15937 | −0.579684 | − | 0.814841i | \(-0.696824\pi\) | ||||
−0.579684 | + | 0.814841i | \(0.696824\pi\) | |||||||
\(830\) | 5942.39i | 0.248510i | ||||||||
\(831\) | 9989.67 | − | 33957.2i | 0.417013 | − | 1.41753i | ||||
\(832\) | − | 5266.09i | − | 0.219434i | ||||||
\(833\) | 22118.0i | 0.919979i | ||||||||
\(834\) | 7969.07 | − | 27088.7i | 0.330871 | − | 1.12471i | ||||
\(835\) | −17412.5 | −0.721659 | ||||||||
\(836\) | −949.230 | −0.0392701 | ||||||||
\(837\) | 2818.20 | + | 3262.51i | 0.116381 | + | 0.134730i | ||||
\(838\) | 13145.2 | 0.541877 | ||||||||
\(839\) | −22478.3 | −0.924956 | −0.462478 | − | 0.886631i | \(-0.653040\pi\) | ||||
−0.462478 | + | 0.886631i | \(0.653040\pi\) | |||||||
\(840\) | −7717.47 | − | 2270.35i | −0.316997 | − | 0.0932555i | ||||
\(841\) | 10388.1 | 0.425934 | ||||||||
\(842\) | 17645.8i | 0.722224i | ||||||||
\(843\) | 23743.8 | + | 6985.03i | 0.970082 | + | 0.285382i | ||||
\(844\) | − | 14093.2i | − | 0.574772i | ||||||
\(845\) | − | 86863.7i | − | 3.53633i | ||||||
\(846\) | −1716.36 | − | 1105.53i | −0.0697513 | − | 0.0449276i | ||||
\(847\) | 12507.4 | 0.507392 | ||||||||
\(848\) | 6544.61i | 0.265027i | ||||||||
\(849\) | 30119.4 | + | 8860.63i | 1.21754 | + | 0.358181i | ||||
\(850\) | − | 43598.2i | − | 1.75930i | ||||||
\(851\) | 8791.69i | 0.354143i | ||||||||
\(852\) | −7217.84 | − | 2123.37i | −0.290234 | − | 0.0853820i | ||||
\(853\) | 35718.4 | 1.43373 | 0.716866 | − | 0.697211i | \(-0.245576\pi\) | ||||
0.716866 | + | 0.697211i | \(0.245576\pi\) | |||||||
\(854\) | − | 14460.8i | − | 0.579436i | ||||||
\(855\) | 6478.76 | − | 10058.5i | 0.259145 | − | 0.402330i | ||||
\(856\) | 8029.42i | 0.320607i | ||||||||
\(857\) | −27395.6 | −1.09197 | −0.545984 | − | 0.837796i | \(-0.683844\pi\) | ||||
−0.545984 | + | 0.837796i | \(0.683844\pi\) | |||||||
\(858\) | 8344.03 | + | 2454.68i | 0.332005 | + | 0.0976705i | ||||
\(859\) | − | 32403.6i | − | 1.28707i | −0.765415 | − | 0.643536i | \(-0.777466\pi\) | ||
0.765415 | − | 0.643536i | \(-0.222534\pi\) | |||||||
\(860\) | −11193.6 | −0.443837 | ||||||||
\(861\) | −3202.12 | − | 942.011i | −0.126746 | − | 0.0372865i | ||||
\(862\) | 19039.6 | 0.752312 | ||||||||
\(863\) | 21545.2 | 0.849835 | 0.424917 | − | 0.905232i | \(-0.360303\pi\) | ||||
0.424917 | + | 0.905232i | \(0.360303\pi\) | |||||||
\(864\) | −3397.44 | + | 2934.76i | −0.133777 | + | 0.115558i | ||||
\(865\) | 33839.8i | 1.33016i | ||||||||
\(866\) | 9236.10 | 0.362420 | ||||||||
\(867\) | 5335.31 | − | 18136.0i | 0.208993 | − | 0.710415i | ||||
\(868\) | − | 1252.40i | − | 0.0489736i | ||||||
\(869\) | 2428.02 | 0.0947813 | ||||||||
\(870\) | −6591.43 | + | 22405.8i | −0.256863 | + | 0.873137i | ||||
\(871\) | −85964.6 | −3.34420 | ||||||||
\(872\) | 15783.5i | 0.612956i | ||||||||
\(873\) | 19504.4 | − | 30281.1i | 0.756156 | − | 1.17395i | ||||
\(874\) | −1852.27 | −0.0716866 | ||||||||
\(875\) | 21429.7i | 0.827950i | ||||||||
\(876\) | 6533.95 | + | 1922.18i | 0.252011 | + | 0.0741376i | ||||
\(877\) | −21365.2 | −0.822635 | −0.411318 | − | 0.911492i | \(-0.634931\pi\) | ||||
−0.411318 | + | 0.911492i | \(0.634931\pi\) | |||||||
\(878\) | 13019.9 | 0.500454 | ||||||||
\(879\) | −7342.60 | − | 2160.07i | −0.281752 | − | 0.0828868i | ||||
\(880\) | − | 3090.96i | − | 0.118405i | ||||||
\(881\) | −39856.6 | −1.52418 | −0.762091 | − | 0.647470i | \(-0.775827\pi\) | ||||
−0.762091 | + | 0.647470i | \(0.775827\pi\) | |||||||
\(882\) | −10858.4 | − | 6994.03i | −0.414537 | − | 0.267008i | ||||
\(883\) | 3668.31 | 0.139806 | 0.0699028 | − | 0.997554i | \(-0.477731\pi\) | ||||
0.0699028 | + | 0.997554i | \(0.477731\pi\) | |||||||
\(884\) | −30435.6 | −1.15798 | ||||||||
\(885\) | −27807.0 | + | 35030.5i | −1.05618 | + | 1.33055i | ||||
\(886\) | 26555.1 | 1.00692 | ||||||||
\(887\) | 33102.6 | 1.25308 | 0.626538 | − | 0.779391i | \(-0.284471\pi\) | ||||
0.626538 | + | 0.779391i | \(0.284471\pi\) | |||||||
\(888\) | 8832.38 | + | 2598.34i | 0.333779 | + | 0.0981922i | ||||
\(889\) | −14262.4 | −0.538071 | ||||||||
\(890\) | 41707.1i | 1.57082i | ||||||||
\(891\) | −3066.43 | − | 6751.16i | −0.115296 | − | 0.253841i | ||||
\(892\) | 19220.9 | 0.721485 | ||||||||
\(893\) | −882.077 | −0.0330544 | ||||||||
\(894\) | −7847.98 | + | 26677.1i | −0.293597 | + | 0.998005i | ||||
\(895\) | − | 16540.1i | − | 0.617738i | ||||||
\(896\) | 1304.19 | 0.0486272 | ||||||||
\(897\) | 16282.1 | + | 4789.92i | 0.606067 | + | 0.178295i | ||||
\(898\) | − | 24795.7i | − | 0.921429i | ||||||
\(899\) | −3636.03 | −0.134893 | ||||||||
\(900\) | 21403.8 | + | 13786.4i | 0.792732 | + | 0.510608i | ||||
\(901\) | 37824.8 | 1.39859 | ||||||||
\(902\) | − | 1282.50i | − | 0.0473420i | ||||||
\(903\) | 7483.52 | + | 2201.53i | 0.275787 | + | 0.0811321i | ||||
\(904\) | −4197.37 | −0.154428 | ||||||||
\(905\) | − | 61680.8i | − | 2.26557i | ||||||
\(906\) | −25882.2 | − | 7614.12i | −0.949094 | − | 0.279208i | ||||
\(907\) | −17757.5 | −0.650084 | −0.325042 | − | 0.945700i | \(-0.605378\pi\) | ||||
−0.325042 | + | 0.945700i | \(0.605378\pi\) | |||||||
\(908\) | 18473.1 | 0.675166 | ||||||||
\(909\) | −18338.1 | − | 11811.8i | −0.669126 | − | 0.430992i | ||||
\(910\) | 31846.7 | 1.16012 | ||||||||
\(911\) | − | 32005.8i | − | 1.16400i | −0.813190 | − | 0.581998i | \(-0.802271\pi\) | ||
0.813190 | − | 0.581998i | \(-0.197729\pi\) | |||||||
\(912\) | −547.431 | + | 1860.85i | −0.0198764 | + | 0.0675645i | ||||
\(913\) | 1591.17 | 0.0576779 | ||||||||
\(914\) | − | 5754.96i | − | 0.208268i | ||||||
\(915\) | −19765.3 | + | 67186.8i | −0.714120 | + | 2.42746i | ||||
\(916\) | − | 14612.3i | − | 0.527077i | ||||||
\(917\) | 21042.2 | 0.757771 | ||||||||
\(918\) | 16961.5 | + | 19635.6i | 0.609819 | + | 0.705960i | ||||
\(919\) | 33130.1i | 1.18919i | 0.804027 | + | 0.594593i | \(0.202687\pi\) | ||||
−0.804027 | + | 0.594593i | \(0.797313\pi\) | |||||||
\(920\) | − | 6031.53i | − | 0.216145i | ||||||
\(921\) | −3043.72 | + | 10346.3i | −0.108897 | + | 0.370166i | ||||
\(922\) | 10443.9i | 0.373049i | ||||||||
\(923\) | 29785.0 | 1.06217 | ||||||||
\(924\) | −607.922 | + | 2066.47i | −0.0216441 | + | 0.0735734i | ||||
\(925\) | − | 52210.3i | − | 1.85585i | ||||||
\(926\) | − | 32127.2i | − | 1.14014i | ||||||
\(927\) | −28008.4 | + | 43483.8i | −0.992359 | + | 1.54066i | ||||
\(928\) | − | 3786.41i | − | 0.133939i | ||||||
\(929\) | −6394.41 | −0.225827 | −0.112914 | − | 0.993605i | \(-0.536018\pi\) | ||||
−0.112914 | + | 0.993605i | \(0.536018\pi\) | |||||||
\(930\) | −1711.79 | + | 5818.79i | −0.0603569 | + | 0.205167i | ||||
\(931\) | −5580.39 | −0.196445 | ||||||||
\(932\) | 5215.59 | 0.183307 | ||||||||
\(933\) | 25524.0 | + | 7508.73i | 0.895623 | + | 0.263478i | ||||
\(934\) | 38421.2 | 1.34602 | ||||||||
\(935\) | −17864.3 | −0.624841 | ||||||||
\(936\) | 9624.18 | − | 14941.8i | 0.336086 | − | 0.521782i | ||||
\(937\) | 30950.9i | 1.07910i | 0.841952 | + | 0.539552i | \(0.181406\pi\) | ||||
−0.841952 | + | 0.539552i | \(0.818594\pi\) | |||||||
\(938\) | − | 21289.9i | − | 0.741086i | ||||||
\(939\) | 20844.7 | + | 6132.16i | 0.724431 | + | 0.213116i | ||||
\(940\) | − | 2872.29i | − | 0.0996637i | ||||||
\(941\) | −6243.39 | −0.216290 | −0.108145 | − | 0.994135i | \(-0.534491\pi\) | ||||
−0.108145 | + | 0.994135i | \(0.534491\pi\) | |||||||
\(942\) | 19671.5 | + | 5787.04i | 0.680396 | + | 0.200161i | ||||
\(943\) | − | 2502.59i | − | 0.0864216i | ||||||
\(944\) | 2722.05 | − | 6720.68i | 0.0938508 | − | 0.231715i | ||||
\(945\) | −17748.0 | − | 20546.0i | −0.610944 | − | 0.707262i | ||||
\(946\) | 2997.26i | 0.103012i | ||||||||
\(947\) | 43732.9i | 1.50067i | 0.661061 | + | 0.750333i | \(0.270107\pi\) | ||||
−0.661061 | + | 0.750333i | \(0.729893\pi\) | |||||||
\(948\) | 1400.26 | − | 4759.83i | 0.0479731 | − | 0.163072i | ||||
\(949\) | −26962.9 | −0.922289 | ||||||||
\(950\) | 10999.9 | 0.375667 | ||||||||
\(951\) | −26992.2 | − | 7940.66i | −0.920380 | − | 0.270761i | ||||
\(952\) | − | 7537.62i | − | 0.256613i | ||||||
\(953\) | 8829.30i | 0.300114i | 0.988677 | + | 0.150057i | \(0.0479458\pi\) | ||||
−0.988677 | + | 0.150057i | \(0.952054\pi\) | |||||||
\(954\) | −11960.8 | + | 18569.4i | −0.405916 | + | 0.630196i | ||||
\(955\) | 30019.4i | 1.01718i | ||||||||
\(956\) | 27743.2i | 0.938576i | ||||||||
\(957\) | 5999.50 | + | 1764.96i | 0.202650 | + | 0.0596164i | ||||
\(958\) | 22306.0i | 0.752268i | ||||||||
\(959\) | 4472.80i | 0.150609i | ||||||||
\(960\) | −6059.45 | − | 1782.59i | −0.203716 | − | 0.0599301i | ||||
\(961\) | 28846.7 | 0.968303 | ||||||||
\(962\) | −36447.5 | −1.22153 | ||||||||
\(963\) | −14674.4 | + | 22782.3i | −0.491043 | + | 0.762358i | ||||
\(964\) | 3897.28 | 0.130210 | ||||||||
\(965\) | 31477.8i | 1.05006i | ||||||||
\(966\) | −1186.26 | + | 4032.39i | −0.0395108 | + | 0.134306i | ||||
\(967\) | − | 28794.6i | − | 0.957572i | −0.877932 | − | 0.478786i | \(-0.841077\pi\) | ||
0.877932 | − | 0.478786i | \(-0.158923\pi\) | |||||||
\(968\) | 9820.35 | 0.326072 | ||||||||
\(969\) | 10754.8 | + | 3163.89i | 0.356548 | + | 0.104891i | ||||
\(970\) | 50674.9 | 1.67739 | ||||||||
\(971\) | 55951.4i | 1.84919i | 0.380947 | + | 0.924597i | \(0.375598\pi\) | ||||
−0.380947 | + | 0.924597i | \(0.624402\pi\) | |||||||
\(972\) | −15003.2 | + | 2117.88i | −0.495092 | + | 0.0698880i | ||||
\(973\) | −27684.2 | −0.912144 | ||||||||
\(974\) | −14712.0 | −0.483986 | ||||||||
\(975\) | −96692.5 | − | 28445.4i | −3.17604 | − | 0.934339i | ||||
\(976\) | − | 11354.1i | − | 0.372371i | ||||||
\(977\) | −5523.97 | −0.180888 | −0.0904440 | − | 0.995902i | \(-0.528829\pi\) | ||||
−0.0904440 | + | 0.995902i | \(0.528829\pi\) | |||||||
\(978\) | 3925.55 | − | 13343.9i | 0.128349 | − | 0.436288i | ||||
\(979\) | 11167.7 | 0.364578 | ||||||||
\(980\) | − | 18171.4i | − | 0.592309i | ||||||
\(981\) | −28845.6 | + | 44783.5i | −0.938806 | + | 1.45752i | ||||
\(982\) | 4800.09i | 0.155985i | ||||||||
\(983\) | 22325.7 | 0.724394 | 0.362197 | − | 0.932101i | \(-0.382027\pi\) | ||||
0.362197 | + | 0.932101i | \(0.382027\pi\) | |||||||
\(984\) | −2514.18 | − | 739.630i | −0.0814522 | − | 0.0239619i | ||||
\(985\) | 33064.4 | 1.06956 | ||||||||
\(986\) | −21883.7 | −0.706814 | ||||||||
\(987\) | −564.914 | + | 1920.28i | −0.0182183 | + | 0.0619282i | ||||
\(988\) | − | 7678.93i | − | 0.247267i | ||||||
\(989\) | 5848.69i | 0.188046i | ||||||||
\(990\) | 5648.97 | − | 8770.17i | 0.181349 | − | 0.281550i | ||||
\(991\) | − | 16996.5i | − | 0.544816i | −0.962182 | − | 0.272408i | \(-0.912180\pi\) | ||
0.962182 | − | 0.272408i | \(-0.0878201\pi\) | |||||||
\(992\) | − | 983.331i | − | 0.0314726i | ||||||
\(993\) | −1622.91 | + | 5516.66i | −0.0518645 | + | 0.176300i | ||||
\(994\) | 7376.50i | 0.235381i | ||||||||
\(995\) | 11679.3i | 0.372118i | ||||||||
\(996\) | 917.642 | − | 3119.28i | 0.0291934 | − | 0.0992351i | ||||
\(997\) | −19053.3 | −0.605241 | −0.302621 | − | 0.953111i | \(-0.597861\pi\) | ||||
−0.302621 | + | 0.953111i | \(0.597861\pi\) | |||||||
\(998\) | −36439.0 | −1.15577 | ||||||||
\(999\) | 20312.0 | + | 23514.3i | 0.643285 | + | 0.744703i |
(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 | 354.4.c.a.353.14 | yes | 30 | |
3.2 | odd | 2 | 354.4.c.b.353.13 | yes | 30 | ||
59.58 | odd | 2 | 354.4.c.b.353.14 | yes | 30 | ||
177.176 | even | 2 | inner | 354.4.c.a.353.13 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.c.a.353.13 | ✓ | 30 | 177.176 | even | 2 | inner | |
354.4.c.a.353.14 | yes | 30 | 1.1 | even | 1 | trivial | |
354.4.c.b.353.13 | yes | 30 | 3.2 | odd | 2 | ||
354.4.c.b.353.14 | yes | 30 | 59.58 | odd | 2 |