Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,5,Mod(34,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.34");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.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: | \(3.61794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 110x^{6} + 7113x^{4} + 190880x^{2} + 4177936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.4 | ||
Root | \(3.16228 - 4.78865i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.34 |
Dual form | 35.5.c.e.34.6 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.78865i | − | 1.19716i | −0.801062 | − | 0.598582i | \(-0.795731\pi\) | ||
0.801062 | − | 0.598582i | \(-0.204269\pi\) | |||||||
\(3\) | 9.48683 | 1.05409 | 0.527046 | − | 0.849837i | \(-0.323299\pi\) | ||||
0.527046 | + | 0.849837i | \(0.323299\pi\) | |||||||
\(4\) | −6.93120 | −0.433200 | ||||||||
\(5\) | 23.8259 | − | 7.57153i | 0.953035 | − | 0.302861i | ||||
\(6\) | − | 45.4292i | − | 1.26192i | ||||||
\(7\) | −9.59562 | + | 48.0513i | −0.195829 | + | 0.980638i | ||||
\(8\) | − | 43.4273i | − | 0.678552i | ||||||
\(9\) | 9.00000 | 0.111111 | ||||||||
\(10\) | −36.2574 | − | 114.094i | −0.362574 | − | 1.14094i | ||||
\(11\) | −134.413 | −1.11085 | −0.555425 | − | 0.831567i | \(-0.687444\pi\) | ||||
−0.555425 | + | 0.831567i | \(0.687444\pi\) | |||||||
\(12\) | −65.7551 | −0.456633 | ||||||||
\(13\) | −54.4114 | −0.321961 | −0.160981 | − | 0.986958i | \(-0.551466\pi\) | ||||
−0.160981 | + | 0.986958i | \(0.551466\pi\) | |||||||
\(14\) | 230.101 | + | 45.9501i | 1.17398 | + | 0.234439i | ||||
\(15\) | 226.032 | − | 71.8298i | 1.00459 | − | 0.319244i | ||||
\(16\) | −318.858 | −1.24554 | ||||||||
\(17\) | 411.531 | 1.42398 | 0.711992 | − | 0.702188i | \(-0.247793\pi\) | ||||
0.711992 | + | 0.702188i | \(0.247793\pi\) | |||||||
\(18\) | − | 43.0979i | − | 0.133018i | ||||||
\(19\) | 561.335i | 1.55494i | 0.628918 | + | 0.777472i | \(0.283498\pi\) | ||||
−0.628918 | + | 0.777472i | \(0.716502\pi\) | |||||||
\(20\) | −165.142 | + | 52.4797i | −0.412855 | + | 0.131199i | ||||
\(21\) | −91.0320 | + | 455.854i | −0.206422 | + | 1.03368i | ||||
\(22\) | 643.656i | 1.32987i | ||||||||
\(23\) | 30.3793i | 0.0574277i | 0.999588 | + | 0.0287139i | \(0.00914116\pi\) | ||||
−0.999588 | + | 0.0287139i | \(0.990859\pi\) | |||||||
\(24\) | − | 411.988i | − | 0.715257i | ||||||
\(25\) | 510.344 | − | 360.796i | 0.816550 | − | 0.577274i | ||||
\(26\) | 260.557i | 0.385440i | ||||||||
\(27\) | −683.052 | −0.936971 | ||||||||
\(28\) | 66.5091 | − | 333.053i | 0.0848331 | − | 0.424812i | ||||
\(29\) | −66.2752 | −0.0788052 | −0.0394026 | − | 0.999223i | \(-0.512545\pi\) | ||||
−0.0394026 | + | 0.999223i | \(0.512545\pi\) | |||||||
\(30\) | −343.968 | − | 1082.39i | −0.382187 | − | 1.20265i | ||||
\(31\) | − | 912.751i | − | 0.949792i | −0.880042 | − | 0.474896i | \(-0.842486\pi\) | ||
0.880042 | − | 0.474896i | \(-0.157514\pi\) | |||||||
\(32\) | 832.061i | 0.812560i | ||||||||
\(33\) | −1275.15 | −1.17094 | ||||||||
\(34\) | − | 1970.68i | − | 1.70474i | ||||||
\(35\) | 135.197 | + | 1217.52i | 0.110365 | + | 0.993891i | ||||
\(36\) | −62.3808 | −0.0481333 | ||||||||
\(37\) | 1602.70i | 1.17071i | 0.810776 | + | 0.585356i | \(0.199045\pi\) | ||||
−0.810776 | + | 0.585356i | \(0.800955\pi\) | |||||||
\(38\) | 2688.04 | 1.86152 | ||||||||
\(39\) | −516.192 | −0.339377 | ||||||||
\(40\) | −328.811 | − | 1034.69i | −0.205507 | − | 0.646684i | ||||
\(41\) | 241.247i | 0.143514i | 0.997422 | + | 0.0717570i | \(0.0228606\pi\) | ||||
−0.997422 | + | 0.0717570i | \(0.977139\pi\) | |||||||
\(42\) | 2182.93 | + | 435.921i | 1.23749 | + | 0.247121i | ||||
\(43\) | − | 2134.40i | − | 1.15435i | −0.816619 | − | 0.577176i | \(-0.804154\pi\) | ||
0.816619 | − | 0.577176i | \(-0.195846\pi\) | |||||||
\(44\) | 931.642 | 0.481220 | ||||||||
\(45\) | 214.433 | − | 68.1437i | 0.105893 | − | 0.0336512i | ||||
\(46\) | 145.476 | 0.0687504 | ||||||||
\(47\) | 517.961 | 0.234478 | 0.117239 | − | 0.993104i | \(-0.462596\pi\) | ||||
0.117239 | + | 0.993104i | \(0.462596\pi\) | |||||||
\(48\) | −3024.95 | −1.31291 | ||||||||
\(49\) | −2216.85 | − | 922.163i | −0.923302 | − | 0.384075i | ||||
\(50\) | −1727.73 | − | 2443.86i | −0.691091 | − | 0.977544i | ||||
\(51\) | 3904.13 | 1.50101 | ||||||||
\(52\) | 377.136 | 0.139474 | ||||||||
\(53\) | − | 145.636i | − | 0.0518464i | −0.999664 | − | 0.0259232i | \(-0.991747\pi\) | ||
0.999664 | − | 0.0259232i | \(-0.00825253\pi\) | |||||||
\(54\) | 3270.90i | 1.12171i | ||||||||
\(55\) | −3202.50 | + | 1017.71i | −1.05868 | + | 0.336433i | ||||
\(56\) | 2086.74 | + | 416.712i | 0.665414 | + | 0.132880i | ||||
\(57\) | 5325.29i | 1.63905i | ||||||||
\(58\) | 317.369i | 0.0943427i | ||||||||
\(59\) | 4874.46i | 1.40031i | 0.713993 | + | 0.700153i | \(0.246885\pi\) | ||||
−0.713993 | + | 0.700153i | \(0.753115\pi\) | |||||||
\(60\) | −1566.67 | + | 497.867i | −0.435187 | + | 0.138296i | ||||
\(61\) | − | 4940.25i | − | 1.32767i | −0.747881 | − | 0.663833i | \(-0.768929\pi\) | ||
0.747881 | − | 0.663833i | \(-0.231071\pi\) | |||||||
\(62\) | −4370.85 | −1.13706 | ||||||||
\(63\) | −86.3606 | + | 432.461i | −0.0217588 | + | 0.108960i | ||||
\(64\) | −1117.27 | −0.272771 | ||||||||
\(65\) | −1296.40 | + | 411.978i | −0.306840 | + | 0.0975095i | ||||
\(66\) | 6106.26i | 1.40180i | ||||||||
\(67\) | − | 3909.19i | − | 0.870837i | −0.900228 | − | 0.435419i | \(-0.856600\pi\) | ||
0.900228 | − | 0.435419i | \(-0.143400\pi\) | |||||||
\(68\) | −2852.40 | −0.616869 | ||||||||
\(69\) | 288.203i | 0.0605341i | ||||||||
\(70\) | 5830.26 | − | 647.414i | 1.18985 | − | 0.132125i | ||||
\(71\) | 428.660 | 0.0850346 | 0.0425173 | − | 0.999096i | \(-0.486462\pi\) | ||||
0.0425173 | + | 0.999096i | \(0.486462\pi\) | |||||||
\(72\) | − | 390.846i | − | 0.0753947i | ||||||
\(73\) | 8360.13 | 1.56880 | 0.784400 | − | 0.620256i | \(-0.212971\pi\) | ||||
0.784400 | + | 0.620256i | \(0.212971\pi\) | |||||||
\(74\) | 7674.80 | 1.40153 | ||||||||
\(75\) | 4841.55 | − | 3422.81i | 0.860720 | − | 0.608500i | ||||
\(76\) | − | 3890.72i | − | 0.673601i | ||||||
\(77\) | 1289.77 | − | 6458.71i | 0.217537 | − | 1.08934i | ||||
\(78\) | 2471.87i | 0.406290i | ||||||||
\(79\) | −4050.04 | −0.648940 | −0.324470 | − | 0.945896i | \(-0.605186\pi\) | ||||
−0.324470 | + | 0.945896i | \(0.605186\pi\) | |||||||
\(80\) | −7597.06 | + | 2414.24i | −1.18704 | + | 0.377225i | ||||
\(81\) | −7209.00 | −1.09877 | ||||||||
\(82\) | 1155.25 | 0.171810 | ||||||||
\(83\) | −630.599 | −0.0915370 | −0.0457685 | − | 0.998952i | \(-0.514574\pi\) | ||||
−0.0457685 | + | 0.998952i | \(0.514574\pi\) | |||||||
\(84\) | 630.961 | − | 3159.62i | 0.0894219 | − | 0.447791i | ||||
\(85\) | 9805.09 | − | 3115.92i | 1.35711 | − | 0.431269i | ||||
\(86\) | −10220.9 | −1.38195 | ||||||||
\(87\) | −628.742 | −0.0830680 | ||||||||
\(88\) | 5837.19i | 0.753770i | ||||||||
\(89\) | − | 13024.0i | − | 1.64424i | −0.569317 | − | 0.822118i | \(-0.692792\pi\) | ||
0.569317 | − | 0.822118i | \(-0.307208\pi\) | |||||||
\(90\) | −326.317 | − | 1026.84i | −0.0402860 | − | 0.126771i | ||||
\(91\) | 522.111 | − | 2614.54i | 0.0630493 | − | 0.315727i | ||||
\(92\) | − | 210.565i | − | 0.0248777i | ||||||
\(93\) | − | 8659.11i | − | 1.00117i | ||||||
\(94\) | − | 2480.33i | − | 0.280708i | ||||||
\(95\) | 4250.16 | + | 13374.3i | 0.470932 | + | 1.48192i | ||||
\(96\) | 7893.63i | 0.856513i | ||||||||
\(97\) | 61.6477 | 0.00655199 | 0.00327600 | − | 0.999995i | \(-0.498957\pi\) | ||||
0.00327600 | + | 0.999995i | \(0.498957\pi\) | |||||||
\(98\) | −4415.92 | + | 10615.7i | −0.459800 | + | 1.10534i | ||||
\(99\) | −1209.72 | −0.123428 | ||||||||
\(100\) | −3537.30 | + | 2500.75i | −0.353730 | + | 0.250075i | ||||
\(101\) | − | 4375.30i | − | 0.428909i | −0.976734 | − | 0.214454i | \(-0.931203\pi\) | ||
0.976734 | − | 0.214454i | \(-0.0687974\pi\) | |||||||
\(102\) | − | 18695.5i | − | 1.79695i | ||||||
\(103\) | −10327.6 | −0.973478 | −0.486739 | − | 0.873547i | \(-0.661814\pi\) | ||||
−0.486739 | + | 0.873547i | \(0.661814\pi\) | |||||||
\(104\) | 2362.94i | 0.218467i | ||||||||
\(105\) | 1282.60 | + | 11550.4i | 0.116335 | + | 1.04765i | ||||
\(106\) | −697.402 | −0.0620686 | ||||||||
\(107\) | − | 772.444i | − | 0.0674683i | −0.999431 | − | 0.0337341i | \(-0.989260\pi\) | ||
0.999431 | − | 0.0337341i | \(-0.0107399\pi\) | |||||||
\(108\) | 4734.37 | 0.405896 | ||||||||
\(109\) | −10145.5 | −0.853926 | −0.426963 | − | 0.904269i | \(-0.640417\pi\) | ||||
−0.426963 | + | 0.904269i | \(0.640417\pi\) | |||||||
\(110\) | 4873.46 | + | 15335.7i | 0.402765 | + | 1.26741i | ||||
\(111\) | 15204.6i | 1.23404i | ||||||||
\(112\) | 3059.64 | − | 15321.5i | 0.243912 | − | 1.22142i | ||||
\(113\) | − | 7157.54i | − | 0.560541i | −0.959921 | − | 0.280270i | \(-0.909576\pi\) | ||
0.959921 | − | 0.280270i | \(-0.0904241\pi\) | |||||||
\(114\) | 25501.0 | 1.96222 | ||||||||
\(115\) | 230.017 | + | 723.812i | 0.0173926 | + | 0.0547306i | ||||
\(116\) | 459.367 | 0.0341384 | ||||||||
\(117\) | −489.703 | −0.0357735 | ||||||||
\(118\) | 23342.1 | 1.67639 | ||||||||
\(119\) | −3948.90 | + | 19774.6i | −0.278857 | + | 1.39641i | ||||
\(120\) | −3119.38 | − | 9815.97i | −0.216623 | − | 0.681665i | ||||
\(121\) | 3425.80 | 0.233987 | ||||||||
\(122\) | −23657.1 | −1.58943 | ||||||||
\(123\) | 2288.67i | 0.151277i | ||||||||
\(124\) | 6326.45i | 0.411450i | ||||||||
\(125\) | 9427.61 | − | 12460.4i | 0.603367 | − | 0.797464i | ||||
\(126\) | 2070.91 | + | 413.551i | 0.130443 | + | 0.0260488i | ||||
\(127\) | 27311.1i | 1.69329i | 0.532158 | + | 0.846645i | \(0.321381\pi\) | ||||
−0.532158 | + | 0.846645i | \(0.678619\pi\) | |||||||
\(128\) | 18663.2i | 1.13911i | ||||||||
\(129\) | − | 20248.7i | − | 1.21679i | ||||||
\(130\) | 1972.82 | + | 6208.01i | 0.116735 | + | 0.367338i | ||||
\(131\) | 8633.14i | 0.503067i | 0.967849 | + | 0.251534i | \(0.0809349\pi\) | ||||
−0.967849 | + | 0.251534i | \(0.919065\pi\) | |||||||
\(132\) | 8838.33 | 0.507250 | ||||||||
\(133\) | −26972.8 | − | 5386.35i | −1.52484 | − | 0.304503i | ||||
\(134\) | −18719.7 | −1.04253 | ||||||||
\(135\) | −16274.3 | + | 5171.75i | −0.892966 | + | 0.283772i | ||||
\(136\) | − | 17871.7i | − | 0.966247i | ||||||
\(137\) | − | 21972.9i | − | 1.17070i | −0.810780 | − | 0.585350i | \(-0.800957\pi\) | ||
0.810780 | − | 0.585350i | \(-0.199043\pi\) | |||||||
\(138\) | 1380.10 | 0.0724693 | ||||||||
\(139\) | 20725.5i | 1.07269i | 0.843998 | + | 0.536346i | \(0.180196\pi\) | ||||
−0.843998 | + | 0.536346i | \(0.819804\pi\) | |||||||
\(140\) | −937.080 | − | 8438.85i | −0.0478102 | − | 0.430553i | ||||
\(141\) | 4913.81 | 0.247161 | ||||||||
\(142\) | − | 2052.70i | − | 0.101800i | ||||||
\(143\) | 7313.59 | 0.357650 | ||||||||
\(144\) | −2869.72 | −0.138393 | ||||||||
\(145\) | −1579.06 | + | 501.804i | −0.0751041 | + | 0.0238670i | ||||
\(146\) | − | 40033.8i | − | 1.87811i | ||||||
\(147\) | −21030.9 | − | 8748.41i | −0.973246 | − | 0.404850i | ||||
\(148\) | − | 11108.7i | − | 0.507152i | ||||||
\(149\) | 25356.3 | 1.14213 | 0.571063 | − | 0.820906i | \(-0.306531\pi\) | ||||
0.571063 | + | 0.820906i | \(0.306531\pi\) | |||||||
\(150\) | −16390.7 | − | 23184.5i | −0.728474 | − | 1.03042i | ||||
\(151\) | 33662.7 | 1.47637 | 0.738186 | − | 0.674598i | \(-0.235683\pi\) | ||||
0.738186 | + | 0.674598i | \(0.235683\pi\) | |||||||
\(152\) | 24377.3 | 1.05511 | ||||||||
\(153\) | 3703.78 | 0.158220 | ||||||||
\(154\) | −30928.5 | − | 6176.28i | −1.30412 | − | 0.260427i | ||||
\(155\) | −6910.91 | − | 21747.1i | −0.287655 | − | 0.905185i | ||||
\(156\) | 3577.83 | 0.147018 | ||||||||
\(157\) | 14735.6 | 0.597819 | 0.298910 | − | 0.954281i | \(-0.403377\pi\) | ||||
0.298910 | + | 0.954281i | \(0.403377\pi\) | |||||||
\(158\) | 19394.2i | 0.776887i | ||||||||
\(159\) | − | 1381.63i | − | 0.0546509i | ||||||
\(160\) | 6299.97 | + | 19824.6i | 0.246093 | + | 0.774398i | ||||
\(161\) | −1459.76 | − | 291.508i | −0.0563158 | − | 0.0112460i | ||||
\(162\) | 34521.4i | 1.31540i | ||||||||
\(163\) | − | 20294.3i | − | 0.763835i | −0.924196 | − | 0.381918i | \(-0.875264\pi\) | ||
0.924196 | − | 0.381918i | \(-0.124736\pi\) | |||||||
\(164\) | − | 1672.13i | − | 0.0621702i | ||||||
\(165\) | −30381.6 | + | 9654.84i | −1.11594 | + | 0.354632i | ||||
\(166\) | 3019.72i | 0.109585i | ||||||||
\(167\) | 43049.6 | 1.54361 | 0.771803 | − | 0.635862i | \(-0.219355\pi\) | ||||
0.771803 | + | 0.635862i | \(0.219355\pi\) | |||||||
\(168\) | 19796.5 | + | 3953.28i | 0.701408 | + | 0.140068i | ||||
\(169\) | −25600.4 | −0.896341 | ||||||||
\(170\) | −14921.1 | − | 46953.2i | −0.516300 | − | 1.62468i | ||||
\(171\) | 5052.01i | 0.172772i | ||||||||
\(172\) | 14793.9i | 0.500066i | ||||||||
\(173\) | 22174.3 | 0.740898 | 0.370449 | − | 0.928853i | \(-0.379204\pi\) | ||||
0.370449 | + | 0.928853i | \(0.379204\pi\) | |||||||
\(174\) | 3010.83i | 0.0994460i | ||||||||
\(175\) | 12439.7 | + | 27984.7i | 0.406193 | + | 0.913787i | ||||
\(176\) | 42858.6 | 1.38361 | ||||||||
\(177\) | 46243.2i | 1.47605i | ||||||||
\(178\) | −62367.4 | −1.96842 | ||||||||
\(179\) | 45793.4 | 1.42921 | 0.714606 | − | 0.699528i | \(-0.246606\pi\) | ||||
0.714606 | + | 0.699528i | \(0.246606\pi\) | |||||||
\(180\) | −1486.28 | + | 472.318i | −0.0458727 | + | 0.0145777i | ||||
\(181\) | 52068.4i | 1.58934i | 0.607041 | + | 0.794670i | \(0.292356\pi\) | ||||
−0.607041 | + | 0.794670i | \(0.707644\pi\) | |||||||
\(182\) | −12520.1 | − | 2500.21i | −0.377977 | − | 0.0754803i | ||||
\(183\) | − | 46867.3i | − | 1.39948i | ||||||
\(184\) | 1319.29 | 0.0389677 | ||||||||
\(185\) | 12134.9 | + | 38185.8i | 0.354563 | + | 1.11573i | ||||
\(186\) | −41465.5 | −1.19856 | ||||||||
\(187\) | −55315.1 | −1.58183 | ||||||||
\(188\) | −3590.09 | −0.101576 | ||||||||
\(189\) | 6554.31 | − | 32821.5i | 0.183486 | − | 0.918830i | ||||
\(190\) | 64044.8 | − | 20352.5i | 1.77409 | − | 0.563782i | ||||
\(191\) | −64608.3 | −1.77101 | −0.885506 | − | 0.464629i | \(-0.846188\pi\) | ||||
−0.885506 | + | 0.464629i | \(0.846188\pi\) | |||||||
\(192\) | −10599.4 | −0.287526 | ||||||||
\(193\) | − | 15621.6i | − | 0.419383i | −0.977768 | − | 0.209691i | \(-0.932754\pi\) | ||
0.977768 | − | 0.209691i | \(-0.0672459\pi\) | |||||||
\(194\) | − | 295.209i | − | 0.00784381i | ||||||
\(195\) | −12298.7 | + | 3908.36i | −0.323438 | + | 0.102784i | ||||
\(196\) | 15365.4 | + | 6391.70i | 0.399974 | + | 0.166381i | ||||
\(197\) | 50010.7i | 1.28864i | 0.764757 | + | 0.644318i | \(0.222859\pi\) | ||||
−0.764757 | + | 0.644318i | \(0.777141\pi\) | |||||||
\(198\) | 5792.91i | 0.147763i | ||||||||
\(199\) | 47729.6i | 1.20526i | 0.798019 | + | 0.602632i | \(0.205881\pi\) | ||||
−0.798019 | + | 0.602632i | \(0.794119\pi\) | |||||||
\(200\) | −15668.4 | − | 22162.9i | −0.391711 | − | 0.554072i | ||||
\(201\) | − | 37085.8i | − | 0.917943i | ||||||
\(202\) | −20951.8 | −0.513474 | ||||||||
\(203\) | 635.952 | − | 3184.61i | 0.0154323 | − | 0.0772794i | ||||
\(204\) | −27060.3 | −0.650238 | ||||||||
\(205\) | 1826.61 | + | 5747.92i | 0.0434648 | + | 0.136774i | ||||
\(206\) | 49455.4i | 1.16541i | ||||||||
\(207\) | 273.413i | 0.00638086i | ||||||||
\(208\) | 17349.5 | 0.401015 | ||||||||
\(209\) | − | 75450.6i | − | 1.72731i | ||||||
\(210\) | 55310.7 | − | 6141.90i | 1.25421 | − | 0.139272i | ||||
\(211\) | −34019.8 | −0.764129 | −0.382064 | − | 0.924136i | \(-0.624787\pi\) | ||||
−0.382064 | + | 0.924136i | \(0.624787\pi\) | |||||||
\(212\) | 1009.43i | 0.0224598i | ||||||||
\(213\) | 4066.62 | 0.0896344 | ||||||||
\(214\) | −3698.97 | −0.0807706 | ||||||||
\(215\) | −16160.7 | − | 50853.9i | −0.349609 | − | 1.10014i | ||||
\(216\) | 29663.1i | 0.635784i | ||||||||
\(217\) | 43858.8 | + | 8758.41i | 0.931403 | + | 0.185997i | ||||
\(218\) | 48583.2i | 1.02229i | ||||||||
\(219\) | 79311.2 | 1.65366 | ||||||||
\(220\) | 22197.2 | − | 7053.95i | 0.458619 | − | 0.145743i | ||||
\(221\) | −22392.0 | −0.458467 | ||||||||
\(222\) | 72809.5 | 1.47735 | ||||||||
\(223\) | −21688.7 | −0.436137 | −0.218068 | − | 0.975933i | \(-0.569976\pi\) | ||||
−0.218068 | + | 0.975933i | \(0.569976\pi\) | |||||||
\(224\) | −39981.6 | − | 7984.14i | −0.796827 | − | 0.159123i | ||||
\(225\) | 4593.10 | − | 3247.17i | 0.0907278 | − | 0.0641416i | ||||
\(226\) | −34275.0 | −0.671059 | ||||||||
\(227\) | 39551.8 | 0.767563 | 0.383782 | − | 0.923424i | \(-0.374622\pi\) | ||||
0.383782 | + | 0.923424i | \(0.374622\pi\) | |||||||
\(228\) | − | 36910.6i | − | 0.710038i | ||||||
\(229\) | 24575.0i | 0.468622i | 0.972162 | + | 0.234311i | \(0.0752834\pi\) | ||||
−0.972162 | + | 0.234311i | \(0.924717\pi\) | |||||||
\(230\) | 3466.09 | − | 1101.47i | 0.0655215 | − | 0.0208218i | ||||
\(231\) | 12235.9 | − | 61272.7i | 0.229304 | − | 1.14827i | ||||
\(232\) | 2878.16i | 0.0534735i | ||||||||
\(233\) | − | 24450.9i | − | 0.450385i | −0.974314 | − | 0.225192i | \(-0.927699\pi\) | ||
0.974314 | − | 0.225192i | \(-0.0723011\pi\) | |||||||
\(234\) | 2345.02i | 0.0428267i | ||||||||
\(235\) | 12340.9 | − | 3921.75i | 0.223465 | − | 0.0710141i | ||||
\(236\) | − | 33785.9i | − | 0.606612i | ||||||
\(237\) | −38422.0 | −0.684043 | ||||||||
\(238\) | 94693.7 | + | 18909.9i | 1.67173 | + | 0.333838i | ||||
\(239\) | −16698.2 | −0.292330 | −0.146165 | − | 0.989260i | \(-0.546693\pi\) | ||||
−0.146165 | + | 0.989260i | \(0.546693\pi\) | |||||||
\(240\) | −72072.0 | + | 22903.5i | −1.25125 | + | 0.397630i | ||||
\(241\) | − | 29546.7i | − | 0.508715i | −0.967110 | − | 0.254357i | \(-0.918136\pi\) | ||
0.967110 | − | 0.254357i | \(-0.0818639\pi\) | |||||||
\(242\) | − | 16405.0i | − | 0.280121i | ||||||
\(243\) | −13063.4 | −0.221229 | ||||||||
\(244\) | 34241.8i | 0.575145i | ||||||||
\(245\) | −59800.5 | − | 5186.42i | −0.996260 | − | 0.0864043i | ||||
\(246\) | 10959.6 | 0.181103 | ||||||||
\(247\) | − | 30543.0i | − | 0.500632i | ||||||
\(248\) | −39638.3 | −0.644484 | ||||||||
\(249\) | −5982.38 | −0.0964885 | ||||||||
\(250\) | −59668.4 | − | 45145.6i | −0.954694 | − | 0.722329i | ||||
\(251\) | − | 77102.9i | − | 1.22384i | −0.790921 | − | 0.611918i | \(-0.790398\pi\) | ||
0.790921 | − | 0.611918i | \(-0.209602\pi\) | |||||||
\(252\) | 598.582 | − | 2997.48i | 0.00942590 | − | 0.0472014i | ||||
\(253\) | − | 4083.36i | − | 0.0637936i | ||||||
\(254\) | 130783. | 2.02714 | ||||||||
\(255\) | 93019.2 | − | 29560.2i | 1.43052 | − | 0.454598i | ||||
\(256\) | 71495.3 | 1.09093 | ||||||||
\(257\) | −71422.5 | −1.08136 | −0.540678 | − | 0.841230i | \(-0.681832\pi\) | ||||
−0.540678 | + | 0.841230i | \(0.681832\pi\) | |||||||
\(258\) | −96963.9 | −1.45670 | ||||||||
\(259\) | −77012.0 | − | 15378.9i | −1.14804 | − | 0.229259i | ||||
\(260\) | 8985.60 | − | 2855.50i | 0.132923 | − | 0.0422411i | ||||
\(261\) | −596.477 | −0.00875614 | ||||||||
\(262\) | 41341.1 | 0.602254 | ||||||||
\(263\) | 103341.i | 1.49404i | 0.664804 | + | 0.747018i | \(0.268515\pi\) | ||||
−0.664804 | + | 0.747018i | \(0.731485\pi\) | |||||||
\(264\) | 55376.5i | 0.794543i | ||||||||
\(265\) | −1102.69 | − | 3469.91i | −0.0157022 | − | 0.0494114i | ||||
\(266\) | −25793.4 | + | 129164.i | −0.364540 | + | 1.82548i | ||||
\(267\) | − | 123556.i | − | 1.73318i | ||||||
\(268\) | 27095.4i | 0.377247i | ||||||||
\(269\) | 54702.4i | 0.755965i | 0.925813 | + | 0.377983i | \(0.123382\pi\) | ||||
−0.925813 | + | 0.377983i | \(0.876618\pi\) | |||||||
\(270\) | 24765.7 | + | 77932.0i | 0.339721 | + | 1.06903i | ||||
\(271\) | 64266.5i | 0.875077i | 0.899200 | + | 0.437539i | \(0.144150\pi\) | ||||
−0.899200 | + | 0.437539i | \(0.855850\pi\) | |||||||
\(272\) | −131220. | −1.77363 | ||||||||
\(273\) | 4953.18 | − | 24803.7i | 0.0664598 | − | 0.332806i | ||||
\(274\) | −105221. | −1.40152 | ||||||||
\(275\) | −68596.8 | + | 48495.6i | −0.907065 | + | 0.641265i | ||||
\(276\) | − | 1997.59i | − | 0.0262234i | ||||||
\(277\) | 35442.4i | 0.461916i | 0.972964 | + | 0.230958i | \(0.0741861\pi\) | ||||
−0.972964 | + | 0.230958i | \(0.925814\pi\) | |||||||
\(278\) | 99247.1 | 1.28419 | ||||||||
\(279\) | − | 8214.75i | − | 0.105532i | ||||||
\(280\) | 52873.5 | − | 5871.27i | 0.674407 | − | 0.0748886i | ||||
\(281\) | 71637.4 | 0.907250 | 0.453625 | − | 0.891193i | \(-0.350130\pi\) | ||||
0.453625 | + | 0.891193i | \(0.350130\pi\) | |||||||
\(282\) | − | 23530.5i | − | 0.295892i | ||||||
\(283\) | 40369.4 | 0.504056 | 0.252028 | − | 0.967720i | \(-0.418902\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418902\pi\) | |||||||
\(284\) | −2971.12 | −0.0368370 | ||||||||
\(285\) | 40320.6 | + | 126880.i | 0.496406 | + | 1.56208i | ||||
\(286\) | − | 35022.3i | − | 0.428166i | ||||||
\(287\) | −11592.2 | − | 2314.91i | −0.140735 | − | 0.0281042i | ||||
\(288\) | 7488.55i | 0.0902844i | ||||||||
\(289\) | 85837.0 | 1.02773 | ||||||||
\(290\) | 2402.97 | + | 7561.59i | 0.0285727 | + | 0.0899119i | ||||
\(291\) | 584.841 | 0.00690641 | ||||||||
\(292\) | −57945.7 | −0.679604 | ||||||||
\(293\) | −11461.9 | −0.133512 | −0.0667560 | − | 0.997769i | \(-0.521265\pi\) | ||||
−0.0667560 | + | 0.997769i | \(0.521265\pi\) | |||||||
\(294\) | −41893.1 | + | 100710.i | −0.484672 | + | 1.16513i | ||||
\(295\) | 36907.1 | + | 116138.i | 0.424098 | + | 1.33454i | ||||
\(296\) | 69601.2 | 0.794389 | ||||||||
\(297\) | 91810.9 | 1.04083 | ||||||||
\(298\) | − | 121423.i | − | 1.36731i | ||||||
\(299\) | − | 1652.98i | − | 0.0184895i | ||||||
\(300\) | −33557.7 | + | 23724.2i | −0.372864 | + | 0.263602i | ||||
\(301\) | 102561. | + | 20480.9i | 1.13200 | + | 0.226056i | ||||
\(302\) | − | 161199.i | − | 1.76746i | ||||||
\(303\) | − | 41507.7i | − | 0.452110i | ||||||
\(304\) | − | 178986.i | − | 1.93674i | ||||||
\(305\) | −37405.2 | − | 117706.i | −0.402098 | − | 1.26531i | ||||
\(306\) | − | 17736.1i | − | 0.189416i | ||||||
\(307\) | 111649. | 1.18462 | 0.592309 | − | 0.805711i | \(-0.298216\pi\) | ||||
0.592309 | + | 0.805711i | \(0.298216\pi\) | |||||||
\(308\) | −8939.68 | + | 44766.6i | −0.0942368 | + | 0.471903i | ||||
\(309\) | −97976.5 | −1.02614 | ||||||||
\(310\) | −104139. | + | 33094.0i | −1.08365 | + | 0.344370i | ||||
\(311\) | − | 26778.1i | − | 0.276859i | −0.990372 | − | 0.138429i | \(-0.955795\pi\) | ||
0.990372 | − | 0.138429i | \(-0.0442054\pi\) | |||||||
\(312\) | 22416.9i | 0.230285i | ||||||||
\(313\) | −87491.2 | −0.893050 | −0.446525 | − | 0.894771i | \(-0.647339\pi\) | ||||
−0.446525 | + | 0.894771i | \(0.647339\pi\) | |||||||
\(314\) | − | 70563.9i | − | 0.715687i | ||||||
\(315\) | 1216.78 | + | 10957.6i | 0.0122628 | + | 0.110432i | ||||
\(316\) | 28071.6 | 0.281121 | ||||||||
\(317\) | − | 46524.6i | − | 0.462982i | −0.972837 | − | 0.231491i | \(-0.925640\pi\) | ||
0.972837 | − | 0.231491i | \(-0.0743603\pi\) | |||||||
\(318\) | −6616.14 | −0.0654260 | ||||||||
\(319\) | 8908.24 | 0.0875408 | ||||||||
\(320\) | −26619.9 | + | 8459.44i | −0.259960 | + | 0.0826117i | ||||
\(321\) | − | 7328.05i | − | 0.0711178i | ||||||
\(322\) | −1395.93 | + | 6990.30i | −0.0134633 | + | 0.0674192i | ||||
\(323\) | 231007.i | 2.21421i | ||||||||
\(324\) | 49967.0 | 0.475985 | ||||||||
\(325\) | −27768.6 | + | 19631.4i | −0.262898 | + | 0.185860i | ||||
\(326\) | −97182.5 | −0.914435 | ||||||||
\(327\) | −96248.6 | −0.900117 | ||||||||
\(328\) | 10476.7 | 0.0973817 | ||||||||
\(329\) | −4970.15 | + | 24888.7i | −0.0459175 | + | 0.229938i | ||||
\(330\) | 46233.7 | + | 145487.i | 0.424552 | + | 1.33597i | ||||
\(331\) | −53803.7 | −0.491085 | −0.245542 | − | 0.969386i | \(-0.578966\pi\) | ||||
−0.245542 | + | 0.969386i | \(0.578966\pi\) | |||||||
\(332\) | 4370.80 | 0.0396538 | ||||||||
\(333\) | 14424.3i | 0.130079i | ||||||||
\(334\) | − | 206150.i | − | 1.84795i | ||||||
\(335\) | −29598.5 | − | 93139.8i | −0.263743 | − | 0.829938i | ||||
\(336\) | 29026.3 | − | 145353.i | 0.257106 | − | 1.28749i | ||||
\(337\) | − | 90016.3i | − | 0.792614i | −0.918118 | − | 0.396307i | \(-0.870292\pi\) | ||
0.918118 | − | 0.396307i | \(-0.129708\pi\) | |||||||
\(338\) | 122591.i | 1.07307i | ||||||||
\(339\) | − | 67902.4i | − | 0.590862i | ||||||
\(340\) | −67961.0 | + | 21597.1i | −0.587898 | + | 0.186826i | ||||
\(341\) | 122685.i | 1.05508i | ||||||||
\(342\) | 24192.3 | 0.206836 | ||||||||
\(343\) | 65583.1 | − | 97673.6i | 0.557448 | − | 0.830212i | ||||
\(344\) | −92691.3 | −0.783289 | ||||||||
\(345\) | 2182.14 | + | 6866.69i | 0.0183334 | + | 0.0576911i | ||||
\(346\) | − | 106185.i | − | 0.886976i | ||||||
\(347\) | − | 52980.3i | − | 0.440003i | −0.975500 | − | 0.220002i | \(-0.929394\pi\) | ||
0.975500 | − | 0.220002i | \(-0.0706062\pi\) | |||||||
\(348\) | 4357.93 | 0.0359851 | ||||||||
\(349\) | 122033.i | 1.00191i | 0.865474 | + | 0.500954i | \(0.167018\pi\) | ||||
−0.865474 | + | 0.500954i | \(0.832982\pi\) | |||||||
\(350\) | 134009. | − | 59569.2i | 1.09395 | − | 0.486279i | ||||
\(351\) | 37165.8 | 0.301668 | ||||||||
\(352\) | − | 111840.i | − | 0.902632i | ||||||
\(353\) | 26076.8 | 0.209269 | 0.104635 | − | 0.994511i | \(-0.466633\pi\) | ||||
0.104635 | + | 0.994511i | \(0.466633\pi\) | |||||||
\(354\) | 221443. | 1.76707 | ||||||||
\(355\) | 10213.2 | − | 3245.61i | 0.0810410 | − | 0.0257537i | ||||
\(356\) | 90271.9i | 0.712283i | ||||||||
\(357\) | −37462.5 | + | 187598.i | −0.293941 | + | 1.47195i | ||||
\(358\) | − | 219288.i | − | 1.71100i | ||||||
\(359\) | −105933. | −0.821946 | −0.410973 | − | 0.911647i | \(-0.634811\pi\) | ||||
−0.410973 | + | 0.911647i | \(0.634811\pi\) | |||||||
\(360\) | −2959.30 | − | 9312.25i | −0.0228341 | − | 0.0718538i | ||||
\(361\) | −184776. | −1.41785 | ||||||||
\(362\) | 249338. | 1.90270 | ||||||||
\(363\) | 32500.0 | 0.246644 | ||||||||
\(364\) | −3618.86 | + | 18121.9i | −0.0273130 | + | 0.136773i | ||||
\(365\) | 199187. | − | 63299.0i | 1.49512 | − | 0.475128i | ||||
\(366\) | −224431. | −1.67541 | ||||||||
\(367\) | −222111. | −1.64906 | −0.824532 | − | 0.565815i | \(-0.808562\pi\) | ||||
−0.824532 | + | 0.565815i | \(0.808562\pi\) | |||||||
\(368\) | − | 9686.66i | − | 0.0715284i | ||||||
\(369\) | 2171.22i | 0.0159460i | ||||||||
\(370\) | 182859. | − | 58109.9i | 1.33571 | − | 0.424470i | ||||
\(371\) | 6998.01 | + | 1397.47i | 0.0508425 | + | 0.0101530i | ||||
\(372\) | 60018.0i | 0.433706i | ||||||||
\(373\) | 60638.8i | 0.435846i | 0.975966 | + | 0.217923i | \(0.0699281\pi\) | ||||
−0.975966 | + | 0.217923i | \(0.930072\pi\) | |||||||
\(374\) | 264885.i | 1.89371i | ||||||||
\(375\) | 89438.2 | − | 118209.i | 0.636005 | − | 0.840600i | ||||
\(376\) | − | 22493.7i | − | 0.159105i | ||||||
\(377\) | 3606.13 | 0.0253722 | ||||||||
\(378\) | −157171. | − | 31386.3i | −1.09999 | − | 0.219663i | ||||
\(379\) | 187024. | 1.30202 | 0.651011 | − | 0.759068i | \(-0.274345\pi\) | ||||
0.651011 | + | 0.759068i | \(0.274345\pi\) | |||||||
\(380\) | −29458.7 | − | 92699.8i | −0.204008 | − | 0.641966i | ||||
\(381\) | 259096.i | 1.78488i | ||||||||
\(382\) | 309387.i | 2.12019i | ||||||||
\(383\) | 66090.0 | 0.450545 | 0.225272 | − | 0.974296i | \(-0.427673\pi\) | ||||
0.225272 | + | 0.974296i | \(0.427673\pi\) | |||||||
\(384\) | 177055.i | 1.20073i | ||||||||
\(385\) | −18172.3 | − | 163650.i | −0.122599 | − | 1.10406i | ||||
\(386\) | −74806.4 | −0.502070 | ||||||||
\(387\) | − | 19209.6i | − | 0.128261i | ||||||
\(388\) | −427.292 | −0.00283832 | ||||||||
\(389\) | −8595.63 | −0.0568039 | −0.0284020 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284020 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(390\) | 18715.8 | + | 58894.3i | 0.123049 | + | 0.387208i | ||||
\(391\) | 12502.0i | 0.0817761i | ||||||||
\(392\) | −40047.1 | + | 96271.8i | −0.260615 | + | 0.626509i | ||||
\(393\) | 81901.1i | 0.530279i | ||||||||
\(394\) | 239484. | 1.54271 | ||||||||
\(395\) | −96495.6 | + | 30664.9i | −0.618463 | + | 0.196539i | ||||
\(396\) | 8384.78 | 0.0534689 | ||||||||
\(397\) | 250.161 | 0.00158723 | 0.000793614 | − | 1.00000i | \(-0.499747\pi\) | ||||
0.000793614 | 1.00000i | \(0.499747\pi\) | ||||||||
\(398\) | 228561. | 1.44290 | ||||||||
\(399\) | −255887. | − | 51099.4i | −1.60732 | − | 0.320974i | ||||
\(400\) | −162727. | + | 115043.i | −1.01704 | + | 0.719017i | ||||
\(401\) | 92669.2 | 0.576297 | 0.288149 | − | 0.957586i | \(-0.406960\pi\) | ||||
0.288149 | + | 0.957586i | \(0.406960\pi\) | |||||||
\(402\) | −177591. | −1.09893 | ||||||||
\(403\) | 49664.1i | 0.305796i | ||||||||
\(404\) | 30326.1i | 0.185803i | ||||||||
\(405\) | −171761. | + | 54583.1i | −1.04716 | + | 0.332773i | ||||
\(406\) | −15250.0 | − | 3045.35i | −0.0925161 | − | 0.0184750i | ||||
\(407\) | − | 215424.i | − | 1.30049i | ||||||
\(408\) | − | 169546.i | − | 1.01851i | ||||||
\(409\) | 20412.9i | 0.122027i | 0.998137 | + | 0.0610137i | \(0.0194333\pi\) | ||||
−0.998137 | + | 0.0610137i | \(0.980567\pi\) | |||||||
\(410\) | 27524.8 | − | 8746.99i | 0.163741 | − | 0.0520344i | ||||
\(411\) | − | 208453.i | − | 1.23403i | ||||||
\(412\) | 71582.9 | 0.421711 | ||||||||
\(413\) | −234224. | − | 46773.5i | −1.37319 | − | 0.274220i | ||||
\(414\) | 1309.28 | 0.00763893 | ||||||||
\(415\) | −15024.6 | + | 4774.59i | −0.0872380 | + | 0.0277230i | ||||
\(416\) | − | 45273.6i | − | 0.261613i | ||||||
\(417\) | 196619.i | 1.13072i | ||||||||
\(418\) | −361307. | −2.06787 | ||||||||
\(419\) | 21558.5i | 0.122798i | 0.998113 | + | 0.0613988i | \(0.0195562\pi\) | ||||
−0.998113 | + | 0.0613988i | \(0.980444\pi\) | |||||||
\(420\) | −8889.92 | − | 80057.9i | −0.0503964 | − | 0.453843i | ||||
\(421\) | −127669. | −0.720311 | −0.360156 | − | 0.932892i | \(-0.617276\pi\) | ||||
−0.360156 | + | 0.932892i | \(0.617276\pi\) | |||||||
\(422\) | 162909.i | 0.914787i | ||||||||
\(423\) | 4661.65 | 0.0260531 | ||||||||
\(424\) | −6324.60 | −0.0351805 | ||||||||
\(425\) | 210023. | − | 148479.i | 1.16275 | − | 0.822029i | ||||
\(426\) | − | 19473.6i | − | 0.107307i | ||||||
\(427\) | 237385. | + | 47404.7i | 1.30196 | + | 0.259995i | ||||
\(428\) | 5353.96i | 0.0292273i | ||||||||
\(429\) | 69382.8 | 0.376997 | ||||||||
\(430\) | −243522. | + | 77387.8i | −1.31705 | + | 0.418538i | ||||
\(431\) | 281440. | 1.51507 | 0.757533 | − | 0.652797i | \(-0.226405\pi\) | ||||
0.757533 | + | 0.652797i | \(0.226405\pi\) | |||||||
\(432\) | 217796. | 1.16703 | ||||||||
\(433\) | 135595. | 0.723214 | 0.361607 | − | 0.932331i | \(-0.382228\pi\) | ||||
0.361607 | + | 0.932331i | \(0.382228\pi\) | |||||||
\(434\) | 41941.0 | − | 210025.i | 0.222669 | − | 1.11504i | ||||
\(435\) | −14980.3 | + | 4760.53i | −0.0791667 | + | 0.0251581i | ||||
\(436\) | 70320.4 | 0.369921 | ||||||||
\(437\) | −17052.9 | −0.0892969 | ||||||||
\(438\) | − | 379794.i | − | 1.97970i | ||||||
\(439\) | − | 73384.2i | − | 0.380779i | −0.981709 | − | 0.190390i | \(-0.939025\pi\) | ||
0.981709 | − | 0.190390i | \(-0.0609751\pi\) | |||||||
\(440\) | 44196.4 | + | 139076.i | 0.228287 | + | 0.718369i | ||||
\(441\) | −19951.6 | − | 8299.47i | −0.102589 | − | 0.0426750i | ||||
\(442\) | 107228.i | 0.548860i | ||||||||
\(443\) | 72350.0i | 0.368664i | 0.982864 | + | 0.184332i | \(0.0590122\pi\) | ||||
−0.982864 | + | 0.184332i | \(0.940988\pi\) | |||||||
\(444\) | − | 105386.i | − | 0.534585i | ||||||
\(445\) | −98611.5 | − | 310308.i | −0.497975 | − | 1.56701i | ||||
\(446\) | 103859.i | 0.522127i | ||||||||
\(447\) | 240551. | 1.20391 | ||||||||
\(448\) | 10720.9 | − | 53686.3i | 0.0534165 | − | 0.267490i | ||||
\(449\) | −323719. | −1.60574 | −0.802870 | − | 0.596154i | \(-0.796695\pi\) | ||||
−0.802870 | + | 0.596154i | \(0.796695\pi\) | |||||||
\(450\) | −15549.6 | − | 21994.7i | −0.0767879 | − | 0.108616i | ||||
\(451\) | − | 32426.7i | − | 0.159422i | ||||||
\(452\) | 49610.3i | 0.242826i | ||||||||
\(453\) | 319353. | 1.55623 | ||||||||
\(454\) | − | 189400.i | − | 0.918899i | ||||||
\(455\) | −7356.29 | − | 66246.8i | −0.0355333 | − | 0.319994i | ||||
\(456\) | 231263. | 1.11218 | ||||||||
\(457\) | 237414.i | 1.13678i | 0.822761 | + | 0.568388i | \(0.192433\pi\) | ||||
−0.822761 | + | 0.568388i | \(0.807567\pi\) | |||||||
\(458\) | 117681. | 0.561017 | ||||||||
\(459\) | −281097. | −1.33423 | ||||||||
\(460\) | −1594.30 | − | 5016.89i | −0.00753448 | − | 0.0237093i | ||||
\(461\) | − | 85619.6i | − | 0.402876i | −0.979501 | − | 0.201438i | \(-0.935439\pi\) | ||
0.979501 | − | 0.201438i | \(-0.0645614\pi\) | |||||||
\(462\) | −293414. | − | 58593.3i | −1.37466 | − | 0.274514i | ||||
\(463\) | 56174.0i | 0.262044i | 0.991379 | + | 0.131022i | \(0.0418258\pi\) | ||||
−0.991379 | + | 0.131022i | \(0.958174\pi\) | |||||||
\(464\) | 21132.4 | 0.0981549 | ||||||||
\(465\) | −65562.7 | − | 206311.i | −0.303215 | − | 0.954149i | ||||
\(466\) | −117087. | −0.539184 | ||||||||
\(467\) | −117912. | −0.540658 | −0.270329 | − | 0.962768i | \(-0.587132\pi\) | ||||
−0.270329 | + | 0.962768i | \(0.587132\pi\) | |||||||
\(468\) | 3394.23 | 0.0154971 | ||||||||
\(469\) | 187841. | + | 37511.1i | 0.853976 | + | 0.170535i | ||||
\(470\) | −18779.9 | − | 59096.1i | −0.0850155 | − | 0.267524i | ||||
\(471\) | 139795. | 0.630157 | ||||||||
\(472\) | 211685. | 0.950181 | ||||||||
\(473\) | 286891.i | 1.28231i | ||||||||
\(474\) | 183990.i | 0.818911i | ||||||||
\(475\) | 202528. | + | 286474.i | 0.897629 | + | 1.26969i | ||||
\(476\) | 27370.6 | − | 137062.i | 0.120801 | − | 0.604926i | ||||
\(477\) | − | 1310.73i | − | 0.00576071i | ||||||
\(478\) | 79961.9i | 0.349967i | ||||||||
\(479\) | − | 252818.i | − | 1.10189i | −0.834543 | − | 0.550943i | \(-0.814268\pi\) | ||
0.834543 | − | 0.550943i | \(-0.185732\pi\) | |||||||
\(480\) | 59766.8 | + | 188072.i | 0.259404 | + | 0.816287i | ||||
\(481\) | − | 87205.5i | − | 0.376924i | ||||||
\(482\) | −141489. | −0.609015 | ||||||||
\(483\) | −13848.5 | − | 2765.49i | −0.0593621 | − | 0.0118543i | ||||
\(484\) | −23744.9 | −0.101363 | ||||||||
\(485\) | 1468.81 | − | 466.767i | 0.00624428 | − | 0.00198434i | ||||
\(486\) | 62555.9i | 0.264848i | ||||||||
\(487\) | − | 212078.i | − | 0.894207i | −0.894482 | − | 0.447103i | \(-0.852456\pi\) | ||
0.894482 | − | 0.447103i | \(-0.147544\pi\) | |||||||
\(488\) | −214542. | −0.900891 | ||||||||
\(489\) | − | 192529.i | − | 0.805153i | ||||||
\(490\) | −24836.0 | + | 286364.i | −0.103440 | + | 1.19269i | ||||
\(491\) | −116891. | −0.484863 | −0.242432 | − | 0.970168i | \(-0.577945\pi\) | ||||
−0.242432 | + | 0.970168i | \(0.577945\pi\) | |||||||
\(492\) | − | 15863.2i | − | 0.0655332i | ||||||
\(493\) | −27274.3 | −0.112217 | ||||||||
\(494\) | −146260. | −0.599338 | ||||||||
\(495\) | −28822.5 | + | 9159.39i | −0.117631 | + | 0.0373815i | ||||
\(496\) | 291038.i | 1.18300i | ||||||||
\(497\) | −4113.25 | + | 20597.6i | −0.0166522 | + | 0.0833882i | ||||
\(498\) | 28647.6i | 0.115513i | ||||||||
\(499\) | 80616.5 | 0.323760 | 0.161880 | − | 0.986810i | \(-0.448244\pi\) | ||||
0.161880 | + | 0.986810i | \(0.448244\pi\) | |||||||
\(500\) | −65344.6 | + | 86365.3i | −0.261379 | + | 0.345461i | ||||
\(501\) | 408404. | 1.62710 | ||||||||
\(502\) | −369219. | −1.46513 | ||||||||
\(503\) | −162668. | −0.642935 | −0.321467 | − | 0.946921i | \(-0.604176\pi\) | ||||
−0.321467 | + | 0.946921i | \(0.604176\pi\) | |||||||
\(504\) | 18780.7 | + | 3750.41i | 0.0739349 | + | 0.0147645i | ||||
\(505\) | −33127.7 | − | 104245.i | −0.129900 | − | 0.408765i | ||||
\(506\) | −19553.8 | −0.0763713 | ||||||||
\(507\) | −242867. | −0.944826 | ||||||||
\(508\) | − | 189298.i | − | 0.733533i | ||||||
\(509\) | 305987.i | 1.18105i | 0.807020 | + | 0.590524i | \(0.201079\pi\) | ||||
−0.807020 | + | 0.590524i | \(0.798921\pi\) | |||||||
\(510\) | −141554. | − | 445437.i | −0.544227 | − | 1.71256i | ||||
\(511\) | −80220.6 | + | 401715.i | −0.307216 | + | 1.53842i | ||||
\(512\) | − | 43754.8i | − | 0.166911i | ||||||
\(513\) | − | 383421.i | − | 1.45694i | ||||||
\(514\) | 342017.i | 1.29456i | ||||||||
\(515\) | −246065. | + | 78195.9i | −0.927759 | + | 0.294829i | ||||
\(516\) | 140348.i | 0.527115i | ||||||||
\(517\) | −69620.6 | −0.260469 | ||||||||
\(518\) | −73644.4 | + | 368784.i | −0.274461 | + | 1.37440i | ||||
\(519\) | 210364. | 0.780975 | ||||||||
\(520\) | 17891.1 | + | 56299.2i | 0.0661653 | + | 0.208207i | ||||
\(521\) | − | 497976.i | − | 1.83456i | −0.398239 | − | 0.917282i | \(-0.630378\pi\) | ||
0.398239 | − | 0.917282i | \(-0.369622\pi\) | |||||||
\(522\) | 2856.32i | 0.0104825i | ||||||||
\(523\) | −242152. | −0.885288 | −0.442644 | − | 0.896697i | \(-0.645959\pi\) | ||||
−0.442644 | + | 0.896697i | \(0.645959\pi\) | |||||||
\(524\) | − | 59838.0i | − | 0.217929i | ||||||
\(525\) | 118013. | + | 265487.i | 0.428165 | + | 0.963217i | ||||
\(526\) | 494864. | 1.78860 | ||||||||
\(527\) | − | 375625.i | − | 1.35249i | ||||||
\(528\) | 406592. | 1.45845 | ||||||||
\(529\) | 278918. | 0.996702 | ||||||||
\(530\) | −16616.2 | + | 5280.40i | −0.0591535 | + | 0.0187981i | ||||
\(531\) | 43870.2i | 0.155590i | ||||||||
\(532\) | 186954. | + | 37333.9i | 0.660559 | + | 0.131911i | ||||
\(533\) | − | 13126.6i | − | 0.0462059i | ||||||
\(534\) | −591669. | −2.07490 | ||||||||
\(535\) | −5848.58 | − | 18404.2i | −0.0204335 | − | 0.0642996i | ||||
\(536\) | −169766. | −0.590909 | ||||||||
\(537\) | 434434. | 1.50652 | ||||||||
\(538\) | 261951. | 0.905014 | ||||||||
\(539\) | 297973. | + | 123951.i | 1.02565 | + | 0.426649i | ||||
\(540\) | 112800. | − | 35846.4i | 0.386833 | − | 0.122930i | ||||
\(541\) | −400699. | −1.36907 | −0.684533 | − | 0.728982i | \(-0.739994\pi\) | ||||
−0.684533 | + | 0.728982i | \(0.739994\pi\) | |||||||
\(542\) | 307750. | 1.04761 | ||||||||
\(543\) | 493964.i | 1.67531i | ||||||||
\(544\) | 342419.i | 1.15707i | ||||||||
\(545\) | −241725. | + | 76816.9i | −0.813821 | + | 0.258621i | ||||
\(546\) | −118776. | − | 23719.1i | −0.398423 | − | 0.0795633i | ||||
\(547\) | 107818.i | 0.360344i | 0.983635 | + | 0.180172i | \(0.0576655\pi\) | ||||
−0.983635 | + | 0.180172i | \(0.942335\pi\) | |||||||
\(548\) | 152298.i | 0.507147i | ||||||||
\(549\) | − | 44462.2i | − | 0.147518i | ||||||
\(550\) | 232229. | + | 328486.i | 0.767699 | + | 1.08590i | ||||
\(551\) | − | 37202.6i | − | 0.122538i | ||||||
\(552\) | 12515.9 | 0.0410756 | ||||||||
\(553\) | 38862.6 | − | 194609.i | 0.127081 | − | 0.636375i | ||||
\(554\) | 169721. | 0.552989 | ||||||||
\(555\) | 115122. | + | 362263.i | 0.373742 | + | 1.17608i | ||||
\(556\) | − | 143652.i | − | 0.464690i | ||||||
\(557\) | − | 143511.i | − | 0.462567i | −0.972886 | − | 0.231284i | \(-0.925707\pi\) | ||
0.972886 | − | 0.231284i | \(-0.0742926\pi\) | |||||||
\(558\) | −39337.6 | −0.126340 | ||||||||
\(559\) | 116136.i | 0.371657i | ||||||||
\(560\) | −43108.7 | − | 388214.i | −0.137464 | − | 1.23793i | ||||
\(561\) | −524765. | −1.66740 | ||||||||
\(562\) | − | 343047.i | − | 1.08613i | ||||||
\(563\) | 84498.7 | 0.266584 | 0.133292 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133292 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(564\) | −34058.6 | −0.107070 | ||||||||
\(565\) | −54193.5 | − | 170535.i | −0.169766 | − | 0.534215i | ||||
\(566\) | − | 193315.i | − | 0.603438i | ||||||
\(567\) | 69174.8 | − | 346402.i | 0.215170 | − | 1.07749i | ||||
\(568\) | − | 18615.6i | − | 0.0577005i | ||||||
\(569\) | −160937. | −0.497086 | −0.248543 | − | 0.968621i | \(-0.579952\pi\) | ||||
−0.248543 | + | 0.968621i | \(0.579952\pi\) | |||||||
\(570\) | 607583. | − | 193081.i | 1.87006 | − | 0.594279i | ||||
\(571\) | −188608. | −0.578479 | −0.289240 | − | 0.957257i | \(-0.593402\pi\) | ||||
−0.289240 | + | 0.957257i | \(0.593402\pi\) | |||||||
\(572\) | −50692.0 | −0.154934 | ||||||||
\(573\) | −612928. | −1.86681 | ||||||||
\(574\) | −11085.3 | + | 55511.1i | −0.0336453 | + | 0.168483i | ||||
\(575\) | 10960.7 | + | 15503.9i | 0.0331515 | + | 0.0468926i | ||||
\(576\) | −10055.4 | −0.0303079 | ||||||||
\(577\) | −105363. | −0.316474 | −0.158237 | − | 0.987401i | \(-0.550581\pi\) | ||||
−0.158237 | + | 0.987401i | \(0.550581\pi\) | |||||||
\(578\) | − | 411043.i | − | 1.23036i | ||||||
\(579\) | − | 148199.i | − | 0.442068i | ||||||
\(580\) | 10944.8 | − | 3478.11i | 0.0325351 | − | 0.0103392i | ||||
\(581\) | 6050.98 | − | 30301.1i | 0.0179256 | − | 0.0897647i | ||||
\(582\) | − | 2800.60i | − | 0.00826810i | ||||||
\(583\) | 19575.4i | 0.0575935i | ||||||||
\(584\) | − | 363058.i | − | 1.06451i | ||||||
\(585\) | −11667.6 | + | 3707.80i | −0.0340934 | + | 0.0108344i | ||||
\(586\) | 54886.9i | 0.159836i | ||||||||
\(587\) | −544367. | −1.57985 | −0.789925 | − | 0.613204i | \(-0.789880\pi\) | ||||
−0.789925 | + | 0.613204i | \(0.789880\pi\) | |||||||
\(588\) | 145769. | + | 60637.0i | 0.421610 | + | 0.175381i | ||||
\(589\) | 512359. | 1.47687 | ||||||||
\(590\) | 556146. | − | 176735.i | 1.59766 | − | 0.507714i | ||||
\(591\) | 474443.i | 1.35834i | ||||||||
\(592\) | − | 511035.i | − | 1.45817i | ||||||
\(593\) | 532984. | 1.51567 | 0.757835 | − | 0.652447i | \(-0.226257\pi\) | ||||
0.757835 | + | 0.652447i | \(0.226257\pi\) | |||||||
\(594\) | − | 439651.i | − | 1.24605i | ||||||
\(595\) | 55638.0 | + | 501046.i | 0.157158 | + | 1.41528i | ||||
\(596\) | −175750. | −0.494769 | ||||||||
\(597\) | 452803.i | 1.27046i | ||||||||
\(598\) | −7915.55 | −0.0221349 | ||||||||
\(599\) | 68054.5 | 0.189672 | 0.0948360 | − | 0.995493i | \(-0.469767\pi\) | ||||
0.0948360 | + | 0.995493i | \(0.469767\pi\) | |||||||
\(600\) | −148644. | − | 210256.i | −0.412899 | − | 0.584043i | ||||
\(601\) | − | 537130.i | − | 1.48707i | −0.668699 | − | 0.743533i | \(-0.733149\pi\) | ||
0.668699 | − | 0.743533i | \(-0.266851\pi\) | |||||||
\(602\) | 98075.8 | − | 491127.i | 0.270626 | − | 1.35519i | ||||
\(603\) | − | 35182.7i | − | 0.0967597i | ||||||
\(604\) | −233323. | −0.639564 | ||||||||
\(605\) | 81622.8 | − | 25938.6i | 0.222998 | − | 0.0708656i | ||||
\(606\) | −198766. | −0.541249 | ||||||||
\(607\) | −409948. | −1.11263 | −0.556315 | − | 0.830971i | \(-0.687785\pi\) | ||||
−0.556315 | + | 0.830971i | \(0.687785\pi\) | |||||||
\(608\) | −467065. | −1.26348 | ||||||||
\(609\) | 6033.17 | − | 30211.8i | 0.0162671 | − | 0.0814597i | ||||
\(610\) | −563651. | + | 179120.i | −1.51478 | + | 0.481377i | ||||
\(611\) | −28183.0 | −0.0754927 | ||||||||
\(612\) | −25671.6 | −0.0685411 | ||||||||
\(613\) | 336398.i | 0.895224i | 0.894228 | + | 0.447612i | \(0.147725\pi\) | ||||
−0.894228 | + | 0.447612i | \(0.852275\pi\) | |||||||
\(614\) | − | 534649.i | − | 1.41818i | ||||||
\(615\) | 17328.7 | + | 54529.5i | 0.0458159 | + | 0.144172i | ||||
\(616\) | −280484. | − | 56011.5i | −0.739175 | − | 0.147610i | ||||
\(617\) | 494704.i | 1.29950i | 0.760149 | + | 0.649749i | \(0.225126\pi\) | ||||
−0.760149 | + | 0.649749i | \(0.774874\pi\) | |||||||
\(618\) | 469176.i | 1.22845i | ||||||||
\(619\) | 259458.i | 0.677151i | 0.940939 | + | 0.338575i | \(0.109945\pi\) | ||||
−0.940939 | + | 0.338575i | \(0.890055\pi\) | |||||||
\(620\) | 47900.9 | + | 150733.i | 0.124612 | + | 0.392126i | ||||
\(621\) | − | 20750.6i | − | 0.0538081i | ||||||
\(622\) | −128231. | −0.331445 | ||||||||
\(623\) | 625819. | + | 124973.i | 1.61240 | + | 0.321989i | ||||
\(624\) | 164592. | 0.422707 | ||||||||
\(625\) | 130277. | − | 368260.i | 0.333509 | − | 0.942747i | ||||
\(626\) | 418965.i | 1.06913i | ||||||||
\(627\) | − | 715787.i | − | 1.82074i | ||||||
\(628\) | −102136. | −0.258975 | ||||||||
\(629\) | 659563.i | 1.66707i | ||||||||
\(630\) | 52472.4 | − | 5826.72i | 0.132206 | − | 0.0146806i | ||||
\(631\) | −398747. | −1.00147 | −0.500736 | − | 0.865600i | \(-0.666937\pi\) | ||||
−0.500736 | + | 0.865600i | \(0.666937\pi\) | |||||||
\(632\) | 175882.i | 0.440340i | ||||||||
\(633\) | −322740. | −0.805463 | ||||||||
\(634\) | −222790. | −0.554265 | ||||||||
\(635\) | 206786. | + | 650710.i | 0.512831 | + | 1.61376i | ||||
\(636\) | 9576.34i | 0.0236747i | ||||||||
\(637\) | 120622. | + | 50176.2i | 0.297267 | + | 0.123657i | ||||
\(638\) | − | 42658.5i | − | 0.104801i | ||||||
\(639\) | 3857.94 | 0.00944829 | ||||||||
\(640\) | 141309. | + | 444667.i | 0.344992 | + | 1.08561i | ||||
\(641\) | 289434. | 0.704424 | 0.352212 | − | 0.935920i | \(-0.385430\pi\) | ||||
0.352212 | + | 0.935920i | \(0.385430\pi\) | |||||||
\(642\) | −35091.5 | −0.0851396 | ||||||||
\(643\) | 446428. | 1.07977 | 0.539883 | − | 0.841740i | \(-0.318469\pi\) | ||||
0.539883 | + | 0.841740i | \(0.318469\pi\) | |||||||
\(644\) | 10117.9 | + | 2020.50i | 0.0243960 | + | 0.00487177i | ||||
\(645\) | −153313. | − | 482442.i | −0.368520 | − | 1.15965i | ||||
\(646\) | 1.10621e6 | 2.65078 | ||||||||
\(647\) | 379786. | 0.907257 | 0.453628 | − | 0.891191i | \(-0.350129\pi\) | ||||
0.453628 | + | 0.891191i | \(0.350129\pi\) | |||||||
\(648\) | 313068.i | 0.745570i | ||||||||
\(649\) | − | 655190.i | − | 1.55553i | ||||||
\(650\) | 94008.2 | + | 132974.i | 0.222505 | + | 0.314731i | ||||
\(651\) | 416081. | + | 83089.5i | 0.981785 | + | 0.196058i | ||||
\(652\) | 140664.i | 0.330893i | ||||||||
\(653\) | − | 549238.i | − | 1.28806i | −0.765002 | − | 0.644028i | \(-0.777262\pi\) | ||
0.765002 | − | 0.644028i | \(-0.222738\pi\) | |||||||
\(654\) | 460901.i | 1.07759i | ||||||||
\(655\) | 65366.0 | + | 205692.i | 0.152359 | + | 0.479441i | ||||
\(656\) | − | 76923.4i | − | 0.178752i | ||||||
\(657\) | 75241.2 | 0.174311 | ||||||||
\(658\) | 119183. | + | 23800.3i | 0.275273 | + | 0.0549707i | ||||
\(659\) | 101895. | 0.234629 | 0.117314 | − | 0.993095i | \(-0.462571\pi\) | ||||
0.117314 | + | 0.993095i | \(0.462571\pi\) | |||||||
\(660\) | 210581. | − | 66919.6i | 0.483427 | − | 0.153626i | ||||
\(661\) | 339312.i | 0.776597i | 0.921534 | + | 0.388299i | \(0.126937\pi\) | ||||
−0.921534 | + | 0.388299i | \(0.873063\pi\) | |||||||
\(662\) | 257647.i | 0.587909i | ||||||||
\(663\) | −212429. | −0.483267 | ||||||||
\(664\) | 27385.2i | 0.0621127i | ||||||||
\(665\) | −683434. | + | 75891.0i | −1.54544 | + | 0.171612i | ||||
\(666\) | 69073.2 | 0.155726 | ||||||||
\(667\) | − | 2013.39i | − | 0.00452561i | ||||||
\(668\) | −298385. | −0.668690 | ||||||||
\(669\) | −205757. | −0.459729 | ||||||||
\(670\) | −446014. | + | 141737.i | −0.993571 | + | 0.315743i | ||||
\(671\) | 664032.i | 1.47484i | ||||||||
\(672\) | −379299. | − | 75744.2i | −0.839929 | − | 0.167730i | ||||
\(673\) | − | 685861.i | − | 1.51428i | −0.653253 | − | 0.757140i | \(-0.726596\pi\) | ||
0.653253 | − | 0.757140i | \(-0.273404\pi\) | |||||||
\(674\) | −431057. | −0.948888 | ||||||||
\(675\) | −348591. | + | 246443.i | −0.765084 | + | 0.540889i | ||||
\(676\) | 177441. | 0.388295 | ||||||||
\(677\) | 342300. | 0.746844 | 0.373422 | − | 0.927662i | \(-0.378184\pi\) | ||||
0.373422 | + | 0.927662i | \(0.378184\pi\) | |||||||
\(678\) | −325161. | −0.707358 | ||||||||
\(679\) | −591.548 | + | 2962.25i | −0.00128307 | + | 0.00642513i | ||||
\(680\) | −135316. | − | 425809.i | −0.292639 | − | 0.920867i | ||||
\(681\) | 375221. | 0.809083 | ||||||||
\(682\) | 587498. | 1.26310 | ||||||||
\(683\) | − | 171281.i | − | 0.367170i | −0.983004 | − | 0.183585i | \(-0.941230\pi\) | ||
0.983004 | − | 0.183585i | \(-0.0587703\pi\) | |||||||
\(684\) | − | 35016.5i | − | 0.0748446i | ||||||
\(685\) | −166368. | − | 523523.i | −0.354560 | − | 1.11572i | ||||
\(686\) | −467725. | − | 314055.i | −0.993900 | − | 0.667356i | ||||
\(687\) | 233139.i | 0.493971i | ||||||||
\(688\) | 680569.i | 1.43779i | ||||||||
\(689\) | 7924.29i | 0.0166925i | ||||||||
\(690\) | 32882.2 | − | 10449.5i | 0.0690657 | − | 0.0219481i | ||||
\(691\) | − | 226012.i | − | 0.473343i | −0.971590 | − | 0.236671i | \(-0.923944\pi\) | ||
0.971590 | − | 0.236671i | \(-0.0760565\pi\) | |||||||
\(692\) | −153695. | −0.320957 | ||||||||
\(693\) | 11608.0 | − | 58128.4i | 0.0241707 | − | 0.121038i | ||||
\(694\) | −253704. | −0.526756 | ||||||||
\(695\) | 156924. | + | 493803.i | 0.324877 | + | 1.02231i | ||||
\(696\) | 27304.6i | 0.0563660i | ||||||||
\(697\) | 99280.6i | 0.204361i | ||||||||
\(698\) | 584376. | 1.19945 | ||||||||
\(699\) | − | 231962.i | − | 0.474747i | ||||||
\(700\) | −86221.7 | − | 193968.i | −0.175963 | − | 0.395853i | ||||
\(701\) | 525569. | 1.06953 | 0.534766 | − | 0.845000i | \(-0.320400\pi\) | ||||
0.534766 | + | 0.845000i | \(0.320400\pi\) | |||||||
\(702\) | − | 177974.i | − | 0.361146i | ||||||
\(703\) | −899654. | −1.82039 | ||||||||
\(704\) | 150175. | 0.303008 | ||||||||
\(705\) | 117076. | − | 37205.0i | 0.235553 | − | 0.0748554i | ||||
\(706\) | − | 124873.i | − | 0.250529i | ||||||
\(707\) | 210239. | + | 41983.7i | 0.420604 | + | 0.0839928i | ||||
\(708\) | − | 320521.i | − | 0.639425i | ||||||
\(709\) | −819495. | −1.63025 | −0.815124 | − | 0.579287i | \(-0.803331\pi\) | ||||
−0.815124 | + | 0.579287i | \(0.803331\pi\) | |||||||
\(710\) | −15542.1 | − | 48907.4i | −0.0308314 | − | 0.0970193i | ||||
\(711\) | −36450.3 | −0.0721045 | ||||||||
\(712\) | −565597. | −1.11570 | ||||||||
\(713\) | 27728.7 | 0.0545444 | ||||||||
\(714\) | 898343. | + | 179395.i | 1.76216 | + | 0.351896i | ||||
\(715\) | 174253. | − | 55375.1i | 0.340853 | − | 0.108318i | ||||
\(716\) | −317403. | −0.619134 | ||||||||
\(717\) | −158413. | −0.308143 | ||||||||
\(718\) | 507278.i | 0.984004i | ||||||||
\(719\) | − | 113789.i | − | 0.220111i | −0.993925 | − | 0.110056i | \(-0.964897\pi\) | ||
0.993925 | − | 0.110056i | \(-0.0351029\pi\) | |||||||
\(720\) | −68373.5 | + | 21728.1i | −0.131893 | + | 0.0419139i | ||||
\(721\) | 99100.0 | − | 496256.i | 0.190635 | − | 0.954630i | ||||
\(722\) | 884827.i | 1.69740i | ||||||||
\(723\) | − | 280304.i | − | 0.536232i | ||||||
\(724\) | − | 360896.i | − | 0.688502i | ||||||
\(725\) | −33823.2 | + | 23911.9i | −0.0643485 | + | 0.0454922i | ||||
\(726\) | − | 155631.i | − | 0.295273i | ||||||
\(727\) | 281594. | 0.532788 | 0.266394 | − | 0.963864i | \(-0.414168\pi\) | ||||
0.266394 | + | 0.963864i | \(0.414168\pi\) | |||||||
\(728\) | −113542. | − | 22673.9i | −0.214238 | − | 0.0427823i | ||||
\(729\) | 459999. | 0.865569 | ||||||||
\(730\) | −303117. | − | 953839.i | −0.568806 | − | 1.78990i | ||||
\(731\) | − | 878372.i | − | 1.64378i | ||||||
\(732\) | 324846.i | 0.606256i | ||||||||
\(733\) | 401713. | 0.747666 | 0.373833 | − | 0.927496i | \(-0.378043\pi\) | ||||
0.373833 | + | 0.927496i | \(0.378043\pi\) | |||||||
\(734\) | 1.06361e6i | 1.97420i | ||||||||
\(735\) | −567318. | − | 49202.7i | −1.05015 | − | 0.0910781i | ||||
\(736\) | −25277.4 | −0.0466635 | ||||||||
\(737\) | 525445.i | 0.967369i | ||||||||
\(738\) | 10397.2 | 0.0190900 | ||||||||
\(739\) | −331954. | −0.607839 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(740\) | −84109.5 | − | 264674.i | −0.153597 | − | 0.483334i | ||||
\(741\) | − | 289757.i | − | 0.527712i | ||||||
\(742\) | 6692.01 | − | 33511.1i | 0.0121548 | − | 0.0608668i | ||||
\(743\) | 132862.i | 0.240671i | 0.992733 | + | 0.120335i | \(0.0383970\pi\) | ||||
−0.992733 | + | 0.120335i | \(0.961603\pi\) | |||||||
\(744\) | −376042. | −0.679346 | ||||||||
\(745\) | 604137. | − | 191986.i | 1.08849 | − | 0.345905i | ||||
\(746\) | 290378. | 0.521778 | ||||||||
\(747\) | −5675.39 | −0.0101708 | ||||||||
\(748\) | 383400. | 0.685249 | ||||||||
\(749\) | 37116.9 | + | 7412.08i | 0.0661620 | + | 0.0132122i | ||||
\(750\) | −566064. | − | 428288.i | −1.00634 | − | 0.761402i | ||||
\(751\) | 6629.17 | 0.0117538 | 0.00587691 | − | 0.999983i | \(-0.498129\pi\) | ||||
0.00587691 | + | 0.999983i | \(0.498129\pi\) | |||||||
\(752\) | −165156. | −0.292051 | ||||||||
\(753\) | − | 731462.i | − | 1.29004i | ||||||
\(754\) | − | 17268.5i | − | 0.0303747i | ||||||
\(755\) | 802044. | − | 254878.i | 1.40703 | − | 0.447135i | ||||
\(756\) | −45429.2 | + | 227492.i | −0.0794861 | + | 0.398037i | ||||
\(757\) | 1.09675e6i | 1.91389i | 0.290273 | + | 0.956944i | \(0.406254\pi\) | ||||
−0.290273 | + | 0.956944i | \(0.593746\pi\) | |||||||
\(758\) | − | 895592.i | − | 1.55873i | ||||||
\(759\) | − | 38738.2i | − | 0.0672443i | ||||||
\(760\) | 580810. | − | 184573.i | 1.00556 | − | 0.319552i | ||||
\(761\) | 1.04930e6i | 1.81188i | 0.423403 | + | 0.905941i | \(0.360835\pi\) | ||||
−0.423403 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(762\) | 1.24072e6 | 2.13680 | ||||||||
\(763\) | 97352.3 | − | 487504.i | 0.167223 | − | 0.837392i | ||||
\(764\) | 447813. | 0.767202 | ||||||||
\(765\) | 88245.8 | − | 28043.3i | 0.150790 | − | 0.0479188i | ||||
\(766\) | − | 316482.i | − | 0.539376i | ||||||
\(767\) | − | 265227.i | − | 0.450844i | ||||||
\(768\) | 678264. | 1.14994 | ||||||||
\(769\) | − | 775397.i | − | 1.31121i | −0.755105 | − | 0.655604i | \(-0.772414\pi\) | ||
0.755105 | − | 0.655604i | \(-0.227586\pi\) | |||||||
\(770\) | −783662. | + | 87020.7i | −1.32174 | + | 0.146771i | ||||
\(771\) | −677573. | −1.13985 | ||||||||
\(772\) | 108276.i | 0.181677i | ||||||||
\(773\) | −184420. | −0.308637 | −0.154319 | − | 0.988021i | \(-0.549318\pi\) | ||||
−0.154319 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(774\) | −91988.1 | −0.153550 | ||||||||
\(775\) | −329317. | − | 465817.i | −0.548291 | − | 0.775553i | ||||
\(776\) | − | 2677.20i | − | 0.00444587i | ||||||
\(777\) | −730600. | − | 145897.i | −1.21015 | − | 0.241661i | ||||
\(778\) | 41161.5i | 0.0680036i | ||||||||
\(779\) | −135420. | −0.223156 | ||||||||
\(780\) | 85244.9 | − | 27089.6i | 0.140113 | − | 0.0445260i | ||||
\(781\) | −57617.3 | −0.0944607 | ||||||||
\(782\) | 59867.8 | 0.0978994 | ||||||||
\(783\) | 45269.4 | 0.0738382 | ||||||||
\(784\) | 706859. | + | 294039.i | 1.15001 | + | 0.478379i | ||||
\(785\) | 351089. | − | 111571.i | 0.569742 | − | 0.181056i | ||||
\(786\) | 392196. | 0.634831 | ||||||||
\(787\) | −367309. | −0.593038 | −0.296519 | − | 0.955027i | \(-0.595826\pi\) | ||||
−0.296519 | + | 0.955027i | \(0.595826\pi\) | |||||||
\(788\) | − | 346634.i | − | 0.558237i | ||||||
\(789\) | 980378.i | 1.57485i | ||||||||
\(790\) | 146844. | + | 462084.i | 0.235289 | + | 0.740401i | ||||
\(791\) | 343929. | + | 68681.0i | 0.549687 | + | 0.109770i | ||||
\(792\) | 52534.7i | 0.0837522i | ||||||||
\(793\) | 268806.i | 0.427457i | ||||||||
\(794\) | − | 1197.94i | − | 0.00190017i | ||||||
\(795\) | −10461.0 | − | 32918.5i | −0.0165516 | − | 0.0520842i | ||||
\(796\) | − | 330824.i | − | 0.522120i | ||||||
\(797\) | −246896. | −0.388685 | −0.194343 | − | 0.980934i | \(-0.562257\pi\) | ||||
−0.194343 | + | 0.980934i | \(0.562257\pi\) | |||||||
\(798\) | −244698. | + | 1.22535e6i | −0.384259 | + | 1.92422i | ||||
\(799\) | 213157. | 0.333892 | ||||||||
\(800\) | 300205. | + | 424637.i | 0.469070 | + | 0.663496i | ||||
\(801\) | − | 117216.i | − | 0.182693i | ||||||
\(802\) | − | 443761.i | − | 0.689922i | ||||||
\(803\) | −1.12371e6 | −1.74270 | ||||||||
\(804\) | 257049.i | 0.397653i | ||||||||
\(805\) | −36987.3 | + | 4107.20i | −0.0570769 | + | 0.00633802i | ||||
\(806\) | 237824. | 0.366088 | ||||||||
\(807\) | 518952.i | 0.796857i | ||||||||
\(808\) | −190008. | −0.291037 | ||||||||
\(809\) | −400601. | −0.612089 | −0.306044 | − | 0.952017i | \(-0.599006\pi\) | ||||
−0.306044 | + | 0.952017i | \(0.599006\pi\) | |||||||
\(810\) | 261380. | + | 822502.i | 0.398384 | + | 1.25362i | ||||
\(811\) | 198723.i | 0.302138i | 0.988523 | + | 0.151069i | \(0.0482716\pi\) | ||||
−0.988523 | + | 0.151069i | \(0.951728\pi\) | |||||||
\(812\) | −4407.91 | + | 22073.1i | −0.00668529 | + | 0.0334774i | ||||
\(813\) | 609686.i | 0.922412i | ||||||||
\(814\) | −1.03159e6 | −1.55689 | ||||||||
\(815\) | −153659. | − | 483530.i | −0.231336 | − | 0.727961i | ||||
\(816\) | −1.24486e6 | −1.86957 | ||||||||
\(817\) | 1.19811e6 | 1.79495 | ||||||||
\(818\) | 97750.2 | 0.146087 | ||||||||
\(819\) | 4699.00 | − | 23530.8i | 0.00700548 | − | 0.0350808i | ||||
\(820\) | −12660.6 | − | 39840.0i | −0.0188289 | − | 0.0592504i | ||||
\(821\) | −509614. | −0.756058 | −0.378029 | − | 0.925794i | \(-0.623398\pi\) | ||||
−0.378029 | + | 0.925794i | \(0.623398\pi\) | |||||||
\(822\) | −998210. | −1.47733 | ||||||||
\(823\) | 637647.i | 0.941414i | 0.882290 | + | 0.470707i | \(0.156001\pi\) | ||||
−0.882290 | + | 0.470707i | \(0.843999\pi\) | |||||||
\(824\) | 448502.i | 0.660556i | ||||||||
\(825\) | −650766. | + | 460070.i | −0.956130 | + | 0.675952i | ||||
\(826\) | −223982. | + | 1.12162e6i | −0.328287 | + | 1.64394i | ||||
\(827\) | − | 1.02274e6i | − | 1.49539i | −0.664041 | − | 0.747696i | \(-0.731160\pi\) | ||
0.664041 | − | 0.747696i | \(-0.268840\pi\) | |||||||
\(828\) | − | 1895.08i | − | 0.00276419i | ||||||
\(829\) | − | 627492.i | − | 0.913059i | −0.889708 | − | 0.456529i | \(-0.849092\pi\) | ||
0.889708 | − | 0.456529i | \(-0.150908\pi\) | |||||||
\(830\) | 22863.9 | + | 71947.4i | 0.0331890 | + | 0.104438i | ||||
\(831\) | 336236.i | 0.486903i | ||||||||
\(832\) | 60792.3 | 0.0878217 | ||||||||
\(833\) | −912302. | − | 379499.i | −1.31477 | − | 0.546916i | ||||
\(834\) | 941541. | 1.35365 | ||||||||
\(835\) | 1.02569e6 | − | 325951.i | 1.47111 | − | 0.467498i | ||||
\(836\) | 522963.i | 0.748270i | ||||||||
\(837\) | 623456.i | 0.889928i | ||||||||
\(838\) | 103236. | 0.147009 | ||||||||
\(839\) | − | 738068.i | − | 1.04851i | −0.851561 | − | 0.524255i | \(-0.824344\pi\) | ||
0.851561 | − | 0.524255i | \(-0.175656\pi\) | |||||||
\(840\) | 501602. | − | 55699.7i | 0.710887 | − | 0.0789395i | ||||
\(841\) | −702889. | −0.993790 | ||||||||
\(842\) | 611361.i | 0.862330i | ||||||||
\(843\) | 679612. | 0.956326 | ||||||||
\(844\) | 235798. | 0.331021 | ||||||||
\(845\) | −609952. | + | 193834.i | −0.854244 | + | 0.271467i | ||||
\(846\) | − | 22323.0i | − | 0.0311898i | ||||||
\(847\) | −32872.7 | + | 164614.i | −0.0458214 | + | 0.229457i | ||||
\(848\) | 46437.3i | 0.0645766i | ||||||||
\(849\) | 382978. | 0.531322 | ||||||||
\(850\) | −711014. | − | 1.00572e6i | −0.984103 | − | 1.39201i | ||||
\(851\) | −48689.0 | −0.0672313 | ||||||||
\(852\) | −28186.6 | −0.0388296 | ||||||||
\(853\) | 789566. | 1.08515 | 0.542576 | − | 0.840007i | \(-0.317449\pi\) | ||||
0.542576 | + | 0.840007i | \(0.317449\pi\) | |||||||
\(854\) | 227005. | − | 1.13675e6i | 0.311257 | − | 1.55866i | ||||
\(855\) | 38251.4 | + | 120369.i | 0.0523258 | + | 0.164657i | ||||
\(856\) | −33545.2 | −0.0457808 | ||||||||
\(857\) | 522419. | 0.711307 | 0.355653 | − | 0.934618i | \(-0.384258\pi\) | ||||
0.355653 | + | 0.934618i | \(0.384258\pi\) | |||||||
\(858\) | − | 332250.i | − | 0.451327i | ||||||
\(859\) | 851038.i | 1.15335i | 0.816972 | + | 0.576677i | \(0.195651\pi\) | ||||
−0.816972 | + | 0.576677i | \(0.804349\pi\) | |||||||
\(860\) | 112013. | + | 352478.i | 0.151450 | + | 0.476580i | ||||
\(861\) | −109973. | − | 21961.2i | −0.148348 | − | 0.0296244i | ||||
\(862\) | − | 1.34772e6i | − | 1.81378i | ||||||
\(863\) | − | 911280.i | − | 1.22357i | −0.791022 | − | 0.611787i | \(-0.790451\pi\) | ||
0.791022 | − | 0.611787i | \(-0.209549\pi\) | |||||||
\(864\) | − | 568341.i | − | 0.761345i | ||||||
\(865\) | 528323. | − | 167894.i | 0.706102 | − | 0.224389i | ||||
\(866\) | − | 649316.i | − | 0.865805i | ||||||
\(867\) | 814321. | 1.08332 | ||||||||
\(868\) | −303994. | − | 60706.2i | −0.403483 | − | 0.0805738i | ||||
\(869\) | 544377. | 0.720875 | ||||||||
\(870\) | 22796.5 | + | 71735.6i | 0.0301183 | + | 0.0947755i | ||||
\(871\) | 212705.i | 0.280376i | ||||||||
\(872\) | 440592.i | 0.579433i | ||||||||
\(873\) | 554.829 | 0.000727999 | ||||||||
\(874\) | 81660.6i | 0.106903i | ||||||||
\(875\) | 508273. | + | 572574.i | 0.663866 | + | 0.747851i | ||||
\(876\) | −549721. | −0.716365 | ||||||||
\(877\) | − | 809992.i | − | 1.05313i | −0.850135 | − | 0.526564i | \(-0.823480\pi\) | ||
0.850135 | − | 0.526564i | \(-0.176520\pi\) | |||||||
\(878\) | −351411. | −0.455855 | ||||||||
\(879\) | −108737. | −0.140734 | ||||||||
\(880\) | 1.02114e6 | − | 324505.i | 1.31862 | − | 0.419040i | ||||
\(881\) | 798132.i | 1.02831i | 0.857698 | + | 0.514153i | \(0.171894\pi\) | ||||
−0.857698 | + | 0.514153i | \(0.828106\pi\) | |||||||
\(882\) | −39743.3 | + | 95541.5i | −0.0510889 | + | 0.122816i | ||||
\(883\) | − | 893487.i | − | 1.14595i | −0.819572 | − | 0.572976i | \(-0.805789\pi\) | ||
0.819572 | − | 0.572976i | \(-0.194211\pi\) | |||||||
\(884\) | 155203. | 0.198608 | ||||||||
\(885\) | 350132. | + | 1.10178e6i | 0.447038 | + | 1.40673i | ||||
\(886\) | 346459. | 0.441352 | ||||||||
\(887\) | −890142. | −1.13139 | −0.565695 | − | 0.824615i | \(-0.691392\pi\) | ||||
−0.565695 | + | 0.824615i | \(0.691392\pi\) | |||||||
\(888\) | 660295. | 0.837360 | ||||||||
\(889\) | −1.31233e6 | − | 262067.i | −1.66050 | − | 0.331595i | ||||
\(890\) | −1.48596e6 | + | 472216.i | −1.87597 | + | 0.596157i | ||||
\(891\) | 968982. | 1.22056 | ||||||||
\(892\) | 150328. | 0.188934 | ||||||||
\(893\) | 290749.i | 0.364599i | ||||||||
\(894\) | − | 1.15192e6i | − | 1.44127i | ||||||
\(895\) | 1.09107e6 | − | 346726.i | 1.36209 | − | 0.432852i | ||||
\(896\) | −896790. | − | 179085.i | −1.11706 | − | 0.223071i | ||||
\(897\) | − | 15681.5i | − | 0.0194896i | ||||||
\(898\) | 1.55018e6i | 1.92233i | ||||||||
\(899\) | 60492.7i | 0.0748486i | ||||||||
\(900\) | −31835.7 | + | 22506.8i | −0.0393033 | + | 0.0277861i | ||||
\(901\) | − | 59933.9i | − | 0.0738284i | ||||||
\(902\) | −155280. | −0.190855 | ||||||||
\(903\) | 972975. | + | 194299.i | 1.19324 | + | 0.238284i | ||||
\(904\) | −310833. | −0.380356 | ||||||||
\(905\) | 394237. | + | 1.24057e6i | 0.481349 | + | 1.51470i | ||||
\(906\) | − | 1.52927e6i | − | 1.86306i | ||||||
\(907\) | − | 91834.0i | − | 0.111632i | −0.998441 | − | 0.0558160i | \(-0.982224\pi\) | ||
0.998441 | − | 0.0558160i | \(-0.0177760\pi\) | |||||||
\(908\) | −274141. | −0.332508 | ||||||||
\(909\) | − | 39377.7i | − | 0.0476565i | ||||||
\(910\) | −317233. | + | 35226.7i | −0.383085 | + | 0.0425392i | ||||
\(911\) | −132543. | −0.159705 | −0.0798526 | − | 0.996807i | \(-0.525445\pi\) | ||||
−0.0798526 | + | 0.996807i | \(0.525445\pi\) | |||||||
\(912\) | − | 1.69801e6i | − | 2.04150i | ||||||
\(913\) | 84760.5 | 0.101684 | ||||||||
\(914\) | 1.13690e6 | 1.36091 | ||||||||
\(915\) | −354857. | − | 1.11665e6i | −0.423849 | − | 1.33376i | ||||
\(916\) | − | 170334.i | − | 0.203007i | ||||||
\(917\) | −414833. | − | 82840.3i | −0.493327 | − | 0.0985151i | ||||
\(918\) | 1.34608e6i | 1.59729i | ||||||||
\(919\) | −903523. | −1.06981 | −0.534907 | − | 0.844911i | \(-0.679653\pi\) | ||||
−0.534907 | + | 0.844911i | \(0.679653\pi\) | |||||||
\(920\) | 31433.3 | − | 9989.05i | 0.0371376 | − | 0.0118018i | ||||
\(921\) | 1.05920e6 | 1.24870 | ||||||||
\(922\) | −410002. | −0.482308 | ||||||||
\(923\) | −23324.0 | −0.0273779 | ||||||||
\(924\) | −84809.2 | + | 424693.i | −0.0993343 | + | 0.497429i | ||||
\(925\) | 578250. | + | 817931.i | 0.675822 | + | 0.955945i | ||||
\(926\) | 268998. | 0.313709 | ||||||||
\(927\) | −92948.7 | −0.108164 | ||||||||
\(928\) | − | 55145.0i | − | 0.0640340i | ||||||
\(929\) | 727404.i | 0.842838i | 0.906866 | + | 0.421419i | \(0.138468\pi\) | ||||
−0.906866 | + | 0.421419i | \(0.861532\pi\) | |||||||
\(930\) | −987951. | + | 313957.i | −1.14227 | + | 0.362998i | ||||
\(931\) | 517642. | − | 1.24439e6i | 0.597215 | − | 1.43568i | ||||
\(932\) | 169474.i | 0.195107i | ||||||||
\(933\) | − | 254039.i | − | 0.291835i | ||||||
\(934\) | 564638.i | 0.647256i | ||||||||
\(935\) | −1.31793e6 | + | 418819.i | −1.50754 | + | 0.479075i | ||||
\(936\) | 21266.5i | 0.0242742i | ||||||||
\(937\) | −1.35820e6 | −1.54698 | −0.773491 | − | 0.633807i | \(-0.781491\pi\) | ||||
−0.773491 | + | 0.633807i | \(0.781491\pi\) | |||||||
\(938\) | 179628. | − | 899507.i | 0.204158 | − | 1.02235i | ||||
\(939\) | −830015. | −0.941357 | ||||||||
\(940\) | −85537.0 | + | 27182.4i | −0.0968051 | + | 0.0307633i | ||||
\(941\) | 635488.i | 0.717675i | 0.933400 | + | 0.358837i | \(0.116827\pi\) | ||||
−0.933400 | + | 0.358837i | \(0.883173\pi\) | |||||||
\(942\) | − | 669428.i | − | 0.754400i | ||||||
\(943\) | −7328.91 | −0.00824168 | ||||||||
\(944\) | − | 1.55426e6i | − | 1.74413i | ||||||
\(945\) | −92346.9 | − | 831627.i | −0.103409 | − | 0.931247i | ||||
\(946\) | 1.37382e6 | 1.53514 | ||||||||
\(947\) | − | 461458.i | − | 0.514555i | −0.966338 | − | 0.257278i | \(-0.917175\pi\) | ||
0.966338 | − | 0.257278i | \(-0.0828255\pi\) | |||||||
\(948\) | 266311. | 0.296327 | ||||||||
\(949\) | −454887. | −0.505092 | ||||||||
\(950\) | 1.37182e6 | − | 969834.i | 1.52003 | − | 1.07461i | ||||
\(951\) | − | 441371.i | − | 0.488026i | ||||||
\(952\) | 858758. | + | 171490.i | 0.947539 | + | 0.189219i | ||||
\(953\) | − | 33374.1i | − | 0.0367471i | −0.999831 | − | 0.0183736i | \(-0.994151\pi\) | ||
0.999831 | − | 0.0183736i | \(-0.00584882\pi\) | |||||||
\(954\) | −6276.62 | −0.00689651 | ||||||||
\(955\) | −1.53935e6 | + | 489183.i | −1.68784 | + | 0.536370i | ||||
\(956\) | 115739. | 0.126637 | ||||||||
\(957\) | 84511.0 | 0.0922761 | ||||||||
\(958\) | −1.21066e6 | −1.31914 | ||||||||
\(959\) | 1.05582e6 | + | 210843.i | 1.14803 | + | 0.229257i | ||||
\(960\) | −252539. | + | 80253.3i | −0.274022 | + | 0.0870804i | ||||
\(961\) | 90407.5 | 0.0978943 | ||||||||
\(962\) | −417597. | −0.451239 | ||||||||
\(963\) | − | 6952.00i | − | 0.00749648i | ||||||
\(964\) | 204794.i | 0.220375i | ||||||||
\(965\) | −118279. | − | 372198.i | −0.127015 | − | 0.399686i | ||||
\(966\) | −13243.0 | + | 66315.8i | −0.0141916 | + | 0.0710661i | ||||
\(967\) | − | 792088.i | − | 0.847073i | −0.905879 | − | 0.423536i | \(-0.860789\pi\) | ||
0.905879 | − | 0.423536i | \(-0.139211\pi\) | |||||||
\(968\) | − | 148774.i | − | 0.158772i | ||||||
\(969\) | 2.19152e6i | 2.33399i | ||||||||
\(970\) | −2235.19 | − | 7033.62i | −0.00237558 | − | 0.00747542i | ||||
\(971\) | − | 1.02728e6i | − | 1.08956i | −0.838580 | − | 0.544779i | \(-0.816614\pi\) | ||
0.838580 | − | 0.544779i | \(-0.183386\pi\) | |||||||
\(972\) | 90544.8 | 0.0958365 | ||||||||
\(973\) | −995886. | − | 198874.i | −1.05192 | − | 0.210064i | ||||
\(974\) | −1.01557e6 | −1.07051 | ||||||||
\(975\) | −263436. | + | 186240.i | −0.277118 | + | 0.195913i | ||||
\(976\) | 1.57524e6i | 1.65366i | ||||||||
\(977\) | 249431.i | 0.261313i | 0.991428 | + | 0.130657i | \(0.0417086\pi\) | ||||
−0.991428 | + | 0.130657i | \(0.958291\pi\) | |||||||
\(978\) | −921954. | −0.963899 | ||||||||
\(979\) | 1.75059e6i | 1.82650i | ||||||||
\(980\) | 414489. | + | 35948.1i | 0.431580 | + | 0.0374303i | ||||
\(981\) | −91309.4 | −0.0948806 | ||||||||
\(982\) | 559752.i | 0.580461i | ||||||||
\(983\) | 1.55175e6 | 1.60589 | 0.802944 | − | 0.596055i | \(-0.203266\pi\) | ||||
0.802944 | + | 0.596055i | \(0.203266\pi\) | |||||||
\(984\) | 99390.8 | 0.102649 | ||||||||
\(985\) | 378657. | + | 1.19155e6i | 0.390278 | + | 1.22812i | ||||
\(986\) | 130607.i | 0.134343i | ||||||||
\(987\) | −47151.0 | + | 236115.i | −0.0484013 | + | 0.242375i | ||||
\(988\) | 211700.i | 0.216874i | ||||||||
\(989\) | 64841.5 | 0.0662919 | ||||||||
\(990\) | 43861.1 | + | 138021.i | 0.0447517 | + | 0.140823i | ||||
\(991\) | 993147. | 1.01127 | 0.505634 | − | 0.862748i | \(-0.331259\pi\) | ||||
0.505634 | + | 0.862748i | \(0.331259\pi\) | |||||||
\(992\) | 759464. | 0.771763 | ||||||||
\(993\) | −510427. | −0.517649 | ||||||||
\(994\) | 98634.9 | + | 19696.9i | 0.0998293 | + | 0.0199355i | ||||
\(995\) | 361386. | + | 1.13720e6i | 0.365027 | + | 1.14866i | ||||
\(996\) | 41465.1 | 0.0417988 | ||||||||
\(997\) | 784005. | 0.788731 | 0.394365 | − | 0.918954i | \(-0.370964\pi\) | ||||
0.394365 | + | 0.918954i | \(0.370964\pi\) | |||||||
\(998\) | − | 386044.i | − | 0.387593i | ||||||
\(999\) | − | 1.09473e6i | − | 1.09692i |
(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 | 35.5.c.e.34.4 | yes | 8 | |
3.2 | odd | 2 | 315.5.e.e.244.5 | 8 | |||
4.3 | odd | 2 | 560.5.p.g.209.3 | 8 | |||
5.2 | odd | 4 | 175.5.d.g.76.5 | 8 | |||
5.3 | odd | 4 | 175.5.d.g.76.4 | 8 | |||
5.4 | even | 2 | inner | 35.5.c.e.34.5 | yes | 8 | |
7.6 | odd | 2 | inner | 35.5.c.e.34.3 | ✓ | 8 | |
15.14 | odd | 2 | 315.5.e.e.244.4 | 8 | |||
20.19 | odd | 2 | 560.5.p.g.209.5 | 8 | |||
21.20 | even | 2 | 315.5.e.e.244.6 | 8 | |||
28.27 | even | 2 | 560.5.p.g.209.6 | 8 | |||
35.13 | even | 4 | 175.5.d.g.76.3 | 8 | |||
35.27 | even | 4 | 175.5.d.g.76.6 | 8 | |||
35.34 | odd | 2 | inner | 35.5.c.e.34.6 | yes | 8 | |
105.104 | even | 2 | 315.5.e.e.244.3 | 8 | |||
140.139 | even | 2 | 560.5.p.g.209.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.c.e.34.3 | ✓ | 8 | 7.6 | odd | 2 | inner | |
35.5.c.e.34.4 | yes | 8 | 1.1 | even | 1 | trivial | |
35.5.c.e.34.5 | yes | 8 | 5.4 | even | 2 | inner | |
35.5.c.e.34.6 | yes | 8 | 35.34 | odd | 2 | inner | |
175.5.d.g.76.3 | 8 | 35.13 | even | 4 | |||
175.5.d.g.76.4 | 8 | 5.3 | odd | 4 | |||
175.5.d.g.76.5 | 8 | 5.2 | odd | 4 | |||
175.5.d.g.76.6 | 8 | 35.27 | even | 4 | |||
315.5.e.e.244.3 | 8 | 105.104 | even | 2 | |||
315.5.e.e.244.4 | 8 | 15.14 | odd | 2 | |||
315.5.e.e.244.5 | 8 | 3.2 | odd | 2 | |||
315.5.e.e.244.6 | 8 | 21.20 | even | 2 | |||
560.5.p.g.209.3 | 8 | 4.3 | odd | 2 | |||
560.5.p.g.209.4 | 8 | 140.139 | even | 2 | |||
560.5.p.g.209.5 | 8 | 20.19 | odd | 2 | |||
560.5.p.g.209.6 | 8 | 28.27 | even | 2 |