Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), 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: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-14.7444i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.7.d.a.43.7 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | + | 4.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | − | 10.7444i | − | 0.397941i | −0.980006 | − | 0.198970i | \(-0.936240\pi\) | ||
0.980006 | − | 0.198970i | \(-0.0637597\pi\) | |||||||
\(4\) | 32.0000i | 0.500000i | ||||||||
\(5\) | 60.1111 | − | 60.1111i | 0.480889 | − | 0.480889i | −0.424527 | − | 0.905415i | \(-0.639559\pi\) |
0.905415 | + | 0.424527i | \(0.139559\pi\) | |||||||
\(6\) | 42.9776 | − | 42.9776i | 0.198970 | − | 0.198970i | ||||
\(7\) | −174.087 | −0.507541 | −0.253770 | − | 0.967264i | \(-0.581671\pi\) | ||||
−0.253770 | + | 0.967264i | \(0.581671\pi\) | |||||||
\(8\) | −128.000 | + | 128.000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 613.558 | 0.841643 | ||||||||
\(10\) | 480.889 | 0.480889 | ||||||||
\(11\) | − | 1127.73i | − | 0.847278i | −0.905831 | − | 0.423639i | \(-0.860753\pi\) | ||
0.905831 | − | 0.423639i | \(-0.139247\pi\) | |||||||
\(12\) | 343.821 | 0.198970 | ||||||||
\(13\) | 739.616 | − | 739.616i | 0.336648 | − | 0.336648i | −0.518456 | − | 0.855104i | \(-0.673493\pi\) |
0.855104 | + | 0.518456i | \(0.173493\pi\) | |||||||
\(14\) | −696.346 | − | 696.346i | −0.253770 | − | 0.253770i | ||||
\(15\) | −645.857 | − | 645.857i | −0.191365 | − | 0.191365i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | 1313.72 | − | 1313.72i | 0.267397 | − | 0.267397i | −0.560653 | − | 0.828051i | \(-0.689450\pi\) |
0.828051 | + | 0.560653i | \(0.189450\pi\) | |||||||
\(18\) | 2454.23 | + | 2454.23i | 0.420822 | + | 0.420822i | ||||
\(19\) | 4161.36 | − | 4161.36i | 0.606700 | − | 0.606700i | −0.335382 | − | 0.942082i | \(-0.608865\pi\) |
0.942082 | + | 0.335382i | \(0.108865\pi\) | |||||||
\(20\) | 1923.55 | + | 1923.55i | 0.240444 | + | 0.240444i | ||||
\(21\) | 1870.45i | 0.201971i | ||||||||
\(22\) | 4510.91 | − | 4510.91i | 0.423639 | − | 0.423639i | ||||
\(23\) | 14825.2 | − | 14825.2i | 1.21848 | − | 1.21848i | 0.250309 | − | 0.968166i | \(-0.419468\pi\) |
0.968166 | − | 0.250309i | \(-0.0805324\pi\) | |||||||
\(24\) | 1375.28 | + | 1375.28i | 0.0994851 | + | 0.0994851i | ||||
\(25\) | 8398.31i | 0.537492i | ||||||||
\(26\) | 5916.92 | 0.336648 | ||||||||
\(27\) | − | 14425.0i | − | 0.732865i | ||||||
\(28\) | − | 5570.77i | − | 0.253770i | ||||||
\(29\) | −2018.87 | − | 2018.87i | −0.0827777 | − | 0.0827777i | 0.664506 | − | 0.747283i | \(-0.268642\pi\) |
−0.747283 | + | 0.664506i | \(0.768642\pi\) | |||||||
\(30\) | − | 5166.86i | − | 0.191365i | ||||||
\(31\) | 10796.7 | + | 10796.7i | 0.362414 | + | 0.362414i | 0.864701 | − | 0.502287i | \(-0.167508\pi\) |
−0.502287 | + | 0.864701i | \(0.667508\pi\) | |||||||
\(32\) | −4096.00 | − | 4096.00i | −0.125000 | − | 0.125000i | ||||
\(33\) | −12116.7 | −0.337166 | ||||||||
\(34\) | 10509.8 | 0.267397 | ||||||||
\(35\) | −10464.5 | + | 10464.5i | −0.244071 | + | 0.244071i | ||||
\(36\) | 19633.9i | 0.420822i | ||||||||
\(37\) | 44063.7 | + | 24982.3i | 0.869913 | + | 0.493205i | ||||
\(38\) | 33290.8 | 0.606700 | ||||||||
\(39\) | −7946.72 | − | 7946.72i | −0.133966 | − | 0.133966i | ||||
\(40\) | 15388.4i | 0.240444i | ||||||||
\(41\) | 7586.85i | 0.110080i | 0.998484 | + | 0.0550402i | \(0.0175287\pi\) | ||||
−0.998484 | + | 0.0550402i | \(0.982471\pi\) | |||||||
\(42\) | −7481.82 | + | 7481.82i | −0.100986 | + | 0.100986i | ||||
\(43\) | 33218.5 | − | 33218.5i | 0.417806 | − | 0.417806i | −0.466641 | − | 0.884447i | \(-0.654536\pi\) |
0.884447 | + | 0.466641i | \(0.154536\pi\) | |||||||
\(44\) | 36087.3 | 0.423639 | ||||||||
\(45\) | 36881.6 | − | 36881.6i | 0.404737 | − | 0.404737i | ||||
\(46\) | 118602. | 1.21848 | ||||||||
\(47\) | −33369.3 | −0.321406 | −0.160703 | − | 0.987003i | \(-0.551376\pi\) | ||||
−0.160703 | + | 0.987003i | \(0.551376\pi\) | |||||||
\(48\) | 11002.3i | 0.0994851i | ||||||||
\(49\) | −87342.9 | −0.742402 | ||||||||
\(50\) | −33593.3 | + | 33593.3i | −0.268746 | + | 0.268746i | ||||
\(51\) | −14115.2 | − | 14115.2i | −0.106408 | − | 0.106408i | ||||
\(52\) | 23667.7 | + | 23667.7i | 0.168324 | + | 0.168324i | ||||
\(53\) | −248937. | −1.67210 | −0.836048 | − | 0.548656i | \(-0.815140\pi\) | ||||
−0.836048 | + | 0.548656i | \(0.815140\pi\) | |||||||
\(54\) | 57699.9 | − | 57699.9i | 0.366432 | − | 0.366432i | ||||
\(55\) | −67788.9 | − | 67788.9i | −0.407446 | − | 0.407446i | ||||
\(56\) | 22283.1 | − | 22283.1i | 0.126885 | − | 0.126885i | ||||
\(57\) | −44711.2 | − | 44711.2i | −0.241431 | − | 0.241431i | ||||
\(58\) | − | 16150.9i | − | 0.0827777i | ||||||
\(59\) | 14581.0 | − | 14581.0i | 0.0709957 | − | 0.0709957i | −0.670717 | − | 0.741713i | \(-0.734014\pi\) |
0.741713 | + | 0.670717i | \(0.234014\pi\) | |||||||
\(60\) | 20667.4 | − | 20667.4i | 0.0956825 | − | 0.0956825i | ||||
\(61\) | −55383.0 | − | 55383.0i | −0.243998 | − | 0.243998i | 0.574504 | − | 0.818502i | \(-0.305195\pi\) |
−0.818502 | + | 0.574504i | \(0.805195\pi\) | |||||||
\(62\) | 86373.4i | 0.362414i | ||||||||
\(63\) | −106812. | −0.427168 | ||||||||
\(64\) | − | 32768.0i | − | 0.125000i | ||||||
\(65\) | − | 88918.2i | − | 0.323780i | ||||||
\(66\) | −48467.0 | − | 48467.0i | −0.168583 | − | 0.168583i | ||||
\(67\) | 86551.8i | 0.287774i | 0.989594 | + | 0.143887i | \(0.0459602\pi\) | ||||
−0.989594 | + | 0.143887i | \(0.954040\pi\) | |||||||
\(68\) | 42039.2 | + | 42039.2i | 0.133699 | + | 0.133699i | ||||
\(69\) | −159288. | − | 159288.i | −0.484881 | − | 0.484881i | ||||
\(70\) | −83716.3 | −0.244071 | ||||||||
\(71\) | −281661. | −0.786959 | −0.393479 | − | 0.919333i | \(-0.628729\pi\) | ||||
−0.393479 | + | 0.919333i | \(0.628729\pi\) | |||||||
\(72\) | −78535.4 | + | 78535.4i | −0.210411 | + | 0.210411i | ||||
\(73\) | 645595.i | 1.65955i | 0.558095 | + | 0.829777i | \(0.311532\pi\) | ||||
−0.558095 | + | 0.829777i | \(0.688468\pi\) | |||||||
\(74\) | 76325.6 | + | 276184.i | 0.188354 | + | 0.681559i | ||||
\(75\) | 90234.8 | 0.213890 | ||||||||
\(76\) | 133163. | + | 133163.i | 0.303350 | + | 0.303350i | ||||
\(77\) | 196322.i | 0.430028i | ||||||||
\(78\) | − | 63573.8i | − | 0.133966i | ||||||
\(79\) | −194161. | + | 194161.i | −0.393804 | + | 0.393804i | −0.876041 | − | 0.482237i | \(-0.839825\pi\) |
0.482237 | + | 0.876041i | \(0.339825\pi\) | |||||||
\(80\) | −61553.8 | + | 61553.8i | −0.120222 | + | 0.120222i | ||||
\(81\) | 292296. | 0.550007 | ||||||||
\(82\) | −30347.4 | + | 30347.4i | −0.0550402 | + | 0.0550402i | ||||
\(83\) | −943610. | −1.65028 | −0.825141 | − | 0.564927i | \(-0.808904\pi\) | ||||
−0.825141 | + | 0.564927i | \(0.808904\pi\) | |||||||
\(84\) | −59854.5 | −0.100986 | ||||||||
\(85\) | − | 157939.i | − | 0.257177i | ||||||
\(86\) | 265748. | 0.417806 | ||||||||
\(87\) | −21691.5 | + | 21691.5i | −0.0329406 | + | 0.0329406i | ||||
\(88\) | 144349. | + | 144349.i | 0.211819 | + | 0.211819i | ||||
\(89\) | −70599.5 | − | 70599.5i | −0.100145 | − | 0.100145i | 0.655259 | − | 0.755404i | \(-0.272560\pi\) |
−0.755404 | + | 0.655259i | \(0.772560\pi\) | |||||||
\(90\) | 295053. | 0.404737 | ||||||||
\(91\) | −128757. | + | 128757.i | −0.170863 | + | 0.170863i | ||||
\(92\) | 474406. | + | 474406.i | 0.609238 | + | 0.609238i | ||||
\(93\) | 116004. | − | 116004.i | 0.144219 | − | 0.144219i | ||||
\(94\) | −133477. | − | 133477.i | −0.160703 | − | 0.160703i | ||||
\(95\) | − | 500287.i | − | 0.583510i | ||||||
\(96\) | −44009.0 | + | 44009.0i | −0.0497426 | + | 0.0497426i | ||||
\(97\) | −55379.7 | + | 55379.7i | −0.0606786 | + | 0.0606786i | −0.736795 | − | 0.676116i | \(-0.763662\pi\) |
0.676116 | + | 0.736795i | \(0.263662\pi\) | |||||||
\(98\) | −349371. | − | 349371.i | −0.371201 | − | 0.371201i | ||||
\(99\) | − | 691926.i | − | 0.713106i | ||||||
\(100\) | −268746. | −0.268746 | ||||||||
\(101\) | − | 462045.i | − | 0.448456i | −0.974537 | − | 0.224228i | \(-0.928014\pi\) | ||
0.974537 | − | 0.224228i | \(-0.0719860\pi\) | |||||||
\(102\) | − | 112921.i | − | 0.106408i | ||||||
\(103\) | 410647. | + | 410647.i | 0.375801 | + | 0.375801i | 0.869585 | − | 0.493784i | \(-0.164387\pi\) |
−0.493784 | + | 0.869585i | \(0.664387\pi\) | |||||||
\(104\) | 189342.i | 0.168324i | ||||||||
\(105\) | 112435. | + | 112435.i | 0.0971256 | + | 0.0971256i | ||||
\(106\) | −995747. | − | 995747.i | −0.836048 | − | 0.836048i | ||||
\(107\) | 1.87384e6 | 1.52961 | 0.764807 | − | 0.644259i | \(-0.222834\pi\) | ||||
0.764807 | + | 0.644259i | \(0.222834\pi\) | |||||||
\(108\) | 461599. | 0.366432 | ||||||||
\(109\) | 319902. | − | 319902.i | 0.247023 | − | 0.247023i | −0.572725 | − | 0.819748i | \(-0.694114\pi\) |
0.819748 | + | 0.572725i | \(0.194114\pi\) | |||||||
\(110\) | − | 542311.i | − | 0.407446i | ||||||
\(111\) | 268420. | − | 473438.i | 0.196266 | − | 0.346174i | ||||
\(112\) | 178265. | 0.126885 | ||||||||
\(113\) | 1.63134e6 | + | 1.63134e6i | 1.13060 | + | 1.13060i | 0.990078 | + | 0.140519i | \(0.0448772\pi\) |
0.140519 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(114\) | − | 357690.i | − | 0.241431i | ||||||
\(115\) | − | 1.78232e6i | − | 1.17190i | ||||||
\(116\) | 64603.7 | − | 64603.7i | 0.0413889 | − | 0.0413889i | ||||
\(117\) | 453797. | − | 453797.i | 0.283337 | − | 0.283337i | ||||
\(118\) | 116648. | 0.0709957 | ||||||||
\(119\) | −228702. | + | 228702.i | −0.135715 | + | 0.135715i | ||||
\(120\) | 165339. | 0.0956825 | ||||||||
\(121\) | 499793. | 0.282120 | ||||||||
\(122\) | − | 443064.i | − | 0.243998i | ||||||
\(123\) | 81516.1 | 0.0438054 | ||||||||
\(124\) | −345493. | + | 345493.i | −0.181207 | + | 0.181207i | ||||
\(125\) | 1.44407e6 | + | 1.44407e6i | 0.739363 | + | 0.739363i | ||||
\(126\) | −427249. | − | 427249.i | −0.213584 | − | 0.213584i | ||||
\(127\) | 1.93108e6 | 0.942734 | 0.471367 | − | 0.881937i | \(-0.343761\pi\) | ||||
0.471367 | + | 0.881937i | \(0.343761\pi\) | |||||||
\(128\) | 131072. | − | 131072.i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −356913. | − | 356913.i | −0.166262 | − | 0.166262i | ||||
\(130\) | 355673. | − | 355673.i | 0.161890 | − | 0.161890i | ||||
\(131\) | 1.94616e6 | + | 1.94616e6i | 0.865696 | + | 0.865696i | 0.991993 | − | 0.126296i | \(-0.0403089\pi\) |
−0.126296 | + | 0.991993i | \(0.540309\pi\) | |||||||
\(132\) | − | 387736.i | − | 0.168583i | ||||||
\(133\) | −724436. | + | 724436.i | −0.307925 | + | 0.307925i | ||||
\(134\) | −346207. | + | 346207.i | −0.143887 | + | 0.143887i | ||||
\(135\) | −867101. | − | 867101.i | −0.352426 | − | 0.352426i | ||||
\(136\) | 336313.i | 0.133699i | ||||||||
\(137\) | −1.80552e6 | −0.702167 | −0.351083 | − | 0.936344i | \(-0.614187\pi\) | ||||
−0.351083 | + | 0.936344i | \(0.614187\pi\) | |||||||
\(138\) | − | 1.27430e6i | − | 0.484881i | ||||||
\(139\) | − | 2.04030e6i | − | 0.759713i | −0.925045 | − | 0.379856i | \(-0.875973\pi\) | ||
0.925045 | − | 0.379856i | \(-0.124027\pi\) | |||||||
\(140\) | −334865. | − | 334865.i | −0.122035 | − | 0.122035i | ||||
\(141\) | 358533.i | 0.127900i | ||||||||
\(142\) | −1.12664e6 | − | 1.12664e6i | −0.393479 | − | 0.393479i | ||||
\(143\) | −834084. | − | 834084.i | −0.285234 | − | 0.285234i | ||||
\(144\) | −628283. | −0.210411 | ||||||||
\(145\) | −242712. | −0.0796137 | ||||||||
\(146\) | −2.58238e6 | + | 2.58238e6i | −0.829777 | + | 0.829777i | ||||
\(147\) | 938446.i | 0.295432i | ||||||||
\(148\) | −799434. | + | 1.41004e6i | −0.246602 | + | 0.434957i | ||||
\(149\) | 1.93410e6 | 0.584682 | 0.292341 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292341 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(150\) | 360939. | + | 360939.i | 0.106945 | + | 0.106945i | ||||
\(151\) | 1.33692e6i | 0.388308i | 0.980971 | + | 0.194154i | \(0.0621961\pi\) | ||||
−0.980971 | + | 0.194154i | \(0.937804\pi\) | |||||||
\(152\) | 1.06531e6i | 0.303350i | ||||||||
\(153\) | 806046. | − | 806046.i | 0.225053 | − | 0.225053i | ||||
\(154\) | −785288. | + | 785288.i | −0.215014 | + | 0.215014i | ||||
\(155\) | 1.29800e6 | 0.348561 | ||||||||
\(156\) | 254295. | − | 254295.i | 0.0669829 | − | 0.0669829i | ||||
\(157\) | −3.18578e6 | −0.823222 | −0.411611 | − | 0.911360i | \(-0.635034\pi\) | ||||
−0.411611 | + | 0.911360i | \(0.635034\pi\) | |||||||
\(158\) | −1.55329e6 | −0.393804 | ||||||||
\(159\) | 2.67467e6i | 0.665395i | ||||||||
\(160\) | −492430. | −0.120222 | ||||||||
\(161\) | −2.58087e6 | + | 2.58087e6i | −0.618426 | + | 0.618426i | ||||
\(162\) | 1.16918e6 | + | 1.16918e6i | 0.275003 | + | 0.275003i | ||||
\(163\) | −1.42695e6 | − | 1.42695e6i | −0.329494 | − | 0.329494i | 0.522900 | − | 0.852394i | \(-0.324850\pi\) |
−0.852394 | + | 0.522900i | \(0.824850\pi\) | |||||||
\(164\) | −242779. | −0.0550402 | ||||||||
\(165\) | −728350. | + | 728350.i | −0.162139 | + | 0.162139i | ||||
\(166\) | −3.77444e6 | − | 3.77444e6i | −0.825141 | − | 0.825141i | ||||
\(167\) | −493922. | + | 493922.i | −0.106049 | + | 0.106049i | −0.758141 | − | 0.652091i | \(-0.773892\pi\) |
0.652091 | + | 0.758141i | \(0.273892\pi\) | |||||||
\(168\) | −239418. | − | 239418.i | −0.0504928 | − | 0.0504928i | ||||
\(169\) | 3.73275e6i | 0.773336i | ||||||||
\(170\) | 631755. | − | 631755.i | 0.128588 | − | 0.128588i | ||||
\(171\) | 2.55323e6 | − | 2.55323e6i | 0.510625 | − | 0.510625i | ||||
\(172\) | 1.06299e6 | + | 1.06299e6i | 0.208903 | + | 0.208903i | ||||
\(173\) | 4.16532e6i | 0.804471i | 0.915536 | + | 0.402235i | \(0.131767\pi\) | ||||
−0.915536 | + | 0.402235i | \(0.868233\pi\) | |||||||
\(174\) | −173532. | −0.0329406 | ||||||||
\(175\) | − | 1.46203e6i | − | 0.272799i | ||||||
\(176\) | 1.15479e6i | 0.211819i | ||||||||
\(177\) | −156664. | − | 156664.i | −0.0282521 | − | 0.0282521i | ||||
\(178\) | − | 564796.i | − | 0.100145i | ||||||
\(179\) | −2.74930e6 | − | 2.74930e6i | −0.479362 | − | 0.479362i | 0.425566 | − | 0.904928i | \(-0.360075\pi\) |
−0.904928 | + | 0.425566i | \(0.860075\pi\) | |||||||
\(180\) | 1.18021e6 | + | 1.18021e6i | 0.202368 | + | 0.202368i | ||||
\(181\) | −8.60548e6 | −1.45124 | −0.725620 | − | 0.688095i | \(-0.758447\pi\) | ||||
−0.725620 | + | 0.688095i | \(0.758447\pi\) | |||||||
\(182\) | −1.03006e6 | −0.170863 | ||||||||
\(183\) | −595056. | + | 595056.i | −0.0970968 | + | 0.0970968i | ||||
\(184\) | 3.79525e6i | 0.609238i | ||||||||
\(185\) | 4.15043e6 | − | 1.14700e6i | 0.655508 | − | 0.181155i | ||||
\(186\) | 928029. | 0.144219 | ||||||||
\(187\) | −1.48152e6 | − | 1.48152e6i | −0.226560 | − | 0.226560i | ||||
\(188\) | − | 1.06782e6i | − | 0.160703i | ||||||
\(189\) | 2.51119e6i | 0.371959i | ||||||||
\(190\) | 2.00115e6 | − | 2.00115e6i | 0.291755 | − | 0.291755i | ||||
\(191\) | 4.33614e6 | − | 4.33614e6i | 0.622305 | − | 0.622305i | −0.323815 | − | 0.946120i | \(-0.604966\pi\) |
0.946120 | + | 0.323815i | \(0.104966\pi\) | |||||||
\(192\) | −352072. | −0.0497426 | ||||||||
\(193\) | −3.19439e6 | + | 3.19439e6i | −0.444341 | + | 0.444341i | −0.893468 | − | 0.449127i | \(-0.851735\pi\) |
0.449127 | + | 0.893468i | \(0.351735\pi\) | |||||||
\(194\) | −443037. | −0.0606786 | ||||||||
\(195\) | −955372. | −0.128845 | ||||||||
\(196\) | − | 2.79497e6i | − | 0.371201i | ||||||
\(197\) | −4.04778e6 | −0.529442 | −0.264721 | − | 0.964325i | \(-0.585280\pi\) | ||||
−0.264721 | + | 0.964325i | \(0.585280\pi\) | |||||||
\(198\) | 2.76770e6 | − | 2.76770e6i | 0.356553 | − | 0.356553i | ||||
\(199\) | 2.50471e6 | + | 2.50471e6i | 0.317833 | + | 0.317833i | 0.847934 | − | 0.530101i | \(-0.177846\pi\) |
−0.530101 | + | 0.847934i | \(0.677846\pi\) | |||||||
\(200\) | −1.07498e6 | − | 1.07498e6i | −0.134373 | − | 0.134373i | ||||
\(201\) | 929947. | 0.114517 | ||||||||
\(202\) | 1.84818e6 | − | 1.84818e6i | 0.224228 | − | 0.224228i | ||||
\(203\) | 351457. | + | 351457.i | 0.0420131 | + | 0.0420131i | ||||
\(204\) | 451685. | − | 451685.i | 0.0532041 | − | 0.0532041i | ||||
\(205\) | 456054. | + | 456054.i | 0.0529364 | + | 0.0529364i | ||||
\(206\) | 3.28518e6i | 0.375801i | ||||||||
\(207\) | 9.09611e6 | − | 9.09611e6i | 1.02552 | − | 1.02552i | ||||
\(208\) | −757366. | + | 757366.i | −0.0841620 | + | 0.0841620i | ||||
\(209\) | −4.69287e6 | − | 4.69287e6i | −0.514043 | − | 0.514043i | ||||
\(210\) | 899480.i | 0.0971256i | ||||||||
\(211\) | −8.67104e6 | −0.923047 | −0.461523 | − | 0.887128i | \(-0.652697\pi\) | ||||
−0.461523 | + | 0.887128i | \(0.652697\pi\) | |||||||
\(212\) | − | 7.96597e6i | − | 0.836048i | ||||||
\(213\) | 3.02628e6i | 0.313163i | ||||||||
\(214\) | 7.49538e6 | + | 7.49538e6i | 0.764807 | + | 0.764807i | ||||
\(215\) | − | 3.99360e6i | − | 0.401837i | ||||||
\(216\) | 1.84640e6 | + | 1.84640e6i | 0.183216 | + | 0.183216i | ||||
\(217\) | −1.87955e6 | − | 1.87955e6i | −0.183940 | − | 0.183940i | ||||
\(218\) | 2.55922e6 | 0.247023 | ||||||||
\(219\) | 6.93652e6 | 0.660404 | ||||||||
\(220\) | 2.16924e6 | − | 2.16924e6i | 0.203723 | − | 0.203723i | ||||
\(221\) | − | 1.94330e6i | − | 0.180038i | ||||||
\(222\) | 2.96743e6 | − | 820073.i | 0.271220 | − | 0.0749538i | ||||
\(223\) | −1.41894e6 | −0.127953 | −0.0639764 | − | 0.997951i | \(-0.520378\pi\) | ||||
−0.0639764 | + | 0.997951i | \(0.520378\pi\) | |||||||
\(224\) | 713059. | + | 713059.i | 0.0634426 | + | 0.0634426i | ||||
\(225\) | 5.15285e6i | 0.452377i | ||||||||
\(226\) | 1.30507e7i | 1.13060i | ||||||||
\(227\) | 1.17994e7 | − | 1.17994e7i | 1.00875 | − | 1.00875i | 0.00878900 | − | 0.999961i | \(-0.497202\pi\) |
0.999961 | − | 0.00878900i | \(-0.00279766\pi\) | |||||||
\(228\) | 1.43076e6 | − | 1.43076e6i | 0.120715 | − | 0.120715i | ||||
\(229\) | 1.85067e6 | 0.154107 | 0.0770536 | − | 0.997027i | \(-0.475449\pi\) | ||||
0.0770536 | + | 0.997027i | \(0.475449\pi\) | |||||||
\(230\) | 7.12927e6 | − | 7.12927e6i | 0.585951 | − | 0.585951i | ||||
\(231\) | 2.10936e6 | 0.171126 | ||||||||
\(232\) | 516830. | 0.0413889 | ||||||||
\(233\) | 1.20765e7i | 0.954710i | 0.878710 | + | 0.477355i | \(0.158404\pi\) | ||||
−0.878710 | + | 0.477355i | \(0.841596\pi\) | |||||||
\(234\) | 3.63038e6 | 0.283337 | ||||||||
\(235\) | −2.00586e6 | + | 2.00586e6i | −0.154560 | + | 0.154560i | ||||
\(236\) | 466593. | + | 466593.i | 0.0354978 | + | 0.0354978i | ||||
\(237\) | 2.08614e6 | + | 2.08614e6i | 0.156711 | + | 0.156711i | ||||
\(238\) | −1.82961e6 | −0.135715 | ||||||||
\(239\) | 2.81267e6 | − | 2.81267e6i | 0.206027 | − | 0.206027i | −0.596549 | − | 0.802577i | \(-0.703462\pi\) |
0.802577 | + | 0.596549i | \(0.203462\pi\) | |||||||
\(240\) | 661358. | + | 661358.i | 0.0478413 | + | 0.0478413i | ||||
\(241\) | −7.53061e6 | + | 7.53061e6i | −0.537996 | + | 0.537996i | −0.922940 | − | 0.384944i | \(-0.874221\pi\) |
0.384944 | + | 0.922940i | \(0.374221\pi\) | |||||||
\(242\) | 1.99917e6 | + | 1.99917e6i | 0.141060 | + | 0.141060i | ||||
\(243\) | − | 1.36564e7i | − | 0.951735i | ||||||
\(244\) | 1.77225e6 | − | 1.77225e6i | 0.121999 | − | 0.121999i | ||||
\(245\) | −5.25027e6 | + | 5.25027e6i | −0.357013 | + | 0.357013i | ||||
\(246\) | 326064. | + | 326064.i | 0.0219027 | + | 0.0219027i | ||||
\(247\) | − | 6.15561e6i | − | 0.408489i | ||||||
\(248\) | −2.76395e6 | −0.181207 | ||||||||
\(249\) | 1.01385e7i | 0.656714i | ||||||||
\(250\) | 1.15525e7i | 0.739363i | ||||||||
\(251\) | −7.17086e6 | − | 7.17086e6i | −0.453471 | − | 0.453471i | 0.443034 | − | 0.896505i | \(-0.353902\pi\) |
−0.896505 | + | 0.443034i | \(0.853902\pi\) | |||||||
\(252\) | − | 3.41799e6i | − | 0.213584i | ||||||
\(253\) | −1.67188e7 | − | 1.67188e7i | −1.03239 | − | 1.03239i | ||||
\(254\) | 7.72432e6 | + | 7.72432e6i | 0.471367 | + | 0.471367i | ||||
\(255\) | −1.69696e6 | −0.102341 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 2.12454e7 | − | 2.12454e7i | 1.25160 | − | 1.25160i | 0.296599 | − | 0.955002i | \(-0.404148\pi\) |
0.955002 | − | 0.296599i | \(-0.0958524\pi\) | |||||||
\(258\) | − | 2.85530e6i | − | 0.166262i | ||||||
\(259\) | −7.67090e6 | − | 4.34908e6i | −0.441517 | − | 0.250322i | ||||
\(260\) | 2.84538e6 | 0.161890 | ||||||||
\(261\) | −1.23869e6 | − | 1.23869e6i | −0.0696693 | − | 0.0696693i | ||||
\(262\) | 1.55693e7i | 0.865696i | ||||||||
\(263\) | 1.66696e7i | 0.916341i | 0.888864 | + | 0.458170i | \(0.151495\pi\) | ||||
−0.888864 | + | 0.458170i | \(0.848505\pi\) | |||||||
\(264\) | 1.55094e6 | − | 1.55094e6i | 0.0842915 | − | 0.0842915i | ||||
\(265\) | −1.49639e7 | + | 1.49639e7i | −0.804092 | + | 0.804092i | ||||
\(266\) | −5.79549e6 | −0.307925 | ||||||||
\(267\) | −758548. | + | 758548.i | −0.0398519 | + | 0.0398519i | ||||
\(268\) | −2.76966e6 | −0.143887 | ||||||||
\(269\) | 2.99869e7 | 1.54055 | 0.770273 | − | 0.637715i | \(-0.220120\pi\) | ||||
0.770273 | + | 0.637715i | \(0.220120\pi\) | |||||||
\(270\) | − | 6.93681e6i | − | 0.352426i | ||||||
\(271\) | −5.00898e6 | −0.251676 | −0.125838 | − | 0.992051i | \(-0.540162\pi\) | ||||
−0.125838 | + | 0.992051i | \(0.540162\pi\) | |||||||
\(272\) | −1.34525e6 | + | 1.34525e6i | −0.0668494 | + | 0.0668494i | ||||
\(273\) | 1.38342e6 | + | 1.38342e6i | 0.0679932 | + | 0.0679932i | ||||
\(274\) | −7.22208e6 | − | 7.22208e6i | −0.351083 | − | 0.351083i | ||||
\(275\) | 9.47100e6 | 0.455405 | ||||||||
\(276\) | 5.09721e6 | − | 5.09721e6i | 0.242440 | − | 0.242440i | ||||
\(277\) | 1.42910e7 | + | 1.42910e7i | 0.672392 | + | 0.672392i | 0.958267 | − | 0.285875i | \(-0.0922842\pi\) |
−0.285875 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(278\) | 8.16120e6 | − | 8.16120e6i | 0.379856 | − | 0.379856i | ||||
\(279\) | 6.62438e6 | + | 6.62438e6i | 0.305023 | + | 0.305023i | ||||
\(280\) | − | 2.67892e6i | − | 0.122035i | ||||||
\(281\) | 1.57080e6 | − | 1.57080e6i | 0.0707948 | − | 0.0707948i | −0.670823 | − | 0.741618i | \(-0.734059\pi\) |
0.741618 | + | 0.670823i | \(0.234059\pi\) | |||||||
\(282\) | −1.43413e6 | + | 1.43413e6i | −0.0639502 | + | 0.0639502i | ||||
\(283\) | −2.15634e7 | − | 2.15634e7i | −0.951389 | − | 0.951389i | 0.0474831 | − | 0.998872i | \(-0.484880\pi\) |
−0.998872 | + | 0.0474831i | \(0.984880\pi\) | |||||||
\(284\) | − | 9.01316e6i | − | 0.393479i | ||||||
\(285\) | −5.37528e6 | −0.232202 | ||||||||
\(286\) | − | 6.67267e6i | − | 0.285234i | ||||||
\(287\) | − | 1.32077e6i | − | 0.0558703i | ||||||
\(288\) | −2.51313e6 | − | 2.51313e6i | −0.105205 | − | 0.105205i | ||||
\(289\) | 2.06858e7i | 0.856997i | ||||||||
\(290\) | −970850. | − | 970850.i | −0.0398069 | − | 0.0398069i | ||||
\(291\) | 595021. | + | 595021.i | 0.0241465 | + | 0.0241465i | ||||
\(292\) | −2.06590e7 | −0.829777 | ||||||||
\(293\) | 1.78427e6 | 0.0709343 | 0.0354672 | − | 0.999371i | \(-0.488708\pi\) | ||||
0.0354672 | + | 0.999371i | \(0.488708\pi\) | |||||||
\(294\) | −3.75378e6 | + | 3.75378e6i | −0.147716 | + | 0.147716i | ||||
\(295\) | − | 1.75296e6i | − | 0.0682820i | ||||||
\(296\) | −8.83789e6 | + | 2.44242e6i | −0.340780 | + | 0.0941771i | ||||
\(297\) | −1.62674e7 | −0.620940 | ||||||||
\(298\) | 7.73640e6 | + | 7.73640e6i | 0.292341 | + | 0.292341i | ||||
\(299\) | − | 2.19299e7i | − | 0.820394i | ||||||
\(300\) | 2.88751e6i | 0.106945i | ||||||||
\(301\) | −5.78290e6 | + | 5.78290e6i | −0.212054 | + | 0.212054i | ||||
\(302\) | −5.34770e6 | + | 5.34770e6i | −0.194154 | + | 0.194154i | ||||
\(303\) | −4.96439e6 | −0.178459 | ||||||||
\(304\) | −4.26123e6 | + | 4.26123e6i | −0.151675 | + | 0.151675i | ||||
\(305\) | −6.65826e6 | −0.234672 | ||||||||
\(306\) | 6.44837e6 | 0.225053 | ||||||||
\(307\) | 2.20472e7i | 0.761971i | 0.924581 | + | 0.380985i | \(0.124415\pi\) | ||||
−0.924581 | + | 0.380985i | \(0.875585\pi\) | |||||||
\(308\) | −6.28231e6 | −0.215014 | ||||||||
\(309\) | 4.41216e6 | − | 4.41216e6i | 0.149546 | − | 0.149546i | ||||
\(310\) | 5.19200e6 | + | 5.19200e6i | 0.174281 | + | 0.174281i | ||||
\(311\) | −2.22545e7 | − | 2.22545e7i | −0.739838 | − | 0.739838i | 0.232708 | − | 0.972547i | \(-0.425241\pi\) |
−0.972547 | + | 0.232708i | \(0.925241\pi\) | |||||||
\(312\) | 2.03436e6 | 0.0669829 | ||||||||
\(313\) | −2.13882e7 | + | 2.13882e7i | −0.697495 | + | 0.697495i | −0.963869 | − | 0.266375i | \(-0.914174\pi\) |
0.266375 | + | 0.963869i | \(0.414174\pi\) | |||||||
\(314\) | −1.27431e7 | − | 1.27431e7i | −0.411611 | − | 0.411611i | ||||
\(315\) | −6.42060e6 | + | 6.42060e6i | −0.205420 | + | 0.205420i | ||||
\(316\) | −6.21315e6 | − | 6.21315e6i | −0.196902 | − | 0.196902i | ||||
\(317\) | 2.73504e7i | 0.858589i | 0.903165 | + | 0.429294i | \(0.141238\pi\) | ||||
−0.903165 | + | 0.429294i | \(0.858762\pi\) | |||||||
\(318\) | −1.06987e7 | + | 1.06987e7i | −0.332697 | + | 0.332697i | ||||
\(319\) | −2.27673e6 | + | 2.27673e6i | −0.0701357 | + | 0.0701357i | ||||
\(320\) | −1.96972e6 | − | 1.96972e6i | −0.0601111 | − | 0.0601111i | ||||
\(321\) | − | 2.01333e7i | − | 0.608696i | ||||||
\(322\) | −2.06469e7 | −0.618426 | ||||||||
\(323\) | − | 1.09337e7i | − | 0.324460i | ||||||
\(324\) | 9.35348e6i | 0.275003i | ||||||||
\(325\) | 6.21152e6 | + | 6.21152e6i | 0.180946 | + | 0.180946i | ||||
\(326\) | − | 1.14156e7i | − | 0.329494i | ||||||
\(327\) | −3.43715e6 | − | 3.43715e6i | −0.0983005 | − | 0.0983005i | ||||
\(328\) | −971116. | − | 971116.i | −0.0275201 | − | 0.0275201i | ||||
\(329\) | 5.80915e6 | 0.163127 | ||||||||
\(330\) | −5.82680e6 | −0.162139 | ||||||||
\(331\) | −3.08628e6 | + | 3.08628e6i | −0.0851043 | + | 0.0851043i | −0.748377 | − | 0.663273i | \(-0.769167\pi\) |
0.663273 | + | 0.748377i | \(0.269167\pi\) | |||||||
\(332\) | − | 3.01955e7i | − | 0.825141i | ||||||
\(333\) | 2.70356e7 | + | 1.53281e7i | 0.732157 | + | 0.415103i | ||||
\(334\) | −3.95137e6 | −0.106049 | ||||||||
\(335\) | 5.20272e6 | + | 5.20272e6i | 0.138387 | + | 0.138387i | ||||
\(336\) | − | 1.91535e6i | − | 0.0504928i | ||||||
\(337\) | 2.62832e7i | 0.686734i | 0.939201 | + | 0.343367i | \(0.111567\pi\) | ||||
−0.939201 | + | 0.343367i | \(0.888433\pi\) | |||||||
\(338\) | −1.49310e7 | + | 1.49310e7i | −0.386668 | + | 0.386668i | ||||
\(339\) | 1.75277e7 | − | 1.75277e7i | 0.449910 | − | 0.449910i | ||||
\(340\) | 5.05404e6 | 0.128588 | ||||||||
\(341\) | 1.21757e7 | − | 1.21757e7i | 0.307065 | − | 0.307065i | ||||
\(342\) | 2.04259e7 | 0.510625 | ||||||||
\(343\) | 3.56863e7 | 0.884341 | ||||||||
\(344\) | 8.50394e6i | 0.208903i | ||||||||
\(345\) | −1.91499e7 | −0.466347 | ||||||||
\(346\) | −1.66613e7 | + | 1.66613e7i | −0.402235 | + | 0.402235i | ||||
\(347\) | 5.19175e7 | + | 5.19175e7i | 1.24258 | + | 1.24258i | 0.958925 | + | 0.283659i | \(0.0915483\pi\) |
0.283659 | + | 0.958925i | \(0.408452\pi\) | |||||||
\(348\) | −694128. | − | 694128.i | −0.0164703 | − | 0.0164703i | ||||
\(349\) | −4.51760e7 | −1.06275 | −0.531376 | − | 0.847136i | \(-0.678325\pi\) | ||||
−0.531376 | + | 0.847136i | \(0.678325\pi\) | |||||||
\(350\) | 5.84813e6 | − | 5.84813e6i | 0.136400 | − | 0.136400i | ||||
\(351\) | −1.06689e7 | − | 1.06689e7i | −0.246717 | − | 0.246717i | ||||
\(352\) | −4.61917e6 | + | 4.61917e6i | −0.105910 | + | 0.105910i | ||||
\(353\) | 2.08582e6 | + | 2.08582e6i | 0.0474191 | + | 0.0474191i | 0.730419 | − | 0.683000i | \(-0.239325\pi\) |
−0.683000 | + | 0.730419i | \(0.739325\pi\) | |||||||
\(354\) | − | 1.25331e6i | − | 0.0282521i | ||||||
\(355\) | −1.69310e7 | + | 1.69310e7i | −0.378440 | + | 0.378440i | ||||
\(356\) | 2.25918e6 | − | 2.25918e6i | 0.0500727 | − | 0.0500727i | ||||
\(357\) | 2.45726e6 | + | 2.45726e6i | 0.0540066 | + | 0.0540066i | ||||
\(358\) | − | 2.19944e7i | − | 0.479362i | ||||||
\(359\) | 5.88696e7 | 1.27235 | 0.636176 | − | 0.771544i | \(-0.280515\pi\) | ||||
0.636176 | + | 0.771544i | \(0.280515\pi\) | |||||||
\(360\) | 9.44170e6i | 0.202368i | ||||||||
\(361\) | 1.24121e7i | 0.263830i | ||||||||
\(362\) | −3.44219e7 | − | 3.44219e7i | −0.725620 | − | 0.725620i | ||||
\(363\) | − | 5.36998e6i | − | 0.112267i | ||||||
\(364\) | −4.12023e6 | − | 4.12023e6i | −0.0854313 | − | 0.0854313i | ||||
\(365\) | 3.88074e7 | + | 3.88074e7i | 0.798061 | + | 0.798061i | ||||
\(366\) | −4.76045e6 | −0.0970968 | ||||||||
\(367\) | −9.47358e7 | −1.91653 | −0.958265 | − | 0.285880i | \(-0.907714\pi\) | ||||
−0.958265 | + | 0.285880i | \(0.907714\pi\) | |||||||
\(368\) | −1.51810e7 | + | 1.51810e7i | −0.304619 | + | 0.304619i | ||||
\(369\) | 4.65497e6i | 0.0926484i | ||||||||
\(370\) | 2.11897e7 | + | 1.20137e7i | 0.418331 | + | 0.237177i | ||||
\(371\) | 4.33365e7 | 0.848657 | ||||||||
\(372\) | 3.71212e6 | + | 3.71212e6i | 0.0721096 | + | 0.0721096i | ||||
\(373\) | − | 2.54683e7i | − | 0.490765i | −0.969426 | − | 0.245382i | \(-0.921086\pi\) | ||
0.969426 | − | 0.245382i | \(-0.0789135\pi\) | |||||||
\(374\) | − | 1.18522e7i | − | 0.226560i | ||||||
\(375\) | 1.55156e7 | − | 1.55156e7i | 0.294222 | − | 0.294222i | ||||
\(376\) | 4.27127e6 | − | 4.27127e6i | 0.0803514 | − | 0.0803514i | ||||
\(377\) | −2.98637e6 | −0.0557339 | ||||||||
\(378\) | −1.00448e7 | + | 1.00448e7i | −0.185979 | + | 0.185979i | ||||
\(379\) | 5.35456e7 | 0.983572 | 0.491786 | − | 0.870716i | \(-0.336344\pi\) | ||||
0.491786 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(380\) | 1.60092e7 | 0.291755 | ||||||||
\(381\) | − | 2.07483e7i | − | 0.375152i | ||||||
\(382\) | 3.46891e7 | 0.622305 | ||||||||
\(383\) | 3.16318e7 | − | 3.16318e7i | 0.563025 | − | 0.563025i | −0.367141 | − | 0.930165i | \(-0.619663\pi\) |
0.930165 | + | 0.367141i | \(0.119663\pi\) | |||||||
\(384\) | −1.40829e6 | − | 1.40829e6i | −0.0248713 | − | 0.0248713i | ||||
\(385\) | 1.18011e7 | + | 1.18011e7i | 0.206796 | + | 0.206796i | ||||
\(386\) | −2.55551e7 | −0.444341 | ||||||||
\(387\) | 2.03815e7 | − | 2.03815e7i | 0.351644 | − | 0.351644i | ||||
\(388\) | −1.77215e6 | − | 1.77215e6i | −0.0303393 | − | 0.0303393i | ||||
\(389\) | 2.53167e7 | − | 2.53167e7i | 0.430089 | − | 0.430089i | −0.458569 | − | 0.888659i | \(-0.651638\pi\) |
0.888659 | + | 0.458569i | \(0.151638\pi\) | |||||||
\(390\) | −3.82149e6 | − | 3.82149e6i | −0.0644227 | − | 0.0644227i | ||||
\(391\) | − | 3.89524e7i | − | 0.651634i | ||||||
\(392\) | 1.11799e7 | − | 1.11799e7i | 0.185601 | − | 0.185601i | ||||
\(393\) | 2.09104e7 | − | 2.09104e7i | 0.344496 | − | 0.344496i | ||||
\(394\) | −1.61911e7 | − | 1.61911e7i | −0.264721 | − | 0.264721i | ||||
\(395\) | 2.33425e7i | 0.378752i | ||||||||
\(396\) | 2.21416e7 | 0.356553 | ||||||||
\(397\) | − | 7.25089e7i | − | 1.15883i | −0.815033 | − | 0.579415i | \(-0.803281\pi\) | ||
0.815033 | − | 0.579415i | \(-0.196719\pi\) | |||||||
\(398\) | 2.00377e7i | 0.317833i | ||||||||
\(399\) | 7.78363e6 | + | 7.78363e6i | 0.122536 | + | 0.122536i | ||||
\(400\) | − | 8.59987e6i | − | 0.134373i | ||||||
\(401\) | −3.23386e7 | − | 3.23386e7i | −0.501519 | − | 0.501519i | 0.410390 | − | 0.911910i | \(-0.365392\pi\) |
−0.911910 | + | 0.410390i | \(0.865392\pi\) | |||||||
\(402\) | 3.71979e6 | + | 3.71979e6i | 0.0572585 | + | 0.0572585i | ||||
\(403\) | 1.59708e7 | 0.244012 | ||||||||
\(404\) | 1.47854e7 | 0.224228 | ||||||||
\(405\) | 1.75702e7 | − | 1.75702e7i | 0.264492 | − | 0.264492i | ||||
\(406\) | 2.81166e6i | 0.0420131i | ||||||||
\(407\) | 2.81732e7 | − | 4.96918e7i | 0.417882 | − | 0.737058i | ||||
\(408\) | 3.61348e6 | 0.0532041 | ||||||||
\(409\) | 6.70387e7 | + | 6.70387e7i | 0.979841 | + | 0.979841i | 0.999801 | − | 0.0199599i | \(-0.00635384\pi\) |
−0.0199599 | + | 0.999801i | \(0.506354\pi\) | |||||||
\(410\) | 3.64843e6i | 0.0529364i | ||||||||
\(411\) | 1.93992e7i | 0.279421i | ||||||||
\(412\) | −1.31407e7 | + | 1.31407e7i | −0.187900 | + | 0.187900i | ||||
\(413\) | −2.53836e6 | + | 2.53836e6i | −0.0360332 | + | 0.0360332i | ||||
\(414\) | 7.27689e7 | 1.02552 | ||||||||
\(415\) | −5.67214e7 | + | 5.67214e7i | −0.793602 | + | 0.793602i | ||||
\(416\) | −6.05893e6 | −0.0841620 | ||||||||
\(417\) | −2.19218e7 | −0.302321 | ||||||||
\(418\) | − | 3.75430e7i | − | 0.514043i | ||||||
\(419\) | 1.91994e7 | 0.261003 | 0.130501 | − | 0.991448i | \(-0.458341\pi\) | ||||
0.130501 | + | 0.991448i | \(0.458341\pi\) | |||||||
\(420\) | −3.59792e6 | + | 3.59792e6i | −0.0485628 | + | 0.0485628i | ||||
\(421\) | −3.19569e7 | − | 3.19569e7i | −0.428270 | − | 0.428270i | 0.459768 | − | 0.888039i | \(-0.347932\pi\) |
−0.888039 | + | 0.459768i | \(0.847932\pi\) | |||||||
\(422\) | −3.46841e7 | − | 3.46841e7i | −0.461523 | − | 0.461523i | ||||
\(423\) | −2.04740e7 | −0.270509 | ||||||||
\(424\) | 3.18639e7 | − | 3.18639e7i | 0.418024 | − | 0.418024i | ||||
\(425\) | 1.10331e7 | + | 1.10331e7i | 0.143724 | + | 0.143724i | ||||
\(426\) | −1.21051e7 | + | 1.21051e7i | −0.156581 | + | 0.156581i | ||||
\(427\) | 9.64143e6 | + | 9.64143e6i | 0.123839 | + | 0.123839i | ||||
\(428\) | 5.99630e7i | 0.764807i | ||||||||
\(429\) | −8.96173e6 | + | 8.96173e6i | −0.113506 | + | 0.113506i | ||||
\(430\) | 1.59744e7 | − | 1.59744e7i | 0.200918 | − | 0.200918i | ||||
\(431\) | −5.49252e7 | − | 5.49252e7i | −0.686025 | − | 0.686025i | 0.275326 | − | 0.961351i | \(-0.411214\pi\) |
−0.961351 | + | 0.275326i | \(0.911214\pi\) | |||||||
\(432\) | 1.47712e7i | 0.183216i | ||||||||
\(433\) | 4.30237e7 | 0.529962 | 0.264981 | − | 0.964254i | \(-0.414634\pi\) | ||||
0.264981 | + | 0.964254i | \(0.414634\pi\) | |||||||
\(434\) | − | 1.50364e7i | − | 0.183940i | ||||||
\(435\) | 2.60780e6i | 0.0316815i | ||||||||
\(436\) | 1.02369e7 | + | 1.02369e7i | 0.123512 | + | 0.123512i | ||||
\(437\) | − | 1.23386e8i | − | 1.47850i | ||||||
\(438\) | 2.77461e7 | + | 2.77461e7i | 0.330202 | + | 0.330202i | ||||
\(439\) | −9.56775e7 | − | 9.56775e7i | −1.13088 | − | 1.13088i | −0.990031 | − | 0.140848i | \(-0.955017\pi\) |
−0.140848 | − | 0.990031i | \(-0.544983\pi\) | |||||||
\(440\) | 1.73540e7 | 0.203723 | ||||||||
\(441\) | −5.35899e7 | −0.624838 | ||||||||
\(442\) | 7.77320e6 | − | 7.77320e6i | 0.0900188 | − | 0.0900188i | ||||
\(443\) | 1.32723e8i | 1.52663i | 0.646027 | + | 0.763315i | \(0.276429\pi\) | ||||
−0.646027 | + | 0.763315i | \(0.723571\pi\) | |||||||
\(444\) | 1.51500e7 | + | 8.58943e6i | 0.173087 | + | 0.0981331i | ||||
\(445\) | −8.48762e6 | −0.0963177 | ||||||||
\(446\) | −5.67576e6 | − | 5.67576e6i | −0.0639764 | − | 0.0639764i | ||||
\(447\) | − | 2.07807e7i | − | 0.232669i | ||||||
\(448\) | 5.70447e6i | 0.0634426i | ||||||||
\(449\) | −6.26817e7 | + | 6.26817e7i | −0.692471 | + | 0.692471i | −0.962775 | − | 0.270304i | \(-0.912876\pi\) |
0.270304 | + | 0.962775i | \(0.412876\pi\) | |||||||
\(450\) | −2.06114e7 | + | 2.06114e7i | −0.226188 | + | 0.226188i | ||||
\(451\) | 8.55589e6 | 0.0932686 | ||||||||
\(452\) | −5.22027e7 | + | 5.22027e7i | −0.565299 | + | 0.565299i | ||||
\(453\) | 1.43644e7 | 0.154523 | ||||||||
\(454\) | 9.43955e7 | 1.00875 | ||||||||
\(455\) | 1.54795e7i | 0.164332i | ||||||||
\(456\) | 1.14461e7 | 0.120715 | ||||||||
\(457\) | 5.16082e7 | − | 5.16082e7i | 0.540717 | − | 0.540717i | −0.383022 | − | 0.923739i | \(-0.625117\pi\) |
0.923739 | + | 0.383022i | \(0.125117\pi\) | |||||||
\(458\) | 7.40269e6 | + | 7.40269e6i | 0.0770536 | + | 0.0770536i | ||||
\(459\) | −1.89504e7 | − | 1.89504e7i | −0.195966 | − | 0.195966i | ||||
\(460\) | 5.70341e7 | 0.585951 | ||||||||
\(461\) | −7.61349e7 | + | 7.61349e7i | −0.777107 | + | 0.777107i | −0.979338 | − | 0.202231i | \(-0.935181\pi\) |
0.202231 | + | 0.979338i | \(0.435181\pi\) | |||||||
\(462\) | 8.43745e6 | + | 8.43745e6i | 0.0855628 | + | 0.0855628i | ||||
\(463\) | −1.34840e8 | + | 1.34840e8i | −1.35855 | + | 1.35855i | −0.482852 | + | 0.875702i | \(0.660399\pi\) |
−0.875702 | + | 0.482852i | \(0.839601\pi\) | |||||||
\(464\) | 2.06732e6 | + | 2.06732e6i | 0.0206944 | + | 0.0206944i | ||||
\(465\) | − | 1.39462e7i | − | 0.138707i | ||||||
\(466\) | −4.83058e7 | + | 4.83058e7i | −0.477355 | + | 0.477355i | ||||
\(467\) | −9.32470e7 | + | 9.32470e7i | −0.915555 | + | 0.915555i | −0.996702 | − | 0.0811476i | \(-0.974141\pi\) |
0.0811476 | + | 0.996702i | \(0.474141\pi\) | |||||||
\(468\) | 1.45215e7 | + | 1.45215e7i | 0.141669 | + | 0.141669i | ||||
\(469\) | − | 1.50675e7i | − | 0.146057i | ||||||
\(470\) | −1.60469e7 | −0.154560 | ||||||||
\(471\) | 3.42293e7i | 0.327593i | ||||||||
\(472\) | 3.73274e6i | 0.0354978i | ||||||||
\(473\) | −3.74614e7 | − | 3.74614e7i | −0.353998 | − | 0.353998i | ||||
\(474\) | 1.66891e7i | 0.156711i | ||||||||
\(475\) | 3.49484e7 | + | 3.49484e7i | 0.326096 | + | 0.326096i | ||||
\(476\) | −7.31845e6 | − | 7.31845e6i | −0.0678576 | − | 0.0678576i | ||||
\(477\) | −1.52737e8 | −1.40731 | ||||||||
\(478\) | 2.25014e7 | 0.206027 | ||||||||
\(479\) | −5.94649e7 | + | 5.94649e7i | −0.541071 | + | 0.541071i | −0.923843 | − | 0.382772i | \(-0.874969\pi\) |
0.382772 | + | 0.923843i | \(0.374969\pi\) | |||||||
\(480\) | 5.29086e6i | 0.0478413i | ||||||||
\(481\) | 5.10675e7 | − | 1.41129e7i | 0.458891 | − | 0.126818i | ||||
\(482\) | −6.02449e7 | −0.537996 | ||||||||
\(483\) | 2.77298e7 | + | 2.77298e7i | 0.246097 | + | 0.246097i | ||||
\(484\) | 1.59934e7i | 0.141060i | ||||||||
\(485\) | 6.65787e6i | 0.0583593i | ||||||||
\(486\) | 5.46254e7 | − | 5.46254e7i | 0.475867 | − | 0.475867i | ||||
\(487\) | −7.43155e7 | + | 7.43155e7i | −0.643417 | + | 0.643417i | −0.951394 | − | 0.307977i | \(-0.900348\pi\) |
0.307977 | + | 0.951394i | \(0.400348\pi\) | |||||||
\(488\) | 1.41780e7 | 0.121999 | ||||||||
\(489\) | −1.53318e7 | + | 1.53318e7i | −0.131119 | + | 0.131119i | ||||
\(490\) | −4.20022e7 | −0.357013 | ||||||||
\(491\) | 3.06751e7 | 0.259144 | 0.129572 | − | 0.991570i | \(-0.458640\pi\) | ||||
0.129572 | + | 0.991570i | \(0.458640\pi\) | |||||||
\(492\) | 2.60851e6i | 0.0219027i | ||||||||
\(493\) | −5.30446e6 | −0.0442691 | ||||||||
\(494\) | 2.46224e7 | − | 2.46224e7i | 0.204244 | − | 0.204244i | ||||
\(495\) | −4.15924e7 | − | 4.15924e7i | −0.342924 | − | 0.342924i | ||||
\(496\) | −1.10558e7 | − | 1.10558e7i | −0.0906034 | − | 0.0906034i | ||||
\(497\) | 4.90334e7 | 0.399414 | ||||||||
\(498\) | −4.05541e7 | + | 4.05541e7i | −0.328357 | + | 0.328357i | ||||
\(499\) | 2.45175e7 | + | 2.45175e7i | 0.197322 | + | 0.197322i | 0.798851 | − | 0.601529i | \(-0.205442\pi\) |
−0.601529 | + | 0.798851i | \(0.705442\pi\) | |||||||
\(500\) | −4.62102e7 | + | 4.62102e7i | −0.369681 | + | 0.369681i | ||||
\(501\) | 5.30689e6 | + | 5.30689e6i | 0.0422014 | + | 0.0422014i | ||||
\(502\) | − | 5.73669e7i | − | 0.453471i | ||||||
\(503\) | −1.85732e7 | + | 1.85732e7i | −0.145943 | + | 0.145943i | −0.776303 | − | 0.630360i | \(-0.782907\pi\) |
0.630360 | + | 0.776303i | \(0.282907\pi\) | |||||||
\(504\) | 1.36720e7 | − | 1.36720e7i | 0.106792 | − | 0.106792i | ||||
\(505\) | −2.77740e7 | − | 2.77740e7i | −0.215657 | − | 0.215657i | ||||
\(506\) | − | 1.33750e8i | − | 1.03239i | ||||||
\(507\) | 4.01061e7 | 0.307742 | ||||||||
\(508\) | 6.17945e7i | 0.471367i | ||||||||
\(509\) | 1.40587e8i | 1.06609i | 0.846087 | + | 0.533044i | \(0.178952\pi\) | ||||
−0.846087 | + | 0.533044i | \(0.821048\pi\) | |||||||
\(510\) | −6.78782e6 | − | 6.78782e6i | −0.0511705 | − | 0.0511705i | ||||
\(511\) | − | 1.12389e8i | − | 0.842292i | ||||||
\(512\) | 4.19430e6 | + | 4.19430e6i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −6.00274e7 | − | 6.00274e7i | −0.444629 | − | 0.444629i | ||||
\(514\) | 1.69963e8 | 1.25160 | ||||||||
\(515\) | 4.93689e7 | 0.361436 | ||||||||
\(516\) | 1.14212e7 | − | 1.14212e7i | 0.0831310 | − | 0.0831310i | ||||
\(517\) | 3.76315e7i | 0.272320i | ||||||||
\(518\) | −1.32873e7 | − | 4.80799e7i | −0.0955975 | − | 0.345919i | ||||
\(519\) | 4.47539e7 | 0.320132 | ||||||||
\(520\) | 1.13815e7 | + | 1.13815e7i | 0.0809451 | + | 0.0809451i | ||||
\(521\) | − | 1.86652e8i | − | 1.31984i | −0.751338 | − | 0.659918i | \(-0.770591\pi\) | ||
0.751338 | − | 0.659918i | \(-0.229409\pi\) | |||||||
\(522\) | − | 9.90953e6i | − | 0.0696693i | ||||||
\(523\) | −5.86978e7 | + | 5.86978e7i | −0.410314 | + | 0.410314i | −0.881848 | − | 0.471534i | \(-0.843701\pi\) |
0.471534 | + | 0.881848i | \(0.343701\pi\) | |||||||
\(524\) | −6.22773e7 | + | 6.22773e7i | −0.432848 | + | 0.432848i | ||||
\(525\) | −1.57087e7 | −0.108558 | ||||||||
\(526\) | −6.66783e7 | + | 6.66783e7i | −0.458170 | + | 0.458170i | ||||
\(527\) | 2.83677e7 | 0.193817 | ||||||||
\(528\) | 1.24075e7 | 0.0842915 | ||||||||
\(529\) | − | 2.91537e8i | − | 1.96936i | ||||||
\(530\) | −1.19711e8 | −0.804092 | ||||||||
\(531\) | 8.94630e6 | − | 8.94630e6i | 0.0597530 | − | 0.0597530i | ||||
\(532\) | −2.31820e7 | − | 2.31820e7i | −0.153963 | − | 0.153963i | ||||
\(533\) | 5.61135e6 | + | 5.61135e6i | 0.0370583 | + | 0.0370583i | ||||
\(534\) | −6.06839e6 | −0.0398519 | ||||||||
\(535\) | 1.12639e8 | − | 1.12639e8i | 0.735574 | − | 0.735574i | ||||
\(536\) | −1.10786e7 | − | 1.10786e7i | −0.0719435 | − | 0.0719435i | ||||
\(537\) | −2.95396e7 | + | 2.95396e7i | −0.190758 | + | 0.190758i | ||||
\(538\) | 1.19948e8 | + | 1.19948e8i | 0.770273 | + | 0.770273i | ||||
\(539\) | 9.84989e7i | 0.629021i | ||||||||
\(540\) | 2.77472e7 | − | 2.77472e7i | 0.176213 | − | 0.176213i | ||||
\(541\) | 1.26758e8 | − | 1.26758e8i | 0.800541 | − | 0.800541i | −0.182639 | − | 0.983180i | \(-0.558464\pi\) |
0.983180 | + | 0.182639i | \(0.0584641\pi\) | |||||||
\(542\) | −2.00359e7 | − | 2.00359e7i | −0.125838 | − | 0.125838i | ||||
\(543\) | 9.24607e7i | 0.577507i | ||||||||
\(544\) | −1.07620e7 | −0.0668494 | ||||||||
\(545\) | − | 3.84593e7i | − | 0.237581i | ||||||
\(546\) | 1.10673e7i | 0.0679932i | ||||||||
\(547\) | −1.75535e8 | − | 1.75535e8i | −1.07251 | − | 1.07251i | −0.997157 | − | 0.0753551i | \(-0.975991\pi\) |
−0.0753551 | − | 0.997157i | \(-0.524009\pi\) | |||||||
\(548\) | − | 5.77766e7i | − | 0.351083i | ||||||
\(549\) | −3.39807e7 | − | 3.39807e7i | −0.205359 | − | 0.205359i | ||||
\(550\) | 3.78840e7 | + | 3.78840e7i | 0.227703 | + | 0.227703i | ||||
\(551\) | −1.68024e7 | −0.100442 | ||||||||
\(552\) | 4.07776e7 | 0.242440 | ||||||||
\(553\) | 3.38008e7 | − | 3.38008e7i | 0.199872 | − | 0.199872i | ||||
\(554\) | 1.14328e8i | 0.672392i | ||||||||
\(555\) | −1.23239e7 | − | 4.45939e7i | −0.0720888 | − | 0.260853i | ||||
\(556\) | 6.52896e7 | 0.379856 | ||||||||
\(557\) | 2.51207e7 | + | 2.51207e7i | 0.145367 | + | 0.145367i | 0.776045 | − | 0.630678i | \(-0.217223\pi\) |
−0.630678 | + | 0.776045i | \(0.717223\pi\) | |||||||
\(558\) | 5.29951e7i | 0.305023i | ||||||||
\(559\) | − | 4.91379e7i | − | 0.281307i | ||||||
\(560\) | 1.07157e7 | − | 1.07157e7i | 0.0610177 | − | 0.0610177i | ||||
\(561\) | −1.59180e7 | + | 1.59180e7i | −0.0901574 | + | 0.0901574i | ||||
\(562\) | 1.25664e7 | 0.0707948 | ||||||||
\(563\) | −6.68578e6 | + | 6.68578e6i | −0.0374651 | + | 0.0374651i | −0.725591 | − | 0.688126i | \(-0.758434\pi\) |
0.688126 | + | 0.725591i | \(0.258434\pi\) | |||||||
\(564\) | −1.14731e7 | −0.0639502 | ||||||||
\(565\) | 1.96123e8 | 1.08738 | ||||||||
\(566\) | − | 1.72507e8i | − | 0.951389i | ||||||
\(567\) | −5.08848e7 | −0.279151 | ||||||||
\(568\) | 3.60526e7 | − | 3.60526e7i | 0.196740 | − | 0.196740i | ||||
\(569\) | 1.68698e8 | + | 1.68698e8i | 0.915742 | + | 0.915742i | 0.996716 | − | 0.0809745i | \(-0.0258032\pi\) |
−0.0809745 | + | 0.996716i | \(0.525803\pi\) | |||||||
\(570\) | −2.15011e7 | − | 2.15011e7i | −0.116101 | − | 0.116101i | ||||
\(571\) | 5.49139e7 | 0.294967 | 0.147484 | − | 0.989064i | \(-0.452883\pi\) | ||||
0.147484 | + | 0.989064i | \(0.452883\pi\) | |||||||
\(572\) | 2.66907e7 | − | 2.66907e7i | 0.142617 | − | 0.142617i | ||||
\(573\) | −4.65892e7 | − | 4.65892e7i | −0.247640 | − | 0.247640i | ||||
\(574\) | 5.28307e6 | − | 5.28307e6i | 0.0279351 | − | 0.0279351i | ||||
\(575\) | 1.24507e8 | + | 1.24507e8i | 0.654921 | + | 0.654921i | ||||
\(576\) | − | 2.01051e7i | − | 0.105205i | ||||||
\(577\) | 1.41186e8 | − | 1.41186e8i | 0.734961 | − | 0.734961i | −0.236637 | − | 0.971598i | \(-0.576045\pi\) |
0.971598 | + | 0.236637i | \(0.0760453\pi\) | |||||||
\(578\) | −8.27433e7 | + | 8.27433e7i | −0.428499 | + | 0.428499i | ||||
\(579\) | 3.43218e7 | + | 3.43218e7i | 0.176821 | + | 0.176821i | ||||
\(580\) | − | 7.76680e6i | − | 0.0398069i | ||||||
\(581\) | 1.64270e8 | 0.837586 | ||||||||
\(582\) | 4.76017e6i | 0.0241465i | ||||||||
\(583\) | 2.80733e8i | 1.41673i | ||||||||
\(584\) | −8.26361e7 | − | 8.26361e7i | −0.414889 | − | 0.414889i | ||||
\(585\) | − | 5.45565e7i | − | 0.272508i | ||||||
\(586\) | 7.13706e6 | + | 7.13706e6i | 0.0354672 | + | 0.0354672i | ||||
\(587\) | 1.78196e8 | + | 1.78196e8i | 0.881014 | + | 0.881014i | 0.993638 | − | 0.112624i | \(-0.0359255\pi\) |
−0.112624 | + | 0.993638i | \(0.535926\pi\) | |||||||
\(588\) | −3.00303e7 | −0.147716 | ||||||||
\(589\) | 8.98575e7 | 0.439753 | ||||||||
\(590\) | 7.01185e6 | − | 7.01185e6i | 0.0341410 | − | 0.0341410i | ||||
\(591\) | 4.34910e7i | 0.210686i | ||||||||
\(592\) | −4.51212e7 | − | 2.55819e7i | −0.217478 | − | 0.123301i | ||||
\(593\) | 1.71632e8 | 0.823067 | 0.411533 | − | 0.911395i | \(-0.364993\pi\) | ||||
0.411533 | + | 0.911395i | \(0.364993\pi\) | |||||||
\(594\) | −6.50697e7 | − | 6.50697e7i | −0.310470 | − | 0.310470i | ||||
\(595\) | 2.74950e7i | 0.130528i | ||||||||
\(596\) | 6.18912e7i | 0.292341i | ||||||||
\(597\) | 2.69116e7 | − | 2.69116e7i | 0.126479 | − | 0.126479i | ||||
\(598\) | 8.77195e7 | − | 8.77195e7i | 0.410197 | − | 0.410197i | ||||
\(599\) | −2.12461e8 | −0.988548 | −0.494274 | − | 0.869306i | \(-0.664566\pi\) | ||||
−0.494274 | + | 0.869306i | \(0.664566\pi\) | |||||||
\(600\) | −1.15501e7 | + | 1.15501e7i | −0.0534725 | + | 0.0534725i | ||||
\(601\) | 2.54871e8 | 1.17408 | 0.587040 | − | 0.809558i | \(-0.300293\pi\) | ||||
0.587040 | + | 0.809558i | \(0.300293\pi\) | |||||||
\(602\) | −4.62632e7 | −0.212054 | ||||||||
\(603\) | 5.31046e7i | 0.242203i | ||||||||
\(604\) | −4.27816e7 | −0.194154 | ||||||||
\(605\) | 3.00431e7 | − | 3.00431e7i | 0.135668 | − | 0.135668i | ||||
\(606\) | −1.98576e7 | − | 1.98576e7i | −0.0892294 | − | 0.0892294i | ||||
\(607\) | 1.19721e8 | + | 1.19721e8i | 0.535311 | + | 0.535311i | 0.922148 | − | 0.386837i | \(-0.126432\pi\) |
−0.386837 | + | 0.922148i | \(0.626432\pi\) | |||||||
\(608\) | −3.40898e7 | −0.151675 | ||||||||
\(609\) | 3.77620e6 | − | 3.77620e6i | 0.0167187 | − | 0.0167187i | ||||
\(610\) | −2.66330e7 | − | 2.66330e7i | −0.117336 | − | 0.117336i | ||||
\(611\) | −2.46805e7 | + | 2.46805e7i | −0.108201 | + | 0.108201i | ||||
\(612\) | 2.57935e7 | + | 2.57935e7i | 0.112527 | + | 0.112527i | ||||
\(613\) | 3.86636e7i | 0.167850i | 0.996472 | + | 0.0839249i | \(0.0267456\pi\) | ||||
−0.996472 | + | 0.0839249i | \(0.973254\pi\) | |||||||
\(614\) | −8.81888e7 | + | 8.81888e7i | −0.380985 | + | 0.380985i | ||||
\(615\) | 4.90002e6 | − | 4.90002e6i | 0.0210655 | − | 0.0210655i | ||||
\(616\) | −2.51292e7 | − | 2.51292e7i | −0.107507 | − | 0.107507i | ||||
\(617\) | 8.56940e7i | 0.364834i | 0.983221 | + | 0.182417i | \(0.0583921\pi\) | ||||
−0.983221 | + | 0.182417i | \(0.941608\pi\) | |||||||
\(618\) | 3.52973e7 | 0.149546 | ||||||||
\(619\) | − | 1.72438e8i | − | 0.727044i | −0.931586 | − | 0.363522i | \(-0.881574\pi\) | ||
0.931586 | − | 0.363522i | \(-0.118426\pi\) | |||||||
\(620\) | 4.15360e7i | 0.174281i | ||||||||
\(621\) | −2.13853e8 | − | 2.13853e8i | −0.892977 | − | 0.892977i | ||||
\(622\) | − | 1.78036e8i | − | 0.739838i | ||||||
\(623\) | 1.22904e7 | + | 1.22904e7i | 0.0508279 | + | 0.0508279i | ||||
\(624\) | 8.13744e6 | + | 8.13744e6i | 0.0334915 | + | 0.0334915i | ||||
\(625\) | 4.23853e7 | 0.173610 | ||||||||
\(626\) | −1.71105e8 | −0.697495 | ||||||||
\(627\) | −5.04221e7 | + | 5.04221e7i | −0.204559 | + | 0.204559i | ||||
\(628\) | − | 1.01945e8i | − | 0.411611i | ||||||
\(629\) | 9.07074e7 | − | 2.50677e7i | 0.364494 | − | 0.100731i | ||||
\(630\) | −5.13648e7 | −0.205420 | ||||||||
\(631\) | −1.06920e8 | − | 1.06920e8i | −0.425570 | − | 0.425570i | 0.461546 | − | 0.887116i | \(-0.347295\pi\) |
−0.887116 | + | 0.461546i | \(0.847295\pi\) | |||||||
\(632\) | − | 4.97052e7i | − | 0.196902i | ||||||
\(633\) | 9.31650e7i | 0.367318i | ||||||||
\(634\) | −1.09401e8 | + | 1.09401e8i | −0.429294 | + | 0.429294i | ||||
\(635\) | 1.16079e8 | − | 1.16079e8i | 0.453350 | − | 0.453350i | ||||
\(636\) | −8.55896e7 | −0.332697 | ||||||||
\(637\) | −6.46001e7 | + | 6.46001e7i | −0.249928 | + | 0.249928i | ||||
\(638\) | −1.82138e7 | −0.0701357 | ||||||||
\(639\) | −1.72815e8 | −0.662339 | ||||||||
\(640\) | − | 1.57578e7i | − | 0.0601111i | ||||||
\(641\) | −2.87915e8 | −1.09318 | −0.546589 | − | 0.837401i | \(-0.684074\pi\) | ||||
−0.546589 | + | 0.837401i | \(0.684074\pi\) | |||||||
\(642\) | 8.05333e7 | − | 8.05333e7i | 0.304348 | − | 0.304348i | ||||
\(643\) | 2.98112e8 | + | 2.98112e8i | 1.12136 | + | 1.12136i | 0.991537 | + | 0.129826i | \(0.0414417\pi\) |
0.129826 | + | 0.991537i | \(0.458558\pi\) | |||||||
\(644\) | −8.25877e7 | − | 8.25877e7i | −0.309213 | − | 0.309213i | ||||
\(645\) | −4.29088e7 | −0.159907 | ||||||||
\(646\) | 4.37350e7 | − | 4.37350e7i | 0.162230 | − | 0.162230i | ||||
\(647\) | −1.47868e8 | − | 1.47868e8i | −0.545961 | − | 0.545961i | 0.379309 | − | 0.925270i | \(-0.376162\pi\) |
−0.925270 | + | 0.379309i | \(0.876162\pi\) | |||||||
\(648\) | −3.74139e7 | + | 3.74139e7i | −0.137502 | + | 0.137502i | ||||
\(649\) | −1.64434e7 | − | 1.64434e7i | −0.0601531 | − | 0.0601531i | ||||
\(650\) | 4.96922e7i | 0.180946i | ||||||||
\(651\) | −2.01947e7 | + | 2.01947e7i | −0.0731971 | + | 0.0731971i | ||||
\(652\) | 4.56625e7 | − | 4.56625e7i | 0.164747 | − | 0.164747i | ||||
\(653\) | 6.68189e7 | + | 6.68189e7i | 0.239971 | + | 0.239971i | 0.816838 | − | 0.576867i | \(-0.195725\pi\) |
−0.576867 | + | 0.816838i | \(0.695725\pi\) | |||||||
\(654\) | − | 2.74972e7i | − | 0.0983005i | ||||||
\(655\) | 2.33972e8 | 0.832607 | ||||||||
\(656\) | − | 7.76893e6i | − | 0.0275201i | ||||||
\(657\) | 3.96110e8i | 1.39675i | ||||||||
\(658\) | 2.32366e7 | + | 2.32366e7i | 0.0815633 | + | 0.0815633i | ||||
\(659\) | − | 4.11029e7i | − | 0.143620i | −0.997418 | − | 0.0718102i | \(-0.977122\pi\) | ||
0.997418 | − | 0.0718102i | \(-0.0228776\pi\) | |||||||
\(660\) | −2.33072e7 | − | 2.33072e7i | −0.0810697 | − | 0.0810697i | ||||
\(661\) | −2.13091e8 | − | 2.13091e8i | −0.737839 | − | 0.737839i | 0.234321 | − | 0.972159i | \(-0.424713\pi\) |
−0.972159 | + | 0.234321i | \(0.924713\pi\) | |||||||
\(662\) | −2.46903e7 | −0.0851043 | ||||||||
\(663\) | −2.08796e7 | −0.0716443 | ||||||||
\(664\) | 1.20782e8 | − | 1.20782e8i | 0.412570 | − | 0.412570i | ||||
\(665\) | 8.70933e7i | 0.296155i | ||||||||
\(666\) | 4.68302e7 | + | 1.69455e8i | 0.158527 | + | 0.573630i | ||||
\(667\) | −5.98601e7 | −0.201725 | ||||||||
\(668\) | −1.58055e7 | − | 1.58055e7i | −0.0530247 | − | 0.0530247i | ||||
\(669\) | 1.52457e7i | 0.0509176i | ||||||||
\(670\) | 4.16218e7i | 0.138387i | ||||||||
\(671\) | −6.24568e7 | + | 6.24568e7i | −0.206734 | + | 0.206734i | ||||
\(672\) | 7.66138e6 | − | 7.66138e6i | 0.0252464 | − | 0.0252464i | ||||
\(673\) | −2.78761e8 | −0.914506 | −0.457253 | − | 0.889337i | \(-0.651167\pi\) | ||||
−0.457253 | + | 0.889337i | \(0.651167\pi\) | |||||||
\(674\) | −1.05133e8 | + | 1.05133e8i | −0.343367 | + | 0.343367i | ||||
\(675\) | 1.21145e8 | 0.393909 | ||||||||
\(676\) | −1.19448e8 | −0.386668 | ||||||||
\(677\) | − | 2.88714e8i | − | 0.930467i | −0.885188 | − | 0.465234i | \(-0.845970\pi\) | ||
0.885188 | − | 0.465234i | \(-0.154030\pi\) | |||||||
\(678\) | 1.40222e8 | 0.449910 | ||||||||
\(679\) | 9.64086e6 | − | 9.64086e6i | 0.0307969 | − | 0.0307969i | ||||
\(680\) | 2.02162e7 | + | 2.02162e7i | 0.0642942 | + | 0.0642942i | ||||
\(681\) | −1.26778e8 | − | 1.26778e8i | −0.401423 | − | 0.401423i | ||||
\(682\) | 9.74055e7 | 0.307065 | ||||||||
\(683\) | 679783. | − | 679783.i | 0.00213358 | − | 0.00213358i | −0.706039 | − | 0.708173i | \(-0.749520\pi\) |
0.708173 | + | 0.706039i | \(0.249520\pi\) | |||||||
\(684\) | 8.17034e7 | + | 8.17034e7i | 0.255312 | + | 0.255312i | ||||
\(685\) | −1.08532e8 | + | 1.08532e8i | −0.337664 | + | 0.337664i | ||||
\(686\) | 1.42745e8 | + | 1.42745e8i | 0.442170 | + | 0.442170i | ||||
\(687\) | − | 1.98843e7i | − | 0.0613255i | ||||||
\(688\) | −3.40158e7 | + | 3.40158e7i | −0.104452 | + | 0.104452i | ||||
\(689\) | −1.84117e8 | + | 1.84117e8i | −0.562908 | + | 0.562908i | ||||
\(690\) | −7.65996e7 | − | 7.65996e7i | −0.233174 | − | 0.233174i | ||||
\(691\) | 3.05221e7i | 0.0925081i | 0.998930 | + | 0.0462540i | \(0.0147284\pi\) | ||||
−0.998930 | + | 0.0462540i | \(0.985272\pi\) | |||||||
\(692\) | −1.33290e8 | −0.402235 | ||||||||
\(693\) | 1.20455e8i | 0.361930i | ||||||||
\(694\) | 4.15340e8i | 1.24258i | ||||||||
\(695\) | −1.22645e8 | − | 1.22645e8i | −0.365337 | − | 0.365337i | ||||
\(696\) | − | 5.55302e6i | − | 0.0164703i | ||||||
\(697\) | 9.96702e6 | + | 9.96702e6i | 0.0294352 | + | 0.0294352i | ||||
\(698\) | −1.80704e8 | − | 1.80704e8i | −0.531376 | − | 0.531376i | ||||
\(699\) | 1.29754e8 | 0.379918 | ||||||||
\(700\) | 4.67851e7 | 0.136400 | ||||||||
\(701\) | 1.36393e8 | − | 1.36393e8i | 0.395947 | − | 0.395947i | −0.480854 | − | 0.876801i | \(-0.659673\pi\) |
0.876801 | + | 0.480854i | \(0.159673\pi\) | |||||||
\(702\) | − | 8.53515e7i | − | 0.246717i | ||||||
\(703\) | 2.87325e8 | − | 7.94045e7i | 0.827004 | − | 0.228549i | ||||
\(704\) | −3.69534e7 | −0.105910 | ||||||||
\(705\) | 2.15518e7 | + | 2.15518e7i | 0.0615058 | + | 0.0615058i | ||||
\(706\) | 1.66866e7i | 0.0474191i | ||||||||
\(707\) | 8.04357e7i | 0.227610i | ||||||||
\(708\) | 5.01326e6 | − | 5.01326e6i | 0.0141260 | − | 0.0141260i | ||||
\(709\) | 9.23054e7 | − | 9.23054e7i | 0.258993 | − | 0.258993i | −0.565651 | − | 0.824645i | \(-0.691375\pi\) |
0.824645 | + | 0.565651i | \(0.191375\pi\) | |||||||
\(710\) | −1.35448e8 | −0.378440 | ||||||||
\(711\) | −1.19129e8 | + | 1.19129e8i | −0.331443 | + | 0.331443i | ||||
\(712\) | 1.80735e7 | 0.0500727 | ||||||||
\(713\) | 3.20125e8 | 0.883185 | ||||||||
\(714\) | 1.96581e7i | 0.0540066i | ||||||||
\(715\) | −1.00275e8 | −0.274332 | ||||||||
\(716\) | 8.79777e7 | − | 8.79777e7i | 0.239681 | − | 0.239681i | ||||
\(717\) | −3.02204e7 | − | 3.02204e7i | −0.0819867 | − | 0.0819867i | ||||
\(718\) | 2.35478e8 | + | 2.35478e8i | 0.636176 | + | 0.636176i | ||||
\(719\) | −5.58546e8 | −1.50270 | −0.751350 | − | 0.659904i | \(-0.770597\pi\) | ||||
−0.751350 | + | 0.659904i | \(0.770597\pi\) | |||||||
\(720\) | −3.77668e7 | + | 3.77668e7i | −0.101184 | + | 0.101184i | ||||
\(721\) | −7.14882e7 | − | 7.14882e7i | −0.190734 | − | 0.190734i | ||||
\(722\) | −4.96485e7 | + | 4.96485e7i | −0.131915 | + | 0.131915i | ||||
\(723\) | 8.09119e7 | + | 8.09119e7i | 0.214090 | + | 0.214090i | ||||
\(724\) | − | 2.75375e8i | − | 0.725620i | ||||||
\(725\) | 1.69551e7 | − | 1.69551e7i | 0.0444924 | − | 0.0444924i | ||||
\(726\) | 2.14799e7 | − | 2.14799e7i | 0.0561336 | − | 0.0561336i | ||||
\(727\) | −3.74737e8 | − | 3.74737e8i | −0.975266 | − | 0.975266i | 0.0244359 | − | 0.999701i | \(-0.492221\pi\) |
−0.999701 | + | 0.0244359i | \(0.992221\pi\) | |||||||
\(728\) | − | 3.29618e7i | − | 0.0854313i | ||||||
\(729\) | 6.63547e7 | 0.171273 | ||||||||
\(730\) | 3.10459e8i | 0.798061i | ||||||||
\(731\) | − | 8.72799e7i | − | 0.223441i | ||||||
\(732\) | −1.90418e7 | − | 1.90418e7i | −0.0485484 | − | 0.0485484i | ||||
\(733\) | 2.97896e8i | 0.756403i | 0.925723 | + | 0.378201i | \(0.123457\pi\) | ||||
−0.925723 | + | 0.378201i | \(0.876543\pi\) | |||||||
\(734\) | −3.78943e8 | − | 3.78943e8i | −0.958265 | − | 0.958265i | ||||
\(735\) | 5.64110e7 | + | 5.64110e7i | 0.142070 | + | 0.142070i | ||||
\(736\) | −1.21448e8 | −0.304619 | ||||||||
\(737\) | 9.76068e7 | 0.243825 | ||||||||
\(738\) | −1.86199e7 | + | 1.86199e7i | −0.0463242 | + | 0.0463242i | ||||
\(739\) | − | 3.51348e8i | − | 0.870571i | −0.900293 | − | 0.435285i | \(-0.856648\pi\) | ||
0.900293 | − | 0.435285i | \(-0.143352\pi\) | |||||||
\(740\) | 3.67041e7 | + | 1.32814e8i | 0.0905774 | + | 0.327754i | ||||
\(741\) | −6.61383e7 | −0.162554 | ||||||||
\(742\) | 1.73346e8 | + | 1.73346e8i | 0.424329 | + | 0.424329i | ||||
\(743\) | 6.49894e8i | 1.58444i | 0.610235 | + | 0.792220i | \(0.291075\pi\) | ||||
−0.610235 | + | 0.792220i | \(0.708925\pi\) | |||||||
\(744\) | 2.96969e7i | 0.0721096i | ||||||||
\(745\) | 1.16261e8 | − | 1.16261e8i | 0.281167 | − | 0.281167i | ||||
\(746\) | 1.01873e8 | − | 1.01873e8i | 0.245382 | − | 0.245382i | ||||
\(747\) | −5.78959e8 | −1.38895 | ||||||||
\(748\) | 4.74087e7 | − | 4.74087e7i | 0.113280 | − | 0.113280i | ||||
\(749\) | −3.26211e8 | −0.776342 | ||||||||
\(750\) | 1.24125e8 | 0.294222 | ||||||||
\(751\) | − | 4.24773e8i | − | 1.00285i | −0.865200 | − | 0.501427i | \(-0.832809\pi\) | ||
0.865200 | − | 0.501427i | \(-0.167191\pi\) | |||||||
\(752\) | 3.41702e7 | 0.0803514 | ||||||||
\(753\) | −7.70465e7 | + | 7.70465e7i | −0.180455 | + | 0.180455i | ||||
\(754\) | −1.19455e7 | − | 1.19455e7i | −0.0278670 | − | 0.0278670i | ||||
\(755\) | 8.03640e7 | + | 8.03640e7i | 0.186733 | + | 0.186733i | ||||
\(756\) | −8.03582e7 | −0.185979 | ||||||||
\(757\) | −3.04769e8 | + | 3.04769e8i | −0.702560 | + | 0.702560i | −0.964959 | − | 0.262399i | \(-0.915486\pi\) |
0.262399 | + | 0.964959i | \(0.415486\pi\) | |||||||
\(758\) | 2.14182e8 | + | 2.14182e8i | 0.491786 | + | 0.491786i | ||||
\(759\) | −1.79633e8 | + | 1.79633e8i | −0.410829 | + | 0.410829i | ||||
\(760\) | 6.40368e7 | + | 6.40368e7i | 0.145878 | + | 0.145878i | ||||
\(761\) | − | 6.23083e8i | − | 1.41381i | −0.707307 | − | 0.706907i | \(-0.750090\pi\) | ||
0.707307 | − | 0.706907i | \(-0.249910\pi\) | |||||||
\(762\) | 8.29931e7 | − | 8.29931e7i | 0.187576 | − | 0.187576i | ||||
\(763\) | −5.56907e7 | + | 5.56907e7i | −0.125374 | + | 0.125374i | ||||
\(764\) | 1.38757e8 | + | 1.38757e8i | 0.311153 | + | 0.311153i | ||||
\(765\) | − | 9.69046e7i | − | 0.216451i | ||||||
\(766\) | 2.53054e8 | 0.563025 | ||||||||
\(767\) | − | 2.15687e7i | − | 0.0478011i | ||||||
\(768\) | − | 1.12663e7i | − | 0.0248713i | ||||||
\(769\) | −1.62617e8 | − | 1.62617e8i | −0.357592 | − | 0.357592i | 0.505332 | − | 0.862925i | \(-0.331370\pi\) |
−0.862925 | + | 0.505332i | \(0.831370\pi\) | |||||||
\(770\) | 9.44091e7i | 0.206796i | ||||||||
\(771\) | −2.28269e8 | − | 2.28269e8i | −0.498063 | − | 0.498063i | ||||
\(772\) | −1.02221e8 | − | 1.02221e8i | −0.222170 | − | 0.222170i | ||||
\(773\) | 7.37384e8 | 1.59645 | 0.798225 | − | 0.602360i | \(-0.205773\pi\) | ||||
0.798225 | + | 0.602360i | \(0.205773\pi\) | |||||||
\(774\) | 1.63052e8 | 0.351644 | ||||||||
\(775\) | −9.06738e7 | + | 9.06738e7i | −0.194795 | + | 0.194795i | ||||
\(776\) | − | 1.41772e7i | − | 0.0303393i | ||||||
\(777\) | −4.67283e7 | + | 8.24192e7i | −0.0996131 | + | 0.175697i | ||||
\(778\) | 2.02534e8 | 0.430089 | ||||||||
\(779\) | 3.15716e7 | + | 3.15716e7i | 0.0667857 | + | 0.0667857i | ||||
\(780\) | − | 3.05719e7i | − | 0.0644227i | ||||||
\(781\) | 3.17637e8i | 0.666773i | ||||||||
\(782\) | 1.55810e8 | − | 1.55810e8i | 0.325817 | − | 0.325817i | ||||
\(783\) | −2.91221e7 | + | 2.91221e7i | −0.0606649 | + | 0.0606649i | ||||
\(784\) | 8.94391e7 | 0.185601 | ||||||||
\(785\) | −1.91501e8 | + | 1.91501e8i | −0.395878 | + | 0.395878i | ||||
\(786\) | 1.67283e8 | 0.344496 | ||||||||
\(787\) | 9.66269e8 | 1.98232 | 0.991160 | − | 0.132672i | \(-0.0423556\pi\) | ||||
0.991160 | + | 0.132672i | \(0.0423556\pi\) | |||||||
\(788\) | − | 1.29529e8i | − | 0.264721i | ||||||
\(789\) | 1.79104e8 | 0.364649 | ||||||||
\(790\) | −9.33698e7 | + | 9.33698e7i | −0.189376 | + | 0.189376i | ||||
\(791\) | −2.83994e8 | − | 2.83994e8i | −0.573824 | − | 0.573824i | ||||
\(792\) | 8.85665e7 | + | 8.85665e7i | 0.178276 | + | 0.178276i | ||||
\(793\) | −8.19242e7 | −0.164283 | ||||||||
\(794\) | 2.90035e8 | − | 2.90035e8i | 0.579415 | − | 0.579415i | ||||
\(795\) | 1.60778e8 | + | 1.60778e8i | 0.319981 | + | 0.319981i | ||||
\(796\) | −8.01508e7 | + | 8.01508e7i | −0.158916 | + | 0.158916i | ||||
\(797\) | 3.97964e8 | + | 3.97964e8i | 0.786084 | + | 0.786084i | 0.980850 | − | 0.194766i | \(-0.0623947\pi\) |
−0.194766 | + | 0.980850i | \(0.562395\pi\) | |||||||
\(798\) | 6.22690e7i | 0.122536i | ||||||||
\(799\) | −4.38380e7 | + | 4.38380e7i | −0.0859431 | + | 0.0859431i | ||||
\(800\) | 3.43995e7 | − | 3.43995e7i | 0.0671865 | − | 0.0671865i | ||||
\(801\) | −4.33169e7 | − | 4.33169e7i | −0.0842868 | − | 0.0842868i | ||||
\(802\) | − | 2.58709e8i | − | 0.501519i | ||||||
\(803\) | 7.28055e8 | 1.40610 | ||||||||
\(804\) | 2.97583e7i | 0.0572585i | ||||||||
\(805\) | 3.10277e8i | 0.594788i | ||||||||
\(806\) | 6.38831e7 | + | 6.38831e7i | 0.122006 | + | 0.122006i | ||||
\(807\) | − | 3.22191e8i | − | 0.613045i | ||||||
\(808\) | 5.91417e7 | + | 5.91417e7i | 0.112114 | + | 0.112114i | ||||
\(809\) | −2.65553e8 | − | 2.65553e8i | −0.501539 | − | 0.501539i | 0.410377 | − | 0.911916i | \(-0.365397\pi\) |
−0.911916 | + | 0.410377i | \(0.865397\pi\) | |||||||
\(810\) | 1.40562e8 | 0.264492 | ||||||||
\(811\) | 9.25828e8 | 1.73567 | 0.867836 | − | 0.496851i | \(-0.165510\pi\) | ||||
0.867836 | + | 0.496851i | \(0.165510\pi\) | |||||||
\(812\) | −1.12466e7 | + | 1.12466e7i | −0.0210065 | + | 0.0210065i | ||||
\(813\) | 5.38185e7i | 0.100152i | ||||||||
\(814\) | 3.11460e8 | − | 8.60745e7i | 0.577470 | − | 0.159588i | ||||
\(815\) | −1.71552e8 | −0.316900 | ||||||||
\(816\) | 1.44539e7 | + | 1.44539e7i | 0.0266021 | + | 0.0266021i | ||||
\(817\) | − | 2.76468e8i | − | 0.506966i | ||||||
\(818\) | 5.36309e8i | 0.979841i | ||||||||
\(819\) | −7.90000e7 | + | 7.90000e7i | −0.143805 | + | 0.143805i | ||||
\(820\) | −1.45937e7 | + | 1.45937e7i | −0.0264682 | + | 0.0264682i | ||||
\(821\) | −7.54703e8 | −1.36379 | −0.681893 | − | 0.731452i | \(-0.738843\pi\) | ||||
−0.681893 | + | 0.731452i | \(0.738843\pi\) | |||||||
\(822\) | −7.75968e7 | + | 7.75968e7i | −0.139710 | + | 0.139710i | ||||
\(823\) | −8.06746e8 | −1.44723 | −0.723615 | − | 0.690204i | \(-0.757521\pi\) | ||||
−0.723615 | + | 0.690204i | \(0.757521\pi\) | |||||||
\(824\) | −1.05126e8 | −0.187900 | ||||||||
\(825\) | − | 1.01760e8i | − | 0.181224i | ||||||
\(826\) | −2.03069e7 | −0.0360332 | ||||||||
\(827\) | 4.22245e7 | − | 4.22245e7i | 0.0746531 | − | 0.0746531i | −0.668794 | − | 0.743447i | \(-0.733189\pi\) |
0.743447 | + | 0.668794i | \(0.233189\pi\) | |||||||
\(828\) | 2.91076e8 | + | 2.91076e8i | 0.512761 | + | 0.512761i | ||||
\(829\) | −2.11031e8 | − | 2.11031e8i | −0.370411 | − | 0.370411i | 0.497216 | − | 0.867627i | \(-0.334356\pi\) |
−0.867627 | + | 0.497216i | \(0.834356\pi\) | |||||||
\(830\) | −4.53771e8 | −0.793602 | ||||||||
\(831\) | 1.53548e8 | − | 1.53548e8i | 0.267572 | − | 0.267572i | ||||
\(832\) | −2.42357e7 | − | 2.42357e7i | −0.0420810 | − | 0.0420810i | ||||
\(833\) | −1.14744e8 | + | 1.14744e8i | −0.198516 | + | 0.198516i | ||||
\(834\) | −8.76871e7 | − | 8.76871e7i | −0.151160 | − | 0.151160i | ||||
\(835\) | 5.93803e7i | 0.101996i | ||||||||
\(836\) | 1.50172e8 | − | 1.50172e8i | 0.257022 | − | 0.257022i | ||||
\(837\) | 1.55742e8 | − | 1.55742e8i | 0.265600 | − | 0.265600i | ||||
\(838\) | 7.67976e7 | + | 7.67976e7i | 0.130501 | + | 0.130501i | ||||
\(839\) | − | 6.74327e8i | − | 1.14179i | −0.821024 | − | 0.570893i | \(-0.806597\pi\) | ||
0.821024 | − | 0.570893i | \(-0.193403\pi\) | |||||||
\(840\) | −2.87834e7 | −0.0485628 | ||||||||
\(841\) | − | 5.86672e8i | − | 0.986296i | ||||||
\(842\) | − | 2.55655e8i | − | 0.428270i | ||||||
\(843\) | −1.68773e7 | − | 1.68773e7i | −0.0281721 | − | 0.0281721i | ||||
\(844\) | − | 2.77473e8i | − | 0.461523i | ||||||
\(845\) | 2.24379e8 | + | 2.24379e8i | 0.371889 | + | 0.371889i | ||||
\(846\) | −8.18960e7 | − | 8.18960e7i | −0.135254 | − | 0.135254i | ||||
\(847\) | −8.70073e7 | −0.143188 | ||||||||
\(848\) | 2.54911e8 | 0.418024 | ||||||||
\(849\) | −2.31686e8 | + | 2.31686e8i | −0.378596 | + | 0.378596i | ||||
\(850\) | 8.82645e7i | 0.143724i | ||||||||
\(851\) | 1.02362e9 | − | 2.82886e8i | 1.66093 | − | 0.459010i | ||||
\(852\) | −9.68409e7 | −0.156581 | ||||||||
\(853\) | 6.10544e8 | + | 6.10544e8i | 0.983717 | + | 0.983717i | 0.999870 | − | 0.0161525i | \(-0.00514173\pi\) |
−0.0161525 | + | 0.999870i | \(0.505142\pi\) | |||||||
\(854\) | 7.71314e7i | 0.123839i | ||||||||
\(855\) | − | 3.06955e8i | − | 0.491108i | ||||||
\(856\) | −2.39852e8 | + | 2.39852e8i | −0.382404 | + | 0.382404i | ||||
\(857\) | 7.64610e8 | − | 7.64610e8i | 1.21478 | − | 1.21478i | 0.245343 | − | 0.969436i | \(-0.421099\pi\) |
0.969436 | − | 0.245343i | \(-0.0789006\pi\) | |||||||
\(858\) | −7.16938e7 | −0.113506 | ||||||||
\(859\) | −6.32535e8 | + | 6.32535e8i | −0.997941 | + | 0.997941i | −0.999998 | − | 0.00205690i | \(-0.999345\pi\) |
0.00205690 | + | 0.999998i | \(0.499345\pi\) | |||||||
\(860\) | 1.27795e8 | 0.200918 | ||||||||
\(861\) | −1.41909e7 | −0.0222330 | ||||||||
\(862\) | − | 4.39402e8i | − | 0.686025i | ||||||
\(863\) | 2.75363e7 | 0.0428424 | 0.0214212 | − | 0.999771i | \(-0.493181\pi\) | ||||
0.0214212 | + | 0.999771i | \(0.493181\pi\) | |||||||
\(864\) | −5.90847e7 | + | 5.90847e7i | −0.0916081 | + | 0.0916081i | ||||
\(865\) | 2.50382e8 | + | 2.50382e8i | 0.386861 | + | 0.386861i | ||||
\(866\) | 1.72095e8 | + | 1.72095e8i | 0.264981 | + | 0.264981i | ||||
\(867\) | 2.22257e8 | 0.341034 | ||||||||
\(868\) | 6.01458e7 | − | 6.01458e7i | 0.0919699 | − | 0.0919699i | ||||
\(869\) | 2.18961e8 | + | 2.18961e8i | 0.333662 | + | 0.333662i | ||||
\(870\) | −1.04312e7 | + | 1.04312e7i | −0.0158408 | + | 0.0158408i | ||||
\(871\) | 6.40151e7 | + | 6.40151e7i | 0.0968786 | + | 0.0968786i | ||||
\(872\) | 8.18949e7i | 0.123512i | ||||||||
\(873\) | −3.39786e7 | + | 3.39786e7i | −0.0510697 | + | 0.0510697i | ||||
\(874\) | 4.93543e8 | − | 4.93543e8i | 0.739249 | − | 0.739249i | ||||
\(875\) | −2.51393e8 | − | 2.51393e8i | −0.375257 | − | 0.375257i | ||||
\(876\) | 2.21969e8i | 0.330202i | ||||||||
\(877\) | −9.49722e8 | −1.40798 | −0.703992 | − | 0.710208i | \(-0.748601\pi\) | ||||
−0.703992 | + | 0.710208i | \(0.748601\pi\) | |||||||
\(878\) | − | 7.65420e8i | − | 1.13088i | ||||||
\(879\) | − | 1.91709e7i | − | 0.0282277i | ||||||
\(880\) | 6.94158e7 | + | 6.94158e7i | 0.101862 | + | 0.101862i | ||||
\(881\) | − | 4.13952e8i | − | 0.605371i | −0.953090 | − | 0.302686i | \(-0.902117\pi\) | ||
0.953090 | − | 0.302686i | \(-0.0978832\pi\) | |||||||
\(882\) | −2.14360e8 | − | 2.14360e8i | −0.312419 | − | 0.312419i | ||||
\(883\) | 4.01091e8 | + | 4.01091e8i | 0.582587 | + | 0.582587i | 0.935614 | − | 0.353026i | \(-0.114847\pi\) |
−0.353026 | + | 0.935614i | \(0.614847\pi\) | |||||||
\(884\) | 6.21856e7 | 0.0900188 | ||||||||
\(885\) | −1.88345e7 | −0.0271722 | ||||||||
\(886\) | −5.30890e8 | + | 5.30890e8i | −0.763315 | + | 0.763315i | ||||
\(887\) | − | 6.14494e8i | − | 0.880535i | −0.897867 | − | 0.440267i | \(-0.854884\pi\) | ||
0.897867 | − | 0.440267i | \(-0.145116\pi\) | |||||||
\(888\) | 2.62423e7 | + | 9.49578e7i | 0.0374769 | + | 0.135610i | ||||
\(889\) | −3.36175e8 | −0.478476 | ||||||||
\(890\) | −3.39505e7 | − | 3.39505e7i | −0.0481588 | − | 0.0481588i | ||||
\(891\) | − | 3.29630e8i | − | 0.466009i | ||||||
\(892\) | − | 4.54061e7i | − | 0.0639764i | ||||||
\(893\) | −1.38862e8 | + | 1.38862e8i | −0.194997 | + | 0.194997i | ||||
\(894\) | 8.31229e7 | − | 8.31229e7i | 0.116334 | − | 0.116334i | ||||
\(895\) | −3.30527e8 | −0.461040 | ||||||||
\(896\) | −2.28179e7 | + | 2.28179e7i | −0.0317213 | + | 0.0317213i | ||||
\(897\) | −2.35623e8 | −0.326468 | ||||||||
\(898\) | −5.01454e8 | −0.692471 | ||||||||
\(899\) | − | 4.35941e7i | − | 0.0599996i | ||||||
\(900\) | −1.64891e8 | −0.226188 | ||||||||
\(901\) | −3.27034e8 | + | 3.27034e8i | −0.447114 | + | 0.447114i | ||||
\(902\) | 3.42236e7 | + | 3.42236e7i | 0.0466343 | + | 0.0466343i | ||||
\(903\) | 6.21337e7 | + | 6.21337e7i | 0.0843848 | + | 0.0843848i | ||||
\(904\) | −4.17622e8 | −0.565299 | ||||||||
\(905\) | −5.17285e8 | + | 5.17285e8i | −0.697885 | + | 0.697885i | ||||
\(906\) | 5.74578e7 | + | 5.74578e7i | 0.0772617 | + | 0.0772617i | ||||
\(907\) | 7.66542e8 | − | 7.66542e8i | 1.02734 | − | 1.02734i | 0.0277236 | − | 0.999616i | \(-0.491174\pi\) |
0.999616 | − | 0.0277236i | \(-0.00882582\pi\) | |||||||
\(908\) | 3.77582e8 | + | 3.77582e8i | 0.504375 | + | 0.504375i | ||||
\(909\) | − | 2.83491e8i | − | 0.377440i | ||||||
\(910\) | −6.19178e7 | + | 6.19178e7i | −0.0821659 | + | 0.0821659i | ||||
\(911\) | 1.50215e8 | − | 1.50215e8i | 0.198681 | − | 0.198681i | −0.600753 | − | 0.799435i | \(-0.705133\pi\) |
0.799435 | + | 0.600753i | \(0.205133\pi\) | |||||||
\(912\) | 4.57843e7 | + | 4.57843e7i | 0.0603576 | + | 0.0603576i | ||||
\(913\) | 1.06413e9i | 1.39825i | ||||||||
\(914\) | 4.12866e8 | 0.540717 | ||||||||
\(915\) | 7.15390e7i | 0.0933855i | ||||||||
\(916\) | 5.92215e7i | 0.0770536i | ||||||||
\(917\) | −3.38801e8 | − | 3.38801e8i | −0.439376 | − | 0.439376i | ||||
\(918\) | − | 1.51603e8i | − | 0.195966i | ||||||
\(919\) | −2.36187e8 | − | 2.36187e8i | −0.304306 | − | 0.304306i | 0.538390 | − | 0.842696i | \(-0.319033\pi\) |
−0.842696 | + | 0.538390i | \(0.819033\pi\) | |||||||
\(920\) | 2.28137e8 | + | 2.28137e8i | 0.292976 | + | 0.292976i | ||||
\(921\) | 2.36884e8 | 0.303219 | ||||||||
\(922\) | −6.09079e8 | −0.777107 | ||||||||
\(923\) | −2.08321e8 | + | 2.08321e8i | −0.264928 | + | 0.264928i | ||||
\(924\) | 6.74996e7i | 0.0855628i | ||||||||
\(925\) | −2.09809e8 | + | 3.70061e8i | −0.265094 | + | 0.467572i | ||||
\(926\) | −1.07872e9 | −1.35855 | ||||||||
\(927\) | 2.51956e8 | + | 2.51956e8i | 0.316290 | + | 0.316290i | ||||
\(928\) | 1.65385e7i | 0.0206944i | ||||||||
\(929\) | 1.45716e9i | 1.81744i | 0.417408 | + | 0.908719i | \(0.362938\pi\) | ||||
−0.417408 | + | 0.908719i | \(0.637062\pi\) | |||||||
\(930\) | 5.57849e7 | − | 5.57849e7i | 0.0693533 | − | 0.0693533i | ||||
\(931\) | −3.63465e8 | + | 3.63465e8i | −0.450415 | + | 0.450415i | ||||
\(932\) | −3.86446e8 | −0.477355 | ||||||||
\(933\) | −2.39111e8 | + | 2.39111e8i | −0.294412 | + | 0.294412i | ||||
\(934\) | −7.45976e8 | −0.915555 | ||||||||
\(935\) | −1.78112e8 | −0.217900 | ||||||||
\(936\) | 1.16172e8i | 0.141669i | ||||||||
\(937\) | −2.91172e7 | −0.0353941 | −0.0176970 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176970 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(938\) | 6.02700e7 | − | 6.02700e7i | 0.0730286 | − | 0.0730286i | ||||
\(939\) | 2.29803e8 | + | 2.29803e8i | 0.277561 | + | 0.277561i | ||||
\(940\) | −6.41877e7 | − | 6.41877e7i | −0.0772802 | − | 0.0772802i | ||||
\(941\) | −6.56222e8 | −0.787556 | −0.393778 | − | 0.919205i | \(-0.628832\pi\) | ||||
−0.393778 | + | 0.919205i | \(0.628832\pi\) | |||||||
\(942\) | −1.36917e8 | + | 1.36917e8i | −0.163797 | + | 0.163797i | ||||
\(943\) | 1.12476e8 | + | 1.12476e8i | 0.134130 | + | 0.134130i | ||||
\(944\) | −1.49310e7 | + | 1.49310e7i | −0.0177489 | + | 0.0177489i | ||||
\(945\) | 1.50951e8 | + | 1.50951e8i | 0.178871 | + | 0.178871i | ||||
\(946\) | − | 2.99691e8i | − | 0.353998i | ||||||
\(947\) | 6.08060e8 | − | 6.08060e8i | 0.715972 | − | 0.715972i | −0.251806 | − | 0.967778i | \(-0.581024\pi\) |
0.967778 | + | 0.251806i | \(0.0810243\pi\) | |||||||
\(948\) | −6.67565e7 | + | 6.67565e7i | −0.0783554 | + | 0.0783554i | ||||
\(949\) | 4.77492e8 | + | 4.77492e8i | 0.558685 | + | 0.558685i | ||||
\(950\) | 2.79587e8i | 0.326096i | ||||||||
\(951\) | 2.93863e8 | 0.341667 | ||||||||
\(952\) | − | 5.85476e7i | − | 0.0678576i | ||||||
\(953\) | 1.32808e9i | 1.53443i | 0.641390 | + | 0.767215i | \(0.278358\pi\) | ||||
−0.641390 | + | 0.767215i | \(0.721642\pi\) | |||||||
\(954\) | −6.10948e8 | − | 6.10948e8i | −0.703654 | − | 0.703654i | ||||
\(955\) | − | 5.21300e8i | − | 0.598519i | ||||||
\(956\) | 9.00054e7 | + | 9.00054e7i | 0.103014 | + | 0.103014i | ||||
\(957\) | 2.44621e7 | + | 2.44621e7i | 0.0279098 | + | 0.0279098i | ||||
\(958\) | −4.75719e8 | −0.541071 | ||||||||
\(959\) | 3.14317e8 | 0.356379 | ||||||||
\(960\) | −2.11634e7 | + | 2.11634e7i | −0.0239206 | + | 0.0239206i | ||||
\(961\) | − | 6.54368e8i | − | 0.737313i | ||||||
\(962\) | 2.60722e8 | + | 1.47818e8i | 0.292854 | + | 0.166036i | ||||
\(963\) | 1.14971e9 | 1.28739 | ||||||||
\(964\) | −2.40980e8 | − | 2.40980e8i | −0.268998 | − | 0.268998i | ||||
\(965\) | 3.84037e8i | 0.427357i | ||||||||
\(966\) | 2.21839e8i | 0.246097i | ||||||||
\(967\) | −8.25481e8 | + | 8.25481e8i | −0.912909 | + | 0.912909i | −0.996500 | − | 0.0835907i | \(-0.973361\pi\) |
0.0835907 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(968\) | −6.39735e7 | + | 6.39735e7i | −0.0705301 | + | 0.0705301i | ||||
\(969\) | −1.17476e8 | −0.129116 | ||||||||
\(970\) | −2.66315e7 | + | 2.66315e7i | −0.0291796 | + | 0.0291796i | ||||
\(971\) | −6.71474e8 | −0.733452 | −0.366726 | − | 0.930329i | \(-0.619521\pi\) | ||||
−0.366726 | + | 0.930329i | \(0.619521\pi\) | |||||||
\(972\) | 4.37003e8 | 0.475867 | ||||||||
\(973\) | 3.55189e8i | 0.385585i | ||||||||
\(974\) | −5.94524e8 | −0.643417 | ||||||||
\(975\) | 6.67391e7 | − | 6.67391e7i | 0.0720056 | − | 0.0720056i | ||||
\(976\) | 5.67121e7 | + | 5.67121e7i | 0.0609996 | + | 0.0609996i | ||||
\(977\) | 3.73876e8 | + | 3.73876e8i | 0.400907 | + | 0.400907i | 0.878553 | − | 0.477646i | \(-0.158510\pi\) |
−0.477646 | + | 0.878553i | \(0.658510\pi\) | |||||||
\(978\) | −1.22654e8 | −0.131119 | ||||||||
\(979\) | −7.96169e7 | + | 7.96169e7i | −0.0848510 | + | 0.0848510i | ||||
\(980\) | −1.68009e8 | − | 1.68009e8i | −0.178506 | − | 0.178506i | ||||
\(981\) | 1.96279e8 | − | 1.96279e8i | 0.207905 | − | 0.207905i | ||||
\(982\) | 1.22700e8 | + | 1.22700e8i | 0.129572 | + | 0.129572i | ||||
\(983\) | − | 1.44822e9i | − | 1.52466i | −0.647187 | − | 0.762331i | \(-0.724055\pi\) | ||
0.647187 | − | 0.762331i | \(-0.275945\pi\) | |||||||
\(984\) | −1.04341e7 | + | 1.04341e7i | −0.0109514 | + | 0.0109514i | ||||
\(985\) | −2.43316e8 | + | 2.43316e8i | −0.254603 | + | 0.254603i | ||||
\(986\) | −2.12179e7 | − | 2.12179e7i | −0.0221346 | − | 0.0221346i | ||||
\(987\) | − | 6.24158e7i | − | 0.0649147i | ||||||
\(988\) | 1.96979e8 | 0.204244 | ||||||||
\(989\) | − | 9.84942e8i | − | 1.01817i | ||||||
\(990\) | − | 3.32739e8i | − | 0.342924i | ||||||
\(991\) | −1.00667e9 | − | 1.00667e9i | −1.03434 | − | 1.03434i | −0.999389 | − | 0.0349531i | \(-0.988872\pi\) |
−0.0349531 | − | 0.999389i | \(-0.511128\pi\) | |||||||
\(992\) | − | 8.84463e7i | − | 0.0906034i | ||||||
\(993\) | 3.31602e7 | + | 3.31602e7i | 0.0338665 | + | 0.0338665i | ||||
\(994\) | 1.96134e8 | + | 1.96134e8i | 0.199707 | + | 0.199707i | ||||
\(995\) | 3.01122e8 | 0.305684 | ||||||||
\(996\) | −3.24432e8 | −0.328357 | ||||||||
\(997\) | −1.29813e9 | + | 1.29813e9i | −1.30989 | + | 1.30989i | −0.388396 | + | 0.921493i | \(0.626971\pi\) |
−0.921493 | + | 0.388396i | \(0.873029\pi\) | |||||||
\(998\) | 1.96140e8i | 0.197322i | ||||||||
\(999\) | 3.60369e8 | − | 6.35618e8i | 0.361452 | − | 0.637529i |
(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 | 74.7.d.a.31.3 | ✓ | 18 | |
37.6 | odd | 4 | inner | 74.7.d.a.43.7 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.a.31.3 | ✓ | 18 | 1.1 | even | 1 | trivial | |
74.7.d.a.43.7 | yes | 18 | 37.6 | odd | 4 | inner |