Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.f (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: | \(1.65391940934\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.6 | ||
Root | \(0.336831 + 2.80830i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.3 |
Dual form | 16.5.f.a.11.6 |
$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47147 | + | 3.14513i | 0.617867 | + | 0.786282i | ||||
\(3\) | −7.86839 | + | 7.86839i | −0.874266 | + | 0.874266i | −0.992934 | − | 0.118668i | \(-0.962138\pi\) |
0.118668 | + | 0.992934i | \(0.462138\pi\) | |||||||
\(4\) | −3.78368 | + | 15.5462i | −0.236480 | + | 0.971636i | ||||
\(5\) | 27.2309 | − | 27.2309i | 1.08924 | − | 1.08924i | 0.0936308 | − | 0.995607i | \(-0.470153\pi\) |
0.995607 | − | 0.0936308i | \(-0.0298473\pi\) | |||||||
\(6\) | −44.1936 | − | 5.30063i | −1.22760 | − | 0.147240i | ||||
\(7\) | 50.3097 | 1.02673 | 0.513365 | − | 0.858171i | \(-0.328399\pi\) | ||||
0.513365 | + | 0.858171i | \(0.328399\pi\) | |||||||
\(8\) | −58.2460 | + | 26.5217i | −0.910094 | + | 0.414402i | ||||
\(9\) | − | 42.8233i | − | 0.528682i | ||||||
\(10\) | 152.945 | + | 18.3444i | 1.52945 | + | 0.183444i | ||||
\(11\) | −53.1047 | − | 53.1047i | −0.438881 | − | 0.438881i | 0.452754 | − | 0.891635i | \(-0.350442\pi\) |
−0.891635 | + | 0.452754i | \(0.850442\pi\) | |||||||
\(12\) | −92.5520 | − | 152.095i | −0.642722 | − | 1.05622i | ||||
\(13\) | −125.128 | − | 125.128i | −0.740404 | − | 0.740404i | 0.232252 | − | 0.972656i | \(-0.425391\pi\) |
−0.972656 | + | 0.232252i | \(0.925391\pi\) | |||||||
\(14\) | 124.339 | + | 158.231i | 0.634382 | + | 0.807299i | ||||
\(15\) | 428.528i | 1.90457i | ||||||||
\(16\) | −227.367 | − | 117.644i | −0.888154 | − | 0.459546i | ||||
\(17\) | 286.271 | 0.990557 | 0.495279 | − | 0.868734i | \(-0.335066\pi\) | ||||
0.495279 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(18\) | 134.685 | − | 105.836i | 0.415694 | − | 0.326655i | ||||
\(19\) | −99.5010 | + | 99.5010i | −0.275626 | + | 0.275626i | −0.831360 | − | 0.555734i | \(-0.812437\pi\) |
0.555734 | + | 0.831360i | \(0.312437\pi\) | |||||||
\(20\) | 320.304 | + | 526.370i | 0.800760 | + | 1.31593i | ||||
\(21\) | −395.857 | + | 395.857i | −0.897635 | + | 0.897635i | ||||
\(22\) | 35.7745 | − | 298.268i | 0.0739143 | − | 0.616255i | ||||
\(23\) | −100.505 | −0.189991 | −0.0949957 | − | 0.995478i | \(-0.530284\pi\) | ||||
−0.0949957 | + | 0.995478i | \(0.530284\pi\) | |||||||
\(24\) | 249.619 | − | 666.986i | 0.433367 | − | 1.15796i | ||||
\(25\) | − | 858.049i | − | 1.37288i | ||||||
\(26\) | 84.2940 | − | 702.795i | 0.124695 | − | 1.03964i | ||||
\(27\) | −300.390 | − | 300.390i | −0.412057 | − | 0.412057i | ||||
\(28\) | −190.356 | + | 782.124i | −0.242801 | + | 0.997607i | ||||
\(29\) | 343.872 | + | 343.872i | 0.408885 | + | 0.408885i | 0.881350 | − | 0.472465i | \(-0.156636\pi\) |
−0.472465 | + | 0.881350i | \(0.656636\pi\) | |||||||
\(30\) | −1347.78 | + | 1059.09i | −1.49753 | + | 1.17677i | ||||
\(31\) | − | 208.400i | − | 0.216858i | −0.994104 | − | 0.108429i | \(-0.965418\pi\) | ||
0.994104 | − | 0.108429i | \(-0.0345820\pi\) | |||||||
\(32\) | −191.927 | − | 1005.85i | −0.187429 | − | 0.982278i | ||||
\(33\) | 835.697 | 0.767398 | ||||||||
\(34\) | 707.510 | + | 900.360i | 0.612033 | + | 0.778858i | ||||
\(35\) | 1369.98 | − | 1369.98i | 1.11835 | − | 1.11835i | ||||
\(36\) | 665.738 | + | 162.030i | 0.513687 | + | 0.125023i | ||||
\(37\) | −1159.47 | + | 1159.47i | −0.846946 | + | 0.846946i | −0.989751 | − | 0.142805i | \(-0.954388\pi\) |
0.142805 | + | 0.989751i | \(0.454388\pi\) | |||||||
\(38\) | −558.857 | − | 67.0299i | −0.387020 | − | 0.0464196i | ||||
\(39\) | 1969.12 | 1.29462 | ||||||||
\(40\) | −863.882 | + | 2308.31i | −0.539927 | + | 1.44269i | ||||
\(41\) | 2335.63i | 1.38943i | 0.719286 | + | 0.694714i | \(0.244469\pi\) | ||||
−0.719286 | + | 0.694714i | \(0.755531\pi\) | |||||||
\(42\) | −2223.37 | − | 266.673i | −1.26041 | − | 0.151175i | ||||
\(43\) | −2079.41 | − | 2079.41i | −1.12461 | − | 1.12461i | −0.991039 | − | 0.133575i | \(-0.957354\pi\) |
−0.133575 | − | 0.991039i | \(-0.542646\pi\) | |||||||
\(44\) | 1026.51 | − | 624.643i | 0.530220 | − | 0.322646i | ||||
\(45\) | −1166.12 | − | 1166.12i | −0.575861 | − | 0.575861i | ||||
\(46\) | −248.396 | − | 316.103i | −0.117389 | − | 0.149387i | ||||
\(47\) | 1054.04i | 0.477159i | 0.971123 | + | 0.238580i | \(0.0766818\pi\) | ||||
−0.971123 | + | 0.238580i | \(0.923318\pi\) | |||||||
\(48\) | 2714.68 | − | 863.350i | 1.17825 | − | 0.374718i | ||||
\(49\) | 130.069 | 0.0541728 | ||||||||
\(50\) | 2698.67 | − | 2120.64i | 1.07947 | − | 0.848256i | ||||
\(51\) | −2252.49 | + | 2252.49i | −0.866011 | + | 0.866011i | ||||
\(52\) | 2418.71 | − | 1471.82i | 0.894494 | − | 0.544312i | ||||
\(53\) | 2136.46 | − | 2136.46i | 0.760576 | − | 0.760576i | −0.215850 | − | 0.976426i | \(-0.569252\pi\) |
0.976426 | + | 0.215850i | \(0.0692523\pi\) | |||||||
\(54\) | 202.361 | − | 1687.17i | 0.0693967 | − | 0.578590i | ||||
\(55\) | −2892.18 | −0.956092 | ||||||||
\(56\) | −2930.34 | + | 1334.30i | −0.934420 | + | 0.425479i | ||||
\(57\) | − | 1565.83i | − | 0.481941i | ||||||
\(58\) | −231.653 | + | 1931.39i | −0.0688625 | + | 0.574136i | ||||
\(59\) | 3721.44 | + | 3721.44i | 1.06907 | + | 1.06907i | 0.997431 | + | 0.0716407i | \(0.0228235\pi\) |
0.0716407 | + | 0.997431i | \(0.477177\pi\) | |||||||
\(60\) | −6661.97 | − | 1621.41i | −1.85055 | − | 0.450393i | ||||
\(61\) | 2496.46 | + | 2496.46i | 0.670912 | + | 0.670912i | 0.957926 | − | 0.287014i | \(-0.0926628\pi\) |
−0.287014 | + | 0.957926i | \(0.592663\pi\) | |||||||
\(62\) | 655.446 | − | 515.055i | 0.170512 | − | 0.133989i | ||||
\(63\) | − | 2154.43i | − | 0.542814i | ||||||
\(64\) | 2689.20 | − | 3089.57i | 0.656542 | − | 0.754289i | ||||
\(65\) | −6814.72 | −1.61295 | ||||||||
\(66\) | 2065.40 | + | 2628.37i | 0.474150 | + | 0.603392i | ||||
\(67\) | −329.116 | + | 329.116i | −0.0733162 | + | 0.0733162i | −0.742814 | − | 0.669498i | \(-0.766509\pi\) |
0.669498 | + | 0.742814i | \(0.266509\pi\) | |||||||
\(68\) | −1083.16 | + | 4450.42i | −0.234247 | + | 0.962461i | ||||
\(69\) | 790.817 | − | 790.817i | 0.166103 | − | 0.166103i | ||||
\(70\) | 7694.64 | + | 922.903i | 1.57033 | + | 0.188348i | ||||
\(71\) | −1040.71 | −0.206449 | −0.103225 | − | 0.994658i | \(-0.532916\pi\) | ||||
−0.103225 | + | 0.994658i | \(0.532916\pi\) | |||||||
\(72\) | 1135.75 | + | 2494.28i | 0.219087 | + | 0.481151i | ||||
\(73\) | − | 2673.24i | − | 0.501639i | −0.968034 | − | 0.250820i | \(-0.919300\pi\) | ||
0.968034 | − | 0.250820i | \(-0.0807001\pi\) | |||||||
\(74\) | −6512.27 | − | 781.089i | −1.18924 | − | 0.142639i | ||||
\(75\) | 6751.46 | + | 6751.46i | 1.20026 | + | 1.20026i | ||||
\(76\) | −1170.38 | − | 1923.34i | −0.202628 | − | 0.332988i | ||||
\(77\) | −2671.68 | − | 2671.68i | −0.450612 | − | 0.450612i | ||||
\(78\) | 4866.61 | + | 6193.13i | 0.799903 | + | 1.01794i | ||||
\(79\) | − | 4475.80i | − | 0.717161i | −0.933499 | − | 0.358580i | \(-0.883261\pi\) | ||
0.933499 | − | 0.358580i | \(-0.116739\pi\) | |||||||
\(80\) | −9394.98 | + | 2987.88i | −1.46797 | + | 0.466857i | ||||
\(81\) | 8195.85 | 1.24918 | ||||||||
\(82\) | −7345.86 | + | 5772.43i | −1.09248 | + | 0.858482i | ||||
\(83\) | 1457.69 | − | 1457.69i | 0.211597 | − | 0.211597i | −0.593349 | − | 0.804945i | \(-0.702195\pi\) |
0.804945 | + | 0.593349i | \(0.202195\pi\) | |||||||
\(84\) | −4656.26 | − | 7651.86i | −0.659901 | − | 1.08445i | ||||
\(85\) | 7795.43 | − | 7795.43i | 1.07895 | − | 1.07895i | ||||
\(86\) | 1400.82 | − | 11679.2i | 0.189402 | − | 1.57913i | ||||
\(87\) | −5411.44 | −0.714948 | ||||||||
\(88\) | 4501.56 | + | 1684.71i | 0.581297 | + | 0.217550i | ||||
\(89\) | 1146.97i | 0.144801i | 0.997376 | + | 0.0724003i | \(0.0230659\pi\) | ||||
−0.997376 | + | 0.0724003i | \(0.976934\pi\) | |||||||
\(90\) | 785.568 | − | 6549.62i | 0.0969838 | − | 0.808595i | ||||
\(91\) | −6295.17 | − | 6295.17i | −0.760194 | − | 0.760194i | ||||
\(92\) | 380.281 | − | 1562.48i | 0.0449292 | − | 0.184603i | ||||
\(93\) | 1639.78 | + | 1639.78i | 0.189592 | + | 0.189592i | ||||
\(94\) | −3315.11 | + | 2605.04i | −0.375182 | + | 0.294821i | ||||
\(95\) | 5419.01i | 0.600444i | ||||||||
\(96\) | 9424.60 | + | 6404.29i | 1.02264 | + | 0.694910i | ||||
\(97\) | −13101.5 | −1.39244 | −0.696222 | − | 0.717826i | \(-0.745137\pi\) | ||||
−0.696222 | + | 0.717826i | \(0.745137\pi\) | |||||||
\(98\) | 321.461 | + | 409.084i | 0.0334716 | + | 0.0425952i | ||||
\(99\) | −2274.11 | + | 2274.11i | −0.232029 | + | 0.232029i | ||||
\(100\) | 13339.4 | + | 3246.59i | 1.33394 | + | 0.324659i | ||||
\(101\) | −7488.18 | + | 7488.18i | −0.734063 | + | 0.734063i | −0.971422 | − | 0.237359i | \(-0.923718\pi\) |
0.237359 | + | 0.971422i | \(0.423718\pi\) | |||||||
\(102\) | −12651.4 | − | 1517.42i | −1.21601 | − | 0.145849i | ||||
\(103\) | 7141.23 | 0.673129 | 0.336565 | − | 0.941660i | \(-0.390735\pi\) | ||||
0.336565 | + | 0.941660i | \(0.390735\pi\) | |||||||
\(104\) | 10606.8 | + | 3969.60i | 0.980662 | + | 0.367012i | ||||
\(105\) | 21559.1i | 1.95547i | ||||||||
\(106\) | 11999.6 | + | 1439.25i | 1.06796 | + | 0.128093i | ||||
\(107\) | 1794.26 | + | 1794.26i | 0.156718 | + | 0.156718i | 0.781111 | − | 0.624393i | \(-0.214654\pi\) |
−0.624393 | + | 0.781111i | \(0.714654\pi\) | |||||||
\(108\) | 5806.49 | − | 3533.33i | 0.497813 | − | 0.302926i | ||||
\(109\) | 5362.57 | + | 5362.57i | 0.451357 | + | 0.451357i | 0.895805 | − | 0.444448i | \(-0.146600\pi\) |
−0.444448 | + | 0.895805i | \(0.646600\pi\) | |||||||
\(110\) | −7147.93 | − | 9096.28i | −0.590738 | − | 0.751759i | ||||
\(111\) | − | 18246.3i | − | 1.48091i | ||||||
\(112\) | −11438.8 | − | 5918.62i | −0.911894 | − | 0.471829i | ||||
\(113\) | −5165.40 | −0.404527 | −0.202263 | − | 0.979331i | \(-0.564830\pi\) | ||||
−0.202263 | + | 0.979331i | \(0.564830\pi\) | |||||||
\(114\) | 4924.73 | − | 3869.89i | 0.378942 | − | 0.297775i | ||||
\(115\) | −2736.86 | + | 2736.86i | −0.206946 | + | 0.206946i | ||||
\(116\) | −6647.00 | + | 4044.80i | −0.493981 | + | 0.300594i | ||||
\(117\) | −5358.40 | + | 5358.40i | −0.391438 | + | 0.391438i | ||||
\(118\) | −2506.99 | + | 20901.8i | −0.180048 | + | 1.50114i | ||||
\(119\) | 14402.2 | 1.01703 | ||||||||
\(120\) | −11365.3 | − | 24960.0i | −0.789256 | − | 1.73334i | ||||
\(121\) | − | 9000.79i | − | 0.614766i | ||||||
\(122\) | −1681.77 | + | 14021.6i | −0.112992 | + | 0.942061i | ||||
\(123\) | −18377.6 | − | 18377.6i | −1.21473 | − | 1.21473i | ||||
\(124\) | 3239.83 | + | 788.521i | 0.210707 | + | 0.0512826i | ||||
\(125\) | −6346.13 | − | 6346.13i | −0.406152 | − | 0.406152i | ||||
\(126\) | 6775.95 | − | 5324.60i | 0.426805 | − | 0.335387i | ||||
\(127\) | 22886.9i | 1.41899i | 0.704711 | + | 0.709495i | \(0.251077\pi\) | ||||
−0.704711 | + | 0.709495i | \(0.748923\pi\) | |||||||
\(128\) | 16363.4 | + | 822.099i | 0.998740 | + | 0.0501770i | ||||
\(129\) | 32723.3 | 1.96642 | ||||||||
\(130\) | −16842.4 | − | 21433.2i | −0.996590 | − | 1.26824i | ||||
\(131\) | 19202.2 | − | 19202.2i | 1.11894 | − | 1.11894i | 0.127048 | − | 0.991897i | \(-0.459450\pi\) |
0.991897 | − | 0.127048i | \(-0.0405502\pi\) | |||||||
\(132\) | −3162.01 | + | 12991.9i | −0.181475 | + | 0.745632i | ||||
\(133\) | −5005.87 | + | 5005.87i | −0.282993 | + | 0.282993i | ||||
\(134\) | −1848.51 | − | 221.713i | −0.102947 | − | 0.0123476i | ||||
\(135\) | −16359.8 | −0.897656 | ||||||||
\(136\) | −16674.1 | + | 7592.40i | −0.901500 | + | 0.410489i | ||||
\(137\) | − | 33680.5i | − | 1.79448i | −0.441547 | − | 0.897238i | \(-0.645570\pi\) | ||
0.441547 | − | 0.897238i | \(-0.354430\pi\) | |||||||
\(138\) | 4441.70 | + | 532.742i | 0.233234 | + | 0.0279743i | ||||
\(139\) | 11747.9 | + | 11747.9i | 0.608036 | + | 0.608036i | 0.942432 | − | 0.334397i | \(-0.108532\pi\) |
−0.334397 | + | 0.942432i | \(0.608532\pi\) | |||||||
\(140\) | 16114.4 | + | 26481.6i | 0.822163 | + | 1.35110i | ||||
\(141\) | −8293.64 | − | 8293.64i | −0.417164 | − | 0.417164i | ||||
\(142\) | −2572.09 | − | 3273.17i | −0.127558 | − | 0.162328i | ||||
\(143\) | 13289.8i | 0.649899i | ||||||||
\(144\) | −5037.89 | + | 9736.62i | −0.242954 | + | 0.469551i | ||||
\(145\) | 18727.9 | 0.890746 | ||||||||
\(146\) | 8407.68 | − | 6606.82i | 0.394430 | − | 0.309947i | ||||
\(147\) | −1023.43 | + | 1023.43i | −0.0473615 | + | 0.0473615i | ||||
\(148\) | −13638.2 | − | 22412.4i | −0.622637 | − | 1.02321i | ||||
\(149\) | −14877.7 | + | 14877.7i | −0.670136 | + | 0.670136i | −0.957747 | − | 0.287611i | \(-0.907139\pi\) |
0.287611 | + | 0.957747i | \(0.407139\pi\) | |||||||
\(150\) | −4548.20 | + | 37920.3i | −0.202142 | + | 1.68535i | ||||
\(151\) | −8005.74 | −0.351114 | −0.175557 | − | 0.984469i | \(-0.556173\pi\) | ||||
−0.175557 | + | 0.984469i | \(0.556173\pi\) | |||||||
\(152\) | 3156.60 | − | 8434.47i | 0.136626 | − | 0.365065i | ||||
\(153\) | − | 12259.1i | − | 0.523690i | ||||||
\(154\) | 1799.81 | − | 15005.8i | 0.0758900 | − | 0.632727i | ||||
\(155\) | −5674.94 | − | 5674.94i | −0.236210 | − | 0.236210i | ||||
\(156\) | −7450.51 | + | 30612.2i | −0.306152 | + | 1.25790i | ||||
\(157\) | 12150.9 | + | 12150.9i | 0.492958 | + | 0.492958i | 0.909237 | − | 0.416279i | \(-0.136666\pi\) |
−0.416279 | + | 0.909237i | \(0.636666\pi\) | |||||||
\(158\) | 14077.0 | − | 11061.8i | 0.563891 | − | 0.443110i | ||||
\(159\) | 33621.0i | 1.32989i | ||||||||
\(160\) | −32616.7 | − | 22164.0i | −1.27409 | − | 0.865780i | ||||
\(161\) | −5056.40 | −0.195070 | ||||||||
\(162\) | 20255.8 | + | 25777.0i | 0.771826 | + | 0.982206i | ||||
\(163\) | −23646.5 | + | 23646.5i | −0.890002 | + | 0.890002i | −0.994523 | − | 0.104520i | \(-0.966669\pi\) |
0.104520 | + | 0.994523i | \(0.466669\pi\) | |||||||
\(164\) | −36310.1 | − | 8837.28i | −1.35002 | − | 0.328572i | ||||
\(165\) | 22756.8 | − | 22756.8i | 0.835879 | − | 0.835879i | ||||
\(166\) | 8187.26 | + | 981.989i | 0.297113 | + | 0.0356361i | ||||
\(167\) | 42493.7 | 1.52367 | 0.761836 | − | 0.647770i | \(-0.224298\pi\) | ||||
0.761836 | + | 0.647770i | \(0.224298\pi\) | |||||||
\(168\) | 12558.3 | − | 33555.9i | 0.444950 | − | 1.18891i | ||||
\(169\) | 2753.14i | 0.0963950i | ||||||||
\(170\) | 43783.8 | + | 5251.48i | 1.51501 | + | 0.181712i | ||||
\(171\) | 4260.96 | + | 4260.96i | 0.145719 | + | 0.145719i | ||||
\(172\) | 40194.7 | − | 24459.1i | 1.35866 | − | 0.826767i | ||||
\(173\) | −16142.1 | − | 16142.1i | −0.539347 | − | 0.539347i | 0.383990 | − | 0.923337i | \(-0.374550\pi\) |
−0.923337 | + | 0.383990i | \(0.874550\pi\) | |||||||
\(174\) | −13374.2 | − | 17019.7i | −0.441743 | − | 0.562151i | ||||
\(175\) | − | 43168.2i | − | 1.40957i | ||||||
\(176\) | 5826.84 | + | 18321.7i | 0.188108 | + | 0.591480i | ||||
\(177\) | −58563.5 | −1.86931 | ||||||||
\(178\) | −3607.36 | + | 2834.69i | −0.113854 | + | 0.0894676i | ||||
\(179\) | −22442.0 | + | 22442.0i | −0.700415 | + | 0.700415i | −0.964500 | − | 0.264084i | \(-0.914930\pi\) |
0.264084 | + | 0.964500i | \(0.414930\pi\) | |||||||
\(180\) | 22540.9 | − | 13716.5i | 0.695707 | − | 0.423347i | ||||
\(181\) | −9891.06 | + | 9891.06i | −0.301916 | + | 0.301916i | −0.841763 | − | 0.539847i | \(-0.818482\pi\) |
0.539847 | + | 0.841763i | \(0.318482\pi\) | |||||||
\(182\) | 4240.81 | − | 35357.4i | 0.128028 | − | 1.06743i | ||||
\(183\) | −39286.3 | −1.17311 | ||||||||
\(184\) | 5854.04 | − | 2665.58i | 0.172910 | − | 0.0787328i | ||||
\(185\) | 63146.9i | 1.84505i | ||||||||
\(186\) | −1104.65 | + | 9209.97i | −0.0319301 | + | 0.266215i | ||||
\(187\) | −15202.3 | − | 15202.3i | −0.434737 | − | 0.434737i | ||||
\(188\) | −16386.4 | − | 3988.17i | −0.463625 | − | 0.112839i | ||||
\(189\) | −15112.5 | − | 15112.5i | −0.423071 | − | 0.423071i | ||||
\(190\) | −17043.5 | + | 13392.9i | −0.472119 | + | 0.370995i | ||||
\(191\) | − | 2033.60i | − | 0.0557442i | −0.999611 | − | 0.0278721i | \(-0.991127\pi\) | ||
0.999611 | − | 0.0278721i | \(-0.00887311\pi\) | |||||||
\(192\) | 3150.29 | + | 45469.6i | 0.0854570 | + | 1.23344i | ||||
\(193\) | 29257.4 | 0.785453 | 0.392727 | − | 0.919655i | \(-0.371532\pi\) | ||||
0.392727 | + | 0.919655i | \(0.371532\pi\) | |||||||
\(194\) | −32380.0 | − | 41206.0i | −0.860346 | − | 1.09486i | ||||
\(195\) | 53620.9 | − | 53620.9i | 1.41015 | − | 1.41015i | ||||
\(196\) | −492.140 | + | 2022.08i | −0.0128108 | + | 0.0526363i | ||||
\(197\) | 28194.9 | − | 28194.9i | 0.726504 | − | 0.726504i | −0.243417 | − | 0.969922i | \(-0.578268\pi\) |
0.969922 | + | 0.243417i | \(0.0782684\pi\) | |||||||
\(198\) | −12772.8 | − | 1531.98i | −0.325803 | − | 0.0390772i | ||||
\(199\) | 54100.9 | 1.36615 | 0.683075 | − | 0.730348i | \(-0.260642\pi\) | ||||
0.683075 | + | 0.730348i | \(0.260642\pi\) | |||||||
\(200\) | 22756.9 | + | 49977.9i | 0.568923 | + | 1.24945i | ||||
\(201\) | − | 5179.24i | − | 0.128196i | ||||||
\(202\) | −42058.1 | − | 5044.49i | −1.03073 | − | 0.123627i | ||||
\(203\) | 17300.1 | + | 17300.1i | 0.419814 | + | 0.419814i | ||||
\(204\) | −26494.9 | − | 43540.4i | −0.636653 | − | 1.04624i | ||||
\(205\) | 63601.4 | + | 63601.4i | 1.51342 | + | 1.51342i | ||||
\(206\) | 17649.3 | + | 22460.1i | 0.415905 | + | 0.529270i | ||||
\(207\) | 4303.97i | 0.100445i | ||||||||
\(208\) | 13729.5 | + | 43170.6i | 0.317343 | + | 0.997842i | ||||
\(209\) | 10567.9 | 0.241934 | ||||||||
\(210\) | −67806.2 | + | 53282.7i | −1.53756 | + | 1.20822i | ||||
\(211\) | −31994.1 | + | 31994.1i | −0.718630 | + | 0.718630i | −0.968325 | − | 0.249694i | \(-0.919670\pi\) |
0.249694 | + | 0.968325i | \(0.419670\pi\) | |||||||
\(212\) | 25130.1 | + | 41297.5i | 0.559142 | + | 0.918865i | ||||
\(213\) | 8188.73 | − | 8188.73i | 0.180492 | − | 0.180492i | ||||
\(214\) | −1208.72 | + | 10077.6i | −0.0263937 | + | 0.220055i | ||||
\(215\) | −113249. | −2.44994 | ||||||||
\(216\) | 25463.3 | + | 9529.65i | 0.545768 | + | 0.204253i | ||||
\(217\) | − | 10484.6i | − | 0.222654i | ||||||
\(218\) | −3612.56 | + | 30119.4i | −0.0760155 | + | 0.633773i | ||||
\(219\) | 21034.1 | + | 21034.1i | 0.438566 | + | 0.438566i | ||||
\(220\) | 10943.1 | − | 44962.3i | 0.226097 | − | 0.928974i | ||||
\(221\) | −35820.6 | − | 35820.6i | −0.733412 | − | 0.733412i | ||||
\(222\) | 57387.0 | − | 45095.2i | 1.16442 | − | 0.915007i | ||||
\(223\) | − | 94185.8i | − | 1.89398i | −0.321261 | − | 0.946991i | \(-0.604107\pi\) | ||
0.321261 | − | 0.946991i | \(-0.395893\pi\) | |||||||
\(224\) | −9655.79 | − | 50604.2i | −0.192438 | − | 1.00853i | ||||
\(225\) | −36744.4 | −0.725816 | ||||||||
\(226\) | −12766.1 | − | 16245.9i | −0.249944 | − | 0.318072i | ||||
\(227\) | 62683.9 | − | 62683.9i | 1.21648 | − | 1.21648i | 0.247622 | − | 0.968857i | \(-0.420351\pi\) |
0.968857 | − | 0.247622i | \(-0.0796490\pi\) | |||||||
\(228\) | 24342.6 | + | 5924.59i | 0.468271 | + | 0.113969i | ||||
\(229\) | −19781.9 | + | 19781.9i | −0.377221 | + | 0.377221i | −0.870099 | − | 0.492877i | \(-0.835945\pi\) |
0.492877 | + | 0.870099i | \(0.335945\pi\) | |||||||
\(230\) | −15371.8 | − | 1843.72i | −0.290583 | − | 0.0348528i | ||||
\(231\) | 42043.7 | 0.787910 | ||||||||
\(232\) | −29149.3 | − | 10909.1i | −0.541566 | − | 0.202681i | ||||
\(233\) | 25062.1i | 0.461642i | 0.972996 | + | 0.230821i | \(0.0741412\pi\) | ||||
−0.972996 | + | 0.230821i | \(0.925859\pi\) | |||||||
\(234\) | −30096.0 | − | 3609.75i | −0.549638 | − | 0.0659242i | ||||
\(235\) | 28702.6 | + | 28702.6i | 0.519740 | + | 0.519740i | ||||
\(236\) | −71934.9 | + | 43773.4i | −1.29156 | + | 0.785934i | ||||
\(237\) | 35217.4 | + | 35217.4i | 0.626989 | + | 0.626989i | ||||
\(238\) | 35594.6 | + | 45296.9i | 0.628392 | + | 0.799676i | ||||
\(239\) | − | 93041.8i | − | 1.62885i | −0.580265 | − | 0.814427i | \(-0.697051\pi\) | ||
0.580265 | − | 0.814427i | \(-0.302949\pi\) | |||||||
\(240\) | 50413.6 | − | 97433.2i | 0.875236 | − | 1.69155i | ||||
\(241\) | −80981.9 | −1.39429 | −0.697146 | − | 0.716929i | \(-0.745547\pi\) | ||||
−0.697146 | + | 0.716929i | \(0.745547\pi\) | |||||||
\(242\) | 28308.7 | − | 22245.2i | 0.483380 | − | 0.379844i | ||||
\(243\) | −40156.6 | + | 40156.6i | −0.680056 | + | 0.680056i | ||||
\(244\) | −48256.3 | + | 29364.6i | −0.810540 | + | 0.493225i | ||||
\(245\) | 3541.90 | − | 3541.90i | 0.0590071 | − | 0.0590071i | ||||
\(246\) | 12380.3 | − | 103220.i | 0.204579 | − | 1.70566i | ||||
\(247\) | 24900.8 | 0.408149 | ||||||||
\(248\) | 5527.14 | + | 12138.5i | 0.0898663 | + | 0.197361i | ||||
\(249\) | 22939.3i | 0.369984i | ||||||||
\(250\) | 4275.14 | − | 35643.7i | 0.0684023 | − | 0.570299i | ||||
\(251\) | 25910.0 | + | 25910.0i | 0.411264 | + | 0.411264i | 0.882179 | − | 0.470915i | \(-0.156076\pi\) |
−0.470915 | + | 0.882179i | \(0.656076\pi\) | |||||||
\(252\) | 33493.1 | + | 8151.67i | 0.527417 | + | 0.128365i | ||||
\(253\) | 5337.31 | + | 5337.31i | 0.0833837 | + | 0.0833837i | ||||
\(254\) | −71982.2 | + | 56564.2i | −1.11573 | + | 0.876747i | ||||
\(255\) | 122675.i | 1.88658i | ||||||||
\(256\) | 37855.9 | + | 53496.7i | 0.577636 | + | 0.816295i | ||||
\(257\) | 15800.6 | 0.239225 | 0.119613 | − | 0.992821i | \(-0.461835\pi\) | ||||
0.119613 | + | 0.992821i | \(0.461835\pi\) | |||||||
\(258\) | 80874.5 | + | 102919.i | 1.21499 | + | 1.54616i | ||||
\(259\) | −58332.6 | + | 58332.6i | −0.869584 | + | 0.869584i | ||||
\(260\) | 25784.7 | − | 105943.i | 0.381431 | − | 1.56720i | ||||
\(261\) | 14725.7 | − | 14725.7i | 0.216170 | − | 0.216170i | ||||
\(262\) | 107851. | + | 12935.8i | 1.57117 | + | 0.188447i | ||||
\(263\) | −82043.7 | −1.18613 | −0.593067 | − | 0.805153i | \(-0.702083\pi\) | ||||
−0.593067 | + | 0.805153i | \(0.702083\pi\) | |||||||
\(264\) | −48676.0 | + | 22164.1i | −0.698405 | + | 0.318011i | ||||
\(265\) | − | 116356.i | − | 1.65690i | ||||||
\(266\) | −28115.9 | − | 3372.26i | −0.397365 | − | 0.0476604i | ||||
\(267\) | −9024.78 | − | 9024.78i | −0.126594 | − | 0.126594i | ||||
\(268\) | −3871.23 | − | 6361.78i | −0.0538988 | − | 0.0885745i | ||||
\(269\) | −30820.2 | − | 30820.2i | −0.425923 | − | 0.425923i | 0.461314 | − | 0.887237i | \(-0.347378\pi\) |
−0.887237 | + | 0.461314i | \(0.847378\pi\) | |||||||
\(270\) | −40432.7 | − | 51453.6i | −0.554632 | − | 0.705811i | ||||
\(271\) | 110808.i | 1.50880i | 0.656412 | + | 0.754402i | \(0.272073\pi\) | ||||
−0.656412 | + | 0.754402i | \(0.727927\pi\) | |||||||
\(272\) | −65088.7 | − | 33678.0i | −0.879768 | − | 0.455206i | ||||
\(273\) | 99065.7 | 1.32922 | ||||||||
\(274\) | 105930. | − | 83240.4i | 1.41097 | − | 1.10875i | ||||
\(275\) | −45566.4 | + | 45566.4i | −0.602531 | + | 0.602531i | ||||
\(276\) | 9301.98 | + | 15286.4i | 0.122112 | + | 0.200672i | ||||
\(277\) | 25634.0 | − | 25634.0i | 0.334084 | − | 0.334084i | −0.520051 | − | 0.854135i | \(-0.674087\pi\) |
0.854135 | + | 0.520051i | \(0.174087\pi\) | |||||||
\(278\) | −7914.08 | + | 65983.0i | −0.102403 | + | 0.853773i | ||||
\(279\) | −8924.39 | −0.114649 | ||||||||
\(280\) | −43461.7 | + | 116130.i | −0.554358 | + | 1.48125i | ||||
\(281\) | 48800.5i | 0.618033i | 0.951057 | + | 0.309017i | \(0.0999999\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(282\) | 5587.10 | − | 46582.0i | 0.0702568 | − | 0.585761i | ||||
\(283\) | −111466. | − | 111466.i | −1.39178 | − | 1.39178i | −0.821340 | − | 0.570439i | \(-0.806773\pi\) |
−0.570439 | − | 0.821340i | \(-0.693227\pi\) | |||||||
\(284\) | 3937.72 | − | 16179.1i | 0.0488212 | − | 0.200594i | ||||
\(285\) | −42638.9 | − | 42638.9i | −0.524948 | − | 0.524948i | ||||
\(286\) | −41798.1 | + | 32845.3i | −0.511004 | + | 0.401551i | ||||
\(287\) | 117505.i | 1.42657i | ||||||||
\(288\) | −43073.9 | + | 8218.94i | −0.519313 | + | 0.0990902i | ||||
\(289\) | −1569.88 | −0.0187963 | ||||||||
\(290\) | 46285.5 | + | 58901.8i | 0.550363 | + | 0.700378i | ||||
\(291\) | 103088. | − | 103088.i | 1.21737 | − | 1.21737i | ||||
\(292\) | 41558.6 | + | 10114.7i | 0.487411 | + | 0.118628i | ||||
\(293\) | 13093.1 | − | 13093.1i | 0.152514 | − | 0.152514i | −0.626726 | − | 0.779240i | \(-0.715605\pi\) |
0.779240 | + | 0.626726i | \(0.215605\pi\) | |||||||
\(294\) | −5748.22 | − | 689.448i | −0.0665026 | − | 0.00797640i | ||||
\(295\) | 202676. | 2.32895 | ||||||||
\(296\) | 36783.3 | − | 98285.6i | 0.419824 | − | 1.12178i | ||||
\(297\) | 31904.2i | 0.361688i | ||||||||
\(298\) | −83562.0 | − | 10022.5i | −0.940971 | − | 0.112861i | ||||
\(299\) | 12576.1 | + | 12576.1i | 0.140670 | + | 0.140670i | ||||
\(300\) | −130505. | + | 79414.1i | −1.45005 | + | 0.882379i | ||||
\(301\) | −104615. | − | 104615.i | −1.15467 | − | 1.15467i | ||||
\(302\) | −19785.9 | − | 25179.1i | −0.216942 | − | 0.276075i | ||||
\(303\) | − | 117840.i | − | 1.28353i | ||||||
\(304\) | 34328.9 | − | 10917.6i | 0.371461 | − | 0.118136i | ||||
\(305\) | 135962. | 1.46156 | ||||||||
\(306\) | 38556.3 | − | 30297.9i | 0.411768 | − | 0.323571i | ||||
\(307\) | 25274.9 | − | 25274.9i | 0.268171 | − | 0.268171i | −0.560192 | − | 0.828363i | \(-0.689273\pi\) |
0.828363 | + | 0.560192i | \(0.189273\pi\) | |||||||
\(308\) | 51643.2 | − | 31425.6i | 0.544392 | − | 0.331270i | ||||
\(309\) | −56190.0 | + | 56190.0i | −0.588494 | + | 0.588494i | ||||
\(310\) | 3822.99 | − | 31873.9i | 0.0397813 | − | 0.331674i | ||||
\(311\) | 53808.0 | 0.556322 | 0.278161 | − | 0.960534i | \(-0.410275\pi\) | ||||
0.278161 | + | 0.960534i | \(0.410275\pi\) | |||||||
\(312\) | −114693. | + | 52224.4i | −1.17823 | + | 0.536493i | ||||
\(313\) | − | 137345.i | − | 1.40192i | −0.713199 | − | 0.700961i | \(-0.752755\pi\) | ||
0.713199 | − | 0.700961i | \(-0.247245\pi\) | |||||||
\(314\) | −8185.60 | + | 68246.8i | −0.0830217 | + | 0.692187i | ||||
\(315\) | −58667.1 | − | 58667.1i | −0.591253 | − | 0.591253i | ||||
\(316\) | 69581.6 | + | 16935.0i | 0.696819 | + | 0.169594i | ||||
\(317\) | 115546. | + | 115546.i | 1.14984 | + | 1.14984i | 0.986584 | + | 0.163252i | \(0.0521982\pi\) |
0.163252 | + | 0.986584i | \(0.447802\pi\) | |||||||
\(318\) | −105742. | + | 83093.3i | −1.04567 | + | 0.821697i | ||||
\(319\) | − | 36522.4i | − | 0.358904i | ||||||
\(320\) | −10902.5 | − | 157361.i | −0.106470 | − | 1.53673i | ||||
\(321\) | −28235.9 | −0.274026 | ||||||||
\(322\) | −12496.7 | − | 15903.0i | −0.120527 | − | 0.153380i | ||||
\(323\) | −28484.2 | + | 28484.2i | −0.273023 | + | 0.273023i | ||||
\(324\) | −31010.5 | + | 127414.i | −0.295406 | + | 1.21375i | ||||
\(325\) | −107366. | + | 107366.i | −1.01648 | + | 1.01648i | ||||
\(326\) | −132813. | − | 15929.7i | −1.24970 | − | 0.149890i | ||||
\(327\) | −84389.7 | −0.789213 | ||||||||
\(328\) | −61944.9 | − | 136041.i | −0.575782 | − | 1.26451i | ||||
\(329\) | 53028.7i | 0.489913i | ||||||||
\(330\) | 127816. | + | 15330.4i | 1.17370 | + | 0.140775i | ||||
\(331\) | 68009.3 | + | 68009.3i | 0.620744 | + | 0.620744i | 0.945722 | − | 0.324978i | \(-0.105357\pi\) |
−0.324978 | + | 0.945722i | \(0.605357\pi\) | |||||||
\(332\) | 17146.1 | + | 28176.9i | 0.155557 | + | 0.255633i | ||||
\(333\) | 49652.2 | + | 49652.2i | 0.447765 | + | 0.447765i | ||||
\(334\) | 105022. | + | 133648.i | 0.941427 | + | 1.19804i | ||||
\(335\) | 17924.3i | 0.159718i | ||||||||
\(336\) | 136575. | − | 43434.9i | 1.20974 | − | 0.384734i | ||||
\(337\) | −146703. | −1.29176 | −0.645878 | − | 0.763440i | \(-0.723509\pi\) | ||||
−0.645878 | + | 0.763440i | \(0.723509\pi\) | |||||||
\(338\) | −8658.97 | + | 6804.29i | −0.0757937 | + | 0.0595593i | ||||
\(339\) | 40643.4 | − | 40643.4i | 0.353664 | − | 0.353664i | ||||
\(340\) | 91693.7 | + | 150685.i | 0.793198 | + | 1.30350i | ||||
\(341\) | −11067.0 | + | 11067.0i | −0.0951749 | + | 0.0951749i | ||||
\(342\) | −2870.44 | + | 23932.1i | −0.0245412 | + | 0.204611i | ||||
\(343\) | −114250. | −0.971108 | ||||||||
\(344\) | 176267. | + | 65967.9i | 1.48955 | + | 0.557462i | ||||
\(345\) | − | 43069.4i | − | 0.361851i | ||||||
\(346\) | 10874.3 | − | 90663.8i | 0.0908343 | − | 0.757324i | ||||
\(347\) | −80120.9 | − | 80120.9i | −0.665406 | − | 0.665406i | 0.291243 | − | 0.956649i | \(-0.405931\pi\) |
−0.956649 | + | 0.291243i | \(0.905931\pi\) | |||||||
\(348\) | 20475.2 | − | 84127.3i | 0.169071 | − | 0.694670i | ||||
\(349\) | 100990. | + | 100990.i | 0.829143 | + | 0.829143i | 0.987398 | − | 0.158255i | \(-0.0505869\pi\) |
−0.158255 | + | 0.987398i | \(0.550587\pi\) | |||||||
\(350\) | 135770. | − | 106689.i | 1.10832 | − | 0.870929i | ||||
\(351\) | 75174.4i | 0.610177i | ||||||||
\(352\) | −43223.3 | + | 63607.7i | −0.348845 | + | 0.513363i | ||||
\(353\) | 129855. | 1.04210 | 0.521052 | − | 0.853525i | \(-0.325540\pi\) | ||||
0.521052 | + | 0.853525i | \(0.325540\pi\) | |||||||
\(354\) | −144738. | − | 184190.i | −1.15498 | − | 1.46980i | ||||
\(355\) | −28339.6 | + | 28339.6i | −0.224873 | + | 0.224873i | ||||
\(356\) | −17830.9 | − | 4339.76i | −0.140694 | − | 0.0342425i | ||||
\(357\) | −113322. | + | 113322.i | −0.889158 | + | 0.889158i | ||||
\(358\) | −126048. | − | 15118.3i | −0.983488 | − | 0.117961i | ||||
\(359\) | −55943.2 | −0.434068 | −0.217034 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217034 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(360\) | 98849.2 | + | 36994.3i | 0.762725 | + | 0.285450i | ||||
\(361\) | 110520.i | 0.848061i | ||||||||
\(362\) | −55554.1 | − | 6663.23i | −0.423935 | − | 0.0508472i | ||||
\(363\) | 70821.8 | + | 70821.8i | 0.537469 | + | 0.537469i | ||||
\(364\) | 121685. | − | 74046.9i | 0.918403 | − | 0.558861i | ||||
\(365\) | −72794.8 | − | 72794.8i | −0.546405 | − | 0.546405i | ||||
\(366\) | −97094.9 | − | 123561.i | −0.724827 | − | 0.922397i | ||||
\(367\) | − | 144947.i | − | 1.07616i | −0.842892 | − | 0.538082i | \(-0.819149\pi\) | ||
0.842892 | − | 0.538082i | \(-0.180851\pi\) | |||||||
\(368\) | 22851.7 | + | 11823.8i | 0.168742 | + | 0.0873097i | ||||
\(369\) | 100019. | 0.734566 | ||||||||
\(370\) | −198605. | + | 156066.i | −1.45073 | + | 1.14000i | ||||
\(371\) | 107485. | − | 107485.i | 0.780906 | − | 0.780906i | ||||
\(372\) | −31696.7 | + | 19287.9i | −0.229049 | + | 0.139379i | ||||
\(373\) | 24034.7 | − | 24034.7i | 0.172751 | − | 0.172751i | −0.615436 | − | 0.788187i | \(-0.711020\pi\) |
0.788187 | + | 0.615436i | \(0.211020\pi\) | |||||||
\(374\) | 10241.2 | − | 85385.4i | 0.0732164 | − | 0.610436i | ||||
\(375\) | 99867.8 | 0.710171 | ||||||||
\(376\) | −27955.1 | − | 61393.9i | −0.197736 | − | 0.434260i | ||||
\(377\) | − | 86056.2i | − | 0.605480i | ||||||
\(378\) | 10180.7 | − | 84881.0i | 0.0712516 | − | 0.594055i | ||||
\(379\) | −27907.2 | − | 27907.2i | −0.194284 | − | 0.194284i | 0.603260 | − | 0.797544i | \(-0.293868\pi\) |
−0.797544 | + | 0.603260i | \(0.793868\pi\) | |||||||
\(380\) | −84244.9 | − | 20503.8i | −0.583414 | − | 0.141993i | ||||
\(381\) | −180083. | − | 180083.i | −1.24057 | − | 1.24057i | ||||
\(382\) | 6395.95 | − | 5025.99i | 0.0438307 | − | 0.0344425i | ||||
\(383\) | 96652.7i | 0.658895i | 0.944174 | + | 0.329448i | \(0.106863\pi\) | ||||
−0.944174 | + | 0.329448i | \(0.893137\pi\) | |||||||
\(384\) | −135222. | + | 122285.i | −0.917033 | + | 0.829297i | ||||
\(385\) | −145505. | −0.981648 | ||||||||
\(386\) | 72308.6 | + | 92018.2i | 0.485306 | + | 0.617588i | ||||
\(387\) | −89047.2 | + | 89047.2i | −0.594564 | + | 0.594564i | ||||
\(388\) | 49572.0 | − | 203678.i | 0.329286 | − | 1.35295i | ||||
\(389\) | 133129. | − | 133129.i | 0.879777 | − | 0.879777i | −0.113734 | − | 0.993511i | \(-0.536281\pi\) |
0.993511 | + | 0.113734i | \(0.0362813\pi\) | |||||||
\(390\) | 301167. | + | 36122.3i | 1.98006 | + | 0.237491i | ||||
\(391\) | −28771.8 | −0.188197 | ||||||||
\(392\) | −7576.00 | + | 3449.65i | −0.0493024 | + | 0.0224493i | ||||
\(393\) | 302181.i | 1.95651i | ||||||||
\(394\) | 158359. | + | 18993.8i | 1.02012 | + | 0.122354i | ||||
\(395\) | −121880. | − | 121880.i | −0.781159 | − | 0.781159i | ||||
\(396\) | −26749.3 | − | 43958.3i | −0.170577 | − | 0.280318i | ||||
\(397\) | 33406.1 | + | 33406.1i | 0.211956 | + | 0.211956i | 0.805098 | − | 0.593142i | \(-0.202113\pi\) |
−0.593142 | + | 0.805098i | \(0.702113\pi\) | |||||||
\(398\) | 133709. | + | 170154.i | 0.844100 | + | 1.07418i | ||||
\(399\) | − | 78776.3i | − | 0.494823i | ||||||
\(400\) | −100944. | + | 195092.i | −0.630900 | + | 1.21933i | ||||
\(401\) | −87329.7 | −0.543092 | −0.271546 | − | 0.962425i | \(-0.587535\pi\) | ||||
−0.271546 | + | 0.962425i | \(0.587535\pi\) | |||||||
\(402\) | 16289.4 | − | 12800.3i | 0.100798 | − | 0.0792079i | ||||
\(403\) | −26076.8 | + | 26076.8i | −0.160562 | + | 0.160562i | ||||
\(404\) | −88079.6 | − | 144745.i | −0.539651 | − | 0.886834i | ||||
\(405\) | 223181. | − | 223181.i | 1.36065 | − | 1.36065i | ||||
\(406\) | −11654.4 | + | 97167.8i | −0.0707031 | + | 0.589482i | ||||
\(407\) | 123146. | 0.743418 | ||||||||
\(408\) | 71458.8 | − | 190939.i | 0.429275 | − | 1.14703i | ||||
\(409\) | − | 47133.9i | − | 0.281765i | −0.990026 | − | 0.140883i | \(-0.955006\pi\) | ||
0.990026 | − | 0.140883i | \(-0.0449940\pi\) | |||||||
\(410\) | −42845.8 | + | 357223.i | −0.254883 | + | 2.12506i | ||||
\(411\) | 265012. | + | 265012.i | 1.56885 | + | 1.56885i | ||||
\(412\) | −27020.2 | + | 111019.i | −0.159182 | + | 0.654037i | ||||
\(413\) | 187224. | + | 187224.i | 1.09765 | + | 1.09765i | ||||
\(414\) | −13536.6 | + | 10637.1i | −0.0789782 | + | 0.0620617i | ||||
\(415\) | − | 79388.5i | − | 0.460958i | ||||||
\(416\) | −101845. | + | 149876.i | −0.588509 | + | 0.866055i | ||||
\(417\) | −184874. | −1.06317 | ||||||||
\(418\) | 26118.3 | + | 33237.5i | 0.149483 | + | 0.190229i | ||||
\(419\) | −70487.1 | + | 70487.1i | −0.401497 | + | 0.401497i | −0.878760 | − | 0.477264i | \(-0.841629\pi\) |
0.477264 | + | 0.878760i | \(0.341629\pi\) | |||||||
\(420\) | −335162. | − | 81572.9i | −1.90001 | − | 0.462431i | ||||
\(421\) | 109929. | − | 109929.i | 0.620225 | − | 0.620225i | −0.325364 | − | 0.945589i | \(-0.605487\pi\) |
0.945589 | + | 0.325364i | \(0.105487\pi\) | |||||||
\(422\) | −179698. | − | 21553.2i | −1.00906 | − | 0.121028i | ||||
\(423\) | 45137.6 | 0.252266 | ||||||||
\(424\) | −67777.6 | + | 181103.i | −0.377012 | + | 1.00738i | ||||
\(425\) | − | 245634.i | − | 1.35991i | ||||||
\(426\) | 45992.8 | + | 5516.43i | 0.253437 | + | 0.0303976i | ||||
\(427\) | 125596. | + | 125596.i | 0.688845 | + | 0.688845i | ||||
\(428\) | −34682.8 | + | 21105.0i | −0.189333 | + | 0.115212i | ||||
\(429\) | −104569. | − | 104569.i | −0.568184 | − | 0.568184i | ||||
\(430\) | −279891. | − | 356182.i | −1.51374 | − | 1.92635i | ||||
\(431\) | 8391.44i | 0.0451733i | 0.999745 | + | 0.0225867i | \(0.00719017\pi\) | ||||
−0.999745 | + | 0.0225867i | \(0.992810\pi\) | |||||||
\(432\) | 32959.9 | + | 103638.i | 0.176611 | + | 0.555329i | ||||
\(433\) | 112221. | 0.598545 | 0.299272 | − | 0.954168i | \(-0.403256\pi\) | ||||
0.299272 | + | 0.954168i | \(0.403256\pi\) | |||||||
\(434\) | 32975.3 | − | 25912.3i | 0.175069 | − | 0.137571i | ||||
\(435\) | −147359. | + | 147359.i | −0.778749 | + | 0.778749i | ||||
\(436\) | −103658. | + | 63077.3i | −0.545292 | + | 0.331818i | ||||
\(437\) | 10000.4 | − | 10000.4i | 0.0523666 | − | 0.0523666i | ||||
\(438\) | −14169.8 | + | 118140.i | −0.0738613 | + | 0.615813i | ||||
\(439\) | −95834.1 | −0.497269 | −0.248634 | − | 0.968597i | \(-0.579982\pi\) | ||||
−0.248634 | + | 0.968597i | \(0.579982\pi\) | |||||||
\(440\) | 168458. | − | 76705.6i | 0.870134 | − | 0.396206i | ||||
\(441\) | − | 5569.98i | − | 0.0286402i | ||||||
\(442\) | 24130.9 | − | 201190.i | 0.123518 | − | 1.02982i | ||||
\(443\) | 48800.8 | + | 48800.8i | 0.248668 | + | 0.248668i | 0.820424 | − | 0.571756i | \(-0.193738\pi\) |
−0.571756 | + | 0.820424i | \(0.693738\pi\) | |||||||
\(444\) | 283661. | + | 69038.3i | 1.43891 | + | 0.350206i | ||||
\(445\) | 31233.0 | + | 31233.0i | 0.157722 | + | 0.157722i | ||||
\(446\) | 296227. | − | 232777.i | 1.48920 | − | 1.17023i | ||||
\(447\) | − | 234127.i | − | 1.17175i | ||||||
\(448\) | 135293. | − | 155435.i | 0.674091 | − | 0.774451i | ||||
\(449\) | −246669. | −1.22355 | −0.611776 | − | 0.791031i | \(-0.709545\pi\) | ||||
−0.611776 | + | 0.791031i | \(0.709545\pi\) | |||||||
\(450\) | −90812.7 | − | 115566.i | −0.448458 | − | 0.570697i | ||||
\(451\) | 124033. | − | 124033.i | 0.609794 | − | 0.609794i | ||||
\(452\) | 19544.3 | − | 80302.3i | 0.0956626 | − | 0.393053i | ||||
\(453\) | 62992.3 | − | 62992.3i | 0.306967 | − | 0.306967i | ||||
\(454\) | 352070. | + | 42227.7i | 1.70812 | + | 0.204874i | ||||
\(455\) | −342847. | −1.65606 | ||||||||
\(456\) | 41528.4 | + | 91203.1i | 0.199717 | + | 0.438611i | ||||
\(457\) | 6030.04i | 0.0288727i | 0.999896 | + | 0.0144364i | \(0.00459540\pi\) | ||||
−0.999896 | + | 0.0144364i | \(0.995405\pi\) | |||||||
\(458\) | −111107. | − | 13326.3i | −0.529675 | − | 0.0635298i | ||||
\(459\) | −85992.8 | − | 85992.8i | −0.408166 | − | 0.408166i | ||||
\(460\) | −32192.3 | − | 52903.1i | −0.152137 | − | 0.250015i | ||||
\(461\) | 13122.6 | + | 13122.6i | 0.0617473 | + | 0.0617473i | 0.737306 | − | 0.675559i | \(-0.236098\pi\) |
−0.675559 | + | 0.737306i | \(0.736098\pi\) | |||||||
\(462\) | 103910. | + | 132233.i | 0.486824 | + | 0.619520i | ||||
\(463\) | 408077.i | 1.90362i | 0.306689 | + | 0.951810i | \(0.400779\pi\) | ||||
−0.306689 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(464\) | −37731.0 | − | 118640.i | −0.175252 | − | 0.551054i | ||||
\(465\) | 89305.3 | 0.413020 | ||||||||
\(466\) | −78823.5 | + | 61940.1i | −0.362981 | + | 0.285233i | ||||
\(467\) | −108240. | + | 108240.i | −0.496311 | + | 0.496311i | −0.910288 | − | 0.413977i | \(-0.864140\pi\) |
0.413977 | + | 0.910288i | \(0.364140\pi\) | |||||||
\(468\) | −63028.1 | − | 103577.i | −0.287768 | − | 0.472903i | ||||
\(469\) | −16557.8 | + | 16557.8i | −0.0752759 | + | 0.0752759i | ||||
\(470\) | −19335.8 | + | 161211.i | −0.0875321 | + | 0.729792i | ||||
\(471\) | −191216. | −0.861953 | ||||||||
\(472\) | −315458. | − | 118060.i | −1.41598 | − | 0.529930i | ||||
\(473\) | 220853.i | 0.987144i | ||||||||
\(474\) | −23724.6 | + | 197802.i | −0.105595 | + | 0.880387i | ||||
\(475\) | 85376.7 | + | 85376.7i | 0.378401 | + | 0.378401i | ||||
\(476\) | −54493.5 | + | 223900.i | −0.240508 | + | 0.988187i | ||||
\(477\) | −91490.1 | − | 91490.1i | −0.402103 | − | 0.402103i | ||||
\(478\) | 292629. | − | 229950.i | 1.28074 | − | 1.00642i | ||||
\(479\) | − | 223150.i | − | 0.972583i | −0.873797 | − | 0.486291i | \(-0.838349\pi\) | ||
0.873797 | − | 0.486291i | \(-0.161651\pi\) | |||||||
\(480\) | 431036. | − | 82246.0i | 1.87081 | − | 0.356970i | ||||
\(481\) | 290165. | 1.25416 | ||||||||
\(482\) | −200144. | − | 254699.i | −0.861488 | − | 1.09631i | ||||
\(483\) | 39785.8 | − | 39785.8i | 0.170543 | − | 0.170543i | ||||
\(484\) | 139928. | + | 34056.2i | 0.597329 | + | 0.145380i | ||||
\(485\) | −356767. | + | 356767.i | −1.51670 | + | 1.51670i | ||||
\(486\) | −225544. | − | 27052.0i | −0.954901 | − | 0.114532i | ||||
\(487\) | 225880. | 0.952399 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(488\) | −211620. | − | 79198.5i | −0.888620 | − | 0.332566i | ||||
\(489\) | − | 372120.i | − | 1.55620i | ||||||
\(490\) | 19893.4 | + | 2386.04i | 0.0828548 | + | 0.00993770i | ||||
\(491\) | −101698. | − | 101698.i | −0.421842 | − | 0.421842i | 0.463996 | − | 0.885837i | \(-0.346415\pi\) |
−0.885837 | + | 0.463996i | \(0.846415\pi\) | |||||||
\(492\) | 355237. | − | 216167.i | 1.46754 | − | 0.893016i | ||||
\(493\) | 98440.7 | + | 98440.7i | 0.405024 | + | 0.405024i | ||||
\(494\) | 61541.4 | + | 78316.1i | 0.252182 | + | 0.320920i | ||||
\(495\) | 123853.i | 0.505469i | ||||||||
\(496\) | −24517.0 | + | 47383.5i | −0.0996561 | + | 0.192603i | ||||
\(497\) | −52357.9 | −0.211968 | ||||||||
\(498\) | −72147.2 | + | 56693.9i | −0.290912 | + | 0.228601i | ||||
\(499\) | 226481. | − | 226481.i | 0.909559 | − | 0.909559i | −0.0866770 | − | 0.996236i | \(-0.527625\pi\) |
0.996236 | + | 0.0866770i | \(0.0276248\pi\) | |||||||
\(500\) | 122670. | − | 74646.4i | 0.490680 | − | 0.298585i | ||||
\(501\) | −334357. | + | 334357.i | −1.33209 | + | 1.33209i | ||||
\(502\) | −17454.6 | + | 145526.i | −0.0692631 | + | 0.577476i | ||||
\(503\) | 125734. | 0.496956 | 0.248478 | − | 0.968637i | \(-0.420070\pi\) | ||||
0.248478 | + | 0.968637i | \(0.420070\pi\) | |||||||
\(504\) | 57139.1 | + | 125487.i | 0.224943 | + | 0.494011i | ||||
\(505\) | 407820.i | 1.59914i | ||||||||
\(506\) | −3595.54 | + | 29977.5i | −0.0140431 | + | 0.117083i | ||||
\(507\) | −21662.8 | − | 21662.8i | −0.0842749 | − | 0.0842749i | ||||
\(508\) | −355804. | − | 86596.7i | −1.37874 | − | 0.335563i | ||||
\(509\) | −82499.2 | − | 82499.2i | −0.318430 | − | 0.318430i | 0.529734 | − | 0.848164i | \(-0.322292\pi\) |
−0.848164 | + | 0.529734i | \(0.822292\pi\) | |||||||
\(510\) | −385829. | + | 303188.i | −1.48339 | + | 1.16566i | ||||
\(511\) | − | 134490.i | − | 0.515048i | ||||||
\(512\) | −74694.3 | + | 251277.i | −0.284936 | + | 0.958546i | ||||
\(513\) | 59778.1 | 0.227147 | ||||||||
\(514\) | 39050.7 | + | 49694.9i | 0.147809 | + | 0.188099i | ||||
\(515\) | 194462. | − | 194462.i | 0.733198 | − | 0.733198i | ||||
\(516\) | −123814. | + | 508722.i | −0.465020 | + | 1.91065i | ||||
\(517\) | 55974.7 | − | 55974.7i | 0.209416 | − | 0.209416i | ||||
\(518\) | −327631. | − | 39296.4i | −1.22103 | − | 0.146451i | ||||
\(519\) | 254025. | 0.943066 | ||||||||
\(520\) | 396930. | − | 180738.i | 1.46794 | − | 0.668410i | ||||
\(521\) | 225057.i | 0.829120i | 0.910022 | + | 0.414560i | \(0.136064\pi\) | ||||
−0.910022 | + | 0.414560i | \(0.863936\pi\) | |||||||
\(522\) | 82708.5 | + | 9920.15i | 0.303535 | + | 0.0364064i | ||||
\(523\) | −230384. | − | 230384.i | −0.842264 | − | 0.842264i | 0.146889 | − | 0.989153i | \(-0.453074\pi\) |
−0.989153 | + | 0.146889i | \(0.953074\pi\) | |||||||
\(524\) | 225866. | + | 371176.i | 0.822599 | + | 1.35182i | ||||
\(525\) | 339664. | + | 339664.i | 1.23234 | + | 1.23234i | ||||
\(526\) | −202768. | − | 258038.i | −0.732873 | − | 0.932636i | ||||
\(527\) | − | 59659.0i | − | 0.214810i | ||||||
\(528\) | −190010. | − | 98314.4i | −0.681568 | − | 0.352655i | ||||
\(529\) | −269740. | −0.963903 | ||||||||
\(530\) | 365953. | − | 287569.i | 1.30279 | − | 1.02374i | ||||
\(531\) | 159364. | − | 159364.i | 0.565199 | − | 0.565199i | ||||
\(532\) | −58881.5 | − | 96762.7i | −0.208044 | − | 0.341889i | ||||
\(533\) | 292253. | − | 292253.i | 1.02874 | − | 1.02874i | ||||
\(534\) | 6079.64 | − | 50688.6i | 0.0213204 | − | 0.177757i | ||||
\(535\) | 97718.9 | 0.341406 | ||||||||
\(536\) | 10441.0 | − | 27898.5i | 0.0363423 | − | 0.0971070i | ||||
\(537\) | − | 353165.i | − | 1.22470i | ||||||
\(538\) | 20762.4 | − | 173105.i | 0.0717319 | − | 0.598060i | ||||
\(539\) | −6907.27 | − | 6907.27i | −0.0237755 | − | 0.0237755i | ||||
\(540\) | 61900.3 | − | 254332.i | 0.212278 | − | 0.872195i | ||||
\(541\) | −183995. | − | 183995.i | −0.628655 | − | 0.628655i | 0.319074 | − | 0.947730i | \(-0.396628\pi\) |
−0.947730 | + | 0.319074i | \(0.896628\pi\) | |||||||
\(542\) | −348506. | + | 273859.i | −1.18635 | + | 0.932241i | ||||
\(543\) | − | 155654.i | − | 0.527909i | ||||||
\(544\) | −54943.1 | − | 287947.i | −0.185659 | − | 0.973003i | ||||
\(545\) | 292056. | 0.983271 | ||||||||
\(546\) | 244838. | + | 311575.i | 0.821284 | + | 1.04515i | ||||
\(547\) | −416851. | + | 416851.i | −1.39318 | + | 1.39318i | −0.575075 | + | 0.818100i | \(0.695027\pi\) |
−0.818100 | + | 0.575075i | \(0.804973\pi\) | |||||||
\(548\) | 523604. | + | 127436.i | 1.74358 | + | 0.424358i | ||||
\(549\) | 106907. | − | 106907.i | 0.354699 | − | 0.354699i | ||||
\(550\) | −255928. | − | 30696.3i | −0.846043 | − | 0.101475i | ||||
\(551\) | −68431.2 | −0.225399 | ||||||||
\(552\) | −25088.1 | + | 67035.7i | −0.0823360 | + | 0.220003i | ||||
\(553\) | − | 225176.i | − | 0.736330i | ||||||
\(554\) | 143976. | + | 17268.6i | 0.469104 | + | 0.0562649i | ||||
\(555\) | −496864. | − | 496864.i | −1.61307 | − | 1.61307i | ||||
\(556\) | −227085. | + | 138184.i | −0.734578 | + | 0.447001i | ||||
\(557\) | −233211. | − | 233211.i | −0.751691 | − | 0.751691i | 0.223104 | − | 0.974795i | \(-0.428381\pi\) |
−0.974795 | + | 0.223104i | \(0.928381\pi\) | |||||||
\(558\) | −22056.3 | − | 28068.4i | −0.0708378 | − | 0.0901465i | ||||
\(559\) | 520386.i | 1.66534i | ||||||||
\(560\) | −472659. | + | 150320.i | −1.50720 | + | 0.479335i | ||||
\(561\) | 239236. | 0.760152 | ||||||||
\(562\) | −153484. | + | 120609.i | −0.485949 | + | 0.381862i | ||||
\(563\) | −82256.5 | + | 82256.5i | −0.259510 | + | 0.259510i | −0.824855 | − | 0.565345i | \(-0.808743\pi\) |
0.565345 | + | 0.824855i | \(0.308743\pi\) | |||||||
\(564\) | 160315. | − | 97553.9i | 0.503983 | − | 0.306681i | ||||
\(565\) | −140659. | + | 140659.i | −0.440626 | + | 0.440626i | ||||
\(566\) | 75090.4 | − | 626061.i | 0.234397 | − | 1.95427i | ||||
\(567\) | 412331. | 1.28257 | ||||||||
\(568\) | 60617.3 | − | 27601.5i | 0.187888 | − | 0.0855530i | ||||
\(569\) | − | 130218.i | − | 0.402203i | −0.979570 | − | 0.201102i | \(-0.935548\pi\) | ||
0.979570 | − | 0.201102i | \(-0.0644522\pi\) | |||||||
\(570\) | 28724.2 | − | 239486.i | 0.0884093 | − | 0.737106i | ||||
\(571\) | 62508.2 | + | 62508.2i | 0.191719 | + | 0.191719i | 0.796438 | − | 0.604720i | \(-0.206715\pi\) |
−0.604720 | + | 0.796438i | \(0.706715\pi\) | |||||||
\(572\) | −206605. | − | 50284.3i | −0.631465 | − | 0.153688i | ||||
\(573\) | 16001.2 | + | 16001.2i | 0.0487353 | + | 0.0487353i | ||||
\(574\) | −369568. | + | 290410.i | −1.12168 | + | 0.881429i | ||||
\(575\) | 86238.6i | 0.260835i | ||||||||
\(576\) | −132305. | − | 115160.i | −0.398779 | − | 0.347102i | ||||
\(577\) | 522256. | 1.56867 | 0.784336 | − | 0.620336i | \(-0.213004\pi\) | ||||
0.784336 | + | 0.620336i | \(0.213004\pi\) | |||||||
\(578\) | −3879.92 | − | 4937.49i | −0.0116136 | − | 0.0147792i | ||||
\(579\) | −230208. | + | 230208.i | −0.686695 | + | 0.686695i | ||||
\(580\) | −70860.6 | + | 291148.i | −0.210644 | + | 0.865481i | ||||
\(581\) | 73336.0 | − | 73336.0i | 0.217252 | − | 0.217252i | ||||
\(582\) | 579003. | + | 69446.3i | 1.70937 | + | 0.205023i | ||||
\(583\) | −226912. | −0.667606 | ||||||||
\(584\) | 70898.8 | + | 155705.i | 0.207880 | + | 0.456539i | ||||
\(585\) | 291829.i | 0.852739i | ||||||||
\(586\) | 73538.9 | + | 8820.34i | 0.214152 | + | 0.0256856i | ||||
\(587\) | 309702. | + | 309702.i | 0.898811 | + | 0.898811i | 0.995331 | − | 0.0965202i | \(-0.0307712\pi\) |
−0.0965202 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(588\) | −12038.1 | − | 19782.8i | −0.0348181 | − | 0.0572182i | ||||
\(589\) | 20736.0 | + | 20736.0i | 0.0597717 | + | 0.0597717i | ||||
\(590\) | 500909. | + | 637444.i | 1.43898 | + | 1.83121i | ||||
\(591\) | 443697.i | 1.27032i | ||||||||
\(592\) | 400030. | − | 127221.i | 1.14143 | − | 0.363008i | ||||
\(593\) | −447350. | −1.27215 | −0.636075 | − | 0.771628i | \(-0.719443\pi\) | ||||
−0.636075 | + | 0.771628i | \(0.719443\pi\) | |||||||
\(594\) | −100343. | + | 78850.2i | −0.284389 | + | 0.223475i | ||||
\(595\) | 392186. | − | 392186.i | 1.10779 | − | 1.10779i | ||||
\(596\) | −174999. | − | 287584.i | −0.492655 | − | 0.809603i | ||||
\(597\) | −425687. | + | 425687.i | −1.19438 | + | 1.19438i | ||||
\(598\) | −8472.01 | + | 70634.7i | −0.0236910 | + | 0.197522i | ||||
\(599\) | 462149. | 1.28804 | 0.644019 | − | 0.765009i | \(-0.277266\pi\) | ||||
0.644019 | + | 0.765009i | \(0.277266\pi\) | |||||||
\(600\) | −572306. | − | 214185.i | −1.58974 | − | 0.594960i | ||||
\(601\) | 374481.i | 1.03677i | 0.855149 | + | 0.518383i | \(0.173466\pi\) | ||||
−0.855149 | + | 0.518383i | \(0.826534\pi\) | |||||||
\(602\) | 70474.8 | − | 587578.i | 0.194465 | − | 1.62134i | ||||
\(603\) | 14093.8 | + | 14093.8i | 0.0387610 | + | 0.0387610i | ||||
\(604\) | 30291.2 | − | 124459.i | 0.0830315 | − | 0.341155i | ||||
\(605\) | −245100. | − | 245100.i | −0.669627 | − | 0.669627i | ||||
\(606\) | 370622. | − | 291238.i | 1.00922 | − | 0.793053i | ||||
\(607\) | 86755.6i | 0.235462i | 0.993046 | + | 0.117731i | \(0.0375620\pi\) | ||||
−0.993046 | + | 0.117731i | \(0.962438\pi\) | |||||||
\(608\) | 119180. | + | 80986.4i | 0.322402 | + | 0.219081i | ||||
\(609\) | −272248. | −0.734058 | ||||||||
\(610\) | 336026. | + | 427618.i | 0.903053 | + | 1.14920i | ||||
\(611\) | 131891. | − | 131891.i | 0.353290 | − | 0.353290i | ||||
\(612\) | 190582. | + | 46384.4i | 0.508836 | + | 0.123842i | ||||
\(613\) | −112325. | + | 112325.i | −0.298920 | + | 0.298920i | −0.840591 | − | 0.541671i | \(-0.817792\pi\) |
0.541671 | + | 0.840591i | \(0.317792\pi\) | |||||||
\(614\) | 141959. | + | 17026.7i | 0.376553 | + | 0.0451642i | ||||
\(615\) | −1.00088e6 | −2.64626 | ||||||||
\(616\) | 226472. | + | 84757.2i | 0.596834 | + | 0.223365i | ||||
\(617\) | − | 602706.i | − | 1.58320i | −0.611041 | − | 0.791599i | \(-0.709249\pi\) | ||
0.611041 | − | 0.791599i | \(-0.290751\pi\) | |||||||
\(618\) | −315597. | − | 37853.0i | −0.826334 | − | 0.0991114i | ||||
\(619\) | −150969. | − | 150969.i | −0.394010 | − | 0.394010i | 0.482104 | − | 0.876114i | \(-0.339873\pi\) |
−0.876114 | + | 0.482104i | \(0.839873\pi\) | |||||||
\(620\) | 109696. | − | 66751.5i | 0.285369 | − | 0.173651i | ||||
\(621\) | 30190.8 | + | 30190.8i | 0.0782873 | + | 0.0782873i | ||||
\(622\) | 132985. | + | 169233.i | 0.343733 | + | 0.437426i | ||||
\(623\) | 57703.6i | 0.148671i | ||||||||
\(624\) | −447713. | − | 231654.i | −1.14982 | − | 0.594937i | ||||
\(625\) | 190658. | 0.488084 | ||||||||
\(626\) | 431968. | − | 339444.i | 1.10231 | − | 0.866202i | ||||
\(627\) | −83152.6 | + | 83152.6i | −0.211515 | + | 0.211515i | ||||
\(628\) | −234876. | + | 142925.i | −0.595551 | + | 0.362401i | ||||
\(629\) | −331922. | + | 331922.i | −0.838948 | + | 0.838948i | ||||
\(630\) | 39521.7 | − | 329509.i | 0.0995761 | − | 0.830208i | ||||
\(631\) | −693714. | −1.74230 | −0.871148 | − | 0.491020i | \(-0.836624\pi\) | ||||
−0.871148 | + | 0.491020i | \(0.836624\pi\) | |||||||
\(632\) | 118706. | + | 260698.i | 0.297193 | + | 0.652684i | ||||
\(633\) | − | 503485.i | − | 1.25655i | ||||||
\(634\) | −77838.8 | + | 648975.i | −0.193650 | + | 1.61454i | ||||
\(635\) | 623231. | + | 623231.i | 1.54562 | + | 1.54562i | ||||
\(636\) | −522678. | − | 127211.i | −1.29217 | − | 0.314493i | ||||
\(637\) | −16275.3 | − | 16275.3i | −0.0401098 | − | 0.0401098i | ||||
\(638\) | 114868. | − | 90264.0i | 0.282200 | − | 0.221755i | ||||
\(639\) | 44566.7i | 0.109146i | ||||||||
\(640\) | 467976. | − | 423203.i | 1.14252 | − | 1.03321i | ||||
\(641\) | −17843.0 | −0.0434261 | −0.0217131 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217131 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(642\) | −69784.2 | − | 88805.6i | −0.169312 | − | 0.215462i | ||||
\(643\) | −230136. | + | 230136.i | −0.556626 | + | 0.556626i | −0.928345 | − | 0.371719i | \(-0.878768\pi\) |
0.371719 | + | 0.928345i | \(0.378768\pi\) | |||||||
\(644\) | 19131.8 | − | 78607.8i | 0.0461301 | − | 0.189537i | ||||
\(645\) | 891085. | − | 891085.i | 2.14190 | − | 2.14190i | ||||
\(646\) | −159985. | − | 19188.7i | −0.383366 | − | 0.0459813i | ||||
\(647\) | 568528. | 1.35814 | 0.679068 | − | 0.734075i | \(-0.262384\pi\) | ||||
0.679068 | + | 0.734075i | \(0.262384\pi\) | |||||||
\(648\) | −477376. | + | 217368.i | −1.13687 | + | 0.517661i | ||||
\(649\) | − | 395251.i | − | 0.938391i | ||||||
\(650\) | −603032. | − | 72328.4i | −1.42730 | − | 0.171191i | ||||
\(651\) | 82496.7 | + | 82496.7i | 0.194659 | + | 0.194659i | ||||
\(652\) | −278142. | − | 457083.i | −0.654291 | − | 1.07523i | ||||
\(653\) | 371799. | + | 371799.i | 0.871932 | + | 0.871932i | 0.992683 | − | 0.120751i | \(-0.0385303\pi\) |
−0.120751 | + | 0.992683i | \(0.538530\pi\) | |||||||
\(654\) | −208567. | − | 265417.i | −0.487629 | − | 0.620544i | ||||
\(655\) | − | 1.04579e6i | − | 2.43759i | ||||||
\(656\) | 274772. | − | 531046.i | 0.638506 | − | 1.23403i | ||||
\(657\) | −114477. | −0.265208 | ||||||||
\(658\) | −166782. | + | 131059.i | −0.385210 | + | 0.302701i | ||||
\(659\) | −71107.3 | + | 71107.3i | −0.163736 | + | 0.163736i | −0.784219 | − | 0.620484i | \(-0.786936\pi\) |
0.620484 | + | 0.784219i | \(0.286936\pi\) | |||||||
\(660\) | 267677. | + | 439886.i | 0.614502 | + | 1.00984i | ||||
\(661\) | 570193. | − | 570193.i | 1.30502 | − | 1.30502i | 0.380065 | − | 0.924960i | \(-0.375902\pi\) |
0.924960 | − | 0.380065i | \(-0.124098\pi\) | |||||||
\(662\) | −45815.2 | + | 381981.i | −0.104543 | + | 0.871617i | ||||
\(663\) | 563701. | 1.28239 | ||||||||
\(664\) | −46244.2 | + | 123565.i | −0.104887 | + | 0.280259i | ||||
\(665\) | 272629.i | 0.616494i | ||||||||
\(666\) | −33448.8 | + | 278877.i | −0.0754105 | + | 0.628730i | ||||
\(667\) | −34561.0 | − | 34561.0i | −0.0776846 | − | 0.0776846i | ||||
\(668\) | −160783. | + | 660615.i | −0.360318 | + | 1.48046i | ||||
\(669\) | 741091. | + | 741091.i | 1.65584 | + | 1.65584i | ||||
\(670\) | −56374.3 | + | 44299.4i | −0.125583 | + | 0.0986842i | ||||
\(671\) | − | 265148.i | − | 0.588901i | ||||||
\(672\) | 474149. | + | 322198.i | 1.04997 | + | 0.713484i | ||||
\(673\) | −57084.2 | −0.126033 | −0.0630167 | − | 0.998012i | \(-0.520072\pi\) | ||||
−0.0630167 | + | 0.998012i | \(0.520072\pi\) | |||||||
\(674\) | −362573. | − | 461402.i | −0.798134 | − | 1.01569i | ||||
\(675\) | −257749. | + | 257749.i | −0.565704 | + | 0.565704i | ||||
\(676\) | −42800.8 | − | 10417.0i | −0.0936609 | − | 0.0227955i | ||||
\(677\) | −107264. | + | 107264.i | −0.234032 | + | 0.234032i | −0.814373 | − | 0.580341i | \(-0.802919\pi\) |
0.580341 | + | 0.814373i | \(0.302919\pi\) | |||||||
\(678\) | 228278. | + | 27379.9i | 0.496597 | + | 0.0595624i | ||||
\(679\) | −659134. | −1.42966 | ||||||||
\(680\) | −247305. | + | 660801.i | −0.534828 | + | 1.42907i | ||||
\(681\) | 986444.i | 2.12705i | ||||||||
\(682\) | −62159.1 | − | 7455.43i | −0.133640 | − | 0.0160289i | ||||
\(683\) | 41763.8 | + | 41763.8i | 0.0895280 | + | 0.0895280i | 0.750452 | − | 0.660924i | \(-0.229836\pi\) |
−0.660924 | + | 0.750452i | \(0.729836\pi\) | |||||||
\(684\) | −82363.7 | + | 50119.5i | −0.176045 | + | 0.107126i | ||||
\(685\) | −917153. | − | 917153.i | −1.95461 | − | 1.95461i | ||||
\(686\) | −282365. | − | 359331.i | −0.600016 | − | 0.763565i | ||||
\(687\) | − | 311303.i | − | 0.659583i | ||||||
\(688\) | 228161. | + | 717420.i | 0.482019 | + | 1.51564i | ||||
\(689\) | −534662. | −1.12627 | ||||||||
\(690\) | 135459. | − | 106445.i | 0.284517 | − | 0.223576i | ||||
\(691\) | 473605. | − | 473605.i | 0.991882 | − | 0.991882i | −0.00808568 | − | 0.999967i | \(-0.502574\pi\) |
0.999967 | + | 0.00808568i | \(0.00257378\pi\) | |||||||
\(692\) | 312025. | − | 189872.i | 0.651594 | − | 0.396504i | ||||
\(693\) | −114410. | + | 114410.i | −0.238231 | + | 0.238231i | ||||
\(694\) | 53974.3 | − | 450007.i | 0.112065 | − | 0.934330i | ||||
\(695\) | 639811. | 1.32459 | ||||||||
\(696\) | 315195. | − | 143521.i | 0.650670 | − | 0.296276i | ||||
\(697\) | 668623.i | 1.37631i | ||||||||
\(698\) | −68033.3 | + | 567223.i | −0.139640 | + | 1.16424i | ||||
\(699\) | −197198. | − | 197198.i | −0.403598 | − | 0.403598i | ||||
\(700\) | 671101. | + | 163335.i | 1.36959 | + | 0.333336i | ||||
\(701\) | −139642. | − | 139642.i | −0.284170 | − | 0.284170i | 0.550599 | − | 0.834770i | \(-0.314399\pi\) |
−0.834770 | + | 0.550599i | \(0.814399\pi\) | |||||||
\(702\) | −236433. | + | 185791.i | −0.479772 | + | 0.377008i | ||||
\(703\) | − | 230737.i | − | 0.466880i | ||||||
\(704\) | −306879. | + | 21261.6i | −0.619188 | + | 0.0428994i | ||||
\(705\) | −451687. | −0.908782 | ||||||||
\(706\) | 320934. | + | 408412.i | 0.643882 | + | 0.819388i | ||||
\(707\) | −376728. | + | 376728.i | −0.753684 | + | 0.753684i | ||||
\(708\) | 221586. | − | 910438.i | 0.442054 | − | 1.81628i | ||||
\(709\) | −161047. | + | 161047.i | −0.320377 | + | 0.320377i | −0.848912 | − | 0.528535i | \(-0.822742\pi\) |
0.528535 | + | 0.848912i | \(0.322742\pi\) | |||||||
\(710\) | −159172. | − | 19091.3i | −0.315755 | − | 0.0378720i | ||||
\(711\) | −191668. | −0.379150 | ||||||||
\(712\) | −30419.5 | − | 66806.2i | −0.0600057 | − | 0.131782i | ||||
\(713\) | 20945.4i | 0.0412011i | ||||||||
\(714\) | −636486. | − | 76340.9i | −1.24851 | − | 0.149748i | ||||
\(715\) | 361893. | + | 361893.i | 0.707894 | + | 0.707894i | ||||
\(716\) | −263974. | − | 433801.i | −0.514914 | − | 0.846183i | ||||
\(717\) | 732090. | + | 732090.i | 1.42405 | + | 1.42405i | ||||
\(718\) | −138262. | − | 175949.i | −0.268197 | − | 0.341300i | ||||
\(719\) | 132212.i | 0.255749i | 0.991790 | + | 0.127874i | \(0.0408154\pi\) | ||||
−0.991790 | + | 0.127874i | \(0.959185\pi\) | |||||||
\(720\) | 127951. | + | 402324.i | 0.246819 | + | 0.776087i | ||||
\(721\) | 359273. | 0.691122 | ||||||||
\(722\) | −347600. | + | 273147.i | −0.666815 | + | 0.523989i | ||||
\(723\) | 637198. | − | 637198.i | 1.21898 | − | 1.21898i | ||||
\(724\) | −116344. | − | 191193.i | −0.221955 | − | 0.364749i | ||||
\(725\) | 295059. | − | 295059.i | 0.561349 | − | 0.561349i | ||||
\(726\) | −47709.9 | + | 397778.i | −0.0905180 | + | 0.754687i | ||||
\(727\) | 98417.4 | 0.186210 | 0.0931050 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931050 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(728\) | 533627. | + | 199710.i | 1.00687 | + | 0.376822i | ||||
\(729\) | 31927.4i | 0.0600770i | ||||||||
\(730\) | 49039.0 | − | 408859.i | 0.0920229 | − | 0.767234i | ||||
\(731\) | −595275. | − | 595275.i | −1.11399 | − | 1.11399i | ||||
\(732\) | 148647. | − | 610752.i | 0.277418 | − | 1.13984i | ||||
\(733\) | −369797. | − | 369797.i | −0.688265 | − | 0.688265i | 0.273584 | − | 0.961848i | \(-0.411791\pi\) |
−0.961848 | + | 0.273584i | \(0.911791\pi\) | |||||||
\(734\) | 455879. | − | 358233.i | 0.846169 | − | 0.664927i | ||||
\(735\) | 55738.2i | 0.103176i | ||||||||
\(736\) | 19289.7 | + | 101094.i | 0.0356098 | + | 0.186624i | ||||
\(737\) | 34955.2 | 0.0643542 | ||||||||
\(738\) | 247194. | + | 314574.i | 0.453864 | + | 0.577576i | ||||
\(739\) | 117481. | − | 117481.i | 0.215120 | − | 0.215120i | −0.591318 | − | 0.806438i | \(-0.701392\pi\) |
0.806438 | + | 0.591318i | \(0.201392\pi\) | |||||||
\(740\) | −981693. | − | 238928.i | −1.79272 | − | 0.436318i | ||||
\(741\) | −195929. | + | 195929.i | −0.356831 | + | 0.356831i | ||||
\(742\) | 603698. | + | 72408.2i | 1.09651 | + | 0.131516i | ||||
\(743\) | −273733. | −0.495849 | −0.247925 | − | 0.968779i | \(-0.579749\pi\) | ||||
−0.247925 | + | 0.968779i | \(0.579749\pi\) | |||||||
\(744\) | −139000. | − | 52020.8i | −0.251113 | − | 0.0939790i | ||||
\(745\) | 810267.i | 1.45988i | ||||||||
\(746\) | 134993. | + | 16191.2i | 0.242568 | + | 0.0290939i | ||||
\(747\) | −62423.0 | − | 62423.0i | −0.111867 | − | 0.111867i | ||||
\(748\) | 293859. | − | 178817.i | 0.525213 | − | 0.319600i | ||||
\(749\) | 90268.8 | + | 90268.8i | 0.160907 | + | 0.160907i | ||||
\(750\) | 246820. | + | 314097.i | 0.438791 | + | 0.558395i | ||||
\(751\) | 875863.i | 1.55295i | 0.630150 | + | 0.776473i | \(0.282993\pi\) | ||||
−0.630150 | + | 0.776473i | \(0.717007\pi\) | |||||||
\(752\) | 124002. | − | 239655.i | 0.219276 | − | 0.423791i | ||||
\(753\) | −407741. | −0.719108 | ||||||||
\(754\) | 270658. | − | 212685.i | 0.476078 | − | 0.374106i | ||||
\(755\) | −218004. | + | 218004.i | −0.382446 | + | 0.382446i | ||||
\(756\) | 292123. | − | 177761.i | 0.511119 | − | 0.311023i | ||||
\(757\) | 66071.4 | − | 66071.4i | 0.115298 | − | 0.115298i | −0.647104 | − | 0.762402i | \(-0.724020\pi\) |
0.762402 | + | 0.647104i | \(0.224020\pi\) | |||||||
\(758\) | 18800.0 | − | 156743.i | 0.0327204 | − | 0.272804i | ||||
\(759\) | −83992.1 | −0.145799 | ||||||||
\(760\) | −143721. | − | 315636.i | −0.248825 | − | 0.546461i | ||||
\(761\) | − | 333176.i | − | 0.575314i | −0.957734 | − | 0.287657i | \(-0.907124\pi\) | ||
0.957734 | − | 0.287657i | \(-0.0928763\pi\) | |||||||
\(762\) | 121315. | − | 1.01145e6i | 0.208932 | − | 1.74195i | ||||
\(763\) | 269790. | + | 269790.i | 0.463422 | + | 0.463422i | ||||
\(764\) | 31614.8 | + | 7694.51i | 0.0541631 | + | 0.0131824i | ||||
\(765\) | −333826. | − | 333826.i | −0.570423 | − | 0.570423i | ||||
\(766\) | −303985. | + | 238874.i | −0.518078 | + | 0.407110i | ||||
\(767\) | − | 931313.i | − | 1.58309i | ||||||
\(768\) | −718798. | − | 123068.i | −1.21867 | − | 0.208652i | ||||
\(769\) | −110911. | −0.187552 | −0.0937762 | − | 0.995593i | \(-0.529894\pi\) | ||||
−0.0937762 | + | 0.995593i | \(0.529894\pi\) | |||||||
\(770\) | −359610. | − | 457631.i | −0.606528 | − | 0.771853i | ||||
\(771\) | −124325. | + | 124325.i | −0.209146 | + | 0.209146i | ||||
\(772\) | −110701. | + | 454840.i | −0.185744 | + | 0.763175i | ||||
\(773\) | −800998. | + | 800998.i | −1.34052 | + | 1.34052i | −0.444972 | + | 0.895544i | \(0.646787\pi\) |
−0.895544 | + | 0.444972i | \(0.853213\pi\) | |||||||
\(774\) | −500142. | − | 59987.6i | −0.834856 | − | 0.100134i | ||||
\(775\) | −178818. | −0.297719 | ||||||||
\(776\) | 763111. | − | 347475.i | 1.26726 | − | 0.577032i | ||||
\(777\) | − | 917967.i | − | 1.52050i | ||||||
\(778\) | 747730. | + | 89683.6i | 1.23534 | + | 0.148168i | ||||
\(779\) | −232397. | − | 232397.i | −0.382962 | − | 0.382962i | ||||
\(780\) | 630716. | + | 1.03648e6i | 1.03668 | + | 1.70362i | ||||
\(781\) | 55266.6 | + | 55266.6i | 0.0906068 | + | 0.0906068i | ||||
\(782\) | −71108.6 | − | 90491.1i | −0.116281 | − | 0.147976i | ||||
\(783\) | − | 206591.i | − | 0.336968i | ||||||
\(784\) | −29573.5 | − | 15301.8i | −0.0481138 | − | 0.0248949i | ||||
\(785\) | 661762. | 1.07390 | ||||||||
\(786\) | −950399. | + | 746831.i | −1.53837 | + | 1.20886i | ||||
\(787\) | −528761. | + | 528761.i | −0.853709 | + | 0.853709i | −0.990588 | − | 0.136879i | \(-0.956293\pi\) |
0.136879 | + | 0.990588i | \(0.456293\pi\) | |||||||
\(788\) | 331643. | + | 545004.i | 0.534094 | + | 0.877702i | ||||
\(789\) | 645552. | − | 645552.i | 1.03700 | − | 1.03700i | ||||
\(790\) | 82106.0 | − | 684553.i | 0.131559 | − | 1.09686i | ||||
\(791\) | −259870. | −0.415340 | ||||||||
\(792\) | 72144.7 | − | 192772.i | 0.115015 | − | 0.307321i | ||||
\(793\) | − | 624756.i | − | 0.993491i | ||||||
\(794\) | −22504.4 | + | 187629.i | −0.0356966 | + | 0.297617i | ||||
\(795\) | 915532. | + | 915532.i | 1.44857 | + | 1.44857i | ||||
\(796\) | −204701. | + | 841063.i | −0.323068 | + | 1.32740i | ||||
\(797\) | 771661. | + | 771661.i | 1.21481 | + | 1.21481i | 0.969424 | + | 0.245390i | \(0.0789161\pi\) |
0.245390 | + | 0.969424i | \(0.421084\pi\) | |||||||
\(798\) | 247762. | − | 194693.i | 0.389070 | − | 0.305735i | ||||
\(799\) | 301742.i | 0.472653i | ||||||||
\(800\) | −863071. | + | 164683.i | −1.34855 | + | 0.257317i | ||||
\(801\) | 49116.8 | 0.0765536 | ||||||||
\(802\) | −215833. | − | 274663.i | −0.335559 | − | 0.427024i | ||||
\(803\) | −141961. | + | 141961.i | −0.220160 | + | 0.220160i | ||||
\(804\) | 80517.3 | + | 19596.6i | 0.124560 | + | 0.0303158i | ||||
\(805\) | −137691. | + | 137691.i | −0.212477 | + | 0.212477i | ||||
\(806\) | −146463. | − | 17566.9i | −0.225454 | − | 0.0270412i | ||||
\(807\) | 485011. | 0.744740 | ||||||||
\(808\) | 237557. | − | 634756.i | 0.363869 | − | 0.972263i | ||||
\(809\) | − | 100893.i | − | 0.154157i | −0.997025 | − | 0.0770783i | \(-0.975441\pi\) | ||
0.997025 | − | 0.0770783i | \(-0.0245592\pi\) | |||||||
\(810\) | 1.25352e6 | + | 150348.i | 1.91056 | + | 0.229154i | ||||
\(811\) | −51769.7 | − | 51769.7i | −0.0787107 | − | 0.0787107i | 0.666655 | − | 0.745366i | \(-0.267725\pi\) |
−0.745366 | + | 0.666655i | \(0.767725\pi\) | |||||||
\(812\) | −334409. | + | 203493.i | −0.507184 | + | 0.308629i | ||||
\(813\) | −871882. | − | 871882.i | −1.31910 | − | 1.31910i | ||||
\(814\) | 304352. | + | 387311.i | 0.459333 | + | 0.584536i | ||||
\(815\) | 1.28783e6i | 1.93885i | ||||||||
\(816\) | 777135. | − | 247152.i | 1.16712 | − | 0.371180i | ||||
\(817\) | 413807. | 0.619946 | ||||||||
\(818\) | 148242. | − | 116490.i | 0.221547 | − | 0.174093i | ||||
\(819\) | −269580. | + | 269580.i | −0.401901 | + | 0.401901i | ||||
\(820\) | −1.22941e6 | + | 748111.i | −1.82838 | + | 1.11260i | ||||
\(821\) | 48584.3 | − | 48584.3i | 0.0720791 | − | 0.0720791i | −0.670148 | − | 0.742227i | \(-0.733769\pi\) |
0.742227 | + | 0.670148i | \(0.233769\pi\) | |||||||
\(822\) | −178528. | + | 1.48846e6i | −0.264218 | + | 2.20290i | ||||
\(823\) | −338093. | −0.499157 | −0.249578 | − | 0.968355i | \(-0.580292\pi\) | ||||
−0.249578 | + | 0.968355i | \(0.580292\pi\) | |||||||
\(824\) | −415948. | + | 189398.i | −0.612611 | + | 0.278946i | ||||
\(825\) | − | 717068.i | − | 1.05354i | ||||||
\(826\) | −126126. | + | 1.05156e6i | −0.184860 | + | 1.54126i | ||||
\(827\) | −458054. | − | 458054.i | −0.669740 | − | 0.669740i | 0.287916 | − | 0.957656i | \(-0.407038\pi\) |
−0.957656 | + | 0.287916i | \(0.907038\pi\) | |||||||
\(828\) | −66910.3 | − | 16284.9i | −0.0975961 | − | 0.0237533i | ||||
\(829\) | 495530. | + | 495530.i | 0.721042 | + | 0.721042i | 0.968818 | − | 0.247775i | \(-0.0796995\pi\) |
−0.247775 | + | 0.968818i | \(0.579699\pi\) | |||||||
\(830\) | 249687. | − | 196206.i | 0.362443 | − | 0.284811i | ||||
\(831\) | 403396.i | 0.584157i | ||||||||
\(832\) | −723087. | + | 50097.9i | −1.04458 | + | 0.0723724i | ||||
\(833\) | 37235.0 | 0.0536613 | ||||||||
\(834\) | −456909. | − | 581452.i | −0.656898 | − | 0.835952i | ||||
\(835\) | 1.15714e6 | − | 1.15714e6i | 1.65964 | − | 1.65964i | ||||
\(836\) | −39985.7 | + | 164291.i | −0.0572127 | + | 0.235072i | ||||
\(837\) | −62601.3 | + | 62601.3i | −0.0893578 | + | 0.0893578i | ||||
\(838\) | −395898. | − | 47484.5i | −0.563761 | − | 0.0676182i | ||||
\(839\) | 696514. | 0.989477 | 0.494739 | − | 0.869042i | \(-0.335264\pi\) | ||||
0.494739 | + | 0.869042i | \(0.335264\pi\) | |||||||
\(840\) | −571785. | − | 1.25573e6i | −0.810352 | − | 1.77967i | ||||
\(841\) | − | 470785.i | − | 0.665626i | ||||||
\(842\) | 617429. | + | 74055.1i | 0.870889 | + | 0.104455i | ||||
\(843\) | −383982. | − | 383982.i | −0.540326 | − | 0.540326i | ||||
\(844\) | −376331. | − | 618443.i | −0.528305 | − | 0.868189i | ||||
\(845\) | 74970.5 | + | 74970.5i | 0.104997 | + | 0.104997i | ||||
\(846\) | 111556. | + | 141964.i | 0.155867 | + | 0.198352i | ||||
\(847\) | − | 452827.i | − | 0.631198i | ||||||
\(848\) | −737102. | + | 234420.i | −1.02503 | + | 0.325989i | ||||
\(849\) | 1.75412e6 | 2.43357 | ||||||||
\(850\) | 772552. | − | 607078.i | 1.06928 | − | 0.840246i | ||||
\(851\) | 116533. | − | 116533.i | 0.160912 | − | 0.160912i | ||||
\(852\) | 96319.9 | + | 158287.i | 0.132690 | + | 0.218055i | ||||
\(853\) | 78365.1 | − | 78365.1i | 0.107702 | − | 0.107702i | −0.651202 | − | 0.758904i | \(-0.725735\pi\) |
0.758904 | + | 0.651202i | \(0.225735\pi\) | |||||||
\(854\) | −84609.4 | + | 705424.i | −0.116012 | + | 0.967241i | ||||
\(855\) | 232060. | 0.317444 | ||||||||
\(856\) | −152096. | − | 56921.7i | −0.207572 | − | 0.0776838i | ||||
\(857\) | − | 576243.i | − | 0.784593i | −0.919839 | − | 0.392296i | \(-0.871681\pi\) | ||
0.919839 | − | 0.392296i | \(-0.128319\pi\) | |||||||
\(858\) | 70444.2 | − | 587323.i | 0.0956909 | − | 0.797816i | ||||
\(859\) | 74196.4 | + | 74196.4i | 0.100553 | + | 0.100553i | 0.755594 | − | 0.655040i | \(-0.227348\pi\) |
−0.655040 | + | 0.755594i | \(0.727348\pi\) | |||||||
\(860\) | 428497. | − | 1.76058e6i | 0.579363 | − | 2.38045i | ||||
\(861\) | −924574. | − | 924574.i | −1.24720 | − | 1.24720i | ||||
\(862\) | −26392.2 | + | 20739.2i | −0.0355190 | + | 0.0279111i | ||||
\(863\) | 299840.i | 0.402594i | 0.979530 | + | 0.201297i | \(0.0645157\pi\) | ||||
−0.979530 | + | 0.201297i | \(0.935484\pi\) | |||||||
\(864\) | −244495. | + | 359801.i | −0.327523 | + | 0.481986i | ||||
\(865\) | −879131. | −1.17495 | ||||||||
\(866\) | 277350. | + | 352948.i | 0.369821 | + | 0.470625i | ||||
\(867\) | 12352.5 | − | 12352.5i | 0.0164329 | − | 0.0164329i | ||||
\(868\) | 162995. | + | 39670.3i | 0.216339 | + | 0.0526534i | ||||
\(869\) | −237686. | + | 237686.i | −0.314749 | + | 0.314749i | ||||
\(870\) | −827655. | − | 99269.9i | −1.09348 | − | 0.131153i | ||||
\(871\) | 82363.5 | 0.108567 | ||||||||
\(872\) | −454573. | − | 170124.i | −0.597821 | − | 0.223734i | ||||
\(873\) | 561050.i | 0.736161i | ||||||||
\(874\) | 56168.2 | + | 6736.87i | 0.0735305 | + | 0.00881933i | ||||
\(875\) | −319272. | − | 319272.i | −0.417009 | − | 0.417009i | ||||
\(876\) | −406586. | + | 247413.i | −0.529839 | + | 0.322415i | ||||
\(877\) | −438353. | − | 438353.i | −0.569934 | − | 0.569934i | 0.362176 | − | 0.932110i | \(-0.382034\pi\) |
−0.932110 | + | 0.362176i | \(0.882034\pi\) | |||||||
\(878\) | −236851. | − | 301411.i | −0.307246 | − | 0.390994i | ||||
\(879\) | 206044.i | 0.266675i | ||||||||
\(880\) | 657588. | + | 340247.i | 0.849157 | + | 0.439368i | ||||
\(881\) | −1526.15 | −0.00196628 | −0.000983142 | − | 1.00000i | \(-0.500313\pi\) | ||||
−0.000983142 | 1.00000i | \(0.500313\pi\) | ||||||||
\(882\) | 17518.3 | − | 13766.0i | 0.0225193 | − | 0.0176959i | ||||
\(883\) | 114980. | − | 114980.i | 0.147469 | − | 0.147469i | −0.629517 | − | 0.776986i | \(-0.716747\pi\) |
0.776986 | + | 0.629517i | \(0.216747\pi\) | |||||||
\(884\) | 692407. | − | 421339.i | 0.886047 | − | 0.539172i | ||||
\(885\) | −1.59474e6 | + | 1.59474e6i | −2.03612 | + | 2.03612i | ||||
\(886\) | −32875.2 | + | 274095.i | −0.0418795 | + | 0.349167i | ||||
\(887\) | −833028. | −1.05880 | −0.529398 | − | 0.848373i | \(-0.677582\pi\) | ||||
−0.529398 | + | 0.848373i | \(0.677582\pi\) | |||||||
\(888\) | 483924. | + | 1.06278e6i | 0.613693 | + | 1.34777i | ||||
\(889\) | 1.15143e6i | 1.45692i | ||||||||
\(890\) | −21040.4 | + | 175423.i | −0.0265629 | + | 0.221466i | ||||
\(891\) | −435238. | − | 435238.i | −0.548241 | − | 0.548241i | ||||
\(892\) | 1.46423e6 | + | 356369.i | 1.84026 | + | 0.447889i | ||||
\(893\) | −104878. | − | 104878.i | −0.131517 | − | 0.131517i | ||||
\(894\) | 736360. | − | 578638.i | 0.921330 | − | 0.723989i | ||||
\(895\) | 1.22223e6i | 1.52584i | ||||||||
\(896\) | 823236. | + | 41359.6i | 1.02544 | + | 0.0515182i | ||||
\(897\) | −197907. | −0.245967 | ||||||||
\(898\) | −609636. | − | 775807.i | −0.755993 | − | 0.962058i | ||||
\(899\) | 71663.1 | − | 71663.1i | 0.0886699 | − | 0.0886699i | ||||
\(900\) | 139029. | − | 571236.i | 0.171641 | − | 0.705229i | ||||
\(901\) | 611606. | − | 611606.i | 0.753394 | − | 0.753394i | ||||
\(902\) | 696642. | + | 83556.0i | 0.856242 | + | 0.102699i | ||||
\(903\) | 1.64630e6 | 2.01898 | ||||||||
\(904\) | 300864. | − | 136995.i | 0.368157 | − | 0.167637i | ||||
\(905\) | 538686.i | 0.657716i | ||||||||
\(906\) | 353803. | + | 42435.5i | 0.431027 | + | 0.0516979i | ||||
\(907\) | −1.13198e6 | − | 1.13198e6i | −1.37602 | − | 1.37602i | −0.851234 | − | 0.524787i | \(-0.824145\pi\) |
−0.524787 | − | 0.851234i | \(-0.675855\pi\) | |||||||
\(908\) | 737319. | + | 1.21167e6i | 0.894302 | + | 1.46965i | ||||
\(909\) | 320668. | + | 320668.i | 0.388086 | + | 0.388086i | ||||
\(910\) | −847335. | − | 1.07830e6i | −1.02323 | − | 1.30213i | ||||
\(911\) | − | 369952.i | − | 0.445768i | −0.974845 | − | 0.222884i | \(-0.928453\pi\) | ||
0.974845 | − | 0.222884i | \(-0.0715471\pi\) | |||||||
\(912\) | −184209. | + | 356018.i | −0.221474 | + | 0.428038i | ||||
\(913\) | −154820. | −0.185732 | ||||||||
\(914\) | −18965.3 | + | 14903.1i | −0.0227021 | + | 0.0178395i | ||||
\(915\) | −1.06980e6 | + | 1.06980e6i | −1.27780 | + | 1.27780i | ||||
\(916\) | −232684. | − | 382381.i | −0.277316 | − | 0.455727i | ||||
\(917\) | 966058. | − | 966058.i | 1.14885 | − | 1.14885i | ||||
\(918\) | 57930.0 | − | 482987.i | 0.0687414 | − | 0.573126i | ||||
\(919\) | 815703. | 0.965831 | 0.482915 | − | 0.875667i | \(-0.339578\pi\) | ||||
0.482915 | + | 0.875667i | \(0.339578\pi\) | |||||||
\(920\) | 86824.9 | − | 231997.i | 0.102581 | − | 0.274099i | ||||
\(921\) | 397746.i | 0.468906i | ||||||||
\(922\) | −8840.19 | + | 73704.4i | −0.0103992 | + | 0.0867025i | ||||
\(923\) | 130222. | + | 130222.i | 0.152856 | + | 0.152856i | ||||
\(924\) | −159080. | + | 653619.i | −0.186325 | + | 0.765562i | ||||
\(925\) | 994881. | + | 994881.i | 1.16275 | + | 1.16275i | ||||
\(926\) | −1.28346e6 | + | 1.00855e6i | −1.49678 | + | 1.17618i | ||||
\(927\) | − | 305811.i | − | 0.355872i | ||||||
\(928\) | 279887. | − | 411883.i | 0.325002 | − | 0.478275i | ||||
\(929\) | 329861. | 0.382208 | 0.191104 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191104 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(930\) | 220715. | + | 280877.i | 0.255192 | + | 0.324751i | ||||
\(931\) | −12942.0 | + | 12942.0i | −0.0149314 | + | 0.0149314i | ||||
\(932\) | −389620. | − | 94827.0i | −0.448548 | − | 0.109169i | ||||
\(933\) | −423383. | + | 423383.i | −0.486374 | + | 0.486374i | ||||
\(934\) | −607940. | − | 72917.1i | −0.696895 | − | 0.0835863i | ||||
\(935\) | −827947. | −0.947064 | ||||||||
\(936\) | 169991. | − | 454219.i | 0.194033 | − | 0.518458i | ||||
\(937\) | 884572.i | 1.00752i | 0.863844 | + | 0.503760i | \(0.168051\pi\) | ||||
−0.863844 | + | 0.503760i | \(0.831949\pi\) | |||||||
\(938\) | −92998.3 | − | 11154.3i | −0.105699 | − | 0.0126776i | ||||
\(939\) | 1.08068e6 | + | 1.08068e6i | 1.22565 | + | 1.22565i | ||||
\(940\) | −554818. | + | 337615.i | −0.627906 | + | 0.382090i | ||||
\(941\) | −441727. | − | 441727.i | −0.498856 | − | 0.498856i | 0.412226 | − | 0.911082i | \(-0.364751\pi\) |
−0.911082 | + | 0.412226i | \(0.864751\pi\) | |||||||
\(942\) | −472586. | − | 601401.i | −0.532572 | − | 0.677738i | ||||
\(943\) | − | 234743.i | − | 0.263979i | ||||||
\(944\) | −408330. | − | 1.28394e6i | −0.458213 | − | 1.44079i | ||||
\(945\) | −823056. | −0.921650 | ||||||||
\(946\) | −694611. | + | 545831.i | −0.776174 | + | 0.609924i | ||||
\(947\) | −98614.4 | + | 98614.4i | −0.109961 | + | 0.109961i | −0.759947 | − | 0.649985i | \(-0.774775\pi\) |
0.649985 | + | 0.759947i | \(0.274775\pi\) | |||||||
\(948\) | −680747. | + | 414244.i | −0.757476 | + | 0.460935i | ||||
\(949\) | −334497. | + | 334497.i | −0.371416 | + | 0.371416i | ||||
\(950\) | −57514.9 | + | 479526.i | −0.0637285 | + | 0.531331i | ||||
\(951\) | −1.81832e6 | −2.01053 | ||||||||
\(952\) | −838872. | + | 381972.i | −0.925597 | + | 0.421461i | ||||
\(953\) | − | 327664.i | − | 0.360780i | −0.983595 | − | 0.180390i | \(-0.942264\pi\) | ||
0.983595 | − | 0.180390i | \(-0.0577360\pi\) | |||||||
\(954\) | 61633.4 | − | 513863.i | 0.0677203 | − | 0.564613i | ||||
\(955\) | −55377.0 | − | 55377.0i | −0.0607187 | − | 0.0607187i | ||||
\(956\) | 1.44644e6 | + | 352041.i | 1.58265 | + | 0.385192i | ||||
\(957\) | 287373. | + | 287373.i | 0.313778 | + | 0.313778i | ||||
\(958\) | 701837. | − | 551509.i | 0.764725 | − | 0.600927i | ||||
\(959\) | − | 1.69446e6i | − | 1.84244i | ||||||
\(960\) | 1.32397e6 | + | 1.15240e6i | 1.43659 | + | 1.25043i | ||||
\(961\) | 880090. | 0.952973 | ||||||||
\(962\) | 717133. | + | 912605.i | 0.774906 | + | 0.986127i | ||||
\(963\) | 76836.2 | − | 76836.2i | 0.0828539 | − | 0.0828539i | ||||
\(964\) | 306410. | − | 1.25896e6i | 0.329723 | − | 1.35475i | ||||
\(965\) | 796705. | − | 796705.i | 0.855545 | − | 0.855545i | ||||
\(966\) | 223461. | + | 26802.1i | 0.239468 | + | 0.0287220i | ||||
\(967\) | 386677. | 0.413519 | 0.206760 | − | 0.978392i | \(-0.433708\pi\) | ||||
0.206760 | + | 0.978392i | \(0.433708\pi\) | |||||||
\(968\) | 238716. | + | 524260.i | 0.254760 | + | 0.559495i | ||||
\(969\) | − | 448251.i | − | 0.477390i | ||||||
\(970\) | −2.00381e6 | − | 240340.i | −2.12968 | − | 0.255436i | ||||
\(971\) | 718740. | + | 718740.i | 0.762313 | + | 0.762313i | 0.976740 | − | 0.214427i | \(-0.0687884\pi\) |
−0.214427 | + | 0.976740i | \(0.568788\pi\) | |||||||
\(972\) | −472342. | − | 776223.i | −0.499947 | − | 0.821587i | ||||
\(973\) | 591032. | + | 591032.i | 0.624288 | + | 0.624288i | ||||
\(974\) | 558254. | + | 710421.i | 0.588456 | + | 0.748855i | ||||
\(975\) | − | 1.68960e6i | − | 1.77735i | ||||||
\(976\) | −273921. | − | 861308.i | −0.287559 | − | 0.904188i | ||||
\(977\) | −1.27845e6 | −1.33935 | −0.669675 | − | 0.742654i | \(-0.733567\pi\) | ||||
−0.669675 | + | 0.742654i | \(0.733567\pi\) | |||||||
\(978\) | 1.17036e6 | − | 919682.i | 1.22361 | − | 0.961524i | ||||
\(979\) | 60909.2 | − | 60909.2i | 0.0635503 | − | 0.0635503i | ||||
\(980\) | 41661.6 | + | 68464.5i | 0.0433794 | + | 0.0712875i | ||||
\(981\) | 229643. | − | 229643.i | 0.238625 | − | 0.238625i | ||||
\(982\) | 68510.0 | − | 571197.i | 0.0710446 | − | 0.592329i | ||||
\(983\) | −414529. | −0.428991 | −0.214495 | − | 0.976725i | \(-0.568811\pi\) | ||||
−0.214495 | + | 0.976725i | \(0.568811\pi\) | |||||||
\(984\) | 1.55783e6 | + | 583018.i | 1.60890 | + | 0.602132i | ||||
\(985\) | − | 1.53555e6i | − | 1.58267i | ||||||
\(986\) | −66315.6 | + | 552902.i | −0.0682122 | + | 0.568714i | ||||
\(987\) | −417251. | − | 417251.i | −0.428314 | − | 0.428314i | ||||
\(988\) | −94216.6 | + | 387112.i | −0.0965192 | + | 0.396572i | ||||
\(989\) | 208992. | + | 208992.i | 0.213667 | + | 0.213667i | ||||
\(990\) | −389532. | + | 306098.i | −0.397442 | + | 0.312313i | ||||
\(991\) | 176697.i | 0.179921i | 0.995945 | + | 0.0899605i | \(0.0286741\pi\) | ||||
−0.995945 | + | 0.0899605i | \(0.971326\pi\) | |||||||
\(992\) | −209620. | + | 39997.7i | −0.213015 | + | 0.0406454i | ||||
\(993\) | −1.07025e6 | −1.08539 | ||||||||
\(994\) | −129401. | − | 164672.i | −0.130968 | − | 0.166666i | ||||
\(995\) | 1.47322e6 | − | 1.47322e6i | 1.48806 | − | 1.48806i | ||||
\(996\) | −356619. | − | 86795.3i | −0.359489 | − | 0.0874938i | ||||
\(997\) | −1.20434e6 | + | 1.20434e6i | −1.21160 | + | 1.21160i | −0.241102 | + | 0.970500i | \(0.577509\pi\) |
−0.970500 | + | 0.241102i | \(0.922491\pi\) | |||||||
\(998\) | 1.27205e6 | + | 152572.i | 1.27716 | + | 0.153184i | ||||
\(999\) | 696585. | 0.697980 |
(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 | 16.5.f.a.3.6 | ✓ | 14 | |
3.2 | odd | 2 | 144.5.m.a.19.2 | 14 | |||
4.3 | odd | 2 | 64.5.f.a.47.6 | 14 | |||
8.3 | odd | 2 | 128.5.f.a.95.2 | 14 | |||
8.5 | even | 2 | 128.5.f.b.95.6 | 14 | |||
12.11 | even | 2 | 576.5.m.a.559.1 | 14 | |||
16.3 | odd | 4 | 128.5.f.b.31.6 | 14 | |||
16.5 | even | 4 | 64.5.f.a.15.6 | 14 | |||
16.11 | odd | 4 | inner | 16.5.f.a.11.6 | yes | 14 | |
16.13 | even | 4 | 128.5.f.a.31.2 | 14 | |||
48.5 | odd | 4 | 576.5.m.a.271.1 | 14 | |||
48.11 | even | 4 | 144.5.m.a.91.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.6 | ✓ | 14 | 1.1 | even | 1 | trivial | |
16.5.f.a.11.6 | yes | 14 | 16.11 | odd | 4 | inner | |
64.5.f.a.15.6 | 14 | 16.5 | even | 4 | |||
64.5.f.a.47.6 | 14 | 4.3 | odd | 2 | |||
128.5.f.a.31.2 | 14 | 16.13 | even | 4 | |||
128.5.f.a.95.2 | 14 | 8.3 | odd | 2 | |||
128.5.f.b.31.6 | 14 | 16.3 | odd | 4 | |||
128.5.f.b.95.6 | 14 | 8.5 | even | 2 | |||
144.5.m.a.19.2 | 14 | 3.2 | odd | 2 | |||
144.5.m.a.91.2 | 14 | 48.11 | even | 4 | |||
576.5.m.a.271.1 | 14 | 48.5 | odd | 4 | |||
576.5.m.a.559.1 | 14 | 12.11 | even | 2 |