Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(65,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.h (of order \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 631 x^{10} - 3100 x^{9} + 142264 x^{8} - 550522 x^{7} + 14083117 x^{6} - 40335478 x^{5} + 638031136 x^{4} - 1209472584 x^{3} + \cdots + 90728724573 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(0.500000 + 9.58497i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.65 |
Dual form | 76.5.h.a.69.2 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.05083 | − | 5.22550i | −1.00565 | − | 0.580611i | −0.0957331 | − | 0.995407i | \(-0.530520\pi\) |
−0.909914 | + | 0.414796i | \(0.863853\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.7505 | + | 22.0845i | −0.510019 | + | 0.883378i | 0.489914 | + | 0.871771i | \(0.337028\pi\) |
−0.999933 | + | 0.0116075i | \(0.996305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.7589 | 0.566508 | 0.283254 | − | 0.959045i | \(-0.408586\pi\) | ||||
0.283254 | + | 0.959045i | \(0.408586\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.1116 | + | 24.4421i | 0.174218 | + | 0.301754i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 143.293 | 1.18424 | 0.592119 | − | 0.805850i | \(-0.298291\pi\) | ||||
0.592119 | + | 0.805850i | \(0.298291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 123.911 | − | 71.5400i | 0.733201 | − | 0.423314i | −0.0863914 | − | 0.996261i | \(-0.527534\pi\) |
0.819592 | + | 0.572948i | \(0.194200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 230.805 | − | 133.255i | 1.02580 | − | 0.592245i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 43.9489 | − | 76.1217i | 0.152072 | − | 0.263397i | −0.779917 | − | 0.625883i | \(-0.784739\pi\) |
0.931989 | + | 0.362486i | \(0.118072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 340.586 | − | 119.675i | 0.943452 | − | 0.331509i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −251.241 | − | 145.054i | −0.569707 | − | 0.328920i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 350.792 | + | 607.590i | 0.663123 | + | 1.14856i | 0.979791 | + | 0.200026i | \(0.0641027\pi\) |
−0.316667 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.6488 | − | 21.9084i | −0.0202381 | − | 0.0350534i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 551.569i | 0.756611i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.5252 | + | 21.6652i | −0.0446197 | + | 0.0257612i | −0.522144 | − | 0.852857i | \(-0.674868\pi\) |
0.477524 | + | 0.878619i | \(0.341534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 111.254i | 0.115769i | 0.998323 | + | 0.0578843i | \(0.0184354\pi\) | ||||
−0.998323 | + | 0.0578843i | \(0.981565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1296.92 | − | 748.776i | −1.19093 | − | 0.687582i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −353.939 | + | 613.040i | −0.288929 | + | 0.500440i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1079.87i | − | 0.788802i | −0.918938 | − | 0.394401i | \(-0.870952\pi\) | ||
0.918938 | − | 0.394401i | \(-0.129048\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1495.33 | −0.983122 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 80.1784 | + | 46.2910i | 0.0476969 | + | 0.0275378i | 0.523659 | − | 0.851928i | \(-0.324567\pi\) |
−0.475962 | + | 0.879466i | \(0.657900\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 945.995 | − | 1638.51i | 0.511625 | − | 0.886161i | −0.488284 | − | 0.872685i | \(-0.662377\pi\) |
0.999909 | − | 0.0134763i | \(-0.00428978\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −719.720 | −0.355417 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1366.72 | + | 2367.22i | 0.618703 | + | 1.07163i | 0.989723 | + | 0.143001i | \(0.0456751\pi\) |
−0.371019 | + | 0.928625i | \(0.620992\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1630.45 | −0.679069 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −795.547 | + | 459.309i | −0.305862 | + | 0.176589i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2153.80 | − | 1243.50i | 0.766749 | − | 0.442683i | −0.0649646 | − | 0.997888i | \(-0.520693\pi\) |
0.831714 | + | 0.555205i | \(0.187360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1827.05 | + | 3164.54i | −0.603984 | + | 1.04613i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3707.95 | − | 696.575i | −1.14126 | − | 0.214397i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5032.93 | − | 2905.77i | −1.44583 | − | 0.834750i | −0.447600 | − | 0.894234i | \(-0.647721\pi\) |
−0.998229 | + | 0.0594837i | \(0.981055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1263.85 | + | 2189.06i | 0.339654 | + | 0.588299i | 0.984368 | − | 0.176126i | \(-0.0563565\pi\) |
−0.644713 | + | 0.764425i | \(0.723023\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 391.723 | + | 678.485i | 0.0986957 | + | 0.170946i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3648.67i | 0.863591i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4300.24 | − | 2482.74i | 0.957950 | − | 0.553073i | 0.0624086 | − | 0.998051i | \(-0.480122\pi\) |
0.895542 | + | 0.444978i | \(0.146788\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 7332.25i | − | 1.54007i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3720.00 | + | 2147.74i | 0.737949 | + | 0.426055i | 0.821323 | − | 0.570463i | \(-0.193236\pi\) |
−0.0833740 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1588.81 | + | 2751.89i | −0.298143 | + | 0.516399i | −0.975711 | − | 0.219061i | \(-0.929701\pi\) |
0.677568 | + | 0.735460i | \(0.263034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 264.385i | 0.0470018i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3977.65 | 0.670880 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4934.57 | + | 2848.97i | 0.790669 | + | 0.456493i | 0.840198 | − | 0.542280i | \(-0.182439\pi\) |
−0.0495288 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4025.27 | − | 6971.97i | 0.613514 | − | 1.06264i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10463.5 | 1.51888 | 0.759439 | − | 0.650579i | \(-0.225474\pi\) | ||||
0.759439 | + | 0.650579i | \(0.225474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1120.74 | + | 1941.17i | 0.155119 | + | 0.268674i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 452.845 | 0.0598289 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4822.97 | − | 2784.54i | 0.608884 | − | 0.351539i | −0.163645 | − | 0.986519i | \(-0.552325\pi\) |
0.772528 | + | 0.634980i | \(0.218992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3439.63 | − | 1985.87i | 0.415364 | − | 0.239810i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 581.355 | − | 1006.94i | 0.0672165 | − | 0.116422i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1699.68 | + | 9047.57i | −0.188330 | + | 1.00250i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15618.3 | − | 9017.22i | −1.65993 | − | 0.958361i | −0.972745 | − | 0.231878i | \(-0.925513\pi\) |
−0.687185 | − | 0.726482i | \(-0.741154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2022.10 | + | 3502.38i | 0.206315 | + | 0.357349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −48.5674 | − | 84.1212i | −0.00476104 | − | 0.00824636i | 0.863635 | − | 0.504118i | \(-0.168182\pi\) |
−0.868396 | + | 0.495871i | \(0.834849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1061.32i | 0.100040i | 0.998748 | + | 0.0500198i | \(0.0159285\pi\) | ||||
−0.998748 | + | 0.0500198i | \(0.984072\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6406.87 | − | 3699.01i | 0.581122 | − | 0.335511i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 86.6771i | 0.00757072i | 0.999993 | + | 0.00378536i | \(0.00120492\pi\) | ||||
−0.999993 | + | 0.00378536i | \(0.998795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17989.3 | − | 10386.1i | −1.51412 | − | 0.874179i | −0.999863 | − | 0.0165449i | \(-0.994733\pi\) |
−0.514260 | − | 0.857634i | \(-0.671933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5642.86 | + | 9773.72i | −0.457987 | + | 0.793257i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18503.4i | 1.44909i | 0.689227 | + | 0.724546i | \(0.257950\pi\) | ||||
−0.689227 | + | 0.724546i | \(0.742050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17891.1 | −1.35282 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3497.17 | + | 2019.09i | 0.255473 | + | 0.147498i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1219.97 | − | 2113.05i | 0.0861500 | − | 0.149216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5891.84 | 0.402421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −483.787 | − | 837.944i | −0.0319775 | − | 0.0553866i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15293.0 | −0.978750 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16075.2 | − | 9281.03i | 0.996665 | − | 0.575425i | 0.0894051 | − | 0.995995i | \(-0.471503\pi\) |
0.907260 | + | 0.420571i | \(0.138170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −17124.1 | + | 9886.59i | −1.02903 | + | 0.594111i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7020.17 | + | 12159.3i | −0.409077 | + | 0.708542i | −0.994787 | − | 0.101979i | \(-0.967483\pi\) |
0.585710 | + | 0.810521i | \(0.300816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9454.29 | − | 3322.04i | 0.534473 | − | 0.187803i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12181.1 | − | 7032.76i | −0.668373 | − | 0.385886i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8900.54 | + | 15416.2i | 0.474215 | + | 0.821364i | 0.999564 | − | 0.0295224i | \(-0.00939864\pi\) |
−0.525349 | + | 0.850887i | \(0.676065\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18227.9 | − | 31571.7i | −0.943426 | − | 1.63406i | −0.758872 | − | 0.651240i | \(-0.774249\pi\) |
−0.184554 | − | 0.982822i | \(-0.559084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 28567.1i | − | 1.43690i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17755.5 | − | 10251.2i | 0.868284 | − | 0.501304i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1104.96i | − | 0.0525548i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14756.9 | + | 8519.89i | 0.682904 | + | 0.394275i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10085.2 | + | 17468.1i | −0.454268 | + | 0.786816i | −0.998646 | − | 0.0520247i | \(-0.983433\pi\) |
0.544378 | + | 0.838840i | \(0.316766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1839.49i | − | 0.0806759i | −0.999186 | − | 0.0403379i | \(-0.987157\pi\) | ||
0.999186 | − | 0.0403379i | \(-0.0128434\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2480.76 | 0.105975 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2456.97 | − | 1418.54i | −0.102267 | − | 0.0590441i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13219.3 | + | 22896.5i | −0.536301 | + | 0.928901i | 0.462798 | + | 0.886464i | \(0.346845\pi\) |
−0.999099 | + | 0.0424369i | \(0.986488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25991.5 | −1.02811 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9737.59 | + | 16866.0i | 0.375664 | + | 0.650670i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13879.3 | −0.522386 | −0.261193 | − | 0.965287i | \(-0.584116\pi\) | ||||
−0.261193 | + | 0.965287i | \(0.584116\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33072.6 | − | 19094.5i | 1.21479 | − | 0.701359i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13289.5 | + | 7672.69i | −0.476514 | + | 0.275115i | −0.718962 | − | 0.695049i | \(-0.755383\pi\) |
0.242449 | + | 0.970164i | \(0.422049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4044.56 | + | 7005.39i | −0.141611 | + | 0.245278i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7731.34 | + | 6635.83i | 0.264401 | + | 0.226936i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14804.8 | + | 8547.56i | 0.494664 | + | 0.285594i | 0.726507 | − | 0.687159i | \(-0.241142\pi\) |
−0.231843 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −351.116 | − | 608.152i | −0.0114650 | − | 0.0198580i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30368.1 | + | 52599.2i | 0.969330 | + | 1.67893i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 30559.4i | − | 0.953758i | −0.878969 | − | 0.476879i | \(-0.841768\pi\) | ||
0.878969 | − | 0.476879i | \(-0.158232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48767.9 | − | 28156.2i | 1.48860 | − | 0.859441i | 0.488681 | − | 0.872463i | \(-0.337478\pi\) |
0.999915 | + | 0.0130215i | \(0.00414497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 26417.1i | − | 0.788828i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23848.3 | + | 13768.9i | 0.696811 | + | 0.402304i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6297.56 | − | 10907.7i | 0.180090 | − | 0.311925i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15310.9i | 0.428626i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20263.1 | −0.555443 | −0.277721 | − | 0.960662i | \(-0.589579\pi\) | ||||
−0.277721 | + | 0.960662i | \(0.589579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 902.539 | + | 521.081i | 0.0242299 | + | 0.0139891i | 0.512066 | − | 0.858946i | \(-0.328880\pi\) |
−0.487836 | + | 0.872935i | \(0.662214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19066.1 | − | 33023.5i | 0.501410 | − | 0.868468i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 59986.7 | 1.54569 | 0.772845 | − | 0.634594i | \(-0.218833\pi\) | ||||
0.772845 | + | 0.634594i | \(0.218833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24312.1 | − | 42109.9i | −0.613928 | − | 1.06335i | −0.990572 | − | 0.136996i | \(-0.956255\pi\) |
0.376644 | − | 0.926358i | \(-0.377078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −51894.3 | −1.28448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1041.66 | + | 601.401i | −0.0252774 | + | 0.0145939i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2044.62 | + | 1180.46i | −0.0486526 | + | 0.0280896i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9900.51 | + | 17148.2i | −0.231056 | + | 0.400200i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 48803.6 | − | 17148.6i | 1.11727 | − | 0.392586i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 30887.6 | + | 17833.0i | 0.693777 | + | 0.400552i | 0.805025 | − | 0.593240i | \(-0.202152\pi\) |
−0.111248 | + | 0.993793i | \(0.535485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22446.1 | − | 38877.7i | −0.494744 | − | 0.856923i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24123.8 | + | 41783.6i | 0.521877 | + | 0.903918i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3088.27i | 0.0655838i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28760.0 | − | 16604.6i | 0.599654 | − | 0.346211i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12576.4i | − | 0.257497i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 31201.2 | + | 18014.0i | 0.627425 | + | 0.362244i | 0.779754 | − | 0.626086i | \(-0.215344\pi\) |
−0.152329 | + | 0.988330i | \(0.548677\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 356.991 | − | 618.326i | 0.00705167 | − | 0.0122139i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 92863.0i | 1.80215i | 0.433663 | + | 0.901075i | \(0.357221\pi\) | ||||
−0.433663 | + | 0.901075i | \(0.642779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −56402.1 | −1.07553 | −0.537767 | − | 0.843094i | \(-0.680732\pi\) | ||||
−0.537767 | + | 0.843094i | \(0.680732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −36001.0 | − | 20785.2i | −0.674669 | − | 0.389520i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23210.6 | + | 40202.0i | −0.427538 | + | 0.740518i | −0.996654 | − | 0.0817394i | \(-0.973952\pi\) |
0.569115 | + | 0.822258i | \(0.307286\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69705.1 | −1.26220 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29774.6 | − | 51571.1i | −0.530090 | − | 0.918142i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −35290.9 | −0.617828 | −0.308914 | − | 0.951090i | \(-0.599965\pi\) | ||||
−0.308914 | + | 0.951090i | \(0.599965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −96639.8 | + | 55795.0i | −1.66388 | + | 0.960642i | −0.693045 | + | 0.720894i | \(0.743731\pi\) |
−0.970835 | + | 0.239748i | \(0.922935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −34172.5 | + | 19729.5i | −0.578714 | + | 0.334121i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20788.9 | − | 36007.5i | 0.346338 | − | 0.599875i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33640.8 | − | 39194.5i | 0.551407 | − | 0.642439i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −94703.8 | − | 54677.2i | −1.52746 | − | 0.881877i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18656.9 | + | 32314.8i | 0.296137 | + | 0.512924i | 0.975249 | − | 0.221111i | \(-0.0709682\pi\) |
−0.679112 | + | 0.734035i | \(0.737635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 50266.0 | + | 87063.3i | 0.785296 | + | 1.36017i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 23425.6i | − | 0.360256i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −54521.2 | + | 31477.8i | −0.825466 | + | 0.476583i | −0.852298 | − | 0.523057i | \(-0.824792\pi\) |
0.0268315 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 29976.0i | − | 0.446862i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1059.08 | − | 611.462i | −0.0155471 | − | 0.00897612i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 43980.5 | − | 76176.4i | 0.635841 | − | 1.10131i | −0.350495 | − | 0.936565i | \(-0.613987\pi\) |
0.986336 | − | 0.164745i | \(-0.0526800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 63420.6i | 0.903106i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −58202.5 | −0.816430 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −51001.2 | − | 29445.6i | −0.704816 | − | 0.406926i | 0.104323 | − | 0.994544i | \(-0.466733\pi\) |
−0.809139 | + | 0.587618i | \(0.800066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 44150.5 | − | 76470.9i | 0.601170 | − | 1.04126i | −0.391475 | − | 0.920189i | \(-0.628035\pi\) |
0.992644 | − | 0.121068i | \(-0.0386318\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −41508.6 | −0.556946 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1812.48 | − | 3139.31i | −0.0239667 | − | 0.0415116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 73761.7 | 0.961327 | 0.480664 | − | 0.876905i | \(-0.340396\pi\) | ||||
0.480664 | + | 0.876905i | \(0.340396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2719.27 | + | 1569.97i | −0.0349336 | + | 0.0201689i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 51830.2 | − | 29924.2i | 0.656403 | − | 0.378975i | −0.134502 | − | 0.990913i | \(-0.542943\pi\) |
0.790905 | + | 0.611939i | \(0.209610\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −70780.2 | + | 122595.i | −0.883769 | + | 1.53073i | −0.0366506 | + | 0.999328i | \(0.511669\pi\) |
−0.847118 | + | 0.531404i | \(0.821664\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 62661.5 | − | 73006.3i | 0.771456 | − | 0.898816i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2225.66 | + | 1284.99i | 0.0270206 | + | 0.0156004i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37897.5 | + | 65640.4i | 0.453748 | + | 0.785915i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 94238.9 | + | 163227.i | 1.11287 | + | 1.92755i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 171279.i | − | 1.99512i | −0.0697935 | − | 0.997561i | \(-0.522234\pi\) | ||
0.0697935 | − | 0.997561i | \(-0.477766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 128344. | − | 74099.7i | 1.47480 | − | 0.851476i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 79035.9i | 0.896007i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 86933.9 | + | 50191.3i | 0.972404 | + | 0.561418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26259.8 | − | 45483.2i | 0.289840 | − | 0.502017i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1015.15i | 0.0110572i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −64458.9 | −0.692921 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23997.7 | + | 13855.1i | 0.254620 | + | 0.147005i | 0.621878 | − | 0.783114i | \(-0.286370\pi\) |
−0.367258 | + | 0.930119i | \(0.619703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5545.93 | − | 9605.83i | 0.0580841 | − | 0.100605i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −189674. | −1.96105 | −0.980524 | − | 0.196401i | \(-0.937075\pi\) | ||||
−0.980524 | + | 0.196401i | \(0.937075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −79050.5 | − | 136919.i | −0.806893 | − | 1.39758i | −0.915006 | − | 0.403441i | \(-0.867814\pi\) |
0.108113 | − | 0.994139i | \(-0.465519\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19978.6 | −0.201347 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 39512.7 | − | 22812.7i | 0.393204 | − | 0.227017i | −0.290343 | − | 0.956923i | \(-0.593769\pi\) |
0.683548 | + | 0.729906i | \(0.260436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5377.09 | + | 3104.46i | −0.0528404 | + | 0.0305074i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 452.931 | − | 784.500i | 0.00439564 | − | 0.00761347i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5858.52 | − | 31185.6i | 0.0561543 | − | 0.298915i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3134.65 | − | 1809.79i | −0.0296771 | − | 0.0171341i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 108545. | + | 188006.i | 1.01512 | + | 1.75823i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37938.5 | + | 65711.4i | 0.350500 | + | 0.607084i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 51241.9i | − | 0.467702i | −0.972272 | − | 0.233851i | \(-0.924867\pi\) | ||
0.972272 | − | 0.233851i | \(-0.0751328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26394.3 | − | 15238.7i | 0.238024 | − | 0.137423i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 126625.i | 1.12831i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7928.49 | + | 4577.52i | 0.0698121 | + | 0.0403060i | 0.534500 | − | 0.845169i | \(-0.320500\pi\) |
−0.464688 | + | 0.885475i | \(0.653833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 96689.7 | − | 167471.i | 0.841358 | − | 1.45727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15941.8i | 0.137098i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −111908. | −0.951205 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 161929. | + | 93489.6i | 1.36046 | + | 0.785462i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 76816.1 | − | 133049.i | 0.637960 | − | 1.10498i | −0.347920 | − | 0.937524i | \(-0.613112\pi\) |
0.985880 | − | 0.167455i | \(-0.0535548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 168335. | 1.38205 | 0.691023 | − | 0.722832i | \(-0.257160\pi\) | ||||
0.691023 | + | 0.722832i | \(0.257160\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39459.2 | + | 68345.4i | 0.320283 | + | 0.554747i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −130340. | −1.04599 | −0.522994 | − | 0.852336i | \(-0.675185\pi\) | ||||
−0.522994 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −94863.5 | + | 54769.5i | −0.752736 | + | 0.434592i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22083.5 | + | 12749.9i | −0.173273 | + | 0.100039i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18849.9 | + | 32649.0i | −0.146258 | + | 0.253327i | −0.929842 | − | 0.367960i | \(-0.880056\pi\) |
0.783583 | + | 0.621287i | \(0.213390\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 101677. | − | 81519.2i | 0.780203 | − | 0.625526i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −53326.0 | − | 30787.8i | −0.404693 | − | 0.233650i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40516.0 | − | 70175.8i | −0.304117 | − | 0.526747i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 48448.8 | + | 83915.8i | 0.359709 | + | 0.623034i | 0.987912 | − | 0.155015i | \(-0.0495427\pi\) |
−0.628203 | + | 0.778049i | \(0.716209\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2612.97i | 0.0191903i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 59787.0 | − | 34518.0i | 0.434369 | − | 0.250783i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 125723.i | − | 0.903644i | −0.892108 | − | 0.451822i | \(-0.850774\pi\) | ||
0.892108 | − | 0.451822i | \(-0.149226\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 138414. | + | 79913.4i | 0.984278 | + | 0.568273i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3099.85 | + | 5369.10i | −0.0218101 | + | 0.0377762i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7410.05i | − | 0.0515873i | −0.999667 | − | 0.0257936i | \(-0.991789\pi\) | ||
0.999667 | − | 0.0257936i | \(-0.00821128\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −193992. | −1.33639 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −105519. | − | 60921.6i | −0.719340 | − | 0.415311i | 0.0951699 | − | 0.995461i | \(-0.469661\pi\) |
−0.814510 | + | 0.580150i | \(0.802994\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −50716.9 | + | 87844.2i | −0.342161 | + | 0.592641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 53398.2 | 0.356537 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −129529. | − | 224351.i | −0.855990 | − | 1.48262i | −0.875724 | − | 0.482812i | \(-0.839615\pi\) |
0.0197344 | − | 0.999805i | \(-0.493718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61667.6 | 0.403370 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 127077. | − | 73367.7i | 0.822774 | − | 0.475029i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −125836. | + | 72651.5i | −0.806512 | + | 0.465640i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −109875. | + | 190310.i | −0.697139 | + | 1.20748i | 0.272315 | + | 0.962208i | \(0.412211\pi\) |
−0.969454 | + | 0.245273i | \(0.921122\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −102928. | − | 19336.1i | −0.646531 | − | 0.121457i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −200338. | − | 115665.i | −1.24588 | − | 0.719307i | −0.275593 | − | 0.961275i | \(-0.588874\pi\) |
−0.970284 | + | 0.241967i | \(0.922207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7959.08 | + | 13785.5i | 0.0490064 | + | 0.0848816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 102648. | + | 177792.i | 0.625807 | + | 1.08393i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 154738.i | − | 0.934130i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36379.7 | − | 21003.8i | 0.217477 | − | 0.125560i | −0.387305 | − | 0.921952i | \(-0.626594\pi\) |
0.604781 | + | 0.796392i | \(0.293261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 186039.i | − | 1.10134i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −139709. | − | 80660.8i | −0.819073 | − | 0.472892i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −133415. | + | 231082.i | −0.774656 | + | 1.34174i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 381000.i | 2.19105i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17406.8 | −0.0991494 | −0.0495747 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495747 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −161802. | − | 93416.2i | −0.912891 | − | 0.527058i | −0.0315305 | − | 0.999503i | \(-0.510038\pi\) |
−0.881360 | + | 0.472445i | \(0.843371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38573.2 | + | 66810.8i | −0.215578 | + | 0.373393i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2223.60 | −0.0123106 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35083.2 | + | 60765.8i | 0.192417 | + | 0.333276i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −214270. | −1.16425 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9163.54 | − | 5290.57i | 0.0493297 | − | 0.0284805i | −0.475132 | − | 0.879914i | \(-0.657600\pi\) |
0.524462 | + | 0.851434i | \(0.324266\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −188173. | + | 108642.i | −1.00365 | + | 0.579458i | −0.909326 | − | 0.416083i | \(-0.863402\pi\) |
−0.0943244 | + | 0.995542i | \(0.530069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5773.99 | + | 10000.8i | −0.0305139 | + | 0.0528516i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 192188. | + | 164956.i | 1.00638 | + | 0.863782i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27000.5 | − | 15588.7i | −0.140101 | − | 0.0808875i | 0.428311 | − | 0.903631i | \(-0.359109\pi\) |
−0.568412 | + | 0.822744i | \(0.692442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23008.3 | − | 39851.5i | −0.118306 | − | 0.204912i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −84484.4 | − | 146331.i | −0.430496 | − | 0.745641i | 0.566420 | − | 0.824117i | \(-0.308328\pi\) |
−0.996916 | + | 0.0784760i | \(0.974995\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 142017.i | 0.717166i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 182559. | − | 105400.i | 0.913667 | − | 0.527506i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 240682.i | − | 1.19385i | −0.802297 | − | 0.596926i | \(-0.796389\pi\) | ||
0.802297 | − | 0.596926i | \(-0.203611\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11489.0 | + | 6633.17i | 0.0564845 | + | 0.0326113i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9612.25 | + | 16648.9i | −0.0468413 | + | 0.0811315i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 101283.i | 0.489231i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 227190. | 1.08782 | 0.543911 | − | 0.839143i | \(-0.316943\pi\) | ||||
0.543911 | + | 0.839143i | \(0.316943\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 41986.4 | + | 24240.8i | 0.199289 | + | 0.115059i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14069.9 | + | 24369.7i | −0.0662046 | + | 0.114670i | −0.897228 | − | 0.441568i | \(-0.854422\pi\) |
0.831023 | + | 0.556238i | \(0.187756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 81970.7 | 0.382381 | 0.191191 | − | 0.981553i | \(-0.438765\pi\) | ||||
0.191191 | + | 0.981553i | \(0.438765\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14825.1 | + | 25677.8i | 0.0685633 | + | 0.118755i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −126102. | −0.578213 | −0.289106 | − | 0.957297i | \(-0.593358\pi\) | ||||
−0.289106 | + | 0.957297i | \(0.593358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 119370. | − | 68918.2i | 0.542686 | − | 0.313320i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 239291. | − | 138155.i | 1.07866 | − | 0.622764i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 135554. | − | 234787.i | 0.605886 | − | 1.04943i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6929.89 | − | 5947.94i | −0.0307142 | − | 0.0263621i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 60787.3 | + | 35095.5i | 0.267163 | + | 0.154246i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −57621.7 | − | 99803.7i | −0.251139 | − | 0.434986i | 0.712700 | − | 0.701469i | \(-0.247472\pi\) |
−0.963840 | + | 0.266482i | \(0.914139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −77253.9 | − | 133808.i | −0.333911 | − | 0.578350i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 203535.i | − | 0.872459i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 398281. | − | 229947.i | 1.69319 | − | 0.977564i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 135408.i | 0.570935i | 0.958388 | + | 0.285467i | \(0.0921488\pi\) | ||||
−0.958388 | + | 0.285467i | \(0.907851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 125619. | + | 72526.1i | 0.525336 | + | 0.303303i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −202101. | + | 350049.i | −0.838312 | + | 1.45200i | 0.0529937 | + | 0.998595i | \(0.483124\pi\) |
−0.891305 | + | 0.453404i | \(0.850210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3808.64i | 0.0156702i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −103131. | −0.420899 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 103263. | + | 59619.0i | 0.418054 | + | 0.241363i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 220006. | − | 381062.i | 0.883557 | − | 1.53037i | 0.0361977 | − | 0.999345i | \(-0.488475\pi\) |
0.847359 | − | 0.531020i | \(-0.178191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 160375. | 0.638940 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 140225. | + | 242877.i | 0.554229 | + | 0.959953i | 0.997963 | + | 0.0637944i | \(0.0203202\pi\) |
−0.443734 | + | 0.896159i | \(0.646346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2477.03 | 0.00971288 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 73213.2 | − | 42269.7i | 0.284822 | − | 0.164442i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −87780.5 | + | 50680.1i | −0.338815 | + | 0.195615i | −0.659748 | − | 0.751487i | \(-0.729337\pi\) |
0.320933 | + | 0.947102i | \(0.396004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44103.5 | + | 76389.4i | −0.168900 | + | 0.292544i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 66009.0 | + | 187857.i | 0.250824 | + | 0.713826i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23438.7 | − | 13532.3i | −0.0883729 | − | 0.0510221i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 195841. | + | 339206.i | 0.732692 | + | 1.26906i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −89330.5 | − | 154725.i | −0.331638 | − | 0.574415i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3847.69i | − | 0.0141751i | −0.999975 | − | 0.00708753i | \(-0.997744\pi\) | ||
0.999975 | − | 0.00708753i | \(-0.00225605\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 126432. | − | 72995.3i | 0.462223 | − | 0.266865i | −0.250755 | − | 0.968051i | \(-0.580679\pi\) |
0.712979 | + | 0.701186i | \(0.247346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7339.03i | 0.0266269i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8468.81 | + | 4889.47i | 0.0304931 | + | 0.0176052i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106190. | + | 183926.i | −0.379464 | + | 0.657252i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 164021.i | − | 0.581713i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13246.6 | 0.0466285 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1914.22 | − | 1105.17i | −0.00668781 | − | 0.00386121i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −159688. | + | 276587.i | −0.553762 | + | 0.959144i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −233631. | −0.804180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 210834. | + | 365176.i | 0.720355 | + | 1.24769i | 0.960857 | + | 0.277043i | \(0.0893546\pi\) |
−0.240502 | + | 0.970649i | \(0.577312\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −588520. | −1.99600 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 458744. | − | 264856.i | 1.54446 | − | 0.891696i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 86529.9 | − | 49958.1i | 0.289196 | − | 0.166967i | −0.348383 | − | 0.937352i | \(-0.613269\pi\) |
0.637579 | + | 0.770385i | \(0.279936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35670.1 | + | 61782.5i | −0.118348 | + | 0.204984i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10187.8 | + | 11869.7i | −0.0335565 | + | 0.0390963i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 136978. | + | 79084.3i | 0.447920 | + | 0.258607i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −143898. | − | 249239.i | −0.467164 | − | 0.809152i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −128227. | − | 222096.i | −0.413304 | − | 0.715864i | 0.581945 | − | 0.813228i | \(-0.302292\pi\) |
−0.995249 | + | 0.0973645i | \(0.968959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 270706.i | − | 0.866312i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −113996. | + | 65815.7i | −0.362213 | + | 0.209124i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5702.78i | 0.0179916i | 0.999960 | + | 0.00899580i | \(0.00286349\pi\) | ||||
−0.999960 | + | 0.00899580i | \(0.997137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −408639. | − | 235928.i | −1.28010 | − | 0.739064i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 111737. | − | 193534.i | 0.347560 | − | 0.601992i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 264278.i | 0.816275i | 0.912920 | + | 0.408138i | \(0.133822\pi\) | ||||
−0.912920 | + | 0.408138i | \(0.866178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −140891. | −0.432126 | −0.216063 | − | 0.976379i | \(-0.569322\pi\) | ||||
−0.216063 | + | 0.976379i | \(0.569322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 183398. | + | 105885.i | 0.558579 | + | 0.322496i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8874.20 | − | 15370.6i | 0.0268407 | − | 0.0464894i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33455.7 | −0.100489 | −0.0502445 | − | 0.998737i | \(-0.516000\pi\) | ||||
−0.0502445 | + | 0.998737i | \(0.516000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5445.82 | − | 9432.43i | −0.0162445 | − | 0.0281363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 290456. | 0.860456 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 308624. | − | 178184.i | 0.908014 | − | 0.524242i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −89181.2 | + | 51488.8i | −0.260592 | + | 0.150453i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −151917. | + | 263128.i | −0.440890 | + | 0.763644i | −0.997756 | − | 0.0669588i | \(-0.978670\pi\) |
0.556866 | + | 0.830602i | \(0.312004\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13314.3 | + | 37891.4i | 0.0383784 | + | 0.109222i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −542929. | − | 313460.i | −1.55442 | − | 0.897445i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −130746. | − | 226459.i | −0.371809 | − | 0.643992i | 0.618035 | − | 0.786151i | \(-0.287929\pi\) |
−0.989844 | + | 0.142158i | \(0.954596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31110.4 | + | 53884.8i | 0.0878763 | + | 0.152206i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 508172.i | 1.42581i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −422627. | + | 244004.i | −1.17789 | + | 0.680053i | −0.955524 | − | 0.294912i | \(-0.904710\pi\) |
−0.222361 | + | 0.974964i | \(0.571376\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 362708.i | − | 1.00417i | −0.864818 | − | 0.502086i | \(-0.832566\pi\) | ||
0.864818 | − | 0.502086i | \(-0.167434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 121367. | + | 70071.2i | 0.333784 | + | 0.192710i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −75123.7 | + | 130118.i | −0.205242 | + | 0.355490i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 560324.i | − | 1.52077i | −0.649475 | − | 0.760383i | \(-0.725011\pi\) | ||
0.649475 | − | 0.760383i | \(-0.274989\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12570.5 | 0.0338935 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 338702. | + | 195550.i | 0.907267 | + | 0.523811i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −197665. | + | 342365.i | −0.526027 | + | 0.911106i | 0.473513 | + | 0.880787i | \(0.342986\pi\) |
−0.999540 | + | 0.0303191i | \(0.990348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24674.1 | 0.0652365 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −47374.0 | − | 82054.2i | −0.124443 | − | 0.215541i | 0.797072 | − | 0.603884i | \(-0.206381\pi\) |
−0.921515 | + | 0.388343i | \(0.873048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 255301. | 0.666303 | 0.333151 | − | 0.942873i | \(-0.391888\pi\) | ||||
0.333151 | + | 0.942873i | \(0.391888\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −335128. | + | 193486.i | −0.869015 | + | 0.501726i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 133880. | − | 77295.7i | 0.344937 | − | 0.199150i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 202898. | − | 351430.i | 0.519419 | − | 0.899660i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −531322. | − | 99814.2i | −1.35152 | − | 0.253897i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −82201.5 | − | 47459.1i | −0.207768 | − | 0.119955i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 392479. | + | 679794.i | 0.985730 | + | 1.70733i | 0.638646 | + | 0.769501i | \(0.279495\pi\) |
0.347084 | + | 0.937834i | \(0.387172\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −186372. | − | 322807.i | −0.465130 | − | 0.805629i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 473350.i | 1.17391i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −202030. | + | 116642.i | −0.497894 | + | 0.287459i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 121233.i | 0.296906i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −55185.8 | − | 31861.5i | −0.134311 | − | 0.0775444i | 0.431339 | − | 0.902190i | \(-0.358041\pi\) |
−0.565650 | + | 0.824646i | \(0.691375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −114558. | + | 198420.i | −0.277079 | + | 0.479915i | −0.970657 | − | 0.240466i | \(-0.922700\pi\) |
0.693579 | + | 0.720381i | \(0.256033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 504235.i | − | 1.21203i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 439341. | 1.04953 | 0.524763 | − | 0.851248i | \(-0.324154\pi\) | ||||
0.524763 | + | 0.851248i | \(0.324154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −721183. | − | 416375.i | −1.71221 | − | 0.988543i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16137.8 | − | 27951.4i | 0.0380786 | − | 0.0659541i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 296297. | 0.694866 | 0.347433 | − | 0.937705i | \(-0.387053\pi\) | ||||
0.347433 | + | 0.937705i | \(0.387053\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −179021. | − | 310073.i | −0.417274 | − | 0.722739i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −89682.7 | −0.207768 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −642280. | + | 370820.i | −1.47895 | + | 0.853872i | −0.999716 | − | 0.0238155i | \(-0.992419\pi\) |
−0.479233 | + | 0.877688i | \(0.659085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −287667. | + | 166084.i | −0.658395 | + | 0.380125i | −0.791665 | − | 0.610955i | \(-0.790786\pi\) |
0.133270 | + | 0.991080i | \(0.457452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −65718.0 | + | 113827.i | −0.149505 | + | 0.258951i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −47181.1 | + | 251150.i | −0.106690 | + | 0.567924i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26327.1 | − | 15199.9i | −0.0591767 | − | 0.0341657i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −188265. | − | 326084.i | −0.420646 | − | 0.728580i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 181101. | + | 313677.i | 0.402232 | + | 0.696686i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40533.1i | 0.0894912i | 0.998998 | + | 0.0447456i | \(0.0142477\pi\) | ||||
−0.998998 | + | 0.0447456i | \(0.985752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12084.0 | − | 6976.69i | 0.0265218 | − | 0.0153123i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 392617.i | 0.856627i | 0.903630 | + | 0.428314i | \(0.140892\pi\) | ||||
−0.903630 | + | 0.428314i | \(0.859108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −433546. | − | 250308.i | −0.940363 | − | 0.542919i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 485255. | − | 840487.i | 1.04635 | − | 1.81233i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 509603.i | 1.09242i | 0.837648 | + | 0.546211i | \(0.183930\pi\) | ||||
−0.837648 | + | 0.546211i | \(0.816070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −453944. | −0.967434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 510485. | + | 294729.i | 1.08161 | + | 0.624466i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 177919. | − | 308165.i | 0.374787 | − | 0.649150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 753165. | 1.57737 | 0.788686 | − | 0.614796i | \(-0.210762\pi\) | ||||
0.788686 | + | 0.614796i | \(0.210762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 56131.2 | + | 97222.0i | 0.116879 | + | 0.202441i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 929659. | 1.92466 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7047.50 | − | 4068.88i | 0.0145067 | − | 0.00837547i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 420151. | − | 242574.i | 0.859906 | − | 0.496467i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 286342. | − | 495960.i | 0.582706 | − | 1.00928i | −0.412451 | − | 0.910980i | \(-0.635327\pi\) |
0.995157 | − | 0.0982968i | \(-0.0313395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −129233. | − | 367789.i | −0.261495 | − | 0.744197i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 630888. | + | 364244.i | 1.26933 | + | 0.732848i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1348.18 | − | 2335.11i | −0.00269717 | − | 0.00467163i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −84487.5 | − | 146337.i | −0.168074 | − | 0.291112i | 0.769669 | − | 0.638443i | \(-0.220421\pi\) |
−0.937743 | + | 0.347331i | \(0.887088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 160815.i | 0.318117i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −67596.5 | + | 39026.9i | −0.132967 | + | 0.0767688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 522829.i | 1.02270i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 319412. | + | 184413.i | 0.621317 | + | 0.358717i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6416.59 | + | 11113.9i | −0.0124121 | + | 0.0214985i | −0.872165 | − | 0.489212i | \(-0.837284\pi\) |
0.859753 | + | 0.510711i | \(0.170618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29461.1i | 0.0566732i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.16623e6 | 2.23104 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 949.297 | + | 548.077i | 0.00180603 | + | 0.00104271i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 385862. | − | 668332.i | 0.730067 | − | 1.26451i | −0.226787 | − | 0.973944i | \(-0.572822\pi\) |
0.956854 | − | 0.290569i | \(-0.0938447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −239708. | −0.451052 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −83150.8 | − | 144021.i | −0.155608 | − | 0.269521i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 598661. | 1.11423 | 0.557113 | − | 0.830437i | \(-0.311909\pi\) | ||||
0.557113 | + | 0.830437i | \(0.311909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −376314. | + | 217265.i | −0.696588 | + | 0.402175i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 616193. | − | 355759.i | 1.13444 | − | 0.654970i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −56363.8 | + | 97624.9i | −0.103207 | + | 0.178761i | −0.913004 | − | 0.407950i | \(-0.866244\pi\) |
0.809797 | + | 0.586710i | \(0.199577\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −509288. | + | 178953.i | −0.927528 | + | 0.325914i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 444706. | + | 256751.i | 0.805555 | + | 0.465088i | 0.845410 | − | 0.534118i | \(-0.179356\pi\) |
−0.0398546 | + | 0.999205i | \(0.512689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −257182. | − | 445453.i | −0.463370 | − | 0.802581i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 147658. | + | 255751.i | 0.264616 | + | 0.458328i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2406.06i | 0.00428887i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −740064. | + | 427276.i | −1.31217 | + | 0.757580i | −0.982455 | − | 0.186501i | \(-0.940285\pi\) |
−0.329713 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 389967.i | − | 0.687761i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 40624.2 | + | 23454.4i | 0.0712673 | + | 0.0411462i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −74063.5 | + | 128282.i | −0.129245 | + | 0.223858i | −0.923384 | − | 0.383877i | \(-0.874589\pi\) |
0.794139 | + | 0.607736i | \(0.207922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.05066e6i | − | 1.82380i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 262528. | 0.453322 | 0.226661 | − | 0.973974i | \(-0.427219\pi\) | ||||
0.226661 | + | 0.973974i | \(0.427219\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −499363. | − | 288307.i | −0.857762 | − | 0.495229i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31630.9 | + | 54786.3i | −0.0540491 | + | 0.0936158i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −831514. | −1.41344 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23000.9 | − | 39838.8i | −0.0388949 | − | 0.0673680i | 0.845923 | − | 0.533306i | \(-0.179050\pi\) |
−0.884818 | + | 0.465938i | \(0.845717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 657950. | 1.10684 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −590492. | + | 340921.i | −0.988224 | + | 0.570551i | −0.904743 | − | 0.425958i | \(-0.859937\pi\) |
−0.0834809 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2437.38 | − | 1407.22i | 0.00405808 | − | 0.00234293i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −156639. | + | 271307.i | −0.259453 | + | 0.449386i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32847.5 | + | 6170.74i | 0.0541287 | + | 0.0101686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 533050. | + | 307756.i | 0.873908 | + | 0.504551i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11949.8 | − | 20697.7i | −0.0194912 | − | 0.0337597i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −337104. | − | 583881.i | −0.547047 | − | 0.947513i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 356499.i | 0.575584i | 0.957693 | + | 0.287792i | \(0.0929212\pi\) | ||||
−0.957693 | + | 0.287792i | \(0.907079\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −796120. | + | 459640.i | −1.27886 | + | 0.738352i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 513635.i | 0.820921i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 313211. | + | 180832.i | 0.498070 | + | 0.287561i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 331404. | − | 574009.i | 0.524353 | − | 0.908206i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 356520.i | − | 0.561265i | −0.959815 | − | 0.280632i | \(-0.909456\pi\) | ||
0.959815 | − | 0.280632i | \(-0.0905442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 240262. | 0.376350 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 136120. | + | 78588.9i | 0.212157 | + | 0.122489i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −227665. | + | 394327.i | −0.353073 | + | 0.611540i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −496635. | −0.766383 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 307735. | + | 533013.i | 0.472531 | + | 0.818448i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 146248. | 0.223456 | 0.111728 | − | 0.993739i | \(-0.464361\pi\) | ||||
0.111728 | + | 0.993739i | \(0.464361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09333e6 | + | 631237.i | −1.66231 | + | 0.959733i | −0.690696 | + | 0.723145i | \(0.742696\pi\) |
−0.971610 | + | 0.236588i | \(0.923971\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −799197. | + | 461417.i | −1.20913 | + | 0.698091i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 176967. | − | 306516.i | 0.266427 | − | 0.461465i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 126104. | − | 671266.i | 0.188923 | − | 1.00566i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 97077.6 | + | 56047.8i | 0.144728 | + | 0.0835585i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −86526.3 | − | 149868.i | −0.128370 | − | 0.222343i | 0.794676 | − | 0.607034i | \(-0.207641\pi\) |
−0.923045 | + | 0.384692i | \(0.874308\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −164144. | − | 284306.i | −0.242340 | − | 0.419745i | 0.719040 | − | 0.694968i | \(-0.244582\pi\) |
−0.961380 | + | 0.275223i | \(0.911248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 37884.5i | 0.0556613i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −894676. | + | 516541.i | −1.30814 | + | 0.755256i | −0.981786 | − | 0.189991i | \(-0.939154\pi\) |
−0.326356 | + | 0.945247i | \(0.605821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 876630.i | 1.27558i | 0.770211 | + | 0.637789i | \(0.220151\pi\) | ||||
−0.770211 | + | 0.637789i | \(0.779849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −667604. | − | 385441.i | −0.966756 | − | 0.558157i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −71656.2 | + | 124112.i | −0.103268 | + | 0.178865i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 391322.i | − | 0.561256i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −61364.0 | −0.0875917 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 228597. | + | 131981.i | 0.324748 | + | 0.187493i | 0.653507 | − | 0.756921i | \(-0.273297\pi\) |
−0.328759 | + | 0.944414i | \(0.606630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −352702. | + | 610897.i | −0.498673 | + | 0.863726i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −625475. | −0.880147 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −103140. | − | 178644.i | −0.144449 | − | 0.250193i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 163551. | 0.227974 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.28124e6 | − | 739723.i | 1.77752 | − | 1.02625i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 656118. | − | 378810.i | 0.905989 | − | 0.523073i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 537972. | − | 931795.i | 0.739370 | − | 1.28063i | −0.213409 | − | 0.976963i | \(-0.568457\pi\) |
0.952779 | − | 0.303664i | \(-0.0982099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −245127. | + | 86132.5i | −0.335319 | + | 0.117824i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 346531. | + | 200070.i | 0.471824 | + | 0.272408i | 0.717003 | − | 0.697070i | \(-0.245513\pi\) |
−0.245179 | + | 0.969478i | \(0.578847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −274871. | − | 476090.i | −0.372514 | − | 0.645213i | 0.617438 | − | 0.786620i | \(-0.288171\pi\) |
−0.989952 | + | 0.141407i | \(0.954837\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13429.4 | − | 23260.4i | −0.0181155 | − | 0.0313769i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 443814.i | 0.595908i | 0.954580 | + | 0.297954i | \(0.0963042\pi\) | ||||
−0.954580 | + | 0.297954i | \(0.903696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −377536. | + | 217971.i | −0.504576 | + | 0.291317i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 792133.i | − | 1.05380i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 707088. | + | 408238.i | 0.936341 | + | 0.540597i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 355231. | − | 615278.i | 0.468246 | − | 0.811027i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 508991.i | − | 0.667854i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −424516. | −0.554469 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −919656. | − | 530964.i | −1.19571 | − | 0.690344i | −0.236115 | − | 0.971725i | \(-0.575874\pi\) |
−0.959596 | + | 0.281381i | \(0.909207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −895020. | + | 1.55022e6i | −1.15839 | + | 2.00639i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −337096. | −0.434312 | −0.217156 | − | 0.976137i | \(-0.569678\pi\) | ||||
−0.217156 | + | 0.976137i | \(0.569678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23184.8 | − | 40157.3i | −0.0297360 | − | 0.0515043i | 0.850774 | − | 0.525531i | \(-0.176133\pi\) |
−0.880510 | + | 0.474027i | \(0.842800\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.54883e6 | −1.97751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −94128.5 | + | 54345.1i | −0.119639 | + | 0.0690738i | −0.558625 | − | 0.829420i | \(-0.688671\pi\) |
0.438986 | + | 0.898494i | \(0.355338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 446230. | − | 257631.i | 0.564618 | − | 0.325982i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 576792. | − | 999033.i | 0.726547 | − | 1.25842i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 748781. | + | 642681.i | 0.938971 | + | 0.805921i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 674887. | + | 389646.i | 0.842529 | + | 0.486434i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −524549. | − | 908546.i | −0.651931 | − | 1.12918i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2410.33 | − | 4174.81i | −0.00298234 | − | 0.00516556i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 218601.i | − | 0.269279i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −475345. | + | 274441.i | −0.582953 | + | 0.336568i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.43602e6i | 1.75332i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −930792. | − | 537393.i | −1.13146 | − | 0.653247i | −0.187156 | − | 0.982330i | \(-0.559927\pi\) |
−0.944301 | + | 0.329083i | \(0.893260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1370.73 | − | 2374.18i | 0.00165892 | − | 0.00287333i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 586315.i | − | 0.706471i | −0.935534 | − | 0.353235i | \(-0.885081\pi\) | ||
0.935534 | − | 0.353235i | \(-0.114919\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.49935e6 | 1.79871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 583407. | + | 336830.i | 0.696834 | + | 0.402317i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −194872. | + | 337528.i | −0.231745 | + | 0.401394i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 678021. | 0.802809 | 0.401405 | − | 0.915901i | \(-0.368522\pi\) | ||||
0.401405 | + | 0.915901i | \(0.368522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −144799. | − | 250800.i | −0.170705 | − | 0.295671i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 614598. | 0.721420 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23658.2 | + | 13659.1i | −0.0276502 | + | 0.0159638i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25940.9 | + | 14977.0i | −0.0301874 | + | 0.0174287i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −364161. | + | 630746.i | −0.421951 | + | 0.730841i | −0.996130 | − | 0.0878888i | \(-0.971988\pi\) |
0.574179 | + | 0.818730i | \(0.305321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −555307. | + | 195123.i | −0.640669 | + | 0.225118i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.71671e6 | + | 991143.i | 1.97212 | + | 1.13861i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 160594. | + | 278156.i | 0.183698 | + | 0.318175i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −338424. | − | 586168.i | −0.385463 | − | 0.667641i | 0.606370 | − | 0.795182i | \(-0.292625\pi\) |
−0.991833 | + | 0.127541i | \(0.959292\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.65231e6i | 1.87396i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −211702. | + | 122226.i | −0.239081 | + | 0.138034i | −0.614754 | − | 0.788719i | \(-0.710745\pi\) |
0.375673 | + | 0.926752i | \(0.377412\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64954.1i | 0.0730438i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −338134. | − | 195222.i | −0.378639 | − | 0.218607i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 392652. | − | 680093.i | 0.437832 | − | 0.758348i | −0.559690 | − | 0.828702i | \(-0.689080\pi\) |
0.997522 | + | 0.0703543i | \(0.0224130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 454653.i | 0.504832i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −476830. | −0.527233 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −504490. | − | 291268.i | −0.555478 | − | 0.320705i | 0.195850 | − | 0.980634i | \(-0.437253\pi\) |
−0.751329 | + | 0.659928i | \(0.770587\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 258364. | − | 447500.i | 0.283286 | − | 0.490666i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64889.5 | 0.0708517 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 247069. | + | 427936.i | 0.268646 | + | 0.465309i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 911144. | 0.986598 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2118.57 | + | 1223.16i | −0.00228450 | + | 0.00131895i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23015.6 | + | 13288.1i | −0.0247154 | + | 0.0142694i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 378832. | − | 656157.i | 0.405130 | − | 0.701705i | −0.589207 | − | 0.807982i | \(-0.700560\pi\) |
0.994337 | + | 0.106277i | \(0.0338930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −215984. | + | 251641.i | −0.230025 | + | 0.268000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −412390. | − | 238093.i | −0.437390 | − | 0.252527i | 0.265100 | − | 0.964221i | \(-0.414595\pi\) |
−0.702490 | + | 0.711694i | \(0.747928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −505987. | − | 876395.i | −0.534458 | − | 0.925709i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18914.1 | + | 32760.2i | 0.0198965 | + | 0.0344617i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 439217.i | − | 0.460140i | −0.973174 | − | 0.230070i | \(-0.926105\pi\) | ||
0.973174 | − | 0.230070i | \(-0.0738955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 691097. | − | 399005.i | 0.721063 | − | 0.416306i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 586261.i | − | 0.609191i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −469744. | − | 271207.i | −0.486132 | − | 0.280668i | 0.236837 | − | 0.971549i | \(-0.423889\pi\) |
−0.722968 | + | 0.690881i | \(0.757223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −764859. | + | 1.32477e6i | −0.788331 | + | 1.36543i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 792990.i | − | 0.814017i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.32739e6 | 1.35708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 560235. | + | 323452.i | 0.570457 | + | 0.329354i | 0.757332 | − | 0.653030i | \(-0.226502\pi\) |
−0.186875 | + | 0.982384i | \(0.559836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −267764. | + | 463781.i | −0.271553 | + | 0.470343i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.23996e6 | 1.25246 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 581238. | + | 1.00673e6i | 0.584741 | + | 1.01280i | 0.994908 | + | 0.100791i | \(0.0321373\pi\) |
−0.410166 | + | 0.912011i | \(0.634529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 595623. | 0.596816 |
(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 | 76.5.h.a.65.2 | ✓ | 12 | |
3.2 | odd | 2 | 684.5.y.c.217.5 | 12 | |||
4.3 | odd | 2 | 304.5.r.b.65.5 | 12 | |||
19.12 | odd | 6 | inner | 76.5.h.a.69.2 | yes | 12 | |
57.50 | even | 6 | 684.5.y.c.145.5 | 12 | |||
76.31 | even | 6 | 304.5.r.b.145.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.h.a.65.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
76.5.h.a.69.2 | yes | 12 | 19.12 | odd | 6 | inner | |
304.5.r.b.65.5 | 12 | 4.3 | odd | 2 | |||
304.5.r.b.145.5 | 12 | 76.31 | even | 6 | |||
684.5.y.c.145.5 | 12 | 57.50 | even | 6 | |||
684.5.y.c.217.5 | 12 | 3.2 | odd | 2 |