Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,6,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.a (trivial) |
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: | yes |
Analytic conductor: | \(36.8882785570\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.27980.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 47x - 106 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(7.78556\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −10.5273 | −0.675326 | −0.337663 | − | 0.941267i | \(-0.609636\pi\) | ||||
−0.337663 | + | 0.941267i | \(0.609636\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 42.1092 | 0.477528 | ||||||||
\(7\) | 156.388 | 1.20631 | 0.603153 | − | 0.797626i | \(-0.293911\pi\) | ||||
0.603153 | + | 0.797626i | \(0.293911\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −132.176 | −0.543935 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | −397.468 | −0.990422 | −0.495211 | − | 0.868773i | \(-0.664909\pi\) | ||||
−0.495211 | + | 0.868773i | \(0.664909\pi\) | |||||||
\(12\) | −168.437 | −0.337663 | ||||||||
\(13\) | −71.8579 | −0.117928 | −0.0589639 | − | 0.998260i | \(-0.518780\pi\) | ||||
−0.0589639 | + | 0.998260i | \(0.518780\pi\) | |||||||
\(14\) | −625.550 | −0.852987 | ||||||||
\(15\) | −263.182 | −0.302015 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 221.370 | 0.185779 | 0.0928896 | − | 0.995676i | \(-0.470390\pi\) | ||||
0.0928896 | + | 0.995676i | \(0.470390\pi\) | |||||||
\(18\) | 528.704 | 0.384620 | ||||||||
\(19\) | −173.333 | −0.110153 | −0.0550767 | − | 0.998482i | \(-0.517540\pi\) | ||||
−0.0550767 | + | 0.998482i | \(0.517540\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −1646.34 | −0.814649 | ||||||||
\(22\) | 1589.87 | 0.700334 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 673.747 | 0.238764 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 287.432 | 0.0833875 | ||||||||
\(27\) | 3949.59 | 1.04266 | ||||||||
\(28\) | 2502.20 | 0.603153 | ||||||||
\(29\) | 6966.29 | 1.53818 | 0.769088 | − | 0.639142i | \(-0.220711\pi\) | ||||
0.769088 | + | 0.639142i | \(0.220711\pi\) | |||||||
\(30\) | 1052.73 | 0.213557 | ||||||||
\(31\) | −2009.47 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 4184.26 | 0.668858 | ||||||||
\(34\) | −885.481 | −0.131366 | ||||||||
\(35\) | 3909.69 | 0.539476 | ||||||||
\(36\) | −2114.82 | −0.271967 | ||||||||
\(37\) | −12305.3 | −1.47771 | −0.738853 | − | 0.673866i | \(-0.764632\pi\) | ||||
−0.738853 | + | 0.673866i | \(0.764632\pi\) | |||||||
\(38\) | 693.333 | 0.0778902 | ||||||||
\(39\) | 756.469 | 0.0796397 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | 420.431 | 0.0390603 | 0.0195301 | − | 0.999809i | \(-0.493783\pi\) | ||||
0.0195301 | + | 0.999809i | \(0.493783\pi\) | |||||||
\(42\) | 6585.35 | 0.576044 | ||||||||
\(43\) | −14261.3 | −1.17622 | −0.588110 | − | 0.808781i | \(-0.700128\pi\) | ||||
−0.588110 | + | 0.808781i | \(0.700128\pi\) | |||||||
\(44\) | −6359.49 | −0.495211 | ||||||||
\(45\) | −3304.40 | −0.243255 | ||||||||
\(46\) | −2116.00 | −0.147442 | ||||||||
\(47\) | 1706.64 | 0.112693 | 0.0563464 | − | 0.998411i | \(-0.482055\pi\) | ||||
0.0563464 | + | 0.998411i | \(0.482055\pi\) | |||||||
\(48\) | −2694.99 | −0.168832 | ||||||||
\(49\) | 7650.08 | 0.455172 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −2330.43 | −0.125462 | ||||||||
\(52\) | −1149.73 | −0.0589639 | ||||||||
\(53\) | −6102.11 | −0.298394 | −0.149197 | − | 0.988807i | \(-0.547669\pi\) | ||||
−0.149197 | + | 0.988807i | \(0.547669\pi\) | |||||||
\(54\) | −15798.4 | −0.737272 | ||||||||
\(55\) | −9936.70 | −0.442930 | ||||||||
\(56\) | −10008.8 | −0.426493 | ||||||||
\(57\) | 1824.73 | 0.0743894 | ||||||||
\(58\) | −27865.1 | −1.08766 | ||||||||
\(59\) | 23220.2 | 0.868432 | 0.434216 | − | 0.900809i | \(-0.357025\pi\) | ||||
0.434216 | + | 0.900809i | \(0.357025\pi\) | |||||||
\(60\) | −4210.92 | −0.151008 | ||||||||
\(61\) | −29339.9 | −1.00957 | −0.504783 | − | 0.863246i | \(-0.668427\pi\) | ||||
−0.504783 | + | 0.863246i | \(0.668427\pi\) | |||||||
\(62\) | 8037.88 | 0.265560 | ||||||||
\(63\) | −20670.7 | −0.656151 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −1796.45 | −0.0527389 | ||||||||
\(66\) | −16737.0 | −0.472954 | ||||||||
\(67\) | −26398.9 | −0.718454 | −0.359227 | − | 0.933250i | \(-0.616960\pi\) | ||||
−0.359227 | + | 0.933250i | \(0.616960\pi\) | |||||||
\(68\) | 3541.92 | 0.0928896 | ||||||||
\(69\) | −5568.94 | −0.140815 | ||||||||
\(70\) | −15638.8 | −0.381467 | ||||||||
\(71\) | −9484.52 | −0.223290 | −0.111645 | − | 0.993748i | \(-0.535612\pi\) | ||||
−0.111645 | + | 0.993748i | \(0.535612\pi\) | |||||||
\(72\) | 8459.27 | 0.192310 | ||||||||
\(73\) | −1769.79 | −0.0388700 | −0.0194350 | − | 0.999811i | \(-0.506187\pi\) | ||||
−0.0194350 | + | 0.999811i | \(0.506187\pi\) | |||||||
\(74\) | 49221.2 | 1.04490 | ||||||||
\(75\) | −6579.56 | −0.135065 | ||||||||
\(76\) | −2773.33 | −0.0550767 | ||||||||
\(77\) | −62159.1 | −1.19475 | ||||||||
\(78\) | −3025.88 | −0.0563138 | ||||||||
\(79\) | −8643.34 | −0.155817 | −0.0779083 | − | 0.996961i | \(-0.524824\pi\) | ||||
−0.0779083 | + | 0.996961i | \(0.524824\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | −9459.68 | −0.160201 | ||||||||
\(82\) | −1681.72 | −0.0276198 | ||||||||
\(83\) | −108289. | −1.72540 | −0.862700 | − | 0.505717i | \(-0.831228\pi\) | ||||
−0.862700 | + | 0.505717i | \(0.831228\pi\) | |||||||
\(84\) | −26341.4 | −0.407325 | ||||||||
\(85\) | 5534.26 | 0.0830830 | ||||||||
\(86\) | 57045.3 | 0.831713 | ||||||||
\(87\) | −73336.1 | −1.03877 | ||||||||
\(88\) | 25438.0 | 0.350167 | ||||||||
\(89\) | −59654.8 | −0.798308 | −0.399154 | − | 0.916884i | \(-0.630696\pi\) | ||||
−0.399154 | + | 0.916884i | \(0.630696\pi\) | |||||||
\(90\) | 13217.6 | 0.172007 | ||||||||
\(91\) | −11237.7 | −0.142257 | ||||||||
\(92\) | 8464.00 | 0.104257 | ||||||||
\(93\) | 21154.3 | 0.253624 | ||||||||
\(94\) | −6826.54 | −0.0796858 | ||||||||
\(95\) | −4333.33 | −0.0492621 | ||||||||
\(96\) | 10779.9 | 0.119382 | ||||||||
\(97\) | −140826. | −1.51968 | −0.759842 | − | 0.650108i | \(-0.774724\pi\) | ||||
−0.759842 | + | 0.650108i | \(0.774724\pi\) | |||||||
\(98\) | −30600.3 | −0.321855 | ||||||||
\(99\) | 52535.8 | 0.538725 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 43468.1 | 0.424001 | 0.212001 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212001 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(102\) | 9321.72 | 0.0887147 | ||||||||
\(103\) | −119511. | −1.10998 | −0.554990 | − | 0.831857i | \(-0.687278\pi\) | ||||
−0.554990 | + | 0.831857i | \(0.687278\pi\) | |||||||
\(104\) | 4598.91 | 0.0416938 | ||||||||
\(105\) | −41158.4 | −0.364322 | ||||||||
\(106\) | 24408.4 | 0.210996 | ||||||||
\(107\) | −74071.6 | −0.625450 | −0.312725 | − | 0.949844i | \(-0.601242\pi\) | ||||
−0.312725 | + | 0.949844i | \(0.601242\pi\) | |||||||
\(108\) | 63193.4 | 0.521330 | ||||||||
\(109\) | 19868.2 | 0.160174 | 0.0800871 | − | 0.996788i | \(-0.474480\pi\) | ||||
0.0800871 | + | 0.996788i | \(0.474480\pi\) | |||||||
\(110\) | 39746.8 | 0.313199 | ||||||||
\(111\) | 129542. | 0.997934 | ||||||||
\(112\) | 40035.2 | 0.301576 | ||||||||
\(113\) | 28794.8 | 0.212138 | 0.106069 | − | 0.994359i | \(-0.466174\pi\) | ||||
0.106069 | + | 0.994359i | \(0.466174\pi\) | |||||||
\(114\) | −7298.92 | −0.0526013 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | 111461. | 0.769088 | ||||||||
\(117\) | 9497.90 | 0.0641450 | ||||||||
\(118\) | −92880.8 | −0.614074 | ||||||||
\(119\) | 34619.6 | 0.224106 | ||||||||
\(120\) | 16843.7 | 0.106778 | ||||||||
\(121\) | −3070.20 | −0.0190635 | ||||||||
\(122\) | 117360. | 0.713871 | ||||||||
\(123\) | −4426.00 | −0.0263784 | ||||||||
\(124\) | −32151.5 | −0.187779 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 82682.8 | 0.463969 | ||||||||
\(127\) | −102984. | −0.566581 | −0.283291 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 150133. | 0.794332 | ||||||||
\(130\) | 7185.79 | 0.0372920 | ||||||||
\(131\) | 11416.3 | 0.0581228 | 0.0290614 | − | 0.999578i | \(-0.490748\pi\) | ||||
0.0290614 | + | 0.999578i | \(0.490748\pi\) | |||||||
\(132\) | 66948.2 | 0.334429 | ||||||||
\(133\) | −27107.2 | −0.132879 | ||||||||
\(134\) | 105596. | 0.508024 | ||||||||
\(135\) | 98739.7 | 0.466291 | ||||||||
\(136\) | −14167.7 | −0.0656828 | ||||||||
\(137\) | −139487. | −0.634938 | −0.317469 | − | 0.948269i | \(-0.602833\pi\) | ||||
−0.317469 | + | 0.948269i | \(0.602833\pi\) | |||||||
\(138\) | 22275.8 | 0.0995714 | ||||||||
\(139\) | −46437.5 | −0.203860 | −0.101930 | − | 0.994792i | \(-0.532502\pi\) | ||||
−0.101930 | + | 0.994792i | \(0.532502\pi\) | |||||||
\(140\) | 62555.0 | 0.269738 | ||||||||
\(141\) | −17966.2 | −0.0761044 | ||||||||
\(142\) | 37938.1 | 0.157890 | ||||||||
\(143\) | 28561.2 | 0.116798 | ||||||||
\(144\) | −33837.1 | −0.135984 | ||||||||
\(145\) | 174157. | 0.687894 | ||||||||
\(146\) | 7079.16 | 0.0274852 | ||||||||
\(147\) | −80534.6 | −0.307390 | ||||||||
\(148\) | −196885. | −0.738853 | ||||||||
\(149\) | −337323. | −1.24475 | −0.622373 | − | 0.782721i | \(-0.713831\pi\) | ||||
−0.622373 | + | 0.782721i | \(0.713831\pi\) | |||||||
\(150\) | 26318.2 | 0.0955055 | ||||||||
\(151\) | 372864. | 1.33079 | 0.665393 | − | 0.746493i | \(-0.268264\pi\) | ||||
0.665393 | + | 0.746493i | \(0.268264\pi\) | |||||||
\(152\) | 11093.3 | 0.0389451 | ||||||||
\(153\) | −29259.9 | −0.101052 | ||||||||
\(154\) | 248636. | 0.844817 | ||||||||
\(155\) | −50236.8 | −0.167955 | ||||||||
\(156\) | 12103.5 | 0.0398199 | ||||||||
\(157\) | −194815. | −0.630772 | −0.315386 | − | 0.948963i | \(-0.602134\pi\) | ||||
−0.315386 | + | 0.948963i | \(0.602134\pi\) | |||||||
\(158\) | 34573.4 | 0.110179 | ||||||||
\(159\) | 64238.7 | 0.201513 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 82729.0 | 0.251532 | ||||||||
\(162\) | 37838.7 | 0.113279 | ||||||||
\(163\) | 332950. | 0.981543 | 0.490772 | − | 0.871288i | \(-0.336715\pi\) | ||||
0.490772 | + | 0.871288i | \(0.336715\pi\) | |||||||
\(164\) | 6726.90 | 0.0195301 | ||||||||
\(165\) | 104607. | 0.299122 | ||||||||
\(166\) | 433157. | 1.22004 | ||||||||
\(167\) | 289233. | 0.802522 | 0.401261 | − | 0.915964i | \(-0.368572\pi\) | ||||
0.401261 | + | 0.915964i | \(0.368572\pi\) | |||||||
\(168\) | 105366. | 0.288022 | ||||||||
\(169\) | −366129. | −0.986093 | ||||||||
\(170\) | −22137.0 | −0.0587485 | ||||||||
\(171\) | 22910.5 | 0.0599162 | ||||||||
\(172\) | −228181. | −0.588110 | ||||||||
\(173\) | −120295. | −0.305584 | −0.152792 | − | 0.988258i | \(-0.548827\pi\) | ||||
−0.152792 | + | 0.988258i | \(0.548827\pi\) | |||||||
\(174\) | 293344. | 0.734522 | ||||||||
\(175\) | 97742.2 | 0.241261 | ||||||||
\(176\) | −101752. | −0.247606 | ||||||||
\(177\) | −244446. | −0.586475 | ||||||||
\(178\) | 238619. | 0.564489 | ||||||||
\(179\) | 93474.3 | 0.218052 | 0.109026 | − | 0.994039i | \(-0.465227\pi\) | ||||
0.109026 | + | 0.994039i | \(0.465227\pi\) | |||||||
\(180\) | −52870.4 | −0.121627 | ||||||||
\(181\) | −578671. | −1.31291 | −0.656456 | − | 0.754364i | \(-0.727945\pi\) | ||||
−0.656456 | + | 0.754364i | \(0.727945\pi\) | |||||||
\(182\) | 44950.7 | 0.100591 | ||||||||
\(183\) | 308870. | 0.681786 | ||||||||
\(184\) | −33856.0 | −0.0737210 | ||||||||
\(185\) | −307633. | −0.660851 | ||||||||
\(186\) | −84617.1 | −0.179339 | ||||||||
\(187\) | −87987.6 | −0.184000 | ||||||||
\(188\) | 27306.2 | 0.0563464 | ||||||||
\(189\) | 617667. | 1.25777 | ||||||||
\(190\) | 17333.3 | 0.0348336 | ||||||||
\(191\) | 334102. | 0.662668 | 0.331334 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331334 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(192\) | −43119.8 | −0.0844158 | ||||||||
\(193\) | −357766. | −0.691362 | −0.345681 | − | 0.938352i | \(-0.612352\pi\) | ||||
−0.345681 | + | 0.938352i | \(0.612352\pi\) | |||||||
\(194\) | 563304. | 1.07458 | ||||||||
\(195\) | 18911.7 | 0.0356160 | ||||||||
\(196\) | 122401. | 0.227586 | ||||||||
\(197\) | 205858. | 0.377923 | 0.188961 | − | 0.981985i | \(-0.439488\pi\) | ||||
0.188961 | + | 0.981985i | \(0.439488\pi\) | |||||||
\(198\) | −210143. | −0.380936 | ||||||||
\(199\) | 992810. | 1.77719 | 0.888594 | − | 0.458695i | \(-0.151683\pi\) | ||||
0.888594 | + | 0.458695i | \(0.151683\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 277909. | 0.485191 | ||||||||
\(202\) | −173872. | −0.299814 | ||||||||
\(203\) | 1.08944e6 | 1.85551 | ||||||||
\(204\) | −37286.9 | −0.0627308 | ||||||||
\(205\) | 10510.8 | 0.0174683 | ||||||||
\(206\) | 478044. | 0.784875 | ||||||||
\(207\) | −69921.2 | −0.113418 | ||||||||
\(208\) | −18395.6 | −0.0294819 | ||||||||
\(209\) | 68894.4 | 0.109098 | ||||||||
\(210\) | 164634. | 0.257615 | ||||||||
\(211\) | −784498. | −1.21307 | −0.606535 | − | 0.795057i | \(-0.707441\pi\) | ||||
−0.606535 | + | 0.795057i | \(0.707441\pi\) | |||||||
\(212\) | −97633.7 | −0.149197 | ||||||||
\(213\) | 99846.3 | 0.150794 | ||||||||
\(214\) | 296287. | 0.442260 | ||||||||
\(215\) | −356533. | −0.526021 | ||||||||
\(216\) | −252774. | −0.368636 | ||||||||
\(217\) | −314256. | −0.453038 | ||||||||
\(218\) | −79472.8 | −0.113260 | ||||||||
\(219\) | 18631.1 | 0.0262499 | ||||||||
\(220\) | −158987. | −0.221465 | ||||||||
\(221\) | −15907.2 | −0.0219085 | ||||||||
\(222\) | −518166. | −0.705646 | ||||||||
\(223\) | 1.25999e6 | 1.69670 | 0.848349 | − | 0.529438i | \(-0.177597\pi\) | ||||
0.848349 | + | 0.529438i | \(0.177597\pi\) | |||||||
\(224\) | −160141. | −0.213247 | ||||||||
\(225\) | −82610.1 | −0.108787 | ||||||||
\(226\) | −115179. | −0.150004 | ||||||||
\(227\) | −1.43471e6 | −1.84799 | −0.923997 | − | 0.382399i | \(-0.875098\pi\) | ||||
−0.923997 | + | 0.382399i | \(0.875098\pi\) | |||||||
\(228\) | 29195.7 | 0.0371947 | ||||||||
\(229\) | −206190. | −0.259824 | −0.129912 | − | 0.991526i | \(-0.541470\pi\) | ||||
−0.129912 | + | 0.991526i | \(0.541470\pi\) | |||||||
\(230\) | −52900.0 | −0.0659380 | ||||||||
\(231\) | 654367. | 0.806847 | ||||||||
\(232\) | −445842. | −0.543828 | ||||||||
\(233\) | 874544. | 1.05534 | 0.527669 | − | 0.849450i | \(-0.323066\pi\) | ||||
0.527669 | + | 0.849450i | \(0.323066\pi\) | |||||||
\(234\) | −37991.6 | −0.0453574 | ||||||||
\(235\) | 42665.9 | 0.0503977 | ||||||||
\(236\) | 371523. | 0.434216 | ||||||||
\(237\) | 90990.9 | 0.105227 | ||||||||
\(238\) | −138478. | −0.158467 | ||||||||
\(239\) | −410321. | −0.464653 | −0.232326 | − | 0.972638i | \(-0.574634\pi\) | ||||
−0.232326 | + | 0.972638i | \(0.574634\pi\) | |||||||
\(240\) | −67374.7 | −0.0755038 | ||||||||
\(241\) | −1.23413e6 | −1.36874 | −0.684368 | − | 0.729137i | \(-0.739922\pi\) | ||||
−0.684368 | + | 0.729137i | \(0.739922\pi\) | |||||||
\(242\) | 12280.8 | 0.0134800 | ||||||||
\(243\) | −860165. | −0.934472 | ||||||||
\(244\) | −469439. | −0.504783 | ||||||||
\(245\) | 191252. | 0.203559 | ||||||||
\(246\) | 17704.0 | 0.0186524 | ||||||||
\(247\) | 12455.4 | 0.0129901 | ||||||||
\(248\) | 128606. | 0.132780 | ||||||||
\(249\) | 1.13999e6 | 1.16521 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | 102403. | 0.102595 | 0.0512977 | − | 0.998683i | \(-0.483664\pi\) | ||||
0.0512977 | + | 0.998683i | \(0.483664\pi\) | |||||||
\(252\) | −330731. | −0.328076 | ||||||||
\(253\) | −210261. | −0.206517 | ||||||||
\(254\) | 411938. | 0.400633 | ||||||||
\(255\) | −58260.7 | −0.0561081 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.73380e6 | −1.63744 | −0.818720 | − | 0.574192i | \(-0.805316\pi\) | ||||
−0.818720 | + | 0.574192i | \(0.805316\pi\) | |||||||
\(258\) | −600532. | −0.561678 | ||||||||
\(259\) | −1.92440e6 | −1.78257 | ||||||||
\(260\) | −28743.2 | −0.0263695 | ||||||||
\(261\) | −920776. | −0.836668 | ||||||||
\(262\) | −45665.1 | −0.0410990 | ||||||||
\(263\) | −1598.98 | −0.00142545 | −0.000712726 | − | 1.00000i | \(-0.500227\pi\) | ||||
−0.000712726 | 1.00000i | \(0.500227\pi\) | ||||||||
\(264\) | −267793. | −0.236477 | ||||||||
\(265\) | −152553. | −0.133446 | ||||||||
\(266\) | 108429. | 0.0939593 | ||||||||
\(267\) | 628004. | 0.539118 | ||||||||
\(268\) | −422382. | −0.359227 | ||||||||
\(269\) | −179772. | −0.151476 | −0.0757378 | − | 0.997128i | \(-0.524131\pi\) | ||||
−0.0757378 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(270\) | −394959. | −0.329718 | ||||||||
\(271\) | 651012. | 0.538475 | 0.269238 | − | 0.963074i | \(-0.413228\pi\) | ||||
0.269238 | + | 0.963074i | \(0.413228\pi\) | |||||||
\(272\) | 56670.8 | 0.0464448 | ||||||||
\(273\) | 118302. | 0.0960698 | ||||||||
\(274\) | 557947. | 0.448969 | ||||||||
\(275\) | −248417. | −0.198084 | ||||||||
\(276\) | −89103.0 | −0.0704076 | ||||||||
\(277\) | 104670. | 0.0819643 | 0.0409821 | − | 0.999160i | \(-0.486951\pi\) | ||||
0.0409821 | + | 0.999160i | \(0.486951\pi\) | |||||||
\(278\) | 185750. | 0.144151 | ||||||||
\(279\) | 265604. | 0.204279 | ||||||||
\(280\) | −250220. | −0.190734 | ||||||||
\(281\) | 951050. | 0.718518 | 0.359259 | − | 0.933238i | \(-0.383030\pi\) | ||||
0.359259 | + | 0.933238i | \(0.383030\pi\) | |||||||
\(282\) | 71865.0 | 0.0538139 | ||||||||
\(283\) | 46711.8 | 0.0346705 | 0.0173353 | − | 0.999850i | \(-0.494482\pi\) | ||||
0.0173353 | + | 0.999850i | \(0.494482\pi\) | |||||||
\(284\) | −151752. | −0.111645 | ||||||||
\(285\) | 45618.2 | 0.0332680 | ||||||||
\(286\) | −114245. | −0.0825889 | ||||||||
\(287\) | 65750.2 | 0.0471186 | ||||||||
\(288\) | 135348. | 0.0961550 | ||||||||
\(289\) | −1.37085e6 | −0.965486 | ||||||||
\(290\) | −696629. | −0.486414 | ||||||||
\(291\) | 1.48252e6 | 1.02628 | ||||||||
\(292\) | −28316.6 | −0.0194350 | ||||||||
\(293\) | 539801. | 0.367337 | 0.183669 | − | 0.982988i | \(-0.441203\pi\) | ||||
0.183669 | + | 0.982988i | \(0.441203\pi\) | |||||||
\(294\) | 322139. | 0.217357 | ||||||||
\(295\) | 580505. | 0.388375 | ||||||||
\(296\) | 787540. | 0.522448 | ||||||||
\(297\) | −1.56984e6 | −1.03267 | ||||||||
\(298\) | 1.34929e6 | 0.880168 | ||||||||
\(299\) | −38012.8 | −0.0245896 | ||||||||
\(300\) | −105273. | −0.0675326 | ||||||||
\(301\) | −2.23029e6 | −1.41888 | ||||||||
\(302\) | −1.49146e6 | −0.941007 | ||||||||
\(303\) | −457601. | −0.286339 | ||||||||
\(304\) | −44373.3 | −0.0275383 | ||||||||
\(305\) | −733498. | −0.451491 | ||||||||
\(306\) | 117039. | 0.0714543 | ||||||||
\(307\) | −1.94725e6 | −1.17917 | −0.589584 | − | 0.807707i | \(-0.700708\pi\) | ||||
−0.589584 | + | 0.807707i | \(0.700708\pi\) | |||||||
\(308\) | −994545. | −0.597376 | ||||||||
\(309\) | 1.25813e6 | 0.749599 | ||||||||
\(310\) | 200947. | 0.118762 | ||||||||
\(311\) | 2.33189e6 | 1.36712 | 0.683560 | − | 0.729894i | \(-0.260431\pi\) | ||||
0.683560 | + | 0.729894i | \(0.260431\pi\) | |||||||
\(312\) | −48414.0 | −0.0281569 | ||||||||
\(313\) | −441207. | −0.254555 | −0.127277 | − | 0.991867i | \(-0.540624\pi\) | ||||
−0.127277 | + | 0.991867i | \(0.540624\pi\) | |||||||
\(314\) | 779259. | 0.446023 | ||||||||
\(315\) | −516768. | −0.293440 | ||||||||
\(316\) | −138293. | −0.0779083 | ||||||||
\(317\) | 815875. | 0.456011 | 0.228005 | − | 0.973660i | \(-0.426780\pi\) | ||||
0.228005 | + | 0.973660i | \(0.426780\pi\) | |||||||
\(318\) | −256955. | −0.142491 | ||||||||
\(319\) | −2.76888e6 | −1.52344 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 779774. | 0.422383 | ||||||||
\(322\) | −330916. | −0.177860 | ||||||||
\(323\) | −38370.8 | −0.0204642 | ||||||||
\(324\) | −151355. | −0.0801003 | ||||||||
\(325\) | −44911.2 | −0.0235856 | ||||||||
\(326\) | −1.33180e6 | −0.694056 | ||||||||
\(327\) | −209158. | −0.108170 | ||||||||
\(328\) | −26907.6 | −0.0138099 | ||||||||
\(329\) | 266897. | 0.135942 | ||||||||
\(330\) | −418426. | −0.211512 | ||||||||
\(331\) | 2.11055e6 | 1.05883 | 0.529415 | − | 0.848363i | \(-0.322412\pi\) | ||||
0.529415 | + | 0.848363i | \(0.322412\pi\) | |||||||
\(332\) | −1.73263e6 | −0.862700 | ||||||||
\(333\) | 1.62647e6 | 0.803776 | ||||||||
\(334\) | −1.15693e6 | −0.567469 | ||||||||
\(335\) | −659973. | −0.321302 | ||||||||
\(336\) | −421463. | −0.203662 | ||||||||
\(337\) | −1.13820e6 | −0.545938 | −0.272969 | − | 0.962023i | \(-0.588006\pi\) | ||||
−0.272969 | + | 0.962023i | \(0.588006\pi\) | |||||||
\(338\) | 1.46452e6 | 0.697273 | ||||||||
\(339\) | −303131. | −0.143262 | ||||||||
\(340\) | 88548.1 | 0.0415415 | ||||||||
\(341\) | 798700. | 0.371961 | ||||||||
\(342\) | −91642.0 | −0.0423672 | ||||||||
\(343\) | −1.43203e6 | −0.657229 | ||||||||
\(344\) | 912724. | 0.415856 | ||||||||
\(345\) | −139223. | −0.0629745 | ||||||||
\(346\) | 481179. | 0.216081 | ||||||||
\(347\) | −1.33256e6 | −0.594103 | −0.297051 | − | 0.954861i | \(-0.596003\pi\) | ||||
−0.297051 | + | 0.954861i | \(0.596003\pi\) | |||||||
\(348\) | −1.17338e6 | −0.519386 | ||||||||
\(349\) | 2.72390e6 | 1.19709 | 0.598545 | − | 0.801089i | \(-0.295746\pi\) | ||||
0.598545 | + | 0.801089i | \(0.295746\pi\) | |||||||
\(350\) | −390969. | −0.170597 | ||||||||
\(351\) | −283809. | −0.122959 | ||||||||
\(352\) | 407007. | 0.175084 | ||||||||
\(353\) | 4.36203e6 | 1.86317 | 0.931585 | − | 0.363524i | \(-0.118427\pi\) | ||||
0.931585 | + | 0.363524i | \(0.118427\pi\) | |||||||
\(354\) | 977783. | 0.414700 | ||||||||
\(355\) | −237113. | −0.0998584 | ||||||||
\(356\) | −954477. | −0.399154 | ||||||||
\(357\) | −364450. | −0.151345 | ||||||||
\(358\) | −373897. | −0.154186 | ||||||||
\(359\) | 3.27980e6 | 1.34311 | 0.671554 | − | 0.740956i | \(-0.265627\pi\) | ||||
0.671554 | + | 0.740956i | \(0.265627\pi\) | |||||||
\(360\) | 211482. | 0.0860036 | ||||||||
\(361\) | −2.44605e6 | −0.987866 | ||||||||
\(362\) | 2.31469e6 | 0.928369 | ||||||||
\(363\) | 32320.9 | 0.0128741 | ||||||||
\(364\) | −179803. | −0.0711285 | ||||||||
\(365\) | −44244.7 | −0.0173832 | ||||||||
\(366\) | −1.23548e6 | −0.482096 | ||||||||
\(367\) | −1.15790e6 | −0.448750 | −0.224375 | − | 0.974503i | \(-0.572034\pi\) | ||||
−0.224375 | + | 0.974503i | \(0.572034\pi\) | |||||||
\(368\) | 135424. | 0.0521286 | ||||||||
\(369\) | −55570.9 | −0.0212462 | ||||||||
\(370\) | 1.23053e6 | 0.467292 | ||||||||
\(371\) | −954294. | −0.359954 | ||||||||
\(372\) | 338468. | 0.126812 | ||||||||
\(373\) | 4.19142e6 | 1.55987 | 0.779936 | − | 0.625859i | \(-0.215252\pi\) | ||||
0.779936 | + | 0.625859i | \(0.215252\pi\) | |||||||
\(374\) | 351950. | 0.130108 | ||||||||
\(375\) | −164489. | −0.0604030 | ||||||||
\(376\) | −109225. | −0.0398429 | ||||||||
\(377\) | −500583. | −0.181394 | ||||||||
\(378\) | −2.47067e6 | −0.889374 | ||||||||
\(379\) | 4.37682e6 | 1.56517 | 0.782583 | − | 0.622546i | \(-0.213902\pi\) | ||||
0.782583 | + | 0.622546i | \(0.213902\pi\) | |||||||
\(380\) | −69333.3 | −0.0246310 | ||||||||
\(381\) | 1.08415e6 | 0.382627 | ||||||||
\(382\) | −1.33641e6 | −0.468577 | ||||||||
\(383\) | 2.90888e6 | 1.01328 | 0.506639 | − | 0.862158i | \(-0.330888\pi\) | ||||
0.506639 | + | 0.862158i | \(0.330888\pi\) | |||||||
\(384\) | 172479. | 0.0596910 | ||||||||
\(385\) | −1.55398e6 | −0.534309 | ||||||||
\(386\) | 1.43106e6 | 0.488867 | ||||||||
\(387\) | 1.88501e6 | 0.639787 | ||||||||
\(388\) | −2.25321e6 | −0.759842 | ||||||||
\(389\) | 723744. | 0.242500 | 0.121250 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121250 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(390\) | −75646.9 | −0.0251843 | ||||||||
\(391\) | 117105. | 0.0387376 | ||||||||
\(392\) | −489605. | −0.160928 | ||||||||
\(393\) | −120183. | −0.0392519 | ||||||||
\(394\) | −823434. | −0.267232 | ||||||||
\(395\) | −216083. | −0.0696833 | ||||||||
\(396\) | 840572. | 0.269362 | ||||||||
\(397\) | −2.05819e6 | −0.655405 | −0.327702 | − | 0.944781i | \(-0.606274\pi\) | ||||
−0.327702 | + | 0.944781i | \(0.606274\pi\) | |||||||
\(398\) | −3.97124e6 | −1.25666 | ||||||||
\(399\) | 285365. | 0.0897364 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −417799. | −0.129750 | −0.0648748 | − | 0.997893i | \(-0.520665\pi\) | ||||
−0.0648748 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(402\) | −1.11164e6 | −0.343082 | ||||||||
\(403\) | 144396. | 0.0442888 | ||||||||
\(404\) | 695489. | 0.212001 | ||||||||
\(405\) | −236492. | −0.0716439 | ||||||||
\(406\) | −4.35776e6 | −1.31204 | ||||||||
\(407\) | 4.89097e6 | 1.46355 | ||||||||
\(408\) | 149147. | 0.0443573 | ||||||||
\(409\) | 2.12284e6 | 0.627493 | 0.313747 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313747 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(410\) | −42043.1 | −0.0123519 | ||||||||
\(411\) | 1.46842e6 | 0.428790 | ||||||||
\(412\) | −1.91218e6 | −0.554990 | ||||||||
\(413\) | 3.63135e6 | 1.04759 | ||||||||
\(414\) | 279685. | 0.0801988 | ||||||||
\(415\) | −2.70723e6 | −0.771622 | ||||||||
\(416\) | 73582.5 | 0.0208469 | ||||||||
\(417\) | 488861. | 0.137672 | ||||||||
\(418\) | −275578. | −0.0771442 | ||||||||
\(419\) | −1.59156e6 | −0.442881 | −0.221440 | − | 0.975174i | \(-0.571076\pi\) | ||||
−0.221440 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(420\) | −658535. | −0.182161 | ||||||||
\(421\) | −2.38860e6 | −0.656808 | −0.328404 | − | 0.944537i | \(-0.606511\pi\) | ||||
−0.328404 | + | 0.944537i | \(0.606511\pi\) | |||||||
\(422\) | 3.13799e6 | 0.857770 | ||||||||
\(423\) | −225576. | −0.0612975 | ||||||||
\(424\) | 390535. | 0.105498 | ||||||||
\(425\) | 138356. | 0.0371558 | ||||||||
\(426\) | −399385. | −0.106627 | ||||||||
\(427\) | −4.58840e6 | −1.21784 | ||||||||
\(428\) | −1.18515e6 | −0.312725 | ||||||||
\(429\) | −300672. | −0.0788770 | ||||||||
\(430\) | 1.42613e6 | 0.371953 | ||||||||
\(431\) | 4.70317e6 | 1.21954 | 0.609772 | − | 0.792577i | \(-0.291261\pi\) | ||||
0.609772 | + | 0.792577i | \(0.291261\pi\) | |||||||
\(432\) | 1.01109e6 | 0.260665 | ||||||||
\(433\) | −5.44455e6 | −1.39554 | −0.697770 | − | 0.716322i | \(-0.745824\pi\) | ||||
−0.697770 | + | 0.716322i | \(0.745824\pi\) | |||||||
\(434\) | 1.25702e6 | 0.320346 | ||||||||
\(435\) | −1.83340e6 | −0.464553 | ||||||||
\(436\) | 317891. | 0.0800871 | ||||||||
\(437\) | −91693.3 | −0.0229686 | ||||||||
\(438\) | −74524.4 | −0.0185615 | ||||||||
\(439\) | 2.90009e6 | 0.718209 | 0.359105 | − | 0.933297i | \(-0.383082\pi\) | ||||
0.359105 | + | 0.933297i | \(0.383082\pi\) | |||||||
\(440\) | 635949. | 0.156600 | ||||||||
\(441\) | −1.01116e6 | −0.247584 | ||||||||
\(442\) | 63628.8 | 0.0154917 | ||||||||
\(443\) | 1.97143e6 | 0.477278 | 0.238639 | − | 0.971108i | \(-0.423299\pi\) | ||||
0.238639 | + | 0.971108i | \(0.423299\pi\) | |||||||
\(444\) | 2.07267e6 | 0.498967 | ||||||||
\(445\) | −1.49137e6 | −0.357014 | ||||||||
\(446\) | −5.03995e6 | −1.19975 | ||||||||
\(447\) | 3.55110e6 | 0.840609 | ||||||||
\(448\) | 640564. | 0.150788 | ||||||||
\(449\) | 2.31589e6 | 0.542128 | 0.271064 | − | 0.962561i | \(-0.412624\pi\) | ||||
0.271064 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(450\) | 330440. | 0.0769240 | ||||||||
\(451\) | −167108. | −0.0386862 | ||||||||
\(452\) | 460717. | 0.106069 | ||||||||
\(453\) | −3.92525e6 | −0.898714 | ||||||||
\(454\) | 5.73886e6 | 1.30673 | ||||||||
\(455\) | −280942. | −0.0636192 | ||||||||
\(456\) | −116783. | −0.0263006 | ||||||||
\(457\) | −4.45559e6 | −0.997964 | −0.498982 | − | 0.866612i | \(-0.666293\pi\) | ||||
−0.498982 | + | 0.866612i | \(0.666293\pi\) | |||||||
\(458\) | 824762. | 0.183724 | ||||||||
\(459\) | 874321. | 0.193704 | ||||||||
\(460\) | 211600. | 0.0466252 | ||||||||
\(461\) | −7.02079e6 | −1.53863 | −0.769314 | − | 0.638871i | \(-0.779402\pi\) | ||||
−0.769314 | + | 0.638871i | \(0.779402\pi\) | |||||||
\(462\) | −2.61747e6 | −0.570527 | ||||||||
\(463\) | 3.69813e6 | 0.801733 | 0.400867 | − | 0.916136i | \(-0.368709\pi\) | ||||
0.400867 | + | 0.916136i | \(0.368709\pi\) | |||||||
\(464\) | 1.78337e6 | 0.384544 | ||||||||
\(465\) | 528857. | 0.113424 | ||||||||
\(466\) | −3.49817e6 | −0.746237 | ||||||||
\(467\) | −1.73226e6 | −0.367553 | −0.183776 | − | 0.982968i | \(-0.558832\pi\) | ||||
−0.183776 | + | 0.982968i | \(0.558832\pi\) | |||||||
\(468\) | 151966. | 0.0320725 | ||||||||
\(469\) | −4.12846e6 | −0.866675 | ||||||||
\(470\) | −170664. | −0.0356366 | ||||||||
\(471\) | 2.05087e6 | 0.425977 | ||||||||
\(472\) | −1.48609e6 | −0.307037 | ||||||||
\(473\) | 5.66842e6 | 1.16495 | ||||||||
\(474\) | −363964. | −0.0744067 | ||||||||
\(475\) | −108333. | −0.0220307 | ||||||||
\(476\) | 553913. | 0.112053 | ||||||||
\(477\) | 806553. | 0.162307 | ||||||||
\(478\) | 1.64128e6 | 0.328559 | ||||||||
\(479\) | 2.57714e6 | 0.513215 | 0.256607 | − | 0.966516i | \(-0.417395\pi\) | ||||
0.256607 | + | 0.966516i | \(0.417395\pi\) | |||||||
\(480\) | 269499. | 0.0533892 | ||||||||
\(481\) | 884234. | 0.174263 | ||||||||
\(482\) | 4.93654e6 | 0.967843 | ||||||||
\(483\) | −870913. | −0.169866 | ||||||||
\(484\) | −49123.2 | −0.00953177 | ||||||||
\(485\) | −3.52065e6 | −0.679623 | ||||||||
\(486\) | 3.44066e6 | 0.660771 | ||||||||
\(487\) | 7.56663e6 | 1.44571 | 0.722854 | − | 0.691001i | \(-0.242830\pi\) | ||||
0.722854 | + | 0.691001i | \(0.242830\pi\) | |||||||
\(488\) | 1.87776e6 | 0.356935 | ||||||||
\(489\) | −3.50506e6 | −0.662862 | ||||||||
\(490\) | −765008. | −0.143938 | ||||||||
\(491\) | −522784. | −0.0978630 | −0.0489315 | − | 0.998802i | \(-0.515582\pi\) | ||||
−0.0489315 | + | 0.998802i | \(0.515582\pi\) | |||||||
\(492\) | −70816.0 | −0.0131892 | ||||||||
\(493\) | 1.54213e6 | 0.285761 | ||||||||
\(494\) | −49821.4 | −0.00918542 | ||||||||
\(495\) | 1.31339e6 | 0.240925 | ||||||||
\(496\) | −514424. | −0.0938896 | ||||||||
\(497\) | −1.48326e6 | −0.269356 | ||||||||
\(498\) | −4.55997e6 | −0.823926 | ||||||||
\(499\) | 9.66184e6 | 1.73703 | 0.868517 | − | 0.495659i | \(-0.165073\pi\) | ||||
0.868517 | + | 0.495659i | \(0.165073\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | −3.04484e6 | −0.541964 | ||||||||
\(502\) | −409612. | −0.0725459 | ||||||||
\(503\) | −3.77794e6 | −0.665787 | −0.332893 | − | 0.942964i | \(-0.608025\pi\) | ||||
−0.332893 | + | 0.942964i | \(0.608025\pi\) | |||||||
\(504\) | 1.32293e6 | 0.231984 | ||||||||
\(505\) | 1.08670e6 | 0.189619 | ||||||||
\(506\) | 841042. | 0.146030 | ||||||||
\(507\) | 3.85435e6 | 0.665934 | ||||||||
\(508\) | −1.64775e6 | −0.283291 | ||||||||
\(509\) | 3.05552e6 | 0.522747 | 0.261373 | − | 0.965238i | \(-0.415825\pi\) | ||||
0.261373 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(510\) | 233043. | 0.0396744 | ||||||||
\(511\) | −276773. | −0.0468891 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −684595. | −0.114852 | ||||||||
\(514\) | 6.93519e6 | 1.15785 | ||||||||
\(515\) | −2.98778e6 | −0.496398 | ||||||||
\(516\) | 2.40213e6 | 0.397166 | ||||||||
\(517\) | −678333. | −0.111613 | ||||||||
\(518\) | 7.69759e6 | 1.26046 | ||||||||
\(519\) | 1.26638e6 | 0.206369 | ||||||||
\(520\) | 114973. | 0.0186460 | ||||||||
\(521\) | 1.06262e7 | 1.71507 | 0.857537 | − | 0.514422i | \(-0.171993\pi\) | ||||
0.857537 | + | 0.514422i | \(0.171993\pi\) | |||||||
\(522\) | 3.68311e6 | 0.591613 | ||||||||
\(523\) | −6.76874e6 | −1.08207 | −0.541033 | − | 0.841002i | \(-0.681967\pi\) | ||||
−0.541033 | + | 0.841002i | \(0.681967\pi\) | |||||||
\(524\) | 182661. | 0.0290614 | ||||||||
\(525\) | −1.02896e6 | −0.162930 | ||||||||
\(526\) | 6395.91 | 0.00100795 | ||||||||
\(527\) | −444837. | −0.0697709 | ||||||||
\(528\) | 1.07117e6 | 0.167215 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 610211. | 0.0943605 | ||||||||
\(531\) | −3.06916e6 | −0.472370 | ||||||||
\(532\) | −433715. | −0.0664393 | ||||||||
\(533\) | −30211.3 | −0.00460629 | ||||||||
\(534\) | −2.51202e6 | −0.381214 | ||||||||
\(535\) | −1.85179e6 | −0.279710 | ||||||||
\(536\) | 1.68953e6 | 0.254012 | ||||||||
\(537\) | −984031. | −0.147256 | ||||||||
\(538\) | 719090. | 0.107109 | ||||||||
\(539\) | −3.04066e6 | −0.450813 | ||||||||
\(540\) | 1.57984e6 | 0.233146 | ||||||||
\(541\) | 1.40510e6 | 0.206402 | 0.103201 | − | 0.994661i | \(-0.467092\pi\) | ||||
0.103201 | + | 0.994661i | \(0.467092\pi\) | |||||||
\(542\) | −2.60405e6 | −0.380759 | ||||||||
\(543\) | 6.09184e6 | 0.886644 | ||||||||
\(544\) | −226683. | −0.0328414 | ||||||||
\(545\) | 496705. | 0.0716320 | ||||||||
\(546\) | −473210. | −0.0679316 | ||||||||
\(547\) | 5.89133e6 | 0.841870 | 0.420935 | − | 0.907091i | \(-0.361702\pi\) | ||||
0.420935 | + | 0.907091i | \(0.361702\pi\) | |||||||
\(548\) | −2.23179e6 | −0.317469 | ||||||||
\(549\) | 3.87804e6 | 0.549138 | ||||||||
\(550\) | 993670. | 0.140067 | ||||||||
\(551\) | −1.20749e6 | −0.169435 | ||||||||
\(552\) | 356412. | 0.0497857 | ||||||||
\(553\) | −1.35171e6 | −0.187962 | ||||||||
\(554\) | −418682. | −0.0579575 | ||||||||
\(555\) | 3.23854e6 | 0.446290 | ||||||||
\(556\) | −743000. | −0.101930 | ||||||||
\(557\) | 1.63738e6 | 0.223621 | 0.111810 | − | 0.993730i | \(-0.464335\pi\) | ||||
0.111810 | + | 0.993730i | \(0.464335\pi\) | |||||||
\(558\) | −1.06242e6 | −0.144447 | ||||||||
\(559\) | 1.02479e6 | 0.138709 | ||||||||
\(560\) | 1.00088e6 | 0.134869 | ||||||||
\(561\) | 926271. | 0.124260 | ||||||||
\(562\) | −3.80420e6 | −0.508069 | ||||||||
\(563\) | 7.94633e6 | 1.05656 | 0.528282 | − | 0.849069i | \(-0.322837\pi\) | ||||
0.528282 | + | 0.849069i | \(0.322837\pi\) | |||||||
\(564\) | −287460. | −0.0380522 | ||||||||
\(565\) | 719870. | 0.0948708 | ||||||||
\(566\) | −186847. | −0.0245157 | ||||||||
\(567\) | −1.47938e6 | −0.193251 | ||||||||
\(568\) | 607009. | 0.0789450 | ||||||||
\(569\) | −6.68375e6 | −0.865445 | −0.432722 | − | 0.901527i | \(-0.642447\pi\) | ||||
−0.432722 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(570\) | −182473. | −0.0235240 | ||||||||
\(571\) | 5.30348e6 | 0.680723 | 0.340362 | − | 0.940295i | \(-0.389451\pi\) | ||||
0.340362 | + | 0.940295i | \(0.389451\pi\) | |||||||
\(572\) | 456979. | 0.0583992 | ||||||||
\(573\) | −3.51719e6 | −0.447517 | ||||||||
\(574\) | −263001. | −0.0333179 | ||||||||
\(575\) | 330625. | 0.0417029 | ||||||||
\(576\) | −541393. | −0.0679918 | ||||||||
\(577\) | −1.06295e7 | −1.32915 | −0.664573 | − | 0.747223i | \(-0.731387\pi\) | ||||
−0.664573 | + | 0.747223i | \(0.731387\pi\) | |||||||
\(578\) | 5.48341e6 | 0.682702 | ||||||||
\(579\) | 3.76630e6 | 0.466895 | ||||||||
\(580\) | 2.78651e6 | 0.343947 | ||||||||
\(581\) | −1.69351e7 | −2.08136 | ||||||||
\(582\) | −5.93006e6 | −0.725691 | ||||||||
\(583\) | 2.42539e6 | 0.295536 | ||||||||
\(584\) | 113267. | 0.0137426 | ||||||||
\(585\) | 237447. | 0.0286865 | ||||||||
\(586\) | −2.15920e6 | −0.259747 | ||||||||
\(587\) | −560366. | −0.0671238 | −0.0335619 | − | 0.999437i | \(-0.510685\pi\) | ||||
−0.0335619 | + | 0.999437i | \(0.510685\pi\) | |||||||
\(588\) | −1.28855e6 | −0.153695 | ||||||||
\(589\) | 348308. | 0.0413690 | ||||||||
\(590\) | −2.32202e6 | −0.274622 | ||||||||
\(591\) | −2.16713e6 | −0.255221 | ||||||||
\(592\) | −3.15016e6 | −0.369427 | ||||||||
\(593\) | 9.64020e6 | 1.12577 | 0.562885 | − | 0.826535i | \(-0.309692\pi\) | ||||
0.562885 | + | 0.826535i | \(0.309692\pi\) | |||||||
\(594\) | 6.27934e6 | 0.730210 | ||||||||
\(595\) | 865489. | 0.100223 | ||||||||
\(596\) | −5.39717e6 | −0.622373 | ||||||||
\(597\) | −1.04516e7 | −1.20018 | ||||||||
\(598\) | 152051. | 0.0173875 | ||||||||
\(599\) | −1.27940e7 | −1.45693 | −0.728465 | − | 0.685083i | \(-0.759766\pi\) | ||||
−0.728465 | + | 0.685083i | \(0.759766\pi\) | |||||||
\(600\) | 421092. | 0.0477528 | ||||||||
\(601\) | −4.10663e6 | −0.463767 | −0.231883 | − | 0.972744i | \(-0.574489\pi\) | ||||
−0.231883 | + | 0.972744i | \(0.574489\pi\) | |||||||
\(602\) | 8.92117e6 | 1.00330 | ||||||||
\(603\) | 3.48930e6 | 0.390792 | ||||||||
\(604\) | 5.96582e6 | 0.665393 | ||||||||
\(605\) | −76755.1 | −0.00852548 | ||||||||
\(606\) | 1.83040e6 | 0.202472 | ||||||||
\(607\) | −606045. | −0.0667626 | −0.0333813 | − | 0.999443i | \(-0.510628\pi\) | ||||
−0.0333813 | + | 0.999443i | \(0.510628\pi\) | |||||||
\(608\) | 177493. | 0.0194725 | ||||||||
\(609\) | −1.14689e7 | −1.25307 | ||||||||
\(610\) | 2.93399e6 | 0.319253 | ||||||||
\(611\) | −122635. | −0.0132896 | ||||||||
\(612\) | −468158. | −0.0505259 | ||||||||
\(613\) | −1.12941e7 | −1.21395 | −0.606976 | − | 0.794720i | \(-0.707618\pi\) | ||||
−0.606976 | + | 0.794720i | \(0.707618\pi\) | |||||||
\(614\) | 7.78900e6 | 0.833798 | ||||||||
\(615\) | −110650. | −0.0117968 | ||||||||
\(616\) | 3.97818e6 | 0.422408 | ||||||||
\(617\) | −1.04308e7 | −1.10308 | −0.551539 | − | 0.834149i | \(-0.685959\pi\) | ||||
−0.551539 | + | 0.834149i | \(0.685959\pi\) | |||||||
\(618\) | −5.03251e6 | −0.530046 | ||||||||
\(619\) | −6.00861e6 | −0.630300 | −0.315150 | − | 0.949042i | \(-0.602055\pi\) | ||||
−0.315150 | + | 0.949042i | \(0.602055\pi\) | |||||||
\(620\) | −803788. | −0.0839774 | ||||||||
\(621\) | 2.08933e6 | 0.217410 | ||||||||
\(622\) | −9.32756e6 | −0.966700 | ||||||||
\(623\) | −9.32928e6 | −0.963003 | ||||||||
\(624\) | 193656. | 0.0199099 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.76483e6 | 0.179997 | ||||||||
\(627\) | −725272. | −0.0736770 | ||||||||
\(628\) | −3.11704e6 | −0.315386 | ||||||||
\(629\) | −2.72403e6 | −0.274527 | ||||||||
\(630\) | 2.06707e6 | 0.207493 | ||||||||
\(631\) | −1.10118e7 | −1.10099 | −0.550496 | − | 0.834838i | \(-0.685561\pi\) | ||||
−0.550496 | + | 0.834838i | \(0.685561\pi\) | |||||||
\(632\) | 553174. | 0.0550895 | ||||||||
\(633\) | 8.25864e6 | 0.819218 | ||||||||
\(634\) | −3.26350e6 | −0.322448 | ||||||||
\(635\) | −2.57461e6 | −0.253383 | ||||||||
\(636\) | 1.02782e6 | 0.100757 | ||||||||
\(637\) | −549719. | −0.0536775 | ||||||||
\(638\) | 1.10755e7 | 1.07724 | ||||||||
\(639\) | 1.25363e6 | 0.121455 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 5.54887e6 | 0.533408 | 0.266704 | − | 0.963778i | \(-0.414065\pi\) | ||||
0.266704 | + | 0.963778i | \(0.414065\pi\) | |||||||
\(642\) | −3.11909e6 | −0.298670 | ||||||||
\(643\) | −3.29092e6 | −0.313899 | −0.156949 | − | 0.987607i | \(-0.550166\pi\) | ||||
−0.156949 | + | 0.987607i | \(0.550166\pi\) | |||||||
\(644\) | 1.32366e6 | 0.125766 | ||||||||
\(645\) | 3.75333e6 | 0.355236 | ||||||||
\(646\) | 153483. | 0.0144704 | ||||||||
\(647\) | −5.30849e6 | −0.498551 | −0.249276 | − | 0.968433i | \(-0.580193\pi\) | ||||
−0.249276 | + | 0.968433i | \(0.580193\pi\) | |||||||
\(648\) | 605420. | 0.0566394 | ||||||||
\(649\) | −9.22929e6 | −0.860115 | ||||||||
\(650\) | 179645. | 0.0166775 | ||||||||
\(651\) | 3.30827e6 | 0.305948 | ||||||||
\(652\) | 5.32719e6 | 0.490772 | ||||||||
\(653\) | −3.53529e6 | −0.324445 | −0.162223 | − | 0.986754i | \(-0.551866\pi\) | ||||
−0.162223 | + | 0.986754i | \(0.551866\pi\) | |||||||
\(654\) | 836634. | 0.0764876 | ||||||||
\(655\) | 285407. | 0.0259933 | ||||||||
\(656\) | 107630. | 0.00976506 | ||||||||
\(657\) | 233924. | 0.0211427 | ||||||||
\(658\) | −1.06759e6 | −0.0961254 | ||||||||
\(659\) | −1.61264e7 | −1.44652 | −0.723260 | − | 0.690575i | \(-0.757357\pi\) | ||||
−0.723260 | + | 0.690575i | \(0.757357\pi\) | |||||||
\(660\) | 1.67370e6 | 0.149561 | ||||||||
\(661\) | 8.53766e6 | 0.760038 | 0.380019 | − | 0.924979i | \(-0.375917\pi\) | ||||
0.380019 | + | 0.924979i | \(0.375917\pi\) | |||||||
\(662\) | −8.44221e6 | −0.748706 | ||||||||
\(663\) | 167460. | 0.0147954 | ||||||||
\(664\) | 6.93050e6 | 0.610021 | ||||||||
\(665\) | −677679. | −0.0594251 | ||||||||
\(666\) | −6.50587e6 | −0.568355 | ||||||||
\(667\) | 3.68516e6 | 0.320732 | ||||||||
\(668\) | 4.62773e6 | 0.401261 | ||||||||
\(669\) | −1.32643e7 | −1.14582 | ||||||||
\(670\) | 2.63989e6 | 0.227195 | ||||||||
\(671\) | 1.16617e7 | 0.999896 | ||||||||
\(672\) | 1.68585e6 | 0.144011 | ||||||||
\(673\) | −2.02365e7 | −1.72226 | −0.861128 | − | 0.508388i | \(-0.830242\pi\) | ||||
−0.861128 | + | 0.508388i | \(0.830242\pi\) | |||||||
\(674\) | 4.55279e6 | 0.386036 | ||||||||
\(675\) | 2.46849e6 | 0.208532 | ||||||||
\(676\) | −5.85807e6 | −0.493047 | ||||||||
\(677\) | −1.31785e7 | −1.10508 | −0.552542 | − | 0.833485i | \(-0.686342\pi\) | ||||
−0.552542 | + | 0.833485i | \(0.686342\pi\) | |||||||
\(678\) | 1.21252e6 | 0.101302 | ||||||||
\(679\) | −2.20234e7 | −1.83320 | ||||||||
\(680\) | −354192. | −0.0293743 | ||||||||
\(681\) | 1.51037e7 | 1.24800 | ||||||||
\(682\) | −3.19480e6 | −0.263016 | ||||||||
\(683\) | −1.61463e7 | −1.32441 | −0.662205 | − | 0.749323i | \(-0.730379\pi\) | ||||
−0.662205 | + | 0.749323i | \(0.730379\pi\) | |||||||
\(684\) | 366568. | 0.0299581 | ||||||||
\(685\) | −3.48717e6 | −0.283953 | ||||||||
\(686\) | 5.72811e6 | 0.464731 | ||||||||
\(687\) | 2.17063e6 | 0.175466 | ||||||||
\(688\) | −3.65090e6 | −0.294055 | ||||||||
\(689\) | 438485. | 0.0351890 | ||||||||
\(690\) | 556894. | 0.0445297 | ||||||||
\(691\) | −7.39037e6 | −0.588805 | −0.294402 | − | 0.955682i | \(-0.595121\pi\) | ||||
−0.294402 | + | 0.955682i | \(0.595121\pi\) | |||||||
\(692\) | −1.92471e6 | −0.152792 | ||||||||
\(693\) | 8.21594e6 | 0.649867 | ||||||||
\(694\) | 5.33022e6 | 0.420094 | ||||||||
\(695\) | −1.16094e6 | −0.0911689 | ||||||||
\(696\) | 4.69351e6 | 0.367261 | ||||||||
\(697\) | 93070.9 | 0.00725658 | ||||||||
\(698\) | −1.08956e7 | −0.846471 | ||||||||
\(699\) | −9.20658e6 | −0.712698 | ||||||||
\(700\) | 1.56388e6 | 0.120631 | ||||||||
\(701\) | 2.20579e7 | 1.69538 | 0.847692 | − | 0.530488i | \(-0.177991\pi\) | ||||
0.847692 | + | 0.530488i | \(0.177991\pi\) | |||||||
\(702\) | 1.13524e6 | 0.0869448 | ||||||||
\(703\) | 2.13292e6 | 0.162774 | ||||||||
\(704\) | −1.62803e6 | −0.123803 | ||||||||
\(705\) | −449156. | −0.0340349 | ||||||||
\(706\) | −1.74481e7 | −1.31746 | ||||||||
\(707\) | 6.79787e6 | 0.511475 | ||||||||
\(708\) | −3.91113e6 | −0.293237 | ||||||||
\(709\) | −7.51982e6 | −0.561813 | −0.280906 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280906 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(710\) | 948452. | 0.0706105 | ||||||||
\(711\) | 1.14244e6 | 0.0847540 | ||||||||
\(712\) | 3.81791e6 | 0.282245 | ||||||||
\(713\) | −1.06301e6 | −0.0783093 | ||||||||
\(714\) | 1.45780e6 | 0.107017 | ||||||||
\(715\) | 714030. | 0.0522338 | ||||||||
\(716\) | 1.49559e6 | 0.109026 | ||||||||
\(717\) | 4.31957e6 | 0.313792 | ||||||||
\(718\) | −1.31192e7 | −0.949721 | ||||||||
\(719\) | −1.09180e7 | −0.787628 | −0.393814 | − | 0.919190i | \(-0.628845\pi\) | ||||
−0.393814 | + | 0.919190i | \(0.628845\pi\) | |||||||
\(720\) | −845927. | −0.0608137 | ||||||||
\(721\) | −1.86901e7 | −1.33897 | ||||||||
\(722\) | 9.78422e6 | 0.698527 | ||||||||
\(723\) | 1.29921e7 | 0.924344 | ||||||||
\(724\) | −9.25874e6 | −0.656456 | ||||||||
\(725\) | 4.35393e6 | 0.307635 | ||||||||
\(726\) | −129284. | −0.00910337 | ||||||||
\(727\) | 2.27274e7 | 1.59483 | 0.797414 | − | 0.603432i | \(-0.206201\pi\) | ||||
0.797414 | + | 0.603432i | \(0.206201\pi\) | |||||||
\(728\) | 719212. | 0.0502954 | ||||||||
\(729\) | 1.13539e7 | 0.791274 | ||||||||
\(730\) | 176979. | 0.0122918 | ||||||||
\(731\) | −3.15703e6 | −0.218517 | ||||||||
\(732\) | 4.94192e6 | 0.340893 | ||||||||
\(733\) | −1.86812e7 | −1.28423 | −0.642117 | − | 0.766607i | \(-0.721944\pi\) | ||||
−0.642117 | + | 0.766607i | \(0.721944\pi\) | |||||||
\(734\) | 4.63159e6 | 0.317314 | ||||||||
\(735\) | −2.01337e6 | −0.137469 | ||||||||
\(736\) | −541696. | −0.0368605 | ||||||||
\(737\) | 1.04927e7 | 0.711573 | ||||||||
\(738\) | 222284. | 0.0150234 | ||||||||
\(739\) | −2.04129e6 | −0.137497 | −0.0687486 | − | 0.997634i | \(-0.521901\pi\) | ||||
−0.0687486 | + | 0.997634i | \(0.521901\pi\) | |||||||
\(740\) | −4.92212e6 | −0.330425 | ||||||||
\(741\) | −131121. | −0.00877258 | ||||||||
\(742\) | 3.81718e6 | 0.254526 | ||||||||
\(743\) | −4.75711e6 | −0.316134 | −0.158067 | − | 0.987428i | \(-0.550526\pi\) | ||||
−0.158067 | + | 0.987428i | \(0.550526\pi\) | |||||||
\(744\) | −1.35387e6 | −0.0896697 | ||||||||
\(745\) | −8.43308e6 | −0.556667 | ||||||||
\(746\) | −1.67657e7 | −1.10300 | ||||||||
\(747\) | 1.43132e7 | 0.938504 | ||||||||
\(748\) | −1.40780e6 | −0.0919999 | ||||||||
\(749\) | −1.15839e7 | −0.754483 | ||||||||
\(750\) | 657956. | 0.0427114 | ||||||||
\(751\) | 1.92465e7 | 1.24524 | 0.622619 | − | 0.782525i | \(-0.286069\pi\) | ||||
0.622619 | + | 0.782525i | \(0.286069\pi\) | |||||||
\(752\) | 436899. | 0.0281732 | ||||||||
\(753\) | −1.07803e6 | −0.0692854 | ||||||||
\(754\) | 2.00233e6 | 0.128265 | ||||||||
\(755\) | 9.32160e6 | 0.595145 | ||||||||
\(756\) | 9.88267e6 | 0.628883 | ||||||||
\(757\) | 2.32757e7 | 1.47626 | 0.738131 | − | 0.674658i | \(-0.235709\pi\) | ||||
0.738131 | + | 0.674658i | \(0.235709\pi\) | |||||||
\(758\) | −1.75073e7 | −1.10674 | ||||||||
\(759\) | 2.21347e6 | 0.139467 | ||||||||
\(760\) | 277333. | 0.0174168 | ||||||||
\(761\) | −1.23815e7 | −0.775019 | −0.387509 | − | 0.921866i | \(-0.626665\pi\) | ||||
−0.387509 | + | 0.921866i | \(0.626665\pi\) | |||||||
\(762\) | −4.33659e6 | −0.270558 | ||||||||
\(763\) | 3.10714e6 | 0.193219 | ||||||||
\(764\) | 5.34564e6 | 0.331334 | ||||||||
\(765\) | −731496. | −0.0451917 | ||||||||
\(766\) | −1.16355e7 | −0.716495 | ||||||||
\(767\) | −1.66855e6 | −0.102412 | ||||||||
\(768\) | −689917. | −0.0422079 | ||||||||
\(769\) | −3.09591e7 | −1.88787 | −0.943936 | − | 0.330128i | \(-0.892908\pi\) | ||||
−0.943936 | + | 0.330128i | \(0.892908\pi\) | |||||||
\(770\) | 6.21591e6 | 0.377814 | ||||||||
\(771\) | 1.82522e7 | 1.10581 | ||||||||
\(772\) | −5.72425e6 | −0.345681 | ||||||||
\(773\) | 2.73438e7 | 1.64593 | 0.822963 | − | 0.568094i | \(-0.192319\pi\) | ||||
0.822963 | + | 0.568094i | \(0.192319\pi\) | |||||||
\(774\) | −7.54002e6 | −0.452397 | ||||||||
\(775\) | −1.25592e6 | −0.0751117 | ||||||||
\(776\) | 9.01286e6 | 0.537289 | ||||||||
\(777\) | 2.02587e7 | 1.20381 | ||||||||
\(778\) | −2.89498e6 | −0.171473 | ||||||||
\(779\) | −72874.7 | −0.00430262 | ||||||||
\(780\) | 302588. | 0.0178080 | ||||||||
\(781\) | 3.76979e6 | 0.221152 | ||||||||
\(782\) | −468419. | −0.0273916 | ||||||||
\(783\) | 2.75140e7 | 1.60379 | ||||||||
\(784\) | 1.95842e6 | 0.113793 | ||||||||
\(785\) | −4.87037e6 | −0.282090 | ||||||||
\(786\) | 480730. | 0.0277553 | ||||||||
\(787\) | 1.78586e7 | 1.02781 | 0.513903 | − | 0.857848i | \(-0.328199\pi\) | ||||
0.513903 | + | 0.857848i | \(0.328199\pi\) | |||||||
\(788\) | 3.29373e6 | 0.188961 | ||||||||
\(789\) | 16832.9 | 0.000962645 0 | ||||||||
\(790\) | 864334. | 0.0492735 | ||||||||
\(791\) | 4.50315e6 | 0.255903 | ||||||||
\(792\) | −3.36229e6 | −0.190468 | ||||||||
\(793\) | 2.10831e6 | 0.119056 | ||||||||
\(794\) | 8.23277e6 | 0.463441 | ||||||||
\(795\) | 1.60597e6 | 0.0901195 | ||||||||
\(796\) | 1.58850e7 | 0.888594 | ||||||||
\(797\) | −8.37462e6 | −0.467003 | −0.233501 | − | 0.972356i | \(-0.575018\pi\) | ||||
−0.233501 | + | 0.972356i | \(0.575018\pi\) | |||||||
\(798\) | −1.14146e6 | −0.0634532 | ||||||||
\(799\) | 377798. | 0.0209360 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 7.88494e6 | 0.434227 | ||||||||
\(802\) | 1.67119e6 | 0.0917468 | ||||||||
\(803\) | 703435. | 0.0384977 | ||||||||
\(804\) | 4.44654e6 | 0.242595 | ||||||||
\(805\) | 2.06823e6 | 0.112489 | ||||||||
\(806\) | −577585. | −0.0313169 | ||||||||
\(807\) | 1.89252e6 | 0.102295 | ||||||||
\(808\) | −2.78196e6 | −0.149907 | ||||||||
\(809\) | −5.71291e6 | −0.306892 | −0.153446 | − | 0.988157i | \(-0.549037\pi\) | ||||
−0.153446 | + | 0.988157i | \(0.549037\pi\) | |||||||
\(810\) | 945968. | 0.0506599 | ||||||||
\(811\) | 1.92032e6 | 0.102523 | 0.0512616 | − | 0.998685i | \(-0.483676\pi\) | ||||
0.0512616 | + | 0.998685i | \(0.483676\pi\) | |||||||
\(812\) | 1.74310e7 | 0.927755 | ||||||||
\(813\) | −6.85339e6 | −0.363646 | ||||||||
\(814\) | −1.95639e7 | −1.03489 | ||||||||
\(815\) | 8.32374e6 | 0.438959 | ||||||||
\(816\) | −596590. | −0.0313654 | ||||||||
\(817\) | 2.47196e6 | 0.129565 | ||||||||
\(818\) | −8.49136e6 | −0.443705 | ||||||||
\(819\) | 1.48535e6 | 0.0773785 | ||||||||
\(820\) | 168172. | 0.00873414 | ||||||||
\(821\) | 8.63223e6 | 0.446956 | 0.223478 | − | 0.974709i | \(-0.428259\pi\) | ||||
0.223478 | + | 0.974709i | \(0.428259\pi\) | |||||||
\(822\) | −5.87367e6 | −0.303201 | ||||||||
\(823\) | 2.49722e7 | 1.28516 | 0.642580 | − | 0.766218i | \(-0.277864\pi\) | ||||
0.642580 | + | 0.766218i | \(0.277864\pi\) | |||||||
\(824\) | 7.64871e6 | 0.392437 | ||||||||
\(825\) | 2.61516e6 | 0.133772 | ||||||||
\(826\) | −1.45254e7 | −0.740761 | ||||||||
\(827\) | 2.77371e7 | 1.41025 | 0.705127 | − | 0.709081i | \(-0.250890\pi\) | ||||
0.705127 | + | 0.709081i | \(0.250890\pi\) | |||||||
\(828\) | −1.11874e6 | −0.0567091 | ||||||||
\(829\) | 1.15754e6 | 0.0584991 | 0.0292496 | − | 0.999572i | \(-0.490688\pi\) | ||||
0.0292496 | + | 0.999572i | \(0.490688\pi\) | |||||||
\(830\) | 1.08289e7 | 0.545619 | ||||||||
\(831\) | −1.10190e6 | −0.0553526 | ||||||||
\(832\) | −294330. | −0.0147410 | ||||||||
\(833\) | 1.69350e6 | 0.0845615 | ||||||||
\(834\) | −1.95544e6 | −0.0973488 | ||||||||
\(835\) | 7.23083e6 | 0.358899 | ||||||||
\(836\) | 1.10231e6 | 0.0545492 | ||||||||
\(837\) | −7.93658e6 | −0.391579 | ||||||||
\(838\) | 6.36622e6 | 0.313164 | ||||||||
\(839\) | 1.00284e7 | 0.491846 | 0.245923 | − | 0.969289i | \(-0.420909\pi\) | ||||
0.245923 | + | 0.969289i | \(0.420909\pi\) | |||||||
\(840\) | 2.63414e6 | 0.128807 | ||||||||
\(841\) | 2.80180e7 | 1.36599 | ||||||||
\(842\) | 9.55440e6 | 0.464433 | ||||||||
\(843\) | −1.00120e7 | −0.485234 | ||||||||
\(844\) | −1.25520e7 | −0.606535 | ||||||||
\(845\) | −9.15324e6 | −0.440994 | ||||||||
\(846\) | 902306. | 0.0433439 | ||||||||
\(847\) | −480142. | −0.0229965 | ||||||||
\(848\) | −1.56214e6 | −0.0745985 | ||||||||
\(849\) | −491748. | −0.0234139 | ||||||||
\(850\) | −553426. | −0.0262731 | ||||||||
\(851\) | −6.50951e6 | −0.308123 | ||||||||
\(852\) | 1.59754e6 | 0.0753968 | ||||||||
\(853\) | 5.61703e6 | 0.264323 | 0.132161 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132161 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(854\) | 1.83536e7 | 0.861146 | ||||||||
\(855\) | 572763. | 0.0267954 | ||||||||
\(856\) | 4.74058e6 | 0.221130 | ||||||||
\(857\) | 1.85480e7 | 0.862670 | 0.431335 | − | 0.902192i | \(-0.358043\pi\) | ||||
0.431335 | + | 0.902192i | \(0.358043\pi\) | |||||||
\(858\) | 1.20269e6 | 0.0557744 | ||||||||
\(859\) | −5.66092e6 | −0.261761 | −0.130880 | − | 0.991398i | \(-0.541780\pi\) | ||||
−0.130880 | + | 0.991398i | \(0.541780\pi\) | |||||||
\(860\) | −5.70453e6 | −0.263011 | ||||||||
\(861\) | −692172. | −0.0318204 | ||||||||
\(862\) | −1.88127e7 | −0.862348 | ||||||||
\(863\) | 2.77686e7 | 1.26919 | 0.634596 | − | 0.772844i | \(-0.281166\pi\) | ||||
0.634596 | + | 0.772844i | \(0.281166\pi\) | |||||||
\(864\) | −4.04438e6 | −0.184318 | ||||||||
\(865\) | −3.00737e6 | −0.136661 | ||||||||
\(866\) | 2.17782e7 | 0.986795 | ||||||||
\(867\) | 1.44314e7 | 0.652018 | ||||||||
\(868\) | −5.02810e6 | −0.226519 | ||||||||
\(869\) | 3.43545e6 | 0.154324 | ||||||||
\(870\) | 7.33361e6 | 0.328488 | ||||||||
\(871\) | 1.89697e6 | 0.0847257 | ||||||||
\(872\) | −1.27157e6 | −0.0566301 | ||||||||
\(873\) | 1.86138e7 | 0.826609 | ||||||||
\(874\) | 366773. | 0.0162412 | ||||||||
\(875\) | 2.44356e6 | 0.107895 | ||||||||
\(876\) | 298098. | 0.0131250 | ||||||||
\(877\) | −2.09926e7 | −0.921653 | −0.460827 | − | 0.887490i | \(-0.652447\pi\) | ||||
−0.460827 | + | 0.887490i | \(0.652447\pi\) | |||||||
\(878\) | −1.16004e7 | −0.507850 | ||||||||
\(879\) | −5.68264e6 | −0.248072 | ||||||||
\(880\) | −2.54380e6 | −0.110733 | ||||||||
\(881\) | −1.66100e7 | −0.720992 | −0.360496 | − | 0.932761i | \(-0.617393\pi\) | ||||
−0.360496 | + | 0.932761i | \(0.617393\pi\) | |||||||
\(882\) | 4.04463e6 | 0.175068 | ||||||||
\(883\) | −4.19946e7 | −1.81256 | −0.906280 | − | 0.422679i | \(-0.861090\pi\) | ||||
−0.906280 | + | 0.422679i | \(0.861090\pi\) | |||||||
\(884\) | −254515. | −0.0109543 | ||||||||
\(885\) | −6.11115e6 | −0.262280 | ||||||||
\(886\) | −7.88570e6 | −0.337486 | ||||||||
\(887\) | −3.01036e7 | −1.28472 | −0.642361 | − | 0.766402i | \(-0.722045\pi\) | ||||
−0.642361 | + | 0.766402i | \(0.722045\pi\) | |||||||
\(888\) | −8.29066e6 | −0.352823 | ||||||||
\(889\) | −1.61055e7 | −0.683470 | ||||||||
\(890\) | 5.96548e6 | 0.252447 | ||||||||
\(891\) | 3.75992e6 | 0.158666 | ||||||||
\(892\) | 2.01598e7 | 0.848349 | ||||||||
\(893\) | −295817. | −0.0124135 | ||||||||
\(894\) | −1.42044e7 | −0.594401 | ||||||||
\(895\) | 2.33686e6 | 0.0975157 | ||||||||
\(896\) | −2.56225e6 | −0.106623 | ||||||||
\(897\) | 400172. | 0.0166060 | ||||||||
\(898\) | −9.26356e6 | −0.383343 | ||||||||
\(899\) | −1.39985e7 | −0.577675 | ||||||||
\(900\) | −1.32176e6 | −0.0543935 | ||||||||
\(901\) | −1.35083e6 | −0.0554354 | ||||||||
\(902\) | 668431. | 0.0273552 | ||||||||
\(903\) | 2.34789e7 | 0.958207 | ||||||||
\(904\) | −1.84287e6 | −0.0750020 | ||||||||
\(905\) | −1.44668e7 | −0.587152 | ||||||||
\(906\) | 1.57010e7 | 0.635487 | ||||||||
\(907\) | −2.41762e7 | −0.975818 | −0.487909 | − | 0.872894i | \(-0.662240\pi\) | ||||
−0.487909 | + | 0.872894i | \(0.662240\pi\) | |||||||
\(908\) | −2.29554e7 | −0.923997 | ||||||||
\(909\) | −5.74544e6 | −0.230629 | ||||||||
\(910\) | 1.12377e6 | 0.0449856 | ||||||||
\(911\) | 2.73957e7 | 1.09367 | 0.546834 | − | 0.837241i | \(-0.315833\pi\) | ||||
0.546834 | + | 0.837241i | \(0.315833\pi\) | |||||||
\(912\) | 467131. | 0.0185974 | ||||||||
\(913\) | 4.30415e7 | 1.70887 | ||||||||
\(914\) | 1.78224e7 | 0.705667 | ||||||||
\(915\) | 7.72175e6 | 0.304904 | ||||||||
\(916\) | −3.29905e6 | −0.129912 | ||||||||
\(917\) | 1.78537e6 | 0.0701138 | ||||||||
\(918\) | −3.49729e6 | −0.136970 | ||||||||
\(919\) | 2.81548e7 | 1.09967 | 0.549837 | − | 0.835272i | \(-0.314690\pi\) | ||||
0.549837 | + | 0.835272i | \(0.314690\pi\) | |||||||
\(920\) | −846400. | −0.0329690 | ||||||||
\(921\) | 2.04993e7 | 0.796323 | ||||||||
\(922\) | 2.80831e7 | 1.08797 | ||||||||
\(923\) | 681538. | 0.0263321 | ||||||||
\(924\) | 1.04699e7 | 0.403424 | ||||||||
\(925\) | −7.69082e6 | −0.295541 | ||||||||
\(926\) | −1.47925e7 | −0.566911 | ||||||||
\(927\) | 1.57965e7 | 0.603757 | ||||||||
\(928\) | −7.13348e6 | −0.271914 | ||||||||
\(929\) | 2.61544e6 | 0.0994272 | 0.0497136 | − | 0.998764i | \(-0.484169\pi\) | ||||
0.0497136 | + | 0.998764i | \(0.484169\pi\) | |||||||
\(930\) | −2.11543e6 | −0.0802031 | ||||||||
\(931\) | −1.32601e6 | −0.0501388 | ||||||||
\(932\) | 1.39927e7 | 0.527669 | ||||||||
\(933\) | −2.45485e7 | −0.923252 | ||||||||
\(934\) | 6.92903e6 | 0.259899 | ||||||||
\(935\) | −2.19969e6 | −0.0822872 | ||||||||
\(936\) | −607866. | −0.0226787 | ||||||||
\(937\) | 4.13839e7 | 1.53986 | 0.769932 | − | 0.638126i | \(-0.220290\pi\) | ||||
0.769932 | + | 0.638126i | \(0.220290\pi\) | |||||||
\(938\) | 1.65138e7 | 0.612831 | ||||||||
\(939\) | 4.64471e6 | 0.171908 | ||||||||
\(940\) | 682654. | 0.0251989 | ||||||||
\(941\) | −3.00692e7 | −1.10700 | −0.553500 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553500 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(942\) | −8.20349e6 | −0.301211 | ||||||||
\(943\) | 222408. | 0.00814463 | ||||||||
\(944\) | 5.94437e6 | 0.217108 | ||||||||
\(945\) | 1.54417e7 | 0.562490 | ||||||||
\(946\) | −2.26737e7 | −0.823747 | ||||||||
\(947\) | −1.33174e7 | −0.482551 | −0.241276 | − | 0.970457i | \(-0.577566\pi\) | ||||
−0.241276 | + | 0.970457i | \(0.577566\pi\) | |||||||
\(948\) | 1.45586e6 | 0.0526135 | ||||||||
\(949\) | 127173. | 0.00458385 | ||||||||
\(950\) | 433333. | 0.0155780 | ||||||||
\(951\) | −8.58895e6 | −0.307956 | ||||||||
\(952\) | −2.21565e6 | −0.0792336 | ||||||||
\(953\) | 3.89545e7 | 1.38939 | 0.694697 | − | 0.719302i | \(-0.255538\pi\) | ||||
0.694697 | + | 0.719302i | \(0.255538\pi\) | |||||||
\(954\) | −3.22621e6 | −0.114768 | ||||||||
\(955\) | 8.35256e6 | 0.296354 | ||||||||
\(956\) | −6.56513e6 | −0.232326 | ||||||||
\(957\) | 2.91488e7 | 1.02882 | ||||||||
\(958\) | −1.03086e7 | −0.362898 | ||||||||
\(959\) | −2.18140e7 | −0.765929 | ||||||||
\(960\) | −1.07799e6 | −0.0377519 | ||||||||
\(961\) | −2.45912e7 | −0.858956 | ||||||||
\(962\) | −3.53694e6 | −0.123222 | ||||||||
\(963\) | 9.79050e6 | 0.340204 | ||||||||
\(964\) | −1.97462e7 | −0.684368 | ||||||||
\(965\) | −8.94414e6 | −0.309186 | ||||||||
\(966\) | 3.48365e6 | 0.120114 | ||||||||
\(967\) | −1.83987e7 | −0.632734 | −0.316367 | − | 0.948637i | \(-0.602463\pi\) | ||||
−0.316367 | + | 0.948637i | \(0.602463\pi\) | |||||||
\(968\) | 196493. | 0.00673998 | ||||||||
\(969\) | 403941. | 0.0138200 | ||||||||
\(970\) | 1.40826e7 | 0.480566 | ||||||||
\(971\) | 9.56759e6 | 0.325653 | 0.162826 | − | 0.986655i | \(-0.447939\pi\) | ||||
0.162826 | + | 0.986655i | \(0.447939\pi\) | |||||||
\(972\) | −1.37626e7 | −0.467236 | ||||||||
\(973\) | −7.26225e6 | −0.245917 | ||||||||
\(974\) | −3.02665e7 | −1.02227 | ||||||||
\(975\) | 472793. | 0.0159279 | ||||||||
\(976\) | −7.51102e6 | −0.252391 | ||||||||
\(977\) | −2.84840e7 | −0.954695 | −0.477347 | − | 0.878715i | \(-0.658402\pi\) | ||||
−0.477347 | + | 0.878715i | \(0.658402\pi\) | |||||||
\(978\) | 1.40202e7 | 0.468714 | ||||||||
\(979\) | 2.37109e7 | 0.790662 | ||||||||
\(980\) | 3.06003e6 | 0.101780 | ||||||||
\(981\) | −2.62610e6 | −0.0871242 | ||||||||
\(982\) | 2.09114e6 | 0.0691996 | ||||||||
\(983\) | −1.41641e7 | −0.467527 | −0.233763 | − | 0.972294i | \(-0.575104\pi\) | ||||
−0.233763 | + | 0.972294i | \(0.575104\pi\) | |||||||
\(984\) | 283264. | 0.00932618 | ||||||||
\(985\) | 5.14646e6 | 0.169012 | ||||||||
\(986\) | −6.16851e6 | −0.202064 | ||||||||
\(987\) | −2.80970e6 | −0.0918051 | ||||||||
\(988\) | 199286. | 0.00649507 | ||||||||
\(989\) | −7.54424e6 | −0.245259 | ||||||||
\(990\) | −5.25358e6 | −0.170360 | ||||||||
\(991\) | 9.12692e6 | 0.295216 | 0.147608 | − | 0.989046i | \(-0.452843\pi\) | ||||
0.147608 | + | 0.989046i | \(0.452843\pi\) | |||||||
\(992\) | 2.05770e6 | 0.0663899 | ||||||||
\(993\) | −2.22184e7 | −0.715055 | ||||||||
\(994\) | 5.93304e6 | 0.190463 | ||||||||
\(995\) | 2.48202e7 | 0.794783 | ||||||||
\(996\) | 1.82399e7 | 0.582604 | ||||||||
\(997\) | −2.74140e7 | −0.873442 | −0.436721 | − | 0.899597i | \(-0.643860\pi\) | ||||
−0.436721 | + | 0.899597i | \(0.643860\pi\) | |||||||
\(998\) | −3.86474e7 | −1.22827 | ||||||||
\(999\) | −4.86009e7 | −1.54074 |
(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 | 230.6.a.c.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.6.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |