Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.16 | ||
Root | \(-8.95007 - 5.16733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.c.146.2 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.3347i | 1.82693i | 0.406922 | + | 0.913463i | \(0.366602\pi\) | ||||
−0.406922 | + | 0.913463i | \(0.633398\pi\) | |||||||
\(3\) | 12.5210 | − | 9.28579i | 0.803219 | − | 0.595683i | ||||
\(4\) | −74.8050 | −2.33766 | ||||||||
\(5\) | 31.7408 | 0.567798 | 0.283899 | − | 0.958854i | \(-0.408372\pi\) | ||||
0.283899 | + | 0.958854i | \(0.408372\pi\) | |||||||
\(6\) | 95.9654 | + | 129.400i | 1.08827 | + | 1.46742i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 442.375i | − | 2.44380i | ||||||
\(9\) | 70.5484 | − | 232.534i | 0.290323 | − | 0.956929i | ||||
\(10\) | 328.031i | 1.03732i | ||||||||
\(11\) | 453.489i | 1.13002i | 0.825085 | + | 0.565008i | \(0.191127\pi\) | ||||
−0.825085 | + | 0.565008i | \(0.808873\pi\) | |||||||
\(12\) | −936.630 | + | 694.623i | −1.87765 | + | 1.39250i | ||||
\(13\) | 551.786i | 0.905550i | 0.891625 | + | 0.452775i | \(0.149566\pi\) | ||||
−0.891625 | + | 0.452775i | \(0.850434\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 397.426 | − | 294.739i | 0.456066 | − | 0.338228i | ||||
\(16\) | 2178.03 | 2.12698 | ||||||||
\(17\) | 538.161 | 0.451637 | 0.225819 | − | 0.974169i | \(-0.427494\pi\) | ||||
0.225819 | + | 0.974169i | \(0.427494\pi\) | |||||||
\(18\) | 2403.15 | + | 729.093i | 1.74824 | + | 0.530398i | ||||
\(19\) | 1366.77i | 0.868586i | 0.900772 | + | 0.434293i | \(0.143002\pi\) | ||||
−0.900772 | + | 0.434293i | \(0.856998\pi\) | |||||||
\(20\) | −2374.38 | −1.32732 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4686.65 | −2.06446 | ||||||||
\(23\) | 3237.97i | 1.27630i | 0.769912 | + | 0.638150i | \(0.220300\pi\) | ||||
−0.769912 | + | 0.638150i | \(0.779700\pi\) | |||||||
\(24\) | −4107.80 | − | 5538.96i | −1.45573 | − | 1.96291i | ||||
\(25\) | −2117.52 | −0.677606 | ||||||||
\(26\) | −5702.52 | −1.65437 | ||||||||
\(27\) | −1275.93 | − | 3566.64i | −0.336834 | − | 0.941564i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1604.88i | 0.354363i | 0.984178 | + | 0.177181i | \(0.0566979\pi\) | ||||
−0.984178 | + | 0.177181i | \(0.943302\pi\) | |||||||
\(30\) | 3046.02 | + | 4107.25i | 0.617917 | + | 0.833199i | ||||
\(31\) | 7069.92i | 1.32133i | 0.750683 | + | 0.660663i | \(0.229725\pi\) | ||||
−0.750683 | + | 0.660663i | \(0.770275\pi\) | |||||||
\(32\) | 8353.19i | 1.44204i | ||||||||
\(33\) | 4211.00 | + | 5678.11i | 0.673132 | + | 0.907651i | ||||
\(34\) | 5561.71i | 0.825108i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5277.37 | + | 17394.7i | −0.678675 | + | 2.23697i | ||||
\(37\) | −1951.06 | −0.234297 | −0.117149 | − | 0.993114i | \(-0.537375\pi\) | ||||
−0.117149 | + | 0.993114i | \(0.537375\pi\) | |||||||
\(38\) | −14125.1 | −1.58684 | ||||||||
\(39\) | 5123.77 | + | 6908.89i | 0.539421 | + | 0.727355i | ||||
\(40\) | − | 14041.4i | − | 1.38758i | ||||||
\(41\) | 1800.47 | 0.167273 | 0.0836365 | − | 0.996496i | \(-0.473347\pi\) | ||||
0.0836365 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7882.36 | 0.650107 | 0.325054 | − | 0.945696i | \(-0.394618\pi\) | ||||
0.325054 | + | 0.945696i | \(0.394618\pi\) | |||||||
\(44\) | − | 33923.2i | − | 2.64159i | ||||||
\(45\) | 2239.27 | − | 7380.82i | 0.164844 | − | 0.543342i | ||||
\(46\) | −33463.3 | −2.33170 | ||||||||
\(47\) | −6090.22 | −0.402150 | −0.201075 | − | 0.979576i | \(-0.564444\pi\) | ||||
−0.201075 | + | 0.979576i | \(0.564444\pi\) | |||||||
\(48\) | 27271.0 | − | 20224.7i | 1.70843 | − | 1.26701i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 21883.8i | − | 1.23794i | ||||||
\(51\) | 6738.29 | − | 4997.25i | 0.362764 | − | 0.269033i | ||||
\(52\) | − | 41276.4i | − | 2.11687i | ||||||
\(53\) | − | 14177.9i | − | 0.693302i | −0.937994 | − | 0.346651i | \(-0.887319\pi\) | ||
0.937994 | − | 0.346651i | \(-0.112681\pi\) | |||||||
\(54\) | 36860.0 | − | 13186.2i | 1.72017 | − | 0.615370i | ||||
\(55\) | 14394.1i | 0.641621i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12691.6 | + | 17113.3i | 0.517402 | + | 0.697665i | ||||
\(58\) | −16585.9 | −0.647394 | ||||||||
\(59\) | 16918.9 | 0.632764 | 0.316382 | − | 0.948632i | \(-0.397532\pi\) | ||||
0.316382 | + | 0.948632i | \(0.397532\pi\) | |||||||
\(60\) | −29729.4 | + | 22047.9i | −1.06613 | + | 0.790660i | ||||
\(61\) | − | 29718.9i | − | 1.02261i | −0.859401 | − | 0.511303i | \(-0.829163\pi\) | ||
0.859401 | − | 0.511303i | \(-0.170837\pi\) | |||||||
\(62\) | −73065.1 | −2.41396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −16630.3 | −0.507518 | ||||||||
\(65\) | 17514.2i | 0.514169i | ||||||||
\(66\) | −58681.3 | + | 43519.2i | −1.65821 | + | 1.22976i | ||||
\(67\) | 13614.3 | 0.370516 | 0.185258 | − | 0.982690i | \(-0.440688\pi\) | ||||
0.185258 | + | 0.982690i | \(0.440688\pi\) | |||||||
\(68\) | −40257.1 | −1.05577 | ||||||||
\(69\) | 30067.1 | + | 40542.4i | 0.760271 | + | 1.02515i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 31338.5i | 0.737790i | 0.929471 | + | 0.368895i | \(0.120264\pi\) | ||||
−0.929471 | + | 0.368895i | \(0.879736\pi\) | |||||||
\(72\) | −102867. | − | 31208.8i | −2.33854 | − | 0.709490i | ||||
\(73\) | − | 9821.33i | − | 0.215707i | −0.994167 | − | 0.107853i | \(-0.965602\pi\) | ||
0.994167 | − | 0.107853i | \(-0.0343977\pi\) | |||||||
\(74\) | − | 20163.6i | − | 0.428044i | ||||||
\(75\) | −26513.3 | + | 19662.8i | −0.544266 | + | 0.403639i | ||||
\(76\) | − | 102242.i | − | 2.03046i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −71401.0 | + | 52952.4i | −1.32882 | + | 0.985482i | ||||
\(79\) | 99798.2 | 1.79910 | 0.899550 | − | 0.436818i | \(-0.143895\pi\) | ||||
0.899550 | + | 0.436818i | \(0.143895\pi\) | |||||||
\(80\) | 69132.6 | 1.20770 | ||||||||
\(81\) | −49094.8 | − | 32809.8i | −0.831426 | − | 0.555636i | ||||
\(82\) | 18607.2i | 0.305595i | ||||||||
\(83\) | −79557.4 | −1.26761 | −0.633804 | − | 0.773493i | \(-0.718508\pi\) | ||||
−0.633804 | + | 0.773493i | \(0.718508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17081.7 | 0.256439 | ||||||||
\(86\) | 81461.4i | 1.18770i | ||||||||
\(87\) | 14902.6 | + | 20094.6i | 0.211088 | + | 0.284631i | ||||
\(88\) | 200612. | 2.76154 | ||||||||
\(89\) | 953.735 | 0.0127630 | 0.00638150 | − | 0.999980i | \(-0.497969\pi\) | ||||
0.00638150 | + | 0.999980i | \(0.497969\pi\) | |||||||
\(90\) | 76278.2 | + | 23142.0i | 0.992645 | + | 0.301159i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 242216.i | − | 2.98355i | ||||||
\(93\) | 65649.7 | + | 88522.1i | 0.787092 | + | 1.06131i | ||||
\(94\) | − | 62940.3i | − | 0.734699i | ||||||
\(95\) | 43382.6i | 0.493181i | ||||||||
\(96\) | 77566.0 | + | 104590.i | 0.859000 | + | 1.15828i | ||||
\(97\) | 115552.i | 1.24695i | 0.781842 | + | 0.623476i | \(0.214280\pi\) | ||||
−0.781842 | + | 0.623476i | \(0.785720\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 105451. | + | 31992.9i | 1.08135 | + | 0.328069i | ||||
\(100\) | 158401. | 1.58401 | ||||||||
\(101\) | −89983.4 | −0.877726 | −0.438863 | − | 0.898554i | \(-0.644619\pi\) | ||||
−0.438863 | + | 0.898554i | \(0.644619\pi\) | |||||||
\(102\) | 51644.8 | + | 69637.9i | 0.491503 | + | 0.662743i | ||||
\(103\) | 156663.i | 1.45503i | 0.686089 | + | 0.727517i | \(0.259326\pi\) | ||||
−0.686089 | + | 0.727517i | \(0.740674\pi\) | |||||||
\(104\) | 244096. | 2.21298 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 146524. | 1.26661 | ||||||||
\(107\) | − | 139107.i | − | 1.17460i | −0.809370 | − | 0.587299i | \(-0.800191\pi\) | ||
0.809370 | − | 0.587299i | \(-0.199809\pi\) | |||||||
\(108\) | 95445.6 | + | 266803.i | 0.787402 | + | 2.20105i | ||||
\(109\) | 24226.4 | 0.195309 | 0.0976547 | − | 0.995220i | \(-0.468866\pi\) | ||||
0.0976547 | + | 0.995220i | \(0.468866\pi\) | |||||||
\(110\) | −148758. | −1.17219 | ||||||||
\(111\) | −24429.2 | + | 18117.2i | −0.188192 | + | 0.139567i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 38230.9i | 0.281655i | 0.990034 | + | 0.140828i | \(0.0449763\pi\) | ||||
−0.990034 | + | 0.140828i | \(0.955024\pi\) | |||||||
\(114\) | −176860. | + | 131163.i | −1.27458 | + | 0.945255i | ||||
\(115\) | 102776.i | 0.724680i | ||||||||
\(116\) | − | 120053.i | − | 0.828378i | ||||||
\(117\) | 128309. | + | 38927.6i | 0.866547 | + | 0.262902i | ||||
\(118\) | 174851.i | 1.15601i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −130385. | − | 175811.i | −0.826561 | − | 1.11453i | ||||
\(121\) | −44601.2 | −0.276938 | ||||||||
\(122\) | 307135. | 1.86822 | ||||||||
\(123\) | 22543.6 | − | 16718.8i | 0.134357 | − | 0.0996417i | ||||
\(124\) | − | 528865.i | − | 3.08881i | ||||||
\(125\) | −166402. | −0.952541 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −65650.6 | −0.361184 | −0.180592 | − | 0.983558i | \(-0.557801\pi\) | ||||
−0.180592 | + | 0.983558i | \(0.557801\pi\) | |||||||
\(128\) | 95433.4i | 0.514844i | ||||||||
\(129\) | 98694.6 | − | 73193.9i | 0.522179 | − | 0.387258i | ||||
\(130\) | −181003. | −0.939349 | ||||||||
\(131\) | 205595. | 1.04673 | 0.523364 | − | 0.852109i | \(-0.324677\pi\) | ||||
0.523364 | + | 0.852109i | \(0.324677\pi\) | |||||||
\(132\) | −315004. | − | 424751.i | −1.57355 | − | 2.12178i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 140699.i | 0.676905i | ||||||||
\(135\) | −40498.9 | − | 113208.i | −0.191253 | − | 0.534618i | ||||
\(136\) | − | 238069.i | − | 1.10371i | ||||||
\(137\) | − | 410472.i | − | 1.86845i | −0.356683 | − | 0.934225i | \(-0.616092\pi\) | ||
0.356683 | − | 0.934225i | \(-0.383908\pi\) | |||||||
\(138\) | −418992. | + | 310733.i | −1.87287 | + | 1.38896i | ||||
\(139\) | − | 73875.8i | − | 0.324314i | −0.986765 | − | 0.162157i | \(-0.948155\pi\) | ||
0.986765 | − | 0.162157i | \(-0.0518450\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −76255.4 | + | 56552.5i | −0.323015 | + | 0.239554i | ||||
\(142\) | −323873. | −1.34789 | ||||||||
\(143\) | −250229. | −1.02329 | ||||||||
\(144\) | 153657. | − | 506466.i | 0.617511 | − | 2.03537i | ||||
\(145\) | 50940.3i | 0.201206i | ||||||||
\(146\) | 101500. | 0.394080 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 145949. | 0.547707 | ||||||||
\(149\) | 57972.3i | 0.213922i | 0.994263 | + | 0.106961i | \(0.0341119\pi\) | ||||
−0.994263 | + | 0.106961i | \(0.965888\pi\) | |||||||
\(150\) | −203208. | − | 274006.i | −0.737418 | − | 0.994334i | ||||
\(151\) | −172435. | −0.615435 | −0.307718 | − | 0.951478i | \(-0.599565\pi\) | ||||
−0.307718 | + | 0.951478i | \(0.599565\pi\) | |||||||
\(152\) | 604627. | 2.12265 | ||||||||
\(153\) | 37966.4 | − | 125141.i | 0.131121 | − | 0.432185i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 224405.i | 0.750246i | ||||||||
\(156\) | −383284. | − | 516820.i | −1.26098 | − | 1.70031i | ||||
\(157\) | 239287.i | 0.774764i | 0.921919 | + | 0.387382i | \(0.126620\pi\) | ||||
−0.921919 | + | 0.387382i | \(0.873380\pi\) | |||||||
\(158\) | 1.03138e6i | 3.28682i | ||||||||
\(159\) | −131653. | − | 177521.i | −0.412989 | − | 0.556874i | ||||
\(160\) | 265137.i | 0.818787i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 339077. | − | 507378.i | 1.01511 | − | 1.51895i | ||||
\(163\) | 148378. | 0.437422 | 0.218711 | − | 0.975790i | \(-0.429815\pi\) | ||||
0.218711 | + | 0.975790i | \(0.429815\pi\) | |||||||
\(164\) | −134684. | −0.391027 | ||||||||
\(165\) | 133661. | + | 180228.i | 0.382203 | + | 0.515362i | ||||
\(166\) | − | 822198.i | − | 2.31583i | ||||||
\(167\) | 549931. | 1.52587 | 0.762934 | − | 0.646476i | \(-0.223758\pi\) | ||||
0.762934 | + | 0.646476i | \(0.223758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 66825.0 | 0.179979 | ||||||||
\(170\) | 176533.i | 0.468494i | ||||||||
\(171\) | 317821. | + | 96423.7i | 0.831175 | + | 0.252170i | ||||
\(172\) | −589640. | −1.51973 | ||||||||
\(173\) | 316273. | 0.803428 | 0.401714 | − | 0.915765i | \(-0.368415\pi\) | ||||
0.401714 | + | 0.915765i | \(0.368415\pi\) | |||||||
\(174\) | −207671. | + | 154013.i | −0.520000 | + | 0.385642i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 987713.i | 2.40353i | ||||||||
\(177\) | 211840. | − | 157105.i | 0.508248 | − | 0.376927i | ||||
\(178\) | 9856.52i | 0.0233170i | ||||||||
\(179\) | − | 563606.i | − | 1.31475i | −0.753564 | − | 0.657374i | \(-0.771667\pi\) | ||
0.753564 | − | 0.657374i | \(-0.228333\pi\) | |||||||
\(180\) | −167508. | + | 552122.i | −0.385350 | + | 1.27015i | ||||
\(181\) | 329274.i | 0.747069i | 0.927616 | + | 0.373535i | \(0.121854\pi\) | ||||
−0.927616 | + | 0.373535i | \(0.878146\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −275963. | − | 372109.i | −0.609149 | − | 0.821377i | ||||
\(184\) | 1.43240e6 | 3.11902 | ||||||||
\(185\) | −61928.4 | −0.133033 | ||||||||
\(186\) | −914845. | + | 678467.i | −1.93894 | + | 1.43796i | ||||
\(187\) | 244050.i | 0.510358i | ||||||||
\(188\) | 455579. | 0.940090 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −448344. | −0.901004 | ||||||||
\(191\) | − | 805475.i | − | 1.59760i | −0.601595 | − | 0.798801i | \(-0.705468\pi\) | ||
0.601595 | − | 0.798801i | \(-0.294532\pi\) | |||||||
\(192\) | −208228. | + | 154426.i | −0.407648 | + | 0.302320i | ||||
\(193\) | 635701. | 1.22846 | 0.614228 | − | 0.789128i | \(-0.289467\pi\) | ||||
0.614228 | + | 0.789128i | \(0.289467\pi\) | |||||||
\(194\) | −1.19419e6 | −2.27809 | ||||||||
\(195\) | 162633. | + | 219294.i | 0.306282 | + | 0.412991i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 137701.i | − | 0.252796i | −0.991980 | − | 0.126398i | \(-0.959658\pi\) | ||
0.991980 | − | 0.126398i | \(-0.0403417\pi\) | |||||||
\(198\) | −330636. | + | 1.08980e6i | −0.599358 | + | 1.97554i | ||||
\(199\) | − | 895559.i | − | 1.60310i | −0.597926 | − | 0.801552i | \(-0.704008\pi\) | ||
0.597926 | − | 0.801552i | \(-0.295992\pi\) | |||||||
\(200\) | 936737.i | 1.65593i | ||||||||
\(201\) | 170463. | − | 126419.i | 0.297606 | − | 0.220710i | ||||
\(202\) | − | 929947.i | − | 1.60354i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −504058. | + | 373819.i | −0.848018 | + | 0.628907i | ||||
\(205\) | 57148.4 | 0.0949772 | ||||||||
\(206\) | −1.61906e6 | −2.65824 | ||||||||
\(207\) | 752936. | + | 228433.i | 1.22133 | + | 0.370539i | ||||
\(208\) | 1.20181e6i | 1.92609i | ||||||||
\(209\) | −619817. | −0.981516 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −392533. | −0.606974 | −0.303487 | − | 0.952836i | \(-0.598151\pi\) | ||||
−0.303487 | + | 0.952836i | \(0.598151\pi\) | |||||||
\(212\) | 1.06058e6i | 1.62070i | ||||||||
\(213\) | 291003. | + | 392388.i | 0.439489 | + | 0.592607i | ||||
\(214\) | 1.43762e6 | 2.14590 | ||||||||
\(215\) | 250193. | 0.369129 | ||||||||
\(216\) | −1.57779e6 | + | 564437.i | −2.30099 | + | 0.823155i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 250372.i | 0.356816i | ||||||||
\(219\) | −91198.8 | − | 122972.i | −0.128493 | − | 0.173260i | ||||
\(220\) | − | 1.07675e6i | − | 1.49989i | ||||||
\(221\) | 296950.i | 0.408980i | ||||||||
\(222\) | −187235. | − | 252467.i | −0.254979 | − | 0.343813i | ||||
\(223\) | − | 1.01457e6i | − | 1.36622i | −0.730317 | − | 0.683109i | \(-0.760628\pi\) | ||
0.730317 | − | 0.683109i | \(-0.239372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −149388. | + | 492394.i | −0.196724 | + | 0.648421i | ||||
\(226\) | −395103. | −0.514563 | ||||||||
\(227\) | −313370. | −0.403639 | −0.201820 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201820 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(228\) | −949393. | − | 1.28016e6i | −1.20951 | − | 1.63090i | ||||
\(229\) | 450743.i | 0.567990i | 0.958826 | + | 0.283995i | \(0.0916599\pi\) | ||||
−0.958826 | + | 0.283995i | \(0.908340\pi\) | |||||||
\(230\) | −1.06215e6 | −1.32394 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 709960. | 0.865992 | ||||||||
\(233\) | − | 134459.i | − | 0.162255i | −0.996704 | − | 0.0811276i | \(-0.974148\pi\) | ||
0.996704 | − | 0.0811276i | \(-0.0258521\pi\) | |||||||
\(234\) | −402303. | + | 1.32603e6i | −0.480302 | + | 1.58312i | ||||
\(235\) | −193309. | −0.228340 | ||||||||
\(236\) | −1.26562e6 | −1.47918 | ||||||||
\(237\) | 1.24957e6 | − | 926705.i | 1.44507 | − | 1.07169i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.26368e6i | − | 1.43101i | −0.698605 | − | 0.715507i | \(-0.746196\pi\) | ||
0.698605 | − | 0.715507i | \(-0.253804\pi\) | |||||||
\(240\) | 865605. | − | 641950.i | 0.970045 | − | 0.719405i | ||||
\(241\) | − | 486586.i | − | 0.539656i | −0.962909 | − | 0.269828i | \(-0.913033\pi\) | ||
0.962909 | − | 0.269828i | \(-0.0869668\pi\) | |||||||
\(242\) | − | 460938.i | − | 0.505945i | ||||||
\(243\) | −919379. | + | 45074.9i | −0.998800 | + | 0.0489687i | ||||
\(244\) | 2.22312e6i | 2.39050i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 172783. | + | 232980.i | 0.182038 | + | 0.245460i | ||||
\(247\) | −754167. | −0.786548 | ||||||||
\(248\) | 3.12755e6 | 3.22906 | ||||||||
\(249\) | −996134. | + | 738753.i | −1.01817 | + | 0.755093i | ||||
\(250\) | − | 1.71971e6i | − | 1.74022i | ||||||
\(251\) | 453648. | 0.454501 | 0.227250 | − | 0.973836i | \(-0.427026\pi\) | ||||
0.227250 | + | 0.973836i | \(0.427026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.46838e6 | −1.44224 | ||||||||
\(254\) | − | 678476.i | − | 0.659857i | ||||||
\(255\) | 213879. | − | 158617.i | 0.205976 | − | 0.152756i | ||||
\(256\) | −1.51844e6 | −1.44810 | ||||||||
\(257\) | 1.98345e6 | 1.87322 | 0.936610 | − | 0.350373i | \(-0.113945\pi\) | ||||
0.936610 | + | 0.350373i | \(0.113945\pi\) | |||||||
\(258\) | 756433. | + | 1.01997e6i | 0.707492 | + | 0.953982i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.31015e6i | − | 1.20195i | ||||||
\(261\) | 373189. | + | 113222.i | 0.339100 | + | 0.102879i | ||||
\(262\) | 2.12475e6i | 1.91229i | ||||||||
\(263\) | − | 782254.i | − | 0.697363i | −0.937241 | − | 0.348681i | \(-0.886630\pi\) | ||
0.937241 | − | 0.348681i | \(-0.113370\pi\) | |||||||
\(264\) | 2.51186e6 | − | 1.86284e6i | 2.21812 | − | 1.64500i | ||||
\(265\) | − | 450019.i | − | 0.393655i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11941.7 | − | 8856.17i | 0.0102515 | − | 0.00760270i | ||||
\(268\) | −1.01841e6 | −0.866139 | ||||||||
\(269\) | 1.68301e6 | 1.41809 | 0.709047 | − | 0.705161i | \(-0.249125\pi\) | ||||
0.709047 | + | 0.705161i | \(0.249125\pi\) | |||||||
\(270\) | 1.16997e6 | − | 418543.i | 0.976707 | − | 0.349406i | ||||
\(271\) | 813635.i | 0.672986i | 0.941686 | + | 0.336493i | \(0.109241\pi\) | ||||
−0.941686 | + | 0.336493i | \(0.890759\pi\) | |||||||
\(272\) | 1.17213e6 | 0.960625 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.24208e6 | 3.41352 | ||||||||
\(275\) | − | 960271.i | − | 0.765706i | ||||||
\(276\) | −2.24917e6 | − | 3.03278e6i | −1.77725 | − | 2.39645i | ||||
\(277\) | 375524. | 0.294062 | 0.147031 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147031 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(278\) | 763481. | 0.592497 | ||||||||
\(279\) | 1.64399e6 | + | 498771.i | 1.26441 | + | 0.383611i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 264282.i | 0.199665i | 0.995004 | + | 0.0998326i | \(0.0318307\pi\) | ||||
−0.995004 | + | 0.0998326i | \(0.968169\pi\) | |||||||
\(282\) | −584450. | − | 788073.i | −0.437648 | − | 0.590124i | ||||
\(283\) | 1.84525e6i | 1.36959i | 0.728738 | + | 0.684793i | \(0.240107\pi\) | ||||
−0.728738 | + | 0.684793i | \(0.759893\pi\) | |||||||
\(284\) | − | 2.34428e6i | − | 1.72470i | ||||||
\(285\) | 402841. | + | 543191.i | 0.293780 | + | 0.396132i | ||||
\(286\) | − | 2.58603e6i | − | 1.86947i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.94240e6 | + | 589304.i | 1.37993 | + | 0.418657i | ||||
\(289\) | −1.13024e6 | −0.796024 | ||||||||
\(290\) | −526450. | −0.367589 | ||||||||
\(291\) | 1.07300e6 | + | 1.44683e6i | 0.742789 | + | 1.00158i | ||||
\(292\) | 734685.i | 0.504248i | ||||||||
\(293\) | −1.96922e6 | −1.34006 | −0.670032 | − | 0.742332i | \(-0.733720\pi\) | ||||
−0.670032 | + | 0.742332i | \(0.733720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 537020. | 0.359282 | ||||||||
\(296\) | 863102.i | 0.572576i | ||||||||
\(297\) | 1.61743e6 | − | 578618.i | 1.06398 | − | 0.380628i | ||||
\(298\) | −599123. | −0.390819 | ||||||||
\(299\) | −1.78667e6 | −1.15575 | ||||||||
\(300\) | 1.98333e6 | − | 1.47088e6i | 1.27231 | − | 0.943569i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1.78205e6i | − | 1.12435i | ||||||
\(303\) | −1.12668e6 | + | 835566.i | −0.705006 | + | 0.522847i | ||||
\(304\) | 2.97688e6i | 1.84747i | ||||||||
\(305\) | − | 943303.i | − | 0.580633i | ||||||
\(306\) | 1.29328e6 | + | 392369.i | 0.789570 | + | 0.239547i | ||||
\(307\) | 2.38073e6i | 1.44166i | 0.693110 | + | 0.720832i | \(0.256240\pi\) | ||||
−0.693110 | + | 0.720832i | \(0.743760\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.45474e6 | + | 1.96157e6i | 0.866740 | + | 1.16871i | ||||
\(310\) | −2.31915e6 | −1.37064 | ||||||||
\(311\) | −3.37378e6 | −1.97795 | −0.988976 | − | 0.148078i | \(-0.952691\pi\) | ||||
−0.988976 | + | 0.148078i | \(0.952691\pi\) | |||||||
\(312\) | 3.05632e6 | − | 2.26663e6i | 1.77751 | − | 1.31824i | ||||
\(313\) | − | 2.68664e6i | − | 1.55006i | −0.631923 | − | 0.775031i | \(-0.717734\pi\) | ||
0.631923 | − | 0.775031i | \(-0.282266\pi\) | |||||||
\(314\) | −2.47294e6 | −1.41544 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.46541e6 | −4.20568 | ||||||||
\(317\) | 690592.i | 0.385988i | 0.981200 | + | 0.192994i | \(0.0618197\pi\) | ||||
−0.981200 | + | 0.192994i | \(0.938180\pi\) | |||||||
\(318\) | 1.83462e6 | − | 1.36059e6i | 1.01737 | − | 0.754500i | ||||
\(319\) | −727796. | −0.400436 | ||||||||
\(320\) | −527861. | −0.288167 | ||||||||
\(321\) | −1.29172e6 | − | 1.74175e6i | −0.699689 | − | 0.943460i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 735544.i | 0.392286i | ||||||||
\(324\) | 3.67254e6 | + | 2.45433e6i | 1.94359 | + | 1.29889i | ||||
\(325\) | − | 1.16842e6i | − | 0.613606i | ||||||
\(326\) | 1.53344e6i | 0.799138i | ||||||||
\(327\) | 303338. | − | 224961.i | 0.156876 | − | 0.116343i | ||||
\(328\) | − | 796482.i | − | 0.408782i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.86259e6 | + | 1.38134e6i | −0.941528 | + | 0.698256i | ||||
\(331\) | 3.23377e6 | 1.62233 | 0.811164 | − | 0.584819i | \(-0.198834\pi\) | ||||
0.811164 | + | 0.584819i | \(0.198834\pi\) | |||||||
\(332\) | 5.95129e6 | 2.96323 | ||||||||
\(333\) | −137644. | + | 453688.i | −0.0680218 | + | 0.224206i | ||||
\(334\) | 5.68335e6i | 2.78765i | ||||||||
\(335\) | 432128. | 0.210378 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −751164. | −0.360296 | −0.180148 | − | 0.983639i | \(-0.557658\pi\) | ||||
−0.180148 | + | 0.983639i | \(0.557658\pi\) | |||||||
\(338\) | 690613.i | 0.328808i | ||||||||
\(339\) | 355003. | + | 478687.i | 0.167777 | + | 0.226231i | ||||
\(340\) | −1.27780e6 | −0.599466 | ||||||||
\(341\) | −3.20613e6 | −1.49312 | ||||||||
\(342\) | −996505. | + | 3.28457e6i | −0.460696 | + | 1.51849i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3.48696e6i | − | 1.58873i | ||||||
\(345\) | 954354. | + | 1.28685e6i | 0.431680 | + | 0.582077i | ||||
\(346\) | 3.26857e6i | 1.46780i | ||||||||
\(347\) | − | 2.12687e6i | − | 0.948236i | −0.880461 | − | 0.474118i | \(-0.842767\pi\) | ||
0.880461 | − | 0.474118i | \(-0.157233\pi\) | |||||||
\(348\) | −1.11479e6 | − | 1.50318e6i | −0.493451 | − | 0.665370i | ||||
\(349\) | 1.87399e6i | 0.823575i | 0.911280 | + | 0.411787i | \(0.135095\pi\) | ||||
−0.911280 | + | 0.411787i | \(0.864905\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.96802e6 | − | 704038.i | 0.852633 | − | 0.305020i | ||||
\(352\) | −3.78808e6 | −1.62953 | ||||||||
\(353\) | −3.19891e6 | −1.36636 | −0.683180 | − | 0.730250i | \(-0.739403\pi\) | ||||
−0.683180 | + | 0.730250i | \(0.739403\pi\) | |||||||
\(354\) | 1.62363e6 | + | 2.18930e6i | 0.688617 | + | 0.928531i | ||||
\(355\) | 994711.i | 0.418915i | ||||||||
\(356\) | −71344.1 | −0.0298355 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.82467e6 | 2.40195 | ||||||||
\(359\) | 246921.i | 0.101117i | 0.998721 | + | 0.0505583i | \(0.0161001\pi\) | ||||
−0.998721 | + | 0.0505583i | \(0.983900\pi\) | |||||||
\(360\) | −3.26509e6 | − | 990595.i | −1.32782 | − | 0.402847i | ||||
\(361\) | 608029. | 0.245559 | ||||||||
\(362\) | −3.40293e6 | −1.36484 | ||||||||
\(363\) | −558449. | + | 414157.i | −0.222442 | + | 0.164967i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 311737.i | − | 0.122478i | ||||||
\(366\) | 3.84562e6 | − | 2.85199e6i | 1.50059 | − | 1.11287i | ||||
\(367\) | 454308.i | 0.176070i | 0.996117 | + | 0.0880349i | \(0.0280587\pi\) | ||||
−0.996117 | + | 0.0880349i | \(0.971941\pi\) | |||||||
\(368\) | 7.05239e6i | 2.71467i | ||||||||
\(369\) | 127020. | − | 418670.i | 0.0485631 | − | 0.160068i | ||||
\(370\) | − | 640009.i | − | 0.243042i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.91093e6 | − | 6.62189e6i | −1.83995 | − | 2.48099i | ||||
\(373\) | 2.35605e6 | 0.876825 | 0.438412 | − | 0.898774i | \(-0.355541\pi\) | ||||
0.438412 | + | 0.898774i | \(0.355541\pi\) | |||||||
\(374\) | −2.52217e6 | −0.932386 | ||||||||
\(375\) | −2.08351e6 | + | 1.54517e6i | −0.765099 | + | 0.567413i | ||||
\(376\) | 2.69416e6i | 0.982775i | ||||||||
\(377\) | −885551. | −0.320893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.39242e6 | 0.497935 | 0.248968 | − | 0.968512i | \(-0.419909\pi\) | ||||
0.248968 | + | 0.968512i | \(0.419909\pi\) | |||||||
\(380\) | − | 3.24523e6i | − | 1.15289i | ||||||
\(381\) | −822007. | + | 609617.i | −0.290110 | + | 0.215152i | ||||
\(382\) | 8.32431e6 | 2.91870 | ||||||||
\(383\) | 4.55786e6 | 1.58768 | 0.793841 | − | 0.608125i | \(-0.208078\pi\) | ||||
0.793841 | + | 0.608125i | \(0.208078\pi\) | |||||||
\(384\) | 886174. | + | 1.19492e6i | 0.306684 | + | 0.413532i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.56975e6i | 2.24430i | ||||||||
\(387\) | 556088. | − | 1.83291e6i | 0.188741 | − | 0.622106i | ||||
\(388\) | − | 8.64391e6i | − | 2.91495i | ||||||
\(389\) | − | 1.66786e6i | − | 0.558839i | −0.960169 | − | 0.279420i | \(-0.909858\pi\) | ||
0.960169 | − | 0.279420i | \(-0.0901420\pi\) | |||||||
\(390\) | −2.26633e6 | + | 1.68075e6i | −0.754503 | + | 0.559554i | ||||
\(391\) | 1.74255e6i | 0.576425i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.57424e6 | − | 1.90911e6i | 0.840752 | − | 0.623518i | ||||
\(394\) | 1.42309e6 | 0.461840 | ||||||||
\(395\) | 3.16768e6 | 1.02152 | ||||||||
\(396\) | −7.88830e6 | − | 2.39323e6i | −2.52782 | − | 0.766914i | ||||
\(397\) | 1.72340e6i | 0.548793i | 0.961617 | + | 0.274397i | \(0.0884781\pi\) | ||||
−0.961617 | + | 0.274397i | \(0.911522\pi\) | |||||||
\(398\) | 9.25529e6 | 2.92875 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.61202e6 | −1.44126 | ||||||||
\(401\) | 5.66032e6i | 1.75784i | 0.476966 | + | 0.878922i | \(0.341737\pi\) | ||||
−0.476966 | + | 0.878922i | \(0.658263\pi\) | |||||||
\(402\) | 1.30650e6 | + | 1.76168e6i | 0.403221 | + | 0.543703i | ||||
\(403\) | −3.90108e6 | −1.19653 | ||||||||
\(404\) | 6.73121e6 | 2.05182 | ||||||||
\(405\) | −1.55831e6 | − | 1.04141e6i | −0.472081 | − | 0.315489i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 884786.i | − | 0.264760i | ||||||
\(408\) | −2.21066e6 | − | 2.98085e6i | −0.657463 | − | 0.886522i | ||||
\(409\) | − | 2.24354e6i | − | 0.663170i | −0.943425 | − | 0.331585i | \(-0.892417\pi\) | ||
0.943425 | − | 0.331585i | \(-0.107583\pi\) | |||||||
\(410\) | 590609.i | 0.173516i | ||||||||
\(411\) | −3.81155e6 | − | 5.13949e6i | −1.11301 | − | 1.50078i | ||||
\(412\) | − | 1.17192e7i | − | 3.40137i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.36078e6 | + | 7.78133e6i | −0.676947 | + | 2.23128i | ||||
\(415\) | −2.52522e6 | −0.719745 | ||||||||
\(416\) | −4.60918e6 | −1.30584 | ||||||||
\(417\) | −685995. | − | 924995.i | −0.193188 | − | 0.260495i | ||||
\(418\) | − | 6.40559e6i | − | 1.79316i | ||||||
\(419\) | −6.62738e6 | −1.84419 | −0.922097 | − | 0.386959i | \(-0.873526\pi\) | ||||
−0.922097 | + | 0.386959i | \(0.873526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −633684. | −0.174248 | −0.0871240 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871240 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(422\) | − | 4.05669e6i | − | 1.10890i | ||||||
\(423\) | −429655. | + | 1.41618e6i | −0.116753 | + | 0.384829i | ||||
\(424\) | −6.27196e6 | −1.69429 | ||||||||
\(425\) | −1.13957e6 | −0.306032 | ||||||||
\(426\) | −4.05519e6 | + | 3.00741e6i | −1.08265 | + | 0.802914i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.04059e7i | 2.74581i | ||||||||
\(429\) | −3.13310e6 | + | 2.32357e6i | −0.821924 | + | 0.609555i | ||||
\(430\) | 2.58565e6i | 0.674372i | ||||||||
\(431\) | 3.73993e6i | 0.969772i | 0.874577 | + | 0.484886i | \(0.161139\pi\) | ||||
−0.874577 | + | 0.484886i | \(0.838861\pi\) | |||||||
\(432\) | −2.77901e6 | − | 7.76825e6i | −0.716440 | − | 2.00269i | ||||
\(433\) | 3.36951e6i | 0.863668i | 0.901953 | + | 0.431834i | \(0.142133\pi\) | ||||
−0.901953 | + | 0.431834i | \(0.857867\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 473021. | + | 637821.i | 0.119855 | + | 0.161613i | ||||
\(436\) | −1.81226e6 | −0.456566 | ||||||||
\(437\) | −4.42557e6 | −1.10858 | ||||||||
\(438\) | 1.27088e6 | − | 942508.i | 0.316533 | − | 0.234747i | ||||
\(439\) | 1.28182e6i | 0.317443i | 0.987323 | + | 0.158722i | \(0.0507372\pi\) | ||||
−0.987323 | + | 0.158722i | \(0.949263\pi\) | |||||||
\(440\) | 6.36760e6 | 1.56799 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.06887e6 | −0.747177 | ||||||||
\(443\) | − | 4.24150e6i | − | 1.02686i | −0.858132 | − | 0.513428i | \(-0.828375\pi\) | ||
0.858132 | − | 0.513428i | \(-0.171625\pi\) | |||||||
\(444\) | 1.82743e6 | − | 1.35525e6i | 0.439929 | − | 0.326260i | ||||
\(445\) | 30272.3 | 0.00724680 | ||||||||
\(446\) | 1.04852e7 | 2.49598 | ||||||||
\(447\) | 538318. | + | 725868.i | 0.127430 | + | 0.171826i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.30045e6i | 1.24079i | 0.784291 | + | 0.620393i | \(0.213027\pi\) | ||||
−0.784291 | + | 0.620393i | \(0.786973\pi\) | |||||||
\(450\) | −5.08873e6 | − | 1.54387e6i | −1.18462 | − | 0.359401i | ||||
\(451\) | 816492.i | 0.189021i | ||||||||
\(452\) | − | 2.85986e6i | − | 0.658413i | ||||||
\(453\) | −2.15905e6 | + | 1.60119e6i | −0.494330 | + | 0.366605i | ||||
\(454\) | − | 3.23857e6i | − | 0.737419i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.57050e6 | − | 5.61443e6i | 1.70495 | − | 1.26443i | ||||
\(457\) | −7.00723e6 | −1.56948 | −0.784741 | − | 0.619824i | \(-0.787204\pi\) | ||||
−0.784741 | + | 0.619824i | \(0.787204\pi\) | |||||||
\(458\) | −4.65827e6 | −1.03768 | ||||||||
\(459\) | −686653. | − | 1.91943e6i | −0.152127 | − | 0.425246i | ||||
\(460\) | − | 7.68815e6i | − | 1.69405i | ||||||
\(461\) | 640032. | 0.140265 | 0.0701325 | − | 0.997538i | \(-0.477658\pi\) | ||||
0.0701325 | + | 0.997538i | \(0.477658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.47378e6 | 0.753096 | 0.376548 | − | 0.926397i | \(-0.377111\pi\) | ||||
0.376548 | + | 0.926397i | \(0.377111\pi\) | |||||||
\(464\) | 3.49548e6i | 0.753724i | ||||||||
\(465\) | 2.08378e6 | + | 2.80977e6i | 0.446909 | + | 0.602612i | ||||
\(466\) | 1.38958e6 | 0.296428 | ||||||||
\(467\) | −1.23565e6 | −0.262182 | −0.131091 | − | 0.991370i | \(-0.541848\pi\) | ||||
−0.131091 | + | 0.991370i | \(0.541848\pi\) | |||||||
\(468\) | −9.59815e6 | − | 2.91198e6i | −2.02569 | − | 0.614574i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.99778e6i | − | 0.417160i | ||||||
\(471\) | 2.22196e6 | + | 2.99610e6i | 0.461514 | + | 0.622305i | ||||
\(472\) | − | 7.48449e6i | − | 1.54635i | ||||||
\(473\) | 3.57456e6i | 0.734632i | ||||||||
\(474\) | 9.57717e6 | + | 1.29139e7i | 1.95790 | + | 2.64004i | ||||
\(475\) | − | 2.89417e6i | − | 0.588559i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.29684e6 | − | 1.00023e6i | −0.663441 | − | 0.201281i | ||||
\(478\) | 1.30597e7 | 2.61436 | ||||||||
\(479\) | 1.56481e6 | 0.311618 | 0.155809 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155809 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(480\) | 2.46201e6 | + | 3.31977e6i | 0.487738 | + | 0.657666i | ||||
\(481\) | − | 1.07657e6i | − | 0.212168i | ||||||
\(482\) | 5.02870e6 | 0.985911 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.33639e6 | 0.647387 | ||||||||
\(485\) | 3.66773e6i | 0.708017i | ||||||||
\(486\) | −465833. | − | 9.50146e6i | −0.0894623 | − | 1.82473i | ||||
\(487\) | −2.89980e6 | −0.554045 | −0.277023 | − | 0.960863i | \(-0.589348\pi\) | ||||
−0.277023 | + | 0.960863i | \(0.589348\pi\) | |||||||
\(488\) | −1.31469e7 | −2.49904 | ||||||||
\(489\) | 1.85784e6 | − | 1.37781e6i | 0.351346 | − | 0.260565i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4.46273e6i | − | 0.835405i | −0.908584 | − | 0.417702i | \(-0.862835\pi\) | ||
0.908584 | − | 0.417702i | \(-0.137165\pi\) | |||||||
\(492\) | −1.68637e6 | + | 1.25065e6i | −0.314080 | + | 0.232928i | ||||
\(493\) | 863685.i | 0.160043i | ||||||||
\(494\) | − | 7.79405e6i | − | 1.43696i | ||||||
\(495\) | 3.34712e6 | + | 1.01548e6i | 0.613985 | + | 0.186277i | ||||
\(496\) | 1.53985e7i | 2.81044i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.63475e6 | − | 1.02947e7i | −1.37950 | − | 1.86012i | ||||
\(499\) | 2.66828e6 | 0.479711 | 0.239855 | − | 0.970809i | \(-0.422900\pi\) | ||||
0.239855 | + | 0.970809i | \(0.422900\pi\) | |||||||
\(500\) | 1.24477e7 | 2.22671 | ||||||||
\(501\) | 6.88566e6 | − | 5.10654e6i | 1.22561 | − | 0.908935i | ||||
\(502\) | 4.68830e6i | 0.830339i | ||||||||
\(503\) | 6.90952e6 | 1.21767 | 0.608833 | − | 0.793299i | \(-0.291638\pi\) | ||||
0.608833 | + | 0.793299i | \(0.291638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.85615e6 | −0.498370 | ||||||||
\(506\) | − | 1.51752e7i | − | 2.63487i | ||||||
\(507\) | 836712. | − | 620522.i | 0.144563 | − | 0.107211i | ||||
\(508\) | 4.91099e6 | 0.844326 | ||||||||
\(509\) | −4.56189e6 | −0.780460 | −0.390230 | − | 0.920717i | \(-0.627604\pi\) | ||||
−0.390230 | + | 0.920717i | \(0.627604\pi\) | |||||||
\(510\) | 1.63925e6 | + | 2.21036e6i | 0.279074 | + | 0.376304i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.26387e7i | − | 2.13073i | ||||||
\(513\) | 4.87479e6 | − | 1.74390e6i | 0.817829 | − | 0.292569i | ||||
\(514\) | 2.04983e7i | 3.42224i | ||||||||
\(515\) | 4.97262e6i | 0.826165i | ||||||||
\(516\) | −7.38285e6 | + | 5.47527e6i | −1.22067 | + | 0.905277i | ||||
\(517\) | − | 2.76185e6i | − | 0.454437i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.96004e6 | − | 2.93684e6i | 0.645329 | − | 0.478589i | ||||
\(520\) | 7.74783e6 | 1.25653 | ||||||||
\(521\) | 532535. | 0.0859515 | 0.0429758 | − | 0.999076i | \(-0.486316\pi\) | ||||
0.0429758 | + | 0.999076i | \(0.486316\pi\) | |||||||
\(522\) | −1.17011e6 | + | 3.85678e6i | −0.187953 | + | 0.619510i | ||||
\(523\) | 1.32596e6i | 0.211971i | 0.994368 | + | 0.105985i | \(0.0337996\pi\) | ||||
−0.994368 | + | 0.105985i | \(0.966200\pi\) | |||||||
\(524\) | −1.53795e7 | −2.44689 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.08433e6 | 1.27403 | ||||||||
\(527\) | 3.80475e6i | 0.596760i | ||||||||
\(528\) | 9.17169e6 | + | 1.23671e7i | 1.43174 | + | 1.93056i | ||||
\(529\) | −4.04808e6 | −0.628941 | ||||||||
\(530\) | 4.65079e6 | 0.719179 | ||||||||
\(531\) | 1.19360e6 | − | 3.93421e6i | 0.183706 | − | 0.605510i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 993473.i | 0.151474i | ||||||||
\(534\) | 91525.5 | + | 123413.i | 0.0138896 | + | 0.0187287i | ||||
\(535\) | − | 4.41537e6i | − | 0.666934i | ||||||
\(536\) | − | 6.02261e6i | − | 0.905467i | ||||||
\(537\) | −5.23352e6 | − | 7.05688e6i | −0.783174 | − | 1.05603i | ||||
\(538\) | 1.73933e7i | 2.59075i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.02952e6 | + | 8.46854e6i | 0.447085 | + | 1.24975i | ||||
\(541\) | −1.12979e7 | −1.65961 | −0.829804 | − | 0.558055i | \(-0.811548\pi\) | ||||
−0.829804 | + | 0.558055i | \(0.811548\pi\) | |||||||
\(542\) | −8.40863e6 | −1.22950 | ||||||||
\(543\) | 3.05757e6 | + | 4.12282e6i | 0.445017 | + | 0.600060i | ||||
\(544\) | 4.49536e6i | 0.651280i | ||||||||
\(545\) | 768967. | 0.110896 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.17217e7 | −1.67503 | −0.837516 | − | 0.546413i | \(-0.815993\pi\) | ||||
−0.837516 | + | 0.546413i | \(0.815993\pi\) | |||||||
\(548\) | 3.07053e7i | 4.36780i | ||||||||
\(549\) | −6.91065e6 | − | 2.09662e6i | −0.978561 | − | 0.296886i | ||||
\(550\) | 9.92407e6 | 1.39889 | ||||||||
\(551\) | −2.19351e6 | −0.307794 | ||||||||
\(552\) | 1.79350e7 | − | 1.33009e7i | 2.50526 | − | 1.85795i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.88091e6i | 0.537229i | ||||||||
\(555\) | −775403. | + | 575054.i | −0.106855 | + | 0.0792458i | ||||
\(556\) | 5.52628e6i | 0.758134i | ||||||||
\(557\) | 5.47372e6i | 0.747558i | 0.927518 | + | 0.373779i | \(0.121938\pi\) | ||||
−0.927518 | + | 0.373779i | \(0.878062\pi\) | |||||||
\(558\) | −5.15463e6 | + | 1.69901e7i | −0.700828 | + | 2.30999i | ||||
\(559\) | 4.34938e6i | 0.588705i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.26620e6 | + | 3.05574e6i | 0.304012 | + | 0.409929i | ||||
\(562\) | −2.73127e6 | −0.364773 | ||||||||
\(563\) | 1.44586e7 | 1.92245 | 0.961224 | − | 0.275769i | \(-0.0889326\pi\) | ||||
0.961224 | + | 0.275769i | \(0.0889326\pi\) | |||||||
\(564\) | 5.70428e6 | − | 4.23041e6i | 0.755098 | − | 0.559996i | ||||
\(565\) | 1.21348e6i | 0.159923i | ||||||||
\(566\) | −1.90700e7 | −2.50213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.38634e7 | 1.80301 | ||||||||
\(569\) | − | 4.69732e6i | − | 0.608233i | −0.952635 | − | 0.304116i | \(-0.901639\pi\) | ||
0.952635 | − | 0.304116i | \(-0.0983612\pi\) | |||||||
\(570\) | −5.61369e6 | + | 4.16322e6i | −0.723704 | + | 0.536713i | ||||
\(571\) | 5.07275e6 | 0.651108 | 0.325554 | − | 0.945523i | \(-0.394449\pi\) | ||||
0.325554 | + | 0.945523i | \(0.394449\pi\) | |||||||
\(572\) | 1.87184e7 | 2.39209 | ||||||||
\(573\) | −7.47947e6 | − | 1.00853e7i | −0.951665 | − | 1.28323i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.85645e6i | − | 0.864828i | ||||||
\(576\) | −1.17324e6 | + | 3.86712e6i | −0.147344 | + | 0.485659i | ||||
\(577\) | − | 7.54076e6i | − | 0.942922i | −0.881887 | − | 0.471461i | \(-0.843727\pi\) | ||
0.881887 | − | 0.471461i | \(-0.156273\pi\) | |||||||
\(578\) | − | 1.16806e7i | − | 1.45428i | ||||||
\(579\) | 7.95959e6 | − | 5.90299e6i | 0.986720 | − | 0.731771i | ||||
\(580\) | − | 3.81059e6i | − | 0.470351i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.49525e7 | + | 1.10890e7i | −1.82981 | + | 1.35702i | ||||
\(583\) | 6.42953e6 | 0.783443 | ||||||||
\(584\) | −4.34471e6 | −0.527144 | ||||||||
\(585\) | 4.07263e6 | + | 1.23560e6i | 0.492023 | + | 0.149275i | ||||
\(586\) | − | 2.03512e7i | − | 2.44820i | ||||||
\(587\) | 1.49725e7 | 1.79349 | 0.896743 | − | 0.442551i | \(-0.145926\pi\) | ||||
0.896743 | + | 0.442551i | \(0.145926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.66297e6 | −1.14768 | ||||||||
\(590\) | 5.54991e6i | 0.656381i | ||||||||
\(591\) | −1.27866e6 | − | 1.72414e6i | −0.150586 | − | 0.203051i | ||||
\(592\) | −4.24948e6 | −0.498347 | ||||||||
\(593\) | −3.02527e6 | −0.353287 | −0.176644 | − | 0.984275i | \(-0.556524\pi\) | ||||
−0.176644 | + | 0.984275i | \(0.556524\pi\) | |||||||
\(594\) | 5.97981e6 | + | 1.67156e7i | 0.695379 | + | 1.94382i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 4.33662e6i | − | 0.500075i | ||||||
\(597\) | −8.31597e6 | − | 1.12132e7i | −0.954942 | − | 1.28764i | ||||
\(598\) | − | 1.84646e7i | − | 2.11148i | ||||||
\(599\) | 5.80456e6i | 0.661001i | 0.943806 | + | 0.330501i | \(0.107218\pi\) | ||||
−0.943806 | + | 0.330501i | \(0.892782\pi\) | |||||||
\(600\) | 8.69834e6 | + | 1.17288e7i | 0.986412 | + | 1.33008i | ||||
\(601\) | − | 8.90296e6i | − | 1.00542i | −0.864455 | − | 0.502711i | \(-0.832336\pi\) | ||
0.864455 | − | 0.502711i | \(-0.167664\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 960464. | − | 3.16577e6i | 0.107569 | − | 0.354557i | ||||
\(604\) | 1.28990e7 | 1.43868 | ||||||||
\(605\) | −1.41568e6 | −0.157245 | ||||||||
\(606\) | −8.63528e6 | − | 1.16438e7i | −0.955202 | − | 1.28799i | ||||
\(607\) | − | 344344.i | − | 0.0379333i | −0.999820 | − | 0.0189667i | \(-0.993962\pi\) | ||
0.999820 | − | 0.0189667i | \(-0.00603764\pi\) | |||||||
\(608\) | −1.14169e7 | −1.25254 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.74871e6 | 1.06077 | ||||||||
\(611\) | − | 3.36050e6i | − | 0.364167i | ||||||
\(612\) | −2.84008e6 | + | 9.36114e6i | −0.306515 | + | 1.01030i | ||||
\(613\) | −40196.2 | −0.00432050 | −0.00216025 | − | 0.999998i | \(-0.500688\pi\) | ||||
−0.00216025 | + | 0.999998i | \(0.500688\pi\) | |||||||
\(614\) | −2.46040e7 | −2.63381 | ||||||||
\(615\) | 715552. | − | 530668.i | 0.0762875 | − | 0.0565763i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.04424e6i | 0.427685i | 0.976868 | + | 0.213843i | \(0.0685980\pi\) | ||||
−0.976868 | + | 0.213843i | \(0.931402\pi\) | |||||||
\(618\) | −2.02721e7 | + | 1.50342e7i | −2.13515 | + | 1.58347i | ||||
\(619\) | − | 7.68259e6i | − | 0.805900i | −0.915222 | − | 0.402950i | \(-0.867985\pi\) | ||
0.915222 | − | 0.402950i | \(-0.132015\pi\) | |||||||
\(620\) | − | 1.67866e7i | − | 1.75382i | ||||||
\(621\) | 1.15487e7 | − | 4.13140e6i | 1.20172 | − | 0.429901i | ||||
\(622\) | − | 3.48668e7i | − | 3.61357i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.11597e7 | + | 1.50478e7i | 1.14734 | + | 1.54707i | ||||
\(625\) | 1.33551e6 | 0.136756 | ||||||||
\(626\) | 2.77655e7 | 2.83185 | ||||||||
\(627\) | −7.76069e6 | + | 5.75548e6i | −0.788373 | + | 0.584673i | ||||
\(628\) | − | 1.78998e7i | − | 1.81113i | ||||||
\(629\) | −1.04999e6 | −0.105817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.42740e7 | 1.42716 | 0.713582 | − | 0.700572i | \(-0.247072\pi\) | ||||
0.713582 | + | 0.700572i | \(0.247072\pi\) | |||||||
\(632\) | − | 4.41483e7i | − | 4.39664i | ||||||
\(633\) | −4.91488e6 | + | 3.64498e6i | −0.487533 | + | 0.361564i | ||||
\(634\) | −7.13703e6 | −0.705171 | ||||||||
\(635\) | −2.08380e6 | −0.205080 | ||||||||
\(636\) | 9.84831e6 | + | 1.32795e7i | 0.965426 | + | 1.30178i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 7.52152e6i | − | 0.731566i | ||||||
\(639\) | 7.28726e6 | + | 2.21088e6i | 0.706012 | + | 0.214197i | ||||
\(640\) | 3.02914e6i | 0.292327i | ||||||||
\(641\) | − | 7.73472e6i | − | 0.743532i | −0.928326 | − | 0.371766i | \(-0.878752\pi\) | ||
0.928326 | − | 0.371766i | \(-0.121248\pi\) | |||||||
\(642\) | 1.80004e7 | − | 1.33494e7i | 1.72363 | − | 1.27828i | ||||
\(643\) | 1.41911e7i | 1.35360i | 0.736168 | + | 0.676799i | \(0.236633\pi\) | ||||
−0.736168 | + | 0.676799i | \(0.763367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.13265e6 | − | 2.32324e6i | 0.296492 | − | 0.219884i | ||||
\(646\) | −7.60159e6 | −0.716677 | ||||||||
\(647\) | −678952. | −0.0637644 | −0.0318822 | − | 0.999492i | \(-0.510150\pi\) | ||||
−0.0318822 | + | 0.999492i | \(0.510150\pi\) | |||||||
\(648\) | −1.45142e7 | + | 2.17183e7i | −1.35786 | + | 2.03184i | ||||
\(649\) | 7.67252e6i | 0.715034i | ||||||||
\(650\) | 1.20752e7 | 1.12101 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.10994e7 | −1.02254 | ||||||||
\(653\) | − | 2.65332e6i | − | 0.243505i | −0.992561 | − | 0.121752i | \(-0.961149\pi\) | ||
0.992561 | − | 0.121752i | \(-0.0388514\pi\) | |||||||
\(654\) | 2.32490e6 | + | 3.13489e6i | 0.212549 | + | 0.286601i | ||||
\(655\) | 6.52575e6 | 0.594329 | ||||||||
\(656\) | 3.92148e6 | 0.355787 | ||||||||
\(657\) | −2.28379e6 | − | 692879.i | −0.206416 | − | 0.0626245i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.07933e7i | − | 0.968149i | −0.875027 | − | 0.484074i | \(-0.839156\pi\) | ||
0.875027 | − | 0.484074i | \(-0.160844\pi\) | |||||||
\(660\) | −9.99849e6 | − | 1.34820e7i | −0.893459 | − | 1.20474i | ||||
\(661\) | 2.05761e7i | 1.83172i | 0.401496 | + | 0.915861i | \(0.368490\pi\) | ||||
−0.401496 | + | 0.915861i | \(0.631510\pi\) | |||||||
\(662\) | 3.34198e7i | 2.96387i | ||||||||
\(663\) | 2.75741e6 | + | 3.71809e6i | 0.243623 | + | 0.328501i | ||||
\(664\) | 3.51942e7i | 3.09778i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.68871e6 | − | 1.42251e6i | −0.409607 | − | 0.124271i | ||||
\(667\) | −5.19655e6 | −0.452273 | ||||||||
\(668\) | −4.11376e7 | −3.56696 | ||||||||
\(669\) | −9.42108e6 | − | 1.27034e7i | −0.813833 | − | 1.09737i | ||||
\(670\) | 4.46589e6i | 0.384345i | ||||||||
\(671\) | 1.34772e7 | 1.15556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.73039e7 | −1.47268 | −0.736338 | − | 0.676614i | \(-0.763447\pi\) | ||||
−0.736338 | + | 0.676614i | \(0.763447\pi\) | |||||||
\(674\) | − | 7.76302e6i | − | 0.658235i | ||||||
\(675\) | 2.70180e6 | + | 7.55243e6i | 0.228241 | + | 0.638009i | ||||
\(676\) | −4.99884e6 | −0.420729 | ||||||||
\(677\) | −2.14664e6 | −0.180006 | −0.0900031 | − | 0.995941i | \(-0.528688\pi\) | ||||
−0.0900031 | + | 0.995941i | \(0.528688\pi\) | |||||||
\(678\) | −4.94706e6 | + | 3.66884e6i | −0.413307 | + | 0.306517i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 7.55651e6i | − | 0.626685i | ||||||
\(681\) | −3.92369e6 | + | 2.90989e6i | −0.324211 | + | 0.240441i | ||||
\(682\) | − | 3.31342e7i | − | 2.72782i | ||||||
\(683\) | − | 2.60907e6i | − | 0.214010i | −0.994258 | − | 0.107005i | \(-0.965874\pi\) | ||
0.994258 | − | 0.107005i | \(-0.0341260\pi\) | |||||||
\(684\) | −2.37746e7 | − | 7.21298e6i | −1.94300 | − | 0.589487i | ||||
\(685\) | − | 1.30287e7i | − | 1.06090i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.18550e6 | + | 5.64373e6i | 0.338342 | + | 0.456220i | ||||
\(688\) | 1.71680e7 | 1.38277 | ||||||||
\(689\) | 7.82318e6 | 0.627820 | ||||||||
\(690\) | −1.32992e7 | + | 9.86292e6i | −1.06341 | + | 0.788647i | ||||
\(691\) | 8.38905e6i | 0.668371i | 0.942507 | + | 0.334185i | \(0.108461\pi\) | ||||
−0.942507 | + | 0.334185i | \(0.891539\pi\) | |||||||
\(692\) | −2.36588e7 | −1.87814 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.19804e7 | 1.73236 | ||||||||
\(695\) | − | 2.34488e6i | − | 0.184144i | ||||||
\(696\) | 8.88937e6 | − | 6.59253e6i | 0.695581 | − | 0.515857i | ||||
\(697\) | 968942. | 0.0755467 | ||||||||
\(698\) | −1.93670e7 | −1.50461 | ||||||||
\(699\) | −1.24855e6 | − | 1.68355e6i | −0.0966527 | − | 0.130327i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.05701e6i | 0.0812425i | 0.999175 | + | 0.0406213i | \(0.0129337\pi\) | ||||
−0.999175 | + | 0.0406213i | \(0.987066\pi\) | |||||||
\(702\) | 7.27599e6 | + | 2.03388e7i | 0.557249 | + | 1.55770i | ||||
\(703\) | − | 2.66666e6i | − | 0.203507i | ||||||
\(704\) | − | 7.54168e6i | − | 0.573504i | ||||||
\(705\) | −2.42041e6 | + | 1.79502e6i | −0.183407 | + | 0.136018i | ||||
\(706\) | − | 3.30596e7i | − | 2.49624i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.58467e7 | + | 1.17523e7i | −1.18811 | + | 0.881126i | ||||
\(709\) | 8.71222e6 | 0.650898 | 0.325449 | − | 0.945560i | \(-0.394485\pi\) | ||||
0.325449 | + | 0.945560i | \(0.394485\pi\) | |||||||
\(710\) | −1.02800e7 | −0.765327 | ||||||||
\(711\) | 7.04061e6 | − | 2.32065e7i | 0.522319 | − | 1.72161i | ||||
\(712\) | − | 421908.i | − | 0.0311902i | ||||||
\(713\) | −2.28921e7 | −1.68641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.94248e6 | −0.581020 | ||||||||
\(716\) | 4.21605e7i | 3.07343i | ||||||||
\(717\) | −1.17343e7 | − | 1.58225e7i | −0.852431 | − | 1.14942i | ||||
\(718\) | −2.55185e6 | −0.184732 | ||||||||
\(719\) | 2.34094e7 | 1.68876 | 0.844380 | − | 0.535744i | \(-0.179969\pi\) | ||||
0.844380 | + | 0.535744i | \(0.179969\pi\) | |||||||
\(720\) | 4.87719e6 | − | 1.60757e7i | 0.350621 | − | 1.15568i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.28377e6i | 0.448618i | ||||||||
\(723\) | −4.51833e6 | − | 6.09252e6i | −0.321464 | − | 0.433462i | ||||
\(724\) | − | 2.46313e7i | − | 1.74639i | ||||||
\(725\) | − | 3.39837e6i | − | 0.240118i | ||||||
\(726\) | −4.28017e6 | − | 5.77138e6i | −0.301383 | − | 0.406385i | ||||
\(727\) | 1.80153e7i | 1.26417i | 0.774899 | + | 0.632085i | \(0.217801\pi\) | ||||
−0.774899 | + | 0.632085i | \(0.782199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.10929e7 | + | 9.10153e6i | −0.773086 | + | 0.634301i | ||||
\(730\) | 3.22170e6 | 0.223758 | ||||||||
\(731\) | 4.24198e6 | 0.293613 | ||||||||
\(732\) | 2.06434e7 | + | 2.78356e7i | 1.42398 | + | 1.92010i | ||||
\(733\) | 7.02971e6i | 0.483256i | 0.970369 | + | 0.241628i | \(0.0776814\pi\) | ||||
−0.970369 | + | 0.241628i | \(0.922319\pi\) | |||||||
\(734\) | −4.69511e6 | −0.321667 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.70474e7 | −1.84048 | ||||||||
\(737\) | 6.17391e6i | 0.418689i | ||||||||
\(738\) | 4.32680e6 | + | 1.31271e6i | 0.292433 | + | 0.0887212i | ||||
\(739\) | 1.59687e7 | 1.07562 | 0.537810 | − | 0.843066i | \(-0.319252\pi\) | ||||
0.537810 | + | 0.843066i | \(0.319252\pi\) | |||||||
\(740\) | 4.63256e6 | 0.310987 | ||||||||
\(741\) | −9.44289e6 | + | 7.00303e6i | −0.631770 | + | 0.468533i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.50742e7i | 1.66630i | 0.553044 | + | 0.833152i | \(0.313466\pi\) | ||||
−0.553044 | + | 0.833152i | \(0.686534\pi\) | |||||||
\(744\) | 3.91600e7 | − | 2.90418e7i | 2.59364 | − | 1.92350i | ||||
\(745\) | 1.84009e6i | 0.121464i | ||||||||
\(746\) | 2.43490e7i | 1.60189i | ||||||||
\(747\) | −5.61264e6 | + | 1.84998e7i | −0.368015 | + | 1.21301i | ||||
\(748\) | − | 1.82562e7i | − | 1.19304i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.59688e7 | − | 2.15324e7i | −1.03662 | − | 1.39778i | ||||
\(751\) | −2.18908e6 | −0.141632 | −0.0708159 | − | 0.997489i | \(-0.522560\pi\) | ||||
−0.0708159 | + | 0.997489i | \(0.522560\pi\) | |||||||
\(752\) | −1.32647e7 | −0.855367 | ||||||||
\(753\) | 5.68011e6 | − | 4.21248e6i | 0.365064 | − | 0.270739i | ||||
\(754\) | − | 9.15187e6i | − | 0.586248i | ||||||
\(755\) | −5.47323e6 | −0.349443 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.44147e6 | −0.0914251 | −0.0457126 | − | 0.998955i | \(-0.514556\pi\) | ||||
−0.0457126 | + | 0.998955i | \(0.514556\pi\) | |||||||
\(758\) | 1.43902e7i | 0.909691i | ||||||||
\(759\) | −1.83855e7 | + | 1.36351e7i | −1.15844 | + | 0.859119i | ||||
\(760\) | 1.91914e7 | 1.20524 | ||||||||
\(761\) | −1.36473e6 | −0.0854253 | −0.0427126 | − | 0.999087i | \(-0.513600\pi\) | ||||
−0.0427126 | + | 0.999087i | \(0.513600\pi\) | |||||||
\(762\) | −6.30018e6 | − | 8.49516e6i | −0.393066 | − | 0.530010i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.02536e7i | 3.73465i | ||||||||
\(765\) | 1.20509e6 | − | 3.97207e6i | 0.0744499 | − | 0.245394i | ||||
\(766\) | 4.71038e7i | 2.90058i | ||||||||
\(767\) | 9.33561e6i | 0.572999i | ||||||||
\(768\) | −1.90123e7 | + | 1.40999e7i | −1.16314 | + | 0.862608i | ||||
\(769\) | 1.59541e7i | 0.972875i | 0.873715 | + | 0.486437i | \(0.161704\pi\) | ||||
−0.873715 | + | 0.486437i | \(0.838296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.48347e7 | − | 1.84179e7i | 1.50461 | − | 1.11585i | ||||
\(772\) | −4.75537e7 | −2.87171 | ||||||||
\(773\) | 1.72753e7 | 1.03986 | 0.519931 | − | 0.854208i | \(-0.325958\pi\) | ||||
0.519931 | + | 0.854208i | \(0.325958\pi\) | |||||||
\(774\) | 1.89425e7 | + | 5.74697e6i | 1.13654 | + | 0.344815i | ||||
\(775\) | − | 1.49707e7i | − | 0.895338i | ||||||
\(776\) | 5.11175e7 | 3.04730 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.72368e7 | 1.02096 | ||||||||
\(779\) | 2.46083e6i | 0.145291i | ||||||||
\(780\) | −1.21657e7 | − | 1.64043e7i | −0.715982 | − | 0.965430i | ||||
\(781\) | −1.42117e7 | −0.833715 | ||||||||
\(782\) | −1.80086e7 | −1.05309 | ||||||||
\(783\) | 5.72403e6 | − | 2.04771e6i | 0.333655 | − | 0.119361i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.59516e6i | 0.439909i | ||||||||
\(786\) | 1.97300e7 | + | 2.66039e7i | 1.13912 | + | 1.53599i | ||||
\(787\) | 6.31579e6i | 0.363489i | 0.983346 | + | 0.181744i | \(0.0581744\pi\) | ||||
−0.983346 | + | 0.181744i | \(0.941826\pi\) | |||||||
\(788\) | 1.03007e7i | 0.590951i | ||||||||
\(789\) | −7.26385e6 | − | 9.79457e6i | −0.415407 | − | 0.560135i | ||||
\(790\) | 3.27369e7i | 1.86625i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.41529e7 | − | 4.66491e7i | 0.801736 | − | 2.64259i | ||||
\(793\) | 1.63985e7 | 0.926021 | ||||||||
\(794\) | −1.78107e7 | −1.00260 | ||||||||
\(795\) | −4.17878e6 | − | 5.63467e6i | −0.234494 | − | 0.316192i | ||||
\(796\) | 6.69923e7i | 3.74751i | ||||||||
\(797\) | 8.89295e6 | 0.495907 | 0.247953 | − | 0.968772i | \(-0.420242\pi\) | ||||
0.247953 | + | 0.968772i | \(0.420242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.27752e6 | −0.181626 | ||||||||
\(800\) | − | 1.76880e7i | − | 0.977136i | ||||||
\(801\) | 67284.4 | − | 221775.i | 0.00370539 | − | 0.0122133i | ||||
\(802\) | −5.84975e7 | −3.21145 | ||||||||
\(803\) | 4.45387e6 | 0.243752 | ||||||||
\(804\) | −1.27515e7 | + | 9.45678e6i | −0.695700 | + | 0.515945i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 4.03163e7i | − | 2.18597i | ||||||
\(807\) | 2.10728e7 | − | 1.56280e7i | 1.13904 | − | 0.844735i | ||||
\(808\) | 3.98064e7i | 2.14499i | ||||||||
\(809\) | − | 276257.i | − | 0.0148403i | −0.999972 | − | 0.00742013i | \(-0.997638\pi\) | ||
0.999972 | − | 0.00742013i | \(-0.00236192\pi\) | |||||||
\(810\) | 1.07626e7 | − | 1.61046e7i | 0.576375 | − | 0.862458i | ||||
\(811\) | 1.88633e7i | 1.00708i | 0.863971 | + | 0.503542i | \(0.167970\pi\) | ||||
−0.863971 | + | 0.503542i | \(0.832030\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.55524e6 | + | 1.01875e7i | 0.400887 | + | 0.540556i | ||||
\(814\) | 9.14395e6 | 0.483697 | ||||||||
\(815\) | 4.70965e6 | 0.248367 | ||||||||
\(816\) | 1.46762e7 | − | 1.08842e7i | 0.771593 | − | 0.572229i | ||||
\(817\) | 1.07734e7i | 0.564674i | ||||||||
\(818\) | 2.31862e7 | 1.21156 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.27499e6 | −0.222024 | ||||||||
\(821\) | 6.93862e6i | 0.359265i | 0.983734 | + | 0.179633i | \(0.0574909\pi\) | ||||
−0.983734 | + | 0.179633i | \(0.942509\pi\) | |||||||
\(822\) | 5.31149e7 | − | 3.93910e7i | 2.74181 | − | 2.03338i | ||||
\(823\) | −2.98167e7 | −1.53448 | −0.767238 | − | 0.641362i | \(-0.778370\pi\) | ||||
−0.767238 | + | 0.641362i | \(0.778370\pi\) | |||||||
\(824\) | 6.93038e7 | 3.55581 | ||||||||
\(825\) | −8.91687e6 | − | 1.20235e7i | −0.456118 | − | 0.615030i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.56391e7i | − | 1.30358i | −0.758398 | − | 0.651792i | \(-0.774018\pi\) | ||
0.758398 | − | 0.651792i | \(-0.225982\pi\) | |||||||
\(828\) | −5.63234e7 | − | 1.70880e7i | −2.85505 | − | 0.866192i | ||||
\(829\) | − | 4.07622e6i | − | 0.206002i | −0.994681 | − | 0.103001i | \(-0.967156\pi\) | ||
0.994681 | − | 0.103001i | \(-0.0328444\pi\) | |||||||
\(830\) | − | 2.60973e7i | − | 1.31492i | ||||||
\(831\) | 4.70192e6 | − | 3.48704e6i | 0.236196 | − | 0.175168i | ||||
\(832\) | − | 9.17640e6i | − | 0.459583i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.55950e6 | − | 7.08952e6i | 0.475905 | − | 0.352941i | ||||
\(835\) | 1.74553e7 | 0.866384 | ||||||||
\(836\) | 4.63654e7 | 2.29445 | ||||||||
\(837\) | 2.52158e7 | − | 9.02068e6i | 1.24411 | − | 0.445067i | ||||
\(838\) | − | 6.84916e7i | − | 3.36921i | ||||||
\(839\) | 2.71420e7 | 1.33118 | 0.665591 | − | 0.746317i | \(-0.268180\pi\) | ||||
0.665591 | + | 0.746317i | \(0.268180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.79355e7 | 0.874427 | ||||||||
\(842\) | − | 6.54891e6i | − | 0.318338i | ||||||
\(843\) | 2.45407e6 | + | 3.30907e6i | 0.118937 | + | 0.160375i | ||||
\(844\) | 2.93634e7 | 1.41890 | ||||||||
\(845\) | 2.12108e6 | 0.102192 | ||||||||
\(846\) | −1.46357e7 | − | 4.44034e6i | −0.703054 | − | 0.213300i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 3.08799e7i | − | 1.47464i | ||||||
\(849\) | 1.71346e7 | + | 2.31043e7i | 0.815840 | + | 1.10008i | ||||
\(850\) | − | 1.17770e7i | − | 0.559098i | ||||||
\(851\) | − | 6.31748e6i | − | 0.299034i | ||||||
\(852\) | −2.17685e7 | − | 2.93526e7i | −1.02737 | − | 1.38531i | ||||
\(853\) | − | 2.48053e6i | − | 0.116727i | −0.998295 | − | 0.0583637i | \(-0.981412\pi\) | ||
0.998295 | − | 0.0583637i | \(-0.0185883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00879e7 | + | 3.06057e6i | 0.471939 | + | 0.143182i | ||||
\(856\) | −6.15374e7 | −2.87048 | ||||||||
\(857\) | −3.71304e7 | −1.72694 | −0.863471 | − | 0.504399i | \(-0.831714\pi\) | ||||
−0.863471 | + | 0.504399i | \(0.831714\pi\) | |||||||
\(858\) | −2.40133e7 | − | 3.23795e7i | −1.11361 | − | 1.50159i | ||||
\(859\) | 4.16270e6i | 0.192483i | 0.995358 | + | 0.0962414i | \(0.0306821\pi\) | ||||
−0.995358 | + | 0.0962414i | \(0.969318\pi\) | |||||||
\(860\) | −1.87157e7 | −0.862898 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.86508e7 | −1.77170 | ||||||||
\(863\) | − | 2.31557e7i | − | 1.05835i | −0.848511 | − | 0.529177i | \(-0.822501\pi\) | ||
0.848511 | − | 0.529177i | \(-0.177499\pi\) | |||||||
\(864\) | 2.97928e7 | − | 1.06581e7i | 1.35777 | − | 0.485728i | ||||
\(865\) | 1.00388e7 | 0.456184 | ||||||||
\(866\) | −3.48227e7 | −1.57786 | ||||||||
\(867\) | −1.41517e7 | + | 1.04952e7i | −0.639382 | + | 0.474178i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.52574e7i | 2.03301i | ||||||||
\(870\) | −6.59166e6 | + | 4.88850e6i | −0.295254 | + | 0.218967i | ||||
\(871\) | 7.51216e6i | 0.335521i | ||||||||
\(872\) | − | 1.07172e7i | − | 0.477297i | ||||||
\(873\) | 2.68698e7 | + | 8.15204e6i | 1.19324 | + | 0.362019i | ||||
\(874\) | − | 4.57367e7i | − | 2.02529i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.82213e6 | + | 9.19896e6i | 0.300372 | + | 0.405022i | ||||
\(877\) | −7.01916e6 | −0.308167 | −0.154084 | − | 0.988058i | \(-0.549243\pi\) | ||||
−0.154084 | + | 0.988058i | \(0.549243\pi\) | |||||||
\(878\) | −1.32472e7 | −0.579945 | ||||||||
\(879\) | −2.46565e7 | + | 1.82858e7i | −1.07637 | + | 0.798254i | ||||
\(880\) | 3.13508e7i | 1.36472i | ||||||||
\(881\) | −1.66384e7 | −0.722224 | −0.361112 | − | 0.932523i | \(-0.617603\pi\) | ||||
−0.361112 | + | 0.932523i | \(0.617603\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.49413e7 | 1.50812 | 0.754062 | − | 0.656803i | \(-0.228092\pi\) | ||||
0.754062 | + | 0.656803i | \(0.228092\pi\) | |||||||
\(884\) | − | 2.22133e7i | − | 0.956056i | ||||||
\(885\) | 6.72400e6 | − | 4.98665e6i | 0.288582 | − | 0.214018i | ||||
\(886\) | 4.38344e7 | 1.87599 | ||||||||
\(887\) | −414512. | −0.0176900 | −0.00884501 | − | 0.999961i | \(-0.502815\pi\) | ||||
−0.00884501 | + | 0.999961i | \(0.502815\pi\) | |||||||
\(888\) | 8.01458e6 | + | 1.08069e7i | 0.341074 | + | 0.459904i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 312854.i | 0.0132394i | ||||||||
\(891\) | 1.48789e7 | − | 2.22640e7i | 0.627878 | − | 0.939525i | ||||
\(892\) | 7.58949e7i | 3.19375i | ||||||||
\(893\) | − | 8.32395e6i | − | 0.349302i | ||||||
\(894\) | −7.50159e6 | + | 5.56333e6i | −0.313913 | + | 0.232804i | ||||
\(895\) | − | 1.78893e7i | − | 0.746511i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.23707e7 | + | 1.65906e7i | −0.928323 | + | 0.688463i | ||||
\(898\) | −5.47783e7 | −2.26682 | ||||||||
\(899\) | −1.13464e7 | −0.468229 | ||||||||
\(900\) | 1.11749e7 | − | 3.68336e7i | 0.459874 | − | 1.51579i | ||||
\(901\) | − | 7.63000e6i | − | 0.313121i | ||||||
\(902\) | −8.43816e6 | −0.345328 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.69124e7 | 0.688309 | ||||||||
\(905\) | 1.04514e7i | 0.424184i | ||||||||
\(906\) | −1.65478e7 | − | 2.23130e7i | −0.669759 | − | 0.903104i | ||||
\(907\) | 3.38278e6 | 0.136539 | 0.0682693 | − | 0.997667i | \(-0.478252\pi\) | ||||
0.0682693 | + | 0.997667i | \(0.478252\pi\) | |||||||
\(908\) | 2.34417e7 | 0.943570 | ||||||||
\(909\) | −6.34818e6 | + | 2.09242e7i | −0.254824 | + | 0.839921i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.26746e7i | 0.905197i | 0.891714 | + | 0.452598i | \(0.149503\pi\) | ||||
−0.891714 | + | 0.452598i | \(0.850497\pi\) | |||||||
\(912\) | 2.76426e7 | + | 3.72733e7i | 1.10051 | + | 1.48392i | ||||
\(913\) | − | 3.60784e7i | − | 1.43242i | ||||||
\(914\) | − | 7.24173e7i | − | 2.86733i | ||||||
\(915\) | −8.75931e6 | − | 1.18111e7i | −0.345873 | − | 0.466376i | ||||
\(916\) | − | 3.37179e7i | − | 1.32777i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.98366e7 | − | 7.09632e6i | 0.776892 | − | 0.277924i | ||||
\(919\) | 1.25070e7 | 0.488500 | 0.244250 | − | 0.969712i | \(-0.421458\pi\) | ||||
0.244250 | + | 0.969712i | \(0.421458\pi\) | |||||||
\(920\) | 4.54654e7 | 1.77097 | ||||||||
\(921\) | 2.21069e7 | + | 2.98090e7i | 0.858775 | + | 1.15797i | ||||
\(922\) | 6.61450e6i | 0.256254i | ||||||||
\(923\) | −1.72922e7 | −0.668105 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.13141e6 | 0.158761 | ||||||||
\(926\) | 3.59003e7i | 1.37585i | ||||||||
\(927\) | 3.64294e7 | + | 1.10523e7i | 1.39236 | + | 0.422429i | ||||
\(928\) | −1.34059e7 | −0.511006 | ||||||||
\(929\) | 5.45557e6 | 0.207396 | 0.103698 | − | 0.994609i | \(-0.466932\pi\) | ||||
0.103698 | + | 0.994609i | \(0.466932\pi\) | |||||||
\(930\) | −2.90379e7 | + | 2.15351e7i | −1.10093 | + | 0.816469i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.00582e7i | 0.379297i | ||||||||
\(933\) | −4.22429e7 | + | 3.13282e7i | −1.58873 | + | 1.17823i | ||||
\(934\) | − | 1.27700e7i | − | 0.478987i | ||||||
\(935\) | 7.74635e6i | 0.289780i | ||||||||
\(936\) | 1.72206e7 | − | 5.67607e7i | 0.642479 | − | 2.11767i | ||||
\(937\) | 2.63266e6i | 0.0979595i | 0.998800 | + | 0.0489797i | \(0.0155970\pi\) | ||||
−0.998800 | + | 0.0489797i | \(0.984403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.49476e7 | − | 3.36393e7i | −0.923346 | − | 1.24504i | ||||
\(940\) | 1.44605e7 | 0.533781 | ||||||||
\(941\) | 1.32478e7 | 0.487720 | 0.243860 | − | 0.969810i | \(-0.421586\pi\) | ||||
0.243860 | + | 0.969810i | \(0.421586\pi\) | |||||||
\(942\) | −3.09636e7 | + | 2.29632e7i | −1.13691 | + | 0.843151i | ||||
\(943\) | 5.82985e6i | 0.213490i | ||||||||
\(944\) | 3.68499e7 | 1.34588 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.69419e7 | −1.34212 | ||||||||
\(947\) | − | 6.01665e6i | − | 0.218012i | −0.994041 | − | 0.109006i | \(-0.965233\pi\) | ||
0.994041 | − | 0.109006i | \(-0.0347667\pi\) | |||||||
\(948\) | −9.34740e7 | + | 6.93222e7i | −3.37808 | + | 2.50525i | ||||
\(949\) | 5.41928e6 | 0.195333 | ||||||||
\(950\) | 2.99102e7 | 1.07525 | ||||||||
\(951\) | 6.41269e6 | + | 8.64687e6i | 0.229926 | + | 0.310033i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.63475e7i | − | 0.939739i | −0.882736 | − | 0.469870i | \(-0.844301\pi\) | ||
0.882736 | − | 0.469870i | \(-0.155699\pi\) | |||||||
\(954\) | 1.03370e7 | − | 3.40717e7i | 0.367726 | − | 1.21206i | ||||
\(955\) | − | 2.55665e7i | − | 0.907115i | ||||||
\(956\) | 9.45300e7i | 3.34522i | ||||||||
\(957\) | −9.11270e6 | + | 6.75816e6i | −0.321638 | + | 0.238533i | ||||
\(958\) | 1.61718e7i | 0.569304i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.60933e6 | + | 4.90161e6i | −0.231462 | + | 0.171657i | ||||
\(961\) | −2.13545e7 | −0.745902 | ||||||||
\(962\) | 1.11260e7 | 0.387615 | ||||||||
\(963\) | −3.23470e7 | − | 9.81377e6i | −1.12401 | − | 0.341012i | ||||
\(964\) | 3.63991e7i | 1.26153i | ||||||||
\(965\) | 2.01777e7 | 0.697515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.11608e7 | −0.383822 | −0.191911 | − | 0.981412i | \(-0.561468\pi\) | ||||
−0.191911 | + | 0.981412i | \(0.561468\pi\) | |||||||
\(968\) | 1.97304e7i | 0.676782i | ||||||||
\(969\) | 6.83011e6 | + | 9.20971e6i | 0.233678 | + | 0.315091i | ||||
\(970\) | −3.79048e7 | −1.29349 | ||||||||
\(971\) | −3.52735e7 | −1.20061 | −0.600303 | − | 0.799772i | \(-0.704954\pi\) | ||||
−0.600303 | + | 0.799772i | \(0.704954\pi\) | |||||||
\(972\) | 6.87741e7 | − | 3.37183e6i | 2.33485 | − | 0.114472i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 2.99684e7i | − | 1.01220i | ||||||
\(975\) | −1.08497e7 | − | 1.46297e7i | −0.365515 | − | 0.492860i | ||||
\(976\) | − | 6.47287e7i | − | 2.17507i | ||||||
\(977\) | − | 2.94174e7i | − | 0.985980i | −0.870035 | − | 0.492990i | \(-0.835904\pi\) | ||
0.870035 | − | 0.492990i | \(-0.164096\pi\) | |||||||
\(978\) | 1.42392e7 | + | 1.92001e7i | 0.476033 | + | 0.641883i | ||||
\(979\) | 432508.i | 0.0144224i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.70913e6 | − | 5.63346e6i | 0.0567027 | − | 0.186897i | ||||
\(982\) | 4.61208e7 | 1.52622 | ||||||||
\(983\) | 2.10765e7 | 0.695688 | 0.347844 | − | 0.937552i | \(-0.386914\pi\) | ||||
0.347844 | + | 0.937552i | \(0.386914\pi\) | |||||||
\(984\) | −7.39596e6 | − | 9.97271e6i | −0.243504 | − | 0.328341i | ||||
\(985\) | − | 4.37073e6i | − | 0.143537i | ||||||
\(986\) | −8.92588e6 | −0.292387 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.64155e7 | 1.83868 | ||||||||
\(989\) | 2.55228e7i | 0.829732i | ||||||||
\(990\) | −1.04947e7 | + | 3.45913e7i | −0.340314 | + | 1.12171i | ||||
\(991\) | 2.90152e7 | 0.938515 | 0.469257 | − | 0.883061i | \(-0.344522\pi\) | ||||
0.469257 | + | 0.883061i | \(0.344522\pi\) | |||||||
\(992\) | −5.90564e7 | −1.90541 | ||||||||
\(993\) | 4.04898e7 | − | 3.00281e7i | 1.30308 | − | 0.966394i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2.84258e7i | − | 0.910238i | ||||||
\(996\) | 7.45158e7 | − | 5.52624e7i | 2.38013 | − | 1.76515i | ||||
\(997\) | 4.09632e7i | 1.30514i | 0.757731 | + | 0.652568i | \(0.226308\pi\) | ||||
−0.757731 | + | 0.652568i | \(0.773692\pi\) | |||||||
\(998\) | 2.75757e7i | 0.876396i | ||||||||
\(999\) | 2.48941e6 | + | 6.95874e6i | 0.0789193 | + | 0.220606i |
(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 | 147.6.c.c.146.16 | 16 | ||
3.2 | odd | 2 | inner | 147.6.c.c.146.1 | 16 | ||
7.2 | even | 3 | 21.6.g.c.17.8 | yes | 16 | ||
7.3 | odd | 6 | 21.6.g.c.5.1 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 147.6.c.c.146.15 | 16 | ||
21.2 | odd | 6 | 21.6.g.c.17.1 | yes | 16 | ||
21.17 | even | 6 | 21.6.g.c.5.8 | yes | 16 | ||
21.20 | even | 2 | inner | 147.6.c.c.146.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.g.c.5.1 | ✓ | 16 | 7.3 | odd | 6 | ||
21.6.g.c.5.8 | yes | 16 | 21.17 | even | 6 | ||
21.6.g.c.17.1 | yes | 16 | 21.2 | odd | 6 | ||
21.6.g.c.17.8 | yes | 16 | 7.2 | even | 3 | ||
147.6.c.c.146.1 | 16 | 3.2 | odd | 2 | inner | ||
147.6.c.c.146.2 | 16 | 21.20 | even | 2 | inner | ||
147.6.c.c.146.15 | 16 | 7.6 | odd | 2 | inner | ||
147.6.c.c.146.16 | 16 | 1.1 | even | 1 | trivial |