Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,6,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("912.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.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: | \(146.270043669\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 4725x^{4} + 92430x^{3} + 1610577x^{2} - 16081740x - 24661341 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 456) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(9.09727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 68.0602 | 1.21750 | 0.608749 | − | 0.793363i | \(-0.291672\pi\) | ||||
0.608749 | + | 0.793363i | \(0.291672\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 181.508 | 1.40007 | 0.700035 | − | 0.714108i | \(-0.253168\pi\) | ||||
0.700035 | + | 0.714108i | \(0.253168\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −56.2292 | −0.140114 | −0.0700568 | − | 0.997543i | \(-0.522318\pi\) | ||||
−0.0700568 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −183.089 | −0.300471 | −0.150236 | − | 0.988650i | \(-0.548003\pi\) | ||||
−0.150236 | + | 0.988650i | \(0.548003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 612.542 | 0.702922 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2031.56 | 1.70493 | 0.852465 | − | 0.522785i | \(-0.175107\pi\) | ||||
0.852465 | + | 0.522785i | \(0.175107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1633.57 | 0.808331 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4003.43 | 1.57802 | 0.789010 | − | 0.614380i | \(-0.210594\pi\) | ||||
0.789010 | + | 0.614380i | \(0.210594\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1507.19 | 0.482300 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4073.95 | −0.899540 | −0.449770 | − | 0.893144i | \(-0.648494\pi\) | ||||
−0.449770 | + | 0.893144i | \(0.648494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6141.15 | −1.14774 | −0.573872 | − | 0.818945i | \(-0.694559\pi\) | ||||
−0.573872 | + | 0.818945i | \(0.694559\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −506.063 | −0.0808947 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12353.4 | 1.70458 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3425.06 | 0.411305 | 0.205653 | − | 0.978625i | \(-0.434068\pi\) | ||||
0.205653 | + | 0.978625i | \(0.434068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1647.80 | −0.173477 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6813.12 | −0.632974 | −0.316487 | − | 0.948597i | \(-0.602503\pi\) | ||||
−0.316487 | + | 0.948597i | \(0.602503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2183.21 | 0.180063 | 0.0900315 | − | 0.995939i | \(-0.471303\pi\) | ||||
0.0900315 | + | 0.995939i | \(0.471303\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5512.87 | 0.405832 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8348.99 | 0.551302 | 0.275651 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275651 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16138.0 | 0.960198 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18284.0 | 0.984341 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 39002.6 | 1.90723 | 0.953616 | − | 0.301027i | \(-0.0973293\pi\) | ||||
0.953616 | + | 0.301027i | \(0.0973293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3826.97 | −0.170588 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 30218.1 | 1.13015 | 0.565076 | − | 0.825039i | \(-0.308847\pi\) | ||||
0.565076 | + | 0.825039i | \(0.308847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12329.1 | 0.424237 | 0.212118 | − | 0.977244i | \(-0.431964\pi\) | ||||
0.212118 | + | 0.977244i | \(0.431964\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14702.1 | 0.466690 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12461.0 | −0.365823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8132.92 | 0.221340 | 0.110670 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110670 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36030.9 | 0.911071 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11559.2 | 0.272134 | 0.136067 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136067 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28897.5 | −0.634677 | −0.317338 | − | 0.948312i | \(-0.602789\pi\) | ||||
−0.317338 | + | 0.948312i | \(0.602789\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13564.7 | 0.278456 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10206.0 | −0.196169 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −164.115 | −0.00295856 | −0.00147928 | − | 0.999999i | \(-0.500471\pi\) | ||||
−0.00147928 | + | 0.999999i | \(0.500471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13470.3 | −0.214625 | −0.107313 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107313 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 138268. | 2.07575 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −36665.5 | −0.519350 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −103567. | −1.38595 | −0.692975 | − | 0.720961i | \(-0.743700\pi\) | ||||
−0.692975 | + | 0.720961i | \(0.743700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −33232.0 | −0.420681 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −55270.3 | −0.662651 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −24569.7 | −0.279313 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −34490.7 | −0.372197 | −0.186099 | − | 0.982531i | \(-0.559584\pi\) | ||||
−0.186099 | + | 0.982531i | \(0.559584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4554.57 | −0.0467046 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −72989.7 | −0.711964 | −0.355982 | − | 0.934493i | \(-0.615854\pi\) | ||||
−0.355982 | + | 0.934493i | \(0.615854\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15482.1 | 0.143793 | 0.0718964 | − | 0.997412i | \(-0.477095\pi\) | ||||
0.0718964 | + | 0.997412i | \(0.477095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 111181. | 0.984141 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 48215.9 | 0.407128 | 0.203564 | − | 0.979062i | \(-0.434748\pi\) | ||||
0.203564 | + | 0.979062i | \(0.434748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −151242. | −1.21929 | −0.609643 | − | 0.792676i | \(-0.708687\pi\) | ||||
−0.609643 | + | 0.792676i | \(0.708687\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 30825.6 | 0.237467 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −233254. | −1.71843 | −0.859217 | − | 0.511612i | \(-0.829049\pi\) | ||||
−0.859217 | + | 0.511612i | \(0.829049\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 272474. | 1.92124 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14830.2 | −0.100157 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 368743. | 2.38702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157889. | −0.980368 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −61318.0 | −0.365448 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −110109. | −0.630299 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 200268. | 1.10180 | 0.550900 | − | 0.834571i | \(-0.314285\pi\) | ||||
0.550900 | + | 0.834571i | \(0.314285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19648.9 | 0.103959 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4663.95 | 0.0237452 | 0.0118726 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118726 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −65524.3 | −0.321198 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49615.9 | 0.234307 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −25589.9 | −0.116484 | −0.0582421 | − | 0.998302i | \(-0.518550\pi\) | ||||
−0.0582421 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 67288.8 | 0.295397 | 0.147698 | − | 0.989032i | \(-0.452813\pi\) | ||||
0.147698 | + | 0.989032i | \(0.452813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 75140.9 | 0.318294 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10294.9 | 0.0421002 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −277274. | −1.09519 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 145242. | 0.554370 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −236573. | −0.872969 | −0.436485 | − | 0.899712i | \(-0.643777\pi\) | ||||
−0.436485 | + | 0.899712i | \(0.643777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 96930.5 | 0.345954 | 0.172977 | − | 0.984926i | \(-0.444661\pi\) | ||||
0.172977 | + | 0.984926i | \(0.444661\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 164556. | 0.568310 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −417968. | −1.39738 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −51875.0 | −0.167961 | −0.0839806 | − | 0.996467i | \(-0.526763\pi\) | ||||
−0.0839806 | + | 0.996467i | \(0.526763\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 351023. | 1.10114 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 726653. | 2.20934 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 194876. | 0.574499 | 0.287250 | − | 0.957856i | \(-0.407259\pi\) | ||||
0.287250 | + | 0.957856i | \(0.407259\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −34442.8 | −0.0984891 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −512937. | −1.42322 | −0.711611 | − | 0.702573i | \(-0.752034\pi\) | ||||
−0.711611 | + | 0.702573i | \(0.752034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −337772. | −0.909717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 344170. | 0.874295 | 0.437148 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437148 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 273566. | 0.675254 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 271963. | 0.652494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 535947. | 1.25023 | 0.625114 | − | 0.780534i | \(-0.285053\pi\) | ||||
0.625114 | + | 0.780534i | \(0.285053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 717175. | 1.62715 | 0.813577 | − | 0.581457i | \(-0.197517\pi\) | ||||
0.813577 | + | 0.581457i | \(0.197517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 110962. | 0.244933 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 233110. | 0.500763 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −114233. | −0.238884 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 132319. | 0.269444 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 616524. | 1.22283 | 0.611416 | − | 0.791310i | \(-0.290600\pi\) | ||||
0.611416 | + | 0.791310i | \(0.290600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −297746. | −0.575377 | −0.287688 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287688 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −112149. | −0.211208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 750295. | 1.37742 | 0.688710 | − | 0.725037i | \(-0.258177\pi\) | ||||
0.688710 | + | 0.725037i | \(0.258177\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 447059. | 0.800262 | 0.400131 | − | 0.916458i | \(-0.368965\pi\) | ||||
0.400131 | + | 0.916458i | \(0.368965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 73196.3 | 0.127791 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −739453. | −1.25942 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −463702. | −0.770645 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 324278. | 0.526007 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20298.8 | 0.0321443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −765080. | −1.18304 | −0.591522 | − | 0.806289i | \(-0.701473\pi\) | ||||
−0.591522 | + | 0.806289i | \(0.701473\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 104033. | 0.157117 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 148590. | 0.219226 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.11467e6 | −1.60692 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −260077. | −0.366431 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −371955. | −0.512283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −624803. | −0.841358 | −0.420679 | − | 0.907210i | \(-0.638208\pi\) | ||||
−0.420679 | + | 0.907210i | \(0.638208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 122082. | 0.160767 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8488.97 | 0.0109343 | 0.00546714 | − | 0.999985i | \(-0.498260\pi\) | ||||
0.00546714 | + | 0.999985i | \(0.498260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 502157. | 0.632777 | 0.316388 | − | 0.948630i | \(-0.397530\pi\) | ||||
0.316388 | + | 0.948630i | \(0.397530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −91854.4 | −0.113258 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −319233. | −0.385228 | −0.192614 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192614 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 568234. | 0.671209 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1477.04 | −0.00170813 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 756618. | 0.856805 | 0.428402 | − | 0.903588i | \(-0.359077\pi\) | ||||
0.428402 | + | 0.903588i | \(0.359077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −645205. | −0.715575 | −0.357788 | − | 0.933803i | \(-0.616469\pi\) | ||||
−0.357788 | + | 0.933803i | \(0.616469\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.09836e6 | 1.16904 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 66095.0 | 0.0689329 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −121232. | −0.123914 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.69048e6 | 1.69366 | 0.846829 | − | 0.531866i | \(-0.178509\pi\) | ||||
0.846829 | + | 0.531866i | \(0.178509\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −225110. | −0.221102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.24441e6 | 1.19843 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −200205. | −0.189079 | −0.0945393 | − | 0.995521i | \(-0.530138\pi\) | ||||
−0.0945393 | + | 0.995521i | \(0.530138\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 621675. | 0.575857 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −329990. | −0.299847 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 791636. | 0.705726 | 0.352863 | − | 0.935675i | \(-0.385208\pi\) | ||||
0.352863 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.65452e6 | 2.32205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −932106. | −0.800179 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 679190. | 0.572283 | 0.286141 | − | 0.958187i | \(-0.407627\pi\) | ||||
0.286141 | + | 0.958187i | \(0.407627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.62480e6 | 1.34393 | 0.671965 | − | 0.740583i | \(-0.265451\pi\) | ||||
0.671965 | + | 0.740583i | \(0.265451\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −299088. | −0.242880 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −84748.0 | −0.0675768 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.46645e6 | −1.93141 | −0.965703 | − | 0.259651i | \(-0.916392\pi\) | ||||
−0.965703 | + | 0.259651i | \(0.916392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −497433. | −0.382582 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 955572. | 0.721934 | 0.360967 | − | 0.932579i | \(-0.382447\pi\) | ||||
0.360967 | + | 0.932579i | \(0.382447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 152472. | 0.113168 | 0.0565841 | − | 0.998398i | \(-0.481979\pi\) | ||||
0.0565841 | + | 0.998398i | \(0.481979\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −221127. | −0.161261 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.23663e6 | −0.886209 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.70736e6 | 1.90678 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −310417. | −0.214888 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.54402e6 | 1.73121 | 0.865607 | − | 0.500724i | \(-0.166933\pi\) | ||||
0.865607 | + | 0.500724i | \(0.166933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.05665e6 | 1.37596 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −40991.1 | −0.0269649 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −732983. | −0.474150 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 396270. | 0.252101 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −656907. | −0.411053 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 839124. | 0.516507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.13060e6 | −0.684644 | −0.342322 | − | 0.939583i | \(-0.611213\pi\) | ||||
−0.342322 | + | 0.939583i | \(0.611213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 139339. | 0.0830188 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.39201e6 | −1.98864 | −0.994320 | − | 0.106428i | \(-0.966058\pi\) | ||||
−0.994320 | + | 0.106428i | \(0.966058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 430684. | 0.248484 | 0.124242 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124242 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00063e6 | 0.568194 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.42810e6 | −1.91604 | −0.958022 | − | 0.286695i | \(-0.907443\pi\) | ||||
−0.958022 | + | 0.286695i | \(0.907443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 229075. | 0.126038 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 433943. | 0.235055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −733392. | −0.391138 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −275949. | −0.144917 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.36118e6 | −0.703955 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.51541e6 | 0.771862 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21956.4 | 0.0110152 | 0.00550758 | − | 0.999985i | \(-0.498247\pi\) | ||||
0.00550758 | + | 0.999985i | \(0.498247\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 277430. | 0.137102 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 553528. | 0.269481 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.54253e6 | 1.21953 | 0.609764 | − | 0.792583i | \(-0.291264\pi\) | ||||
0.609764 | + | 0.792583i | \(0.291264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.09928e6 | −0.992138 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 345312. | 0.160815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −121421. | −0.0557262 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.45227e6 | 1.10923 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.25363e6 | 0.558914 | 0.279457 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279457 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.36606e6 | 0.600352 | 0.300176 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300176 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −133472. | −0.0578258 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.16721e6 | 1.35282 | 0.676411 | − | 0.736525i | \(-0.263534\pi\) | ||||
0.676411 | + | 0.736525i | \(0.263534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 786723. | 0.331322 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.31869e6 | 1.37815 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.40859e6 | −0.986342 | −0.493171 | − | 0.869932i | \(-0.664162\pi\) | ||||
−0.493171 | + | 0.869932i | \(0.664162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.42100e6 | −0.566016 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.96677e6 | −0.772717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.29575e6 | −0.889734 | −0.444867 | − | 0.895597i | \(-0.646749\pi\) | ||||
−0.444867 | + | 0.895597i | \(0.646749\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −551862. | −0.210991 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.07926e6 | 2.67026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.59398e6 | −1.70969 | −0.854844 | − | 0.518885i | \(-0.826347\pi\) | ||||
−0.854844 | + | 0.518885i | \(0.826347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −990978. | −0.363903 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 745894. | 0.270286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.51884e6 | 0.543143 | 0.271572 | − | 0.962418i | \(-0.412457\pi\) | ||||
0.271572 | + | 0.962418i | \(0.412457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.80241e6 | 0.636125 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −796963. | −0.277614 | −0.138807 | − | 0.990319i | \(-0.544327\pi\) | ||||
−0.138807 | + | 0.990319i | \(0.544327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −694625. | −0.238835 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 176840. | 0.0600210 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.08768e6 | 0.364440 | 0.182220 | − | 0.983258i | \(-0.441672\pi\) | ||||
0.182220 | + | 0.983258i | \(0.441672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.13319e6 | 2.69041 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41975.5 | 0.0137093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11169.7 | −0.00360204 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −90856.2 | −0.0289320 | −0.0144660 | − | 0.999895i | \(-0.504605\pi\) | ||||
−0.0144660 | + | 0.999895i | \(0.504605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −589718. | −0.185444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.42123e6 | −1.06248 | −0.531241 | − | 0.847221i | \(-0.678274\pi\) | ||||
−0.531241 | + | 0.847221i | \(0.678274\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.12437e6 | 0.344864 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 446543. | 0.135277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −192589. | −0.0576295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.71976e6 | −0.508346 | −0.254173 | − | 0.967159i | \(-0.581803\pi\) | ||||
−0.254173 | + | 0.967159i | \(0.581803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −230309. | −0.0672522 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.48481e6 | 1.58229 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −916789. | −0.261306 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 605599. | 0.170547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.64727e6 | −1.84973 | −0.924864 | − | 0.380297i | \(-0.875822\pi\) | ||||
−0.924864 | + | 0.380297i | \(0.875822\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.48576e6 | 1.23348 | 0.616739 | − | 0.787168i | \(-0.288454\pi\) | ||||
0.616739 | + | 0.787168i | \(0.288454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 676268. | 0.183767 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.06193e6 | 0.822287 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.23783e6 | 0.593961 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 92654.5 | 0.0243065 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.50573e6 | −1.16835 | −0.584174 | − | 0.811629i | \(-0.698581\pi\) | ||||
−0.584174 | + | 0.811629i | \(0.698581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.74569e6 | 1.72905 | 0.864524 | − | 0.502592i | \(-0.167620\pi\) | ||||
0.864524 | + | 0.502592i | \(0.167620\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.49546e6 | −0.632307 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.44524e6 | −0.362023 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.54556e6 | 1.37336 | 0.686679 | − | 0.726960i | \(-0.259068\pi\) | ||||
0.686679 | + | 0.726960i | \(0.259068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.30718e6 | 0.320066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.36139e6 | −0.329589 | −0.164795 | − | 0.986328i | \(-0.552696\pi\) | ||||
−0.164795 | + | 0.986328i | \(0.552696\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.04881e6 | −1.68739 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.12915e6 | −0.504009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −577806. | −0.135259 | −0.0676295 | − | 0.997711i | \(-0.521544\pi\) | ||||
−0.0676295 | + | 0.997711i | \(0.521544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 383096. | 0.0886884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 872375. | 0.199737 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.26178e6 | −0.512178 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.53412e6 | 1.01555 | 0.507777 | − | 0.861489i | \(-0.330468\pi\) | ||||
0.507777 | + | 0.861489i | \(0.330468\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48100e6 | 0.328114 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.58278e6 | −1.66179 | −0.830895 | − | 0.556429i | \(-0.812171\pi\) | ||||
−0.830895 | + | 0.556429i | \(0.812171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.74510e6 | 1.89589 | 0.947943 | − | 0.318440i | \(-0.103159\pi\) | ||||
0.947943 | + | 0.318440i | \(0.103159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.76171e6 | −0.806775 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.25842e6 | −0.691378 | −0.345689 | − | 0.938349i | \(-0.612355\pi\) | ||||
−0.345689 | + | 0.938349i | \(0.612355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.47619e6 | 0.309891 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −466875. | −0.0969724 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −122760. | −0.0252293 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −544095. | −0.110647 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.15921e6 | 0.635744 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 481496. | 0.0958857 | 0.0479429 | − | 0.998850i | \(-0.484733\pi\) | ||||
0.0479429 | + | 0.998850i | \(0.484733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −627091. | −0.123586 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.53988e6 | 1.27556 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.34745e6 | −0.453149 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.42000e6 | −0.844500 | −0.422250 | − | 0.906479i | \(-0.638760\pi\) | ||||
−0.422250 | + | 0.906479i | \(0.638760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.75388e6 | 0.331687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 257981. | 0.0482930 | 0.0241465 | − | 0.999708i | \(-0.492313\pi\) | ||||
0.0241465 | + | 0.999708i | \(0.492313\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.27645e6 | −1.53365 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −309985. | −0.0568627 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.09809e6 | 0.381007 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.08106e7 | 1.94356 | 0.971782 | − | 0.235882i | \(-0.0757978\pi\) | ||||
0.971782 | + | 0.235882i | \(0.0757978\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.61643e6 | −0.821698 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.13024e7 | −1.99183 | −0.995915 | − | 0.0902925i | \(-0.971220\pi\) | ||||
−0.995915 | + | 0.0902925i | \(0.971220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.96769e6 | −0.866814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.03994e6 | −0.525225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.04265e6 | 0.862708 | 0.431354 | − | 0.902183i | \(-0.358036\pi\) | ||||
0.431354 | + | 0.902183i | \(0.358036\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.24511e6 | −0.888592 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.05372e6 | 0.175067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −469458. | −0.0772449 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.09753e6 | 0.504775 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.51864e6 | −0.890713 | −0.445357 | − | 0.895353i | \(-0.646923\pi\) | ||||
−0.445357 | + | 0.895353i | \(0.646923\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.84641e6 | −0.934621 | −0.467310 | − | 0.884093i | \(-0.654777\pi\) | ||||
−0.467310 | + | 0.884093i | \(0.654777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.46209e6 | 0.389858 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.24761e7 | −1.95682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.59111e6 | 1.49015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.44766e6 | 0.376717 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.24740e6 | 0.190191 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.28158e6 | 0.495677 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.82352e6 | 0.721819 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −907430. | −0.134537 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.21955e6 | −0.326041 | −0.163020 | − | 0.986623i | \(-0.552124\pi\) | ||||
−0.163020 | + | 0.986623i | \(0.552124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.45458e6 | 0.939438 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.02935e7 | −1.48448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.37703e6 | 0.196777 | 0.0983883 | − | 0.995148i | \(-0.468631\pi\) | ||||
0.0983883 | + | 0.995148i | \(0.468631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 998661. | 0.141412 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.47070e6 | 0.206369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29788.2 | −0.00414220 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.09799e6 | 0.289116 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.61215e6 | −0.629891 | −0.314946 | − | 0.949110i | \(-0.601986\pi\) | ||||
−0.314946 | + | 0.949110i | \(0.601986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −399721. | −0.0541038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.02810e6 | −0.137920 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.39621e7 | 1.85643 | 0.928214 | − | 0.372046i | \(-0.121343\pi\) | ||||
0.928214 | + | 0.372046i | \(0.121343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.58753e7 | −2.09219 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.19087e6 | 0.155563 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.25243e7 | −1.62170 | −0.810852 | − | 0.585251i | \(-0.800996\pi\) | ||||
−0.810852 | + | 0.585251i | \(0.800996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.03755e6 | 1.03165 | 0.515826 | − | 0.856693i | \(-0.327485\pi\) | ||||
0.515826 | + | 0.856693i | \(0.327485\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.54872e6 | 0.706002 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.03392e6 | 0.761079 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.33502e7 | 1.66935 | 0.834674 | − | 0.550744i | \(-0.185656\pi\) | ||||
0.834674 | + | 0.550744i | \(0.185656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.67971e6 | −0.332194 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.44496e6 | −0.300491 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.19308e6 | −0.267229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00934e6 | −0.121941 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.01353e6 | 0.480763 | 0.240382 | − | 0.970678i | \(-0.422727\pi\) | ||||
0.240382 | + | 0.970678i | \(0.422727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.21695e6 | 0.263311 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.75265e6 | 0.795254 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.78650e6 | 1.02608 | 0.513038 | − | 0.858366i | \(-0.328520\pi\) | ||||
0.513038 | + | 0.858366i | \(0.328520\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.50967e7 | 2.90619 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.02353e6 | 0.462031 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.36952e7 | −1.55955 | −0.779777 | − | 0.626058i | \(-0.784667\pi\) | ||||
−0.779777 | + | 0.626058i | \(0.784667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.47348e7 | −1.66402 | −0.832010 | − | 0.554760i | \(-0.812810\pi\) | ||||
−0.832010 | + | 0.554760i | \(0.812810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 658767. | 0.0737800 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.07460e7 | −1.19360 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.98391e6 | −0.879516 | −0.439758 | − | 0.898116i | \(-0.644936\pi\) | ||||
−0.439758 | + | 0.898116i | \(0.644936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.65508e6 | −0.727126 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.52861e6 | −0.165650 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.43938e7 | −1.54712 | −0.773558 | − | 0.633725i | \(-0.781525\pi\) | ||||
−0.773558 | + | 0.633725i | \(0.781525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.17332e6 | −0.444932 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.35120e7 | −1.42892 | −0.714459 | − | 0.699677i | \(-0.753327\pi\) | ||||
−0.714459 | + | 0.699677i | \(0.753327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.80703e6 | −0.189557 | −0.0947783 | − | 0.995498i | \(-0.530214\pi\) | ||||
−0.0947783 | + | 0.995498i | \(0.530214\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.91850e6 | 0.303690 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.87983e7 | −1.94043 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.22040e7 | −1.24969 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 182689. | 0.0185585 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.95821e6 | 0.701247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.73492e7 | −1.73463 | −0.867313 | − | 0.497762i | \(-0.834155\pi\) | ||||
−0.867313 | + | 0.497762i | \(0.834155\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.88572e6 | −0.683030 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.36303e7 | 1.34144 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.95469e6 | −0.288512 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 936297. | 0.0907113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.83239e6 | −0.560662 | −0.280331 | − | 0.959903i | \(-0.590444\pi\) | ||||
−0.280331 | + | 0.959903i | \(0.590444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.08231e7 | 1.03235 | 0.516173 | − | 0.856484i | \(-0.327356\pi\) | ||||
0.516173 | + | 0.856484i | \(0.327356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.33731e6 | 0.126570 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.06311e7 | −0.998433 | −0.499217 | − | 0.866477i | \(-0.666379\pi\) | ||||
−0.499217 | + | 0.866477i | \(0.666379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.69914e6 | −0.158350 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.00320e7 | −0.927758 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.53877e7 | 1.41219 | 0.706093 | − | 0.708119i | \(-0.250456\pi\) | ||||
0.706093 | + | 0.708119i | \(0.250456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 317429. | 0.0289097 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.34070e6 | −0.211559 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.66297e6 | −0.149166 | −0.0745832 | − | 0.997215i | \(-0.523763\pi\) | ||||
−0.0745832 | + | 0.997215i | \(0.523763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.97953e6 | 0.354265 | 0.177133 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177133 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.34759e6 | −0.295766 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.45959e6 | −0.391058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.63098e7 | −1.41949 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.62323e6 | −0.485758 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −693259. | −0.0594414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.83424e6 | 0.666744 | 0.333372 | − | 0.942795i | \(-0.391814\pi\) | ||||
0.333372 | + | 0.942795i | \(0.391814\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09874e6 | 0.0928186 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.68877e6 | −0.644741 | −0.322370 | − | 0.946614i | \(-0.604480\pi\) | ||||
−0.322370 | + | 0.946614i | \(0.604480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.26033e6 | −0.521102 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 76400.7 | 0.00631291 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.48293e7 | −1.21638 | −0.608190 | − | 0.793792i | \(-0.708104\pi\) | ||||
−0.608190 | + | 0.793792i | \(0.708104\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.74165e6 | −0.141819 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.51941e6 | 0.365334 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.14093e6 | −0.573069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.34870e7 | 1.87125 | 0.935626 | − | 0.352992i | \(-0.114836\pi\) | ||||
0.935626 | + | 0.352992i | \(0.114836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −826689. | −0.0653897 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.57969e6 | 0.359645 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38412e7 | −1.07918 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.87309e6 | −0.222411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.22661e6 | −0.248000 | −0.124000 | − | 0.992282i | \(-0.539572\pi\) | ||||
−0.124000 | + | 0.992282i | \(0.539572\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.23645e6 | −0.0943599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.11411e6 | 0.387522 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.32482e7 | −0.996800 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.35520e6 | 0.175959 | 0.0879796 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879796 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13293.3 | −0.000986188 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.45857e7 | −1.81116 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 700675. | 0.0512568 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.80956e6 | 0.494677 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.13336e7 | 1.53901 | 0.769507 | − | 0.638638i | \(-0.220502\pi\) | ||||
0.769507 | + | 0.638638i | \(0.220502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81012e6 | 0.201320 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.80685e6 | −0.413138 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.14020e6 | −0.433848 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.88770e6 | −0.132464 | −0.0662319 | − | 0.997804i | \(-0.521098\pi\) | ||||
−0.0662319 | + | 0.997804i | \(0.521098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.43531e6 | 0.306995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −899424. | −0.0618308 | −0.0309154 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309154 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.88522e6 | 0.674944 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −457308. | −0.0310127 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 157022. | 0.0105767 | 0.00528833 | − | 0.999986i | \(-0.498317\pi\) | ||||
0.00528833 | + | 0.999986i | \(0.498317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 594855. | 0.0397984 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.95058e7 | −1.29626 | −0.648128 | − | 0.761531i | \(-0.724448\pi\) | ||||
−0.648128 | + | 0.761531i | \(0.724448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.61012e7 | −1.06284 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.09109e6 | −0.0715418 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.75156e6 | 0.570008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45467e7 | −0.941163 | −0.470582 | − | 0.882356i | \(-0.655956\pi\) | ||||
−0.470582 | + | 0.882356i | \(0.655956\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.52143e7 | 0.977834 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.59711e6 | 0.421198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.20959e7 | −0.767183 | −0.383592 | − | 0.923503i | \(-0.625313\pi\) | ||||
−0.383592 | + | 0.923503i | \(0.625313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.02599e6 | −0.127653 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.04786e7 | −0.655905 | −0.327952 | − | 0.944694i | \(-0.606359\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.74515e7 | −1.70709 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.11997e7 | 0.691916 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.53259e6 | −0.339578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.61815e6 | −0.0986739 | −0.0493370 | − | 0.998782i | \(-0.515711\pi\) | ||||
−0.0493370 | + | 0.998782i | \(0.515711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.80185e6 | −0.109165 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.19651e7 | 1.32216 | 0.661080 | − | 0.750315i | \(-0.270098\pi\) | ||||
0.661080 | + | 0.750315i | \(0.270098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.25586e6 | −0.553557 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.59508e6 | 0.332471 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.45953e6 | 0.145214 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −649966. | −0.0381297 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.96991e6 | −0.173117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.53062e6 | −0.204492 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.02291e7 | −0.588707 | −0.294354 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294354 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.12472e6 | 0.407451 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.23374e7 | −2.40593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.25733e6 | −0.127471 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.38907e7 | 1.34064 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.15124e7 | −1.19962 | −0.599808 | − | 0.800144i | \(-0.704756\pi\) | ||||
−0.599808 | + | 0.800144i | \(0.704756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.69614e7 | 0.939931 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.38895e6 | −0.461983 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.62488e6 | 0.0889269 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.94562e7 | 2.68987 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.11271e6 | 0.330408 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.72326e6 | −0.307448 | −0.153724 | − | 0.988114i | \(-0.549127\pi\) | ||||
−0.153724 | + | 0.988114i | \(0.549127\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.78783e7 | −1.48838 | −0.744191 | − | 0.667967i | \(-0.767165\pi\) | ||||
−0.744191 | + | 0.667967i | \(0.767165\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.46232e7 | 0.775918 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.32633e7 | 0.699451 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −788139. | −0.0413093 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.69179e6 | −0.140227 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.54662e6 | 0.338969 | 0.169484 | − | 0.985533i | \(-0.445790\pi\) | ||||
0.169484 | + | 0.985533i | \(0.445790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.03390e7 | 0.532082 | 0.266041 | − | 0.963962i | \(-0.414284\pi\) | ||||
0.266041 | + | 0.963962i | \(0.414284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −762732. | −0.0390155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.19751e7 | 0.608858 | 0.304429 | − | 0.952535i | \(-0.401534\pi\) | ||||
0.304429 | + | 0.952535i | \(0.401534\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.39945e7 | −0.707249 | −0.353625 | − | 0.935387i | \(-0.615051\pi\) | ||||
−0.353625 | + | 0.935387i | \(0.615051\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.21981e7 | −1.11510 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.27853e7 | 1.63707 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.49106e7 | −1.73277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.47690e6 | −0.220884 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.12669e7 | 1.04303 | 0.521517 | − | 0.853241i | \(-0.325366\pi\) | ||||
0.521517 | + | 0.853241i | \(0.325366\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.91410e6 | −0.190828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.60015e6 | 0.416809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.29888e7 | −1.10758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.86581e7 | −1.37258 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37225e6 | 0.0653377 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.37120e7 | 0.649048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.31526e6 | −0.203065 | −0.101532 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101532 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.99015e6 | −0.0931044 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.59971e6 | 0.0744029 | 0.0372015 | − | 0.999308i | \(-0.488156\pi\) | ||||
0.0372015 | + | 0.999308i | \(0.488156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.97990e7 | −1.37790 | −0.688951 | − | 0.724808i | \(-0.741928\pi\) | ||||
−0.688951 | + | 0.724808i | \(0.741928\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.11297e7 | −0.511653 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.17818e7 | 0.538498 | 0.269249 | − | 0.963071i | \(-0.413225\pi\) | ||||
0.269249 | + | 0.963071i | \(0.413225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.34243e7 | 1.06445 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.43662e7 | 1.10088 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9228.07 | 0.000414535 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.48905e6 | −0.0665063 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.79375e6 | −0.124066 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.99856e7 | −0.882462 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.60831e7 | −0.706108 | −0.353054 | − | 0.935603i | \(-0.614857\pi\) | ||||
−0.353054 | + | 0.935603i | \(0.614857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.28961e7 | 0.999517 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.06461e7 | −0.896187 | −0.448093 | − | 0.893987i | \(-0.647897\pi\) | ||||
−0.448093 | + | 0.893987i | \(0.647897\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.44612e7 | 1.05579 | 0.527894 | − | 0.849310i | \(-0.322982\pi\) | ||||
0.527894 | + | 0.849310i | \(0.322982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.85098e7 | 0.794409 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.49921e7 | −1.06658 | −0.533290 | − | 0.845932i | \(-0.679045\pi\) | ||||
−0.533290 | + | 0.845932i | \(0.679045\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.63502e7 | 1.54260 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −368920. | −0.0155682 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.01399e6 | −0.126477 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.64766e7 | 1.52215 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.59685e6 | −0.273751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.50187e7 | 1.03244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.92359e7 | 3.25169 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.56643e6 | 0.145551 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.88111e7 | 1.98106 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.33799e6 | −0.0540051 | −0.0270026 | − | 0.999635i | \(-0.508596\pi\) | ||||
−0.0270026 | + | 0.999635i | \(0.508596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.91216e6 | −0.237321 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.41172e6 | 0.176121 | 0.0880606 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880606 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 757423. | 0.0300719 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.55211e6 | 0.298206 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 846542. | 0.0332449 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.72978e7 | 0.675619 | 0.337810 | − | 0.941214i | \(-0.390314\pi\) | ||||
0.337810 | + | 0.941214i | \(0.390314\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.01754e7 | −0.395279 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.11636e6 | −0.0817685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.16221e6 | 0.198373 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.25405e6 | 0.0479309 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.09081e7 | −0.414676 | −0.207338 | − | 0.978269i | \(-0.566480\pi\) | ||||
−0.207338 | + | 0.978269i | \(0.566480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.82583e6 | −0.220284 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.05281e7 | −1.14814 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.77471e6 | −0.290841 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85474e7 | 1.43432 | 0.717159 | − | 0.696909i | \(-0.245442\pi\) | ||||
0.717159 | + | 0.696909i | \(0.245442\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.87616e6 | 0.143462 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.02392e6 | 0.0745110 | 0.0372555 | − | 0.999306i | \(-0.488138\pi\) | ||||
0.0372555 | + | 0.999306i | \(0.488138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.72758e7 | −0.998847 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.00566e6 | 0.328047 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.58028e7 | −0.572611 | −0.286306 | − | 0.958138i | \(-0.592427\pi\) | ||||
−0.286306 | + | 0.958138i | \(0.592427\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.29080e6 | 0.190702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.08529e7 | −1.10623 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.55765e7 | −1.62558 | −0.812791 | − | 0.582555i | \(-0.802053\pi\) | ||||
−0.812791 | + | 0.582555i | \(0.802053\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.19607e7 | 1.48879 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.06168e6 | 0.0727680 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.64477e6 | −0.163086 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.08453e6 | 0.317318 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.90549e6 | 0.135709 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.02646e7 | −0.700520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.49937e7 | 1.54734 | 0.773669 | − | 0.633589i | \(-0.218419\pi\) | ||||
0.773669 | + | 0.633589i | \(0.218419\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.60052e6 | −0.225823 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.31949e7 | −1.47023 | −0.735114 | − | 0.677944i | \(-0.762871\pi\) | ||||
−0.735114 | + | 0.677944i | \(0.762871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22134e7 | 0.413577 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.48354e6 | −0.0836681 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.76839e6 | 0.293889 | 0.146945 | − | 0.989145i | \(-0.453056\pi\) | ||||
0.146945 | + | 0.989145i | \(0.453056\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.82351e6 | 0.194191 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.22506e7 | −0.406428 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.18236e7 | 1.38051 | 0.690253 | − | 0.723568i | \(-0.257499\pi\) | ||||
0.690253 | + | 0.723568i | \(0.257499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.10652e7 | 1.67700 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.36387e7 | 0.445634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.74033e6 | 0.284143 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.87743e7 | −0.930723 | −0.465362 | − | 0.885121i | \(-0.654076\pi\) | ||||
−0.465362 | + | 0.885121i | \(0.654076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 197607. | 0.00635960 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.04269e7 | 0.974317 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.50959e6 | −0.302987 | −0.151493 | − | 0.988458i | \(-0.548408\pi\) | ||||
−0.151493 | + | 0.988458i | \(0.548408\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.49687e6 | 0.0791558 |
(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 | 912.6.a.y.1.6 | 6 | ||
4.3 | odd | 2 | 456.6.a.f.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.6.a.f.1.6 | ✓ | 6 | 4.3 | odd | 2 | ||
912.6.a.y.1.6 | 6 | 1.1 | even | 1 | trivial |