Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,6,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("72.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(11.5476350265\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 72.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 34.0000 | 0.608210 | 0.304105 | − | 0.952638i | \(-0.401643\pi\) | ||||
0.304105 | + | 0.952638i | \(0.401643\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −240.000 | −1.85125 | −0.925627 | − | 0.378436i | \(-0.876462\pi\) | ||||
−0.925627 | + | 0.378436i | \(0.876462\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000 | 0.308987 | 0.154493 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154493 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.0000 | 0.0754917 | 0.0377459 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377459 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1954.00 | −1.63984 | −0.819921 | − | 0.572476i | \(-0.805983\pi\) | ||||
−0.819921 | + | 0.572476i | \(0.805983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1924.00 | −1.22270 | −0.611352 | − | 0.791359i | \(-0.709374\pi\) | ||||
−0.611352 | + | 0.791359i | \(0.709374\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2840.00 | −1.11943 | −0.559717 | − | 0.828684i | \(-0.689090\pi\) | ||||
−0.559717 | + | 0.828684i | \(0.689090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1969.00 | −0.630080 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8922.00 | 1.97000 | 0.985002 | − | 0.172541i | \(-0.0551979\pi\) | ||||
0.985002 | + | 0.172541i | \(0.0551979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4648.00 | −0.868684 | −0.434342 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434342 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8160.00 | −1.12595 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4362.00 | −0.523819 | −0.261910 | − | 0.965092i | \(-0.584352\pi\) | ||||
−0.261910 | + | 0.965092i | \(0.584352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2886.00 | 0.268125 | 0.134062 | − | 0.990973i | \(-0.457198\pi\) | ||||
0.134062 | + | 0.990973i | \(0.457198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11332.0 | 0.934621 | 0.467310 | − | 0.884093i | \(-0.345223\pi\) | ||||
0.467310 | + | 0.884093i | \(0.345223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7008.00 | −0.462753 | −0.231377 | − | 0.972864i | \(-0.574323\pi\) | ||||
−0.231377 | + | 0.972864i | \(0.574323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40793.0 | 2.42714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22594.0 | 1.10485 | 0.552425 | − | 0.833562i | \(-0.313703\pi\) | ||||
0.552425 | + | 0.833562i | \(0.313703\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4216.00 | 0.187929 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28.0000 | 0.00104720 | 0.000523598 | − | 1.00000i | \(-0.499833\pi\) | ||||
0.000523598 | 1.00000i | \(0.499833\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6386.00 | −0.219738 | −0.109869 | − | 0.993946i | \(-0.535043\pi\) | ||||
−0.109869 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1564.00 | 0.0459149 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −39076.0 | −1.06346 | −0.531732 | − | 0.846912i | \(-0.678459\pi\) | ||||
−0.531732 | + | 0.846912i | \(0.678459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 54872.0 | 1.29183 | 0.645914 | − | 0.763410i | \(-0.276476\pi\) | ||||
0.645914 | + | 0.763410i | \(0.276476\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 21034.0 | 0.461971 | 0.230986 | − | 0.972957i | \(-0.425805\pi\) | ||||
0.230986 | + | 0.972957i | \(0.425805\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −29760.0 | −0.572013 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26632.0 | 0.480105 | 0.240052 | − | 0.970760i | \(-0.422835\pi\) | ||||
0.240052 | + | 0.970760i | \(0.422835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −56188.0 | −0.895258 | −0.447629 | − | 0.894219i | \(-0.647732\pi\) | ||||
−0.447629 | + | 0.894219i | \(0.647732\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66436.0 | −0.997370 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −64410.0 | −0.861942 | −0.430971 | − | 0.902366i | \(-0.641829\pi\) | ||||
−0.430971 | + | 0.902366i | \(0.641829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11040.0 | −0.139754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65416.0 | −0.743661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −116158. | −1.25349 | −0.626743 | − | 0.779226i | \(-0.715613\pi\) | ||||
−0.626743 | + | 0.779226i | \(0.715613\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66834.0 | 0.651920 | 0.325960 | − | 0.945384i | \(-0.394313\pi\) | ||||
0.325960 | + | 0.945384i | \(0.394313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 64000.0 | 0.594411 | 0.297206 | − | 0.954814i | \(-0.403945\pi\) | ||||
0.297206 | + | 0.954814i | \(0.403945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15084.0 | 0.127367 | 0.0636835 | − | 0.997970i | \(-0.479715\pi\) | ||||
0.0636835 | + | 0.997970i | \(0.479715\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −39698.0 | −0.320039 | −0.160019 | − | 0.987114i | \(-0.551156\pi\) | ||||
−0.160019 | + | 0.987114i | \(0.551156\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −155154. | −1.14305 | −0.571527 | − | 0.820583i | \(-0.693649\pi\) | ||||
−0.571527 | + | 0.820583i | \(0.693649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −96560.0 | −0.680852 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 468960. | 3.03577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145675. | −0.904527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −173196. | −0.991432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 52072.0 | 0.286480 | 0.143240 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143240 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −159964. | −0.814412 | −0.407206 | − | 0.913336i | \(-0.633497\pi\) | ||||
−0.407206 | + | 0.913336i | \(0.633497\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 461760. | 2.26353 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 262278. | 1.19388 | 0.596940 | − | 0.802286i | \(-0.296383\pi\) | ||||
0.596940 | + | 0.802286i | \(0.296383\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 253524. | 1.11297 | 0.556483 | − | 0.830859i | \(-0.312150\pi\) | ||||
0.556483 | + | 0.830859i | \(0.312150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5704.00 | 0.0233260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 303348. | 1.19818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −355630. | −1.31230 | −0.656149 | − | 0.754631i | \(-0.727816\pi\) | ||||
−0.656149 | + | 0.754631i | \(0.727816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1024.00 | −0.00365475 | −0.00182737 | − | 0.999998i | \(-0.500582\pi\) | ||||
−0.00182737 | + | 0.999998i | \(0.500582\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −158032. | −0.528343 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −59954.0 | −0.194119 | −0.0970597 | − | 0.995279i | \(-0.530944\pi\) | ||||
−0.0970597 | + | 0.995279i | \(0.530944\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 681600. | 2.07236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −341556. | −1.00692 | −0.503458 | − | 0.864020i | \(-0.667939\pi\) | ||||
−0.503458 | + | 0.864020i | \(0.667939\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5016.00 | −0.0139177 | −0.00695883 | − | 0.999976i | \(-0.502215\pi\) | ||||
−0.00695883 | + | 0.999976i | \(0.502215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369177. | −0.994301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 228666. | 0.580880 | 0.290440 | − | 0.956893i | \(-0.406198\pi\) | ||||
0.290440 | + | 0.956893i | \(0.406198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 472560. | 1.16644 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −161388. | −0.376477 | −0.188239 | − | 0.982123i | \(-0.560278\pi\) | ||||
−0.188239 | + | 0.982123i | \(0.560278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −291690. | −0.661797 | −0.330899 | − | 0.943666i | \(-0.607352\pi\) | ||||
−0.330899 | + | 0.943666i | \(0.607352\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −148308. | −0.318592 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −242296. | −0.506690 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 55680.0 | 0.110437 | 0.0552187 | − | 0.998474i | \(-0.482414\pi\) | ||||
0.0552187 | + | 0.998474i | \(0.482414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −176254. | −0.340601 | −0.170300 | − | 0.985392i | \(-0.554474\pi\) | ||||
−0.170300 | + | 0.985392i | \(0.554474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 374610. | 0.687723 | 0.343862 | − | 0.939020i | \(-0.388265\pi\) | ||||
0.343862 | + | 0.939020i | \(0.388265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −637760. | −1.14163 | −0.570814 | − | 0.821079i | \(-0.693372\pi\) | ||||
−0.570814 | + | 0.821079i | \(0.693372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.14128e6 | −3.64698 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 98124.0 | 0.163076 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −238576. | −0.377799 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −904628. | −1.39883 | −0.699413 | − | 0.714717i | \(-0.746555\pi\) | ||||
−0.699413 | + | 0.714717i | \(0.746555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 385288. | 0.568446 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.11552e6 | 1.60816 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −89884.0 | −0.123795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 619048. | 0.833609 | 0.416804 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416804 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.46975e6 | 1.89312 | 0.946560 | − | 0.322527i | \(-0.104532\pi\) | ||||
0.946560 | + | 0.322527i | \(0.104532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3290.00 | −0.00414579 | −0.00207289 | − | 0.999998i | \(-0.500660\pi\) | ||||
−0.00207289 | + | 0.999998i | \(0.500660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −935402. | −1.12878 | −0.564389 | − | 0.825509i | \(-0.690888\pi\) | ||||
−0.564389 | + | 0.825509i | \(0.690888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −238272. | −0.281451 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 875600. | 0.991542 | 0.495771 | − | 0.868453i | \(-0.334886\pi\) | ||||
0.495771 | + | 0.868453i | \(0.334886\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −959214. | −1.06383 | −0.531916 | − | 0.846797i | \(-0.678528\pi\) | ||||
−0.531916 | + | 0.846797i | \(0.678528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.38696e6 | 1.47621 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −88504.0 | −0.0923040 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −318868. | −0.319467 | −0.159734 | − | 0.987160i | \(-0.551064\pi\) | ||||
−0.159734 | + | 0.987160i | \(0.551064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −352160. | −0.345891 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.71469e6 | −1.61940 | −0.809698 | − | 0.586847i | \(-0.800369\pi\) | ||||
−0.809698 | + | 0.586847i | \(0.800369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.04688e6 | 0.969723 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.11028e6 | 0.989790 | 0.494895 | − | 0.868953i | \(-0.335206\pi\) | ||||
0.494895 | + | 0.868953i | \(0.335206\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 768196. | 0.671982 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 398378. | 0.335672 | 0.167836 | − | 0.985815i | \(-0.446322\pi\) | ||||
0.167836 | + | 0.985815i | \(0.446322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.44198e6 | 1.19271 | 0.596355 | − | 0.802721i | \(-0.296615\pi\) | ||||
0.596355 | + | 0.802721i | \(0.296615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −244156. | −0.194686 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 117238. | 0.0918056 | 0.0459028 | − | 0.998946i | \(-0.485384\pi\) | ||||
0.0459028 | + | 0.998946i | \(0.485384\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67514e6 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.92468e6 | 1.42854 | 0.714269 | − | 0.699872i | \(-0.246760\pi\) | ||||
0.714269 | + | 0.699872i | \(0.246760\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −692640. | −0.496367 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.39826e6 | 1.68908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.28062e6 | −0.871469 | −0.435734 | − | 0.900075i | \(-0.643511\pi\) | ||||
−0.435734 | + | 0.900075i | \(0.643511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 952.000 | 0.000636916 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −130640. | −0.0845081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.71968e6 | −1.73022 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −217124. | −0.133647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.26319e6 | −1.37049 | −0.685243 | − | 0.728314i | \(-0.740304\pi\) | ||||
−0.685243 | + | 0.728314i | \(0.740304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −247848. | −0.145306 | −0.0726532 | − | 0.997357i | \(-0.523147\pi\) | ||||
−0.0726532 | + | 0.997357i | \(0.523147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.82391e6 | −1.05231 | −0.526154 | − | 0.850390i | \(-0.676366\pi\) | ||||
−0.526154 | + | 0.850390i | \(0.676366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.85629e6 | −1.59645 | −0.798224 | − | 0.602361i | \(-0.794227\pi\) | ||||
−0.798224 | + | 0.602361i | \(0.794227\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10633e6 | 0.608705 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.75950e6 | 2.00504 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −90574.0 | −0.0475658 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.68192e6 | 0.856674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −147148. | −0.0738218 | −0.0369109 | − | 0.999319i | \(-0.511752\pi\) | ||||
−0.0369109 | + | 0.999319i | \(0.511752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.32858e6 | −0.646810 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.24728e6 | −1.55756 | −0.778780 | − | 0.627297i | \(-0.784161\pi\) | ||||
−0.778780 | + | 0.627297i | \(0.784161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −576352. | −0.268412 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.75664e6 | −2.64201 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.55675e6 | 0.694056 | 0.347028 | − | 0.937855i | \(-0.387191\pi\) | ||||
0.347028 | + | 0.937855i | \(0.387191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.03217e6 | 1.77205 | 0.886024 | − | 0.463639i | \(-0.153456\pi\) | ||||
0.886024 | + | 0.463639i | \(0.153456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.79399e6 | −0.766271 | −0.383135 | − | 0.923692i | \(-0.625156\pi\) | ||||
−0.383135 | + | 0.923692i | \(0.625156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.86565e6 | 0.785704 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.55278e6 | −0.635876 | −0.317938 | − | 0.948111i | \(-0.602990\pi\) | ||||
−0.317938 | + | 0.948111i | \(0.602990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.22568e6 | 0.495003 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 715156. | 0.280976 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.11545e6 | −1.20741 | −0.603706 | − | 0.797207i | \(-0.706310\pi\) | ||||
−0.603706 | + | 0.797207i | \(0.706310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.42256e6 | −2.04536 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −630682. | −0.234714 | −0.117357 | − | 0.993090i | \(-0.537442\pi\) | ||||
−0.117357 | + | 0.993090i | \(0.537442\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 410412. | 0.148719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 48404.0 | 0.0173094 | 0.00865472 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865472 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.74182e6 | −0.606747 | −0.303373 | − | 0.952872i | \(-0.598113\pi\) | ||||
−0.303373 | + | 0.952872i | \(0.598113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.01184e6 | −0.347904 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.06819e6 | 1.02804 | 0.514019 | − | 0.857779i | \(-0.328156\pi\) | ||||
0.514019 | + | 0.857779i | \(0.328156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.54936e6 | 1.83570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 905488. | 0.292005 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.35984e6 | 1.70677 | 0.853386 | − | 0.521280i | \(-0.174545\pi\) | ||||
0.853386 | + | 0.521280i | \(0.174545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.76473e6 | 0.858603 | 0.429302 | − | 0.903161i | \(-0.358760\pi\) | ||||
0.429302 | + | 0.903161i | \(0.358760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −213808. | −0.0655785 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −540888. | −0.161853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.20893e6 | −0.357350 | −0.178675 | − | 0.983908i | \(-0.557181\pi\) | ||||
−0.178675 | + | 0.983908i | \(0.557181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6720.00 | −0.00193863 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.91039e6 | −0.544505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.38008e6 | 1.21884 | 0.609421 | − | 0.792847i | \(-0.291402\pi\) | ||||
0.609421 | + | 0.792847i | \(0.291402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −922810. | −0.253751 | −0.126875 | − | 0.991919i | \(-0.540495\pi\) | ||||
−0.126875 | + | 0.991919i | \(0.540495\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.84743e6 | 1.03323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.53264e6 | 0.406790 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.12678e6 | −1.58869 | −0.794345 | − | 0.607466i | \(-0.792186\pi\) | ||||
−0.794345 | + | 0.607466i | \(0.792186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.76315e6 | −0.451928 | −0.225964 | − | 0.974136i | \(-0.572553\pi\) | ||||
−0.225964 | + | 0.974136i | \(0.572553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.46416e6 | 1.36874 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.85906e6 | 0.955696 | 0.477848 | − | 0.878443i | \(-0.341417\pi\) | ||||
0.477848 | + | 0.878443i | \(0.341417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.39396e6 | 1.06377 | 0.531884 | − | 0.846817i | \(-0.321484\pi\) | ||||
0.531884 | + | 0.846817i | \(0.321484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.18994e6 | −0.524242 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 793390. | 0.185725 | 0.0928626 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928626 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 357864. | 0.0828470 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −375360. | −0.0850001 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.04302e6 | 1.57750 | 0.788748 | − | 0.614717i | \(-0.210730\pi\) | ||||
0.788748 | + | 0.614717i | \(0.210730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.43005e6 | −1.62832 | −0.814160 | − | 0.580641i | \(-0.802802\pi\) | ||||
−0.814160 | + | 0.580641i | \(0.802802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.10567e6 | −0.890086 | −0.445043 | − | 0.895509i | \(-0.646812\pi\) | ||||
−0.445043 | + | 0.895509i | \(0.646812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.39817e6 | −0.721030 | −0.360515 | − | 0.932753i | \(-0.617399\pi\) | ||||
−0.360515 | + | 0.932753i | \(0.617399\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.37824e6 | 1.96874 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.40517e6 | 0.288786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.78836e6 | 0.770401 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.78133e6 | −0.553877 | −0.276939 | − | 0.960888i | \(-0.589320\pi\) | ||||
−0.276939 | + | 0.960888i | \(0.589320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −200652. | −0.0395440 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.94937e6 | −0.762384 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.06734e6 | −0.394994 | −0.197497 | − | 0.980304i | \(-0.563281\pi\) | ||||
−0.197497 | + | 0.980304i | \(0.563281\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.65976e6 | 1.43387 | 0.716937 | − | 0.697138i | \(-0.245543\pi\) | ||||
0.716937 | + | 0.697138i | \(0.245543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.74336e7 | −3.23050 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.31693e7 | −2.39150 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −386580. | −0.0695005 | −0.0347503 | − | 0.999396i | \(-0.511064\pi\) | ||||
−0.0347503 | + | 0.999396i | \(0.511064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.57326e6 | 0.453485 | 0.226743 | − | 0.973955i | \(-0.427192\pi\) | ||||
0.226743 | + | 0.973955i | \(0.427192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.27236e6 | 0.396504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −360678. | −0.0617057 | −0.0308528 | − | 0.999524i | \(-0.509822\pi\) | ||||
−0.0308528 | + | 0.999524i | \(0.509822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.04816e6 | −0.855226 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17600e6 | 0.361527 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −868992. | −0.142985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.55908e6 | 0.251636 | 0.125818 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125818 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.18220e6 | −1.46789 | −0.733944 | − | 0.679210i | \(-0.762322\pi\) | ||||
−0.733944 | + | 0.679210i | \(0.762322\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.08219e6 | 1.42451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.62926e6 | 0.253134 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 132756. | 0.0202412 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 512856. | 0.0774660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05833e6 | 0.749955 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.67773e6 | −0.980925 | −0.490462 | − | 0.871462i | \(-0.663172\pi\) | ||||
−0.490462 | + | 0.871462i | \(0.663172\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.34973e6 | −0.194651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.89656e6 | 1.27132 | 0.635658 | − | 0.771971i | \(-0.280729\pi\) | ||||
0.635658 | + | 0.771971i | \(0.280729\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.71659e7 | −2.40873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.39168e6 | −0.888796 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.46070e6 | 0.609207 | 0.304603 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304603 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 521272. | 0.0705562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.37660e6 | −0.847849 | −0.423924 | − | 0.905698i | \(-0.639348\pi\) | ||||
−0.423924 | + | 0.905698i | \(0.639348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.27524e6 | −0.695218 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.51143e6 | −0.713648 | −0.356824 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356824 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.35431e6 | 0.173831 | 0.0869155 | − | 0.996216i | \(-0.472299\pi\) | ||||
0.0869155 | + | 0.996216i | \(0.472299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.59196e6 | 0.705333 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.00736e6 | −0.626137 | −0.313068 | − | 0.949731i | \(-0.601357\pi\) | ||||
−0.313068 | + | 0.949731i | \(0.601357\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.34851e7 | 1.65735 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.80166e6 | 0.341384 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.69964e6 | −0.323378 | −0.161689 | − | 0.986842i | \(-0.551694\pi\) | ||||
−0.161689 | + | 0.986842i | \(0.551694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.94275e6 | 1.06214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.31035e7 | −1.53021 | −0.765103 | − | 0.643908i | \(-0.777312\pi\) | ||||
−0.765103 | + | 0.643908i | \(0.777312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.59446e7 | 1.84639 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.22804e6 | 0.595349 | 0.297675 | − | 0.954667i | \(-0.403789\pi\) | ||||
0.297675 | + | 0.954667i | \(0.403789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.02248e7 | 1.15470 | 0.577351 | − | 0.816496i | \(-0.304087\pi\) | ||||
0.577351 | + | 0.816496i | \(0.304087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.95295e6 | −0.550143 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.81684e6 | 0.971273 | 0.485636 | − | 0.874161i | \(-0.338588\pi\) | ||||
0.485636 | + | 0.874161i | \(0.338588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −322368. | −0.0349340 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.13600e7 | 1.22103 | 0.610514 | − | 0.792006i | \(-0.290963\pi\) | ||||
0.610514 | + | 0.792006i | \(0.290963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.77356e6 | 0.504812 | 0.252406 | − | 0.967621i | \(-0.418778\pi\) | ||||
0.252406 | + | 0.967621i | \(0.418778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.55931e6 | −0.268470 | −0.134235 | − | 0.990950i | \(-0.542858\pi\) | ||||
−0.134235 | + | 0.990950i | \(0.542858\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.54584e7 | 1.59567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 264461. | 0.0270808 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.52335e6 | 0.858981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.41981e6 | −0.841839 | −0.420919 | − | 0.907098i | \(-0.638292\pi\) | ||||
−0.420919 | + | 0.907098i | \(0.638292\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.77045e6 | 0.174240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.87648e6 | 0.183229 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.21494e7 | 1.16791 | 0.583957 | − | 0.811785i | \(-0.301504\pi\) | ||||
0.583957 | + | 0.811785i | \(0.301504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.08968e7 | −1.03937 | −0.519685 | − | 0.854358i | \(-0.673951\pi\) | ||||
−0.519685 | + | 0.854358i | \(0.673951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.32166e7 | −1.24124 | −0.620622 | − | 0.784110i | \(-0.713120\pi\) | ||||
−0.620622 | + | 0.784110i | \(0.713120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3472.00 | 0.000323570 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.65915e7 | −1.52266 | −0.761329 | − | 0.648365i | \(-0.775453\pi\) | ||||
−0.761329 | + | 0.648365i | \(0.775453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.43878e6 | −0.495334 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.29372e6 | 0.205743 | 0.102872 | − | 0.994695i | \(-0.467197\pi\) | ||||
0.102872 | + | 0.994695i | \(0.467197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −719194. | −0.0640239 | −0.0320120 | − | 0.999487i | \(-0.510191\pi\) | ||||
−0.0320120 | + | 0.999487i | \(0.510191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.56998e7 | 1.37671 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.53385e7 | −2.20529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −791864. | −0.0678960 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.64695e6 | 0.735911 | 0.367955 | − | 0.929843i | \(-0.380058\pi\) | ||||
0.367955 | + | 0.929843i | \(0.380058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.69592e7 | 1.42211 | 0.711056 | − | 0.703135i | \(-0.248217\pi\) | ||||
0.711056 | + | 0.703135i | \(0.248217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.78779e7 | 2.32052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.87105e7 | −1.53473 | −0.767367 | − | 0.641209i | \(-0.778433\pi\) | ||||
−0.767367 | + | 0.641209i | \(0.778433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.91745e6 | 0.726130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.03932e6 | 0.0834071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.16204e7 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.61982e6 | 0.676918 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.63924e6 | −0.439682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.23497e7 | −1.71781 | −0.858907 | − | 0.512132i | \(-0.828856\pi\) | ||||
−0.858907 | + | 0.512132i | \(0.828856\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.39249e6 | 0.640475 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.60402e7 | −1.20687 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.02353e7 | 0.764687 | 0.382344 | − | 0.924020i | \(-0.375117\pi\) | ||||
0.382344 | + | 0.924020i | \(0.375117\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.32003e7 | 0.972435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 193936. | 0.0141871 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.70339e7 | 1.22883 | 0.614416 | − | 0.788982i | \(-0.289392\pi\) | ||||
0.614416 | + | 0.788982i | \(0.289392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.53600e7 | −1.10041 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.75674e7 | −1.24126 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.62280e7 | −1.13875 | −0.569377 | − | 0.822077i | \(-0.692815\pi\) | ||||
−0.569377 | + | 0.822077i | \(0.692815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.21427e7 | −1.53263 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.17495e7 | −1.49517 | −0.747583 | − | 0.664168i | \(-0.768786\pi\) | ||||
−0.747583 | + | 0.664168i | \(0.768786\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.84542e6 | −0.328597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.96200e7 | 1.32156 | 0.660781 | − | 0.750578i | \(-0.270225\pi\) | ||||
0.660781 | + | 0.750578i | \(0.270225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.74018e7 | −1.15644 | −0.578218 | − | 0.815882i | \(-0.696252\pi\) | ||||
−0.578218 | + | 0.815882i | \(0.696252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.20914e7 | −0.798154 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.62016e6 | −0.235789 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.62693e7 | −1.69961 | −0.849803 | − | 0.527101i | \(-0.823279\pi\) | ||||
−0.849803 | + | 0.527101i | \(0.823279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34816.0 | −0.00222286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.70356e6 | −0.361748 | −0.180874 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180874 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.13762e7 | 1.33804 | 0.669020 | − | 0.743244i | \(-0.266714\pi\) | ||||
0.669020 | + | 0.743244i | \(0.266714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.52752e6 | 0.592473 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1288.00 | 7.90547e−5 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.01523e6 | −0.122888 | −0.0614439 | − | 0.998111i | \(-0.519571\pi\) | ||||
−0.0614439 | + | 0.998111i | \(0.519571\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.27674e7 | 0.768520 | 0.384260 | − | 0.923225i | \(-0.374457\pi\) | ||||
0.384260 | + | 0.923225i | \(0.374457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.15191e6 | 0.547340 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.55266e6 | −0.327837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.80413e6 | 0.399158 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.03844e6 | −0.118065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.72384e7 | −1.56764 | −0.783818 | − | 0.620990i | \(-0.786731\pi\) | ||||
−0.783818 | + | 0.620990i | \(0.786731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.72370e7 | 2.11608 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −293756. | −0.0165884 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.66724e6 | 0.427556 | 0.213778 | − | 0.976882i | \(-0.431423\pi\) | ||||
0.213778 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36936e7 | 0.758843 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.60822e6 | 0.142743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.31744e7 | 1.26043 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.05541e7 | 0.566956 | 0.283478 | − | 0.958979i | \(-0.408512\pi\) | ||||
0.283478 | + | 0.958979i | \(0.408512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.32883e6 | −0.0709442 | −0.0354721 | − | 0.999371i | \(-0.511293\pi\) | ||||
−0.0354721 | + | 0.999371i | \(0.511293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.16129e7 | −0.612416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.18028e7 | −1.14276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.15933e6 | 0.318915 | 0.159458 | − | 0.987205i | \(-0.449025\pi\) | ||||
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.00734e7 | 0.518414 | 0.259207 | − | 0.965822i | \(-0.416539\pi\) | ||||
0.259207 | + | 0.965822i | \(0.416539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.49152e6 | 0.330052 | 0.165026 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165026 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.93536e7 | −0.978082 | −0.489041 | − | 0.872261i | \(-0.662653\pi\) | ||||
−0.489041 | + | 0.872261i | \(0.662653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.97095e7 | −3.98013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −170544. | −0.00846487 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.78622e7 | 1.36650 | 0.683251 | − | 0.730183i | \(-0.260565\pi\) | ||||
0.683251 | + | 0.730183i | \(0.260565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.90909e7 | 2.88092 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.25520e7 | −0.604744 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49620e7 | 1.67451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.23881e7 | 0.586381 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.07651e7 | 0.506577 | 0.253288 | − | 0.967391i | \(-0.418488\pi\) | ||||
0.253288 | + | 0.967391i | \(0.418488\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22439e7 | −0.569465 | −0.284733 | − | 0.958607i | \(-0.591905\pi\) | ||||
−0.284733 | + | 0.958607i | \(0.591905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.38664e6 | −0.0641179 | −0.0320590 | − | 0.999486i | \(-0.510206\pi\) | ||||
−0.0320590 | + | 0.999486i | \(0.510206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.09856e7 | 0.502109 | 0.251055 | − | 0.967973i | \(-0.419223\pi\) | ||||
0.251055 | + | 0.967973i | \(0.419223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.77464e6 | 0.353297 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.30237e6 | 0.148346 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.79750e6 | −0.0802828 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.15670e7 | 1.83539 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.17798e6 | 0.359044 | 0.179522 | − | 0.983754i | \(-0.442545\pi\) | ||||
0.179522 | + | 0.983754i | \(0.442545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.66520e6 | −0.202503 | −0.101251 | − | 0.994861i | \(-0.532285\pi\) | ||||
−0.101251 | + | 0.994861i | \(0.532285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.82201e7 | 1.64964 | 0.824822 | − | 0.565393i | \(-0.191276\pi\) | ||||
0.824822 | + | 0.565393i | \(0.191276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.72172e6 | 0.329538 | 0.164769 | − | 0.986332i | \(-0.447312\pi\) | ||||
0.164769 | + | 0.986332i | \(0.447312\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.24973e7 | −0.530348 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.34834e7 | 0.565810 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.48719e6 | −0.228977 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.14695e7 | −1.71131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.41487e7 | −1.81178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.91746e6 | −0.402512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.33137e7 | 1.74826 | 0.874131 | − | 0.485689i | \(-0.161431\pi\) | ||||
0.874131 | + | 0.485689i | \(0.161431\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.44456e6 | −0.137511 | −0.0687556 | − | 0.997634i | \(-0.521903\pi\) | ||||
−0.0687556 | + | 0.997634i | \(0.521903\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.96731e6 | −0.276623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.83914e7 | 1.50768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.37073e7 | −1.70712 | −0.853562 | − | 0.520991i | \(-0.825563\pi\) | ||||
−0.853562 | + | 0.520991i | \(0.825563\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.52411e6 | 0.0975224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.58878e6 | 0.330048 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.13022e7 | 1.57012 | 0.785062 | − | 0.619418i | \(-0.212631\pi\) | ||||
0.785062 | + | 0.619418i | \(0.212631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.84857e7 | −2.96768 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.23806e6 | −0.308174 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.57460e6 | 0.356264 | 0.178132 | − | 0.984007i | \(-0.442995\pi\) | ||||
0.178132 | + | 0.984007i | \(0.442995\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.71623e6 | −0.320889 | −0.160444 | − | 0.987045i | \(-0.551293\pi\) | ||||
−0.160444 | + | 0.987045i | \(0.551293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.19624e6 | −0.300148 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.30605e7 | 0.473244 | 0.236622 | − | 0.971602i | \(-0.423960\pi\) | ||||
0.236622 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 967564. | 0.0348750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.13875e7 | −0.406158 | −0.203079 | − | 0.979162i | \(-0.565095\pi\) | ||||
−0.203079 | + | 0.979162i | \(0.565095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.89312e6 | 0.0671691 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.29467e7 | −2.21017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.02525e6 | −0.245388 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.99264e6 | −0.207157 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.62711e7 | 1.59127 | 0.795634 | − | 0.605778i | \(-0.207138\pi\) | ||||
0.795634 | + | 0.605778i | \(0.207138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.63206e7 | −0.555506 | −0.277753 | − | 0.960653i | \(-0.589590\pi\) | ||||
−0.277753 | + | 0.960653i | \(0.589590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.08458e7 | −2.06038 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.95213e7 | 0.654294 | 0.327147 | − | 0.944973i | \(-0.393913\pi\) | ||||
0.327147 | + | 0.944973i | \(0.393913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.98684e6 | −0.266329 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.33962e7 | 1.43241 | 0.716207 | − | 0.697888i | \(-0.245877\pi\) | ||||
0.716207 | + | 0.697888i | \(0.245877\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.27367e7 | 0.418281 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.21829e7 | −1.04625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.83518e7 | 1.24051 | 0.620257 | − | 0.784399i | \(-0.287028\pi\) | ||||
0.620257 | + | 0.784399i | \(0.287028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.16838e7 | −0.694350 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.82206e6 | −0.249220 | −0.124610 | − | 0.992206i | \(-0.539768\pi\) | ||||
−0.124610 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 72.6.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 24.6.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 144.6.a.i.1.1 | 1 | |||
8.3 | odd | 2 | 576.6.a.l.1.1 | 1 | |||
8.5 | even | 2 | 576.6.a.k.1.1 | 1 | |||
12.11 | even | 2 | 48.6.a.d.1.1 | 1 | |||
15.2 | even | 4 | 600.6.f.f.49.2 | 2 | |||
15.8 | even | 4 | 600.6.f.f.49.1 | 2 | |||
15.14 | odd | 2 | 600.6.a.i.1.1 | 1 | |||
24.5 | odd | 2 | 192.6.a.n.1.1 | 1 | |||
24.11 | even | 2 | 192.6.a.f.1.1 | 1 | |||
48.5 | odd | 4 | 768.6.d.r.385.2 | 2 | |||
48.11 | even | 4 | 768.6.d.a.385.1 | 2 | |||
48.29 | odd | 4 | 768.6.d.r.385.1 | 2 | |||
48.35 | even | 4 | 768.6.d.a.385.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.6.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
48.6.a.d.1.1 | 1 | 12.11 | even | 2 | |||
72.6.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
144.6.a.i.1.1 | 1 | 4.3 | odd | 2 | |||
192.6.a.f.1.1 | 1 | 24.11 | even | 2 | |||
192.6.a.n.1.1 | 1 | 24.5 | odd | 2 | |||
576.6.a.k.1.1 | 1 | 8.5 | even | 2 | |||
576.6.a.l.1.1 | 1 | 8.3 | odd | 2 | |||
600.6.a.i.1.1 | 1 | 15.14 | odd | 2 | |||
600.6.f.f.49.1 | 2 | 15.8 | even | 4 | |||
600.6.f.f.49.2 | 2 | 15.2 | even | 4 | |||
768.6.d.a.385.1 | 2 | 48.11 | even | 4 | |||
768.6.d.a.385.2 | 2 | 48.35 | even | 4 | |||
768.6.d.r.385.1 | 2 | 48.29 | odd | 4 | |||
768.6.d.r.385.2 | 2 | 48.5 | odd | 4 |