Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,6,Mod(385,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.385");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(123.174773616\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 385.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.385 |
Dual form | 768.6.d.r.385.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 9.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 34.0000i | 0.608210i | 0.952638 | + | 0.304105i | \(0.0983575\pi\) | ||||
−0.952638 | + | 0.304105i | \(0.901643\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 240.000 | 1.85125 | 0.925627 | − | 0.378436i | \(-0.123538\pi\) | ||||
0.925627 | + | 0.378436i | \(0.123538\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000i | 0.308987i | 0.987994 | + | 0.154493i | \(0.0493745\pi\) | ||||
−0.987994 | + | 0.154493i | \(0.950625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.0000i | 0.0754917i | 0.999287 | + | 0.0377459i | \(0.0120177\pi\) | ||||
−0.999287 | + | 0.0377459i | \(0.987982\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 306.000 | 0.351150 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1954.00 | 1.63984 | 0.819921 | − | 0.572476i | \(-0.194017\pi\) | ||||
0.819921 | + | 0.572476i | \(0.194017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1924.00i | − 1.22270i | −0.791359 | − | 0.611352i | \(-0.790626\pi\) | ||||
0.791359 | − | 0.611352i | \(-0.209374\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2160.00i | − 1.06882i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8922.00i | − 1.97000i | −0.172541 | − | 0.985002i | \(-0.555198\pi\) | ||||
0.172541 | − | 0.985002i | \(-0.444802\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4648.00 | −0.868684 | −0.434342 | − | 0.900748i | \(-0.643019\pi\) | ||||
−0.434342 | + | 0.900748i | \(0.643019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1116.00 | 0.178394 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8160.00i | 1.12595i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4362.00i | 0.523819i | 0.965092 | + | 0.261910i | \(0.0843522\pi\) | ||||
−0.965092 | + | 0.261910i | \(0.915648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 414.000 | 0.0435852 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2886.00 | 0.268125 | 0.134062 | − | 0.990973i | \(-0.457198\pi\) | ||||
0.134062 | + | 0.990973i | \(0.457198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11332.0i | − 0.934621i | −0.884093 | − | 0.467310i | \(-0.845223\pi\) | ||||
0.884093 | − | 0.467310i | \(-0.154777\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2754.00i | − 0.202737i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7008.00 | 0.462753 | 0.231377 | − | 0.972864i | \(-0.425677\pi\) | ||||
0.231377 | + | 0.972864i | \(0.425677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40793.0 | 2.42714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 17586.0i | − 0.946764i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22594.0i | 1.10485i | 0.833562 | + | 0.552425i | \(0.186297\pi\) | ||||
−0.833562 | + | 0.552425i | \(0.813703\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4216.00 | −0.187929 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17316.0 | −0.705928 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28.0000i | 0.00104720i | 1.00000 | 0.000523598i | \(0.000166666\pi\) | |||||
−1.00000 | 0.000523598i | \(0.999833\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6386.00i | − 0.219738i | −0.993946 | − | 0.109869i | \(-0.964957\pi\) | ||||
0.993946 | − | 0.109869i | \(-0.0350431\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19440.0 | −0.617085 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1564.00 | −0.0459149 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 39076.0i | − 1.06346i | −0.846912 | − | 0.531732i | \(-0.821541\pi\) | ||||
0.846912 | − | 0.531732i | \(-0.178459\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 25560.0i | 0.646306i | ||||||||
\(70\) | 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 | \(-0.574195\pi\) | ||||
−0.230986 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 17721.0i | − 0.363777i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29760.0i | 0.572013i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 26632.0 | 0.480105 | 0.240052 | − | 0.970760i | \(-0.422835\pi\) | ||||
0.240052 | + | 0.970760i | \(0.422835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 56188.0i | 0.895258i | 0.894219 | + | 0.447629i | \(0.147732\pi\) | ||||
−0.894219 | + | 0.447629i | \(0.852268\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 66436.0i | 0.997370i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −80298.0 | −1.13738 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −64410.0 | −0.861942 | −0.430971 | − | 0.902366i | \(-0.641829\pi\) | ||||
−0.430971 | + | 0.902366i | \(0.641829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11040.0i | 0.139754i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 41832.0i | 0.501535i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 10044.0i | − 0.102996i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 66834.0i | 0.651920i | 0.945384 | + | 0.325960i | \(0.105687\pi\) | ||||
−0.945384 | + | 0.325960i | \(0.894313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −64000.0 | −0.594411 | −0.297206 | − | 0.954814i | \(-0.596055\pi\) | ||||
−0.297206 | + | 0.954814i | \(0.596055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 73440.0 | 0.650069 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15084.0i | 0.127367i | 0.997970 | + | 0.0636835i | \(0.0202848\pi\) | ||||
−0.997970 | + | 0.0636835i | \(0.979715\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 39698.0i | − 0.320039i | −0.987114 | − | 0.160019i | \(-0.948844\pi\) | ||||
0.987114 | − | 0.160019i | \(-0.0511556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 39258.0 | 0.302427 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 155154. | 1.14305 | 0.571527 | − | 0.820583i | \(-0.306351\pi\) | ||||
0.571527 | + | 0.820583i | \(0.306351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 96560.0i | − 0.680852i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3726.00i | − 0.0251639i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 468960. | 3.03577 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 145675. | 0.904527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 25974.0i | − 0.154802i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 173196.i | 0.991432i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 52072.0 | 0.286480 | 0.143240 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143240 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −101988. | −0.539604 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 159964.i | 0.814412i | 0.913336 | + | 0.407206i | \(0.133497\pi\) | ||||
−0.913336 | + | 0.407206i | \(0.866503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 461760.i | − 2.26353i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24786.0 | −0.117050 | ||||||||
\(136\) | 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.i | − 1.11297i | −0.830859 | − | 0.556483i | \(-0.812150\pi\) | ||||
0.830859 | − | 0.556483i | \(-0.187850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 63072.0i | − 0.267171i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5704.00 | −0.0233260 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 303348. | 1.19818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 367137.i | − 1.40131i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 355630.i | − 1.31230i | −0.754631 | − | 0.656149i | \(-0.772184\pi\) | ||||
0.754631 | − | 0.656149i | \(-0.227816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1024.00 | 0.00365475 | 0.00182737 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182737 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −158274. | −0.546614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 158032.i | − 0.528343i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 59954.0i | − 0.194119i | −0.995279 | − | 0.0970597i | \(-0.969056\pi\) | ||||
0.995279 | − | 0.0970597i | \(-0.0309438\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 203346. | 0.637886 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −681600. | −2.07236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 341556.i | − 1.00692i | −0.864020 | − | 0.503458i | \(-0.832061\pi\) | ||||
0.864020 | − | 0.503458i | \(-0.167939\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 37944.0i | 0.108501i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 155844.i | 0.407568i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 228666.i | − 0.580880i | −0.956893 | − | 0.290440i | \(-0.906198\pi\) | ||||
0.956893 | − | 0.290440i | \(-0.0938016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 472560. | 1.16644 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 252.000 | 0.000604599 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 161388.i | 0.376477i | 0.982123 | + | 0.188239i | \(0.0602778\pi\) | ||||
−0.982123 | + | 0.188239i | \(0.939722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 291690.i | 0.661797i | 0.943666 | + | 0.330899i | \(0.107352\pi\) | ||||
−0.943666 | + | 0.330899i | \(0.892648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −57474.0 | −0.126866 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −148308. | −0.318592 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 242296.i | 0.506690i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 174960.i | 0.356274i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −55680.0 | −0.110437 | −0.0552187 | − | 0.998474i | \(-0.517586\pi\) | ||||
−0.0552187 | + | 0.998474i | \(0.517586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −176254. | −0.340601 | −0.170300 | − | 0.985392i | \(-0.554474\pi\) | ||||
−0.170300 | + | 0.985392i | \(0.554474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14076.0i | 0.0265090i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 374610.i | 0.687723i | 0.939020 | + | 0.343862i | \(0.111735\pi\) | ||||
−0.939020 | + | 0.343862i | \(0.888265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 637760. | 1.14163 | 0.570814 | − | 0.821079i | \(-0.306628\pi\) | ||||
0.570814 | + | 0.821079i | \(0.306628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −351684. | −0.613992 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.14128e6i | − 3.64698i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 98124.0i | 0.163076i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 230040. | 0.373145 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 238576. | 0.377799 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 904628.i | − 1.39883i | −0.714717 | − | 0.699413i | \(-0.753445\pi\) | ||||
0.714717 | − | 0.699413i | \(-0.246555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 493848.i | − 0.745838i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 385288. | 0.568446 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.11552e6 | −1.60816 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 189306.i | 0.266719i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 89884.0i | 0.123795i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 619048. | 0.833609 | 0.416804 | − | 0.908996i | \(-0.363150\pi\) | ||||
0.416804 | + | 0.908996i | \(0.363150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −159489. | −0.210027 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.46975e6i | − 1.89312i | −0.322527 | − | 0.946560i | \(-0.604532\pi\) | ||||
0.322527 | − | 0.946560i | \(-0.395468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3290.00i | 0.00414579i | 0.999998 | + | 0.00207289i | \(0.000659823\pi\) | ||||
−0.999998 | + | 0.00207289i | \(0.999340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 267840. | 0.330252 | ||||||||
\(232\) | 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.i | 0.281451i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 239688.i | − 0.277189i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −875600. | −0.991542 | −0.495771 | − | 0.868453i | \(-0.665114\pi\) | ||||
−0.495771 | + | 0.868453i | \(0.665114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −959214. | −1.06383 | −0.531916 | − | 0.846797i | \(-0.678528\pi\) | ||||
−0.531916 | + | 0.846797i | \(0.678528\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 59049.0i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.38696e6i | 1.47621i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88504.0 | 0.0923040 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 505692. | 0.516878 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 318868.i | − 0.319467i | −0.987160 | − | 0.159734i | \(-0.948936\pi\) | ||||
0.987160 | − | 0.159734i | \(-0.0510636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 352160.i | − 0.345891i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 597924. | 0.575832 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.71469e6 | 1.61940 | 0.809698 | − | 0.586847i | \(-0.199631\pi\) | ||||
0.809698 | + | 0.586847i | \(0.199631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.04688e6i | 0.969723i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 722682.i | 0.656668i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 579690.i | 0.497643i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 398378.i | − 0.335672i | −0.985815 | − | 0.167836i | \(-0.946322\pi\) | ||||
0.985815 | − | 0.167836i | \(-0.0536778\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.44198e6 | 1.19271 | 0.596355 | − | 0.802721i | \(-0.296615\pi\) | ||||
0.596355 | + | 0.802721i | \(0.296615\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 99360.0 | 0.0806873 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 244156.i | 0.194686i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 117238.i | − 0.0918056i | −0.998946 | − | 0.0459028i | \(-0.985384\pi\) | ||||
0.998946 | − | 0.0459028i | \(-0.0146164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 376488. | 0.289561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67514e6 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.92468e6i | − 1.42854i | −0.699872 | − | 0.714269i | \(-0.746760\pi\) | ||||
0.699872 | − | 0.714269i | \(-0.253240\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 588744.i | − 0.429353i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 692640. | 0.496367 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.39826e6 | 1.68908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.04542e6i | 0.723701i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.28062e6i | − 0.871469i | −0.900075 | − | 0.435734i | \(-0.856489\pi\) | ||||
0.900075 | − | 0.435734i | \(-0.143511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −952.000 | −0.000636916 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −90396.0 | −0.0594645 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 130640.i | − 0.0845081i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.71968e6i | − 1.73022i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 601506. | 0.376386 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 217124. | 0.133647 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.26319e6i | − 1.37049i | −0.728314 | − | 0.685243i | \(-0.759696\pi\) | ||||
0.728314 | − | 0.685243i | \(-0.240304\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 576000.i | 0.343183i | ||||||||
\(310\) | 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 | \(-0.323634\pi\) | ||||
0.526154 | + | 0.850390i | \(0.323634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 660960.i | − 0.375317i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.85629e6i | 1.59645i | 0.602361 | + | 0.798224i | \(0.294227\pi\) | ||||
−0.602361 | + | 0.798224i | \(0.705773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10633e6 | 0.608705 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 135756. | 0.0735354 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.75950e6i | − 2.00504i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 90574.0i | 0.0475658i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −357282. | −0.184774 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.68192e6 | 0.856674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 147148.i | 0.0738218i | 0.999319 | + | 0.0369109i | \(0.0117518\pi\) | ||||
−0.999319 | + | 0.0369109i | \(0.988248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 353322.i | − 0.174606i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 1.39639e6i | − 0.659943i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 576352.i | − 0.268412i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.75664e6 | 2.64201 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −869040. | −0.393090 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.55675e6i | 0.694056i | 0.937855 | + | 0.347028i | \(0.112809\pi\) | ||||
−0.937855 | + | 0.347028i | \(0.887191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.03217e6i | 1.77205i | 0.463639 | + | 0.886024i | \(0.346544\pi\) | ||||
−0.463639 | + | 0.886024i | \(0.653456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33534.0 | −0.0145284 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.79399e6 | 0.766271 | 0.383135 | − | 0.923692i | \(-0.374844\pi\) | ||||
0.383135 | + | 0.923692i | \(0.374844\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.86565e6i | 0.785704i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.22064e6i | − 1.75270i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − 1.31108e6i | − 0.522229i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 715156.i | − 0.280976i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.11545e6 | −1.20741 | −0.603706 | − | 0.797207i | \(-0.706310\pi\) | ||||
−0.603706 | + | 0.797207i | \(0.706310\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −233766. | −0.0893749 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.42256e6i | 2.04536i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 630682.i | 0.234714i | 0.993090 | + | 0.117357i | \(0.0374421\pi\) | ||||
−0.993090 | + | 0.117357i | \(0.962558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.55876e6 | 0.572403 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 410412. | 0.148719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 48404.0i | − 0.0173094i | −0.999963 | − | 0.00865472i | \(-0.997245\pi\) | ||||
0.999963 | − | 0.00865472i | \(-0.00275492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 468648.i | − 0.165400i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.74182e6 | 0.606747 | 0.303373 | − | 0.952872i | \(-0.401887\pi\) | ||||
0.303373 | + | 0.952872i | \(0.401887\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.01184e6 | −0.347904 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 917892.i | 0.311540i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.06819e6i | 1.02804i | 0.857779 | + | 0.514019i | \(0.171844\pi\) | ||||
−0.857779 | + | 0.514019i | \(0.828156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.54936e6 | −1.83570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.43968e6 | 0.470201 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 905488.i | 0.292005i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.35984e6i | 1.70677i | 0.521280 | + | 0.853386i | \(0.325455\pi\) | ||||
−0.521280 | + | 0.853386i | \(0.674545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.15584e6 | −1.30685 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.76473e6 | −0.858603 | −0.429302 | − | 0.903161i | \(-0.641240\pi\) | ||||
−0.429302 | + | 0.903161i | \(0.641240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 213808.i | − 0.0655785i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 223074.i | 0.0675789i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −540888. | −0.161853 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.20893e6 | 0.357350 | 0.178675 | − | 0.983908i | \(-0.442819\pi\) | ||||
0.178675 | + | 0.983908i | \(0.442819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2.36050e6i | − 0.689287i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6720.00i | 0.00193863i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.91039e6 | −0.544505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.28172e6 | −0.642571 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 4.38008e6i | − 1.21884i | −0.792847 | − | 0.609421i | \(-0.791402\pi\) | ||||
0.792847 | − | 0.609421i | \(-0.208598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 922810.i | 0.253751i | 0.991919 | + | 0.126875i | \(0.0404948\pi\) | ||||
−0.991919 | + | 0.126875i | \(0.959505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −567648. | −0.154251 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.84743e6 | 1.03323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.53264e6i | − 0.406790i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 51336.0i | 0.0134672i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.12678e6 | 1.58869 | 0.794345 | − | 0.607466i | \(-0.207814\pi\) | ||||
0.794345 | + | 0.607466i | \(0.207814\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.76315e6 | −0.451928 | −0.225964 | − | 0.974136i | \(-0.572553\pi\) | ||||
−0.225964 | + | 0.974136i | \(0.572553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.73013e6i | − 0.691768i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.46416e6i | 1.36874i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.85906e6 | −0.955696 | −0.477848 | − | 0.878443i | \(-0.658583\pi\) | ||||
−0.477848 | + | 0.878443i | \(0.658583\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.30423e6 | −0.809048 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.39396e6i | 1.06377i | 0.846817 | + | 0.531884i | \(0.178516\pi\) | ||||
−0.846817 | + | 0.531884i | \(0.821484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.18994e6i | − 0.524242i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.20067e6 | −0.757656 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −793390. | −0.185725 | −0.0928626 | − | 0.995679i | \(-0.529602\pi\) | ||||
−0.0928626 | + | 0.995679i | \(0.529602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 357864.i | 0.0828470i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 9216.00i | − 0.00211007i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −375360. | −0.0850001 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.04302e6 | −1.57750 | −0.788748 | − | 0.614717i | \(-0.789270\pi\) | ||||
−0.788748 | + | 0.614717i | \(0.789270\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.42447e6i | 0.315588i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.43005e6i | 1.62832i | 0.580641 | + | 0.814160i | \(0.302802\pi\) | ||||
−0.580641 | + | 0.814160i | \(0.697198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.10567e6 | −0.890086 | −0.445043 | − | 0.895509i | \(-0.646812\pi\) | ||||
−0.445043 | + | 0.895509i | \(0.646812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.42229e6 | −0.305039 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.39817e6i | 0.721030i | 0.932753 | + | 0.360515i | \(0.117399\pi\) | ||||
−0.932753 | + | 0.360515i | \(0.882601\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.37824e6i | − 1.96874i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −539586. | −0.112075 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.40517e6 | 0.288786 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 3.78836e6i | − 0.770401i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.83011e6i | − 0.368283i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.78133e6 | 0.553877 | 0.276939 | − | 0.960888i | \(-0.410680\pi\) | ||||
0.276939 | + | 0.960888i | \(0.410680\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −200652. | −0.0395440 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.13440e6i | 1.19648i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 3.94937e6i | − 0.762384i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.06734e6 | 0.394994 | 0.197497 | − | 0.980304i | \(-0.436719\pi\) | ||||
0.197497 | + | 0.980304i | \(0.436719\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.07400e6 | −0.581343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.65976e6i | 1.43387i | 0.697138 | + | 0.716937i | \(0.254457\pi\) | ||||
−0.697138 | + | 0.716937i | \(0.745543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.74336e7i | − 3.23050i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 341496. | 0.0626430 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.31693e7 | 2.39150 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 386580.i | − 0.0695005i | −0.999396 | − | 0.0347503i | \(-0.988936\pi\) | ||||
0.999396 | − | 0.0347503i | \(-0.0110636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 45144.0i | 0.00803537i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 3.32259e6i | − 0.574060i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 360678.i | 0.0617057i | 0.999524 | + | 0.0308528i | \(0.00982232\pi\) | ||||
−0.999524 | + | 0.0308528i | \(0.990178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.04816e6 | −0.855226 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.40260e6 | 0.235309 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.17600e6i | − 0.361527i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 868992.i | 0.142985i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.05799e6 | −0.335371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.55908e6 | 0.251636 | 0.125818 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125818 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.18220e6i | 1.46789i | 0.679210 | + | 0.733944i | \(0.262322\pi\) | ||||
−0.679210 | + | 0.733944i | \(0.737678\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4.25304e6i | − 0.673444i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.08219e6 | −1.42451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.62926e6 | 0.253134 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2268.00i | 0 0.000349065i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 132756.i | 0.0202412i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −512856. | −0.0774660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.45249e6 | 0.217359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05833e6i | 0.749955i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 6.67773e6i | − 0.980925i | −0.871462 | − | 0.490462i | \(-0.836828\pi\) | ||||
0.871462 | − | 0.490462i | \(-0.163172\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.62521e6 | 0.382089 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.34973e6 | 0.194651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.89656e6i | 1.27132i | 0.771971 | + | 0.635658i | \(0.219271\pi\) | ||||
−0.771971 | + | 0.635658i | \(0.780729\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 517266.i | 0.0732459i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.71659e7 | −2.40873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.39168e6 | 0.888796 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.33477e6i | 0.183939i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 4.46070e6i | − 0.609207i | −0.952479 | − | 0.304603i | \(-0.901476\pi\) | ||||
0.952479 | − | 0.304603i | \(-0.0985239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 521272. | 0.0705562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.18066e6 | 0.292538 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.37660e6i | 0.847849i | 0.905698 | + | 0.423924i | \(0.139348\pi\) | ||||
−0.905698 | + | 0.423924i | \(0.860652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.27524e6i | 0.695218i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.57464e6 | 0.205695 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.51143e6 | −0.713648 | −0.356824 | − | 0.934172i | \(-0.616140\pi\) | ||||
−0.356824 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.35431e6i | − 0.173831i | −0.996216 | − | 0.0869155i | \(-0.972299\pi\) | ||||
0.996216 | − | 0.0869155i | \(-0.0277010\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 501120.i | 0.0637610i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 1.58629e6i | 0.196646i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.34851e7i | 1.65735i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.80166e6 | −0.341384 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 126684. | 0.0153050 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.69964e6i | − 0.323378i | −0.986842 | − | 0.161689i | \(-0.948306\pi\) | ||||
0.986842 | − | 0.161689i | \(-0.0516941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.94275e6i | 1.06214i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.37149e6 | 0.397057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.31035e7 | 1.53021 | 0.765103 | − | 0.643908i | \(-0.222688\pi\) | ||||
0.765103 | + | 0.643908i | \(0.222688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.59446e7i | 1.84639i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.73984e6i | − 0.659119i | ||||||||
\(598\) | 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 | \(-0.695913\pi\) | ||||
−0.577351 | + | 0.816496i | \(0.695913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.16516e6i | 0.354488i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.95295e6i | 0.550143i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.81684e6 | 0.971273 | 0.485636 | − | 0.874161i | \(-0.338588\pi\) | ||||
0.485636 | + | 0.874161i | \(0.338588\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.92715e7 | −2.10558 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 322368.i | 0.0349340i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.13600e7i | − 1.22103i | −0.792006 | − | 0.610514i | \(-0.790963\pi\) | ||||
0.792006 | − | 0.610514i | \(-0.209037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 883116. | 0.0941521 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.77356e6 | 0.504812 | 0.252406 | − | 0.967621i | \(-0.418778\pi\) | ||||
0.252406 | + | 0.967621i | \(0.418778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.55931e6i | 0.268470i | 0.990950 | + | 0.134235i | \(0.0428577\pi\) | ||||
−0.990950 | + | 0.134235i | \(0.957142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.07036e6i | − 0.215435i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.54584e7 | −1.59567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 264461. | 0.0270808 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.14718e6i | − 0.218122i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.52335e6i | 0.858981i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.41981e6 | 0.841839 | 0.420919 | − | 0.907098i | \(-0.361708\pi\) | ||||
0.420919 | + | 0.907098i | \(0.361708\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.14165e6 | −0.807613 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.77045e6i | 0.174240i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.87648e6i | 0.183229i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.44463e6 | −0.430610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.21494e7 | −1.16791 | −0.583957 | − | 0.811785i | \(-0.698496\pi\) | ||||
−0.583957 | + | 0.811785i | \(0.698496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.08968e7i | − 1.03937i | −0.854358 | − | 0.519685i | \(-0.826049\pi\) | ||||
0.854358 | − | 0.519685i | \(-0.173951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.46759e6i | − 0.328193i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 1.00397e7i | 0.928469i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.65915e7i | 1.52266i | 0.648365 | + | 0.761329i | \(0.275453\pi\) | ||||
−0.648365 | + | 0.761329i | \(0.724547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.43878e6 | −0.495334 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.70375e6 | 0.153990 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.29372e6i | − 0.205743i | −0.994695 | − | 0.102872i | \(-0.967197\pi\) | ||||
0.994695 | − | 0.102872i | \(-0.0328031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 719194.i | 0.0640239i | 0.999487 | + | 0.0320120i | \(0.0101915\pi\) | ||||
−0.999487 | + | 0.0320120i | \(0.989809\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 808956. | 0.0714728 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.56998e7 | 1.37671 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53385e7i | 2.20529i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 5.57143e6i | − 0.481284i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 1.43540e6i | 0.121259i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.69592e7i | 1.42211i | 0.703135 | + | 0.711056i | \(0.251783\pi\) | ||||
−0.703135 | + | 0.711056i | \(0.748217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.78779e7 | −2.32052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.32277e7 | −1.09299 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.87105e7i | − 1.53473i | −0.641209 | − | 0.767367i | \(-0.721567\pi\) | ||||
0.641209 | − | 0.767367i | \(-0.278433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.91745e6i | 0.726130i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29610.0 | 0.00239357 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.03932e6 | −0.0834071 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.16204e7i | − 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.41056e6i | − 0.190671i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.61982e6 | 0.676918 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.63924e6 | 0.439682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.41862e6i | 0.651700i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.23497e7i | 1.71781i | 0.512132 | + | 0.858907i | \(0.328856\pi\) | ||||
−0.512132 | + | 0.858907i | \(0.671144\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.39249e6 | 0.640475 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.14445e6 | 0.162496 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.60402e7i | 1.20687i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.02353e7i | − 0.764687i | −0.924020 | − | 0.382344i | \(-0.875117\pi\) | ||||
0.924020 | − | 0.382344i | \(-0.124883\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.15719e6 | −0.160035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.32003e7 | 0.972435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 193936.i | − 0.0141871i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.88040e6i | 0.572467i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.70339e7 | −1.22883 | −0.614416 | − | 0.788982i | \(-0.710608\pi\) | ||||
−0.614416 | + | 0.788982i | \(0.710608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.53600e7 | −1.10041 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.63293e6i | 0.614203i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1.75674e7i | − 1.24126i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.62280e7 | 1.13875 | 0.569377 | − | 0.822077i | \(-0.307185\pi\) | ||||
0.569377 | + | 0.822077i | \(0.307185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.21427e7i | − 1.53263i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.17495e7i | − 1.49517i | −0.664168 | − | 0.747583i | \(-0.731214\pi\) | ||||
0.664168 | − | 0.747583i | \(-0.268786\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.24827e7 | 0.852293 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.84542e6 | 0.328597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.96200e7i | 1.32156i | 0.750578 | + | 0.660781i | \(0.229775\pi\) | ||||
−0.750578 | + | 0.660781i | \(0.770225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 796536.i | − 0.0532917i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 4.55123e6i | − 0.298419i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.62016e6i | 0.235789i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.62693e7 | −1.69961 | −0.849803 | − | 0.527101i | \(-0.823279\pi\) | ||||
−0.849803 | + | 0.527101i | \(0.823279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.86981e6 | −0.184445 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34816.0i | 0.00222286i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70356e6i | 0.361748i | 0.983506 | + | 0.180874i | \(0.0578927\pi\) | ||||
−0.983506 | + | 0.180874i | \(0.942107\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.16944e6 | −0.199700 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.13762e7 | 1.33804 | 0.669020 | − | 0.743244i | \(-0.266714\pi\) | ||||
0.669020 | + | 0.743244i | \(0.266714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 9.52752e6i | − 0.592473i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 5.38132e6i | − 0.332457i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 1.54322e7i | − 0.934958i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.27674e7i | 0.768520i | 0.923225 | + | 0.384260i | \(0.125543\pi\) | ||||
−0.923225 | + | 0.384260i | \(0.874457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.15191e6 | −0.547340 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.42192e6 | 0.559870 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5.55266e6i | − 0.327837i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.80413e6i | 0.399158i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.50414e6 | 0.379128 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.03844e6 | 0.118065 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.72384e7i | − 1.56764i | −0.620990 | − | 0.783818i | \(-0.713269\pi\) | ||||
0.620990 | − | 0.783818i | \(-0.286731\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 9.99252e6i | − 0.571456i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.72370e7 | 2.11608 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 293756. | 0.0165884 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.91376e6i | 0.387969i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 7.66724e6i | − 0.427556i | −0.976882 | − | 0.213778i | \(-0.931423\pi\) | ||||
0.976882 | − | 0.213778i | \(-0.0685770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36936e7 | 0.758843 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.21721e6 | 0.287314 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.60822e6i | − 0.142743i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.31744e7i | − 1.26043i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.58540e6 | −0.193800 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.05541e7 | 0.566956 | 0.283478 | − | 0.958979i | \(-0.408512\pi\) | ||||
0.283478 | + | 0.958979i | \(0.408512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.32883e6i | 0.0709442i | 0.999371 | + | 0.0354721i | \(0.0112935\pi\) | ||||
−0.999371 | + | 0.0354721i | \(0.988707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.29778e7i | − 0.688611i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.16129e7 | 0.612416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.18028e7 | −1.14276 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 894240.i | − 0.0465848i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.15933e6i | 0.318915i | 0.987205 | + | 0.159458i | \(0.0509746\pi\) | ||||
−0.987205 | + | 0.159458i | \(0.949025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.00734e7 | −0.518414 | −0.259207 | − | 0.965822i | \(-0.583461\pi\) | ||||
−0.259207 | + | 0.965822i | \(0.583461\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.19740e6 | 0.112402 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.49152e6i | 0.330052i | 0.986289 | + | 0.165026i | \(0.0527708\pi\) | ||||
−0.986289 | + | 0.165026i | \(0.947229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.93536e7i | − 0.978082i | −0.872261 | − | 0.489041i | \(-0.837347\pi\) | ||||
0.872261 | − | 0.489041i | \(-0.162653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.05514e6 | −0.0530040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.97095e7 | 3.98013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 170544.i | − 0.00846487i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.38839e6i | − 0.167178i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | − 1.50763e7i | − 0.730677i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.25520e7i | 0.604744i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49620e7 | 1.67451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.73221e7 | −0.824766 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.23881e7i | − 0.586381i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.07651e7i | − 0.506577i | −0.967391 | − | 0.253288i | \(-0.918488\pi\) | ||||
0.967391 | − | 0.253288i | \(-0.0815121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.29870e6 | −0.247887 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.22439e7 | −0.569465 | −0.284733 | − | 0.958607i | \(-0.591905\pi\) | ||||
−0.284733 | + | 0.958607i | \(0.591905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.38664e6i | 0.0641179i | 0.999486 | + | 0.0320590i | \(0.0102064\pi\) | ||||
−0.999486 | + | 0.0320590i | \(0.989794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 6.23376e6i | − 0.286578i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.09856e7 | −0.502109 | −0.251055 | − | 0.967973i | \(-0.580777\pi\) | ||||
−0.251055 | + | 0.967973i | \(0.580777\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.77464e6 | 0.353297 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.15843e7i | − 0.975194i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.30237e6i | 0.148346i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.79750e6 | 0.0802828 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.40880e6 | 0.417829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.15670e7i | 1.83539i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.17798e6i | 0.359044i | 0.983754 | + | 0.179522i | \(0.0574550\pi\) | ||||
−0.983754 | + | 0.179522i | \(0.942545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.15256e7 | −0.503143 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.66520e6 | 0.202503 | 0.101251 | − | 0.994861i | \(-0.467715\pi\) | ||||
0.101251 | + | 0.994861i | \(0.467715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.82201e7i | 1.64964i | 0.565393 | + | 0.824822i | \(0.308724\pi\) | ||||
−0.565393 | + | 0.824822i | \(0.691276\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8568.00i | 0 0.000367723i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 813564.i | 0.0343319i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.34834e7i | − 0.565810i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.48719e6 | −0.228977 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17576e6 | −0.0487908 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.14695e7i | 1.71131i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.41487e7i | 1.81178i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.44771e7 | −0.998944 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.91746e6 | −0.402512 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.33137e7i | − 1.74826i | −0.485689 | − | 0.874131i | \(-0.661431\pi\) | ||||
0.485689 | − | 0.874131i | \(-0.338569\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 5.41355e6i | − 0.217307i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.44456e6 | 0.137511 | 0.0687556 | − | 0.997634i | \(-0.478097\pi\) | ||||
0.0687556 | + | 0.997634i | \(0.478097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.96731e6 | −0.276623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.95412e6i | − 0.0771610i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.83914e7i | 1.50768i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.37073e7 | 1.70712 | 0.853562 | − | 0.520991i | \(-0.174437\pi\) | ||||
0.853562 | + | 0.520991i | \(0.174437\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.03687e7 | −0.791251 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.52411e6i | 0.0975224i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.58878e6i | 0.330048i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.18400e6 | 0.198137 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.13022e7 | −1.57012 | −0.785062 | − | 0.619418i | \(-0.787369\pi\) | ||||
−0.785062 | + | 0.619418i | \(0.787369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 7.84857e7i | − 2.96768i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.23063e6i | 0.0838926i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.23806e6 | −0.308174 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.57460e6 | −0.356264 | −0.178132 | − | 0.984007i | \(-0.557005\pi\) | ||||
−0.178132 | + | 0.984007i | \(0.557005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.64152e7i | − 0.607550i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.71623e6i | 0.320889i | 0.987045 | + | 0.160444i | \(0.0512927\pi\) | ||||
−0.987045 | + | 0.160444i | \(0.948707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.19624e6 | −0.300148 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.94864e6 | −0.216690 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.30605e7i | − 0.473244i | −0.971602 | − | 0.236622i | \(-0.923960\pi\) | ||||
0.971602 | − | 0.236622i | \(-0.0760403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 967564.i | − 0.0348750i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.57066e7 | 0.921710 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.13875e7 | −0.406158 | −0.203079 | − | 0.979162i | \(-0.565095\pi\) | ||||
−0.203079 | + | 0.979162i | \(0.565095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.89312e6i | − 0.0671691i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.95695e6i | − 0.351436i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.29467e7 | 2.21017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.02525e6 | −0.245388 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.22180e6i | − 0.0424557i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 5.99264e6i | − 0.207157i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.62711e7 | −1.59127 | −0.795634 | − | 0.605778i | \(-0.792862\pi\) | ||||
−0.795634 | + | 0.605778i | \(0.792862\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.38355e7 | −1.15761 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.63206e7i | − 0.555506i | −0.960653 | − | 0.277753i | \(-0.910410\pi\) | ||||
0.960653 | − | 0.277753i | \(-0.0895896\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.08458e7i | − 2.06038i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 815166. | 0.0274621 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.95213e7 | −0.654294 | −0.327147 | − | 0.944973i | \(-0.606087\pi\) | ||||
−0.327147 | + | 0.944973i | \(0.606087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.98684e6i | − 0.266329i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21554e6i | 0.106680i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | − 1.51373e7i | − 0.494601i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.21829e7i | 1.04625i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.83518e7 | 1.24051 | 0.620257 | − | 0.784399i | \(-0.287028\pi\) | ||||
0.620257 | + | 0.784399i | \(0.287028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.32433e6 | 0.0426210 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.16838e7i | 0.694350i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.82206e6i | 0.249220i | 0.992206 | + | 0.124610i | \(0.0397680\pi\) | ||||
−0.992206 | + | 0.124610i | \(0.960232\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.17990e6 | −0.100809 |
(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 | 768.6.d.r.385.1 | 2 | ||
4.3 | odd | 2 | 768.6.d.a.385.2 | 2 | |||
8.3 | odd | 2 | 768.6.d.a.385.1 | 2 | |||
8.5 | even | 2 | inner | 768.6.d.r.385.2 | 2 | ||
16.3 | odd | 4 | 192.6.a.f.1.1 | 1 | |||
16.5 | even | 4 | 24.6.a.a.1.1 | ✓ | 1 | ||
16.11 | odd | 4 | 48.6.a.d.1.1 | 1 | |||
16.13 | even | 4 | 192.6.a.n.1.1 | 1 | |||
48.5 | odd | 4 | 72.6.a.e.1.1 | 1 | |||
48.11 | even | 4 | 144.6.a.i.1.1 | 1 | |||
48.29 | odd | 4 | 576.6.a.k.1.1 | 1 | |||
48.35 | even | 4 | 576.6.a.l.1.1 | 1 | |||
80.37 | odd | 4 | 600.6.f.f.49.2 | 2 | |||
80.53 | odd | 4 | 600.6.f.f.49.1 | 2 | |||
80.69 | even | 4 | 600.6.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.6.a.a.1.1 | ✓ | 1 | 16.5 | even | 4 | ||
48.6.a.d.1.1 | 1 | 16.11 | odd | 4 | |||
72.6.a.e.1.1 | 1 | 48.5 | odd | 4 | |||
144.6.a.i.1.1 | 1 | 48.11 | even | 4 | |||
192.6.a.f.1.1 | 1 | 16.3 | odd | 4 | |||
192.6.a.n.1.1 | 1 | 16.13 | even | 4 | |||
576.6.a.k.1.1 | 1 | 48.29 | odd | 4 | |||
576.6.a.l.1.1 | 1 | 48.35 | even | 4 | |||
600.6.a.i.1.1 | 1 | 80.69 | even | 4 | |||
600.6.f.f.49.1 | 2 | 80.53 | odd | 4 | |||
600.6.f.f.49.2 | 2 | 80.37 | odd | 4 | |||
768.6.d.a.385.1 | 2 | 8.3 | odd | 2 | |||
768.6.d.a.385.2 | 2 | 4.3 | odd | 2 | |||
768.6.d.r.385.1 | 2 | 1.1 | even | 1 | trivial | ||
768.6.d.r.385.2 | 2 | 8.5 | even | 2 | inner |