Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 343 x^{10} - 696 x^{9} + 44406 x^{8} + 179640 x^{7} - 2401691 x^{6} - 15554592 x^{5} + 26901210 x^{4} + 434775816 x^{3} + 1271335685 x^{2} + \cdots + 653157349 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(-1.02698 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.c.161.9 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 5.98217i | − 0.383756i | −0.981419 | − | 0.191878i | \(-0.938542\pi\) | ||||
0.981419 | − | 0.191878i | \(-0.0614578\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 25.0000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −86.0039 | −0.663396 | −0.331698 | − | 0.943386i | \(-0.607622\pi\) | ||||
−0.331698 | + | 0.943386i | \(0.607622\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 207.214 | 0.852731 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 562.865i | 1.40256i | 0.712884 | + | 0.701282i | \(0.247389\pi\) | ||||
−0.712884 | + | 0.701282i | \(0.752611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 659.925i | − 1.08302i | −0.840694 | − | 0.541510i | \(-0.817853\pi\) | ||||
0.840694 | − | 0.541510i | \(-0.182147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −149.554 | −0.171621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −989.843 | −0.830700 | −0.415350 | − | 0.909662i | \(-0.636341\pi\) | ||||
−0.415350 | + | 0.909662i | \(0.636341\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1610.12i | − 1.02323i | −0.859214 | − | 0.511616i | \(-0.829047\pi\) | ||||
0.859214 | − | 0.511616i | \(-0.170953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 514.490i | 0.254582i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2932.96 | 1.15608 | 0.578039 | − | 0.816009i | \(-0.303818\pi\) | ||||
0.578039 | + | 0.816009i | \(0.303818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2693.25i | − 0.710997i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5656.43i | − 1.24896i | −0.781042 | − | 0.624478i | \(-0.785312\pi\) | ||||
0.781042 | − | 0.624478i | \(-0.214688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6876.28 | −1.28514 | −0.642568 | − | 0.766228i | \(-0.722131\pi\) | ||||
−0.642568 | + | 0.766228i | \(0.722131\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3367.15 | 0.538243 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2150.10i | 0.296680i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10863.8i | 1.30460i | 0.757960 | + | 0.652302i | \(0.226196\pi\) | ||||
−0.757960 | + | 0.652302i | \(0.773804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3947.78 | −0.415616 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18053.4 | −1.67726 | −0.838628 | − | 0.544704i | \(-0.816642\pi\) | ||||
−0.838628 | + | 0.544704i | \(0.816642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14898.2i | 1.22875i | 0.789014 | + | 0.614375i | \(0.210592\pi\) | ||||
−0.789014 | + | 0.614375i | \(0.789408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 5180.34i | − 0.381353i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7542.31 | 0.498035 | 0.249017 | − | 0.968499i | \(-0.419892\pi\) | ||||
0.249017 | + | 0.968499i | \(0.419892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9410.33 | −0.559906 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5921.41i | 0.318786i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 23275.2i | − 1.13816i | −0.822282 | − | 0.569080i | \(-0.807299\pi\) | ||||
0.822282 | − | 0.569080i | \(-0.192701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14071.6 | 0.627246 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9632.01 | −0.392672 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9083.21i | − 0.339711i | −0.985469 | − | 0.169855i | \(-0.945670\pi\) | ||||
0.985469 | − | 0.169855i | \(-0.0543301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6457.10i | 0.222184i | 0.993810 | + | 0.111092i | \(0.0354348\pi\) | ||||
−0.993810 | + | 0.111092i | \(0.964565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −17821.2 | −0.565699 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16498.1 | −0.484341 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62015.4i | 1.68777i | 0.536527 | + | 0.843883i | \(0.319736\pi\) | ||||
−0.536527 | + | 0.843883i | \(0.680264\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 17545.5i | − 0.443652i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −49547.0 | −1.16646 | −0.583232 | − | 0.812306i | \(-0.698212\pi\) | ||||
−0.583232 | + | 0.812306i | \(0.698212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2157.48 | 0.0473850 | 0.0236925 | − | 0.999719i | \(-0.492458\pi\) | ||||
0.0236925 | + | 0.999719i | \(0.492458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3738.86i | 0.0767513i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 48408.6i | − 0.930456i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −25663.1 | −0.462638 | −0.231319 | − | 0.972878i | \(-0.574304\pi\) | ||||
−0.231319 | + | 0.972878i | \(0.574304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34241.4 | 0.579881 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 54850.1i | 0.873940i | 0.899476 | + | 0.436970i | \(0.143948\pi\) | ||||
−0.899476 | + | 0.436970i | \(0.856052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24746.1i | 0.371500i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −33837.7 | −0.479295 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −115200. | −1.54162 | −0.770808 | − | 0.637068i | \(-0.780147\pi\) | ||||
−0.770808 | + | 0.637068i | \(0.780147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 56756.1i | 0.718471i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 41135.1i | 0.493179i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −40253.0 | −0.457603 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114285. | −1.23328 | −0.616639 | − | 0.787246i | \(-0.711506\pi\) | ||||
−0.616639 | + | 0.787246i | \(0.711506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 116633.i | 1.19601i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 56833.6i | − 0.554372i | −0.960816 | − | 0.277186i | \(-0.910598\pi\) | ||||
0.960816 | − | 0.277186i | \(-0.0894019\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −136106. | −1.26411 | −0.632053 | − | 0.774925i | \(-0.717788\pi\) | ||||
−0.632053 | + | 0.774925i | \(0.717788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12862.2 | 0.113853 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 51245.3i | 0.432708i | 0.976315 | + | 0.216354i | \(0.0694165\pi\) | ||||
−0.976315 | + | 0.216354i | \(0.930584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 160990.i | − 1.29787i | −0.760843 | − | 0.648937i | \(-0.775214\pi\) | ||||
0.760843 | − | 0.648937i | \(-0.224786\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 64989.2 | 0.500650 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −197348. | −1.45390 | −0.726952 | − | 0.686688i | \(-0.759064\pi\) | ||||
−0.726952 | + | 0.686688i | \(0.759064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 73324.1i | − 0.517014i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 136745.i | − 0.923524i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 85130.4 | 0.551083 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −155766. | −0.967186 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 107998.i | 0.643658i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −54027.0 | −0.297236 | −0.148618 | − | 0.988895i | \(-0.547482\pi\) | ||||
−0.148618 | + | 0.988895i | \(0.547482\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 89123.7 | 0.471540 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44661.0i | 0.227379i | 0.993516 | + | 0.113689i | \(0.0362669\pi\) | ||||
−0.993516 | + | 0.113689i | \(0.963733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 138477.i | 0.678808i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −67331.4 | −0.317968 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 250220. | 1.13899 | 0.569497 | − | 0.821994i | \(-0.307138\pi\) | ||||
0.569497 | + | 0.821994i | \(0.307138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97606.2i | 0.428490i | 0.976780 | + | 0.214245i | \(0.0687290\pi\) | ||||
−0.976780 | + | 0.214245i | \(0.931271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 45119.4i | − 0.191124i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 371449. | 1.51900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −141411. | −0.558550 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 56294.2i | 0.214867i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 274545.i | 1.01309i | 0.862213 | + | 0.506545i | \(0.169078\pi\) | ||||
−0.862213 | + | 0.506545i | \(0.830922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −331973. | −1.18484 | −0.592420 | − | 0.805629i | \(-0.701828\pi\) | ||||
−0.592420 | + | 0.805629i | \(0.701828\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −205109. | −0.708364 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 171907.i | 0.574730i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 289482.i | − 0.937288i | −0.883387 | − | 0.468644i | \(-0.844743\pi\) | ||||
0.883387 | − | 0.468644i | \(-0.155257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −139236. | −0.436776 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −252246. | −0.766938 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 232604.i | − 0.685721i | −0.939386 | − | 0.342861i | \(-0.888604\pi\) | ||||
0.939386 | − | 0.342861i | \(-0.111396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 84178.9i | − 0.240710i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 51950.4 | 0.144144 | 0.0720722 | − | 0.997399i | \(-0.477039\pi\) | ||||
0.0720722 | + | 0.997399i | \(0.477039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64208.1 | −0.172931 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 333639.i | − 0.872542i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 364659.i | − 0.926342i | −0.886269 | − | 0.463171i | \(-0.846712\pi\) | ||||
0.886269 | − | 0.463171i | \(-0.153288\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53752.4 | 0.132679 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −54337.3 | −0.130366 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 84272.6i | − 0.196587i | −0.995157 | − | 0.0982933i | \(-0.968662\pi\) | ||||
0.995157 | − | 0.0982933i | \(-0.0313383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 91685.0i | 0.208018i | 0.994576 | + | 0.104009i | \(0.0331671\pi\) | ||||
−0.994576 | + | 0.104009i | \(0.966833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38627.5 | 0.0852645 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 271596. | 0.583436 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 557148.i | − 1.16511i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 231630.i | 0.471673i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −550876. | −1.09262 | −0.546312 | − | 0.837582i | \(-0.683969\pi\) | ||||
−0.546312 | + | 0.837582i | \(0.683969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 705787. | 1.36389 | 0.681946 | − | 0.731402i | \(-0.261134\pi\) | ||||
0.681946 | + | 0.731402i | \(0.261134\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 98694.6i | 0.185869i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 407510.i | 0.748123i | 0.927404 | + | 0.374061i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374061i | \(0.877965\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 123380. | 0.220857 | 0.110428 | − | 0.993884i | \(-0.464778\pi\) | ||||
0.110428 | + | 0.993884i | \(0.464778\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 370986. | 0.647691 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 486475.i | 0.828553i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 451335.i | 0.750092i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 607750. | 0.985824 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 906281. | 1.43515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 421862.i | − 0.652325i | −0.945314 | − | 0.326163i | \(-0.894244\pi\) | ||||
0.945314 | − | 0.326163i | \(-0.105756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 296398.i | 0.447638i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 372456. | 0.549514 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 591387. | 0.852555 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 12906.4i | − 0.0181843i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 653222.i | 0.899664i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.32959e6 | 1.79042 | 0.895208 | − | 0.445648i | \(-0.147027\pi\) | ||||
0.895208 | + | 0.445648i | \(0.147027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −129509. | −0.170546 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 164830.i | 0.212311i | 0.994350 | + | 0.106155i | \(0.0338541\pi\) | ||||
−0.994350 | + | 0.106155i | \(0.966146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 881880.i | − 1.11127i | −0.831425 | − | 0.555637i | \(-0.812475\pi\) | ||||
0.831425 | − | 0.555637i | \(-0.187525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −289588. | −0.357068 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −525527. | −0.634170 | −0.317085 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317085 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 188558.i | − 0.222728i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 153521.i | 0.177540i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 322839. | 0.365587 | 0.182794 | − | 0.983151i | \(-0.441486\pi\) | ||||
0.182794 | + | 0.983151i | \(0.441486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.17177e6 | 1.29956 | 0.649782 | − | 0.760120i | \(-0.274860\pi\) | ||||
0.649782 | + | 0.760120i | \(0.274860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 859299.i | − 0.933530i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 235258.i | 0.250397i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.06256e6 | −1.10818 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 328122. | 0.335380 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.68512e6i | − 1.68829i | −0.536119 | − | 0.844143i | \(-0.680110\pi\) | ||||
0.536119 | − | 0.844143i | \(-0.319890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.65086e6i | 1.62147i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 148035. | 0.142566 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −516986. | −0.488255 | −0.244127 | − | 0.969743i | \(-0.578501\pi\) | ||||
−0.244127 | + | 0.969743i | \(0.578501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 934331.i | − 0.865469i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1.17209e6i | − 1.06502i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 101121. | 0.0901467 | 0.0450734 | − | 0.998984i | \(-0.485648\pi\) | ||||
0.0450734 | + | 0.998984i | \(0.485648\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −581880. | −0.509001 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 689144.i | 0.591605i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 17814.9i | − 0.0150107i | −0.999972 | − | 0.00750537i | \(-0.997611\pi\) | ||||
0.999972 | − | 0.00750537i | \(-0.00238906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.82431e6 | 1.50895 | 0.754474 | − | 0.656330i | \(-0.227892\pi\) | ||||
0.754474 | + | 0.656330i | \(0.227892\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 339525. | 0.275718 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 351791.i | − 0.280513i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 250172.i | 0.195903i | 0.995191 | + | 0.0979513i | \(0.0312289\pi\) | ||||
−0.995191 | + | 0.0979513i | \(0.968771\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.42486e6 | −1.09588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.21044e6 | 0.914490 | 0.457245 | − | 0.889341i | \(-0.348836\pi\) | ||||
0.457245 | + | 0.889341i | \(0.348836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 739043.i | 0.548534i | 0.961654 | + | 0.274267i | \(0.0884352\pi\) | ||||
−0.961654 | + | 0.274267i | \(0.911565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 240800.i | 0.175608i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.55266e6 | 1.11269 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −440067. | −0.309938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 683674.i | 0.473279i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.11599e6i | 1.43994i | 0.694006 | + | 0.719969i | \(0.255844\pi\) | ||||
−0.694006 | + | 0.719969i | \(0.744156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −227080. | −0.151923 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.51594e6 | 0.997219 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.93554e6i | − 1.25206i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.28131e6i | − 0.815148i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −339988. | −0.212744 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 161427. | 0.0993637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.32583e6i | − 1.40842i | −0.709992 | − | 0.704210i | \(-0.751301\pi\) | ||||
0.709992 | − | 0.704210i | \(-0.248699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 814208.i | 0.485109i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00391e6 | −1.76111 | −0.880554 | − | 0.473945i | \(-0.842830\pi\) | ||||
−0.880554 | + | 0.473945i | \(0.842830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.07318e6 | −0.619172 | −0.309586 | − | 0.950871i | \(-0.600190\pi\) | ||||
−0.309586 | + | 0.950871i | \(0.600190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 445529.i | 0.252988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.09103e6i | − 1.72765i | −0.503795 | − | 0.863823i | \(-0.668063\pi\) | ||||
0.503795 | − | 0.863823i | \(-0.331937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.18381e6 | 1.75174 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 306558. | 0.166054 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.59377e6i | 0.849999i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 412453.i | 0.216604i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −963068. | −0.498067 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −648668. | −0.330394 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198204.i | 0.0994356i | 0.998763 | + | 0.0497178i | \(0.0158322\pi\) | ||||
−0.998763 | + | 0.0497178i | \(0.984168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.25113e6i | 1.11248i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.55038e6 | 0.754792 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.06781e6 | 0.991828 | 0.495914 | − | 0.868372i | \(-0.334833\pi\) | ||||
0.495914 | + | 0.868372i | \(0.334833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.18057e6i | 0.557945i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.87042e6i | − 1.80249i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.25479e6 | 1.03484 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −438637. | −0.198407 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.97453e6i | − 0.880319i | −0.897920 | − | 0.440160i | \(-0.854922\pi\) | ||||
0.897920 | − | 0.440160i | \(-0.145078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1.07261e6i | − 0.471388i | −0.971827 | − | 0.235694i | \(-0.924264\pi\) | ||||
0.971827 | − | 0.235694i | \(-0.0757363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.77735e6 | −0.770024 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.81294e6 | −1.20150 | −0.600750 | − | 0.799437i | \(-0.705131\pi\) | ||||
−0.600750 | + | 0.799437i | \(0.705131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.23867e6i | 0.521658i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 509264.i | − 0.211482i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.16815e6 | −0.887877 | −0.443939 | − | 0.896057i | \(-0.646419\pi\) | ||||
−0.443939 | + | 0.896057i | \(0.646419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −116388. | −0.0470048 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 931820.i | 0.371164i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 53937.1i | − 0.0211912i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.48484e6 | −1.73813 | −0.869064 | − | 0.494700i | \(-0.835278\pi\) | ||||
−0.869064 | + | 0.494700i | \(0.835278\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.74091e6 | −1.43025 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00176e6i | 0.755052i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5669.92i | − 0.00211011i | −0.999999 | − | 0.00105505i | \(-0.999664\pi\) | ||||
0.999999 | − | 0.00105505i | \(-0.000335834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 93471.4 | 0.0343242 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.73282e6 | −1.35264 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.47374e6i | 1.24222i | 0.783723 | + | 0.621110i | \(0.213318\pi\) | ||||
−0.783723 | + | 0.621110i | \(0.786682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 323199.i | 0.114066i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.16714e6 | 1.79992 | 0.899960 | − | 0.435972i | \(-0.143595\pi\) | ||||
0.899960 | + | 0.435972i | \(0.143595\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.21021e6 | −0.416112 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.08712e6i | 1.04779i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.58648e6i | 0.866634i | 0.901242 | + | 0.433317i | \(0.142657\pi\) | ||||
−0.901242 | + | 0.433317i | \(0.857343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.90318e6 | −0.960354 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 267169. | 0.0872580 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 641578.i | 0.206898i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.62059e6i | 1.15293i | 0.817122 | + | 0.576465i | \(0.195568\pi\) | ||||
−0.817122 | + | 0.576465i | \(0.804432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 828390. | 0.260497 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33479.2 | 0.0103971 | 0.00519857 | − | 0.999986i | \(-0.498345\pi\) | ||||
0.00519857 | + | 0.999986i | \(0.498345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.53783e6i | 1.39183i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 856035.i | − 0.259331i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.11487e6 | −1.82979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.73047e6 | 1.69388 | 0.846939 | − | 0.531690i | \(-0.178443\pi\) | ||||
0.846939 | + | 0.531690i | \(0.178443\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.49686e6i | − 0.437096i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 781191.i | 0.225363i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.37125e6 | 0.390838 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 583897. | 0.164436 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 831585.i | − 0.231404i | −0.993284 | − | 0.115702i | \(-0.963088\pi\) | ||||
0.993284 | − | 0.115702i | \(-0.0369118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.09206e6i | − 1.12522i | −0.826723 | − | 0.562609i | \(-0.809798\pi\) | ||||
0.826723 | − | 0.562609i | \(-0.190202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.56287e6 | 0.424690 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 618652. | 0.166140 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 555336.i | − 0.147396i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.22207e6i | − 0.582927i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.02709e6 | −0.784932 | −0.392466 | − | 0.919766i | \(-0.628378\pi\) | ||||
−0.392466 | + | 0.919766i | \(0.628378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.34502e6 | −1.11371 | −0.556855 | − | 0.830609i | \(-0.687992\pi\) | ||||
−0.556855 | + | 0.830609i | \(0.687992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 845943.i | 0.214347i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.72243e6i | − 1.18294i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.30491e6 | −1.80906 | −0.904532 | − | 0.426406i | \(-0.859779\pi\) | ||||
−0.904532 | + | 0.426406i | \(0.859779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.94995e6 | −0.477449 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.50733e6i | 1.57541i | 0.616053 | + | 0.787705i | \(0.288731\pi\) | ||||
−0.616053 | + | 0.787705i | \(0.711269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.87999e6i | 0.689431i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.64238e6 | 0.388780 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.22440e6 | −0.754802 | −0.377401 | − | 0.926050i | \(-0.623182\pi\) | ||||
−0.377401 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1.01616e7i | − 2.35246i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.98592e6i | 0.454690i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.41890e6 | 0.321310 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.81776e6 | −1.30306 | −0.651531 | − | 0.758622i | \(-0.725873\pi\) | ||||
−0.651531 | + | 0.758622i | \(0.725873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.66590e6i | 0.590625i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 7.60005e6i | − 1.66557i | −0.553594 | − | 0.832787i | \(-0.686744\pi\) | ||||
0.553594 | − | 0.832787i | \(-0.313256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.98478e6 | 1.94785 | 0.973923 | − | 0.226877i | \(-0.0728517\pi\) | ||||
0.973923 | + | 0.226877i | \(0.0728517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.02838e6 | 0.220556 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.10558e6i | 0.234584i | 0.993097 | + | 0.117292i | \(0.0374214\pi\) | ||||
−0.993097 | + | 0.117292i | \(0.962579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5.33356e6i | − 1.11966i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.73173e6 | −0.359690 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.38569e6 | −1.72340 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00633e6i | 0.204647i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.82294e6i | − 0.970545i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.48384e6 | −0.693777 | −0.346888 | − | 0.937906i | \(-0.612762\pi\) | ||||
−0.346888 | + | 0.937906i | \(0.612762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.16931e6 | 1.41291 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.50898e6i | 0.294317i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.85713e6i | 0.551539i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57518e6 | −0.300958 | −0.150479 | − | 0.988613i | \(-0.548082\pi\) | ||||
−0.150479 | + | 0.988613i | \(0.548082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.39148e6 | −0.263150 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.61403e6i | 1.61251i | 0.591568 | + | 0.806255i | \(0.298509\pi\) | ||||
−0.591568 | + | 0.806255i | \(0.701491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.59898e6i | 1.03751i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.91583e6 | 0.534872 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.26123e6 | 0.773827 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 385806.i | 0.0693613i | 0.999398 | + | 0.0346806i | \(0.0110414\pi\) | ||||
−0.999398 | + | 0.0346806i | \(0.988959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 310776.i | − 0.0553163i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.61083e6 | −0.812567 | −0.406283 | − | 0.913747i | \(-0.633175\pi\) | ||||
−0.406283 | + | 0.913747i | \(0.633175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.42084e6 | −0.247923 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 384104.i | 0.0663634i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 57696.0i | − 0.00987078i | −0.999988 | − | 0.00493539i | \(-0.998429\pi\) | ||||
0.999988 | − | 0.00493539i | \(-0.00157099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −185552. | −0.0314350 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.33646e6 | −0.727516 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.40265e6i | 0.565326i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.24530e6i | 0.698526i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.18145e6 | −0.355490 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.74455e6 | 1.08858 | 0.544288 | − | 0.838898i | \(-0.316800\pi\) | ||||
0.544288 | + | 0.838898i | \(0.316800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.12870e7i | − 1.80436i | −0.431356 | − | 0.902182i | \(-0.641965\pi\) | ||||
0.431356 | − | 0.902182i | \(-0.358035\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 321556.i | − 0.0509165i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.80644e6 | 1.06756 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.16594e6 | 0.336517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.88217e6i | − 0.289682i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19139e7i | 1.81650i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.28113e6 | 0.193513 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −504133. | −0.0754413 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.29675e6i | − 0.785303i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 8.45796e6i | − 1.24243i | −0.783640 | − | 0.621216i | \(-0.786639\pi\) | ||||
0.783640 | − | 0.621216i | \(-0.213361\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 548475. | 0.0798284 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.02475e6 | −0.580426 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.58748e6i | − 0.655550i | −0.944756 | − | 0.327775i | \(-0.893701\pi\) | ||||
0.944756 | − | 0.327775i | \(-0.106299\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.33800e6i | 0.189463i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.10753e6 | −1.27797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.20713e6 | 0.306913 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.62473e6i | − 0.223897i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.35598e6i | − 0.731478i | −0.930718 | − | 0.365739i | \(-0.880816\pi\) | ||||
0.930718 | − | 0.365739i | \(-0.119184\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.83171e6 | 1.33076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33296e6 | −0.447118 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.30053e6i | 0.305884i | 0.988235 | + | 0.152942i | \(0.0488747\pi\) | ||||
−0.988235 | + | 0.152942i | \(0.951125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.93369e6i | 0.650206i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.94489e6 | −0.384691 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.12794e6 | 0.663991 | 0.331996 | − | 0.943281i | \(-0.392278\pi\) | ||||
0.331996 | + | 0.943281i | \(0.392278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 7.88741e6i | − 1.01238i | −0.862421 | − | 0.506191i | \(-0.831053\pi\) | ||||
0.862421 | − | 0.506191i | \(-0.168947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.29543e6i | 0.419301i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.83310e6 | −0.231216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.38694e6 | 0.798644 | 0.399322 | − | 0.916811i | \(-0.369246\pi\) | ||||
0.399322 | + | 0.916811i | \(0.369246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.22213e6i | − 0.523402i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.71732e6i | − 0.579769i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.31008e7 | 1.59634 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.41864e6 | −0.413013 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 2.32088e6i | − 0.278009i | −0.990292 | − | 0.139004i | \(-0.955610\pi\) | ||||
0.990292 | − | 0.139004i | \(-0.0443902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.10716e7i | 1.31499i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.43779e6 | 0.287097 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.95109e6 | 0.461403 | 0.230701 | − | 0.973025i | \(-0.425898\pi\) | ||||
0.230701 | + | 0.973025i | \(0.425898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2.12826e6i | − 0.246452i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 738078.i | − 0.0847553i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.10428e7 | 1.25751 | 0.628755 | − | 0.777603i | \(-0.283565\pi\) | ||||
0.628755 | + | 0.777603i | \(0.283565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.97957e6 | 0.336486 | 0.168243 | − | 0.985746i | \(-0.446191\pi\) | ||||
0.168243 | + | 0.985746i | \(0.446191\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.28504e7i | 1.43921i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.89416e6i | 0.432539i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.18732e6 | −0.461280 | −0.230640 | − | 0.973039i | \(-0.574082\pi\) | ||||
−0.230640 | + | 0.973039i | \(0.574082\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.91017e6 | 0.317962 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4.97736e6i | − 0.539381i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.29891e7i | 1.39613i | 0.716033 | + | 0.698066i | \(0.245956\pi\) | ||||
−0.716033 | + | 0.698066i | \(0.754044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.69996e6 | 0.287852 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.67330e7 | 1.76954 | 0.884769 | − | 0.466030i | \(-0.154316\pi\) | ||||
0.884769 | + | 0.466030i | \(0.154316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 3.29552e6i | − 0.345699i | −0.984948 | − | 0.172849i | \(-0.944703\pi\) | ||||
0.984948 | − | 0.172849i | \(-0.0552974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7.89922e6i | − 0.821968i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.90762e6 | 1.02270 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5.42152e6i | − 0.550748i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.07535e7i | − 1.08373i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.18430e7 | −1.18410 | −0.592050 | − | 0.805901i | \(-0.701681\pi\) | ||||
−0.592050 | + | 0.805901i | \(0.701681\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.52365e6 | −0.250334 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.35067e6i | 0.132928i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.21011e6i | 0.606389i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.02668e7 | −0.994680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.99649e6 | 0.864824 | 0.432412 | − | 0.901676i | \(-0.357663\pi\) | ||||
0.432412 | + | 0.901676i | \(0.357663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.77796e6i | 0.932655i | 0.884612 | + | 0.466327i | \(0.154423\pi\) | ||||
−0.884612 | + | 0.466327i | \(0.845577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 2.22809e6i | − 0.210879i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.52186e6 | −0.424675 | −0.212337 | − | 0.977196i | \(-0.568108\pi\) | ||||
−0.212337 | + | 0.977196i | \(0.568108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.11262e6 | 0.476466 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.53777e6i | − 0.327173i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.59880e6i | 0.605594i | 0.953055 | + | 0.302797i | \(0.0979204\pi\) | ||||
−0.953055 | + | 0.302797i | \(0.902080\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11652e6 | 0.101687 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 447060. | 0.0404066 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.23865e6i | − 0.200804i | −0.994947 | − | 0.100402i | \(-0.967987\pi\) | ||||
0.994947 | − | 0.100402i | \(-0.0320130\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.30535e7i | 1.16205i | 0.813887 | + | 0.581023i | \(0.197348\pi\) | ||||
−0.813887 | + | 0.581023i | \(0.802652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.90769e6 | 0.345252 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.46191e6 | 0.303572 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.65901e7i | − 1.44389i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 7.95380e6i | − 0.687084i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.63448e6 | −0.311627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.18780e7 | 1.86196 | 0.930980 | − | 0.365071i | \(-0.118955\pi\) | ||||
0.930980 | + | 0.365071i | \(0.118955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.68328e6i | 0.142199i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.11662e7i | − 0.936344i | −0.883637 | − | 0.468172i | \(-0.844913\pi\) | ||||
0.883637 | − | 0.468172i | \(-0.155087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.82898e6 | 0.818152 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 986043. | 0.0814757 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.63440e6i | − 0.462164i | −0.972934 | − | 0.231082i | \(-0.925773\pi\) | ||||
0.972934 | − | 0.231082i | \(-0.0742266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 6.25551e6i | − 0.509373i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.27556e6 | −0.426458 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53599e7 | −1.23265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.17015e6i | − 0.650931i | −0.945554 | − | 0.325466i | \(-0.894479\pi\) | ||||
0.945554 | − | 0.325466i | \(-0.105521\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.00309e7i | − 0.793428i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.44015e6 | 0.191626 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.78700e7 | 1.39330 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.14379e6i | 0.243367i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.43711e7i | 1.87318i | 0.350421 | + | 0.936592i | \(0.386038\pi\) | ||||
−0.350421 | + | 0.936592i | \(0.613962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.74921e7 | 1.33491 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.12798e6 | −0.0854733 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.88791e6i | 0.367768i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.61049e7i | 1.20322i | 0.798791 | + | 0.601608i | \(0.205473\pi\) | ||||
−0.798791 | + | 0.601608i | \(0.794527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.31775e6 | −0.394506 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.01679e7 | −1.48572 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 9.28622e6i | − 0.679319i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.93128e6i | − 0.140296i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.41860e6 | −0.535180 | −0.267590 | − | 0.963533i | \(-0.586227\pi\) | ||||
−0.267590 | + | 0.963533i | \(0.586227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17056e7 | 0.838604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7.00970e6i | − 0.498716i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.53527e6i | 0.249791i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.45557e7 | 1.02140 | 0.510702 | − | 0.859758i | \(-0.329386\pi\) | ||||
0.510702 | + | 0.859758i | \(0.329386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.18019e6 | 0.221633 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.47469e7i | − 1.02072i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.37973e7i | 0.948492i | 0.880392 | + | 0.474246i | \(0.157279\pi\) | ||||
−0.880392 | + | 0.474246i | \(0.842721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.40736e6 | 0.0960916 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.49063e7 | −2.36720 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.41030e7i | − 1.62353i | −0.583984 | − | 0.811765i | \(-0.698507\pi\) | ||||
0.583984 | − | 0.811765i | \(-0.301493\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.35641e6i | 0.425271i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.09987e7 | 0.730919 | 0.365459 | − | 0.930827i | \(-0.380912\pi\) | ||||
0.365459 | + | 0.930827i | \(0.380912\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.86363e6 | 0.453068 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.13657e7i | 0.745236i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.40729e6i | − 0.287057i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.89927e7 | −1.22882 | −0.614408 | − | 0.788988i | \(-0.710605\pi\) | ||||
−0.614408 | + | 0.788988i | \(0.710605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.00807e7 | −0.647890 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.29932e6i | 0.529877i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 2.30676e7i | − 1.46306i | −0.681810 | − | 0.731530i | \(-0.738807\pi\) | ||||
0.681810 | − | 0.731530i | \(-0.261193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.87575e6 | 0.622251 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.19864e6 | −0.0750287 | −0.0375143 | − | 0.999296i | \(-0.511944\pi\) | ||||
−0.0375143 | + | 0.999296i | \(0.511944\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.38458e7i | 0.861004i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.12773e6i | 0.316790i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.99424e6 | −0.367913 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.94617e7 | 1.18677 | 0.593384 | − | 0.804919i | \(-0.297792\pi\) | ||||
0.593384 | + | 0.804919i | \(0.297792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.09270e6i | 0.187371i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.46693e6i | − 0.208688i | −0.994541 | − | 0.104344i | \(-0.966726\pi\) | ||||
0.994541 | − | 0.104344i | \(-0.0332742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.29767e6 | 0.257027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.58933e6 | −0.332129 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.90681e7i | 1.71622i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 2.78883e7i | − 1.63604i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.52342e7 | −0.888005 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.23706e6 | −0.419168 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.32482e7i | 1.33799i | 0.743266 | + | 0.668996i | \(0.233276\pi\) | ||||
−0.743266 | + | 0.668996i | \(0.766724\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 604920.i | − 0.0345944i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.69727e7 | 0.964515 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.26120e6 | 0.240630 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.48090e6i | 0.195332i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.84771e6i | 0.549148i | 0.961566 | + | 0.274574i | \(0.0885368\pi\) | ||||
−0.961566 | + | 0.274574i | \(0.911463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.46570e6 | −0.413717 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.38709e7 | −1.31458 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.21437e6i | 0.0664605i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.30616e6i | 0.342985i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −106572. | −0.00576047 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.27282e7 | −1.22094 | −0.610470 | − | 0.792040i | \(-0.709019\pi\) | ||||
−0.610470 | + | 0.792040i | \(0.709019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 6.46981e6i | − 0.345413i | −0.984973 | − | 0.172707i | \(-0.944749\pi\) | ||||
0.984973 | − | 0.172707i | \(-0.0552513\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.09133e7i | − 0.579068i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.81509e6 | −0.306664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.39879e7 | 1.25730 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.17606e7i | 0.612663i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.40123e7i | − 1.24330i | −0.783295 | − | 0.621651i | \(-0.786462\pi\) | ||||
0.783295 | − | 0.621651i | \(-0.213538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.96788e7 | −1.01274 | −0.506372 | − | 0.862315i | \(-0.669014\pi\) | ||||
−0.506372 | + | 0.862315i | \(0.669014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.10447e6 | −0.107649 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.32667e7i | − 0.674525i | −0.941411 | − | 0.337263i | \(-0.890499\pi\) | ||||
0.941411 | − | 0.337263i | \(-0.109501\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 3.47443e6i | − 0.175589i | −0.996139 | − | 0.0877945i | \(-0.972018\pi\) | ||||
0.996139 | − | 0.0877945i | \(-0.0279819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.49657e6 | 0.0751788 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.31475e6 | 0.465113 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.29876e6i | − 0.0644633i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.85196e7i | 0.913728i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.38012e7 | −1.16733 | −0.583667 | − | 0.811993i | \(-0.698382\pi\) | ||||
−0.583667 | + | 0.811993i | \(0.698382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.14840e7 | −0.559893 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 7.24108e6i | − 0.350941i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.60520e6i | 0.0773372i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.33965e7 | 0.641628 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.42108e6 | 0.210503 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.18632e7i | 1.50822i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.71488e7i | − 0.806978i | −0.914984 | − | 0.403489i | \(-0.867797\pi\) | ||||
0.914984 | − | 0.403489i | \(-0.132203\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.34097e6 | −0.390213 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.72604e7 | −0.802782 | −0.401391 | − | 0.915907i | \(-0.631473\pi\) | ||||
−0.401391 | + | 0.915907i | \(0.631473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 4.82808e6i | − 0.223250i | −0.993750 | − | 0.111625i | \(-0.964394\pi\) | ||||
0.993750 | − | 0.111625i | \(-0.0356056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 9.28829e6i | − 0.427000i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.74637e7 | −0.798197 | −0.399098 | − | 0.916908i | \(-0.630677\pi\) | ||||
−0.399098 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.11647e6 | −0.414273 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.63256e6i | 0.118941i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.44449e7i | − 0.648880i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.09255e7 | 1.82788 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.36815e7 | −1.05166 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.34381e6i | − 0.0593360i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.08269e7i | 0.475343i | 0.971346 | + | 0.237671i | \(0.0763842\pi\) | ||||
−0.971346 | + | 0.237671i | \(0.923616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.26582e7 | 0.552585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.30776e6 | −0.143580 | −0.0717900 | − | 0.997420i | \(-0.522871\pi\) | ||||
−0.0717900 | + | 0.997420i | \(0.522871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4.32516e7i | − 1.86681i | −0.358821 | − | 0.933407i | \(-0.616821\pi\) | ||||
0.358821 | − | 0.933407i | \(-0.383179\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.35843e6i | 0.0583015i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.05387e6 | 0.301036 | 0.150518 | − | 0.988607i | \(-0.451906\pi\) | ||||
0.150518 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.64653e6 | 0.197185 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.92733e7i | 0.813321i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.21440e7i | − 0.509605i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.10681e6 | −0.0879162 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.15787e7 | −0.480484 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.88952e7i | 1.60508i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.30388e7i | 0.945470i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.66498e6 | −0.312818 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.29212e6 | 0.0930287 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 370745.i | 0.0149643i | 0.999972 | + | 0.00748216i | \(0.00238167\pi\) | ||||
−0.999972 | + | 0.00748216i | \(0.997618\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1.17767e7i | − 0.472730i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.25833e7 | −1.69998 | −0.849989 | − | 0.526800i | \(-0.823392\pi\) | ||||
−0.849989 | + | 0.526800i | \(0.823392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.08732e7 | −1.22576 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 965686.i | − 0.0381315i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 3.84102e6i | − 0.150842i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.10538e7 | −0.431742 | −0.215871 | − | 0.976422i | \(-0.569259\pi\) | ||||
−0.215871 | + | 0.976422i | \(0.569259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.39135e7 | −0.540490 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.26973e7i | 1.26330i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.78989e6i | − 0.260921i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.82030e7 | −1.07794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.17601e7 | 0.447068 | 0.223534 | − | 0.974696i | \(-0.428241\pi\) | ||||
0.223534 | + | 0.974696i | \(0.428241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.51518e7i | 0.572914i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.79699e7i | 0.675837i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39287e7 | −0.521053 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.73257e6 | 0.101677 | 0.0508384 | − | 0.998707i | \(-0.483811\pi\) | ||||
0.0508384 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.41993e6i | 0.237611i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.09153e7i | 0.401850i | 0.979607 | + | 0.200925i | \(0.0643947\pi\) | ||||
−0.979607 | + | 0.200925i | \(0.935605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.29500e7 | −1.93904 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.79076e6 | 0.210938 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.45793e7i | 0.890624i | 0.895375 | + | 0.445312i | \(0.146907\pi\) | ||||
−0.895375 | + | 0.445312i | \(0.853093\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.42378e6i | − 0.0513188i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.84911e7 | −0.662995 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.84534e7 | 0.658179 | 0.329090 | − | 0.944299i | \(-0.393258\pi\) | ||||
0.329090 | + | 0.944299i | \(0.393258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.37719e7i | 0.488636i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.90461e7i | − 0.672242i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.15199e7 | −0.755604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.86541e7 | 0.651576 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.06187e7i | 0.368983i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.76447e7i | − 0.609951i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.26565e7 | 1.46696 | 0.733482 | − | 0.679709i | \(-0.237894\pi\) | ||||
0.733482 | + | 0.679709i | \(0.237894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.53418e6 | 0.326193 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.69578e7i | 1.59831i | 0.601127 | + | 0.799153i | \(0.294718\pi\) | ||||
−0.601127 | + | 0.799153i | \(0.705282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.39451e6i | − 0.284258i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.46736e6 | 0.0831231 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.67491e7 | −0.561376 | −0.280688 | − | 0.959799i | \(-0.590563\pi\) | ||||
−0.280688 | + | 0.959799i | \(0.590563\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6.48419e7i | − 2.16221i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 3.33593e7i | − 1.10674i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.08679e7 | 1.67904 | 0.839518 | − | 0.543332i | \(-0.182837\pi\) | ||||
0.839518 | + | 0.543332i | \(0.182837\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.01878e7 | 0.334571 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.88044e6i | 0.126791i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.36960e7i | 1.42053i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.37887e7 | 1.73983 | 0.869916 | − | 0.493200i | \(-0.164173\pi\) | ||||
0.869916 | + | 0.493200i | \(0.164173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.18569e6 | 0.0381591 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.08449e6i | − 0.0987703i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.20907e7i | 0.703837i | 0.936031 | + | 0.351919i | \(0.114471\pi\) | ||||
−0.936031 | + | 0.351919i | \(0.885529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.92590e7 | 0.927569 |
(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 | 320.6.d.c.161.4 | ✓ | 12 | |
4.3 | odd | 2 | 320.6.d.d.161.9 | yes | 12 | ||
8.3 | odd | 2 | 320.6.d.d.161.4 | yes | 12 | ||
8.5 | even | 2 | inner | 320.6.d.c.161.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.c.161.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
320.6.d.c.161.9 | yes | 12 | 8.5 | even | 2 | inner | |
320.6.d.d.161.4 | yes | 12 | 8.3 | odd | 2 | ||
320.6.d.d.161.9 | yes | 12 | 4.3 | odd | 2 |