Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (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: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{241})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 121x^{2} + 3600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-7.26209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.6.c.o.49.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 19.5242i | 1.25248i | 0.779632 | + | 0.626238i | \(0.215406\pi\) | ||||
−0.779632 | + | 0.626238i | \(0.784594\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.0483i | 0.270348i | 0.990822 | + | 0.135174i | \(0.0431593\pi\) | ||||
−0.990822 | + | 0.135174i | \(0.956841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −138.193 | −0.568697 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 426.008 | 1.06154 | 0.530769 | − | 0.847516i | \(-0.321903\pi\) | ||||
0.530769 | + | 0.847516i | \(0.321903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1103.26i | 1.81058i | 0.424791 | + | 0.905291i | \(0.360347\pi\) | ||||
−0.424791 | + | 0.905291i | \(0.639653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 109.387i | − 0.0918000i | −0.998946 | − | 0.0459000i | \(-0.985384\pi\) | ||||
0.998946 | − | 0.0459000i | \(-0.0146156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 495.926 | 0.315161 | 0.157581 | − | 0.987506i | \(-0.449631\pi\) | ||||
0.157581 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −684.290 | −0.338604 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2497.37i | − 0.984381i | −0.870488 | − | 0.492190i | \(-0.836196\pi\) | ||||
0.870488 | − | 0.492190i | \(-0.163804\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2046.26i | 0.540197i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.4221 | 0.00936694 | 0.00468347 | − | 0.999989i | \(-0.498509\pi\) | ||||
0.00468347 | + | 0.999989i | \(0.498509\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7999.56 | 1.49507 | 0.747535 | − | 0.664222i | \(-0.231237\pi\) | ||||
0.747535 | + | 0.664222i | \(0.231237\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8317.45i | 1.32955i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13763.7i | 1.65284i | 0.563054 | + | 0.826420i | \(0.309626\pi\) | ||||
−0.563054 | + | 0.826420i | \(0.690374\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21540.2 | −2.26771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11863.6 | 1.10219 | 0.551097 | − | 0.834441i | \(-0.314210\pi\) | ||||
0.551097 | + | 0.834441i | \(0.314210\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16816.0i | 1.38692i | 0.720494 | + | 0.693461i | \(0.243915\pi\) | ||||
−0.720494 | + | 0.693461i | \(0.756085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 13036.0i | − 0.860795i | −0.902639 | − | 0.430397i | \(-0.858373\pi\) | ||||
0.902639 | − | 0.430397i | \(-0.141627\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15578.6 | 0.926912 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2135.69 | 0.114977 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17817.3i | 0.871269i | 0.900124 | + | 0.435634i | \(0.143476\pi\) | ||||
−0.900124 | + | 0.435634i | \(0.856524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9682.55i | 0.394732i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −47346.1 | −1.77074 | −0.885368 | − | 0.464891i | \(-0.846094\pi\) | ||||
−0.885368 | + | 0.464891i | \(0.846094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22782.9 | −0.783944 | −0.391972 | − | 0.919977i | \(-0.628207\pi\) | ||||
−0.391972 | + | 0.919977i | \(0.628207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4843.45i | − 0.153746i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 39418.3i | − 1.07278i | −0.843970 | − | 0.536390i | \(-0.819787\pi\) | ||||
0.843970 | − | 0.536390i | \(-0.180213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48759.1 | 1.23291 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1616.32 | 0.0380523 | 0.0190261 | − | 0.999819i | \(-0.493943\pi\) | ||||
0.0190261 | + | 0.999819i | \(0.493943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53293.3i | 1.17048i | 0.810859 | + | 0.585242i | \(0.199000\pi\) | ||||
−0.810859 | + | 0.585242i | \(0.801000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14930.9i | 0.286984i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6516.98 | −0.117484 | −0.0587420 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587420 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73532.6 | −1.24528 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 46016.4i | − 0.733191i | −0.930380 | − | 0.366595i | \(-0.880523\pi\) | ||||
0.930380 | − | 0.366595i | \(-0.119477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 828.257i | 0.0117319i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −113488. | −1.51872 | −0.759358 | − | 0.650673i | \(-0.774487\pi\) | ||||
−0.759358 | + | 0.650673i | \(0.774487\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38667.3 | −0.489487 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 156185.i | 1.87254i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 107418.i | − 1.15917i | −0.814912 | − | 0.579585i | \(-0.803215\pi\) | ||||
0.814912 | − | 0.579585i | \(-0.196785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −58871.4 | −0.603694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −197554. | −1.92700 | −0.963502 | − | 0.267703i | \(-0.913736\pi\) | ||||
−0.963502 | + | 0.267703i | \(0.913736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 81026.0i | 0.752543i | 0.926509 | + | 0.376272i | \(0.122794\pi\) | ||||
−0.926509 | + | 0.376272i | \(0.877206\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 137442.i | − 1.16054i | −0.814423 | − | 0.580271i | \(-0.802946\pi\) | ||||
0.814423 | − | 0.580271i | \(-0.197054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68693.1 | 0.553792 | 0.276896 | − | 0.960900i | \(-0.410694\pi\) | ||||
0.276896 | + | 0.960900i | \(0.410694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −268725. | −2.07014 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 139632.i | − 1.02870i | −0.857579 | − | 0.514352i | \(-0.828033\pi\) | ||||
0.857579 | − | 0.514352i | \(-0.171967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 152463.i | − 1.02967i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3833.83 | 0.0248179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20431.5 | 0.126864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 231628.i | 1.38047i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 65230.1i | − 0.358871i | −0.983770 | − | 0.179436i | \(-0.942573\pi\) | ||||
0.983770 | − | 0.179436i | \(-0.0574271\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −328319. | −1.73709 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −118542. | −0.603524 | −0.301762 | − | 0.953383i | \(-0.597575\pi\) | ||||
−0.301762 | + | 0.953383i | \(0.597575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17381.4i | 0.0852031i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 84757.8i | − 0.385814i | −0.981217 | − | 0.192907i | \(-0.938208\pi\) | ||||
0.981217 | − | 0.192907i | \(-0.0617916\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 168334. | 0.738982 | 0.369491 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369491 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 254517. | 1.07813 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 469996.i | 1.92200i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 304160.i | 1.16094i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −67628.6 | −0.249554 | −0.124777 | − | 0.992185i | \(-0.539822\pi\) | ||||
−0.124777 | + | 0.992185i | \(0.539822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65622.3 | 0.234212 | 0.117106 | − | 0.993119i | \(-0.462638\pi\) | ||||
0.117106 | + | 0.993119i | \(0.462638\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15116.5i | 0.0522064i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 297885.i | 0.964495i | 0.876035 | + | 0.482247i | \(0.160179\pi\) | ||||
−0.876035 | + | 0.482247i | \(0.839821\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −347868. | −1.09124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87528.7 | 0.266125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 473879.i | 1.39701i | 0.715607 | + | 0.698503i | \(0.246150\pi\) | ||||
−0.715607 | + | 0.698503i | \(0.753850\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 267673.i | 0.742701i | 0.928493 | + | 0.371351i | \(0.121105\pi\) | ||||
−0.928493 | + | 0.371351i | \(0.878895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −845883. | −2.27821 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −68533.7 | −0.179231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 703284.i | 1.78655i | 0.449509 | + | 0.893276i | \(0.351599\pi\) | ||||
−0.449509 | + | 0.893276i | \(0.648401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 924393.i | − 2.21780i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 635322. | 1.48204 | 0.741022 | − | 0.671481i | \(-0.234341\pi\) | ||||
0.741022 | + | 0.671481i | \(0.234341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −547906. | −1.24311 | −0.621555 | − | 0.783370i | \(-0.713499\pi\) | ||||
−0.621555 | + | 0.783370i | \(0.713499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 444818.i | − 0.981872i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 46599.6i | − 0.0974492i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −71718.1 | −0.146041 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 80607.9 | 0.159880 | 0.0799400 | − | 0.996800i | \(-0.474527\pi\) | ||||
0.0799400 | + | 0.996800i | \(0.474527\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 26549.3i | − 0.0513049i | −0.999671 | − | 0.0256525i | \(-0.991834\pi\) | ||||
0.999671 | − | 0.0256525i | \(-0.00816633\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 703676.i | 1.29184i | 0.763407 | + | 0.645918i | \(0.223525\pi\) | ||||
−0.763407 | + | 0.645918i | \(0.776475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 73599.5 | 0.131747 | 0.0658737 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658737 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 769610. | 1.34363 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1486.83i | 0.00253233i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 345120.i | 0.559815i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 211268. | 0.334556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00808e6 | 1.55879 | 0.779395 | − | 0.626533i | \(-0.215526\pi\) | ||||
0.779395 | + | 0.626533i | \(0.215526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31557.2i | 0.0476596i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 280371.i | 0.404189i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.04051e6 | −1.46600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 120682. | 0.166211 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 141067.i | − 0.189961i | −0.995479 | − | 0.0949805i | \(-0.969721\pi\) | ||||
0.995479 | − | 0.0949805i | \(-0.0302789\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.14301e6i | − 1.47226i | −0.676842 | − | 0.736129i | \(-0.736652\pi\) | ||||
0.676842 | − | 0.736129i | \(-0.263348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.29731e6 | 1.63476 | 0.817380 | − | 0.576099i | \(-0.195426\pi\) | ||||
0.817380 | + | 0.576099i | \(0.195426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −291513. | −0.359441 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 626232.i | − 0.755693i | −0.925868 | − | 0.377846i | \(-0.876665\pi\) | ||||
0.925868 | − | 0.377846i | \(-0.123335\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 127239.i | − 0.147146i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 270281. | 0.306070 | 0.153035 | − | 0.988221i | \(-0.451095\pi\) | ||||
0.153035 | + | 0.988221i | \(0.451095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −694339. | −0.770068 | −0.385034 | − | 0.922902i | \(-0.625810\pi\) | ||||
−0.385034 | + | 0.922902i | \(0.625810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 938421.i | − 1.01949i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 547134.i | 0.570626i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 898431. | 0.918304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −864085. | −0.865710 | −0.432855 | − | 0.901464i | \(-0.642494\pi\) | ||||
−0.432855 | + | 0.901464i | \(0.642494\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.06390e6i | − 1.04496i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.00660e6i | 0.950660i | 0.879808 | + | 0.475330i | \(0.157671\pi\) | ||||
−0.879808 | + | 0.475330i | \(0.842329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −482395. | −0.446841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5862.46 | −0.00532695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 931373.i | − 0.830299i | −0.909753 | − | 0.415149i | \(-0.863729\pi\) | ||||
0.909753 | − | 0.415149i | \(-0.136271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.21577e6i | − 1.90216i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.96236e6 | 1.65348 | 0.826738 | − | 0.562587i | \(-0.190194\pi\) | ||||
0.826738 | + | 0.562587i | \(0.190194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12152e6 | −0.927649 | −0.463825 | − | 0.885927i | \(-0.653523\pi\) | ||||
−0.463825 | + | 0.885927i | \(0.653523\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 754948.i | − 0.613070i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 105917.i | 0.0829401i | 0.999140 | + | 0.0414701i | \(0.0132041\pi\) | ||||
−0.999140 | + | 0.0414701i | \(0.986796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.10549e6 | −0.850242 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.05276e6 | −0.795362 | −0.397681 | − | 0.917524i | \(-0.630185\pi\) | ||||
−0.397681 | + | 0.917524i | \(0.630185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 950210.i | − 0.705267i | −0.935762 | − | 0.352633i | \(-0.885286\pi\) | ||||
0.935762 | − | 0.352633i | \(-0.114714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 415801.i | 0.297975i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.40789e6 | 0.991573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.09725e6 | 1.45183 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 381801.i | 0.259817i | 0.991526 | + | 0.129909i | \(0.0414684\pi\) | ||||
−0.991526 | + | 0.129909i | \(0.958532\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 871723.i | 0.573440i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.75524e6 | 1.78230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −589373. | −0.374951 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3.85708e6i | − 2.41353i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.61048e6i | 0.975238i | 0.873057 | + | 0.487619i | \(0.162134\pi\) | ||||
−0.873057 | + | 0.487619i | \(0.837866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.58197e6 | −0.942543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.15652e6 | 1.26431 | 0.632153 | − | 0.774843i | \(-0.282171\pi\) | ||||
0.632153 | + | 0.774843i | \(0.282171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 364108.i | 0.210073i | 0.994468 | + | 0.105036i | \(0.0334959\pi\) | ||||
−0.994468 | + | 0.105036i | \(0.966504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.03846e6i | − 0.580420i | −0.956963 | − | 0.290210i | \(-0.906275\pi\) | ||||
0.956963 | − | 0.290210i | \(-0.0937252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18072.2 | 0.00994336 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.68345e6 | 1.45355 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 54247.8i | − 0.0289318i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.34118e6i | 0.693612i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 456890. | 0.232714 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.82942e6 | 1.41948 | 0.709738 | − | 0.704466i | \(-0.248814\pi\) | ||||
0.709738 | + | 0.704466i | \(0.248814\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.90205e6i | − 0.939966i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 804843.i | 0.386043i | 0.981194 | + | 0.193022i | \(0.0618288\pi\) | ||||
−0.981194 | + | 0.193022i | \(0.938171\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.72621e6 | 1.28843 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.40787e6 | 1.58708 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.13506e6i | 0.520936i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 759889.i | − 0.338787i | −0.985549 | − | 0.169393i | \(-0.945819\pi\) | ||||
0.985549 | − | 0.169393i | \(-0.0541809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −580673. | −0.255193 | −0.127596 | − | 0.991826i | \(-0.540726\pi\) | ||||
−0.127596 | + | 0.991826i | \(0.540726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.25755e6 | −0.978071 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.64210e6i | 0.701393i | 0.936489 | + | 0.350697i | \(0.114055\pi\) | ||||
−0.936489 | + | 0.350697i | \(0.885945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 74852.3i | 0.0310838i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.88181e6 | −1.18013 | −0.590065 | − | 0.807356i | \(-0.700898\pi\) | ||||
−0.590065 | + | 0.807356i | \(0.700898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.23016e6 | −0.900673 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 398909.i | 0.158894i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.83418e6i | 1.48596i | 0.669314 | + | 0.742980i | \(0.266588\pi\) | ||||
−0.669314 | + | 0.742980i | \(0.733412\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.63947e6 | −0.626814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −624467. | −0.235545 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.19341e6i | − 1.18845i | −0.804298 | − | 0.594227i | \(-0.797458\pi\) | ||||
0.804298 | − | 0.594227i | \(-0.202542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 46802.5i | 0.0169596i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.47338e6 | 1.24209 | 0.621046 | − | 0.783774i | \(-0.286708\pi\) | ||||
0.621046 | + | 0.783774i | \(0.286708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27356e6 | 0.449478 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.56341e6i | 0.544599i | 0.962213 | + | 0.272299i | \(0.0877841\pi\) | ||||
−0.962213 | + | 0.272299i | \(0.912216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.32386e6i | − 0.788738i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.98980e6 | −1.67190 | −0.835949 | − | 0.548808i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548808i | \(0.815082\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −273179. | −0.0903661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 2.31444e6i | − 0.755899i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.37245e6i | − 0.437038i | −0.975833 | − | 0.218519i | \(-0.929877\pi\) | ||||
0.975833 | − | 0.218519i | \(-0.0701226\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −339357. | −0.106715 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.44247e6 | 1.69019 | 0.845094 | − | 0.534617i | \(-0.179544\pi\) | ||||
0.845094 | + | 0.534617i | \(0.179544\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.82557e6i | 2.70695i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.86344e6i | 1.75455i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.03830e6 | 1.78487 | 0.892435 | − | 0.451176i | \(-0.148995\pi\) | ||||
0.892435 | + | 0.451176i | \(0.148995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.65483e6 | 0.483223 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.65940e6i | − 0.478714i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.28657e6i | 0.925557i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 770366. | 0.214369 | 0.107184 | − | 0.994239i | \(-0.465816\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00249e6 | 0.550636 | 0.275318 | − | 0.961353i | \(-0.411217\pi\) | ||||
0.275318 | + | 0.961353i | \(0.411217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.80149e6i | 0.489532i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 798504.i | − 0.211937i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.17628e6 | −2.40726 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.56690e6 | −1.44351 | −0.721756 | − | 0.692148i | \(-0.756665\pi\) | ||||
−0.721756 | + | 0.692148i | \(0.756665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.22941e6i | 0.571441i | 0.958313 | + | 0.285720i | \(0.0922328\pi\) | ||||
−0.958313 | + | 0.285720i | \(0.907767\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.23851e6i | − 0.310239i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 543061. | 0.134489 | 0.0672446 | − | 0.997737i | \(-0.478579\pi\) | ||||
0.0672446 | + | 0.997737i | \(0.478579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.15286e6 | −0.527132 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.53358e6i | − 1.09757i | −0.835964 | − | 0.548785i | \(-0.815091\pi\) | ||||
0.835964 | − | 0.548785i | \(-0.184909\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.32039e6i | − 0.312561i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.39468e6 | 0.794662 | 0.397331 | − | 0.917675i | \(-0.369936\pi\) | ||||
0.397331 | + | 0.917675i | \(0.369936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.05400e6 | 1.17002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28122e6i | 0.293345i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 8.34100e6i | − 1.86822i | −0.356988 | − | 0.934109i | \(-0.616196\pi\) | ||||
0.356988 | − | 0.934109i | \(-0.383804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 223834. | 0.0495900 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.18453e6 | −0.697900 | −0.348950 | − | 0.937141i | \(-0.613462\pi\) | ||||
−0.348950 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.05943e6i | − 0.880061i | −0.897983 | − | 0.440030i | \(-0.854968\pi\) | ||||
0.897983 | − | 0.440030i | \(-0.145032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.98706e6i | − 1.69471i | −0.531029 | − | 0.847353i | \(-0.678195\pi\) | ||||
0.531029 | − | 0.847353i | \(-0.321805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.38155e6 | 0.290024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.81596e6 | −1.20801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.16375e6i | 1.47227i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.46223e6i | − 0.495488i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.27553e6 | 1.05058 | 0.525288 | − | 0.850924i | \(-0.323958\pi\) | ||||
0.525288 | + | 0.850924i | \(0.323958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.51849e7 | −2.99260 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.70892e6i | 0.333315i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76969e6i | 1.67557i | 0.546002 | + | 0.837784i | \(0.316149\pi\) | ||||
−0.546002 | + | 0.837784i | \(0.683851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.25209e6 | −1.74972 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.83080e6 | −1.46589 | −0.732946 | − | 0.680286i | \(-0.761855\pi\) | ||||
−0.732946 | + | 0.680286i | \(0.761855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4640.42i | 0 0.000859885i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 56649.2i | 0.0102873i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.54560e6 | −1.17679 | −0.588394 | − | 0.808574i | \(-0.700240\pi\) | ||||
−0.588394 | + | 0.808574i | \(0.700240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.22610e6 | −0.930216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.07773e6i | 0.366158i | 0.983098 | + | 0.183079i | \(0.0586064\pi\) | ||||
−0.983098 | + | 0.183079i | \(0.941394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1.65152e7i | − 2.85340i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.25093e6 | 1.06942 | 0.534712 | − | 0.845034i | \(-0.320420\pi\) | ||||
0.534712 | + | 0.845034i | \(0.320420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.86784e6 | −0.316437 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.01480e6i | 0.170249i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.55344e6i | − 0.913767i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.37310e7 | −2.23761 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.19897e6 | 0.354916 | 0.177458 | − | 0.984128i | \(-0.443213\pi\) | ||||
0.177458 | + | 0.984128i | \(0.443213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.10298e6i | 0.336187i | 0.985771 | + | 0.168093i | \(0.0537610\pi\) | ||||
−0.985771 | + | 0.168093i | \(0.946239\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 875046.i | − 0.137247i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 199490. | 0.0309944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.54291e6 | 1.00701 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.30886e7i | 1.99561i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.24041e7i | 1.85623i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.63661e6 | 0.983953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.83729e6 | −0.269889 | −0.134944 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134944 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.06974e7i | − 1.55697i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.31872e6i | 0.617145i | 0.951201 | + | 0.308572i | \(0.0998512\pi\) | ||||
−0.951201 | + | 0.308572i | \(0.900149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.14845e6 | 0.445827 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21038.3 | 0.00295210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 228409.i | − 0.0317615i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.26837e6i | 0.582940i | 0.956580 | + | 0.291470i | \(0.0941444\pi\) | ||||
−0.956580 | + | 0.291470i | \(0.905856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.85524e7 | −2.51114 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 909819. | 0.122053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.26350e7i | 1.67998i | 0.542605 | + | 0.839988i | \(0.317438\pi\) | ||||
−0.542605 | + | 0.839988i | \(0.682562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2.57720e6i | − 0.336659i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.67409e6 | 1.12316 | 0.561582 | − | 0.827421i | \(-0.310193\pi\) | ||||
0.561582 | + | 0.827421i | \(0.310193\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.28781e6 | −0.422004 | −0.211002 | − | 0.977486i | \(-0.567673\pi\) | ||||
−0.211002 | + | 0.977486i | \(0.567673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.57380e6i | 0.200246i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 117668.i | 0.0147135i | 0.999973 | + | 0.00735677i | \(0.00234175\pi\) | ||||
−0.999973 | + | 0.00735677i | \(0.997658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 518352. | 0.0642582 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.61280e6 | 0.198216 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.59031e6i | 0.924885i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.10151e7i | − 1.31945i | −0.751509 | − | 0.659723i | \(-0.770674\pi\) | ||||
0.751509 | − | 0.659723i | \(-0.229326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.96719e6 | 0.471189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.37387e7 | −1.61799 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 5.33879e6i | − 0.623456i | −0.950171 | − | 0.311728i | \(-0.899092\pi\) | ||||
0.950171 | − | 0.311728i | \(-0.100908\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.43697e6i | 0.165011i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.17784e6 | −0.817385 | −0.408692 | − | 0.912672i | \(-0.634015\pi\) | ||||
−0.408692 | + | 0.912672i | \(0.634015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −809127. | −0.0913756 | −0.0456878 | − | 0.998956i | \(-0.514548\pi\) | ||||
−0.0456878 | + | 0.998956i | \(0.514548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.44735e6i | 0.610087i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 591991.i | 0.0652143i | 0.999468 | + | 0.0326072i | \(0.0103810\pi\) | ||||
−0.999468 | + | 0.0326072i | \(0.989619\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29029.1 | −0.00317168 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.43821e7 | 1.55854 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 4.01173e6i | − 0.431201i | −0.976482 | − | 0.215601i | \(-0.930829\pi\) | ||||
0.976482 | − | 0.215601i | \(-0.0691710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.24093e6i | − 0.871491i | −0.900070 | − | 0.435746i | \(-0.856485\pi\) | ||||
0.900070 | − | 0.435746i | \(-0.143515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.96985e6 | 0.206636 | 0.103318 | − | 0.994648i | \(-0.467054\pi\) | ||||
0.103318 | + | 0.994648i | \(0.467054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.11027e6 | 0.531759 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 3.97758e6i | − 0.410581i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.12484e6i | 0.419024i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.50557e6 | 0.151731 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.82360e7 | 1.82329 | 0.911646 | − | 0.410977i | \(-0.134813\pi\) | ||||
0.911646 | + | 0.410977i | \(0.134813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.96819e7i | 1.95235i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.71872e7i | 1.67825i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −223364. | −0.0216402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.65378e6 | 0.735752 | 0.367876 | − | 0.929875i | \(-0.380085\pi\) | ||||
0.367876 | + | 0.929875i | \(0.380085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.47762e6i | − 0.236323i | −0.992994 | − | 0.118162i | \(-0.962300\pi\) | ||||
0.992994 | − | 0.118162i | \(-0.0377001\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.79533e6i | 0.450358i | 0.974317 | + | 0.225179i | \(0.0722967\pi\) | ||||
−0.974317 | + | 0.225179i | \(0.927703\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.01698e7 | −1.87970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.47402e6 | −0.506237 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.67125e7i | 1.53376i | 0.641789 | + | 0.766881i | \(0.278193\pi\) | ||||
−0.641789 | + | 0.766881i | \(0.721807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 7.36478e6i | − 0.665650i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.28380e6 | 0.294553 | 0.147277 | − | 0.989095i | \(-0.452949\pi\) | ||||
0.147277 | + | 0.989095i | \(0.452949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.98880e7 | −1.77047 | −0.885234 | − | 0.465145i | \(-0.846002\pi\) | ||||
−0.885234 | + | 0.465145i | \(0.846002\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.35621e6i | 0.208176i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 105944.i | − 0.00922063i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.75423e6 | 0.237922 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.70571e6 | −0.832187 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1.39915e7i | − 1.19076i | −0.803443 | − | 0.595381i | \(-0.797001\pi\) | ||||
0.803443 | − | 0.595381i | \(-0.202999\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.13032e6i | − 0.262493i | −0.991350 | − | 0.131246i | \(-0.958102\pi\) | ||||
0.991350 | − | 0.131246i | \(-0.0418979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.76482e6 | 0.313379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.23162e7 | 1.84397 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8.94034e6i | − 0.733335i | −0.930352 | − | 0.366667i | \(-0.880499\pi\) | ||||
0.930352 | − | 0.366667i | \(-0.119501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.53288e7i | 2.04750i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.96571e7 | −1.57750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.38378e7 | 1.89920 | 0.949599 | − | 0.313466i | \(-0.101490\pi\) | ||||
0.949599 | + | 0.313466i | \(0.101490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.06335e6i | − 0.163207i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.29772e6i | − 0.101181i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.22267e7 | 0.946487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.57226e7 | 1.20845 | 0.604225 | − | 0.796814i | \(-0.293483\pi\) | ||||
0.604225 | + | 0.796814i | \(0.293483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.82578e6i | 0.520912i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6.92394e6i | − 0.520961i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.05866e6 | 0.228515 | 0.114258 | − | 0.993451i | \(-0.463551\pi\) | ||||
0.114258 | + | 0.993451i | \(0.463551\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 900603. | 0.0668128 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.99778e7i | − 1.47172i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.27701e6i | 0.383345i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.16146e7 | 1.55929 | 0.779643 | − | 0.626224i | \(-0.215400\pi\) | ||||
0.779643 | + | 0.626224i | \(0.215400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.83983e6 | −0.203448 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.35564e7i | − 0.964492i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.73589e7i | 1.91983i | 0.280287 | + | 0.959916i | \(0.409570\pi\) | ||||
−0.280287 | + | 0.959916i | \(0.590430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 453482. | 0.0316039 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.83945e6 | 0.127319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.54693e7i | − 1.06344i | −0.846921 | − | 0.531718i | \(-0.821547\pi\) | ||||
0.846921 | − | 0.531718i | \(-0.178453\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.67925e7i | − 1.13880i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56327e6 | 0.374731 | 0.187365 | − | 0.982290i | \(-0.440005\pi\) | ||||
0.187365 | + | 0.982290i | \(0.440005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.06823e7 | −0.714695 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.55089e7i | − 1.03064i | −0.856997 | − | 0.515322i | \(-0.827672\pi\) | ||||
0.856997 | − | 0.515322i | \(-0.172328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.35916e6i | 0.416963i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.81713e6 | 0.313750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.20221e7 | −1.42482 | −0.712409 | − | 0.701765i | \(-0.752396\pi\) | ||||
−0.712409 | + | 0.701765i | \(0.752396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 1.68706e7i | − 1.08428i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.75653e6i | − 0.111408i | −0.998447 | − | 0.0557040i | \(-0.982260\pi\) | ||||
0.998447 | − | 0.0557040i | \(-0.0177403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.07717e7 | 1.30879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.16974e6 | −0.135814 | −0.0679072 | − | 0.997692i | \(-0.521632\pi\) | ||||
−0.0679072 | + | 0.997692i | \(0.521632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.40758e6i | 0.149716i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 5.22349e7i | − 3.20606i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.12131e7 | 0.683769 | 0.341884 | − | 0.939742i | \(-0.388935\pi\) | ||||
0.341884 | + | 0.939742i | \(0.388935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.96531e7 | −1.19068 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.43367e7i | − 0.862980i | −0.902118 | − | 0.431490i | \(-0.857988\pi\) | ||||
0.902118 | − | 0.431490i | \(-0.142012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 9.41836e6i | − 0.559658i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.88348e6 | 0.347369 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 688563. | 0.0403939 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 86806.8i | 0.00505999i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.00549e6i | − 0.115421i | −0.998333 | − | 0.0577103i | \(-0.981620\pi\) | ||||
0.998333 | − | 0.0577103i | \(-0.0183800\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.81843e7 | 1.03993 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.89389e6 | 0.278108 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 2.51354e7i | − 1.41940i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 448115.i | 0.0249887i | 0.999922 | + | 0.0124944i | \(0.00397718\pi\) | ||||
−0.999922 | + | 0.0124944i | \(0.996023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.42597e6 | −0.0790210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.56834e7 | 0.863690 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.27033e7i | 1.24251i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.83134e7i | 2.07094i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.28425e7 | −0.689889 | −0.344944 | − | 0.938623i | \(-0.612102\pi\) | ||||
−0.344944 | + | 0.938623i | \(0.612102\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.78700e7 | −0.954054 | −0.477027 | − | 0.878889i | \(-0.658286\pi\) | ||||
−0.477027 | + | 0.878889i | \(0.658286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.18968e7i | − 1.16186i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.33950e6i | 0.437104i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.34357e6 | 0.278370 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.73336e7 | 1.41527 | 0.707634 | − | 0.706580i | \(-0.249763\pi\) | ||||
0.707634 | + | 0.706580i | \(0.249763\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.05819e6i | 0.157385i | 0.996899 | + | 0.0786927i | \(0.0250746\pi\) | ||||
−0.996899 | + | 0.0786927i | \(0.974925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.23961e7i | − 0.630261i | −0.949048 | − | 0.315131i | \(-0.897952\pi\) | ||||
0.949048 | − | 0.315131i | \(-0.102048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 399873. | 0.0202086 | 0.0101043 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101043 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.06793e6 | −0.103881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.70409e6i | − 0.0850905i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.63692e7i | 0.807632i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.08411e6 | −0.102215 | −0.0511075 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511075 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05093e7 | −0.999912 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.05543e7i | − 0.996172i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 716092.i | 0.0342973i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.85521e7 | 0.883330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.43730e7 | 1.62702 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.14298e7i | 1.00843i | 0.863579 | + | 0.504214i | \(0.168218\pi\) | ||||
−0.863579 | + | 0.504214i | \(0.831782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.49123e6i | − 0.162377i | −0.996699 | − | 0.0811887i | \(-0.974128\pi\) | ||||
0.996699 | − | 0.0811887i | \(-0.0258717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −568043. | −0.0262662 | −0.0131331 | − | 0.999914i | \(-0.504181\pi\) | ||||
−0.0131331 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.11816e6 | −0.373207 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.28678e7i | − 1.50226i | −0.660157 | − | 0.751128i | \(-0.729510\pi\) | ||||
0.660157 | − | 0.751128i | \(-0.270490\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.74879e7i | 1.24192i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.77628e6 | −0.124714 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.34885e7 | 1.94236 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.48444e7i | 0.659217i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.92945e7i | − 1.28614i | −0.765808 | − | 0.643069i | \(-0.777661\pi\) | ||||
0.765808 | − | 0.643069i | \(-0.222339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.45435e6 | −0.325415 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.88332e6 | 0.125156 | 0.0625782 | − | 0.998040i | \(-0.480068\pi\) | ||||
0.0625782 | + | 0.998040i | \(0.480068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.79477e7i | − 1.20627i | −0.797639 | − | 0.603135i | \(-0.793918\pi\) | ||||
0.797639 | − | 0.603135i | \(-0.206082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.89567e7i | − 1.23578i | −0.786266 | − | 0.617888i | \(-0.787989\pi\) | ||||
0.786266 | − | 0.617888i | \(-0.212011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.28621e6 | 0.0970199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.13254e7 | −1.32191 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.46490e6i | − 0.271289i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37938e7i | 2.23229i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 339358. | 0.0140042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.94898e6 | 0.0799825 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.15070e7i | − 0.469617i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.18508e6i | − 0.0478333i | −0.999714 | − | 0.0239166i | \(-0.992386\pi\) | ||||
0.999714 | − | 0.0239166i | \(-0.00761363\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.73007e7 | 1.09588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.14346e7 | 0.456485 | 0.228242 | − | 0.973604i | \(-0.426702\pi\) | ||||
0.228242 | + | 0.973604i | \(0.426702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.96033e7i | − 0.778310i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 4.15471e6i | − 0.163161i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.48904e7 | −0.581589 | −0.290795 | − | 0.956785i | \(-0.593920\pi\) | ||||
−0.290795 | + | 0.956785i | \(0.593920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.14434e7 | −1.22146 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.78321e6i | 0.0688968i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.11973e7i | − 0.427969i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.02580e7 | 0.770117 | 0.385058 | − | 0.922892i | \(-0.374181\pi\) | ||||
0.385058 | + | 0.922892i | \(0.374181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.72584e6 | 0.292127 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.21043e7i | 1.58351i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.96237e7i | 0.730182i | 0.930972 | + | 0.365091i | \(0.118962\pi\) | ||||
−0.930972 | + | 0.365091i | \(0.881038\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.10891e6 | −0.263111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.62854e6 | 0.280846 | 0.140423 | − | 0.990092i | \(-0.455154\pi\) | ||||
0.140423 | + | 0.990092i | \(0.455154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.96279e7i | − 1.08498i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.93605e7i | 1.42622i | 0.701054 | + | 0.713108i | \(0.252713\pi\) | ||||
−0.701054 | + | 0.713108i | \(0.747287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.87962e7 | −2.11926 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.02751e7 | 0.726963 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.09953e7i | 1.81886i | 0.415861 | + | 0.909428i | \(0.363480\pi\) | ||||
−0.415861 | + | 0.909428i | \(0.636520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 352844.i | 0.0124538i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.97062e6 | 0.104304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.53638e7 | 1.23524 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.89936e7i | 0.659997i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 5.17740e7i | − 1.78051i | −0.455458 | − | 0.890257i | \(-0.650524\pi\) | ||||
0.455458 | − | 0.890257i | \(-0.349476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.05914e6 | 0.0362364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.69158e7 | 1.25651 | 0.628253 | − | 0.778009i | \(-0.283770\pi\) | ||||
0.628253 | + | 0.778009i | \(0.283770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.89981e6i | 0.199782i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.14468e7i | − 1.05400i | −0.849866 | − | 0.526999i | \(-0.823317\pi\) | ||||
0.849866 | − | 0.526999i | \(-0.176683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.83470e7 | −1.61218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.49293e6 | −0.314940 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.15823e7i | 1.70262i | 0.524667 | + | 0.851308i | \(0.324190\pi\) | ||||
−0.524667 | + | 0.851308i | \(0.675810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.92041e6i | 0.291469i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.19958e7 | 1.36526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.30562e7 | 0.422312 | 0.211156 | − | 0.977452i | \(-0.432277\pi\) | ||||
0.211156 | + | 0.977452i | \(0.432277\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.52421e7i | 1.77786i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.97672e7i | 1.58564i | 0.609454 | + | 0.792821i | \(0.291389\pi\) | ||||
−0.609454 | + | 0.792821i | \(0.708611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.81641e7 | −0.892859 |
(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 | 400.6.c.o.49.4 | 4 | ||
4.3 | odd | 2 | 200.6.c.f.49.1 | 4 | |||
5.2 | odd | 4 | 400.6.a.u.1.2 | 2 | |||
5.3 | odd | 4 | 400.6.a.r.1.1 | 2 | |||
5.4 | even | 2 | inner | 400.6.c.o.49.1 | 4 | ||
20.3 | even | 4 | 200.6.a.f.1.2 | yes | 2 | ||
20.7 | even | 4 | 200.6.a.e.1.1 | ✓ | 2 | ||
20.19 | odd | 2 | 200.6.c.f.49.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.e.1.1 | ✓ | 2 | 20.7 | even | 4 | ||
200.6.a.f.1.2 | yes | 2 | 20.3 | even | 4 | ||
200.6.c.f.49.1 | 4 | 4.3 | odd | 2 | |||
200.6.c.f.49.4 | 4 | 20.19 | odd | 2 | |||
400.6.a.r.1.1 | 2 | 5.3 | odd | 4 | |||
400.6.a.u.1.2 | 2 | 5.2 | odd | 4 | |||
400.6.c.o.49.1 | 4 | 5.4 | even | 2 | inner | ||
400.6.c.o.49.4 | 4 | 1.1 | even | 1 | trivial |