Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(97,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.c (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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4694952902656.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 20x^{6} + 56x^{4} + 20x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(-0.244539i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.97 |
Dual form | 224.3.c.a.97.7 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 5.43734i | − | 1.81245i | −0.422800 | − | 0.906223i | \(-0.638953\pi\) | ||
0.422800 | − | 0.906223i | \(-0.361047\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.12900i | 1.22580i | 0.790160 | + | 0.612900i | \(0.209997\pi\) | ||||
−0.790160 | + | 0.612900i | \(0.790003\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.21005 | − | 3.23038i | −0.887149 | − | 0.461483i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.5647 | −2.28496 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.2485 | −1.38623 | −0.693114 | − | 0.720828i | \(-0.743762\pi\) | ||||
−0.693114 | + | 0.720828i | \(0.743762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00789i | 0.231376i | 0.993286 | + | 0.115688i | \(0.0369073\pi\) | ||||
−0.993286 | + | 0.115688i | \(0.963093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 33.3255 | 2.22170 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 21.6213i | − | 1.27184i | −0.771753 | − | 0.635922i | \(-0.780620\pi\) | ||
0.771753 | − | 0.635922i | \(-0.219380\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.8981i | 0.626216i | 0.949718 | + | 0.313108i | \(0.101370\pi\) | ||||
−0.949718 | + | 0.313108i | \(0.898630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −17.5647 | + | 33.7661i | −0.836412 | + | 1.60791i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.72205 | −0.0748715 | −0.0374358 | − | 0.999299i | \(-0.511919\pi\) | ||||
−0.0374358 | + | 0.999299i | \(0.511919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5647 | −0.502586 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 62.8810i | 2.32893i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −41.1293 | −1.41825 | −0.709126 | − | 0.705082i | \(-0.750910\pi\) | ||||
−0.709126 | + | 0.705082i | \(0.750910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.50759i | − | 0.274438i | −0.990541 | − | 0.137219i | \(-0.956184\pi\) | ||
0.990541 | − | 0.137219i | \(-0.0438165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 82.9114i | 2.51247i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.7990 | − | 38.0614i | 0.565685 | − | 1.08747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.1293 | 1.43593 | 0.717964 | − | 0.696080i | \(-0.245074\pi\) | ||||
0.717964 | + | 0.696080i | \(0.245074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.3549 | 0.419356 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 43.0162i | − | 1.04918i | −0.851356 | − | 0.524588i | \(-0.824219\pi\) | ||
0.851356 | − | 0.524588i | \(-0.175781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −36.6446 | −0.852200 | −0.426100 | − | 0.904676i | \(-0.640113\pi\) | ||||
−0.426100 | + | 0.904676i | \(0.640113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 126.041i | − | 2.80091i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 30.2569i | − | 0.643765i | −0.946780 | − | 0.321882i | \(-0.895684\pi\) | ||
0.946780 | − | 0.321882i | \(-0.104316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.1293 | + | 40.1216i | 0.574068 | + | 0.818808i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −117.563 | −2.30515 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −30.0000 | −0.566038 | −0.283019 | − | 0.959114i | \(-0.591336\pi\) | ||||
−0.283019 | + | 0.959114i | \(0.591336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 93.4582i | − | 1.69924i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 64.6940 | 1.13498 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 73.0525i | − | 1.23818i | −0.785321 | − | 0.619089i | \(-0.787502\pi\) | ||
0.785321 | − | 0.619089i | \(-0.212498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.67609i | − | 0.0930506i | −0.998917 | − | 0.0465253i | \(-0.985185\pi\) | ||
0.998917 | − | 0.0465253i | \(-0.0148148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 127.707 | + | 66.4316i | 2.02710 | + | 1.05447i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.4353 | −0.283621 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 28.7750 | 0.429477 | 0.214739 | − | 0.976672i | \(-0.431110\pi\) | ||||
0.214739 | + | 0.976672i | \(0.431110\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.36335i | 0.135701i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.53191 | −0.0779142 | −0.0389571 | − | 0.999241i | \(-0.512404\pi\) | ||||
−0.0389571 | + | 0.999241i | \(0.512404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 94.9429i | − | 1.30059i | −0.759683 | − | 0.650294i | \(-0.774646\pi\) | ||
0.759683 | − | 0.650294i | \(-0.225354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 68.3183i | 0.910911i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 94.6940 | + | 49.2585i | 1.22979 | + | 0.639720i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −81.5337 | −1.03207 | −0.516036 | − | 0.856567i | \(-0.672593\pi\) | ||||
−0.516036 | + | 0.856567i | \(0.672593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 156.823 | 1.93609 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 86.2943i | 1.03969i | 0.854261 | + | 0.519845i | \(0.174010\pi\) | ||||
−0.854261 | + | 0.519845i | \(0.825990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 132.517 | 1.55903 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 223.634i | 2.57051i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 27.6371i | 0.310529i | 0.987873 | + | 0.155265i | \(0.0496231\pi\) | ||||
−0.987873 | + | 0.155265i | \(0.950377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.71661 | − | 18.6791i | 0.106776 | − | 0.205265i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −46.2586 | −0.497405 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −72.9234 | −0.767615 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 100.959i | − | 1.04081i | −0.853919 | − | 0.520406i | \(-0.825781\pi\) | ||
0.853919 | − | 0.520406i | \(-0.174219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 313.581 | 3.16748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.541i | 1.06476i | 0.846506 | + | 0.532379i | \(0.178702\pi\) | ||||
−0.846506 | + | 0.532379i | \(0.821298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 59.1076i | − | 0.573860i | −0.957952 | − | 0.286930i | \(-0.907365\pi\) | ||
0.957952 | − | 0.286930i | \(-0.0926347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −206.953 | − | 107.654i | −1.97098 | − | 1.02527i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −45.9954 | −0.429864 | −0.214932 | − | 0.976629i | \(-0.568953\pi\) | ||||
−0.214932 | + | 0.976629i | \(0.568953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −23.7414 | −0.217811 | −0.108905 | − | 0.994052i | \(-0.534735\pi\) | ||||
−0.108905 | + | 0.994052i | \(0.534735\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 288.882i | − | 2.60254i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −187.211 | −1.65674 | −0.828368 | − | 0.560184i | \(-0.810731\pi\) | ||||
−0.828368 | + | 0.560184i | \(0.810731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 10.5544i | − | 0.0917776i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 61.8562i | − | 0.528685i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −69.8451 | + | 134.270i | −0.586934 | + | 1.12832i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 111.517 | 0.921630 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −233.894 | −1.90158 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 76.2162i | 0.609730i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 206.350 | 1.62480 | 0.812402 | − | 0.583097i | \(-0.198159\pi\) | ||||
0.812402 | + | 0.583097i | \(0.198159\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 199.249i | 1.54457i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 186.979i | − | 1.42732i | −0.700492 | − | 0.713660i | \(-0.747036\pi\) | ||
0.700492 | − | 0.713660i | \(-0.252964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 38.4353 | − | 73.8877i | 0.288988 | − | 0.555547i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −385.398 | −2.85480 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.51728 | −0.0183743 | −0.00918715 | − | 0.999958i | \(-0.502924\pi\) | ||||
−0.00918715 | + | 0.999958i | \(0.502924\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6791i | 0.134382i | 0.997740 | + | 0.0671910i | \(0.0214037\pi\) | ||||
−0.997740 | + | 0.0671910i | \(0.978596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −164.517 | −1.16679 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 45.8658i | − | 0.320740i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 252.082i | − | 1.73849i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 218.155 | − | 152.949i | 1.48405 | − | 1.04047i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.51728 | −0.0168945 | −0.00844725 | − | 0.999964i | \(-0.502689\pi\) | ||||
−0.00844725 | + | 0.999964i | \(0.502689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −78.4553 | −0.519572 | −0.259786 | − | 0.965666i | \(-0.583652\pi\) | ||||
−0.259786 | + | 0.965666i | \(0.583652\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 444.636i | 2.90612i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 52.1430 | 0.336407 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 298.559i | 1.90165i | 0.309732 | + | 0.950824i | \(0.399761\pi\) | ||||
−0.309732 | + | 0.950824i | \(0.600239\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 163.120i | 1.02591i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.6940 | + | 5.56286i | 0.0664222 | + | 0.0345519i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.86012 | −0.0543566 | −0.0271783 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271783 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −508.164 | −3.07978 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 252.930i | 1.51455i | 0.653095 | + | 0.757276i | \(0.273470\pi\) | ||||
−0.653095 | + | 0.757276i | \(0.726530\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 159.953 | 0.946465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 244.680i | − | 1.43088i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.89137i | 0.0456149i | 0.999740 | + | 0.0228074i | \(0.00726046\pi\) | ||||
−0.999740 | + | 0.0228074i | \(0.992740\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 78.0271 | + | 40.5886i | 0.445869 | + | 0.231935i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −397.211 | −2.24413 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 298.573 | 1.66800 | 0.834002 | − | 0.551761i | \(-0.186044\pi\) | ||||
0.834002 | + | 0.551761i | \(0.186044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 281.821i | − | 1.55702i | −0.627631 | − | 0.778511i | \(-0.715975\pi\) | ||
0.627631 | − | 0.778511i | \(-0.284025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.8628 | −0.168649 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 325.630i | 1.76016i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 329.694i | 1.76307i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 203.129 | − | 390.494i | 1.07476 | − | 2.06610i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.5396 | −0.107537 | −0.0537686 | − | 0.998553i | \(-0.517123\pi\) | ||||
−0.0537686 | + | 0.998553i | \(0.517123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 191.565 | 0.992563 | 0.496282 | − | 0.868162i | \(-0.334698\pi\) | ||||
0.496282 | + | 0.868162i | \(0.334698\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 100.239i | 0.514047i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −113.129 | −0.574261 | −0.287130 | − | 0.957892i | \(-0.592701\pi\) | ||||
−0.287130 | + | 0.957892i | \(0.592701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 132.543i | 0.666045i | 0.942919 | + | 0.333023i | \(0.108069\pi\) | ||||
−0.942919 | + | 0.333023i | \(0.891931\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 156.459i | − | 0.778405i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 255.415 | + | 132.863i | 1.25820 | + | 0.654499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 263.647 | 1.28608 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.4133 | 0.171079 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 181.428i | − | 0.868078i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −235.366 | −1.11548 | −0.557739 | − | 0.830016i | \(-0.688331\pi\) | ||||
−0.557739 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.0789i | 0.141215i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 224.595i | − | 1.04463i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.4827 | + | 52.8325i | −0.126648 | + | 0.243468i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −516.237 | −2.35725 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 65.0346 | 0.294274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 209.306i | 0.938593i | 0.883041 | + | 0.469297i | \(0.155492\pi\) | ||||
−0.883041 | + | 0.469297i | \(0.844508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 258.388 | 1.14839 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 217.751i | 0.959256i | 0.877472 | + | 0.479628i | \(0.159228\pi\) | ||||
−0.877472 | + | 0.479628i | \(0.840772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 51.1341i | − | 0.223293i | −0.993748 | − | 0.111646i | \(-0.964388\pi\) | ||
0.993748 | − | 0.111646i | \(-0.0356124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 267.835 | − | 514.883i | 1.15946 | − | 2.22893i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −242.517 | −1.04085 | −0.520423 | − | 0.853908i | \(-0.674226\pi\) | ||||
−0.520423 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 185.445 | 0.789127 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 443.326i | 1.87057i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4613 | −0.0730598 | −0.0365299 | − | 0.999333i | \(-0.511630\pi\) | ||||
−0.0365299 | + | 0.999333i | \(0.511630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 68.8417i | − | 0.285650i | −0.989748 | − | 0.142825i | \(-0.954381\pi\) | ||
0.989748 | − | 0.142825i | \(-0.0456186\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 286.773i | − | 1.18013i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −245.905 | + | 172.405i | −1.00369 | + | 0.703692i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.7881 | −0.144891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 469.211 | 1.88438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 122.246i | − | 0.487037i | −0.969896 | − | 0.243518i | \(-0.921698\pi\) | ||
0.969896 | − | 0.243518i | \(-0.0783016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.2586 | 0.103789 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 720.541i | − | 2.82565i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 312.466i | − | 1.21582i | −0.794006 | − | 0.607910i | \(-0.792008\pi\) | ||
0.794006 | − | 0.607910i | \(-0.207992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −329.935 | − | 171.628i | −1.27388 | − | 0.662655i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 845.810 | 3.24065 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −373.959 | −1.42190 | −0.710949 | − | 0.703244i | \(-0.751734\pi\) | ||||
−0.710949 | + | 0.703244i | \(0.751734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 183.870i | − | 0.693849i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 150.272 | 0.562818 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 180.636i | − | 0.671508i | −0.941950 | − | 0.335754i | \(-0.891009\pi\) | ||
0.941950 | − | 0.335754i | \(-0.108991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 275.195i | 1.01548i | 0.861511 | + | 0.507740i | \(0.169519\pi\) | ||||
−0.861511 | + | 0.507740i | \(0.830481\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −101.565 | − | 52.8325i | −0.372032 | − | 0.193526i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 191.592 | 0.696700 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 376.940 | 1.36079 | 0.680397 | − | 0.732844i | \(-0.261807\pi\) | ||||
0.680397 | + | 0.732844i | \(0.261807\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 174.956i | 0.627081i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 62.5173 | 0.222481 | 0.111241 | − | 0.993793i | \(-0.464518\pi\) | ||||
0.111241 | + | 0.993793i | \(0.464518\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 103.435i | 0.365494i | 0.983160 | + | 0.182747i | \(0.0584989\pi\) | ||||
−0.983160 | + | 0.182747i | \(0.941501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 396.510i | 1.39126i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −138.959 | + | 267.133i | −0.484177 | + | 0.930776i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −178.483 | −0.617587 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −548.947 | −1.88641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 507.624i | − | 1.73251i | −0.499606 | − | 0.866253i | \(-0.666522\pi\) | ||
0.499606 | − | 0.866253i | \(-0.333478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 447.739 | 1.51776 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 958.842i | − | 3.22842i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 5.17972i | − | 0.0173235i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 227.565 | + | 118.376i | 0.756029 | + | 0.393275i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 584.735 | 1.92982 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.7887 | 0.114061 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 419.316i | − | 1.36585i | −0.730489 | − | 0.682925i | \(-0.760708\pi\) | ||
0.730489 | − | 0.682925i | \(-0.239292\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −321.388 | −1.04009 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 171.628i | 0.551858i | 0.961178 | + | 0.275929i | \(0.0889854\pi\) | ||||
−0.961178 | + | 0.275929i | \(0.911015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 503.484i | 1.60857i | 0.594240 | + | 0.804287i | \(0.297453\pi\) | ||||
−0.594240 | + | 0.804287i | \(0.702547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −407.159 | + | 782.719i | −1.29257 | + | 2.48482i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −205.647 | −0.648727 | −0.324364 | − | 0.945932i | \(-0.605150\pi\) | ||||
−0.324364 | + | 0.945932i | \(0.605150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 627.161 | 1.96602 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 250.093i | 0.779105i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 257.253 | 0.796448 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 37.7931i | − | 0.116286i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 129.090i | 0.394770i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −97.7414 | + | 187.897i | −0.297086 | + | 0.571115i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6740 | −0.0594382 | −0.0297191 | − | 0.999558i | \(-0.509461\pi\) | ||||
−0.0297191 | + | 0.999558i | \(0.509461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1092.59 | −3.28104 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 176.362i | 0.526454i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 317.823 | 0.943096 | 0.471548 | − | 0.881840i | \(-0.343695\pi\) | ||||
0.471548 | + | 0.881840i | \(0.343695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1017.93i | 3.00275i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 129.728i | 0.380434i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −45.0765 | − | 340.025i | −0.131418 | − | 0.991327i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −57.3880 | −0.166342 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −416.385 | −1.19996 | −0.599979 | − | 0.800016i | \(-0.704824\pi\) | ||||
−0.599979 | + | 0.800016i | \(0.704824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 333.344i | − | 0.955140i | −0.878594 | − | 0.477570i | \(-0.841518\pi\) | ||
0.878594 | − | 0.477570i | \(-0.158482\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −189.139 | −0.538857 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 230.864i | 0.654005i | 0.945023 | + | 0.327003i | \(0.106039\pi\) | ||||
−0.945023 | + | 0.327003i | \(0.893961\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 33.9051i | − | 0.0955073i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 730.069 | + | 379.772i | 2.04501 | + | 1.06379i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.9796 | 0.0472970 | 0.0236485 | − | 0.999720i | \(-0.492472\pi\) | ||||
0.0236485 | + | 0.999720i | \(0.492472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 219.435 | 0.607854 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 606.357i | − | 1.67041i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 581.905 | 1.59426 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 457.377i | − | 1.24626i | −0.782119 | − | 0.623129i | \(-0.785861\pi\) | ||
0.782119 | − | 0.623129i | \(-0.214139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 884.614i | 2.39733i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 186.301 | + | 96.9113i | 0.502160 | + | 0.261217i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −541.974 | −1.45301 | −0.726507 | − | 0.687159i | \(-0.758858\pi\) | ||||
−0.726507 | + | 0.687159i | \(0.758858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 414.413 | 1.10510 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 123.712i | − | 0.328149i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −254.799 | −0.672294 | −0.336147 | − | 0.941810i | \(-0.609124\pi\) | ||||
−0.336147 | + | 0.941810i | \(0.609124\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1122.00i | − | 2.94487i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 295.983i | − | 0.772803i | −0.922331 | − | 0.386401i | \(-0.873718\pi\) | ||
0.922331 | − | 0.386401i | \(-0.126282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −301.905 | + | 580.380i | −0.784169 | + | 1.50748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 753.584 | 1.94725 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −538.164 | −1.38345 | −0.691727 | − | 0.722159i | \(-0.743150\pi\) | ||||
−0.691727 | + | 0.722159i | \(0.743150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.2329i | 0.0952249i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1016.67 | −2.58694 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 499.720i | − | 1.26511i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 547.293i | − | 1.37857i | −0.724490 | − | 0.689286i | \(-0.757925\pi\) | ||
0.724490 | − | 0.689286i | \(-0.242075\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −401.753 | − | 208.986i | −1.00690 | − | 0.523774i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 203.375 | 0.507170 | 0.253585 | − | 0.967313i | \(-0.418390\pi\) | ||||
0.253585 | + | 0.967313i | \(0.418390\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.5899 | 0.0634984 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 961.170i | 2.37326i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −810.143 | −1.99052 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 103.627i | 0.253366i | 0.991943 | + | 0.126683i | \(0.0404332\pi\) | ||||
−0.991943 | + | 0.126683i | \(0.959567\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6873i | 0.0333024i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −235.987 | + | 453.659i | −0.571398 | + | 1.09845i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −528.898 | −1.27445 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 101.565 | 0.243560 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 438.503i | − | 1.04655i | −0.852165 | − | 0.523273i | \(-0.824711\pi\) | ||
0.852165 | − | 0.523273i | \(-0.175289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −741.293 | −1.76079 | −0.880396 | − | 0.474240i | \(-0.842723\pi\) | ||||
−0.880396 | + | 0.474240i | \(0.842723\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 622.224i | 1.47098i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 271.665i | 0.639212i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.3359 | + | 35.2488i | −0.0429412 | + | 0.0825498i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −249.388 | −0.581324 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −82.8809 | −0.192299 | −0.0961495 | − | 0.995367i | \(-0.530653\pi\) | ||||
−0.0961495 | + | 0.995367i | \(0.530653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 607.840i | − | 1.40379i | −0.712282 | − | 0.701893i | \(-0.752338\pi\) | ||
0.712282 | − | 0.701893i | \(-0.247662\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1370.65 | −3.15093 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.4891i | − | 0.0468857i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 654.207i | − | 1.49022i | −0.666941 | − | 0.745111i | \(-0.732397\pi\) | ||
0.666941 | − | 0.745111i | \(-0.267603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −578.470 | − | 825.087i | −1.31172 | − | 1.87094i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 566.176 | 1.27805 | 0.639025 | − | 0.769186i | \(-0.279338\pi\) | ||||
0.639025 | + | 0.769186i | \(0.279338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −169.388 | −0.380647 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.6873i | 0.0306204i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 348.776 | 0.776784 | 0.388392 | − | 0.921494i | \(-0.373031\pi\) | ||||
0.388392 | + | 0.921494i | \(0.373031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 655.934i | 1.45440i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 426.588i | 0.941696i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 114.484 | + | 59.5531i | 0.251614 | + | 0.130886i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 354.694 | 0.776136 | 0.388068 | − | 0.921631i | \(-0.373143\pi\) | ||||
0.388068 | + | 0.921631i | \(0.373143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1359.57 | 2.96203 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 220.531i | − | 0.478375i | −0.970973 | − | 0.239187i | \(-0.923119\pi\) | ||
0.970973 | − | 0.239187i | \(-0.0768810\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −497.178 | −1.07382 | −0.536910 | − | 0.843640i | \(-0.680408\pi\) | ||||
−0.536910 | + | 0.843640i | \(0.680408\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 283.519i | − | 0.609719i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 299.499i | − | 0.641326i | −0.947193 | − | 0.320663i | \(-0.896094\pi\) | ||
0.947193 | − | 0.320663i | \(-0.103906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −178.694 | − | 92.9541i | −0.381011 | − | 0.198196i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1623.37 | 3.44663 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 558.776 | 1.18134 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 149.496i | − | 0.314727i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 616.940 | 1.29337 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 524.867i | − | 1.09576i | −0.836558 | − | 0.547878i | \(-0.815436\pi\) | ||
0.836558 | − | 0.547878i | \(-0.184564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 159.807i | 0.332239i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.2471 | − | 58.1468i | 0.0626235 | − | 0.120387i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 618.776 | 1.27583 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 62.2345 | 0.127792 | 0.0638958 | − | 0.997957i | \(-0.479647\pi\) | ||||
0.0638958 | + | 0.997957i | \(0.479647\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.1755i | 0.0985184i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 127.136 | 0.258933 | 0.129467 | − | 0.991584i | \(-0.458674\pi\) | ||||
0.129467 | + | 0.991584i | \(0.458674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 889.271i | 1.80380i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1921.94i | 3.88270i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.3534 | + | 17.8702i | 0.0691215 | + | 0.0359560i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −699.460 | −1.40172 | −0.700862 | − | 0.713297i | \(-0.747201\pi\) | ||||
−0.700862 | + | 0.713297i | \(0.747201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1375.27 | 2.74505 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 856.217i | 1.70222i | 0.524986 | + | 0.851111i | \(0.324070\pi\) | ||||
−0.524986 | + | 0.851111i | \(0.675930\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −659.116 | −1.30518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 869.717i | − | 1.71542i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 83.6547i | − | 0.164351i | −0.996618 | − | 0.0821755i | \(-0.973813\pi\) | ||
0.996618 | − | 0.0821755i | \(-0.0261868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −306.701 | + | 589.600i | −0.600199 | + | 1.15382i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −748.164 | −1.45841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 362.270 | 0.703438 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 461.374i | 0.892405i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.9081 | 0.0826745 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 563.287i | 1.08117i | 0.841291 | + | 0.540583i | \(0.181796\pi\) | ||||
−0.841291 | + | 0.540583i | \(0.818204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 414.011i | 0.791607i | 0.918335 | + | 0.395804i | \(0.129534\pi\) | ||||
−0.918335 | + | 0.395804i | \(0.870466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 220.694 | − | 424.260i | 0.420369 | − | 0.808114i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −183.946 | −0.349043 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −526.035 | −0.994394 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1502.30i | 2.82919i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 129.388 | 0.242754 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 281.906i | − | 0.526927i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1623.44i | − | 3.02317i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −428.930 | − | 611.795i | −0.795789 | − | 1.13505i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −86.7068 | −0.160271 | −0.0801357 | − | 0.996784i | \(-0.525535\pi\) | ||||
−0.0801357 | + | 0.996784i | \(0.525535\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1532.36 | −2.82202 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 145.511i | − | 0.266992i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 827.355 | 1.51253 | 0.756266 | − | 0.654265i | \(-0.227022\pi\) | ||||
0.756266 | + | 0.654265i | \(0.227022\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 116.727i | 0.212617i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 489.361i | − | 0.888132i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 506.328 | + | 263.385i | 0.915602 | + | 0.476283i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1770.56 | 3.19020 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −343.741 | −0.617130 | −0.308565 | − | 0.951203i | \(-0.599849\pi\) | ||||
−0.308565 | + | 0.951203i | \(0.599849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 110.223i | − | 0.197179i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1792.66 | 3.19546 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 308.968i | − | 0.548788i | −0.961617 | − | 0.274394i | \(-0.911523\pi\) | ||
0.961617 | − | 0.274394i | \(-0.0884772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1147.42i | − | 2.03083i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −973.880 | − | 506.598i | −1.71760 | − | 0.893472i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 182.177 | 0.320170 | 0.160085 | − | 0.987103i | \(-0.448823\pi\) | ||||
0.160085 | + | 0.987103i | \(0.448823\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 378.037 | 0.662061 | 0.331031 | − | 0.943620i | \(-0.392604\pi\) | ||||
0.331031 | + | 0.943620i | \(0.392604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 111.681i | 0.194905i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.6369 | 0.0376294 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 81.6019i | 0.141424i | 0.997497 | + | 0.0707122i | \(0.0225272\pi\) | ||||
−0.997497 | + | 0.0707122i | \(0.977473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1041.60i | − | 1.79897i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 278.763 | − | 535.891i | 0.479799 | − | 0.922360i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 457.456 | 0.784658 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 379.116 | 0.648062 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 37.9917i | − | 0.0647217i | −0.999476 | − | 0.0323609i | \(-0.989697\pi\) | ||
0.999476 | − | 0.0323609i | \(-0.0103026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 101.224 | 0.171858 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 615.123i | 1.04082i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 406.099i | − | 0.684822i | −0.939550 | − | 0.342411i | \(-0.888757\pi\) | ||
0.939550 | − | 0.342411i | \(-0.111243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −822.938 | − | 428.081i | −1.38309 | − | 0.719464i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 720.681 | 1.20717 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −292.800 | −0.488815 | −0.244407 | − | 0.969673i | \(-0.578593\pi\) | ||||
−0.244407 | + | 0.969673i | \(0.578593\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.6997i | − | 0.0244588i | −0.999925 | − | 0.0122294i | \(-0.996107\pi\) | ||
0.999925 | − | 0.0122294i | \(-0.00389284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −591.748 | −0.981340 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 683.490i | 1.12973i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 959.534i | − | 1.58078i | −0.612604 | − | 0.790390i | \(-0.709878\pi\) | ||
0.612604 | − | 0.790390i | \(-0.290122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 722.423 | − | 1388.78i | 1.18624 | − | 2.28042i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 91.0095 | 0.148952 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −896.397 | −1.46231 | −0.731156 | − | 0.682211i | \(-0.761019\pi\) | ||||
−0.731156 | + | 0.682211i | \(0.761019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1433.54i | − | 2.33095i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 137.280 | 0.222497 | 0.111248 | − | 0.993793i | \(-0.464515\pi\) | ||||
0.111248 | + | 0.993793i | \(0.464515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 703.714i | − | 1.13686i | −0.822733 | − | 0.568428i | \(-0.807552\pi\) | ||
0.822733 | − | 0.568428i | \(-0.192448\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 108.284i | − | 0.174370i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 89.2783 | − | 171.628i | 0.143304 | − | 0.275486i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −781.246 | −1.24999 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −986.487 | −1.57334 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1148.73i | − | 1.82628i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −87.6903 | −0.138970 | −0.0694852 | − | 0.997583i | \(-0.522136\pi\) | ||||
−0.0694852 | + | 0.997583i | \(0.522136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1279.77i | 2.02175i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1264.72i | 1.99169i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −120.681 | + | 84.6098i | −0.189452 | + | 0.132825i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 113.762 | 0.178031 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −380.953 | −0.594310 | −0.297155 | − | 0.954829i | \(-0.596038\pi\) | ||||
−0.297155 | + | 0.954829i | \(0.596038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 441.511i | 0.686642i | 0.939218 | + | 0.343321i | \(0.111552\pi\) | ||||
−0.939218 | + | 0.343321i | \(0.888448\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1221.20 | −1.89333 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 844.897i | 1.30587i | 0.757414 | + | 0.652934i | \(0.226462\pi\) | ||||
−0.757414 | + | 0.652934i | \(0.773538\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1113.94i | 1.71640i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 287.268 | + | 149.433i | 0.441272 | + | 0.229544i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 478.845 | 0.733300 | 0.366650 | − | 0.930359i | \(-0.380505\pi\) | ||||
0.366650 | + | 0.930359i | \(0.380505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1145.99 | 1.74961 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1952.47i | 2.97179i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 257.012 | 0.390003 | 0.195002 | − | 0.980803i | \(-0.437529\pi\) | ||||
0.195002 | + | 0.980803i | \(0.437529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 788.652i | 1.19312i | 0.802568 | + | 0.596560i | \(0.203466\pi\) | ||||
−0.802568 | + | 0.596560i | \(0.796534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 353.615i | − | 0.533356i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 452.858 | + | 235.570i | 0.680989 | + | 0.354241i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 70.8266 | 0.106187 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1138.07 | 1.70115 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 86.5519i | 0.128989i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −511.362 | −0.759825 | −0.379913 | − | 0.925022i | \(-0.624046\pi\) | ||||
−0.379913 | + | 0.925022i | \(0.624046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 790.078i | − | 1.17049i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 543.542i | − | 0.802868i | −0.915888 | − | 0.401434i | \(-0.868512\pi\) | ||
0.915888 | − | 0.401434i | \(-0.131488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −326.135 | + | 626.958i | −0.480316 | + | 0.923355i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1183.99 | 1.73860 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −785.312 | −1.14980 | −0.574899 | − | 0.818224i | \(-0.694959\pi\) | ||||
−0.574899 | + | 0.818224i | \(0.694959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.4284i | − | 0.0225232i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −278.033 | −0.404706 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 90.2366i | − | 0.130967i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1063.98i | 1.53978i | 0.638179 | + | 0.769888i | \(0.279688\pi\) | ||||
−0.638179 | + | 0.769888i | \(0.720312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1947.35 | − | 1012.98i | −2.81003 | − | 1.46174i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −114.484 | −0.164726 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −930.069 | −1.33439 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1318.65i | 1.88648i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −113.810 | −0.162354 | −0.0811772 | − | 0.996700i | \(-0.525868\pi\) | ||||
−0.0811772 | + | 0.996700i | \(0.525868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 632.138i | 0.899200i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1008.33i | − | 1.43025i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 347.397 | − | 667.832i | 0.491367 | − | 0.944600i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 418.000 | 0.589563 | 0.294781 | − | 0.955565i | \(-0.404753\pi\) | ||||
0.294781 | + | 0.955565i | \(0.404753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1676.71 | 2.35824 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6505i | 0.0205476i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 281.112 | 0.393163 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 94.9429i | 0.132417i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 752.720i | 1.04690i | 0.852057 | + | 0.523449i | \(0.175355\pi\) | ||||
−0.852057 | + | 0.523449i | \(0.824645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −190.940 | + | 367.061i | −0.264826 | + | 0.509099i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −374.316 | −0.517726 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 516.776 | 0.712794 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 269.945i | − | 0.371314i | −0.982615 | − | 0.185657i | \(-0.940559\pi\) | ||
0.982615 | − | 0.185657i | \(-0.0594414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −147.871 | −0.202840 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 792.306i | 1.08387i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 805.971i | 1.09955i | 0.835312 | + | 0.549776i | \(0.185287\pi\) | ||||
−0.835312 | + | 0.549776i | \(0.814713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 937.423 | + | 1337.07i | 1.27540 | + | 1.81914i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −438.776 | −0.595354 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 672.425 | 0.909912 | 0.454956 | − | 0.890514i | \(-0.349655\pi\) | ||||
0.454956 | + | 0.890514i | \(0.349655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 194.592i | 0.262607i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −367.686 | −0.494867 | −0.247434 | − | 0.968905i | \(-0.579587\pi\) | ||||
−0.247434 | + | 0.968905i | \(0.579587\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 15.4284i | − | 0.0207093i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1774.61i | − | 2.37565i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 285.634 | + | 148.583i | 0.381354 | + | 0.198375i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −181.778 | −0.242048 | −0.121024 | − | 0.992650i | \(-0.538618\pi\) | ||||
−0.121024 | + | 0.992650i | \(0.538618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −664.694 | −0.882728 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 480.853i | − | 0.636891i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −63.7414 | −0.0842026 | −0.0421013 | − | 0.999113i | \(-0.513405\pi\) | ||||
−0.0421013 | + | 0.999113i | \(0.513405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 142.777i | − | 0.188112i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1279.94i | − | 1.68192i | −0.541096 | − | 0.840961i | \(-0.681990\pi\) | ||
0.541096 | − | 0.840961i | \(-0.318010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 147.435 | + | 76.6936i | 0.193231 | + | 0.100516i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2725.17 | −3.56232 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 219.734 | 0.286485 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 321.701i | − | 0.418337i | −0.977880 | − | 0.209169i | \(-0.932924\pi\) | ||
0.977880 | − | 0.209169i | \(-0.0670758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1698.98 | −2.20361 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 697.333i | − | 0.902112i | −0.892496 | − | 0.451056i | \(-0.851047\pi\) | ||
0.892496 | − | 0.451056i | \(-0.148953\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 106.895i | 0.137929i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −933.198 | + | 1793.97i | −1.20103 | + | 2.30884i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 511.811 | 0.657011 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 84.3534 | 0.108007 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2586.25i | − | 3.30300i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1829.87 | −2.33104 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 330.202i | 0.419570i | 0.977748 | + | 0.209785i | \(0.0672764\pi\) | ||||
−0.977748 | + | 0.209785i | \(0.932724\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2033.34i | 2.57711i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1162.59 | + | 604.763i | 1.46977 | + | 0.764555i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0730 | 0.0215297 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −999.764 | −1.25756 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 456.879i | 0.573248i | 0.958043 | + | 0.286624i | \(0.0925331\pi\) | ||||
−0.958043 | + | 0.286624i | \(0.907467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −654.196 | −0.818768 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 568.348i | − | 0.709548i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1447.74i | 1.80291i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.0948 | + | 65.5434i | −0.0423537 | + | 0.0814204i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −982.178 | −1.21707 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 175.211 | 0.216578 | 0.108289 | − | 0.994119i | \(-0.465463\pi\) | ||||
0.108289 | + | 0.994119i | \(0.465463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 149.621i | − | 0.184489i | −0.995736 | − | 0.0922446i | \(-0.970596\pi\) | ||
0.995736 | − | 0.0922446i | \(-0.0294042\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1496.33 | 1.84050 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 54.3037i | − | 0.0666303i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 436.001i | − | 0.533661i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −199.819 | + | 384.130i | −0.243979 | + | 0.469023i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −880.750 | −1.07278 | −0.536389 | − | 0.843971i | \(-0.680212\pi\) | ||||
−0.536389 | + | 0.843971i | \(0.680212\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1149.93 | 1.39724 | 0.698621 | − | 0.715492i | \(-0.253798\pi\) | ||||
0.698621 | + | 0.715492i | \(0.253798\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1041.75i | − | 1.26273i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −633.041 | −0.765466 | −0.382733 | − | 0.923859i | \(-0.625017\pi\) | ||||
−0.382733 | + | 0.923859i | \(0.625017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 900.963i | 1.08681i | 0.839472 | + | 0.543404i | \(0.182865\pi\) | ||||
−0.839472 | + | 0.543404i | \(0.817135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2049.55i | − | 2.46637i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 867.483 | − | 608.194i | 1.04140 | − | 0.730125i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1550.21 | −1.85654 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 534.965 | 0.639146 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1587.19i | − | 1.89176i | −0.324514 | − | 0.945881i | \(-0.605201\pi\) | ||
0.324514 | − | 0.945881i | \(-0.394799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 850.621 | 1.01144 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 339.928i | − | 0.403236i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 980.350i | 1.16018i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −692.527 | − | 360.243i | −0.817624 | − | 0.425316i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 562.410 | 0.662438 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −91.4911 | −0.107510 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 614.776i | 0.720722i | 0.932813 | + | 0.360361i | \(0.117346\pi\) | ||||
−0.932813 | + | 0.360361i | \(0.882654\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1499.65 | 1.75397 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 741.142i | − | 0.864809i | −0.901680 | − | 0.432405i | \(-0.857665\pi\) | ||
0.901680 | − | 0.432405i | \(-0.142335\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 686.448i | − | 0.799125i | −0.916706 | − | 0.399563i | \(-0.869162\pi\) | ||
0.916706 | − | 0.399563i | \(-0.130838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1452.49 | + | 755.566i | 1.68698 | + | 0.877544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1375.44 | 1.59378 | 0.796892 | − | 0.604122i | \(-0.206476\pi\) | ||||
0.796892 | + | 0.604122i | \(0.206476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48.3662 | −0.0559147 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 970.471i | 1.11934i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1243.27 | 1.43069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 86.5519i | 0.0993707i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2076.18i | 2.37821i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 246.207 | − | 473.306i | 0.281380 | − | 0.540921i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1319.39 | −1.50443 | −0.752217 | − | 0.658916i | \(-0.771015\pi\) | ||||
−0.752217 | + | 0.658916i | \(0.771015\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2760.12 | −3.14007 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 270.582i | − | 0.307130i | −0.988139 | − | 0.153565i | \(-0.950924\pi\) | ||
0.988139 | − | 0.153565i | \(-0.0490755\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1491.67 | 1.68932 | 0.844660 | − | 0.535303i | \(-0.179803\pi\) | ||||
0.844660 | + | 0.535303i | \(0.179803\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 2434.51i | − | 2.75086i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 79.8264i | 0.0899960i | 0.998987 | + | 0.0449980i | \(0.0143281\pi\) | ||||
−0.998987 | + | 0.0449980i | \(0.985672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1281.44 | − | 666.589i | −1.44144 | − | 0.749819i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2391.32 | −2.68386 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 360.000 | 0.403135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1829.95i | 2.04464i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.1639 | −0.0313979 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 349.911i | 0.389223i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 648.640i | 0.719912i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 643.650 | − | 1237.35i | 0.712791 | − | 1.37026i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1727.28 | 1.90860 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 845.557 | 0.932256 | 0.466128 | − | 0.884717i | \(-0.345649\pi\) | ||||
0.466128 | + | 0.884717i | \(0.345649\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2211.54i | − | 2.43293i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1377.51 | 1.51209 | 0.756045 | − | 0.654519i | \(-0.227129\pi\) | ||||
0.756045 | + | 0.654519i | \(0.227129\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1315.86i | − | 1.44125i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 189.158i | − | 0.206730i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −604.013 | + | 1161.15i | −0.658684 | + | 1.26625i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −648.950 | −0.706148 | −0.353074 | − | 0.935595i | \(-0.614864\pi\) | ||||
−0.353074 | + | 0.935595i | \(0.614864\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2279.96 | −2.47553 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 16.6394i | − | 0.0180275i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −667.552 | −0.721678 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1215.53i | 1.31125i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1394.62i | 1.50120i | 0.660756 | + | 0.750601i | \(0.270236\pi\) | ||||
−0.660756 | + | 0.750601i | \(0.729764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −477.370 | + | 334.685i | −0.512750 | + | 0.359490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 933.198 | 1.00021 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2020.69 | −2.16117 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 433.382i | 0.462521i | 0.972892 | + | 0.231260i | \(0.0742850\pi\) | ||||
−0.972892 | + | 0.231260i | \(0.925715\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2737.61 | 2.91546 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 891.147i | − | 0.947021i | −0.880788 | − | 0.473511i | \(-0.842987\pi\) | ||
0.880788 | − | 0.473511i | \(-0.157013\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.0759i | 0.0785535i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2393.34 | + | 1244.98i | 2.53263 | + | 1.31744i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1021.88 | 1.07907 | 0.539537 | − | 0.841962i | \(-0.318599\pi\) | ||||
0.539537 | + | 0.841962i | \(0.318599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 285.577 | 0.300925 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1118.17i | 1.17578i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1322.52 | −1.38774 | −0.693871 | − | 0.720100i | \(-0.744096\pi\) | ||||
−0.693871 | + | 0.720100i | \(0.744096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 125.887i | − | 0.131819i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3410.09i | − | 3.56331i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.6324 | + | 8.13176i | 0.0163008 | + | 0.00847942i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 888.621 | 0.924684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 945.881 | 0.982223 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1174.10i | 1.21668i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1681.56 | 1.73894 | 0.869471 | − | 0.493983i | \(-0.164460\pi\) | ||||
0.869471 | + | 0.493983i | \(0.164460\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1398.77i | − | 1.44352i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1177.91i | 1.21309i | 0.795049 | + | 0.606546i | \(0.207445\pi\) | ||||
−0.795049 | + | 0.606546i | \(0.792555\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 60.3406 | − | 115.998i | 0.0620150 | − | 0.119217i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −205.494 | −0.210763 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1440.21 | 1.47411 | 0.737056 | − | 0.675832i | \(-0.236215\pi\) | ||||
0.737056 | + | 0.675832i | \(0.236215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 421.425i | − | 0.430465i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 488.233 | 0.497689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 283.257i | − | 0.288156i | −0.989566 | − | 0.144078i | \(-0.953978\pi\) | ||
0.989566 | − | 0.144078i | \(-0.0460215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 693.370i | − | 0.703929i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1021.66 | + | 531.453i | 1.03512 | + | 0.538453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.1037 | 0.0638055 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1079.85 | 1.08966 | 0.544830 | − | 0.838547i | \(-0.316594\pi\) | ||||
0.544830 | + | 0.838547i | \(0.316594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 106.974i | 0.107729i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −812.356 | −0.816438 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1572.31i | − | 1.57704i | −0.615010 | − | 0.788520i | \(-0.710848\pi\) | ||
0.615010 | − | 0.788520i | \(-0.289152\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3340.82i | 3.34417i |
(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 | 224.3.c.a.97.2 | yes | 8 | |
3.2 | odd | 2 | 2016.3.f.c.1441.1 | 8 | |||
4.3 | odd | 2 | inner | 224.3.c.a.97.8 | yes | 8 | |
7.6 | odd | 2 | inner | 224.3.c.a.97.7 | yes | 8 | |
8.3 | odd | 2 | 448.3.c.g.321.1 | 8 | |||
8.5 | even | 2 | 448.3.c.g.321.7 | 8 | |||
12.11 | even | 2 | 2016.3.f.c.1441.2 | 8 | |||
21.20 | even | 2 | 2016.3.f.c.1441.7 | 8 | |||
28.27 | even | 2 | inner | 224.3.c.a.97.1 | ✓ | 8 | |
56.13 | odd | 2 | 448.3.c.g.321.2 | 8 | |||
56.27 | even | 2 | 448.3.c.g.321.8 | 8 | |||
84.83 | odd | 2 | 2016.3.f.c.1441.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.c.a.97.1 | ✓ | 8 | 28.27 | even | 2 | inner | |
224.3.c.a.97.2 | yes | 8 | 1.1 | even | 1 | trivial | |
224.3.c.a.97.7 | yes | 8 | 7.6 | odd | 2 | inner | |
224.3.c.a.97.8 | yes | 8 | 4.3 | odd | 2 | inner | |
448.3.c.g.321.1 | 8 | 8.3 | odd | 2 | |||
448.3.c.g.321.2 | 8 | 56.13 | odd | 2 | |||
448.3.c.g.321.7 | 8 | 8.5 | even | 2 | |||
448.3.c.g.321.8 | 8 | 56.27 | even | 2 | |||
2016.3.f.c.1441.1 | 8 | 3.2 | odd | 2 | |||
2016.3.f.c.1441.2 | 8 | 12.11 | even | 2 | |||
2016.3.f.c.1441.7 | 8 | 21.20 | even | 2 | |||
2016.3.f.c.1441.8 | 8 | 84.83 | odd | 2 |