Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,3,Mod(1049,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.1049");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.p (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: | \(38.1472370104\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.8 | ||
Root | \(0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.1049 |
Dual form | 1400.3.p.a.1049.7 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.69552 | 1.23184 | 0.615920 | − | 0.787809i | \(-0.288785\pi\) | ||||
0.615920 | + | 0.787809i | \(0.288785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.75699 | + | 1.82843i | −0.965284 | + | 0.261204i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.65685 | 0.517428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.3137 | 1.21034 | 0.605169 | − | 0.796097i | \(-0.293106\pi\) | ||||
0.605169 | + | 0.796097i | \(0.293106\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.5391 | −1.65685 | −0.828425 | − | 0.560100i | \(-0.810763\pi\) | ||||
−0.828425 | + | 0.560100i | \(0.810763\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.12293 | −0.360173 | −0.180086 | − | 0.983651i | \(-0.557638\pi\) | ||||
−0.180086 | + | 0.983651i | \(0.557638\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.7457i | − | 1.03925i | −0.854395 | − | 0.519623i | \(-0.826072\pi\) | ||
0.854395 | − | 0.519623i | \(-0.173928\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.9706 | + | 6.75699i | −1.18907 | + | 0.321761i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 28.6274i | − | 1.24467i | −0.782751 | − | 0.622335i | \(-0.786184\pi\) | ||
0.782751 | − | 0.622335i | \(-0.213816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.0502 | −0.594451 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.3137 | −1.28668 | −0.643340 | − | 0.765581i | \(-0.722452\pi\) | ||||
−0.643340 | + | 0.765581i | \(0.722452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.9050i | 0.674355i | 0.941441 | + | 0.337178i | \(0.109472\pi\) | ||||
−0.941441 | + | 0.337178i | \(0.890528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.2011 | 1.49094 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.9411i | 0.647057i | 0.946218 | + | 0.323529i | \(0.104869\pi\) | ||||
−0.946218 | + | 0.323529i | \(0.895131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −79.5980 | −2.04097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 70.1061i | − | 1.70990i | −0.518707 | − | 0.854952i | \(-0.673587\pi\) | ||
0.518707 | − | 0.854952i | \(-0.326413\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 46.0000i | − | 1.06977i | −0.844926 | − | 0.534884i | \(-0.820355\pi\) | ||
0.844926 | − | 0.534884i | \(-0.179645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.05053 | 0.0223517 | 0.0111758 | − | 0.999938i | \(-0.496443\pi\) | ||||
0.0111758 | + | 0.999938i | \(0.496443\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 42.3137 | − | 24.7093i | 0.863545 | − | 0.504272i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.6274 | −0.443675 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 15.3726i | − | 0.290049i | −0.989428 | − | 0.145024i | \(-0.953674\pi\) | ||
0.989428 | − | 0.145024i | \(-0.0463261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 72.9706i | − | 1.28019i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 14.8909i | − | 0.252387i | −0.992006 | − | 0.126194i | \(-0.959724\pi\) | ||
0.992006 | − | 0.126194i | \(-0.0402761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86.7903i | 1.42279i | 0.702792 | + | 0.711396i | \(0.251937\pi\) | ||||
−0.702792 | + | 0.711396i | \(0.748063\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −31.4663 | + | 8.51472i | −0.499465 | + | 0.135154i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 24.6274i | − | 0.367573i | −0.982966 | − | 0.183787i | \(-0.941164\pi\) | ||
0.982966 | − | 0.183787i | \(-0.0588356\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 105.793i | − | 1.53323i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45.0294 | −0.634217 | −0.317109 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317109 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −51.7373 | −0.708730 | −0.354365 | − | 0.935107i | \(-0.615303\pi\) | ||||
−0.354365 | + | 0.935107i | \(0.615303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −89.9605 | + | 24.3431i | −1.16832 | + | 0.316145i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33.7157 | 0.426781 | 0.213391 | − | 0.976967i | \(-0.431549\pi\) | ||||
0.213391 | + | 0.976967i | \(0.431549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.225 | −1.24970 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −77.3883 | −0.932389 | −0.466195 | − | 0.884682i | \(-0.654375\pi\) | ||||
−0.466195 | + | 0.884682i | \(0.654375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −137.893 | −1.58498 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 78.7652i | − | 0.885002i | −0.896768 | − | 0.442501i | \(-0.854091\pi\) | ||
0.896768 | − | 0.442501i | \(-0.145909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 145.539 | − | 39.3826i | 1.59933 | − | 0.432776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 77.2548i | 0.830697i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −90.1781 | −0.929671 | −0.464836 | − | 0.885397i | \(-0.653887\pi\) | ||||
−0.464836 | + | 0.885397i | \(0.653887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 62.0000 | 0.626263 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 129.651i | − | 1.28367i | −0.766842 | − | 0.641836i | \(-0.778173\pi\) | ||
0.766842 | − | 0.641836i | \(-0.221827\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 34.4190 | 0.334165 | 0.167082 | − | 0.985943i | \(-0.446565\pi\) | ||||
0.167082 | + | 0.985943i | \(0.446565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 149.882i | − | 1.40077i | −0.713766 | − | 0.700384i | \(-0.753012\pi\) | ||
0.713766 | − | 0.700384i | \(-0.246988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 67.2548 | 0.617017 | 0.308508 | − | 0.951222i | \(-0.400170\pi\) | ||||
0.308508 | + | 0.951222i | \(0.400170\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 88.4749i | 0.797071i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 70.2843i | 0.621985i | 0.950412 | + | 0.310992i | \(0.100661\pi\) | ||||
−0.950412 | + | 0.310992i | \(0.899339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −100.304 | −0.857301 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 41.3726 | − | 11.1953i | 0.347669 | − | 0.0940785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 56.2548 | 0.464916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 259.078i | − | 2.10633i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.7645i | 0.738303i | 0.929369 | + | 0.369152i | \(0.120352\pi\) | ||||
−0.929369 | + | 0.369152i | \(0.879648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 169.994i | − | 1.31778i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 146.226i | 1.11623i | 0.829763 | + | 0.558116i | \(0.188475\pi\) | ||||
−0.829763 | + | 0.558116i | \(0.811525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36.1036 | + | 133.421i | 0.271455 | + | 1.00317i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 149.765i | 1.09317i | 0.837403 | + | 0.546586i | \(0.184073\pi\) | ||||
−0.837403 | + | 0.546586i | \(0.815927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 120.249i | 0.865100i | 0.901610 | + | 0.432550i | \(0.142386\pi\) | ||||
−0.901610 | + | 0.432550i | \(0.857614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.88225 | 0.0275337 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −286.765 | −2.00535 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 156.371 | − | 91.3137i | 1.06375 | − | 0.621182i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −33.7645 | −0.226607 | −0.113304 | − | 0.993560i | \(-0.536143\pi\) | ||||
−0.113304 | + | 0.993560i | \(0.536143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 144.627 | 0.957797 | 0.478899 | − | 0.877870i | \(-0.341036\pi\) | ||||
0.478899 | + | 0.877870i | \(0.341036\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28.5136 | −0.186363 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −128.818 | −0.820496 | −0.410248 | − | 0.911974i | \(-0.634558\pi\) | ||||
−0.410248 | + | 0.911974i | \(0.634558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 56.8097i | − | 0.357293i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 52.3431 | + | 193.435i | 0.325113 | + | 1.20146i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 57.4315i | 0.352340i | 0.984360 | + | 0.176170i | \(0.0563709\pi\) | ||||
−0.984360 | + | 0.176170i | \(0.943629\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −229.122 | −1.37199 | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 294.931 | 1.74515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 91.9528i | − | 0.537736i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 123.310 | 0.712776 | 0.356388 | − | 0.934338i | \(-0.384008\pi\) | ||||
0.356388 | + | 0.934338i | \(0.384008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 55.0294i | − | 0.310901i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 271.941 | 1.51922 | 0.759612 | − | 0.650376i | \(-0.225389\pi\) | ||||
0.759612 | + | 0.650376i | \(0.225389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 30.6333i | − | 0.169245i | −0.996413 | − | 0.0846225i | \(-0.973032\pi\) | ||
0.996413 | − | 0.0846225i | \(-0.0269684\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 320.735i | 1.75265i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −81.5190 | −0.435930 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 108.451 | − | 29.3466i | 0.573814 | − | 0.155273i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69.5980 | −0.364387 | −0.182194 | − | 0.983263i | \(-0.558320\pi\) | ||||
−0.182194 | + | 0.983263i | \(0.558320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 279.421i | 1.44778i | 0.689916 | + | 0.723890i | \(0.257647\pi\) | ||||
−0.689916 | + | 0.723890i | \(0.742353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 102.451i | − | 0.520055i | −0.965601 | − | 0.260027i | \(-0.916268\pi\) | ||
0.965601 | − | 0.260027i | \(-0.0837316\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 161.950i | 0.813820i | 0.913468 | + | 0.406910i | \(0.133394\pi\) | ||||
−0.913468 | + | 0.406910i | \(0.866606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 91.0111i | − | 0.452791i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 252.128 | − | 68.2254i | 1.24201 | − | 0.336086i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 133.314i | − | 0.644028i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 262.888i | − | 1.25784i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −51.0193 | −0.241798 | −0.120899 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120899 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −166.407 | −0.781254 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.2233 | − | 141.255i | −0.176144 | − | 0.650944i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −191.196 | −0.873041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 131.882 | 0.596752 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −221.296 | −0.992358 | −0.496179 | − | 0.868220i | \(-0.665264\pi\) | ||||
−0.496179 | + | 0.868220i | \(0.665264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −101.047 | −0.445141 | −0.222571 | − | 0.974917i | \(-0.571445\pi\) | ||||
−0.222571 | + | 0.974917i | \(0.571445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 170.193i | − | 0.743200i | −0.928393 | − | 0.371600i | \(-0.878809\pi\) | ||
0.928393 | − | 0.371600i | \(-0.121191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −332.451 | + | 89.9605i | −1.43918 | + | 0.389440i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 451.019i | − | 1.93571i | −0.251518 | − | 0.967853i | \(-0.580930\pi\) | ||
0.251518 | − | 0.967853i | \(-0.419070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 124.597 | 0.525726 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −219.137 | −0.916892 | −0.458446 | − | 0.888722i | \(-0.651594\pi\) | ||||
−0.458446 | + | 0.888722i | \(0.651594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 325.386i | − | 1.35015i | −0.737750 | − | 0.675074i | \(-0.764112\pi\) | ||
0.737750 | − | 0.675074i | \(-0.235888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −229.629 | −0.944974 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 425.304i | 1.72188i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −285.990 | −1.14855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 260.063i | 1.03611i | 0.855348 | + | 0.518054i | \(0.173343\pi\) | ||||
−0.855348 | + | 0.518054i | \(0.826657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 381.137i | − | 1.50647i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 184.558 | 0.718126 | 0.359063 | − | 0.933313i | \(-0.383096\pi\) | ||||
0.359063 | + | 0.933313i | \(0.383096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −43.7746 | − | 161.770i | −0.169014 | − | 0.624594i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −173.765 | −0.665764 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 246.853i | 0.938604i | 0.883038 | + | 0.469302i | \(0.155494\pi\) | ||||
−0.883038 | + | 0.469302i | \(0.844506\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 291.078i | − | 1.09018i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 105.159i | − | 0.390926i | −0.980711 | − | 0.195463i | \(-0.937379\pi\) | ||
0.980711 | − | 0.195463i | \(-0.0626210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 71.8093i | − | 0.264979i | −0.991184 | − | 0.132489i | \(-0.957703\pi\) | ||
0.991184 | − | 0.132489i | \(-0.0422971\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 537.842 | − | 145.539i | 1.97012 | − | 0.533110i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 402.098i | − | 1.45162i | −0.687898 | − | 0.725808i | \(-0.741466\pi\) | ||
0.687898 | − | 0.725808i | \(-0.258534\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 97.3516i | 0.348930i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.529 | 1.14423 | 0.572116 | − | 0.820173i | \(-0.306123\pi\) | ||||
0.572116 | + | 0.820173i | \(0.306123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −485.561 | −1.71576 | −0.857882 | − | 0.513847i | \(-0.828220\pi\) | ||||
−0.857882 | + | 0.513847i | \(0.828220\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 128.184 | + | 473.706i | 0.446634 | + | 1.65054i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −251.510 | −0.870276 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −333.255 | −1.14521 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 480.218 | 1.63897 | 0.819485 | − | 0.573100i | \(-0.194259\pi\) | ||||
0.819485 | + | 0.573100i | \(0.194259\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −213.687 | −0.719486 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 616.608i | 2.06223i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 84.1076 | + | 310.821i | 0.279427 | + | 1.03263i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 479.127i | − | 1.58128i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1876 | 0.0429564 | 0.0214782 | − | 0.999769i | \(-0.493163\pi\) | ||||
0.0214782 | + | 0.999769i | \(0.493163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 127.196 | 0.411637 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 393.211i | − | 1.26434i | −0.774829 | − | 0.632171i | \(-0.782164\pi\) | ||
0.774829 | − | 0.632171i | \(-0.217836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 221.694 | 0.708287 | 0.354143 | − | 0.935191i | \(-0.384772\pi\) | ||||
0.354143 | + | 0.935191i | \(0.384772\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 94.5685i | 0.298323i | 0.988813 | + | 0.149162i | \(0.0476575\pi\) | ||||
−0.988813 | + | 0.149162i | \(0.952342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −496.784 | −1.55732 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 553.893i | − | 1.72552i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 120.902i | 0.374308i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 248.541 | 0.760066 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.09841 | + | 1.92082i | −0.0215757 | + | 0.00583835i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −190.333 | −0.575024 | −0.287512 | − | 0.957777i | \(-0.592828\pi\) | ||||
−0.287512 | + | 0.957777i | \(0.592828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 111.490i | 0.334806i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 430.735i | 1.27815i | 0.769146 | + | 0.639073i | \(0.220682\pi\) | ||||
−0.769146 | + | 0.639073i | \(0.779318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 259.737i | 0.766185i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 278.323i | 0.816197i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −240.734 | + | 244.328i | −0.701848 | + | 0.712327i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 251.255i | 0.724077i | 0.932163 | + | 0.362039i | \(0.117919\pi\) | ||||
−0.932163 | + | 0.362039i | \(0.882081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 78.3487i | 0.224495i | 0.993680 | + | 0.112247i | \(0.0358049\pi\) | ||||
−0.993680 | + | 0.112247i | \(0.964195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 345.706 | 0.984916 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −43.9111 | −0.124394 | −0.0621970 | − | 0.998064i | \(-0.519811\pi\) | ||||
−0.0621970 | + | 0.998064i | \(0.519811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 152.893 | − | 41.3726i | 0.428272 | − | 0.115890i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −546.431 | −1.52209 | −0.761045 | − | 0.648699i | \(-0.775314\pi\) | ||||
−0.761045 | + | 0.648699i | \(0.775314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.8924 | −0.0800342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 207.891 | 0.572702 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 481.505 | 1.31200 | 0.656002 | − | 0.754759i | \(-0.272246\pi\) | ||||
0.656002 | + | 0.754759i | \(0.272246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 326.474i | − | 0.884753i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.1076 | + | 103.872i | 0.0757619 | + | 0.279979i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 432.843i | − | 1.16044i | −0.814461 | − | 0.580218i | \(-0.802967\pi\) | ||
0.814461 | − | 0.580218i | \(-0.197033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 803.702 | 2.13184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 512.607 | 1.35253 | 0.676263 | − | 0.736660i | \(-0.263598\pi\) | ||||
0.676263 | + | 0.736660i | \(0.263598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 346.508i | 0.909471i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 651.897 | 1.70208 | 0.851040 | − | 0.525100i | \(-0.175972\pi\) | ||||
0.851040 | + | 0.525100i | \(0.175972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 214.215i | − | 0.553528i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 523.352 | 1.34538 | 0.672689 | − | 0.739925i | \(-0.265139\pi\) | ||||
0.672689 | + | 0.739925i | \(0.265139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 175.284i | 0.448296i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 540.382i | 1.37502i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8513 | 0.0399276 | 0.0199638 | − | 0.999801i | \(-0.493645\pi\) | ||||
0.0199638 | + | 0.999801i | \(0.493645\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 133.421 | + | 493.061i | 0.334389 | + | 1.23574i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7746 | 0.0293631 | 0.0146816 | − | 0.999892i | \(-0.495327\pi\) | ||||
0.0146816 | + | 0.999892i | \(0.495327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 450.274i | − | 1.11731i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 318.745i | 0.783158i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 492.483i | 1.20411i | 0.798453 | + | 0.602057i | \(0.205652\pi\) | ||||
−0.798453 | + | 0.602057i | \(0.794348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 553.457i | 1.34661i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.2268 | + | 100.617i | 0.0659246 | + | 0.243625i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 444.382i | 1.06566i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 276.946i | 0.660970i | 0.943811 | + | 0.330485i | \(0.107212\pi\) | ||||
−0.943811 | + | 0.330485i | \(0.892788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3532 | 0.0340932 | 0.0170466 | − | 0.999855i | \(-0.494574\pi\) | ||||
0.0170466 | + | 0.999855i | \(0.494574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.89216 | 0.0115654 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −158.690 | − | 586.441i | −0.371639 | − | 1.37340i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1059.74 | −2.47027 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 250.471 | 0.581139 | 0.290570 | − | 0.956854i | \(-0.406155\pi\) | ||||
0.290570 | + | 0.956854i | \(0.406155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −656.534 | −1.51625 | −0.758123 | − | 0.652112i | \(-0.773883\pi\) | ||||
−0.758123 | + | 0.652112i | \(0.773883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −565.268 | −1.29352 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 356.398i | − | 0.811841i | −0.913908 | − | 0.405921i | \(-0.866951\pi\) | ||
0.913908 | − | 0.405921i | \(-0.133049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 197.049 | − | 115.068i | 0.446823 | − | 0.260924i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 253.785i | 0.572877i | 0.958099 | + | 0.286439i | \(0.0924715\pi\) | ||||
−0.958099 | + | 0.286439i | \(0.907529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −124.777 | −0.279144 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 107.921 | 0.240358 | 0.120179 | − | 0.992752i | \(-0.461653\pi\) | ||||
0.120179 | + | 0.992752i | \(0.461653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 933.372i | − | 2.06956i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 534.473 | 1.17985 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 143.990i | − | 0.315076i | −0.987513 | − | 0.157538i | \(-0.949644\pi\) | ||
0.987513 | − | 0.157538i | \(-0.0503557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 98.2742 | 0.214105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 380.728i | − | 0.825875i | −0.910759 | − | 0.412938i | \(-0.864503\pi\) | ||
0.910759 | − | 0.412938i | \(-0.135497\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 227.990i | − | 0.492419i | −0.969217 | − | 0.246209i | \(-0.920815\pi\) | ||
0.969217 | − | 0.246209i | \(-0.0791851\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 502.917 | 1.07691 | 0.538455 | − | 0.842654i | \(-0.319008\pi\) | ||||
0.538455 | + | 0.842654i | \(0.319008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 45.0294 | + | 166.407i | 0.0960116 | + | 0.354813i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −476.049 | −1.01072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 612.431i | − | 1.29478i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 71.5879i | − | 0.150079i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 212.637i | − | 0.443918i | −0.975056 | − | 0.221959i | \(-0.928755\pi\) | ||
0.975056 | − | 0.221959i | \(-0.0712451\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 515.669i | − | 1.07208i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 193.435 | + | 714.843i | 0.400487 | + | 1.48001i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 121.411i | 0.249304i | 0.992200 | + | 0.124652i | \(0.0397815\pi\) | ||||
−0.992200 | + | 0.124652i | \(0.960218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 212.239i | 0.434027i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −130.353 | −0.265485 | −0.132743 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 228.469 | 0.463427 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 304.263 | − | 82.3330i | 0.612200 | − | 0.165660i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −157.980 | −0.316593 | −0.158296 | − | 0.987392i | \(-0.550600\pi\) | ||||
−0.158296 | + | 0.987392i | \(0.550600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −846.725 | −1.69007 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −323.502 | −0.643146 | −0.321573 | − | 0.946885i | \(-0.604212\pi\) | ||||
−0.321573 | + | 0.946885i | \(0.604212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1089.92 | 2.14975 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 505.723i | 0.993563i | 0.867876 | + | 0.496781i | \(0.165485\pi\) | ||||
−0.867876 | + | 0.496781i | \(0.834515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 349.588 | − | 94.5978i | 0.684125 | − | 0.185123i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 316.922i | 0.617781i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9864 | 0.0270531 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 455.696 | 0.878026 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 827.833i | 1.58893i | 0.607309 | + | 0.794466i | \(0.292249\pi\) | ||||
−0.607309 | + | 0.794466i | \(0.707751\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 114.306 | 0.218559 | 0.109279 | − | 0.994011i | \(-0.465146\pi\) | ||||
0.109279 | + | 0.994011i | \(0.465146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 128.000i | − | 0.242884i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −290.529 | −0.549204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 69.3446i | − | 0.130592i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1510.02i | 2.83306i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1004.96 | 1.87144 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 563.352 | − | 328.973i | 1.04518 | − | 0.610339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 529.098 | 0.978001 | 0.489000 | − | 0.872284i | \(-0.337362\pi\) | ||||
0.489000 | + | 0.872284i | \(0.337362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 113.206i | − | 0.208483i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 281.314i | 0.514285i | 0.966374 | + | 0.257142i | \(0.0827809\pi\) | ||||
−0.966374 | + | 0.257142i | \(0.917219\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 404.170i | 0.736193i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 736.785i | 1.33718i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −227.817 | + | 61.6468i | −0.411965 | + | 0.111477i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 198.471i | 0.356321i | 0.984001 | + | 0.178161i | \(0.0570147\pi\) | ||||
−0.984001 | + | 0.178161i | \(0.942985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 990.797i | 1.77244i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −301.255 | −0.536996 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −98.2933 | −0.174588 | −0.0872942 | − | 0.996183i | \(-0.527822\pi\) | ||||
−0.0872942 | + | 0.996183i | \(0.527822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 683.979 | − | 185.083i | 1.20631 | − | 0.326426i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 709.029 | 1.24610 | 0.623049 | − | 0.782183i | \(-0.285894\pi\) | ||||
0.623049 | + | 0.782183i | \(0.285894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 462.118 | 0.809313 | 0.404657 | − | 0.914469i | \(-0.367391\pi\) | ||||
0.404657 | + | 0.914469i | \(0.367391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −257.201 | −0.448867 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 586.571 | 1.01659 | 0.508294 | − | 0.861184i | \(-0.330276\pi\) | ||||
0.508294 | + | 0.861184i | \(0.330276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1032.61i | 1.78343i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 522.912 | − | 141.499i | 0.900020 | − | 0.243544i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 204.666i | − | 0.351057i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −441.613 | −0.752322 | −0.376161 | − | 0.926554i | \(-0.622756\pi\) | ||||
−0.376161 | + | 0.926554i | \(0.622756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 412.784 | 0.700821 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 378.609i | − | 0.640624i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 87.0265 | 0.146756 | 0.0733782 | − | 0.997304i | \(-0.476622\pi\) | ||||
0.0733782 | + | 0.997304i | \(0.476622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 598.489i | 1.00249i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −484.108 | −0.808193 | −0.404097 | − | 0.914716i | \(-0.632414\pi\) | ||||
−0.404097 | + | 0.914716i | \(0.632414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 904.895i | − | 1.50565i | −0.658221 | − | 0.752825i | \(-0.728691\pi\) | ||
0.658221 | − | 0.752825i | \(-0.271309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 114.686i | − | 0.190193i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −940.980 | −1.55021 | −0.775107 | − | 0.631830i | \(-0.782304\pi\) | ||||
−0.775107 | + | 0.631830i | \(0.782304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 931.744 | − | 252.128i | 1.52996 | − | 0.414004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6274 | −0.0370334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 240.627i | 0.392541i | 0.980550 | + | 0.196270i | \(0.0628830\pi\) | ||||
−0.980550 | + | 0.196270i | \(0.937117\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 781.716i | − | 1.26696i | −0.773758 | − | 0.633481i | \(-0.781625\pi\) | ||
0.773758 | − | 0.633481i | \(-0.218375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.99870i | − | 0.0161530i | −0.999967 | − | 0.00807649i | \(-0.997429\pi\) | ||
0.999967 | − | 0.00807649i | \(-0.00257085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 459.475i | 0.739895i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 144.016 | + | 532.215i | 0.231166 | + | 0.854278i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 971.509i | − | 1.54946i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 146.590i | − | 0.233052i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 908.538 | 1.43984 | 0.719919 | − | 0.694058i | \(-0.244179\pi\) | ||||
0.719919 | + | 0.694058i | \(0.244179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −188.543 | −0.297856 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −911.397 | + | 532.215i | −1.43077 | + | 0.835503i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −209.696 | −0.328162 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 193.460 | 0.301810 | 0.150905 | − | 0.988548i | \(-0.451781\pi\) | ||||
0.150905 | + | 0.988548i | \(0.451781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 362.412 | 0.563627 | 0.281814 | − | 0.959469i | \(-0.409064\pi\) | ||||
0.281814 | + | 0.959469i | \(0.409064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −359.625 | −0.555834 | −0.277917 | − | 0.960605i | \(-0.589644\pi\) | ||||
−0.277917 | + | 0.960605i | \(0.589644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 198.253i | − | 0.305474i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −141.255 | − | 522.010i | −0.216981 | − | 0.801858i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 715.685i | − | 1.09600i | −0.836480 | − | 0.547998i | \(-0.815390\pi\) | ||
0.836480 | − | 0.547998i | \(-0.184610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −240.933 | −0.366717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 390.431 | 0.592459 | 0.296230 | − | 0.955117i | \(-0.404271\pi\) | ||||
0.296230 | + | 0.955117i | \(0.404271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 350.474i | 0.530218i | 0.964218 | + | 0.265109i | \(0.0854080\pi\) | ||||
−0.964218 | + | 0.265109i | \(0.914592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 487.373 | 0.735103 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1068.20i | 1.60149i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −817.803 | −1.22243 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1155.50i | 1.72206i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 487.214i | 0.723944i | 0.932189 | + | 0.361972i | \(0.117896\pi\) | ||||
−0.932189 | + | 0.361972i | \(0.882104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 451.742 | 0.667271 | 0.333635 | − | 0.942702i | \(-0.391725\pi\) | ||||
0.333635 | + | 0.942702i | \(0.391725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 609.332 | − | 164.884i | 0.897396 | − | 0.242834i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −373.421 | −0.548343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 224.745i | − | 0.329056i | −0.986372 | − | 0.164528i | \(-0.947390\pi\) | ||
0.986372 | − | 0.164528i | \(-0.0526101\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 628.950i | − | 0.915503i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 331.111i | 0.480567i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 56.0855i | − | 0.0811657i | −0.999176 | − | 0.0405828i | \(-0.987079\pi\) | ||
0.999176 | − | 0.0405828i | \(-0.0129215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −418.933 | + | 113.362i | −0.604521 | + | 0.163582i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 429.255i | 0.615861i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1666.75i | − | 2.38448i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −769.647 | −1.09793 | −0.548963 | − | 0.835846i | \(-0.684977\pi\) | ||||
−0.548963 | + | 0.835846i | \(0.684977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 472.734 | 0.672452 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 237.057 | + | 876.049i | 0.335300 | + | 1.23911i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −465.960 | −0.657207 | −0.328603 | − | 0.944468i | \(-0.606578\pi\) | ||||
−0.328603 | + | 0.944468i | \(0.606578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 157.009 | 0.220829 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 598.456 | 0.839350 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −809.825 | −1.12946 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1051.88i | − | 1.46298i | −0.681852 | − | 0.731490i | \(-0.738825\pi\) | ||
0.681852 | − | 0.731490i | \(-0.261175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −232.569 | + | 62.9326i | −0.322564 | + | 0.0872852i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1202.47i | − | 1.66317i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 161.080 | 0.221568 | 0.110784 | − | 0.993845i | \(-0.464664\pi\) | ||||
0.110784 | + | 0.993845i | \(0.464664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 62.4315 | 0.0856399 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 281.655i | 0.385301i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1438.70 | −1.96275 | −0.981376 | − | 0.192097i | \(-0.938471\pi\) | ||||
−0.981376 | + | 0.192097i | \(0.938471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 327.882i | − | 0.444888i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1137.39 | −1.53909 | −0.769547 | − | 0.638590i | \(-0.779518\pi\) | ||||
−0.769547 | + | 0.638590i | \(0.779518\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1571.72i | 2.12108i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 745.882i | − | 1.00388i | −0.864903 | − | 0.501940i | \(-0.832620\pi\) | ||
0.864903 | − | 0.501940i | \(-0.167380\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −360.386 | −0.482445 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 274.049 | + | 1012.75i | 0.365886 | + | 1.35214i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −153.882 | −0.204903 | −0.102452 | − | 0.994738i | \(-0.532669\pi\) | ||||
−0.102452 | + | 0.994738i | \(0.532669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 961.068i | 1.27632i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 119.137i | 0.157381i | 0.996899 | + | 0.0786903i | \(0.0250738\pi\) | ||||
−0.996899 | + | 0.0786903i | \(0.974926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1408.50i | − | 1.85573i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1385.20i | − | 1.82024i | −0.414348 | − | 0.910119i | \(-0.635990\pi\) | ||
0.414348 | − | 0.910119i | \(-0.364010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −454.440 | + | 122.971i | −0.595596 | + | 0.161167i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 320.735i | 0.418168i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 55.9020i | 0.0726945i | 0.999339 | + | 0.0363472i | \(0.0115722\pi\) | ||||
−0.999339 | + | 0.0363472i | \(0.988428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 682.039 | 0.884616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 179.759 | 0.232548 | 0.116274 | − | 0.993217i | \(-0.462905\pi\) | ||||
0.116274 | + | 0.993217i | \(0.462905\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −161.770 | − | 597.823i | −0.208198 | − | 0.769399i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1384.29 | −1.77701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −599.509 | −0.767617 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 598.892 | 0.764868 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −208.363 | −0.264756 | −0.132378 | − | 0.991199i | \(-0.542261\pi\) | ||||
−0.132378 | + | 0.991199i | \(0.542261\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 912.249i | 1.15621i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −128.510 | − | 474.910i | −0.162465 | − | 0.600392i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1869.38i | − | 2.35735i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 237.327 | 0.297776 | 0.148888 | − | 0.988854i | \(-0.452431\pi\) | ||||
0.148888 | + | 0.988854i | \(0.452431\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.43232 | −0.00805047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 366.798i | − | 0.457925i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −688.815 | −0.857802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 388.617i | − | 0.481558i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −513.793 | −0.635097 | −0.317548 | − | 0.948242i | \(-0.602860\pi\) | ||||
−0.317548 | + | 0.948242i | \(0.602860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 452.373i | − | 0.557797i | −0.960321 | − | 0.278898i | \(-0.910031\pi\) | ||
0.960321 | − | 0.278898i | \(-0.0899692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 265.373i | − | 0.326412i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −908.302 | −1.11175 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 677.754 | − | 183.399i | 0.827539 | − | 0.223930i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1441.04 | −1.75522 | −0.877611 | − | 0.479373i | \(-0.840864\pi\) | ||||
−0.877611 | + | 0.479373i | \(0.840864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1603.66i | − | 1.94855i | −0.225362 | − | 0.974275i | \(-0.572356\pi\) | ||
0.225362 | − | 0.974275i | \(-0.427644\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 933.549i | − | 1.12884i | −0.825488 | − | 0.564419i | \(-0.809100\pi\) | ||
0.825488 | − | 0.564419i | \(-0.190900\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 418.809i | − | 0.505198i | −0.967571 | − | 0.252599i | \(-0.918715\pi\) | ||
0.967571 | − | 0.252599i | \(-0.0812853\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1485.96i | − | 1.78816i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −259.084 | + | 151.294i | −0.311025 | + | 0.181625i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 335.529i | − | 0.400871i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 995.689i | 1.18676i | 0.804924 | + | 0.593378i | \(0.202206\pi\) | ||||
−0.804924 | + | 0.593378i | \(0.797794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 551.313 | 0.655544 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1188.22 | 1.40951 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −380.113 | + | 102.858i | −0.448776 | + | 0.121438i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1794.40 | −2.11355 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 685.373 | 0.805373 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −315.117 | −0.369422 | −0.184711 | − | 0.982793i | \(-0.559135\pi\) | ||||
−0.184711 | + | 0.982793i | \(0.559135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 218.287 | 0.254711 | 0.127355 | − | 0.991857i | \(-0.459351\pi\) | ||||
0.127355 | + | 0.991857i | \(0.459351\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1441.76i | − | 1.67842i | −0.543811 | − | 0.839208i | \(-0.683019\pi\) | ||
0.543811 | − | 0.839208i | \(-0.316981\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 473.706 | + | 1750.59i | 0.550181 | + | 2.03320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 874.873i | 1.01376i | 0.862017 | + | 0.506879i | \(0.169201\pi\) | ||||
−0.862017 | + | 0.506879i | \(0.830799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −929.459 | −1.07204 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 448.881 | 0.516549 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 530.451i | 0.609014i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −419.946 | −0.481038 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1702.65i | − | 1.94144i | −0.240207 | − | 0.970722i | \(-0.577215\pi\) | ||
0.240207 | − | 0.970722i | \(-0.422785\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1774.66 | 2.01895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1018.58i | − | 1.15617i | −0.815978 | − | 0.578083i | \(-0.803801\pi\) | ||
0.815978 | − | 0.578083i | \(-0.196199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1646.04i | 1.86414i | 0.362276 | + | 0.932071i | \(0.382000\pi\) | ||||
−0.362276 | + | 0.932071i | \(0.618000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −688.597 | −0.776321 | −0.388161 | − | 0.921592i | \(-0.626889\pi\) | ||||
−0.388161 | + | 0.921592i | \(0.626889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −171.442 | − | 633.565i | −0.192848 | − | 0.712672i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1347.69 | −1.51255 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 20.7434i | − | 0.0232289i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2278.68i | 2.54034i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 780.043i | − | 0.867679i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 94.1253i | 0.104468i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 310.821 | + | 1148.65i | 0.344210 | + | 1.27203i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 212.018i | 0.233758i | 0.993146 | + | 0.116879i | \(0.0372890\pi\) | ||||
−0.993146 | + | 0.116879i | \(0.962711\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 603.765i | − | 0.664208i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −601.882 | −0.660683 | −0.330342 | − | 0.943861i | \(-0.607164\pi\) | ||||
−0.330342 | + | 0.943861i | \(0.607164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1030.33 | −1.12851 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −267.364 | − | 988.049i | −0.291564 | − | 1.07748i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1118.34 | −1.21691 | −0.608456 | − | 0.793588i | \(-0.708211\pi\) | ||||
−0.608456 | + | 0.793588i | \(0.708211\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.7351 | 0.0529154 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 969.892 | 1.05080 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 160.284 | 0.172906 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 401.907i | − | 0.432623i | −0.976324 | − | 0.216312i | \(-0.930597\pi\) | ||
0.976324 | − | 0.216312i | \(-0.0694027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −487.902 | − | 835.513i | −0.524063 | − | 0.897437i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1453.12i | − | 1.55747i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1597.84 | 1.70527 | 0.852635 | − | 0.522507i | \(-0.175003\pi\) | ||||
0.852635 | + | 0.522507i | \(0.175003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 819.273 | 0.872496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1537.71i | 1.63413i | 0.576547 | + | 0.817064i | \(0.304400\pi\) | ||||
−0.576547 | + | 0.817064i | \(0.695600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2006.96 | −2.12827 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 320.274i | 0.338199i | 0.985599 | + | 0.169099i | \(0.0540859\pi\) | ||||
−0.985599 | + | 0.169099i | \(0.945914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1114.37 | 1.17426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 349.480i | 0.367487i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 734.861i | − | 0.771103i | −0.922686 | − | 0.385552i | \(-0.874011\pi\) | ||
0.922686 | − | 0.385552i | \(-0.125989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1835.87 | −1.91836 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −273.833 | − | 1011.96i | −0.285541 | − | 1.05522i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 523.981 | 0.545245 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 697.980i | − | 0.724797i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1446.98i | − | 1.49636i | −0.663497 | − | 0.748179i | \(-0.730928\pi\) | ||
0.663497 | − | 0.748179i | \(-0.269072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 446.794i | 0.461088i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 966.084i | − | 0.994937i | −0.867482 | − | 0.497469i | \(-0.834263\pi\) | ||
0.867482 | − | 0.497469i | \(-0.165737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −219.866 | − | 812.520i | −0.225967 | − | 0.835067i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 609.606i | 0.623957i | 0.950089 | + | 0.311979i | \(0.100992\pi\) | ||||
−0.950089 | + | 0.311979i | \(0.899008\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1048.66i | − | 1.07115i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 313.196 | 0.319262 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1277.27 | 1.29936 | 0.649679 | − | 0.760209i | \(-0.274903\pi\) | ||||
0.649679 | + | 0.760209i | \(0.274903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.2323 | + | 7.09841i | −0.0265778 | + | 0.00719191i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1316.86 | −1.33151 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1669.99 | −1.68515 | −0.842577 | − | 0.538575i | \(-0.818963\pi\) | ||||
−0.842577 | + | 0.538575i | \(0.818963\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −703.379 | −0.708338 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −789.952 | −0.792329 | −0.396164 | − | 0.918180i | \(-0.629659\pi\) | ||||
−0.396164 | + | 0.918180i | \(0.629659\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 384.259i | − | 0.384644i |
(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 | 1400.3.p.a.1049.8 | 8 | ||
5.2 | odd | 4 | 56.3.c.a.41.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1400.3.f.a.601.4 | 4 | |||
5.4 | even | 2 | inner | 1400.3.p.a.1049.1 | 8 | ||
7.6 | odd | 2 | inner | 1400.3.p.a.1049.2 | 8 | ||
15.2 | even | 4 | 504.3.f.a.433.3 | 4 | |||
20.7 | even | 4 | 112.3.c.c.97.4 | 4 | |||
35.2 | odd | 12 | 392.3.o.b.129.4 | 8 | |||
35.12 | even | 12 | 392.3.o.b.129.1 | 8 | |||
35.13 | even | 4 | 1400.3.f.a.601.1 | 4 | |||
35.17 | even | 12 | 392.3.o.b.313.4 | 8 | |||
35.27 | even | 4 | 56.3.c.a.41.4 | yes | 4 | ||
35.32 | odd | 12 | 392.3.o.b.313.1 | 8 | |||
35.34 | odd | 2 | inner | 1400.3.p.a.1049.7 | 8 | ||
40.27 | even | 4 | 448.3.c.e.321.1 | 4 | |||
40.37 | odd | 4 | 448.3.c.f.321.4 | 4 | |||
60.47 | odd | 4 | 1008.3.f.h.433.3 | 4 | |||
105.62 | odd | 4 | 504.3.f.a.433.2 | 4 | |||
140.27 | odd | 4 | 112.3.c.c.97.1 | 4 | |||
140.47 | odd | 12 | 784.3.s.f.129.4 | 8 | |||
140.67 | even | 12 | 784.3.s.f.705.4 | 8 | |||
140.87 | odd | 12 | 784.3.s.f.705.1 | 8 | |||
140.107 | even | 12 | 784.3.s.f.129.1 | 8 | |||
280.27 | odd | 4 | 448.3.c.e.321.4 | 4 | |||
280.237 | even | 4 | 448.3.c.f.321.1 | 4 | |||
420.167 | even | 4 | 1008.3.f.h.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.c.a.41.1 | ✓ | 4 | 5.2 | odd | 4 | ||
56.3.c.a.41.4 | yes | 4 | 35.27 | even | 4 | ||
112.3.c.c.97.1 | 4 | 140.27 | odd | 4 | |||
112.3.c.c.97.4 | 4 | 20.7 | even | 4 | |||
392.3.o.b.129.1 | 8 | 35.12 | even | 12 | |||
392.3.o.b.129.4 | 8 | 35.2 | odd | 12 | |||
392.3.o.b.313.1 | 8 | 35.32 | odd | 12 | |||
392.3.o.b.313.4 | 8 | 35.17 | even | 12 | |||
448.3.c.e.321.1 | 4 | 40.27 | even | 4 | |||
448.3.c.e.321.4 | 4 | 280.27 | odd | 4 | |||
448.3.c.f.321.1 | 4 | 280.237 | even | 4 | |||
448.3.c.f.321.4 | 4 | 40.37 | odd | 4 | |||
504.3.f.a.433.2 | 4 | 105.62 | odd | 4 | |||
504.3.f.a.433.3 | 4 | 15.2 | even | 4 | |||
784.3.s.f.129.1 | 8 | 140.107 | even | 12 | |||
784.3.s.f.129.4 | 8 | 140.47 | odd | 12 | |||
784.3.s.f.705.1 | 8 | 140.87 | odd | 12 | |||
784.3.s.f.705.4 | 8 | 140.67 | even | 12 | |||
1008.3.f.h.433.2 | 4 | 420.167 | even | 4 | |||
1008.3.f.h.433.3 | 4 | 60.47 | odd | 4 | |||
1400.3.f.a.601.1 | 4 | 35.13 | even | 4 | |||
1400.3.f.a.601.4 | 4 | 5.3 | odd | 4 | |||
1400.3.p.a.1049.1 | 8 | 5.4 | even | 2 | inner | ||
1400.3.p.a.1049.2 | 8 | 7.6 | odd | 2 | inner | ||
1400.3.p.a.1049.7 | 8 | 35.34 | odd | 2 | inner | ||
1400.3.p.a.1049.8 | 8 | 1.1 | even | 1 | trivial |