Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [528,2,Mod(175,528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(528, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("528.175");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.o (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: | \(4.21610122672\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.454201344.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 4x^{6} + 24x^{5} - 25x^{4} - 12x^{3} + 128x^{2} - 182x + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 175.7 | ||
Root | \(1.02715 - 1.10132i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 528.175 |
Dual form | 528.2.o.b.175.3 |
$q$-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 \(\left(\mathbb{Z}/528\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(145\) | \(353\) | \(463\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73205 | 1.22181 | 0.610905 | − | 0.791704i | \(-0.290806\pi\) | ||||
0.610905 | + | 0.791704i | \(0.290806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.13734 | −1.94173 | −0.970867 | − | 0.239620i | \(-0.922977\pi\) | ||||
−0.970867 | + | 0.239620i | \(0.922977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.88040 | + | 2.73205i | 0.566961 | + | 0.823744i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.13734i | 1.42484i | 0.701752 | + | 0.712421i | \(0.252402\pi\) | ||||
−0.701752 | + | 0.712421i | \(0.747598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.73205i | 0.705412i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.76080i | 0.912127i | 0.889947 | + | 0.456064i | \(0.150741\pi\) | ||||
−0.889947 | + | 0.456064i | \(0.849259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.76080 | 0.862786 | 0.431393 | − | 0.902164i | \(-0.358022\pi\) | ||||
0.431393 | + | 0.902164i | \(0.358022\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.13734i | − | 1.12106i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.26795i | 0.264386i | 0.991224 | + | 0.132193i | \(0.0422018\pi\) | ||||
−0.991224 | + | 0.132193i | \(0.957798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.46410 | 0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.73205 | + | 1.88040i | −0.475589 | + | 0.327335i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.0355 | −2.37243 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.535898 | 0.0881012 | 0.0440506 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440506 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.13734 | −0.822633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.2747i | − | 1.60464i | −0.596896 | − | 0.802318i | \(-0.703600\pi\) | ||
0.596896 | − | 0.802318i | \(-0.296400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.76080 | 0.573516 | 0.286758 | − | 0.958003i | \(-0.407422\pi\) | ||||
0.286758 | + | 0.958003i | \(0.407422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.73205 | −0.407270 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.19615i | 0.612072i | 0.952020 | + | 0.306036i | \(0.0990028\pi\) | ||||
−0.952020 | + | 0.306036i | \(0.900997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.3923 | 2.77033 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.76080 | −0.526617 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7321 | −1.47416 | −0.737080 | − | 0.675805i | \(-0.763796\pi\) | ||||
−0.737080 | + | 0.675805i | \(0.763796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.13734 | + | 7.46410i | 0.692719 | + | 1.00646i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.76080i | 0.498130i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.46410i | 1.23212i | 0.787699 | + | 0.616061i | \(0.211272\pi\) | ||||
−0.787699 | + | 0.616061i | \(0.788728\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.38425i | − | 0.305272i | −0.988282 | − | 0.152636i | \(-0.951224\pi\) | ||
0.988282 | − | 0.152636i | \(-0.0487762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.13734 | 0.647245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.0355i | 1.74089i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.3923i | − | 1.26962i | −0.772667 | − | 0.634811i | \(-0.781078\pi\) | ||
0.772667 | − | 0.634811i | \(-0.218922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.26795 | −0.152643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.7321i | − | 1.27366i | −0.771004 | − | 0.636830i | \(-0.780245\pi\) | ||
0.771004 | − | 0.636830i | \(-0.219755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2747i | 1.20256i | 0.799038 | + | 0.601281i | \(0.205343\pi\) | ||||
−0.799038 | + | 0.601281i | \(0.794657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.46410i | 0.284530i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.66025 | − | 14.0355i | −1.10089 | − | 1.59949i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.13734 | 0.577996 | 0.288998 | − | 0.957330i | \(-0.406678\pi\) | ||||
0.288998 | + | 0.957330i | \(0.406678\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2747 | 1.12779 | 0.563897 | − | 0.825845i | \(-0.309302\pi\) | ||||
0.563897 | + | 0.825845i | \(0.309302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2747i | 1.11445i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 26.3923i | − | 2.76667i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2747 | 1.05416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.46410 | 0.554795 | 0.277398 | − | 0.960755i | \(-0.410528\pi\) | ||||
0.277398 | + | 0.960755i | \(0.410528\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.88040 | − | 2.73205i | −0.188987 | − | 0.274581i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 17.7963i | − | 1.77080i | −0.464833 | − | 0.885398i | \(-0.653886\pi\) | ||
0.464833 | − | 0.885398i | \(-0.346114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.0000i | − | 0.985329i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) | ||
0.870219 | − | 0.492665i | \(-0.163977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 14.0355i | − | 1.36972i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.76080 | −0.363570 | −0.181785 | − | 0.983338i | \(-0.558187\pi\) | ||||
−0.181785 | + | 0.983338i | \(0.558187\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.6589i | − | 1.21251i | −0.795272 | − | 0.606253i | \(-0.792672\pi\) | ||
0.795272 | − | 0.606253i | \(-0.207328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.535898i | 0.0508652i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3205 | 1.62938 | 0.814688 | − | 0.579899i | \(-0.196908\pi\) | ||||
0.814688 | + | 0.579899i | \(0.196908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.46410i | 0.323029i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.13734i | − | 0.474948i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 19.3205i | − | 1.77111i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.92820 | + | 10.2747i | −0.357109 | + | 0.934063i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2747 | 0.926437 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.13734 | −0.455866 | −0.227933 | − | 0.973677i | \(-0.573197\pi\) | ||||
−0.227933 | + | 0.973677i | \(0.573197\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.76080i | 0.331120i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.75309 | 0.240539 | 0.120269 | − | 0.992741i | \(-0.461624\pi\) | ||||
0.120269 | + | 0.992741i | \(0.461624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.3205 | −1.67530 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 2.73205i | − | 0.235137i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.92820 | 0.421045 | 0.210522 | − | 0.977589i | \(-0.432484\pi\) | ||||
0.210522 | + | 0.977589i | \(0.432484\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0355 | 1.19047 | 0.595237 | − | 0.803550i | \(-0.297058\pi\) | ||||
0.595237 | + | 0.803550i | \(0.297058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.19615 | −0.353380 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.0355 | + | 9.66025i | −1.17371 | + | 0.807831i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.3923i | 1.59945i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7963i | 1.45793i | 0.684552 | + | 0.728964i | \(0.259998\pi\) | ||||
−0.684552 | + | 0.728964i | \(0.740002\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.38425 | −0.194027 | −0.0970137 | − | 0.995283i | \(-0.530929\pi\) | ||||
−0.0970137 | + | 0.995283i | \(0.530929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.76080i | − | 0.304042i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.46410i | 0.438887i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8564 | 0.946244 | 0.473122 | − | 0.880997i | \(-0.343127\pi\) | ||||
0.473122 | + | 0.880997i | \(0.343127\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 10.7321i | − | 0.851107i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.51389i | − | 0.513367i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.92820i | 0.229355i | 0.993403 | + | 0.114677i | \(0.0365834\pi\) | ||||
−0.993403 | + | 0.114677i | \(0.963417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.46410 | + | 5.13734i | −0.581080 | + | 0.399942i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7963 | 1.37712 | 0.688559 | − | 0.725180i | \(-0.258244\pi\) | ||||
0.688559 | + | 0.725180i | \(0.258244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.3923 | −1.03018 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.76080 | −0.287595 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0278i | 0.990484i | 0.868755 | + | 0.495242i | \(0.164921\pi\) | ||||
−0.868755 | + | 0.495242i | \(0.835079\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.6589 | −0.956926 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.46410 | −0.711365 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.392305i | 0.0293222i | 0.999893 | + | 0.0146611i | \(0.00466695\pi\) | ||||
−0.999893 | + | 0.0146611i | \(0.995333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.39230 | 0.177819 | 0.0889093 | − | 0.996040i | \(-0.471662\pi\) | ||||
0.0889093 | + | 0.996040i | \(0.471662\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.38425 | 0.176249 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.46410 | 0.107643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.2747 | + | 7.07180i | −0.751360 | + | 0.517141i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.13734i | 0.373687i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.1244i | − | 0.804930i | −0.915435 | − | 0.402465i | \(-0.868153\pi\) | ||
0.915435 | − | 0.402465i | \(-0.131847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.0278i | − | 0.937760i | −0.883262 | − | 0.468880i | \(-0.844658\pi\) | ||
0.883262 | − | 0.468880i | \(-0.155342\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.0355 | −1.00510 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.75309i | − | 0.196150i | −0.995179 | − | 0.0980749i | \(-0.968732\pi\) | ||
0.995179 | − | 0.0980749i | \(-0.0312685\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.4641i | 1.66333i | 0.555281 | + | 0.831663i | \(0.312611\pi\) | ||||
−0.555281 | + | 0.831663i | \(0.687389\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3923 | 0.733017 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 28.0710i | − | 1.96056i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.26795i | − | 0.0881286i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.07180 | + | 10.2747i | 0.489166 | + | 0.710715i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5571 | 1.48405 | 0.742025 | − | 0.670372i | \(-0.233865\pi\) | ||||
0.742025 | + | 0.670372i | \(0.233865\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.7321 | 0.735348 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.2747 | 0.700728 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.2747i | − | 0.697491i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2747 | −0.694299 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.3205 | −1.29964 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.4641i | − | 0.767693i | −0.923397 | − | 0.383847i | \(-0.874599\pi\) | ||
0.923397 | − | 0.383847i | \(-0.125401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7886 | −1.11430 | −0.557149 | − | 0.830413i | \(-0.688105\pi\) | ||||
−0.557149 | + | 0.830413i | \(0.688105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.8564 | 1.57648 | 0.788238 | − | 0.615371i | \(-0.210994\pi\) | ||||
0.788238 | + | 0.615371i | \(0.210994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.0355 | − | 9.66025i | 0.923467 | − | 0.635598i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.2747i | − | 0.673117i | −0.941663 | − | 0.336559i | \(-0.890737\pi\) | ||
0.941663 | − | 0.336559i | \(-0.109263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4641i | 0.747836i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.13734i | 0.333706i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.3025 | −1.50731 | −0.753656 | − | 0.657269i | \(-0.771711\pi\) | ||||
−0.753656 | + | 0.657269i | \(0.771711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.0710i | 1.80821i | 0.427310 | + | 0.904105i | \(0.359461\pi\) | ||||
−0.427310 | + | 0.904105i | \(0.640539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 52.9808 | 3.38482 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.3205i | 1.22933i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2747i | 0.651132i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.8564i | − | 1.37956i | −0.724017 | − | 0.689782i | \(-0.757706\pi\) | ||
0.724017 | − | 0.689782i | \(-0.242294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.46410 | + | 2.38425i | −0.217786 | + | 0.149896i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.2747 | −0.643426 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.4641 | −0.964624 | −0.482312 | − | 0.875999i | \(-0.660203\pi\) | ||||
−0.482312 | + | 0.875999i | \(0.660203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.75309 | −0.171069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.76850 | 0.294038 | 0.147019 | − | 0.989134i | \(-0.453032\pi\) | ||||
0.147019 | + | 0.989134i | \(0.453032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.3205 | −1.80114 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 10.3923i | − | 0.635999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.875644 | −0.0533890 | −0.0266945 | − | 0.999644i | \(-0.508498\pi\) | ||||
−0.0266945 | + | 0.999644i | \(0.508498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.38425 | −0.144833 | −0.0724164 | − | 0.997374i | \(-0.523071\pi\) | ||||
−0.0724164 | + | 0.997374i | \(0.523071\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.3923 | 1.59733 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.63349 | + | 6.73205i | 0.279410 | + | 0.405958i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.90584i | 0.595184i | 0.954693 | + | 0.297592i | \(0.0961836\pi\) | ||||
−0.954693 | + | 0.297592i | \(0.903816\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.00000i | − | 0.119737i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.26699i | 0.552822i | 0.961040 | + | 0.276411i | \(0.0891451\pi\) | ||||
−0.961040 | + | 0.276411i | \(0.910855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0355 | −0.834323 | −0.417161 | − | 0.908832i | \(-0.636975\pi\) | ||||
−0.417161 | + | 0.908832i | \(0.636975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.2747i | 0.608620i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 52.7846i | 3.11578i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.85641 | 0.168024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.46410i | 0.320311i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.5494i | 1.20051i | 0.799810 | + | 0.600254i | \(0.204934\pi\) | ||||
−0.799810 | + | 0.600254i | \(0.795066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.8564i | 1.50542i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.73205 | − | 1.88040i | 0.158530 | − | 0.109112i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.51389 | −0.376708 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.3205 | −1.11362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.7963 | 1.02237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.51389i | − | 0.372984i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.51389 | −0.371767 | −0.185884 | − | 0.982572i | \(-0.559515\pi\) | ||||
−0.185884 | + | 0.982572i | \(0.559515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9808i | 1.18971i | 0.803833 | + | 0.594855i | \(0.202791\pi\) | ||||
−0.803833 | + | 0.594855i | \(0.797209\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8564 | 0.670164 | 0.335082 | − | 0.942189i | \(-0.391236\pi\) | ||||
0.335082 | + | 0.942189i | \(0.391236\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.0355 | 0.790810 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.66025 | 0.542574 | 0.271287 | − | 0.962499i | \(-0.412551\pi\) | ||||
0.271287 | + | 0.962499i | \(0.412551\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3.76080i | − | 0.209907i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.1436i | 0.786971i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6589i | 0.702192i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.6589 | 0.700041 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 21.5571i | − | 1.18848i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.07180i | − | 0.0589113i | −0.999566 | − | 0.0294556i | \(-0.990623\pi\) | ||
0.999566 | − | 0.0294556i | \(-0.00937738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.535898 | −0.0293671 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 28.3923i | − | 1.55124i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.75309i | − | 0.149971i | −0.997185 | − | 0.0749853i | \(-0.976109\pi\) | ||
0.997185 | − | 0.0749853i | \(-0.0238910\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3205i | 0.940721i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.46410 | + | 3.76080i | −0.295898 | + | 0.203659i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −63.6635 | −3.43751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.46410 | −0.186501 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.8241 | −1.65472 | −0.827361 | − | 0.561670i | \(-0.810159\pi\) | ||||
−0.827361 | + | 0.561670i | \(0.810159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.89044i | − | 0.422365i | −0.977447 | − | 0.211183i | \(-0.932268\pi\) | ||
0.977447 | − | 0.211183i | \(-0.0677315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.13734 | 0.274211 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.14359 | 0.433440 | 0.216720 | − | 0.976234i | \(-0.430464\pi\) | ||||
0.216720 | + | 0.976234i | \(0.430464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 29.3205i | − | 1.55617i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.3205 | 1.02255 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.52159 | −0.396975 | −0.198487 | − | 0.980103i | \(-0.563603\pi\) | ||||
−0.198487 | + | 0.980103i | \(0.563603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.85641 | −0.255600 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2747 | − | 3.92820i | −0.539281 | − | 0.206177i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.0710i | 1.46930i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3923i | 0.542474i | 0.962513 | + | 0.271237i | \(0.0874327\pi\) | ||||
−0.962513 | + | 0.271237i | \(0.912567\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.2747i | 0.534879i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55.1342 | 2.86243 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.1651i | − | 0.940555i | −0.882519 | − | 0.470277i | \(-0.844154\pi\) | ||
0.882519 | − | 0.470277i | \(-0.155846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 6.92820i | − | 0.357771i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.92820i | − | 0.150412i | −0.997168 | − | 0.0752058i | \(-0.976039\pi\) | ||
0.997168 | − | 0.0752058i | \(-0.0239614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 5.13734i | − | 0.263194i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 20.9808i | − | 1.07207i | −0.844197 | − | 0.536033i | \(-0.819922\pi\) | ||
0.844197 | − | 0.536033i | \(-0.180078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.3923 | − | 38.3457i | −1.34508 | − | 1.95428i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.76080 | −0.191172 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.26795 | −0.0642876 | −0.0321438 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321438 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76850 | −0.241153 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.75309i | 0.138875i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0355 | 0.706202 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.3205 | −1.07005 | −0.535023 | − | 0.844838i | \(-0.679697\pi\) | ||||
−0.535023 | + | 0.844838i | \(0.679697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 19.3205i | − | 0.967235i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.46410 | 0.172989 | 0.0864945 | − | 0.996252i | \(-0.472434\pi\) | ||||
0.0864945 | + | 0.996252i | \(0.472434\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2747 | −0.511819 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.73205 | 0.135757 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00770 | + | 1.46410i | 0.0499500 | + | 0.0725728i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.3179i | − | 1.25189i | −0.779868 | − | 0.625944i | \(-0.784714\pi\) | ||
0.779868 | − | 0.625944i | \(-0.215286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.92820i | 0.243090i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 48.6203i | − | 2.39245i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.0710 | 1.37795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0355i | 0.687321i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.14359i | − | 0.300134i | −0.988676 | − | 0.150067i | \(-0.952051\pi\) | ||
0.988676 | − | 0.150067i | \(-0.0479490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32051 | 0.454254 | 0.227127 | − | 0.973865i | \(-0.427067\pi\) | ||||
0.227127 | + | 0.973865i | \(0.427067\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.19615i | − | 0.204024i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.26699i | 0.449515i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2487i | 0.592757i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.66025 | − | 14.0355i | −0.466401 | − | 0.677640i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3025 | 1.12244 | 0.561220 | − | 0.827666i | \(-0.310332\pi\) | ||||
0.561220 | + | 0.827666i | \(0.310332\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.9282 | −0.813518 | −0.406759 | − | 0.913536i | \(-0.633341\pi\) | ||||
−0.406759 | + | 0.913536i | \(0.633341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.76850i | 0.228108i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.4398 | 1.35736 | 0.678679 | − | 0.734435i | \(-0.262553\pi\) | ||||
0.678679 | + | 0.734435i | \(0.262553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3923 | −0.923443 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.14359i | − | 0.101845i | −0.998703 | − | 0.0509226i | \(-0.983784\pi\) | ||
0.998703 | − | 0.0509226i | \(-0.0162162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.3923 | −1.34592 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.7963 | −0.841735 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0718 | −0.711282 | −0.355641 | − | 0.934623i | \(-0.615737\pi\) | ||||
−0.355641 | + | 0.934623i | \(0.615737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.0710 | − | 19.3205i | 1.32181 | − | 0.909767i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 2.38425i | − | 0.112022i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 72.1051i | − | 3.38034i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.75309i | 0.128784i | 0.997925 | + | 0.0643922i | \(0.0205109\pi\) | ||||
−0.997925 | + | 0.0643922i | \(0.979489\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.76080 | 0.175539 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.50619i | 0.256449i | 0.991745 | + | 0.128224i | \(0.0409278\pi\) | ||||
−0.991745 | + | 0.128224i | \(0.959072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9282i | 1.53030i | 0.643850 | + | 0.765152i | \(0.277336\pi\) | ||||
−0.643850 | + | 0.765152i | \(0.722664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.46410 | −0.253392 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 9.46410i | − | 0.437946i | −0.975731 | − | 0.218973i | \(-0.929729\pi\) | ||
0.975731 | − | 0.218973i | \(-0.0702707\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 53.3888i | 2.46527i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8564i | 0.546314i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.07180 | + | 10.2747i | 0.325162 | + | 0.472431i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.26699 | 0.425198 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7321 | 0.491387 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2747 | −0.469462 | −0.234731 | − | 0.972060i | \(-0.575421\pi\) | ||||
−0.234731 | + | 0.972060i | \(0.575421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.75309i | 0.125530i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.51389 | 0.296392 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.9282 | 0.677855 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3923i | 0.833435i | 0.909036 | + | 0.416717i | \(0.136820\pi\) | ||||
−0.909036 | + | 0.416717i | \(0.863180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.92820 | −0.132418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.2824 | −0.509167 | −0.254584 | − | 0.967051i | \(-0.581938\pi\) | ||||
−0.254584 | + | 0.967051i | \(0.581938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.13734 | − | 7.46410i | −0.230906 | − | 0.335486i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 55.1342i | 2.47311i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0718i | 0.764239i | 0.924113 | + | 0.382119i | \(0.124806\pi\) | ||||
−0.924113 | + | 0.382119i | \(0.875194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7963i | 0.795079i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.75309 | 0.122754 | 0.0613772 | − | 0.998115i | \(-0.480451\pi\) | ||||
0.0613772 | + | 0.998115i | \(0.480451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 48.6203i | − | 2.16358i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 13.3923i | − | 0.594773i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.7321 | 1.18488 | 0.592439 | − | 0.805616i | \(-0.298165\pi\) | ||||
0.592439 | + | 0.805616i | \(0.298165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 52.7846i | − | 2.33505i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.76080i | − | 0.166043i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 27.3205i | − | 1.20389i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.4641 | + | 7.89044i | −0.504191 | + | 0.347021i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.0278 | −0.571856 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.3205 | −1.81028 | −0.905142 | − | 0.425109i | \(-0.860236\pi\) | ||||
−0.905142 | + | 0.425109i | \(0.860236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.3380 | 1.63267 | 0.816337 | − | 0.577575i | \(-0.196001\pi\) | ||||
0.816337 | + | 0.577575i | \(0.196001\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 12.6589i | − | 0.552481i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.52159 | −0.327646 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3923 | 0.930100 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.46410i | − | 0.410707i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.7846 | 2.28636 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2747 | −0.444214 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.392305 | −0.0169292 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.4653 | + | 52.9808i | 1.57067 | + | 2.28204i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 27.7021i | − | 1.19101i | −0.803353 | − | 0.595504i | \(-0.796953\pi\) | ||
0.803353 | − | 0.595504i | \(-0.203047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.39230i | 0.102664i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 34.5849i | − | 1.48145i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.26699 | −0.396228 | −0.198114 | − | 0.980179i | \(-0.563482\pi\) | ||||
−0.198114 | + | 0.980179i | \(0.563482\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.38425i | 0.101757i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.3923 | −1.12231 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.46410i | 0.0621477i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.5494i | − | 0.870705i | −0.900260 | − | 0.435353i | \(-0.856624\pi\) | ||
0.900260 | − | 0.435353i | \(-0.143376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.3205i | 0.817170i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.07180 | − | 10.2747i | −0.298571 | − | 0.433798i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.8318 | −1.34155 | −0.670775 | − | 0.741661i | \(-0.734038\pi\) | ||||
−0.670775 | + | 0.741661i | \(0.734038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 47.3205 | 1.99079 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.13734 | −0.215748 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.26699i | 0.388492i | 0.980953 | + | 0.194246i | \(0.0622260\pi\) | ||||
−0.980953 | + | 0.194246i | \(0.937774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0355 | −0.587367 | −0.293683 | − | 0.955903i | \(-0.594881\pi\) | ||||
−0.293683 | + | 0.955903i | \(0.594881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.1244 | 0.464727 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12436i | 0.130295i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.3923 | 1.68155 | 0.840777 | − | 0.541382i | \(-0.182099\pi\) | ||||
0.840777 | + | 0.541382i | \(0.182099\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.0278 | 0.541416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −52.7846 | −2.18987 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.1805 | − | 29.3205i | −0.835792 | − | 1.21433i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 14.0355i | − | 0.580296i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.1769i | − | 1.36936i | −0.728845 | − | 0.684679i | \(-0.759942\pi\) | ||
0.728845 | − | 0.684679i | \(-0.240058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.52159i | 0.309922i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.75309 | 0.113247 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.3102i | − | 0.998299i | −0.866516 | − | 0.499150i | \(-0.833646\pi\) | ||
0.866516 | − | 0.499150i | \(-0.166354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 52.7846i | − | 2.16396i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.4641 | −0.960322 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8038i | 0.645728i | 0.946445 | + | 0.322864i | \(0.104646\pi\) | ||||
−0.946445 | + | 0.322864i | \(0.895354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.8395i | − | 1.33955i | −0.742564 | − | 0.669775i | \(-0.766391\pi\) | ||
0.742564 | − | 0.669775i | \(-0.233609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3923i | 0.423207i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.7321 | + | 28.0710i | −0.436320 | + | 1.14125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7021 | 1.12439 | 0.562197 | − | 0.827003i | \(-0.309956\pi\) | ||||
0.562197 | + | 0.827003i | \(0.309956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.5571 | −0.872106 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 33.2083i | − | 1.34127i | −0.741787 | − | 0.670636i | \(-0.766021\pi\) | ||
0.741787 | − | 0.670636i | \(-0.233979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.0710 | 1.13193 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.53590 | 0.343642 | 0.171821 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171821 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.53590i | 0.343087i | 0.985177 | + | 0.171543i | \(0.0548754\pi\) | ||||
−0.985177 | + | 0.171543i | \(0.945125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.26795 | 0.0508810 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 53.3888 | 2.13898 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.2747 | + | 7.07180i | −0.410332 | + | 0.282420i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.01540i | 0.0803595i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.78461i | 0.270091i | 0.990839 | + | 0.135046i | \(0.0431181\pi\) | ||||
−0.990839 | + | 0.135046i | \(0.956882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.5571i | 0.856817i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.0355 | −0.556981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 99.6249i | 3.94728i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.7321i | 0.424553i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.53590 | −0.179157 | −0.0895786 | − | 0.995980i | \(-0.528552\pi\) | ||||
−0.0895786 | + | 0.995980i | \(0.528552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.4641i | − | 0.609845i | −0.952377 | − | 0.304922i | \(-0.901369\pi\) | ||
0.952377 | − | 0.304922i | \(-0.0986305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2747i | 0.404565i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.8756i | 0.506194i | 0.967441 | + | 0.253097i | \(0.0814492\pi\) | ||||
−0.967441 | + | 0.253097i | \(0.918551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.8564 | + | 17.7963i | −1.01495 | + | 0.698565i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.2747 | 0.402697 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.2679 | −0.832279 | −0.416140 | − | 0.909301i | \(-0.636617\pi\) | ||||
−0.416140 | + | 0.909301i | \(0.636617\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.52159 | 0.293893 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.2747i | − | 0.400854i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.3380 | −1.45448 | −0.727240 | − | 0.686383i | \(-0.759197\pi\) | ||||
−0.727240 | + | 0.686383i | \(0.759197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8564 | 1.23907 | 0.619535 | − | 0.784969i | \(-0.287321\pi\) | ||||
0.619535 | + | 0.784969i | \(0.287321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 19.3205i | − | 0.750346i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −52.7846 | −2.04690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.4641 | 0.443228 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.51389 | − | 4.48334i | 0.251466 | − | 0.173077i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.8395i | 1.26587i | 0.774206 | + | 0.632934i | \(0.218150\pi\) | ||||
−0.774206 | + | 0.632934i | \(0.781850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.46410i | − | 0.0948433i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.76850i | − | 0.183268i | −0.995793 | − | 0.0916342i | \(-0.970791\pi\) | ||
0.995793 | − | 0.0916342i | \(-0.0292090\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.0710 | −1.07726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 16.7886i | − | 0.643340i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.7128i | 0.754290i | 0.926154 | + | 0.377145i | \(0.123094\pi\) | ||||
−0.926154 | + | 0.377145i | \(0.876906\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.4641 | 0.514437 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.8564i | 0.910179i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 55.1342i | − | 2.10045i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 30.3923i | − | 1.15618i | −0.815974 | − | 0.578089i | \(-0.803799\pi\) | ||
0.815974 | − | 0.578089i | \(-0.196201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.66025 | + | 14.0355i | 0.366963 | + | 0.533164i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38.3457 | 1.45453 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.6410 | 1.46363 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.2747 | 0.388624 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.0278i | − | 0.492053i | −0.969263 | − | 0.246026i | \(-0.920875\pi\) | ||
0.969263 | − | 0.246026i | \(-0.0791250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.01540 | 0.0760124 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.4641 | −0.431763 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 91.4256i | 3.43841i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.7846 | −0.855694 | −0.427847 | − | 0.903851i | \(-0.640728\pi\) | ||||
−0.427847 | + | 0.903851i | \(0.640728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.13734 | −0.192665 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.53590 | −0.0949701 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.3457 | + | 26.3923i | −1.43405 | + | 0.987016i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 23.3025i | − | 0.870247i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.66025i | 0.211092i | 0.994414 | + | 0.105546i | \(0.0336590\pi\) | ||||
−0.994414 | + | 0.105546i | \(0.966341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.3734i | 1.91325i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.0710 | −1.04397 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.248711i | − | 0.00922419i | −0.999989 | − | 0.00461210i | \(-0.998532\pi\) | ||
0.999989 | − | 0.00461210i | \(-0.00146808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1436i | 0.523120i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12.6589i | − | 0.467569i | −0.972288 | − | 0.233784i | \(-0.924889\pi\) | ||
0.972288 | − | 0.233784i | \(-0.0751109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 52.9808i | 1.95422i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.3923 | − | 19.5417i | 1.04584 | − | 0.719827i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.00770 | 0.0370689 | 0.0185345 | − | 0.999828i | \(-0.494100\pi\) | ||||
0.0185345 | + | 0.999828i | \(0.494100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.3205 | −0.709757 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5648 | 0.827822 | 0.413911 | − | 0.910317i | \(-0.364163\pi\) | ||||
0.413911 | + | 0.910317i | \(0.364163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.6203i | 1.78131i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.2747 | −0.375931 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.3205 | 0.705956 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.5692i | − | 1.15198i | −0.817458 | − | 0.575989i | \(-0.804617\pi\) | ||
0.817458 | − | 0.575989i | \(-0.195383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.8564 | 0.796492 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.51389 | −0.237065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1769 | 1.56929 | 0.784646 | − | 0.619944i | \(-0.212845\pi\) | ||||
0.784646 | + | 0.619944i | \(0.212845\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.38425 | − | 3.46410i | −0.0865428 | − | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 37.3380i | − | 1.35350i | −0.736213 | − | 0.676750i | \(-0.763388\pi\) | ||
0.736213 | − | 0.676750i | \(-0.236612\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 65.0333i | 2.35436i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10.2747i | − | 0.371482i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.6203 | −1.75558 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50619i | 0.198558i | 0.995060 | + | 0.0992791i | \(0.0316537\pi\) | ||||
−0.995060 | + | 0.0992791i | \(0.968346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.4641i | − | 0.556926i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.8372 | −1.25301 | −0.626503 | − | 0.779419i | \(-0.715514\pi\) | ||||
−0.626503 | + | 0.779419i | \(0.715514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.92820i | 0.177026i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.75309i | − | 0.0987667i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 38.6410i | − | 1.38446i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.3205 | − | 20.1805i | 1.04917 | − | 0.722116i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.3923 | 1.15613 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.26699 | −0.330332 | −0.165166 | − | 0.986266i | \(-0.552816\pi\) | ||||
−0.165166 | + | 0.986266i | \(0.552816\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.76850i | 0.169763i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −88.9814 | −3.16381 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2487 | 0.434964 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 29.3205i | − | 1.03989i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.6603 | 0.625558 | 0.312779 | − | 0.949826i | \(-0.398740\pi\) | ||||
0.312779 | + | 0.949826i | \(0.398740\pi\) | |||||||
\(798\) | 0 |