Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [352,2,Mod(351,352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("352.351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.e (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: | \(2.81073415115\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 351.7 | ||
Root | \(-1.16947 + 0.795191i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.351 |
Dual form | 352.2.e.a.351.5 |
$q$-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 \(\left(\mathbb{Z}/352\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(287\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.529317i | 0.305601i | 0.988257 | + | 0.152801i | \(0.0488292\pi\) | ||||
−0.988257 | + | 0.152801i | \(0.951171\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.77846 | −1.24256 | −0.621282 | − | 0.783587i | \(-0.713388\pi\) | ||||
−0.621282 | + | 0.783587i | \(0.713388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.18077 | −1.20222 | −0.601108 | − | 0.799168i | \(-0.705274\pi\) | ||||
−0.601108 | + | 0.799168i | \(0.705274\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.71982 | 0.906608 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.665647 | − | 3.24914i | −0.200700 | − | 0.979653i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.00919i | − | 1.66665i | −0.552783 | − | 0.833325i | \(-0.686434\pi\) | ||
0.552783 | − | 0.833325i | \(-0.313566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.47068i | − | 0.379729i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.67790i | − | 1.13456i | −0.823526 | − | 0.567279i | \(-0.807996\pi\) | ||
0.823526 | − | 0.567279i | \(-0.192004\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.50633 | −1.72207 | −0.861035 | − | 0.508546i | \(-0.830183\pi\) | ||||
−0.861035 | + | 0.508546i | \(0.830183\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.68363i | − | 0.367399i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.02760i | 1.04833i | 0.851618 | + | 0.524163i | \(0.175622\pi\) | ||||
−0.851618 | + | 0.524163i | \(0.824378\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.71982 | 0.543965 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02760i | 0.582661i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.03024i | 0.934091i | 0.884233 | + | 0.467046i | \(0.154682\pi\) | ||||
−0.884233 | + | 0.467046i | \(0.845318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.96896i | − | 0.712847i | −0.934324 | − | 0.356424i | \(-0.883996\pi\) | ||
0.934324 | − | 0.356424i | \(-0.116004\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.71982 | − | 0.352338i | 0.299383 | − | 0.0613342i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.83762 | 1.49383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.77846 | −0.456776 | −0.228388 | − | 0.973570i | \(-0.573345\pi\) | ||||
−0.228388 | + | 0.973570i | \(0.573345\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.18077 | 0.509330 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34049i | 1.14639i | 0.819419 | + | 0.573196i | \(0.194297\pi\) | ||||
−0.819419 | + | 0.573196i | \(0.805703\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.33129 | −0.203020 | −0.101510 | − | 0.994834i | \(-0.532367\pi\) | ||||
−0.101510 | + | 0.994834i | \(0.532367\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.55691 | −1.12652 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.61555i | − | 1.25671i | −0.777928 | − | 0.628353i | \(-0.783729\pi\) | ||
0.777928 | − | 0.628353i | \(-0.216271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.11727 | 0.445324 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47609 | 0.346722 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.117266 | 0.0161078 | 0.00805388 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805388 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84947 | + | 9.02760i | 0.249383 | + | 1.21728i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.97322i | − | 0.526266i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.41205i | 0.834778i | 0.908728 | + | 0.417389i | \(0.137055\pi\) | ||||
−0.908728 | + | 0.417389i | \(0.862945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.32556i | − | 0.553831i | −0.960894 | − | 0.276916i | \(-0.910688\pi\) | ||
0.960894 | − | 0.276916i | \(-0.0893123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.65112 | −1.08994 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.6963i | 2.07092i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.5845i | − | 1.29310i | −0.762870 | − | 0.646552i | \(-0.776210\pi\) | ||
0.762870 | − | 0.646552i | \(-0.223790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.66119 | −0.320370 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.91377i | 0.227123i | 0.993531 | + | 0.113561i | \(0.0362258\pi\) | ||||
−0.993531 | + | 0.113561i | \(0.963774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.34049i | − | 0.859139i | −0.903034 | − | 0.429569i | \(-0.858665\pi\) | ||
0.903034 | − | 0.429569i | \(-0.141335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43965i | 0.166236i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.11727 | + | 10.3348i | 0.241285 | + | 1.17775i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3137 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.55691 | 0.728546 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.69282 | 0.844397 | 0.422199 | − | 0.906503i | \(-0.361259\pi\) | ||||
0.422199 | + | 0.906503i | \(0.361259\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9973i | 1.40976i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.66259 | −0.285459 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.95436 | 0.207161 | 0.103581 | − | 0.994621i | \(-0.466970\pi\) | ||||
0.103581 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.1138i | 2.00367i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.10084 | 0.217847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.8560 | 2.13978 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.3940 | −1.35996 | −0.679978 | − | 0.733233i | \(-0.738010\pi\) | ||||
−0.679978 | + | 0.733233i | \(0.738010\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.81044 | − | 8.83709i | −0.181956 | − | 0.888161i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 5.30452i | − | 0.527819i | −0.964547 | − | 0.263910i | \(-0.914988\pi\) | ||
0.964547 | − | 0.263910i | \(-0.0850120\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.50172i | − | 0.542100i | −0.962565 | − | 0.271050i | \(-0.912629\pi\) | ||
0.962565 | − | 0.271050i | \(-0.0873710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.67790i | 0.456516i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.55415 | 0.246919 | 0.123459 | − | 0.992350i | \(-0.460601\pi\) | ||||
0.123459 | + | 0.992350i | \(0.460601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.98815i | 0.669343i | 0.942335 | + | 0.334672i | \(0.108625\pi\) | ||||
−0.942335 | + | 0.334672i | \(0.891375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.47068i | − | 0.139591i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2767 | −1.06083 | −0.530413 | − | 0.847739i | \(-0.677963\pi\) | ||||
−0.530413 | + | 0.847739i | \(0.677963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.9690i | − | 1.30261i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 16.3439i | − | 1.51100i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.8793i | 1.36398i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1138 | + | 4.32556i | −0.919439 | + | 0.393233i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.88544 | −0.350338 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.33537 | 0.566653 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.87971 | −0.610475 | −0.305238 | − | 0.952276i | \(-0.598736\pi\) | ||||
−0.305238 | + | 0.952276i | \(0.598736\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 0.704676i | − | 0.0620432i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50633 | −0.655831 | −0.327915 | − | 0.944707i | \(-0.606346\pi\) | ||||
−0.327915 | + | 0.944707i | \(0.606346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.8759 | 2.07030 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.41205i | − | 0.723994i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.162910 | −0.0139183 | −0.00695916 | − | 0.999976i | \(-0.502215\pi\) | ||||
−0.00695916 | + | 0.999976i | \(0.502215\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8679 | 1.17626 | 0.588128 | − | 0.808768i | \(-0.299865\pi\) | ||||
0.588128 | + | 0.808768i | \(0.299865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.56035 | 0.384051 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.5247 | + | 4.00000i | −1.63274 | + | 0.334497i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13.9763i | − | 1.16067i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.65002i | 0.136091i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00919i | 0.492292i | 0.969233 | + | 0.246146i | \(0.0791643\pi\) | ||||
−0.969233 | + | 0.246146i | \(0.920836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.3378 | −1.65507 | −0.827534 | − | 0.561415i | \(-0.810257\pi\) | ||||
−0.827534 | + | 0.561415i | \(0.810257\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 12.7231i | − | 1.02860i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.0276i | 0.885758i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2181 | 1.13473 | 0.567364 | − | 0.823467i | \(-0.307963\pi\) | ||||
0.567364 | + | 0.823467i | \(0.307963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0620710i | 0.00492255i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 15.9916i | − | 1.26032i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.2637i | − | 0.803919i | −0.915657 | − | 0.401959i | \(-0.868329\pi\) | ||
0.915657 | − | 0.401959i | \(-0.131671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.77846 | + | 0.978956i | −0.372002 | + | 0.0762116i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4945 | 1.12162 | 0.560808 | − | 0.827946i | \(-0.310491\pi\) | ||||
0.560808 | + | 0.827946i | \(0.310491\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.1104 | −1.77772 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.4159 | −1.56124 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 5.73491i | − | 0.436017i | −0.975947 | − | 0.218009i | \(-0.930044\pi\) | ||
0.975947 | − | 0.218009i | \(-0.0699561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.65112 | −0.653963 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.39400 | −0.255109 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.29478i | 0.321007i | 0.987035 | + | 0.160504i | \(0.0513118\pi\) | ||||
−0.987035 | + | 0.160504i | \(0.948688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10428 | 0.230739 | 0.115370 | − | 0.993323i | \(-0.463195\pi\) | ||||
0.115370 | + | 0.993323i | \(0.463195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.28959 | 0.169251 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.71982 | 0.567573 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.1991 | + | 3.11383i | −1.11147 | + | 0.227706i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 9.63008i | − | 0.700485i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 19.9690i | − | 1.44490i | −0.691421 | − | 0.722452i | \(-0.743015\pi\) | ||
0.691421 | − | 0.722452i | \(-0.256985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.95791i | − | 0.140934i | −0.997514 | − | 0.0704668i | \(-0.977551\pi\) | ||
0.997514 | − | 0.0704668i | \(-0.0224489\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.83762 | −0.632875 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.69282i | 0.548091i | 0.961717 | + | 0.274046i | \(0.0883619\pi\) | ||||
−0.961717 | + | 0.274046i | \(0.911638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.38101i | − | 0.310562i | −0.987870 | − | 0.155281i | \(-0.950372\pi\) | ||
0.987870 | − | 0.155281i | \(-0.0496283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.60256 | 0.395174 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 16.0000i | − | 1.12298i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 20.3952i | − | 1.42446i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.6742i | 0.950421i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.99656 | + | 24.3891i | 0.345619 | + | 1.68703i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.6450 | 0.870518 | 0.435259 | − | 0.900305i | \(-0.356657\pi\) | ||||
0.435259 | + | 0.900305i | \(0.356657\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.01299 | −0.0694089 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.69894 | 0.252266 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6243i | 0.856996i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.88544 | 0.262554 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.1104 | −1.89091 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.9690i | − | 1.33722i | −0.743613 | − | 0.668610i | \(-0.766889\pi\) | ||
0.743613 | − | 0.668610i | \(-0.233111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.39744 | 0.493163 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.55415 | −0.169525 | −0.0847624 | − | 0.996401i | \(-0.527013\pi\) | ||||
−0.0847624 | + | 0.996401i | \(0.527013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.33193 | 0.616672 | 0.308336 | − | 0.951278i | \(-0.400228\pi\) | ||||
0.308336 | + | 0.951278i | \(0.400228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.47036 | + | 1.12070i | −0.359923 | + | 0.0737369i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.3856i | − | 1.00795i | −0.863719 | − | 0.503974i | \(-0.831871\pi\) | ||
0.863719 | − | 0.503974i | \(-0.168129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.9379i | 1.56154i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.98853i | 0.388997i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0731 | 1.62185 | 0.810923 | − | 0.585153i | \(-0.198966\pi\) | ||||
0.810923 | + | 0.585153i | \(0.198966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.0789i | − | 1.42222i | −0.703079 | − | 0.711112i | \(-0.748192\pi\) | ||
0.703079 | − | 0.711112i | \(-0.251808\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.5535i | 0.805306i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.66119 | −0.553343 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 45.1070i | 2.87009i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.07194i | 0.258049i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.7018i | − | 1.30668i | −0.757063 | − | 0.653342i | \(-0.773366\pi\) | ||
0.757063 | − | 0.653342i | \(-0.226634\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.3354 | − | 3.34660i | 1.02700 | − | 0.210399i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.87971 | −0.430824 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.1104 | 1.37921 | 0.689604 | − | 0.724187i | \(-0.257785\pi\) | ||||
0.689604 | + | 0.724187i | \(0.257785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.83762 | 0.549143 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.6814i | 0.846855i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.16930 | −0.565403 | −0.282702 | − | 0.959208i | \(-0.591231\pi\) | ||||
−0.282702 | + | 0.959208i | \(0.591231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.325819 | −0.0200149 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.03447i | 0.0633087i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.88273 | −0.480619 | −0.240309 | − | 0.970696i | \(-0.577249\pi\) | ||||
−0.240309 | + | 0.970696i | \(0.577249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.47036 | −0.332300 | −0.166150 | − | 0.986100i | \(-0.553134\pi\) | ||||
−0.166150 | + | 0.986100i | \(0.553134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.1173 | −0.612325 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.81044 | − | 8.83709i | −0.109174 | − | 0.532897i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.98815i | − | 0.419877i | −0.977715 | − | 0.209939i | \(-0.932674\pi\) | ||
0.977715 | − | 0.209939i | \(-0.0673264\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.7949i | − | 0.646273i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.66259i | 0.158837i | 0.996841 | + | 0.0794183i | \(0.0253063\pi\) | ||||
−0.996841 | + | 0.0794183i | \(0.974694\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0065 | −1.12982 | −0.564911 | − | 0.825152i | \(-0.691089\pi\) | ||||
−0.564911 | + | 0.825152i | \(0.691089\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.0394i | 0.653919i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 23.3484i | − | 1.37821i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.88273 | −0.287220 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 7.08967i | − | 0.415604i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.05128i | 0.236678i | 0.992973 | + | 0.118339i | \(0.0377570\pi\) | ||||
−0.992973 | + | 0.118339i | \(0.962243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 17.8156i | − | 1.03726i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.83709 | − | 2.01531i | 0.570806 | − | 0.116940i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.2118 | 1.74719 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23453 | 0.244074 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.80777 | 0.161302 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0184i | 0.688171i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.14480 | −0.0653369 | −0.0326685 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326685 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.91215 | 0.165666 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8466i | 1.01199i | 0.862536 | + | 0.505995i | \(0.168875\pi\) | ||||
−0.862536 | + | 0.505995i | \(0.831125\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.5078 | −1.83745 | −0.918726 | − | 0.394896i | \(-0.870781\pi\) | ||||
−0.918726 | + | 0.394896i | \(0.870781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.0368 | 1.35432 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8923 | −0.780268 | −0.390134 | − | 0.920758i | \(-0.627571\pi\) | ||||
−0.390134 | + | 0.920758i | \(0.627571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3439 | − | 3.34836i | 0.915085 | − | 0.187472i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.35195i | 0.0754586i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.1138i | 1.95379i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 16.3439i | − | 0.906599i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.69894 | −0.204552 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.4040i | 1.51083i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64658i | 0.145469i | 0.997351 | + | 0.0727347i | \(0.0231726\pi\) | ||||
−0.997351 | + | 0.0727347i | \(0.976827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.55691 | −0.414116 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.4086i | 1.60676i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7147i | 1.56419i | 0.623161 | + | 0.782094i | \(0.285848\pi\) | ||||
−0.623161 | + | 0.782094i | \(0.714152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 5.96896i | − | 0.324190i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8957 | + | 2.64193i | −0.698343 | + | 0.143068i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3501 | 0.666841 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.39400 | 0.398080 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.5909 | 1.42748 | 0.713738 | − | 0.700413i | \(-0.247001\pi\) | ||||
0.713738 | + | 0.700413i | \(0.247001\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.7392i | 1.96660i | 0.181985 | + | 0.983301i | \(0.441748\pi\) | ||||
−0.181985 | + | 0.983301i | \(0.558252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.1934 | 0.971093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.60600 | 0.138703 | 0.0693516 | − | 0.997592i | \(-0.477907\pi\) | ||||
0.0693516 | + | 0.997592i | \(0.477907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.31733i | − | 0.282214i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.87586 | −0.416835 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.21712 | −0.222571 | −0.111286 | − | 0.993788i | \(-0.535497\pi\) | ||||
−0.111286 | + | 0.993788i | \(0.535497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.3449 | 1.96552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.28959 | − | 5.35342i | −0.120172 | − | 0.280982i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.3952i | 1.06753i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 15.7344i | − | 0.821331i | −0.911786 | − | 0.410665i | \(-0.865296\pi\) | ||
0.911786 | − | 0.410665i | \(-0.134704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.9648i | 1.03933i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.372997 | −0.0193650 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0206587i | 0.00106967i | 1.00000 | 0.000534833i | \(0.000170243\pi\) | |||||
−1.00000 | 0.000534833i | \(0.999830\pi\) | ||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.35342i | 0.173170i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.2277 | 1.55680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.8156i | − | 1.63426i | −0.576455 | − | 0.817129i | \(-0.695564\pi\) | ||
0.576455 | − | 0.817129i | \(-0.304436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3.64154i | − | 0.186562i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3794i | 0.990241i | 0.868824 | + | 0.495120i | \(0.164876\pi\) | ||||
−0.868824 | + | 0.495120i | \(0.835124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.88273 | − | 28.7147i | −0.299812 | − | 1.46343i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.62088 | −0.184060 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.6543 | −1.35143 | −0.675714 | − | 0.737164i | \(-0.736164\pi\) | ||||
−0.675714 | + | 0.737164i | \(0.736164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.5186 | 1.18939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.97322i | − | 0.200423i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.4347 | −1.58165 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1173 | −0.608148 | −0.304074 | − | 0.952648i | \(-0.598347\pi\) | ||||
−0.304074 | + | 0.952648i | \(0.598347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.6379i | 0.632686i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.8759 | 1.69168 | 0.845840 | − | 0.533437i | \(-0.179100\pi\) | ||||
0.845840 | + | 0.533437i | \(0.179100\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.8503 | −1.18807 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.2181 | −0.905265 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.84947 | + | 9.02760i | 0.0916749 | + | 0.447481i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.704676i | 0.0348440i | 0.999848 | + | 0.0174220i | \(0.00554587\pi\) | ||||
−0.999848 | + | 0.0174220i | \(0.994454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 0.0862308i | − | 0.00425345i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 20.3952i | − | 1.00358i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.3742 | −1.04922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.34049i | 0.359465i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4948i | 1.34321i | 0.740909 | + | 0.671605i | \(0.234395\pi\) | ||||
−0.740909 | + | 0.671605i | \(0.765605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.11727 | −0.200663 | −0.100332 | − | 0.994954i | \(-0.531990\pi\) | ||||
−0.100332 | + | 0.994954i | \(0.531990\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 23.4328i | − | 1.13934i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 12.7231i | − | 0.617159i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.7586i | 0.665825i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.11727 | − | 10.3348i | −0.102223 | − | 0.498967i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.1571 | −0.826427 | −0.413213 | − | 0.910634i | \(-0.635594\pi\) | ||||
−0.413213 | + | 0.910634i | \(0.635594\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.39400 | −0.259219 | −0.129610 | − | 0.991565i | \(-0.541372\pi\) | ||||
−0.129610 | + | 0.991565i | \(0.541372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.39789 | 0.354701 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 37.7388i | − | 1.80529i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.66259 | −0.127078 | −0.0635392 | − | 0.997979i | \(-0.520239\pi\) | ||||
−0.0635392 | + | 0.997979i | \(0.520239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.47842 | 0.403734 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.2327i | − | 0.581194i | −0.956846 | − | 0.290597i | \(-0.906146\pi\) | ||
0.956846 | − | 0.290597i | \(-0.0938538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.43010 | −0.257411 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.18077 | −0.150445 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0422 | −0.709886 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.8503 | − | 4.88617i | 1.12307 | − | 0.230081i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 10.7651i | − | 0.505791i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 53.1070i | − | 2.48969i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 32.6879i | − | 1.52907i | −0.644579 | − | 0.764537i | \(-0.722967\pi\) | ||
0.644579 | − | 0.764537i | \(-0.277033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.1628 | 0.661063 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 22.3738i | − | 1.04205i | −0.853541 | − | 0.521026i | \(-0.825550\pi\) | ||
0.853541 | − | 0.521026i | \(-0.174450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.1449i | 0.703842i | 0.936030 | + | 0.351921i | \(0.114471\pi\) | ||||
−0.936030 | + | 0.351921i | \(0.885529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.83709 | −0.270689 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 19.2362i | − | 0.890143i | −0.895495 | − | 0.445071i | \(-0.853178\pi\) | ||
0.895495 | − | 0.445071i | \(-0.146822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.6668i | 1.55459i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.52588i | 0.346774i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.886172 | + | 4.32556i | 0.0407462 | + | 0.198889i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.4159 | −0.936745 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.318944 | 0.0146034 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.7841 | −0.766883 | −0.383442 | − | 0.923565i | \(-0.625261\pi\) | ||||
−0.383442 | + | 0.923565i | \(0.625261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.6963i | 0.761285i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.46462 | 0.385154 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.2147 | 1.68983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.9655i | − | 1.31255i | −0.754520 | − | 0.656277i | \(-0.772130\pi\) | ||
0.754520 | − | 0.656277i | \(-0.227870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.43277 | 0.245678 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.4044 | −1.19161 | −0.595807 | − | 0.803127i | \(-0.703168\pi\) | ||||
−0.595807 | + | 0.803127i | \(0.703168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.5309 | 1.05978 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.03024 | + | 24.5535i | 0.226092 | + | 1.10360i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.08725i | − | 0.273050i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.4948i | 1.23084i | 0.788200 | + | 0.615419i | \(0.211013\pi\) | ||||
−0.788200 | + | 0.615419i | \(0.788987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.67217i | 0.342767i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.69894 | −0.164928 | −0.0824638 | − | 0.996594i | \(-0.526279\pi\) | ||||
−0.0824638 | + | 0.996594i | \(0.526279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7384i | 0.655849i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.2327i | − | 0.543274i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.10771 | 0.0934228 | 0.0467114 | − | 0.998908i | \(-0.485126\pi\) | ||||
0.0467114 | + | 0.998908i | \(0.485126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.3484i | 1.03287i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 22.7261i | − | 1.00338i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.2863i | 0.673594i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.9931 | + | 5.73491i | −1.23114 | + | 0.252221i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.03558 | 0.133247 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8596 | −1.00150 | −0.500749 | − | 0.865592i | \(-0.666942\pi\) | ||||
−0.500749 | + | 0.865592i | \(0.666942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6146 | −0.551599 | −0.275799 | − | 0.961215i | \(-0.588943\pi\) | ||||
−0.275799 | + | 0.961215i | \(0.588943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 4.57918i | − | 0.199852i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.5664 | −0.808766 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.27674 | −0.0989886 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.4396i | 0.756816i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 44.1104 | 1.91063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.09659 | −0.306812 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.27330 | −0.0981002 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.07500 | − | 10.1284i | −0.0893765 | − | 0.436263i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16.7743i | − | 0.721185i | −0.932723 | − | 0.360593i | \(-0.882574\pi\) | ||
0.932723 | − | 0.360593i | \(-0.117426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.64315i | 0.0705141i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19.4163i | − | 0.831702i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0544 | 0.600921 | 0.300460 | − | 0.953794i | \(-0.402860\pi\) | ||||
0.300460 | + | 0.953794i | \(0.402860\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 11.7648i | − | 0.502108i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 37.7586i | − | 1.60857i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.9862 | −1.53029 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.08623i | 0.173451i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0811i | 0.427151i | 0.976927 | + | 0.213576i | \(0.0685110\pi\) | ||||
−0.976927 | + | 0.213576i | \(0.931489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.64820 | − | 8.04516i | −0.0695871 | − | 0.339667i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.7059 | −1.92627 | −0.963137 | − | 0.269012i | \(-0.913303\pi\) | ||||
−0.963137 | + | 0.269012i | \(0.913303\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.3319 | 1.31814 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.8560 | −0.875870 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 44.0016i | − | 1.84464i | −0.386423 | − | 0.922321i | \(-0.626290\pi\) | ||
0.386423 | − | 0.922321i | \(-0.373710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.4285 | 1.48264 | 0.741319 | − | 0.671153i | \(-0.234201\pi\) | ||||
0.741319 | + | 0.671153i | \(0.234201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.5699 | 0.441564 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6742i | 0.570253i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.25420 | 0.177105 | 0.0885523 | − | 0.996072i | \(-0.471776\pi\) | ||||
0.0885523 | + | 0.996072i | \(0.471776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.03636 | 0.0430694 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.4691 | −1.01515 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0780580 | − | 0.381015i | −0.00323283 | − | 0.0157800i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 45.4109i | 1.87751i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.61211i | − | 0.396734i | −0.980128 | − | 0.198367i | \(-0.936436\pi\) | ||
0.980128 | − | 0.198367i | \(-0.0635638\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.7923i | 1.22757i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.07194 | −0.167497 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 37.3084i | − | 1.53207i | −0.642798 | − | 0.766036i | \(-0.722226\pi\) | ||
0.642798 | − | 0.766036i | \(-0.277774\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 41.3415i | − | 1.69484i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.31894 | 0.0949080 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 10.6087i | − | 0.433459i | −0.976232 | − | 0.216729i | \(-0.930461\pi\) | ||
0.976232 | − | 0.216729i | \(-0.0695389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2448i | 0.703432i | 0.936107 | + | 0.351716i | \(0.114402\pi\) | ||||
−0.936107 | + | 0.351716i | \(0.885598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 28.7880i | − | 1.17234i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28.1008 | − | 12.0184i | 1.14246 | − | 0.488617i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7231 | 0.516413 | 0.258207 | − | 0.966090i | \(-0.416868\pi\) | ||||
0.258207 | + | 0.966090i | \(0.416868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.46907 | 0.343184 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51.7725 | −2.09449 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.3746i | − | 0.822921i | −0.911428 | − | 0.411460i | \(-0.865019\pi\) | ||
0.911428 | − | 0.411460i | \(-0.134981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.7955 | 0.435318 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.1173 | −0.648857 | −0.324428 | − | 0.945910i | \(-0.605172\pi\) | ||||
−0.324428 | + | 0.945910i | \(0.605172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.8742i | 1.32133i | 0.750682 | + | 0.660664i | \(0.229725\pi\) | ||||
−0.750682 | + | 0.660664i | \(0.770275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.2215 | −0.610819 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.21635 | −0.249053 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2017 | −1.24807 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.9096 | + | 2.64476i | −0.515558 | + | 0.105622i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.9973i | 0.518238i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9069i | 0.792481i | 0.918147 | + | 0.396240i | \(0.129685\pi\) | ||||
−0.918147 | + | 0.396240i | \(0.870315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.69321i | 0.266031i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.1150 | 0.758555 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 18.7323i | − | 0.742199i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.20512i | 0.205911i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.71639 | 0.265281 | 0.132641 | − | 0.991164i | \(-0.457654\pi\) | ||||
0.132641 | + | 0.991164i | \(0.457654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.58451i | − | 0.101923i | −0.998701 | − | 0.0509616i | \(-0.983771\pi\) | ||
0.998701 | − | 0.0509616i | \(-0.0162286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.95791i | 0.0770927i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 14.0862i | − | 0.553787i | −0.960901 | − | 0.276893i | \(-0.910695\pi\) | ||
0.960901 | − | 0.276893i | \(-0.0893049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.8337 | − | 4.26816i | 0.817792 | − | 0.167540i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.68227 | −0.261899 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.3354 | 0.952317 | 0.476158 | − | 0.879360i | \(-0.342029\pi\) | ||||
0.476158 | + | 0.879360i | \(0.342029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8560 | 0.814911 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 19.9648i | − | 0.778902i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.4044 | 1.02857 | 0.514285 | − | 0.857619i | \(-0.328057\pi\) | ||||
0.514285 | + | 0.857619i | \(0.328057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.5370 | −0.643217 | −0.321608 | − | 0.946873i | \(-0.604223\pi\) | ||||
−0.321608 | + | 0.946873i | \(0.604223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 14.8793i | − | 0.577864i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −66.3380 | −2.57248 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.2900 | −0.979233 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.5699 | 0.408656 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0544 | + | 2.87930i | −0.542562 | + | 0.111154i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.7369i | 1.87867i | 0.343002 | + | 0.939335i | \(0.388556\pi\) | ||||
−0.343002 | + | 0.939335i | \(0.611444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.23453i | 0.316947i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.6902i | 0.795188i | 0.917562 | + | 0.397594i | \(0.130155\pi\) | ||||
−0.917562 | + | 0.397594i | \(0.869845\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.6032 | 1.63496 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.35195i | − | 0.0518069i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.50172i | 0.0574617i | 0.999587 | + | 0.0287308i | \(0.00914657\pi\) | ||||
−0.999587 | + | 0.0287308i | \(0.990853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.452638 | 0.0172944 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.93955i | 0.188455i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.704676i | − | 0.0268460i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8777i | 0.908350i | 0.890913 | + | 0.454175i | \(0.150066\pi\) | ||||
−0.890913 | + | 0.454175i | \(0.849934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.75859 | + | 28.1087i | 0.218751 | + | 1.06776i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.5312 | −1.46157 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.3380 | 1.30065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.14388 | 0.308030 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.4018i | − | 1.48818i | −0.668077 | − | 0.744092i | \(-0.732882\pi\) | ||
0.668077 | − | 0.744092i | \(-0.267118\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.8560 | 0.786599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.6707 | −0.477208 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.8724i | 0.634553i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.5665 | 1.71128 | 0.855642 | − | 0.517568i | \(-0.173162\pi\) | ||||
0.855642 | + | 0.517568i | \(0.173162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.7713 | 1.15401 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.9544 | 0.747297 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 54.2486 | − | 11.1138i | 2.02878 | − | 0.415634i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.2716i | 0.495638i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.2518i | 1.35196i | 0.736918 | + | 0.675982i | \(0.236280\pi\) | ||||
−0.736918 | + | 0.675982i | \(0.763720\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.4997i | 0.651722i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6867 | 0.434633 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.6814i | 0.508113i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.1346i | 1.56268i | 0.624103 | + | 0.781342i | \(0.285465\pi\) | ||||
−0.624103 | + | 0.781342i | \(0.714535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0260 | 0.482444 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.22766i | 0.230338i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.9293i | 1.51176i | 0.654712 | + | 0.755879i | \(0.272790\pi\) | ||||
−0.654712 | + | 0.755879i | \(0.727210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 4.58451i | − | 0.169102i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34.3906 | + | 7.04555i | −1.26679 | + | 0.259526i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0429 | 0.737290 | 0.368645 | − | 0.929570i | \(-0.379822\pi\) | ||||
0.368645 | + | 0.929570i | \(0.379822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.8759 | −0.877102 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.7721 | −1.05554 | −0.527772 | − | 0.849386i | \(-0.676973\pi\) | ||||
−0.527772 | + | 0.849386i | \(0.676973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.6963i | − | 0.611704i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.9231 | 0.765537 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.12414 | −0.296850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 53.7795i | − | 1.96244i | −0.192886 | − | 0.981221i | \(-0.561785\pi\) | ||
0.192886 | − | 0.981221i | \(-0.438215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.9578 | 0.399324 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.5078 | 2.05653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8827 | −0.577268 | −0.288634 | − | 0.957440i | \(-0.593201\pi\) | ||||
−0.288634 | + | 0.957440i | \(0.593201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.77141 | + | 8.64658i | 0.0642982 | + | 0.313851i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.42466i | − | 0.124144i | −0.998072 | − | 0.0620720i | \(-0.980229\pi\) | ||
0.998072 | − | 0.0620720i | \(-0.0197708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 22.2277i | − | 0.804695i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35.3505i | 1.27810i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.5312 | 1.39128 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.7147i | 1.03548i | 0.855539 | + | 0.517739i | \(0.173226\pi\) | ||||
−0.855539 | + | 0.517739i | \(0.826774\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7034i | 0.421488i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.7586 | 0.710667 | 0.355334 | − | 0.934740i | \(-0.384367\pi\) | ||||
0.355334 | + | 0.934740i | \(0.384367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.7949i | − | 0.387764i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.67790i | 0.167819i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 55.1001i | − | 1.97417i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.21811 | − | 1.27389i | 0.222501 | − | 0.0455835i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.2295 | −0.544259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −39.5044 | −1.40997 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.9702 | 0.640568 | 0.320284 | − | 0.947322i | \(-0.396222\pi\) | ||||
0.320284 | + | 0.947322i | \(0.396222\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 4.85346i | − | 0.172788i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.8687 | 1.27534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.9931 | −0.923043 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 0.172462i | − | 0.00611658i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.5336 | −1.75457 | −0.877285 | − | 0.479969i | \(-0.840648\pi\) | ||||
−0.877285 | + | 0.479969i | \(0.840648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.3027 | −1.42581 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.31551 | 0.187814 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.8503 | + | 4.88617i | −0.841658 | + | 0.172429i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.4320i | 1.56602i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.17246i | − | 0.146878i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.9564i | 1.26416i | 0.774903 | + | 0.632080i | \(0.217799\pi\) | ||||
−0.774903 | + | 0.632080i | \(0.782201\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.65724 | 0.163538 | 0.0817689 | − | 0.996651i | \(-0.473943\pi\) | ||||
0.0817689 | + | 0.996651i | \(0.473943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 2.89555i | − | 0.101551i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.5174i | 0.998920i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.99312 | 0.349615 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 51.9862i | 1.81655i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 25.6997i | − | 0.896927i | −0.893801 | − | 0.448464i | \(-0.851971\pi\) | ||
0.893801 | − | 0.448464i | \(-0.148029\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5585i | 0.437763i | 0.975751 | + | 0.218881i | \(0.0702408\pi\) | ||||
−0.975751 | + | 0.218881i | \(0.929759\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.67762 | − | 0.958297i | 0.162854 | − | 0.0333636i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.5557 | −1.61890 | −0.809451 | − | 0.587188i | \(-0.800235\pi\) | ||||
−0.809451 | + | 0.587188i | \(0.800235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.8923 | −1.03820 | −0.519101 | − | 0.854713i | \(-0.673733\pi\) | ||||
−0.519101 | + | 0.854713i | \(0.673733\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.69894 | 0.128315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 14.5823i | − | 0.505245i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.2723 | −1.39368 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.0164 | 0.415348 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 19.1932i | − | 0.662622i | −0.943522 | − | 0.331311i | \(-0.892509\pi\) | ||
0.943522 | − | 0.331311i | \(-0.107491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.69672 | 0.127473 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.40935 | −0.0485407 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.2112 | 2.20893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.1697 | − | 13.7586i | 1.10536 | − | 0.472751i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 10.0605i | − | 0.345275i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.9690i | − | 0.478850i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.6944i | − | 1.76998i | −0.465607 | − | 0.884992i | \(-0.654164\pi\) | ||
0.465607 | − | 0.884992i | \(-0.345836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.7247 | 1.93994 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.7300i | − | 1.04972i | −0.851190 | − | 0.524858i | \(-0.824118\pi\) | ||
0.851190 | − | 0.524858i | \(-0.175882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.05681i | 0.0360580i | 0.999837 | + | 0.0180290i | \(0.00573912\pi\) | ||||
−0.999837 | + | 0.0180290i | \(0.994261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.3587 | 0.421183 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.146482i | − | 0.00498631i | −0.999997 | − | 0.00249315i | \(-0.999206\pi\) | ||
0.999997 | − | 0.00249315i | \(-0.000793597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.9342i | 0.541779i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.58451i | − | 0.0877746i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.53093 | − | 36.7598i | −0.255469 | − | 1.24699i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63.6044 | −2.15515 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.4293 | −1.23295 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.1513 | −0.681239 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.0206587i | − | 0.000697594i | −1.00000 | 0.000348797i | \(-0.999889\pi\) | |||
1.00000 | 0.000348797i | \(-0.000111026\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.14441 | −0.0723292 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.0682 | 1.51839 | 0.759193 | − | 0.650866i | \(-0.225594\pi\) | ||||
0.759193 | + | 0.650866i | \(0.225594\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.6087i | 1.03006i | 0.857171 | + | 0.515032i | \(0.172220\pi\) | ||||
−0.857171 | + | 0.515032i | \(0.827780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.43010 | 0.316989 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6033 | −0.456754 | −0.228377 | − | 0.973573i | \(-0.573342\pi\) | ||||
−0.228377 | + | 0.973573i | \(0.573342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.8827 | 0.733923 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.36459 | − | 21.3043i | −0.146219 | − | 0.713722i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.6711i | 2.16414i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.9329i | − | 0.398872i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9916i | 0.533944i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.9648 | 0.665864 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.548560i | − | 0.0182752i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.24141i | 0.0745894i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.62510 | −0.286708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.50172i | 0.0498638i | 0.999689 | + | 0.0249319i | \(0.00793689\pi\) | ||||
−0.999689 | + | 0.0249319i | \(0.992063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 14.4274i | − | 0.478525i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6121i | 0.450989i | 0.974244 | + | 0.225495i | \(0.0723998\pi\) | ||||
−0.974244 | + | 0.225495i | \(0.927600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.12070 | − | 24.9951i | −0.169471 | − | 0.827216i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.36153 | −0.210306 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.8759 | 0.788450 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.3856 | −0.507526 | −0.253763 | − | 0.967266i | \(-0.581668\pi\) | ||||
−0.253763 | + | 0.967266i | \(0.581668\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 0.605959i | − | 0.0199670i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.5002 | 0.378534 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.55691 | −0.248470 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 14.9637i | − | 0.491473i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6482 | 0.644637 | 0.322318 | − | 0.946631i | \(-0.395538\pi\) | ||||
0.322318 | + | 0.946631i | \(0.395538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.3992 | −0.766878 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.44652 | −0.309265 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.2302 | − | 8.65164i | 1.38107 | − | 0.282939i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.04593i | − | 0.197512i | −0.995112 | − | 0.0987560i | \(-0.968514\pi\) | ||
0.995112 | − | 0.0987560i | \(-0.0314863\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 17.2069i | − | 0.561527i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 31.7296i | − | 1.03436i | −0.855878 | − | 0.517178i | \(-0.826983\pi\) | ||
0.855878 | − | 0.517178i | \(-0.173017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.9050 | −1.20179 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 26.7568i | 0.870397i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.7638i | 0.674734i | 0.941373 | + | 0.337367i | \(0.109536\pi\) | ||||
−0.941373 | + | 0.337367i | \(0.890464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.1104 | −1.43188 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.35342i | − | 0.238451i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7269i | 0.671410i | 0.941967 | + | 0.335705i | \(0.108975\pi\) | ||||
−0.941967 | + | 0.335705i | \(0.891025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.4829i | 1.79538i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.77234 | + | 8.65112i | 0.0572917 | + | 0.279651i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.518178 | 0.0167328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2473 | 0.491849 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.94683 | 0.223858 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.43997i | 0.175119i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.65112 | 0.278201 | 0.139101 | − | 0.990278i | \(-0.455579\pi\) | ||||
0.139101 | + | 0.990278i | \(0.455579\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.5863 | −0.597079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.3534i | − | 0.941996i | −0.882134 | − | 0.470998i | \(-0.843894\pi\) | ||
0.882134 | − | 0.470998i | \(-0.156106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.1104 | −1.41411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.65112 | 0.277058 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.8268 | 0.602322 | 0.301161 | − | 0.953573i | \(-0.402626\pi\) | ||||
0.301161 | + | 0.953573i | \(0.402626\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.30091 | − | 6.34998i | −0.0415773 | − | 0.202946i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.0065i | 0.606832i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2553i | 0.358987i | 0.983759 | + | 0.179493i | \(0.0574459\pi\) | ||||
−0.983759 | + | 0.179493i | \(0.942554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 21.3742i | − | 0.681038i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.5054 | −0.461712 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.69321i | − | 0.212832i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.14304i | 0.163374i | 0.996658 | + | 0.0816871i | \(0.0260308\pi\) | ||||
−0.996658 | + | 0.0816871i | \(0.973969\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.40088 | −0.0444556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.1725i | 0.385893i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5884i | 0.335337i | 0.985843 | + | 0.167669i | \(0.0536239\pi\) | ||||
−0.985843 | + | 0.167669i | \(0.946376\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.41205i | − | 0.266145i |
(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 | 352.2.e.a.351.7 | yes | 12 | |
3.2 | odd | 2 | 3168.2.o.e.703.10 | 12 | |||
4.3 | odd | 2 | inner | 352.2.e.a.351.6 | yes | 12 | |
8.3 | odd | 2 | 704.2.e.d.703.8 | 12 | |||
8.5 | even | 2 | 704.2.e.d.703.5 | 12 | |||
11.10 | odd | 2 | inner | 352.2.e.a.351.8 | yes | 12 | |
12.11 | even | 2 | 3168.2.o.e.703.11 | 12 | |||
16.3 | odd | 4 | 2816.2.g.i.1407.7 | 12 | |||
16.5 | even | 4 | 2816.2.g.i.1407.6 | 12 | |||
16.11 | odd | 4 | 2816.2.g.d.1407.5 | 12 | |||
16.13 | even | 4 | 2816.2.g.d.1407.8 | 12 | |||
33.32 | even | 2 | 3168.2.o.e.703.12 | 12 | |||
44.43 | even | 2 | inner | 352.2.e.a.351.5 | ✓ | 12 | |
88.21 | odd | 2 | 704.2.e.d.703.6 | 12 | |||
88.43 | even | 2 | 704.2.e.d.703.7 | 12 | |||
132.131 | odd | 2 | 3168.2.o.e.703.9 | 12 | |||
176.21 | odd | 4 | 2816.2.g.i.1407.5 | 12 | |||
176.43 | even | 4 | 2816.2.g.d.1407.6 | 12 | |||
176.109 | odd | 4 | 2816.2.g.d.1407.7 | 12 | |||
176.131 | even | 4 | 2816.2.g.i.1407.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.e.a.351.5 | ✓ | 12 | 44.43 | even | 2 | inner | |
352.2.e.a.351.6 | yes | 12 | 4.3 | odd | 2 | inner | |
352.2.e.a.351.7 | yes | 12 | 1.1 | even | 1 | trivial | |
352.2.e.a.351.8 | yes | 12 | 11.10 | odd | 2 | inner | |
704.2.e.d.703.5 | 12 | 8.5 | even | 2 | |||
704.2.e.d.703.6 | 12 | 88.21 | odd | 2 | |||
704.2.e.d.703.7 | 12 | 88.43 | even | 2 | |||
704.2.e.d.703.8 | 12 | 8.3 | odd | 2 | |||
2816.2.g.d.1407.5 | 12 | 16.11 | odd | 4 | |||
2816.2.g.d.1407.6 | 12 | 176.43 | even | 4 | |||
2816.2.g.d.1407.7 | 12 | 176.109 | odd | 4 | |||
2816.2.g.d.1407.8 | 12 | 16.13 | even | 4 | |||
2816.2.g.i.1407.5 | 12 | 176.21 | odd | 4 | |||
2816.2.g.i.1407.6 | 12 | 16.5 | even | 4 | |||
2816.2.g.i.1407.7 | 12 | 16.3 | odd | 4 | |||
2816.2.g.i.1407.8 | 12 | 176.131 | even | 4 | |||
3168.2.o.e.703.9 | 12 | 132.131 | odd | 2 | |||
3168.2.o.e.703.10 | 12 | 3.2 | odd | 2 | |||
3168.2.o.e.703.11 | 12 | 12.11 | even | 2 | |||
3168.2.o.e.703.12 | 12 | 33.32 | even | 2 |