Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), 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: | \(1.79663404548\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.143 |
Dual form | 225.2.f.a.107.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | 0.411438 | − | 0.911438i | \(-0.365027\pi\) |
−0.911438 | + | 0.411438i | \(0.865027\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 2.00000i | 0.755929 | − | 0.755929i | −0.219650 | − | 0.975579i | \(-0.570491\pi\) |
0.975579 | + | 0.219650i | \(0.0704915\pi\) | |||||||
\(8\) | −2.12132 | + | 2.12132i | −0.750000 | + | 0.750000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | − | 1.00000i | −0.277350 | − | 0.277350i | 0.554700 | − | 0.832050i | \(-0.312833\pi\) |
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | −2.82843 | −0.755929 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.82843 | − | 2.82843i | −0.685994 | − | 0.685994i | 0.275350 | − | 0.961344i | \(-0.411206\pi\) |
−0.961344 | + | 0.275350i | \(0.911206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | + | 2.00000i | −0.426401 | + | 0.426401i | ||||
\(23\) | 2.82843 | − | 2.82843i | 0.589768 | − | 0.589768i | −0.347801 | − | 0.937568i | \(-0.613071\pi\) |
0.937568 | + | 0.347801i | \(0.113071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.41421i | 0.277350i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 2.00000i | −0.377964 | − | 0.377964i | ||||
\(29\) | 4.24264 | 0.787839 | 0.393919 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 3.53553 | + | 3.53553i | 0.625000 | + | 0.625000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −0.164399 | + | 0.164399i | −0.784512 | − | 0.620113i | \(-0.787087\pi\) |
0.620113 | + | 0.784512i | \(0.287087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41421i | 0.220863i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | + | 8.00000i | 1.21999 | + | 1.21999i | 0.967635 | + | 0.252353i | \(0.0812046\pi\) |
0.252353 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(44\) | −2.82843 | −0.426401 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 5.65685 | + | 5.65685i | 0.825137 | + | 0.825137i | 0.986840 | − | 0.161703i | \(-0.0516985\pi\) |
−0.161703 | + | 0.986840i | \(0.551699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | + | 1.00000i | −0.138675 | + | 0.138675i | ||||
\(53\) | 2.82843 | − | 2.82843i | 0.388514 | − | 0.388514i | −0.485643 | − | 0.874157i | \(-0.661414\pi\) |
0.874157 | + | 0.485643i | \(0.161414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.48528i | 1.13389i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.00000 | − | 3.00000i | −0.393919 | − | 0.393919i | ||||
\(59\) | 8.48528 | 1.10469 | 0.552345 | − | 0.833616i | \(-0.313733\pi\) | ||||
0.552345 | + | 0.833616i | \(0.313733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 2.82843 | + | 2.82843i | 0.359211 | + | 0.359211i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 7.00000i | − | 0.875000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 4.00000i | −0.488678 | + | 0.488678i | −0.907889 | − | 0.419211i | \(-0.862307\pi\) |
0.419211 | + | 0.907889i | \(0.362307\pi\) | |||||||
\(68\) | −2.82843 | + | 2.82843i | −0.342997 | + | 0.342997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.00000i | −0.117041 | − | 0.117041i | 0.646160 | − | 0.763202i | \(-0.276374\pi\) |
−0.763202 | + | 0.646160i | \(0.776374\pi\) | |||||||
\(74\) | 1.41421 | 0.164399 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.65685 | − | 5.65685i | −0.644658 | − | 0.644658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000i | 1.35011i | 0.737769 | + | 0.675053i | \(0.235879\pi\) | ||||
−0.737769 | + | 0.675053i | \(0.764121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.00000 | − | 1.00000i | 0.110432 | − | 0.110432i | ||||
\(83\) | 2.82843 | − | 2.82843i | 0.310460 | − | 0.310460i | −0.534628 | − | 0.845088i | \(-0.679548\pi\) |
0.845088 | + | 0.534628i | \(0.179548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 11.3137i | − | 1.21999i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.00000 | + | 6.00000i | 0.639602 | + | 0.639602i | ||||
\(89\) | −12.7279 | −1.34916 | −0.674579 | − | 0.738203i | \(-0.735675\pi\) | ||||
−0.674579 | + | 0.738203i | \(0.735675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | −2.82843 | − | 2.82843i | −0.294884 | − | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 8.00000i | − | 0.825137i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0000 | − | 11.0000i | 1.11688 | − | 1.11688i | 0.124684 | − | 0.992196i | \(-0.460208\pi\) |
0.992196 | − | 0.124684i | \(-0.0397918\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.5563i | − | 1.54791i | −0.633238 | − | 0.773957i | \(-0.718274\pi\) | ||
0.633238 | − | 0.773957i | \(-0.281726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | − | 10.0000i | −0.985329 | − | 0.985329i | 0.0145647 | − | 0.999894i | \(-0.495364\pi\) |
−0.999894 | + | 0.0145647i | \(0.995364\pi\) | |||||||
\(104\) | 4.24264 | 0.416025 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −2.82843 | − | 2.82843i | −0.273434 | − | 0.273434i | 0.557047 | − | 0.830481i | \(-0.311934\pi\) |
−0.830481 | + | 0.557047i | \(0.811934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | − | 2.00000i | 0.188982 | − | 0.188982i | ||||
\(113\) | −9.89949 | + | 9.89949i | −0.931266 | + | 0.931266i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) |
0.0665190 | + | 0.997785i | \(0.478811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.24264i | − | 0.393919i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | − | 6.00000i | −0.552345 | − | 0.552345i | ||||
\(119\) | −11.3137 | −1.03713 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −5.65685 | − | 5.65685i | −0.512148 | − | 0.512148i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000i | 0.359211i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | + | 10.0000i | −0.887357 | + | 0.887357i | −0.994268 | − | 0.106912i | \(-0.965904\pi\) |
0.106912 | + | 0.994268i | \(0.465904\pi\) | |||||||
\(128\) | 2.12132 | − | 2.12132i | 0.187500 | − | 0.187500i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1421i | 1.23560i | 0.786334 | + | 0.617802i | \(0.211977\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.65685 | 0.488678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | 1.02899 | ||||||||
\(137\) | −7.07107 | − | 7.07107i | −0.604122 | − | 0.604122i | 0.337282 | − | 0.941404i | \(-0.390493\pi\) |
−0.941404 | + | 0.337282i | \(0.890493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | − | 4.00000i | 0.335673 | − | 0.335673i | ||||
\(143\) | −2.82843 | + | 2.82843i | −0.236525 | + | 0.236525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.41421i | 0.117041i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | + | 1.00000i | 0.0821995 | + | 0.0821995i | ||||
\(149\) | −4.24264 | −0.347571 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00000i | 0.644658i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | − | 5.00000i | 0.399043 | − | 0.399043i | −0.478852 | − | 0.877896i | \(-0.658947\pi\) |
0.877896 | + | 0.478852i | \(0.158947\pi\) | |||||||
\(158\) | 8.48528 | − | 8.48528i | 0.675053 | − | 0.675053i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.3137i | − | 0.891645i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | + | 8.00000i | 0.626608 | + | 0.626608i | 0.947213 | − | 0.320605i | \(-0.103886\pi\) |
−0.320605 | + | 0.947213i | \(0.603886\pi\) | |||||||
\(164\) | 1.41421 | 0.110432 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.00000 | −0.310460 | ||||||||
\(167\) | 14.1421 | + | 14.1421i | 1.09435 | + | 1.09435i | 0.995058 | + | 0.0992931i | \(0.0316581\pi\) |
0.0992931 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | − | 8.00000i | 0.609994 | − | 0.609994i | ||||
\(173\) | −9.89949 | + | 9.89949i | −0.752645 | + | 0.752645i | −0.974972 | − | 0.222327i | \(-0.928635\pi\) |
0.222327 | + | 0.974972i | \(0.428635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.82843i | − | 0.213201i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.00000 | + | 9.00000i | 0.674579 | + | 0.674579i | ||||
\(179\) | 25.4558 | 1.90266 | 0.951330 | − | 0.308175i | \(-0.0997184\pi\) | ||||
0.951330 | + | 0.308175i | \(0.0997184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 2.82843 | + | 2.82843i | 0.209657 | + | 0.209657i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000i | 0.884652i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00000 | + | 8.00000i | −0.585018 | + | 0.585018i | ||||
\(188\) | 5.65685 | − | 5.65685i | 0.412568 | − | 0.412568i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274i | 1.63726i | 0.574320 | + | 0.818631i | \(0.305267\pi\) | ||||
−0.574320 | + | 0.818631i | \(0.694733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.00000i | −0.0719816 | − | 0.0719816i | 0.670199 | − | 0.742181i | \(-0.266209\pi\) |
−0.742181 | + | 0.670199i | \(0.766209\pi\) | |||||||
\(194\) | −15.5563 | −1.11688 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 9.89949 | + | 9.89949i | 0.705310 | + | 0.705310i | 0.965545 | − | 0.260235i | \(-0.0838002\pi\) |
−0.260235 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.0000 | + | 11.0000i | −0.773957 | + | 0.773957i | ||||
\(203\) | 8.48528 | − | 8.48528i | 0.595550 | − | 0.595550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.1421i | 0.985329i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | − | 1.00000i | −0.0693375 | − | 0.0693375i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | −2.82843 | − | 2.82843i | −0.194257 | − | 0.194257i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000i | 0.273434i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | + | 8.00000i | −0.543075 | + | 0.543075i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685i | 0.380521i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | − | 10.0000i | −0.669650 | − | 0.669650i | 0.287985 | − | 0.957635i | \(-0.407015\pi\) |
−0.957635 | + | 0.287985i | \(0.907015\pi\) | |||||||
\(224\) | 14.1421 | 0.944911 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.0000 | 0.931266 | ||||||||
\(227\) | 5.65685 | + | 5.65685i | 0.375459 | + | 0.375459i | 0.869461 | − | 0.494002i | \(-0.164466\pi\) |
−0.494002 | + | 0.869461i | \(0.664466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.00000 | + | 9.00000i | −0.590879 | + | 0.590879i | ||||
\(233\) | 2.82843 | − | 2.82843i | 0.185296 | − | 0.185296i | −0.608363 | − | 0.793659i | \(-0.708173\pi\) |
0.793659 | + | 0.608363i | \(0.208173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 8.48528i | − | 0.552345i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.00000 | + | 8.00000i | 0.518563 | + | 0.518563i | ||||
\(239\) | −16.9706 | −1.09773 | −0.548867 | − | 0.835910i | \(-0.684941\pi\) | ||||
−0.548867 | + | 0.835910i | \(0.684941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | −2.12132 | − | 2.12132i | −0.136364 | − | 0.136364i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.00000i | − | 0.512148i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.48528 | − | 8.48528i | 0.538816 | − | 0.538816i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.7990i | − | 1.24970i | −0.780744 | − | 0.624851i | \(-0.785160\pi\) | ||
0.780744 | − | 0.624851i | \(-0.214840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | − | 8.00000i | −0.502956 | − | 0.502956i | ||||
\(254\) | 14.1421 | 0.887357 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 1.41421 | + | 1.41421i | 0.0882162 | + | 0.0882162i | 0.749838 | − | 0.661622i | \(-0.230131\pi\) |
−0.661622 | + | 0.749838i | \(0.730131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.0000 | − | 10.0000i | 0.617802 | − | 0.617802i | ||||
\(263\) | 2.82843 | − | 2.82843i | 0.174408 | − | 0.174408i | −0.614505 | − | 0.788913i | \(-0.710644\pi\) |
0.788913 | + | 0.614505i | \(0.210644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | + | 4.00000i | 0.244339 | + | 0.244339i | ||||
\(269\) | −12.7279 | −0.776035 | −0.388018 | − | 0.921652i | \(-0.626840\pi\) | ||||
−0.388018 | + | 0.921652i | \(0.626840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | −2.82843 | − | 2.82843i | −0.171499 | − | 0.171499i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000i | 0.604122i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 11.0000i | 0.660926 | − | 0.660926i | −0.294672 | − | 0.955598i | \(-0.595211\pi\) |
0.955598 | + | 0.294672i | \(0.0952105\pi\) | |||||||
\(278\) | −8.48528 | + | 8.48528i | −0.508913 | + | 0.508913i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.89949i | 0.590554i | 0.955412 | + | 0.295277i | \(0.0954120\pi\) | ||||
−0.955412 | + | 0.295277i | \(0.904588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | + | 8.00000i | 0.475551 | + | 0.475551i | 0.903705 | − | 0.428155i | \(-0.140836\pi\) |
−0.428155 | + | 0.903705i | \(0.640836\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 2.82843 | + | 2.82843i | 0.166957 | + | 0.166957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | + | 1.00000i | −0.0585206 | + | 0.0585206i | ||||
\(293\) | −9.89949 | + | 9.89949i | −0.578335 | + | 0.578335i | −0.934444 | − | 0.356110i | \(-0.884103\pi\) |
0.356110 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 3.00000i | 0.173785 | + | 0.173785i | ||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.0000 | 1.84445 | ||||||||
\(302\) | −5.65685 | − | 5.65685i | −0.325515 | − | 0.325515i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.00000 | − | 8.00000i | 0.456584 | − | 0.456584i | −0.440948 | − | 0.897532i | \(-0.645358\pi\) |
0.897532 | + | 0.440948i | \(0.145358\pi\) | |||||||
\(308\) | −5.65685 | + | 5.65685i | −0.322329 | + | 0.322329i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.3137i | − | 0.641542i | −0.947157 | − | 0.320771i | \(-0.896058\pi\) | ||
0.947157 | − | 0.320771i | \(-0.103942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0000 | − | 19.0000i | −1.07394 | − | 1.07394i | −0.997038 | − | 0.0769051i | \(-0.975496\pi\) |
−0.0769051 | − | 0.997038i | \(-0.524504\pi\) | |||||||
\(314\) | −7.07107 | −0.399043 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | −19.7990 | − | 19.7990i | −1.11202 | − | 1.11202i | −0.992877 | − | 0.119145i | \(-0.961985\pi\) |
−0.119145 | − | 0.992877i | \(-0.538015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.0000i | − | 0.671871i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | + | 8.00000i | −0.445823 | + | 0.445823i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 11.3137i | − | 0.626608i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | − | 3.00000i | −0.165647 | − | 0.165647i | ||||
\(329\) | 22.6274 | 1.24749 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −2.82843 | − | 2.82843i | −0.155230 | − | 0.155230i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 20.0000i | − | 1.09435i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | − | 5.00000i | 0.272367 | − | 0.272367i | −0.557685 | − | 0.830053i | \(-0.688310\pi\) |
0.830053 | + | 0.557685i | \(0.188310\pi\) | |||||||
\(338\) | −7.77817 | + | 7.77817i | −0.423077 | + | 0.423077i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.3137i | 0.612672i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | −33.9411 | −1.82998 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | −11.3137 | − | 11.3137i | −0.607352 | − | 0.607352i | 0.334901 | − | 0.942253i | \(-0.391297\pi\) |
−0.942253 | + | 0.334901i | \(0.891297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.0000i | − | 1.28469i | −0.766415 | − | 0.642345i | \(-0.777962\pi\) | ||
0.766415 | − | 0.642345i | \(-0.222038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.0000 | − | 10.0000i | 0.533002 | − | 0.533002i | ||||
\(353\) | 2.82843 | − | 2.82843i | 0.150542 | − | 0.150542i | −0.627818 | − | 0.778360i | \(-0.716052\pi\) |
0.778360 | + | 0.627818i | \(0.216052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.7279i | 0.674579i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.0000 | − | 18.0000i | −0.951330 | − | 0.951330i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 11.3137 | + | 11.3137i | 0.594635 | + | 0.594635i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000i | 0.209657i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | − | 2.00000i | 0.104399 | − | 0.104399i | −0.652978 | − | 0.757377i | \(-0.726481\pi\) |
0.757377 | + | 0.652978i | \(0.226481\pi\) | |||||||
\(368\) | 2.82843 | − | 2.82843i | 0.147442 | − | 0.147442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.3137i | − | 0.587378i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0000 | + | 17.0000i | 0.880227 | + | 0.880227i | 0.993557 | − | 0.113331i | \(-0.0361520\pi\) |
−0.113331 | + | 0.993557i | \(0.536152\pi\) | |||||||
\(374\) | 11.3137 | 0.585018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | −1.23771 | ||||||||
\(377\) | −4.24264 | − | 4.24264i | −0.218507 | − | 0.218507i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0000i | 1.84920i | 0.380945 | + | 0.924598i | \(0.375599\pi\) | ||||
−0.380945 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0000 | − | 16.0000i | 0.818631 | − | 0.818631i | ||||
\(383\) | −22.6274 | + | 22.6274i | −1.15621 | + | 1.15621i | −0.170923 | + | 0.985284i | \(0.554675\pi\) |
−0.985284 | + | 0.170923i | \(0.945325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.41421i | 0.0719816i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.0000 | − | 11.0000i | −0.558440 | − | 0.558440i | ||||
\(389\) | 4.24264 | 0.215110 | 0.107555 | − | 0.994199i | \(-0.465698\pi\) | ||||
0.107555 | + | 0.994199i | \(0.465698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 2.12132 | + | 2.12132i | 0.107143 | + | 0.107143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 14.0000i | − | 0.705310i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0000 | + | 19.0000i | −0.953583 | + | 0.953583i | −0.998969 | − | 0.0453868i | \(-0.985548\pi\) |
0.0453868 | + | 0.998969i | \(0.485548\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 24.0416i | − | 1.20058i | −0.799782 | − | 0.600291i | \(-0.795051\pi\) | ||
0.799782 | − | 0.600291i | \(-0.204949\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000 | + | 4.00000i | 0.199254 | + | 0.199254i | ||||
\(404\) | −15.5563 | −0.773957 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 2.82843 | + | 2.82843i | 0.140200 | + | 0.140200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0000i | 1.18672i | 0.804936 | + | 0.593362i | \(0.202200\pi\) | ||||
−0.804936 | + | 0.593362i | \(0.797800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.0000 | + | 10.0000i | −0.492665 | + | 0.492665i | ||||
\(413\) | 16.9706 | − | 16.9706i | 0.835067 | − | 0.835067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 7.07107i | − | 0.346688i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.48528 | 0.414533 | 0.207267 | − | 0.978285i | \(-0.433543\pi\) | ||||
0.207267 | + | 0.978285i | \(0.433543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 2.82843 | + | 2.82843i | 0.137686 | + | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0000i | 0.582772i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.0000 | − | 16.0000i | 0.774294 | − | 0.774294i | ||||
\(428\) | −2.82843 | + | 2.82843i | −0.136717 | + | 0.136717i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.65685i | 0.272481i | 0.990676 | + | 0.136241i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136241i | \(0.956498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | + | 17.0000i | 0.816968 | + | 0.816968i | 0.985668 | − | 0.168700i | \(-0.0539568\pi\) |
−0.168700 | + | 0.985668i | \(0.553957\pi\) | |||||||
\(434\) | 11.3137 | 0.543075 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 24.0000i | − | 1.14546i | −0.819745 | − | 0.572729i | \(-0.805885\pi\) | ||
0.819745 | − | 0.572729i | \(-0.194115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | − | 4.00000i | 0.190261 | − | 0.190261i | ||||
\(443\) | 28.2843 | − | 28.2843i | 1.34383 | − | 1.34383i | 0.451612 | − | 0.892215i | \(-0.350849\pi\) |
0.892215 | − | 0.451612i | \(-0.149151\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.1421i | 0.669650i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.0000 | − | 14.0000i | −0.661438 | − | 0.661438i | ||||
\(449\) | −12.7279 | −0.600668 | −0.300334 | − | 0.953834i | \(-0.597098\pi\) | ||||
−0.300334 | + | 0.953834i | \(0.597098\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 9.89949 | + | 9.89949i | 0.465633 | + | 0.465633i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 8.00000i | − | 0.375459i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.0000 | + | 25.0000i | −1.16945 | + | 1.16945i | −0.187112 | + | 0.982339i | \(0.559913\pi\) |
−0.982339 | + | 0.187112i | \(0.940087\pi\) | |||||||
\(458\) | 4.24264 | − | 4.24264i | 0.198246 | − | 0.198246i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.89949i | 0.461065i | 0.973065 | + | 0.230533i | \(0.0740469\pi\) | ||||
−0.973065 | + | 0.230533i | \(0.925953\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0000 | − | 10.0000i | −0.464739 | − | 0.464739i | 0.435466 | − | 0.900205i | \(-0.356584\pi\) |
−0.900205 | + | 0.435466i | \(0.856584\pi\) | |||||||
\(464\) | 4.24264 | 0.196960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00000 | −0.185296 | ||||||||
\(467\) | −2.82843 | − | 2.82843i | −0.130884 | − | 0.130884i | 0.638630 | − | 0.769514i | \(-0.279501\pi\) |
−0.769514 | + | 0.638630i | \(0.779501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000i | 0.738811i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.0000 | + | 18.0000i | −0.828517 | + | 0.828517i | ||||
\(473\) | 22.6274 | − | 22.6274i | 1.04041 | − | 1.04041i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.3137i | 0.518563i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | + | 12.0000i | 0.548867 | + | 0.548867i | ||||
\(479\) | 16.9706 | 0.775405 | 0.387702 | − | 0.921785i | \(-0.373269\pi\) | ||||
0.387702 | + | 0.921785i | \(0.373269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | 7.07107 | + | 7.07107i | 0.322078 | + | 0.322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | + | 10.0000i | −0.453143 | + | 0.453143i | −0.896396 | − | 0.443253i | \(-0.853824\pi\) |
0.443253 | + | 0.896396i | \(0.353824\pi\) | |||||||
\(488\) | −16.9706 | + | 16.9706i | −0.768221 | + | 0.768221i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1421i | 0.638226i | 0.947717 | + | 0.319113i | \(0.103385\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | − | 12.0000i | −0.540453 | − | 0.540453i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 11.3137 | + | 11.3137i | 0.507489 | + | 0.507489i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000i | 1.07439i | 0.843459 | + | 0.537194i | \(0.180516\pi\) | ||||
−0.843459 | + | 0.537194i | \(0.819484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.0000 | + | 14.0000i | −0.624851 | + | 0.624851i | ||||
\(503\) | −22.6274 | + | 22.6274i | −1.00891 | + | 1.00891i | −0.00894668 | + | 0.999960i | \(0.502848\pi\) |
−0.999960 | + | 0.00894668i | \(0.997152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.3137i | 0.502956i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0000 | + | 10.0000i | 0.443678 | + | 0.443678i | ||||
\(509\) | −4.24264 | −0.188052 | −0.0940259 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940259 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00000 | −0.176950 | ||||||||
\(512\) | 7.77817 | + | 7.77817i | 0.343750 | + | 0.343750i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.00000i | − | 0.0882162i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | − | 16.0000i | 0.703679 | − | 0.703679i | ||||
\(518\) | 2.82843 | − | 2.82843i | 0.124274 | − | 0.124274i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3848i | 0.805452i | 0.915321 | + | 0.402726i | \(0.131937\pi\) | ||||
−0.915321 | + | 0.402726i | \(0.868063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | + | 8.00000i | 0.349816 | + | 0.349816i | 0.860041 | − | 0.510225i | \(-0.170438\pi\) |
−0.510225 | + | 0.860041i | \(0.670438\pi\) | |||||||
\(524\) | 14.1421 | 0.617802 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.00000 | −0.174408 | ||||||||
\(527\) | 11.3137 | + | 11.3137i | 0.492833 | + | 0.492833i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000i | 0.304348i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.41421 | − | 1.41421i | 0.0612564 | − | 0.0612564i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 16.9706i | − | 0.733017i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.00000 | + | 9.00000i | 0.388018 | + | 0.388018i | ||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | 11.3137 | + | 11.3137i | 0.485965 | + | 0.485965i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 20.0000i | − | 0.857493i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | − | 20.0000i | 0.855138 | − | 0.855138i | −0.135622 | − | 0.990761i | \(-0.543303\pi\) |
0.990761 | + | 0.135622i | \(0.0433034\pi\) | |||||||
\(548\) | −7.07107 | + | 7.07107i | −0.302061 | + | 0.302061i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.0000 | + | 24.0000i | 1.02058 | + | 1.02058i | ||||
\(554\) | −15.5563 | −0.660926 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.0000 | −0.508913 | ||||||||
\(557\) | −2.82843 | − | 2.82843i | −0.119844 | − | 0.119844i | 0.644641 | − | 0.764485i | \(-0.277007\pi\) |
−0.764485 | + | 0.644641i | \(0.777007\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16.0000i | − | 0.676728i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.00000 | − | 7.00000i | 0.295277 | − | 0.295277i | ||||
\(563\) | 28.2843 | − | 28.2843i | 1.19204 | − | 1.19204i | 0.215546 | − | 0.976494i | \(-0.430847\pi\) |
0.976494 | − | 0.215546i | \(-0.0691532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 11.3137i | − | 0.475551i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | − | 12.0000i | −0.503509 | − | 0.503509i | ||||
\(569\) | 29.6985 | 1.24503 | 0.622513 | − | 0.782610i | \(-0.286112\pi\) | ||||
0.622513 | + | 0.782610i | \(0.286112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 2.82843 | + | 2.82843i | 0.118262 | + | 0.118262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 4.00000i | − | 0.166957i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | − | 17.0000i | 0.707719 | − | 0.707719i | −0.258336 | − | 0.966055i | \(-0.583174\pi\) |
0.966055 | + | 0.258336i | \(0.0831741\pi\) | |||||||
\(578\) | −0.707107 | + | 0.707107i | −0.0294118 | + | 0.0294118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.3137i | − | 0.469372i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | − | 8.00000i | −0.331326 | − | 0.331326i | ||||
\(584\) | 4.24264 | 0.175562 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0000 | 0.578335 | ||||||||
\(587\) | −19.7990 | − | 19.7990i | −0.817192 | − | 0.817192i | 0.168508 | − | 0.985700i | \(-0.446105\pi\) |
−0.985700 | + | 0.168508i | \(0.946105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | + | 1.00000i | −0.0410997 | + | 0.0410997i | ||||
\(593\) | −9.89949 | + | 9.89949i | −0.406524 | + | 0.406524i | −0.880524 | − | 0.474001i | \(-0.842809\pi\) |
0.474001 | + | 0.880524i | \(0.342809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.24264i | 0.173785i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.00000 | + | 4.00000i | 0.163572 | + | 0.163572i | ||||
\(599\) | −16.9706 | −0.693398 | −0.346699 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346699 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.00000 | 0.326327 | 0.163163 | − | 0.986599i | \(-0.447830\pi\) | ||||
0.163163 | + | 0.986599i | \(0.447830\pi\) | |||||||
\(602\) | −22.6274 | − | 22.6274i | −0.922225 | − | 0.922225i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 8.00000i | − | 0.325515i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.0000 | + | 22.0000i | −0.892952 | + | 0.892952i | −0.994800 | − | 0.101848i | \(-0.967525\pi\) |
0.101848 | + | 0.994800i | \(0.467525\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.3137i | − | 0.457704i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.00000i | −0.0403896 | − | 0.0403896i | 0.686624 | − | 0.727013i | \(-0.259092\pi\) |
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | −11.3137 | −0.456584 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 24.0000 | 0.966988 | ||||||||
\(617\) | 14.1421 | + | 14.1421i | 0.569341 | + | 0.569341i | 0.931944 | − | 0.362603i | \(-0.118112\pi\) |
−0.362603 | + | 0.931944i | \(0.618112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000i | 0.482321i | 0.970485 | + | 0.241160i | \(0.0775280\pi\) | ||||
−0.970485 | + | 0.241160i | \(0.922472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.00000 | + | 8.00000i | −0.320771 | + | 0.320771i | ||||
\(623\) | −25.4558 | + | 25.4558i | −1.01987 | + | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.8701i | 1.07394i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.00000 | − | 5.00000i | −0.199522 | − | 0.199522i | ||||
\(629\) | 5.65685 | 0.225554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | −25.4558 | − | 25.4558i | −1.01258 | − | 1.01258i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.0000i | 1.11202i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | + | 1.00000i | −0.0396214 | + | 0.0396214i | ||||
\(638\) | −8.48528 | + | 8.48528i | −0.335936 | + | 0.335936i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 15.5563i | − | 0.614439i | −0.951639 | − | 0.307219i | \(-0.900601\pi\) | ||
0.951639 | − | 0.307219i | \(-0.0993986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0000 | − | 28.0000i | −1.10421 | − | 1.10421i | −0.993897 | − | 0.110316i | \(-0.964814\pi\) |
−0.110316 | − | 0.993897i | \(-0.535186\pi\) | |||||||
\(644\) | −11.3137 | −0.445823 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.2843 | − | 28.2843i | −1.11197 | − | 1.11197i | −0.992884 | − | 0.119085i | \(-0.962004\pi\) |
−0.119085 | − | 0.992884i | \(-0.537996\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00000 | − | 8.00000i | 0.313304 | − | 0.313304i | ||||
\(653\) | 2.82843 | − | 2.82843i | 0.110685 | − | 0.110685i | −0.649595 | − | 0.760280i | \(-0.725062\pi\) |
0.760280 | + | 0.649595i | \(0.225062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.41421i | 0.0552158i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.0000 | − | 16.0000i | −0.623745 | − | 0.623745i | ||||
\(659\) | −8.48528 | −0.330540 | −0.165270 | − | 0.986248i | \(-0.552849\pi\) | ||||
−0.165270 | + | 0.986248i | \(0.552849\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.0000 | −1.55582 | −0.777910 | − | 0.628376i | \(-0.783720\pi\) | ||||
−0.777910 | + | 0.628376i | \(0.783720\pi\) | |||||||
\(662\) | −5.65685 | − | 5.65685i | −0.219860 | − | 0.219860i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000i | 0.465690i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | − | 12.0000i | 0.464642 | − | 0.464642i | ||||
\(668\) | 14.1421 | − | 14.1421i | 0.547176 | − | 0.547176i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 22.6274i | − | 0.873522i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.00000i | −0.0385472 | − | 0.0385472i | 0.687570 | − | 0.726118i | \(-0.258677\pi\) |
−0.726118 | + | 0.687570i | \(0.758677\pi\) | |||||||
\(674\) | −7.07107 | −0.272367 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | 31.1127 | + | 31.1127i | 1.19576 | + | 1.19576i | 0.975425 | + | 0.220334i | \(0.0707146\pi\) |
0.220334 | + | 0.975425i | \(0.429285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 44.0000i | − | 1.68857i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.00000 | − | 8.00000i | 0.306336 | − | 0.306336i | ||||
\(683\) | 2.82843 | − | 2.82843i | 0.108227 | − | 0.108227i | −0.650920 | − | 0.759147i | \(-0.725617\pi\) |
0.759147 | + | 0.650920i | \(0.225617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 16.9706i | − | 0.647939i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | + | 8.00000i | 0.304997 | + | 0.304997i | ||||
\(689\) | −5.65685 | −0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 9.89949 | + | 9.89949i | 0.376322 | + | 0.376322i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000i | 0.607352i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | − | 4.00000i | 0.151511 | − | 0.151511i | ||||
\(698\) | −16.9706 | + | 16.9706i | −0.642345 | + | 0.642345i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.07107i | − | 0.267071i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) | ||
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −19.7990 | −0.746203 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00000 | −0.150542 | ||||||||
\(707\) | −31.1127 | − | 31.1127i | −1.17011 | − | 1.17011i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.00000i | − | 0.225335i | −0.993633 | − | 0.112667i | \(-0.964061\pi\) | ||
0.993633 | − | 0.112667i | \(-0.0359394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.0000 | − | 27.0000i | 1.01187 | − | 1.01187i | ||||
\(713\) | −11.3137 | + | 11.3137i | −0.423702 | + | 0.423702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 25.4558i | − | 0.951330i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0000 | −1.48968 | ||||||||
\(722\) | −13.4350 | − | 13.4350i | −0.500000 | − | 0.500000i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.0000i | 0.594635i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | − | 2.00000i | 0.0741759 | − | 0.0741759i | −0.669046 | − | 0.743221i | \(-0.733297\pi\) |
0.743221 | + | 0.669046i | \(0.233297\pi\) | |||||||
\(728\) | 8.48528 | − | 8.48528i | 0.314485 | − | 0.314485i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 45.2548i | − | 1.67381i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.00000 | − | 1.00000i | −0.0369358 | − | 0.0369358i | 0.688398 | − | 0.725333i | \(-0.258314\pi\) |
−0.725333 | + | 0.688398i | \(0.758314\pi\) | |||||||
\(734\) | −2.82843 | −0.104399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.0000 | 0.737210 | ||||||||
\(737\) | 11.3137 | + | 11.3137i | 0.416746 | + | 0.416746i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.00000 | + | 8.00000i | −0.293689 | + | 0.293689i | ||||
\(743\) | −22.6274 | + | 22.6274i | −0.830119 | + | 0.830119i | −0.987533 | − | 0.157413i | \(-0.949684\pi\) |
0.157413 | + | 0.987533i | \(0.449684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 24.0416i | − | 0.880227i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00000 | + | 8.00000i | 0.292509 | + | 0.292509i | ||||
\(749\) | −11.3137 | −0.413394 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | 5.65685 | + | 5.65685i | 0.206284 | + | 0.206284i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000i | 0.218507i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0000 | + | 19.0000i | −0.690567 | + | 0.690567i | −0.962357 | − | 0.271790i | \(-0.912384\pi\) |
0.271790 | + | 0.962357i | \(0.412384\pi\) | |||||||
\(758\) | 25.4558 | − | 25.4558i | 0.924598 | − | 0.924598i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.3259i | 1.89681i | 0.317058 | + | 0.948406i | \(0.397305\pi\) | ||||
−0.317058 | + | 0.948406i | \(0.602695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.6274 | 0.818631 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.0000 | 1.15621 | ||||||||
\(767\) | −8.48528 | − | 8.48528i | −0.306386 | − | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0000i | 0.865462i | 0.901523 | + | 0.432731i | \(0.142450\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | + | 1.00000i | −0.0359908 | + | 0.0359908i | ||||
\(773\) | 2.82843 | − | 2.82843i | 0.101731 | − | 0.101731i | −0.654409 | − | 0.756141i | \(-0.727083\pi\) |
0.756141 | + | 0.654409i | \(0.227083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 46.6690i | 1.67532i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.00000 | − | 3.00000i | −0.107555 | − | 0.107555i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 11.3137 | + | 11.3137i | 0.404577 | + | 0.404577i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | + | 4.00000i | −0.142585 | + | 0.142585i | −0.774796 | − | 0.632211i | \(-0.782147\pi\) |
0.632211 | + | 0.774796i | \(0.282147\pi\) | |||||||
\(788\) | 9.89949 | − | 9.89949i | 0.352655 | − | 0.352655i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.5980i | 1.40794i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | − | 8.00000i | −0.284088 | − | 0.284088i | ||||
\(794\) | 26.8701 | 0.953583 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.41421 | + | 1.41421i | 0.0500940 | + | 0.0500940i | 0.731710 | − | 0.681616i | \(-0.238723\pi\) |
−0.681616 | + | 0.731710i | \(0.738723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 32.0000i | − | 1.13208i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.0000 | + | 17.0000i | −0.600291 | + | 0.600291i | ||||
\(803\) | −2.82843 | + | 2.82843i | −0.0998130 | + | 0.0998130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 5.65685i | − | 0.199254i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.0000 | + | 33.0000i | 1.16094 | + | 1.16094i | ||||
\(809\) | 12.7279 | 0.447490 | 0.223745 | − | 0.974648i | \(-0.428172\pi\) | ||||
0.223745 | + | 0.974648i | \(0.428172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −8.48528 | − | 8.48528i | −0.297775 | − | 0.297775i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 4.00000i | − | 0.140200i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.9706 | − | 16.9706i | 0.593362 | − | 0.593362i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.3553i | 1.23391i | 0.786998 | + | 0.616955i | \(0.211634\pi\) | ||||
−0.786998 | + | 0.616955i | \(0.788366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0000 | − | 10.0000i | −0.348578 | − | 0.348578i | 0.511002 | − | 0.859580i | \(-0.329275\pi\) |
−0.859580 | + | 0.511002i | \(0.829275\pi\) | |||||||
\(824\) | 42.4264 | 1.47799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0000 | −0.835067 | ||||||||
\(827\) | 22.6274 | + | 22.6274i | 0.786832 | + | 0.786832i | 0.980974 | − | 0.194141i | \(-0.0621920\pi\) |
−0.194141 | + | 0.980974i | \(0.562192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.00000 | + | 7.00000i | −0.242681 | + | 0.242681i | ||||
\(833\) | −2.82843 | + | 2.82843i | −0.0979992 | + | 0.0979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | − | 6.00000i | −0.207267 | − | 0.207267i | ||||
\(839\) | −33.9411 | −1.17178 | −0.585889 | − | 0.810391i | \(-0.699255\pi\) | ||||
−0.585889 | + | 0.810391i | \(0.699255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | 7.07107 | + | 7.07107i | 0.243685 | + | 0.243685i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000i | 0.137686i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000 | − | 6.00000i | 0.206162 | − | 0.206162i | ||||
\(848\) | 2.82843 | − | 2.82843i | 0.0971286 | − | 0.0971286i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.65685i | 0.193914i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0000 | + | 17.0000i | 0.582069 | + | 0.582069i | 0.935471 | − | 0.353402i | \(-0.114975\pi\) |
−0.353402 | + | 0.935471i | \(0.614975\pi\) | |||||||
\(854\) | −22.6274 | −0.774294 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 31.1127 | + | 31.1127i | 1.06279 | + | 1.06279i | 0.997892 | + | 0.0648976i | \(0.0206721\pi\) |
0.0648976 | + | 0.997892i | \(0.479328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.0000i | − | 0.409435i | −0.978821 | − | 0.204717i | \(-0.934372\pi\) | ||
0.978821 | − | 0.204717i | \(-0.0656275\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.00000 | − | 4.00000i | 0.136241 | − | 0.136241i | ||||
\(863\) | 2.82843 | − | 2.82843i | 0.0962808 | − | 0.0962808i | −0.657326 | − | 0.753607i | \(-0.728312\pi\) |
0.753607 | + | 0.657326i | \(0.228312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 24.0416i | − | 0.816968i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.00000 | + | 8.00000i | 0.271538 | + | 0.271538i | ||||
\(869\) | 33.9411 | 1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0000 | + | 13.0000i | −0.438979 | + | 0.438979i | −0.891668 | − | 0.452689i | \(-0.850465\pi\) |
0.452689 | + | 0.891668i | \(0.350465\pi\) | |||||||
\(878\) | −16.9706 | + | 16.9706i | −0.572729 | + | 0.572729i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.07107i | − | 0.238230i | −0.992880 | − | 0.119115i | \(-0.961994\pi\) | ||
0.992880 | − | 0.119115i | \(-0.0380058\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | + | 8.00000i | 0.269221 | + | 0.269221i | 0.828786 | − | 0.559565i | \(-0.189032\pi\) |
−0.559565 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.0000 | −1.34383 | ||||||||
\(887\) | 14.1421 | + | 14.1421i | 0.474846 | + | 0.474846i | 0.903479 | − | 0.428632i | \(-0.141004\pi\) |
−0.428632 | + | 0.903479i | \(0.641004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.0000i | 1.34156i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.0000 | + | 10.0000i | −0.334825 | + | 0.334825i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 8.48528i | − | 0.283473i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.00000 | + | 9.00000i | 0.300334 | + | 0.300334i | ||||
\(899\) | −16.9706 | −0.566000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | −2.82843 | − | 2.82843i | −0.0941763 | − | 0.0941763i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 42.0000i | − | 1.39690i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | − | 20.0000i | 0.664089 | − | 0.664089i | −0.292252 | − | 0.956341i | \(-0.594405\pi\) |
0.956341 | + | 0.292252i | \(0.0944047\pi\) | |||||||
\(908\) | 5.65685 | − | 5.65685i | 0.187729 | − | 0.187729i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6274i | 0.749680i | 0.927090 | + | 0.374840i | \(0.122302\pi\) | ||||
−0.927090 | + | 0.374840i | \(0.877698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | − | 8.00000i | −0.264761 | − | 0.264761i | ||||
\(914\) | 35.3553 | 1.16945 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000 | 0.198246 | ||||||||
\(917\) | 28.2843 | + | 28.2843i | 0.934029 | + | 0.934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0000i | 1.18753i | 0.804638 | + | 0.593765i | \(0.202359\pi\) | ||||
−0.804638 | + | 0.593765i | \(0.797641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.00000 | − | 7.00000i | 0.230533 | − | 0.230533i | ||||
\(923\) | 5.65685 | − | 5.65685i | 0.186198 | − | 0.186198i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.1421i | 0.464739i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.0000 | + | 15.0000i | 0.492399 | + | 0.492399i | ||||
\(929\) | −46.6690 | −1.53116 | −0.765581 | − | 0.643340i | \(-0.777548\pi\) | ||||
−0.765581 | + | 0.643340i | \(0.777548\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.82843 | − | 2.82843i | −0.0926482 | − | 0.0926482i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.00000i | 0.130884i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0000 | + | 37.0000i | −1.20874 | + | 1.20874i | −0.237301 | + | 0.971436i | \(0.576263\pi\) |
−0.971436 | + | 0.237301i | \(0.923737\pi\) | |||||||
\(938\) | 11.3137 | − | 11.3137i | 0.369406 | − | 0.369406i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.41421i | 0.0461020i | 0.999734 | + | 0.0230510i | \(0.00733802\pi\) | ||||
−0.999734 | + | 0.0230510i | \(0.992662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | + | 4.00000i | 0.130258 | + | 0.130258i | ||||
\(944\) | 8.48528 | 0.276172 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.0000 | −1.04041 | ||||||||
\(947\) | 5.65685 | + | 5.65685i | 0.183823 | + | 0.183823i | 0.793019 | − | 0.609196i | \(-0.208508\pi\) |
−0.609196 | + | 0.793019i | \(0.708508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.00000i | 0.0649227i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 24.0000 | − | 24.0000i | 0.777844 | − | 0.777844i | ||||
\(953\) | 15.5563 | − | 15.5563i | 0.503920 | − | 0.503920i | −0.408734 | − | 0.912654i | \(-0.634030\pi\) |
0.912654 | + | 0.408734i | \(0.134030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.9706i | 0.548867i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0000 | − | 12.0000i | −0.387702 | − | 0.387702i | ||||
\(959\) | −28.2843 | −0.913347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | −1.41421 | − | 1.41421i | −0.0455961 | − | 0.0455961i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000i | 0.322078i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | + | 22.0000i | −0.707472 | + | 0.707472i | −0.966003 | − | 0.258531i | \(-0.916762\pi\) |
0.258531 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(968\) | −6.36396 | + | 6.36396i | −0.204545 | + | 0.204545i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 19.7990i | − | 0.635380i | −0.948195 | − | 0.317690i | \(-0.897093\pi\) | ||
0.948195 | − | 0.317690i | \(-0.102907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | − | 24.0000i | −0.769405 | − | 0.769405i | ||||
\(974\) | 14.1421 | 0.453143 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | −36.7696 | − | 36.7696i | −1.17636 | − | 1.17636i | −0.980664 | − | 0.195698i | \(-0.937303\pi\) |
−0.195698 | − | 0.980664i | \(-0.562697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000i | 1.15056i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.0000 | − | 10.0000i | 0.319113 | − | 0.319113i | ||||
\(983\) | −22.6274 | + | 22.6274i | −0.721703 | + | 0.721703i | −0.968952 | − | 0.247249i | \(-0.920473\pi\) |
0.247249 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.9706i | 0.540453i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.2548 | 1.43902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | −14.1421 | − | 14.1421i | −0.449013 | − | 0.449013i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 16.0000i | − | 0.507489i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.0000 | + | 25.0000i | −0.791758 | + | 0.791758i | −0.981780 | − | 0.190022i | \(-0.939144\pi\) |
0.190022 | + | 0.981780i | \(0.439144\pi\) | |||||||
\(998\) | 16.9706 | − | 16.9706i | 0.537194 | − | 0.537194i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))