Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(199,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.199 |
Dual form | 675.2.k.a.424.2 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | −0.161521 | − | 0.986869i | \(-0.551640\pi\) |
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59808 | − | 1.50000i | 0.981981 | − | 0.566947i | 0.0791130 | − | 0.996866i | \(-0.474791\pi\) |
0.902867 | + | 0.429919i | \(0.141458\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.73205 | + | 1.00000i | 0.480384 | + | 0.277350i | 0.720577 | − | 0.693375i | \(-0.243877\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | 1.50000 | − | 2.59808i | 0.400892 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 4.00000i | 0.970143i | 0.874475 | + | 0.485071i | \(0.161206\pi\) | ||||
−0.874475 | + | 0.485071i | \(0.838794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.00000 | 1.83533 | 0.917663 | − | 0.397360i | \(-0.130073\pi\) | ||||
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.73205 | − | 1.00000i | −0.369274 | − | 0.213201i | ||||
\(23\) | 2.59808 | + | 1.50000i | 0.541736 | + | 0.312772i | 0.745782 | − | 0.666190i | \(-0.232076\pi\) |
−0.204046 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00000i | 0.566947i | ||||||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | −4.33013 | − | 2.50000i | −0.765466 | − | 0.441942i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 6.92820 | − | 4.00000i | 1.12390 | − | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | − | 4.33013i | 0.390434 | − | 0.676252i | −0.602072 | − | 0.798441i | \(-0.705658\pi\) |
0.992507 | + | 0.122189i | \(0.0389915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.92820 | + | 4.00000i | −1.05654 | + | 0.609994i | −0.924473 | − | 0.381246i | \(-0.875495\pi\) |
−0.132068 | + | 0.991241i | \(0.542162\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | 0.442326 | ||||||||
\(47\) | 6.06218 | − | 3.50000i | 0.884260 | − | 0.510527i | 0.0121990 | − | 0.999926i | \(-0.496117\pi\) |
0.872060 | + | 0.489398i | \(0.162783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 1.73205i | 0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.73205 | + | 1.00000i | −0.240192 | + | 0.138675i | ||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.50000 | + | 7.79423i | 0.601338 | + | 1.04155i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.866025 | + | 0.500000i | 0.113715 | + | 0.0656532i | ||||
\(59\) | 7.00000 | − | 12.1244i | 0.911322 | − | 1.57846i | 0.0991242 | − | 0.995075i | \(-0.468396\pi\) |
0.812198 | − | 0.583382i | \(-0.198271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.50000 | − | 6.06218i | −0.448129 | − | 0.776182i | 0.550135 | − | 0.835076i | \(-0.314576\pi\) |
−0.998264 | + | 0.0588933i | \(0.981243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.59808 | − | 1.50000i | −0.317406 | − | 0.183254i | 0.332830 | − | 0.942987i | \(-0.391996\pi\) |
−0.650236 | + | 0.759733i | \(0.725330\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 2.00000 | + | 3.46410i | 0.232495 | + | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | + | 6.92820i | −0.458831 | + | 0.794719i | ||||
\(77\) | −5.19615 | − | 3.00000i | −0.592157 | − | 0.341882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | − | 5.19615i | −0.337526 | − | 0.584613i | 0.646440 | − | 0.762964i | \(-0.276257\pi\) |
−0.983967 | + | 0.178352i | \(0.942924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 5.00000i | − | 0.552158i | ||||||
\(83\) | −7.79423 | + | 4.50000i | −0.855528 | + | 0.493939i | −0.862512 | − | 0.506036i | \(-0.831110\pi\) |
0.00698436 | + | 0.999976i | \(0.497777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.19615 | − | 3.00000i | 0.553912 | − | 0.319801i | ||||
\(89\) | −15.0000 | −1.59000 | −0.794998 | − | 0.606612i | \(-0.792528\pi\) | ||||
−0.794998 | + | 0.606612i | \(0.792528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | −2.59808 | + | 1.50000i | −0.270868 | + | 0.156386i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.50000 | − | 6.06218i | 0.360997 | − | 0.625266i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.73205 | + | 1.00000i | −0.175863 | + | 0.101535i | −0.585348 | − | 0.810782i | \(-0.699042\pi\) |
0.409484 | + | 0.912317i | \(0.365709\pi\) | |||||||
\(98\) | − | 2.00000i | − | 0.202031i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | −3.00000 | + | 5.19615i | −0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | + | 1.73205i | 0.0971286 | + | 0.168232i | ||||
\(107\) | 3.00000i | 0.290021i | 0.989430 | + | 0.145010i | \(0.0463216\pi\) | ||||
−0.989430 | + | 0.145010i | \(0.953678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.59808 | + | 1.50000i | 0.245495 | + | 0.141737i | ||||
\(113\) | −6.92820 | − | 4.00000i | −0.651751 | − | 0.376288i | 0.137376 | − | 0.990519i | \(-0.456133\pi\) |
−0.789127 | + | 0.614231i | \(0.789466\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.0000i | − | 1.28880i | ||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | −6.06218 | − | 3.50000i | −0.548844 | − | 0.316875i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000i | 0.443678i | 0.975083 | + | 0.221839i | \(0.0712060\pi\) | ||||
−0.975083 | + | 0.221839i | \(0.928794\pi\) | |||||||
\(128\) | 2.59808 | − | 1.50000i | 0.229640 | − | 0.132583i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.7846 | − | 12.0000i | 1.80225 | − | 1.04053i | ||||
\(134\) | −3.00000 | −0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | −1.02899 | ||||||||
\(137\) | 10.3923 | − | 6.00000i | 0.887875 | − | 0.512615i | 0.0146279 | − | 0.999893i | \(-0.495344\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | + | 13.8564i | −0.678551 | + | 1.17529i | 0.296866 | + | 0.954919i | \(0.404058\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.73205 | + | 1.00000i | −0.145350 | + | 0.0839181i | ||||
\(143\) | − | 4.00000i | − | 0.334497i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | + | 3.46410i | 0.165521 | + | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | −8.50000 | + | 14.7224i | −0.696347 | + | 1.20611i | 0.273377 | + | 0.961907i | \(0.411859\pi\) |
−0.969724 | + | 0.244202i | \(0.921474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 24.0000i | 1.94666i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1244 | + | 7.00000i | 0.967629 | + | 0.558661i | 0.898513 | − | 0.438948i | \(-0.144649\pi\) |
0.0691164 | + | 0.997609i | \(0.477982\pi\) | |||||||
\(158\) | −5.19615 | − | 3.00000i | −0.413384 | − | 0.238667i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.00000 | 0.709299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 2.50000 | + | 4.33013i | 0.195217 | + | 0.338126i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | 7.79423 | + | 4.50000i | 0.603136 | + | 0.348220i | 0.770274 | − | 0.637713i | \(-0.220119\pi\) |
−0.167139 | + | 0.985933i | \(0.553453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.50000 | − | 7.79423i | −0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | − | 1.73205i | 0.0753778 | − | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9904 | + | 7.50000i | −0.973670 | + | 0.562149i | ||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 5.19615 | − | 3.00000i | 0.385164 | − | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.50000 | + | 7.79423i | −0.331744 | + | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92820 | − | 4.00000i | 0.506640 | − | 0.292509i | ||||
\(188\) | 7.00000i | 0.510527i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | + | 6.92820i | 0.289430 | + | 0.501307i | 0.973674 | − | 0.227946i | \(-0.0732010\pi\) |
−0.684244 | + | 0.729253i | \(0.739868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.66025 | + | 5.00000i | 0.623379 | + | 0.359908i | 0.778183 | − | 0.628037i | \(-0.216141\pi\) |
−0.154805 | + | 0.987945i | \(0.549475\pi\) | |||||||
\(194\) | −1.00000 | + | 1.73205i | −0.0717958 | + | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 1.73205i | 0.0714286 | + | 0.123718i | ||||
\(197\) | − | 12.0000i | − | 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.5885 | − | 9.00000i | −1.09680 | − | 0.633238i | ||||
\(203\) | 2.59808 | + | 1.50000i | 0.182349 | + | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | −8.00000 | − | 13.8564i | −0.553372 | − | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0000 | − | 19.0526i | 0.757271 | − | 1.31163i | −0.186966 | − | 0.982366i | \(-0.559865\pi\) |
0.944237 | − | 0.329266i | \(-0.106801\pi\) | |||||||
\(212\) | −1.73205 | − | 1.00000i | −0.118958 | − | 0.0686803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.33013 | + | 2.50000i | −0.293273 | + | 0.169321i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | + | 6.92820i | −0.269069 | + | 0.466041i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.4545 | + | 9.50000i | −1.10187 | + | 0.636167i | −0.936713 | − | 0.350100i | \(-0.886148\pi\) |
−0.165161 | + | 0.986267i | \(0.552814\pi\) | |||||||
\(224\) | −15.0000 | −1.00223 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | −3.46410 | + | 2.00000i | −0.229920 | + | 0.132745i | −0.610535 | − | 0.791989i | \(-0.709046\pi\) |
0.380615 | + | 0.924734i | \(0.375712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.50000 | − | 12.9904i | 0.495614 | − | 0.858429i | −0.504373 | − | 0.863486i | \(-0.668276\pi\) |
0.999987 | + | 0.00505719i | \(0.00160976\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.59808 | + | 1.50000i | −0.170572 | + | 0.0984798i | ||||
\(233\) | − | 24.0000i | − | 1.57229i | −0.618041 | − | 0.786146i | \(-0.712073\pi\) | ||
0.618041 | − | 0.786146i | \(-0.287927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | + | 12.1244i | 0.455661 | + | 0.789228i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.3923 | + | 6.00000i | 0.673633 | + | 0.388922i | ||||
\(239\) | 4.00000 | − | 6.92820i | 0.258738 | − | 0.448148i | −0.707166 | − | 0.707048i | \(-0.750027\pi\) |
0.965904 | + | 0.258900i | \(0.0833599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.50000 | + | 9.52628i | 0.354286 | + | 0.613642i | 0.986996 | − | 0.160748i | \(-0.0513906\pi\) |
−0.632709 | + | 0.774389i | \(0.718057\pi\) | |||||||
\(242\) | − | 7.00000i | − | 0.449977i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.00000 | 0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8564 | + | 8.00000i | 0.881662 | + | 0.509028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 2.50000 | + | 4.33013i | 0.156864 | + | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 5.19615 | + | 3.00000i | 0.324127 | + | 0.187135i | 0.653231 | − | 0.757159i | \(-0.273413\pi\) |
−0.329104 | + | 0.944294i | \(0.606747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | + | 10.3923i | 0.372822 | + | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000i | 0.370681i | ||||||||
\(263\) | 13.8564 | − | 8.00000i | 0.854423 | − | 0.493301i | −0.00771799 | − | 0.999970i | \(-0.502457\pi\) |
0.862141 | + | 0.506669i | \(0.169123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.0000 | − | 20.7846i | 0.735767 | − | 1.27439i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.59808 | − | 1.50000i | 0.158703 | − | 0.0916271i | ||||
\(269\) | 25.0000 | 1.52428 | 0.762138 | − | 0.647414i | \(-0.224150\pi\) | ||||
0.762138 | + | 0.647414i | \(0.224150\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −3.46410 | + | 2.00000i | −0.210042 | + | 0.121268i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3923 | + | 6.00000i | −0.624413 | + | 0.360505i | −0.778585 | − | 0.627539i | \(-0.784062\pi\) |
0.154172 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.50000 | − | 12.9904i | −0.447412 | − | 0.774941i | 0.550804 | − | 0.834634i | \(-0.314321\pi\) |
−0.998217 | + | 0.0596933i | \(0.980988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1865 | − | 10.5000i | −1.08108 | − | 0.624160i | −0.149890 | − | 0.988703i | \(-0.547892\pi\) |
−0.931187 | + | 0.364542i | \(0.881225\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | − | 3.46410i | −0.118262 | − | 0.204837i | ||||
\(287\) | − | 15.0000i | − | 0.885422i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.46410 | − | 2.00000i | −0.202721 | − | 0.117041i | ||||
\(293\) | 10.3923 | + | 6.00000i | 0.607125 | + | 0.350524i | 0.771839 | − | 0.635818i | \(-0.219337\pi\) |
−0.164714 | + | 0.986341i | \(0.552670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.0000 | −0.697486 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.0000i | 0.984784i | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | + | 20.7846i | −0.691669 | + | 1.19800i | ||||
\(302\) | 1.73205 | + | 1.00000i | 0.0996683 | + | 0.0575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | + | 6.92820i | 0.229416 | + | 0.397360i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.00000i | − | 0.399511i | −0.979846 | − | 0.199756i | \(-0.935985\pi\) | ||
0.979846 | − | 0.199756i | \(-0.0640148\pi\) | |||||||
\(308\) | 5.19615 | − | 3.00000i | 0.296078 | − | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1244 | − | 7.00000i | 0.685309 | − | 0.395663i | −0.116543 | − | 0.993186i | \(-0.537181\pi\) |
0.801852 | + | 0.597522i | \(0.203848\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | −29.4449 | + | 17.0000i | −1.65379 | + | 0.954815i | −0.678294 | + | 0.734791i | \(0.737280\pi\) |
−0.975494 | + | 0.220024i | \(0.929386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.00000 | − | 1.73205i | 0.0559893 | − | 0.0969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.79423 | − | 4.50000i | 0.434355 | − | 0.250775i | ||||
\(323\) | 32.0000i | 1.78053i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00000 | − | 3.46410i | −0.110770 | − | 0.191859i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.9904 | + | 7.50000i | 0.717274 | + | 0.414118i | ||||
\(329\) | 10.5000 | − | 18.1865i | 0.578884 | − | 1.00266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.00000 | + | 5.19615i | 0.164895 | + | 0.285606i | 0.936618 | − | 0.350352i | \(-0.113938\pi\) |
−0.771723 | + | 0.635959i | \(0.780605\pi\) | |||||||
\(332\) | − | 9.00000i | − | 0.493939i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.00000 | 0.492458 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.92820 | − | 4.00000i | −0.377403 | − | 0.217894i | 0.299285 | − | 0.954164i | \(-0.403252\pi\) |
−0.676688 | + | 0.736270i | \(0.736585\pi\) | |||||||
\(338\) | −7.79423 | − | 4.50000i | −0.423950 | − | 0.244768i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −12.0000 | − | 20.7846i | −0.646997 | − | 1.12063i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.46410 | − | 2.00000i | −0.185963 | − | 0.107366i | 0.404128 | − | 0.914702i | \(-0.367575\pi\) |
−0.590091 | + | 0.807337i | \(0.700908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.50000 | − | 4.33013i | −0.133822 | − | 0.231786i | 0.791325 | − | 0.611396i | \(-0.209392\pi\) |
−0.925147 | + | 0.379610i | \(0.876058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.0000i | 0.533002i | ||||||||
\(353\) | −20.7846 | + | 12.0000i | −1.10625 | + | 0.638696i | −0.937856 | − | 0.347024i | \(-0.887192\pi\) |
−0.168397 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.50000 | − | 12.9904i | 0.397499 | − | 0.688489i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.73205 | + | 1.00000i | −0.0915417 | + | 0.0528516i | ||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | −6.06218 | + | 3.50000i | −0.318621 | + | 0.183956i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | + | 5.19615i | −0.157243 | + | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.7846 | + | 12.0000i | −1.08495 | + | 0.626395i | −0.932227 | − | 0.361874i | \(-0.882137\pi\) |
−0.152721 | + | 0.988269i | \(0.548804\pi\) | |||||||
\(368\) | 3.00000i | 0.156386i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | + | 5.19615i | 0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.66025 | − | 5.00000i | −0.448411 | − | 0.258890i | 0.258748 | − | 0.965945i | \(-0.416690\pi\) |
−0.707159 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5000 | + | 18.1865i | 0.541496 | + | 0.937899i | ||||
\(377\) | 2.00000i | 0.103005i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.92820 | + | 4.00000i | 0.354478 | + | 0.204658i | ||||
\(383\) | 31.1769 | + | 18.0000i | 1.59307 | + | 0.919757i | 0.992777 | + | 0.119974i | \(0.0382810\pi\) |
0.600289 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | −16.5000 | − | 28.5788i | −0.836583 | − | 1.44900i | −0.892735 | − | 0.450582i | \(-0.851216\pi\) |
0.0561516 | − | 0.998422i | \(-0.482117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | + | 10.3923i | −0.303433 | + | 0.525561i | ||||
\(392\) | 5.19615 | + | 3.00000i | 0.262445 | + | 0.151523i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | − | 10.3923i | −0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.0000i | − | 1.70641i | −0.521575 | − | 0.853206i | \(-0.674655\pi\) | ||
0.521575 | − | 0.853206i | \(-0.325345\pi\) | |||||||
\(398\) | −3.46410 | + | 2.00000i | −0.173640 | + | 0.100251i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | 0.148888 | ||||||||
\(407\) | 6.92820 | − | 4.00000i | 0.343418 | − | 0.198273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.92820 | − | 4.00000i | 0.341328 | − | 0.197066i | ||||
\(413\) | − | 42.0000i | − | 2.06668i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.00000 | − | 8.66025i | −0.245145 | − | 0.424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.8564 | − | 8.00000i | −0.677739 | − | 0.391293i | ||||
\(419\) | −13.0000 | + | 22.5167i | −0.635092 | + | 1.10001i | 0.351404 | + | 0.936224i | \(0.385704\pi\) |
−0.986496 | + | 0.163787i | \(0.947629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0000 | − | 29.4449i | −0.828529 | − | 1.43505i | −0.899192 | − | 0.437555i | \(-0.855845\pi\) |
0.0706626 | − | 0.997500i | \(-0.477489\pi\) | |||||||
\(422\) | − | 22.0000i | − | 1.07094i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.1865 | − | 10.5000i | −0.880108 | − | 0.508131i | ||||
\(428\) | −2.59808 | − | 1.50000i | −0.125583 | − | 0.0725052i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000 | 1.44505 | 0.722525 | − | 0.691345i | \(-0.242982\pi\) | ||||
0.722525 | + | 0.691345i | \(0.242982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000i | 1.34559i | 0.739827 | + | 0.672797i | \(0.234907\pi\) | ||||
−0.739827 | + | 0.672797i | \(0.765093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.50000 | − | 4.33013i | 0.119728 | − | 0.207375i | ||||
\(437\) | 20.7846 | + | 12.0000i | 0.994263 | + | 0.574038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | −12.9904 | + | 7.50000i | −0.617192 | + | 0.356336i | −0.775775 | − | 0.631010i | \(-0.782641\pi\) |
0.158583 | + | 0.987346i | \(0.449307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.50000 | + | 16.4545i | −0.449838 | + | 0.779142i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.1865 | + | 10.5000i | −0.859233 | + | 0.496078i | ||||
\(449\) | −26.0000 | −1.22702 | −0.613508 | − | 0.789689i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789689i | \(0.710242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | −0.470882 | ||||||||
\(452\) | 6.92820 | − | 4.00000i | 0.325875 | − | 0.188144i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.00000 | + | 3.46410i | −0.0938647 | + | 0.162578i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3205 | − | 10.0000i | 0.810219 | − | 0.467780i | −0.0368128 | − | 0.999322i | \(-0.511721\pi\) |
0.847032 | + | 0.531542i | \(0.178387\pi\) | |||||||
\(458\) | − | 15.0000i | − | 0.700904i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50000 | + | 7.79423i | 0.209586 | + | 0.363013i | 0.951584 | − | 0.307388i | \(-0.0994551\pi\) |
−0.741998 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.1769 | + | 18.0000i | 1.44891 | + | 0.836531i | 0.998417 | − | 0.0562469i | \(-0.0179134\pi\) |
0.450497 | + | 0.892778i | \(0.351247\pi\) | |||||||
\(464\) | −0.500000 | + | 0.866025i | −0.0232119 | + | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | − | 20.7846i | −0.555889 | − | 0.962828i | ||||
\(467\) | 20.0000i | 0.925490i | 0.886492 | + | 0.462745i | \(0.153135\pi\) | ||||
−0.886492 | + | 0.462745i | \(0.846865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.00000 | −0.415581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.3731 | + | 21.0000i | 1.67421 | + | 0.966603i | ||||
\(473\) | 13.8564 | + | 8.00000i | 0.637118 | + | 0.367840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.0000 | −0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 8.00000i | − | 0.365911i | ||||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | 9.52628 | + | 5.50000i | 0.433910 | + | 0.250518i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000i | 0.725029i | 0.931978 | + | 0.362515i | \(0.118082\pi\) | ||||
−0.931978 | + | 0.362515i | \(0.881918\pi\) | |||||||
\(488\) | 18.1865 | − | 10.5000i | 0.823266 | − | 0.475313i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0000 | − | 17.3205i | 0.451294 | − | 0.781664i | −0.547173 | − | 0.837020i | \(-0.684296\pi\) |
0.998467 | + | 0.0553560i | \(0.0176294\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.46410 | + | 2.00000i | −0.156015 | + | 0.0900755i | ||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.19615 | + | 3.00000i | −0.233079 | + | 0.134568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0000 | + | 27.7128i | −0.716258 | + | 1.24060i | 0.246214 | + | 0.969216i | \(0.420813\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00000i | 0.312115i | 0.987748 | + | 0.156057i | \(0.0498784\pi\) | ||||
−0.987748 | + | 0.156057i | \(0.950122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.00000 | − | 5.19615i | −0.133366 | − | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.33013 | − | 2.50000i | −0.192118 | − | 0.110920i | ||||
\(509\) | −21.5000 | + | 37.2391i | −0.952971 | + | 1.65059i | −0.214026 | + | 0.976828i | \(0.568658\pi\) |
−0.738945 | + | 0.673766i | \(0.764676\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 10.3923i | 0.265424 | + | 0.459728i | ||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.1244 | − | 7.00000i | −0.533229 | − | 0.307860i | ||||
\(518\) | 10.3923 | + | 6.00000i | 0.456612 | + | 0.263625i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0000 | −0.481919 | −0.240959 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240959 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 29.0000i | − | 1.26808i | −0.773300 | − | 0.634041i | \(-0.781395\pi\) | ||
0.773300 | − | 0.634041i | \(-0.218605\pi\) | |||||||
\(524\) | −3.00000 | − | 5.19615i | −0.131056 | − | 0.226995i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.00000 | − | 13.8564i | 0.348817 | − | 0.604168i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.0000i | 1.04053i | ||||||||
\(533\) | 8.66025 | − | 5.00000i | 0.375117 | − | 0.216574i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.50000 | − | 7.79423i | 0.194370 | − | 0.336659i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.6506 | − | 12.5000i | 0.933425 | − | 0.538913i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.0000 | −1.67674 | −0.838370 | − | 0.545101i | \(-0.816491\pi\) | ||||
−0.838370 | + | 0.545101i | \(0.816491\pi\) | |||||||
\(542\) | −6.92820 | + | 4.00000i | −0.297592 | + | 0.171815i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.0000 | − | 17.3205i | 0.428746 | − | 0.742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.1147 | − | 14.5000i | 1.07383 | − | 0.619975i | 0.144604 | − | 0.989490i | \(-0.453809\pi\) |
0.929225 | + | 0.369514i | \(0.120476\pi\) | |||||||
\(548\) | 12.0000i | 0.512615i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | + | 6.92820i | 0.170406 | + | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.5885 | − | 9.00000i | −0.662889 | − | 0.382719i | ||||
\(554\) | −6.00000 | + | 10.3923i | −0.254916 | + | 0.441527i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | − | 13.8564i | −0.339276 | − | 0.587643i | ||||
\(557\) | − | 30.0000i | − | 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.9904 | − | 7.50000i | −0.547966 | − | 0.316368i | ||||
\(563\) | −18.1865 | − | 10.5000i | −0.766471 | − | 0.442522i | 0.0651433 | − | 0.997876i | \(-0.479250\pi\) |
−0.831614 | + | 0.555354i | \(0.812583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.0000 | −0.882696 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | 3.46410 | + | 2.00000i | 0.144841 | + | 0.0836242i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.50000 | − | 12.9904i | −0.313044 | − | 0.542208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0000i | 0.416305i | 0.978096 | + | 0.208153i | \(0.0667451\pi\) | ||||
−0.978096 | + | 0.208153i | \(0.933255\pi\) | |||||||
\(578\) | 0.866025 | − | 0.500000i | 0.0360219 | − | 0.0207973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.5000 | + | 23.3827i | −0.560074 | + | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.46410 | − | 2.00000i | 0.143468 | − | 0.0828315i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | −28.5788 | + | 16.5000i | −1.17957 | + | 0.681028i | −0.955916 | − | 0.293640i | \(-0.905133\pi\) |
−0.223659 | + | 0.974668i | \(0.571800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.46410 | + | 2.00000i | −0.142374 | + | 0.0821995i | ||||
\(593\) | − | 20.0000i | − | 0.821302i | −0.911793 | − | 0.410651i | \(-0.865302\pi\) | ||
0.911793 | − | 0.410651i | \(-0.134698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.50000 | − | 14.7224i | −0.348174 | − | 0.603054i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.19615 | + | 3.00000i | 0.212486 | + | 0.122679i | ||||
\(599\) | 5.00000 | − | 8.66025i | 0.204294 | − | 0.353848i | −0.745613 | − | 0.666379i | \(-0.767843\pi\) |
0.949908 | + | 0.312531i | \(0.101177\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00000 | − | 1.73205i | −0.0407909 | − | 0.0706518i | 0.844909 | − | 0.534910i | \(-0.179654\pi\) |
−0.885700 | + | 0.464258i | \(0.846321\pi\) | |||||||
\(602\) | 24.0000i | 0.978167i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.5070 | − | 20.5000i | −1.44119 | − | 0.832069i | −0.443257 | − | 0.896394i | \(-0.646177\pi\) |
−0.997929 | + | 0.0643251i | \(0.979511\pi\) | |||||||
\(608\) | −34.6410 | − | 20.0000i | −1.40488 | − | 0.811107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.0000 | 0.566379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 44.0000i | − | 1.77714i | −0.458738 | − | 0.888572i | \(-0.651698\pi\) | ||
0.458738 | − | 0.888572i | \(-0.348302\pi\) | |||||||
\(614\) | −3.50000 | − | 6.06218i | −0.141249 | − | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.00000 | − | 15.5885i | 0.362620 | − | 0.628077i | ||||
\(617\) | 31.1769 | + | 18.0000i | 1.25514 | + | 0.724653i | 0.972125 | − | 0.234464i | \(-0.0753335\pi\) |
0.283011 | + | 0.959117i | \(0.408667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | − | 3.46410i | −0.0803868 | − | 0.139234i | 0.823029 | − | 0.567999i | \(-0.192282\pi\) |
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.9711 | + | 22.5000i | −1.56135 | + | 0.901443i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.00000 | − | 12.1244i | 0.279776 | − | 0.484587i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.1244 | + | 7.00000i | −0.483814 | + | 0.279330i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 15.5885 | − | 9.00000i | 0.620076 | − | 0.358001i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.0000 | + | 29.4449i | −0.675156 | + | 1.16940i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.46410 | − | 2.00000i | 0.137253 | − | 0.0792429i | ||||
\(638\) | − | 2.00000i | − | 0.0791808i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | + | 28.5788i | 0.651711 | + | 1.12880i | 0.982708 | + | 0.185164i | \(0.0592817\pi\) |
−0.330997 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.79423 | + | 4.50000i | 0.307374 | + | 0.177463i | 0.645751 | − | 0.763548i | \(-0.276544\pi\) |
−0.338377 | + | 0.941011i | \(0.609878\pi\) | |||||||
\(644\) | −4.50000 | + | 7.79423i | −0.177325 | + | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.0000 | + | 27.7128i | 0.629512 | + | 1.09035i | ||||
\(647\) | − | 17.0000i | − | 0.668339i | −0.942513 | − | 0.334169i | \(-0.891544\pi\) | ||
0.942513 | − | 0.334169i | \(-0.108456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.46410 | + | 2.00000i | 0.135665 | + | 0.0783260i | ||||
\(653\) | −3.46410 | − | 2.00000i | −0.135561 | − | 0.0782660i | 0.430686 | − | 0.902502i | \(-0.358272\pi\) |
−0.566247 | + | 0.824236i | \(0.691605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.00000 | 0.195217 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 21.0000i | − | 0.818665i | ||||||
\(659\) | 4.00000 | + | 6.92820i | 0.155818 | + | 0.269884i | 0.933357 | − | 0.358951i | \(-0.116865\pi\) |
−0.777539 | + | 0.628835i | \(0.783532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.00000 | − | 12.1244i | 0.272268 | − | 0.471583i | −0.697174 | − | 0.716902i | \(-0.745559\pi\) |
0.969442 | + | 0.245319i | \(0.0788928\pi\) | |||||||
\(662\) | 5.19615 | + | 3.00000i | 0.201954 | + | 0.116598i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.5000 | − | 23.3827i | −0.523902 | − | 0.907424i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.00000i | 0.116160i | ||||||||
\(668\) | −7.79423 | + | 4.50000i | −0.301568 | + | 0.174110i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.00000 | + | 12.1244i | −0.270232 | + | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.19615 | − | 3.00000i | 0.200297 | − | 0.115642i | −0.396497 | − | 0.918036i | \(-0.629774\pi\) |
0.596794 | + | 0.802395i | \(0.296441\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −36.3731 | + | 21.0000i | −1.39793 | + | 0.807096i | −0.994176 | − | 0.107772i | \(-0.965628\pi\) |
−0.403755 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00000 | + | 5.19615i | −0.115129 | + | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 12.0000i | − | 0.459167i | −0.973289 | − | 0.229584i | \(-0.926264\pi\) | ||
0.973289 | − | 0.229584i | \(-0.0737364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.50000 | + | 12.9904i | 0.286351 | + | 0.495975i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.92820 | − | 4.00000i | −0.264135 | − | 0.152499i | ||||
\(689\) | −2.00000 | + | 3.46410i | −0.0761939 | + | 0.131972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.00000 | + | 12.1244i | 0.266293 | + | 0.461232i | 0.967901 | − | 0.251330i | \(-0.0808679\pi\) |
−0.701609 | + | 0.712562i | \(0.747535\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3205 | + | 10.0000i | 0.656061 | + | 0.378777i | ||||
\(698\) | −4.33013 | − | 2.50000i | −0.163898 | − | 0.0946264i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.0000 | −0.868698 | −0.434349 | − | 0.900745i | \(-0.643022\pi\) | ||||
−0.434349 | + | 0.900745i | \(0.643022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.0000i | 1.20690i | ||||||||
\(704\) | 7.00000 | + | 12.1244i | 0.263822 | + | 0.456954i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | + | 20.7846i | −0.451626 | + | 0.782239i | ||||
\(707\) | −46.7654 | − | 27.0000i | −1.75879 | − | 1.01544i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.5000 | − | 35.5070i | −0.769894 | − | 1.33349i | −0.937620 | − | 0.347661i | \(-0.886976\pi\) |
0.167727 | − | 0.985834i | \(-0.446357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 45.0000i | − | 1.68645i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.00000 | − | 1.73205i | 0.0373718 | − | 0.0647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.7846 | − | 12.0000i | 0.775675 | − | 0.447836i | ||||
\(719\) | 6.00000 | 0.223762 | 0.111881 | − | 0.993722i | \(-0.464312\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | 38.9711 | − | 22.5000i | 1.45036 | − | 0.837363i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9186 | + | 11.5000i | −0.738739 | + | 0.426511i | −0.821611 | − | 0.570049i | \(-0.806924\pi\) |
0.0828714 | + | 0.996560i | \(0.473591\pi\) | |||||||
\(728\) | 18.0000i | 0.667124i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.0000 | − | 27.7128i | −0.591781 | − | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4449 | + | 17.0000i | 1.08757 | + | 0.627909i | 0.932929 | − | 0.360061i | \(-0.117244\pi\) |
0.154642 | + | 0.987971i | \(0.450578\pi\) | |||||||
\(734\) | −12.0000 | + | 20.7846i | −0.442928 | + | 0.767174i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.50000 | − | 12.9904i | −0.276454 | − | 0.478832i | ||||
\(737\) | 6.00000i | 0.221013i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | 0.0735712 | 0.0367856 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.19615 | + | 3.00000i | 0.190757 | + | 0.110133i | ||||
\(743\) | −25.1147 | − | 14.5000i | −0.921370 | − | 0.531953i | −0.0372984 | − | 0.999304i | \(-0.511875\pi\) |
−0.884072 | + | 0.467351i | \(0.845209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | 4.50000 | + | 7.79423i | 0.164426 | + | 0.284795i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.00000 | + | 8.66025i | −0.182453 | + | 0.316017i | −0.942715 | − | 0.333599i | \(-0.891737\pi\) |
0.760263 | + | 0.649616i | \(0.225070\pi\) | |||||||
\(752\) | 6.06218 | + | 3.50000i | 0.221065 | + | 0.127632i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.00000 | + | 1.73205i | 0.0364179 | + | 0.0630776i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000i | 0.944986i | 0.881334 | + | 0.472493i | \(0.156646\pi\) | ||||
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | 22.5167 | − | 13.0000i | 0.817842 | − | 0.472181i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.50000 | − | 12.9904i | 0.271875 | − | 0.470901i | −0.697467 | − | 0.716617i | \(-0.745690\pi\) |
0.969342 | + | 0.245716i | \(0.0790230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.9904 | + | 7.50000i | −0.470283 | + | 0.271518i | ||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | 24.2487 | − | 14.0000i | 0.875570 | − | 0.505511i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | − | 4.33013i | 0.0901523 | − | 0.156148i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.66025 | + | 5.00000i | −0.311689 | + | 0.179954i | ||||
\(773\) | 24.0000i | 0.863220i | 0.902060 | + | 0.431610i | \(0.142054\pi\) | ||||
−0.902060 | + | 0.431610i | \(0.857946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.00000 | − | 5.19615i | −0.107694 | − | 0.186531i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.5788 | − | 16.5000i | −1.02460 | − | 0.591554i | ||||
\(779\) | 20.0000 | − | 34.6410i | 0.716574 | − | 1.24114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 12.0000i | 0.429119i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2487 | + | 14.0000i | 0.864373 | + | 0.499046i | 0.865474 | − | 0.500953i | \(-0.167017\pi\) |
−0.00110111 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(788\) | 10.3923 | + | 6.00000i | 0.370211 | + | 0.213741i | ||||
\(789\) | 0 | 0 |