Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,2,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(1.79663404548\) |
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 | 49.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.2.k.a.124.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | −0.773893 | − | 0.633316i | \(-0.781693\pi\) |
0.161521 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 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 | ||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0.866025 | + | 1.50000i | 0.250000 | + | 0.433013i | ||||
\(13\) | 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 | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 2.59808 | + | 1.50000i | 0.612372 | + | 0.353553i | ||||
\(19\) | 8.00000 | 1.83533 | 0.917663 | − | 0.397360i | \(-0.130073\pi\) | ||||
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 5.19615i | − | 1.13389i | ||||||
\(22\) | −1.73205 | − | 1.00000i | −0.369274 | − | 0.213201i | ||||
\(23\) | −2.59808 | − | 1.50000i | −0.541736 | − | 0.312772i | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | −4.50000 | − | 2.59808i | −0.918559 | − | 0.530330i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 3.00000i | 0.566947i | ||||||||
\(29\) | −0.500000 | − | 0.866025i | −0.0928477 | − | 0.160817i | 0.815861 | − | 0.578249i | \(-0.196264\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 3.46410 | 0.603023 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | 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 | ||||
\(39\) | 3.00000 | − | 1.73205i | 0.480384 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50000 | + | 4.33013i | −0.390434 | + | 0.676252i | −0.992507 | − | 0.122189i | \(-0.961009\pi\) |
0.602072 | + | 0.798441i | \(0.294342\pi\) | |||||||
\(42\) | 2.59808 | + | 4.50000i | 0.400892 | + | 0.694365i | ||||
\(43\) | −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 | −0.872060 | − | 0.489398i | \(-0.837217\pi\) |
−0.0121990 | + | 0.999926i | \(0.503883\pi\) | |||||||
\(48\) | 1.73205 | 0.250000 | ||||||||
\(49\) | 1.00000 | − | 1.73205i | 0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | − | 3.46410i | −0.840168 | − | 0.485071i | ||||
\(52\) | −1.73205 | + | 1.00000i | −0.240192 | + | 0.138675i | ||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.50000 | − | 7.79423i | −0.601338 | − | 1.04155i | ||||
\(57\) | 6.92820 | − | 12.0000i | 0.917663 | − | 1.58944i | ||||
\(58\) | 0.866025 | + | 0.500000i | 0.113715 | + | 0.0656532i | ||||
\(59\) | −7.00000 | + | 12.1244i | −0.911322 | + | 1.57846i | −0.0991242 | + | 0.995075i | \(0.531604\pi\) |
−0.812198 | + | 0.583382i | \(0.801729\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | −7.79423 | − | 4.50000i | −0.981981 | − | 0.566947i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | + | 1.73205i | −0.369274 | + | 0.213201i | ||||
\(67\) | −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 | ||||
\(69\) | −4.50000 | + | 2.59808i | −0.541736 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −7.79423 | + | 4.50000i | −0.918559 | + | 0.530330i | ||||
\(73\) | 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 | ||||
\(78\) | −1.73205 | + | 3.00000i | −0.196116 | + | 0.339683i | ||||
\(79\) | −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 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | − | 5.00000i | − | 0.552158i | ||||||
\(83\) | 7.79423 | − | 4.50000i | 0.855528 | − | 0.493939i | −0.00698436 | − | 0.999976i | \(-0.502223\pi\) |
0.862512 | + | 0.506036i | \(0.168890\pi\) | |||||||
\(84\) | 4.50000 | + | 2.59808i | 0.490990 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | −1.73205 | −0.185695 | ||||||||
\(88\) | 5.19615 | − | 3.00000i | 0.553912 | − | 0.319801i | ||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 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 | ||||||||
\(96\) | 7.50000 | − | 4.33013i | 0.765466 | − | 0.441942i | ||||
\(97\) | −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 | ||||||||
\(99\) | 3.00000 | − | 5.19615i | 0.301511 | − | 0.522233i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 6.92820 | 0.685994 | ||||||||
\(103\) | −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 | \(-0.953678\pi\) | ||
0.989430 | − | 0.145010i | \(-0.0463216\pi\) | |||||||
\(108\) | 2.59808 | − | 4.50000i | 0.250000 | − | 0.433013i | ||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | + | 3.46410i | 0.569495 | + | 0.328798i | ||||
\(112\) | 2.59808 | + | 1.50000i | 0.245495 | + | 0.141737i | ||||
\(113\) | 6.92820 | + | 4.00000i | 0.651751 | + | 0.376288i | 0.789127 | − | 0.614231i | \(-0.210534\pi\) |
−0.137376 | + | 0.990519i | \(0.543867\pi\) | |||||||
\(114\) | 13.8564i | 1.29777i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | − | 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 | ||||
\(123\) | 4.33013 | + | 7.50000i | 0.390434 | + | 0.676252i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.00000 | 0.801784 | ||||||||
\(127\) | 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 | ||||
\(129\) | 13.8564i | 1.21999i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | −1.73205 | + | 3.00000i | −0.150756 | + | 0.261116i | ||||
\(133\) | 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 | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | 2.59808 | − | 4.50000i | 0.221163 | − | 0.383065i | ||||
\(139\) | −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 | ||||||||
\(141\) | 12.1244i | 1.02105i | ||||||||
\(142\) | −1.73205 | + | 1.00000i | −0.145350 | + | 0.0839181i | ||||
\(143\) | 4.00000i | 0.334497i | ||||||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | − | 3.46410i | −0.165521 | − | 0.286691i | ||||
\(147\) | −1.73205 | − | 3.00000i | −0.142857 | − | 0.247436i | ||||
\(148\) | −3.46410 | − | 2.00000i | −0.284747 | − | 0.164399i | ||||
\(149\) | 8.50000 | − | 14.7224i | 0.696347 | − | 1.20611i | −0.273377 | − | 0.961907i | \(-0.588141\pi\) |
0.969724 | − | 0.244202i | \(-0.0785259\pi\) | |||||||
\(150\) | 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 | ||||||
\(153\) | −10.3923 | + | 6.00000i | −0.840168 | + | 0.485071i | ||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.46410i | 0.277350i | ||||||||
\(157\) | 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 | ||||
\(159\) | −3.00000 | − | 1.73205i | −0.237915 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | −0.709299 | ||||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | − | 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 | 0.167139 | − | 0.985933i | \(-0.446547\pi\) |
−0.770274 | + | 0.637713i | \(0.779881\pi\) | |||||||
\(168\) | −15.5885 | −1.20268 | ||||||||
\(169\) | −4.50000 | − | 7.79423i | −0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0000 | − | 20.7846i | −0.917663 | − | 1.58944i | ||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 1.50000 | − | 0.866025i | 0.113715 | − | 0.0656532i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 12.1244 | + | 21.0000i | 0.911322 | + | 1.57846i | ||||
\(178\) | −12.9904 | + | 7.50000i | −0.973670 | + | 0.562149i | ||||
\(179\) | 2.00000 | 0.149487 | 0.0747435 | − | 0.997203i | \(-0.476186\pi\) | ||||
0.0747435 | + | 0.997203i | \(0.476186\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | −12.1244 | −0.896258 | ||||||||
\(184\) | −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 | ||||||
\(189\) | −13.5000 | + | 7.79423i | −0.981981 | + | 0.566947i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | − | 6.92820i | −0.289430 | − | 0.501307i | 0.684244 | − | 0.729253i | \(-0.260132\pi\) |
−0.973674 | + | 0.227946i | \(0.926799\pi\) | |||||||
\(192\) | −6.06218 | + | 10.5000i | −0.437500 | + | 0.757772i | ||||
\(193\) | 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 | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 6.00000i | 0.426401i | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.50000 | + | 2.59808i | −0.317406 | + | 0.183254i | ||||
\(202\) | −15.5885 | − | 9.00000i | −1.09680 | − | 0.633238i | ||||
\(203\) | −2.59808 | − | 1.50000i | −0.182349 | − | 0.105279i | ||||
\(204\) | 6.00000 | − | 3.46410i | 0.420084 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 9.00000i | 0.625543i | ||||||||
\(208\) | 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 | ||||
\(213\) | 1.73205 | − | 3.00000i | 0.118678 | − | 0.205557i | ||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 15.5885i | 1.06066i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.33013 | − | 2.50000i | 0.293273 | − | 0.169321i | ||||
\(219\) | 6.00000 | + | 3.46410i | 0.405442 | + | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | − | 6.92820i | 0.269069 | − | 0.466041i | ||||
\(222\) | −6.92820 | −0.464991 | ||||||||
\(223\) | −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 | −0.380615 | − | 0.924734i | \(-0.624288\pi\) |
0.610535 | + | 0.791989i | \(0.290954\pi\) | |||||||
\(228\) | 6.92820 | + | 12.0000i | 0.458831 | + | 0.794719i | ||||
\(229\) | 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 | ||||||||
\(231\) | 9.00000 | − | 5.19615i | 0.592157 | − | 0.341882i | ||||
\(232\) | −2.59808 | + | 1.50000i | −0.170572 | + | 0.0984798i | ||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.00000 | − | 12.1244i | −0.455661 | − | 0.789228i | ||||
\(237\) | −10.3923 | −0.675053 | ||||||||
\(238\) | 10.3923 | + | 6.00000i | 0.673633 | + | 0.388922i | ||||
\(239\) | −4.00000 | + | 6.92820i | −0.258738 | + | 0.448148i | −0.965904 | − | 0.258900i | \(-0.916640\pi\) |
0.707166 | + | 0.707048i | \(0.249973\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 7.79423 | + | 13.5000i | 0.500000 | + | 0.866025i | ||||
\(244\) | 7.00000 | 0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.50000 | − | 4.33013i | −0.478183 | − | 0.276079i | ||||
\(247\) | 13.8564 | + | 8.00000i | 0.881662 | + | 0.509028i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 7.79423 | − | 4.50000i | 0.490990 | − | 0.283473i | ||||
\(253\) | − | 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 | 0.329104 | − | 0.944294i | \(-0.393253\pi\) |
−0.653231 | + | 0.757159i | \(0.726587\pi\) | |||||||
\(258\) | −6.92820 | − | 12.0000i | −0.431331 | − | 0.747087i | ||||
\(259\) | 6.00000 | + | 10.3923i | 0.372822 | + | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 6.00000i | 0.370681i | ||||||||
\(263\) | −13.8564 | + | 8.00000i | −0.854423 | + | 0.493301i | −0.862141 | − | 0.506669i | \(-0.830877\pi\) |
0.00771799 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(264\) | − | 10.3923i | − | 0.639602i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.0000 | + | 20.7846i | −0.735767 | + | 1.27439i | ||||
\(267\) | 12.9904 | − | 22.5000i | 0.794998 | − | 1.37698i | ||||
\(268\) | 2.59808 | − | 1.50000i | 0.158703 | − | 0.0916271i | ||||
\(269\) | −25.0000 | −1.52428 | −0.762138 | − | 0.647414i | \(-0.775850\pi\) | ||||
−0.762138 | + | 0.647414i | \(0.775850\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 5.19615 | − | 9.00000i | 0.314485 | − | 0.544705i | ||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 5.19615i | − | 0.312772i | ||||||
\(277\) | −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 | 0.998217 | − | 0.0596933i | \(-0.0190123\pi\) |
−0.550804 | + | 0.834634i | \(0.685679\pi\) | |||||||
\(282\) | −6.06218 | − | 10.5000i | −0.360997 | − | 0.625266i | ||||
\(283\) | −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 | ||||||||
\(288\) | − | 15.0000i | − | 0.883883i | ||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.46410i | 0.203069i | ||||||||
\(292\) | −3.46410 | − | 2.00000i | −0.202721 | − | 0.117041i | ||||
\(293\) | −10.3923 | − | 6.00000i | −0.607125 | − | 0.350524i | 0.164714 | − | 0.986341i | \(-0.447330\pi\) |
−0.771839 | + | 0.635818i | \(0.780663\pi\) | |||||||
\(294\) | 3.00000 | + | 1.73205i | 0.174964 | + | 0.101015i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.0000 | 0.697486 | ||||||||
\(297\) | −5.19615 | − | 9.00000i | −0.301511 | − | 0.522233i | ||||
\(298\) | 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 | ||||
\(303\) | 31.1769 | 1.79107 | ||||||||
\(304\) | 4.00000 | + | 6.92820i | 0.229416 | + | 0.397360i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | − | 10.3923i | 0.342997 | − | 0.594089i | ||||
\(307\) | − | 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 | ||||
\(309\) | −12.0000 | + | 6.92820i | −0.682656 | + | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | −5.19615 | − | 9.00000i | −0.294174 | − | 0.509525i | ||||
\(313\) | 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 | \(-0.262720\pi\) |
0.975494 | − | 0.220024i | \(-0.0706137\pi\) | |||||||
\(318\) | 3.46410 | 0.194257 | ||||||||
\(319\) | 1.00000 | − | 1.73205i | 0.0559893 | − | 0.0969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | − | 2.59808i | −0.251166 | − | 0.145010i | ||||
\(322\) | 7.79423 | − | 4.50000i | 0.434355 | − | 0.250775i | ||||
\(323\) | − | 32.0000i | − | 1.78053i | ||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −4.33013 | + | 7.50000i | −0.239457 | + | 0.414751i | ||||
\(328\) | 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 | ||||||||
\(333\) | 10.3923 | − | 6.00000i | 0.569495 | − | 0.328798i | ||||
\(334\) | 9.00000 | 0.492458 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.50000 | − | 2.59808i | 0.245495 | − | 0.141737i | ||||
\(337\) | −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 | ||||
\(339\) | 12.0000 | − | 6.92820i | 0.651751 | − | 0.376288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 20.7846 | + | 12.0000i | 1.12390 | + | 0.648886i | ||||
\(343\) | 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 | 0.590091 | − | 0.807337i | \(-0.299092\pi\) |
−0.404128 | + | 0.914702i | \(0.632425\pi\) | |||||||
\(348\) | 0.866025 | − | 1.50000i | 0.0464238 | − | 0.0804084i | ||||
\(349\) | −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 | ||||||||
\(351\) | −9.00000 | − | 5.19615i | −0.480384 | − | 0.277350i | ||||
\(352\) | 10.0000i | 0.533002i | ||||||||
\(353\) | 20.7846 | − | 12.0000i | 1.10625 | − | 0.638696i | 0.168397 | − | 0.985719i | \(-0.446141\pi\) |
0.937856 | + | 0.347024i | \(0.112808\pi\) | |||||||
\(354\) | −21.0000 | − | 12.1244i | −1.11614 | − | 0.644402i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.50000 | + | 12.9904i | −0.397499 | + | 0.688489i | ||||
\(357\) | −20.7846 | −1.10004 | ||||||||
\(358\) | −1.73205 | + | 1.00000i | −0.0915417 | + | 0.0528516i | ||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 45.0000 | 2.36842 | ||||||||
\(362\) | 6.06218 | − | 3.50000i | 0.318621 | − | 0.183956i | ||||
\(363\) | −6.06218 | − | 10.5000i | −0.318182 | − | 0.551107i | ||||
\(364\) | −3.00000 | + | 5.19615i | −0.157243 | + | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.5000 | − | 6.06218i | 0.548844 | − | 0.316875i | ||||
\(367\) | −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 | ||||||
\(369\) | 15.0000 | 0.780869 | ||||||||
\(370\) | 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 | ||||||
\(378\) | 7.79423 | − | 13.5000i | 0.400892 | − | 0.694365i | ||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.50000 | + | 4.33013i | 0.384237 | + | 0.221839i | ||||
\(382\) | 6.92820 | + | 4.00000i | 0.354478 | + | 0.204658i | ||||
\(383\) | −31.1769 | − | 18.0000i | −1.59307 | − | 0.919757i | −0.992777 | − | 0.119974i | \(-0.961719\pi\) |
−0.600289 | − | 0.799783i | \(-0.704948\pi\) | |||||||
\(384\) | 5.19615i | 0.265165i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | 20.7846 | + | 12.0000i | 1.05654 | + | 0.609994i | ||||
\(388\) | − | 2.00000i | − | 0.101535i | ||||||
\(389\) | 16.5000 | + | 28.5788i | 0.836583 | + | 1.44900i | 0.892735 | + | 0.450582i | \(0.148784\pi\) |
−0.0561516 | + | 0.998422i | \(0.517883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | + | 10.3923i | −0.303433 | + | 0.525561i | ||||
\(392\) | −5.19615 | − | 3.00000i | −0.262445 | − | 0.151523i | ||||
\(393\) | −5.19615 | − | 9.00000i | −0.262111 | − | 0.453990i | ||||
\(394\) | −6.00000 | − | 10.3923i | −0.302276 | − | 0.523557i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.00000 | + | 5.19615i | 0.150756 | + | 0.261116i | ||||
\(397\) | − | 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 | ||||
\(399\) | − | 41.5692i | − | 2.08106i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | − | 15.5885i | 0.449439 | − | 0.778450i | −0.548911 | − | 0.835881i | \(-0.684957\pi\) |
0.998350 | + | 0.0574304i | \(0.0182907\pi\) | |||||||
\(402\) | 2.59808 | − | 4.50000i | 0.129580 | − | 0.224440i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | 0.148888 | ||||||||
\(407\) | −6.92820 | + | 4.00000i | −0.343418 | + | 0.198273i | ||||
\(408\) | −10.3923 | + | 18.0000i | −0.514496 | + | 0.891133i | ||||
\(409\) | 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 | ||||||||
\(411\) | 20.7846i | 1.02523i | ||||||||
\(412\) | 6.92820 | − | 4.00000i | 0.341328 | − | 0.197066i | ||||
\(413\) | 42.0000i | 2.06668i | ||||||||
\(414\) | −4.50000 | − | 7.79423i | −0.221163 | − | 0.383065i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.00000 | + | 8.66025i | 0.245145 | + | 0.424604i | ||||
\(417\) | 13.8564 | + | 24.0000i | 0.678551 | + | 1.17529i | ||||
\(418\) | −13.8564 | − | 8.00000i | −0.677739 | − | 0.391293i | ||||
\(419\) | 13.0000 | − | 22.5167i | 0.635092 | − | 1.10001i | −0.351404 | − | 0.936224i | \(-0.614296\pi\) |
0.986496 | − | 0.163787i | \(-0.0523710\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 18.1865 | + | 10.5000i | 0.884260 | + | 0.510527i | ||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.46410i | 0.167836i | ||||||||
\(427\) | −18.1865 | − | 10.5000i | −0.880108 | − | 0.508131i | ||||
\(428\) | 2.59808 | + | 1.50000i | 0.125583 | + | 0.0725052i | ||||
\(429\) | 6.00000 | + | 3.46410i | 0.289683 | + | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.0000 | −1.44505 | −0.722525 | − | 0.691345i | \(-0.757018\pi\) | ||||
−0.722525 | + | 0.691345i | \(0.757018\pi\) | |||||||
\(432\) | −2.59808 | − | 4.50000i | −0.125000 | − | 0.216506i | ||||
\(433\) | 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 | ||||
\(438\) | −6.92820 | −0.331042 | ||||||||
\(439\) | 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 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | 12.9904 | − | 7.50000i | 0.617192 | − | 0.356336i | −0.158583 | − | 0.987346i | \(-0.550693\pi\) |
0.775775 | + | 0.631010i | \(0.217359\pi\) | |||||||
\(444\) | −6.00000 | + | 3.46410i | −0.284747 | + | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.50000 | − | 16.4545i | 0.449838 | − | 0.779142i | ||||
\(447\) | −14.7224 | − | 25.5000i | −0.696347 | − | 1.20611i | ||||
\(448\) | −18.1865 | + | 10.5000i | −0.859233 | + | 0.496078i | ||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | −0.470882 | ||||||||
\(452\) | −6.92820 | + | 4.00000i | −0.325875 | + | 0.188144i | ||||
\(453\) | 3.46410 | 0.162758 | ||||||||
\(454\) | −2.00000 | + | 3.46410i | −0.0938647 | + | 0.162578i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −36.0000 | − | 20.7846i | −1.68585 | − | 0.973329i | ||||
\(457\) | 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 | ||||||||
\(459\) | 20.7846i | 0.970143i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50000 | − | 7.79423i | −0.209586 | − | 0.363013i | 0.741998 | − | 0.670402i | \(-0.233878\pi\) |
−0.951584 | + | 0.307388i | \(0.900545\pi\) | |||||||
\(462\) | −5.19615 | + | 9.00000i | −0.241747 | + | 0.418718i | ||||
\(463\) | 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 | \(-0.846865\pi\) | ||
0.886492 | − | 0.462745i | \(-0.153135\pi\) | |||||||
\(468\) | 5.19615 | + | 3.00000i | 0.240192 | + | 0.138675i | ||||
\(469\) | −9.00000 | −0.415581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.0000 | − | 12.1244i | 0.967629 | − | 0.558661i | ||||
\(472\) | 36.3731 | + | 21.0000i | 1.67421 | + | 0.966603i | ||||
\(473\) | −13.8564 | − | 8.00000i | −0.637118 | − | 0.367840i | ||||
\(474\) | 9.00000 | − | 5.19615i | 0.413384 | − | 0.238667i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | −5.19615 | + | 3.00000i | −0.237915 | + | 0.137361i | ||||
\(478\) | − | 8.00000i | − | 0.365911i | ||||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | −9.52628 | − | 5.50000i | −0.433910 | − | 0.250518i | ||||
\(483\) | −7.79423 | + | 13.5000i | −0.354650 | + | 0.614271i | ||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | 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 | ||||
\(489\) | −6.00000 | − | 3.46410i | −0.271329 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0000 | + | 17.3205i | −0.451294 | + | 0.781664i | −0.998467 | − | 0.0553560i | \(-0.982371\pi\) |
0.547173 | + | 0.837020i | \(0.315704\pi\) | |||||||
\(492\) | −8.66025 | −0.390434 | ||||||||
\(493\) | −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 | ||||
\(498\) | 7.79423 | + | 13.5000i | 0.349268 | + | 0.604949i | ||||
\(499\) | −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 | ||||||||
\(501\) | −13.5000 | + | 7.79423i | −0.603136 | + | 0.348220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.00000i | − | 0.312115i | −0.987748 | − | 0.156057i | \(-0.950122\pi\) | ||
0.987748 | − | 0.156057i | \(-0.0498784\pi\) | |||||||
\(504\) | −13.5000 | + | 23.3827i | −0.601338 | + | 1.04155i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −15.5885 | −0.692308 | ||||||||
\(508\) | −4.33013 | − | 2.50000i | −0.192118 | − | 0.110920i | ||||
\(509\) | 21.5000 | − | 37.2391i | 0.952971 | − | 1.65059i | 0.214026 | − | 0.976828i | \(-0.431342\pi\) |
0.738945 | − | 0.673766i | \(-0.235324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 10.3923i | 0.265424 | + | 0.459728i | ||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | −41.5692 | −1.83533 | ||||||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.0000 | − | 6.92820i | −0.528271 | − | 0.304997i | ||||
\(517\) | −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 | \(-0.422538\pi\) | ||||
0.240959 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(522\) | − | 3.00000i | − | 0.131306i | ||||||
\(523\) | − | 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 | ||||||||
\(528\) | 1.73205 | + | 3.00000i | 0.0753778 | + | 0.130558i | ||||
\(529\) | −7.00000 | − | 12.1244i | −0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.0000 | 1.82264 | ||||||||
\(532\) | 24.0000i | 1.04053i | ||||||||
\(533\) | −8.66025 | + | 5.00000i | −0.375117 | + | 0.216574i | ||||
\(534\) | 25.9808i | 1.12430i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | 1.73205 | − | 3.00000i | 0.0747435 | − | 0.129460i | ||||
\(538\) | 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 | ||||
\(543\) | −6.06218 | + | 10.5000i | −0.260153 | + | 0.450598i | ||||
\(544\) | 10.0000 | − | 17.3205i | 0.428746 | − | 0.742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3923i | 0.444750i | ||||||||
\(547\) | 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 | ||||||
\(549\) | −10.5000 | + | 18.1865i | −0.448129 | + | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.00000 | − | 6.92820i | −0.170406 | − | 0.295151i | ||||
\(552\) | 7.79423 | + | 13.5000i | 0.331744 | + | 0.574598i | ||||
\(553\) | −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 | \(0.219235\pi\) | ||||
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 13.8564i | − | 0.585018i | ||||||
\(562\) | −12.9904 | − | 7.50000i | −0.547966 | − | 0.316368i | ||||
\(563\) | 18.1865 | + | 10.5000i | 0.766471 | + | 0.442522i | 0.831614 | − | 0.555354i | \(-0.187417\pi\) |
−0.0651433 | + | 0.997876i | \(0.520750\pi\) | |||||||
\(564\) | −10.5000 | − | 6.06218i | −0.442130 | − | 0.255264i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.0000 | 0.882696 | ||||||||
\(567\) | 27.0000i | 1.13389i | ||||||||
\(568\) | − | 6.00000i | − | 0.251754i | ||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | −13.8564 | −0.578860 | ||||||||
\(574\) | −7.50000 | − | 12.9904i | −0.313044 | − | 0.542208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.5000 | + | 18.1865i | 0.437500 | + | 0.757772i | ||||
\(577\) | 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 | ||||
\(579\) | 15.0000 | − | 8.66025i | 0.623379 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5000 | − | 23.3827i | 0.560074 | − | 0.970077i | ||||
\(582\) | −1.73205 | − | 3.00000i | −0.0717958 | − | 0.124354i | ||||
\(583\) | 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 | 0.223659 | − | 0.974668i | \(-0.428200\pi\) |
0.955916 | + | 0.293640i | \(0.0948666\pi\) | |||||||
\(588\) | 3.46410 | 0.142857 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | + | 10.3923i | 0.740421 | + | 0.427482i | ||||
\(592\) | −3.46410 | + | 2.00000i | −0.142374 | + | 0.0821995i | ||||
\(593\) | 20.0000i | 0.821302i | 0.911793 | + | 0.410651i | \(0.134698\pi\) | ||||
−0.911793 | + | 0.410651i | \(0.865302\pi\) | |||||||
\(594\) | 9.00000 | + | 5.19615i | 0.369274 | + | 0.213201i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.50000 | + | 14.7224i | 0.348174 | + | 0.603054i | ||||
\(597\) | −3.46410 | + | 6.00000i | −0.141776 | + | 0.245564i | ||||
\(598\) | 5.19615 | + | 3.00000i | 0.212486 | + | 0.122679i | ||||
\(599\) | −5.00000 | + | 8.66025i | −0.204294 | + | 0.353848i | −0.949908 | − | 0.312531i | \(-0.898823\pi\) |
0.745613 | + | 0.666379i | \(0.232157\pi\) | |||||||
\(600\) | 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 | ||||||
\(603\) | 9.00000i | 0.366508i | ||||||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −27.0000 | + | 15.5885i | −1.09680 | + | 0.633238i | ||||
\(607\) | −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 | ||||
\(609\) | −4.50000 | + | 2.59808i | −0.182349 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.0000 | −0.566379 | ||||||||
\(612\) | − | 12.0000i | − | 0.485071i | ||||||
\(613\) | − | 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 | −0.283011 | − | 0.959117i | \(-0.591333\pi\) |
−0.972125 | + | 0.234464i | \(0.924666\pi\) | |||||||
\(618\) | 6.92820 | − | 12.0000i | 0.278693 | − | 0.482711i | ||||
\(619\) | −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 | ||||||||
\(621\) | 13.5000 | + | 7.79423i | 0.541736 | + | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.9711 | − | 22.5000i | 1.56135 | − | 0.901443i | ||||
\(624\) | 3.00000 | + | 1.73205i | 0.120096 | + | 0.0693375i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.00000 | + | 12.1244i | −0.279776 | + | 0.484587i | ||||
\(627\) | 27.7128 | 1.10674 | ||||||||
\(628\) | −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 | ||||
\(633\) | −19.0526 | − | 33.0000i | −0.757271 | − | 1.31163i | ||||
\(634\) | −17.0000 | + | 29.4449i | −0.675156 | + | 1.16940i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.00000 | − | 1.73205i | 0.118958 | − | 0.0686803i | ||||
\(637\) | 3.46410 | − | 2.00000i | 0.137253 | − | 0.0792429i | ||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | −3.00000 | − | 5.19615i | −0.118678 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.5000 | − | 28.5788i | −0.651711 | − | 1.12880i | −0.982708 | − | 0.185164i | \(-0.940718\pi\) |
0.330997 | − | 0.943632i | \(-0.392615\pi\) | |||||||
\(642\) | 5.19615 | 0.205076 | ||||||||
\(643\) | 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 | \(0.108456\pi\) | ||||
−0.942513 | + | 0.334169i | \(0.891544\pi\) | |||||||
\(648\) | 23.3827 | + | 13.5000i | 0.918559 | + | 0.530330i | ||||
\(649\) | −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 | 0.566247 | − | 0.824236i | \(-0.308395\pi\) |
−0.430686 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(654\) | − | 8.66025i | − | 0.338643i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.00000 | −0.195217 | ||||||||
\(657\) | 10.3923 | − | 6.00000i | 0.405442 | − | 0.234082i | ||||
\(658\) | − | 21.0000i | − | 0.818665i | ||||||
\(659\) | −4.00000 | − | 6.92820i | −0.155818 | − | 0.269884i | 0.777539 | − | 0.628835i | \(-0.216468\pi\) |
−0.933357 | + | 0.358951i | \(0.883135\pi\) | |||||||
\(660\) | 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 | ||||
\(663\) | −6.92820 | − | 12.0000i | −0.269069 | − | 0.466041i | ||||
\(664\) | −13.5000 | − | 23.3827i | −0.523902 | − | 0.907424i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.00000 | + | 10.3923i | −0.232495 | + | 0.402694i | ||||
\(667\) | 3.00000i | 0.116160i | ||||||||
\(668\) | 7.79423 | − | 4.50000i | 0.301568 | − | 0.174110i | ||||
\(669\) | 32.9090i | 1.27233i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.00000 | − | 12.1244i | 0.270232 | − | 0.468056i | ||||
\(672\) | 12.9904 | − | 22.5000i | 0.501115 | − | 0.867956i | ||||
\(673\) | 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 | 0.403755 | − | 0.914867i | \(-0.367705\pi\) |
0.994176 | + | 0.107772i | \(0.0343715\pi\) | |||||||
\(678\) | −6.92820 | + | 12.0000i | −0.266076 | + | 0.460857i | ||||
\(679\) | −3.00000 | + | 5.19615i | −0.115129 | + | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.92820i | − | 0.265489i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 24.0000 | 0.917663 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | −12.9904 | − | 22.5000i | −0.495614 | − | 0.858429i | ||||
\(688\) | −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 | ||||||||
\(693\) | − | 18.0000i | − | 0.683763i | ||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.19615i | 0.196960i | ||||||||
\(697\) | 17.3205 | + | 10.0000i | 0.656061 | + | 0.378777i | ||||
\(698\) | 4.33013 | + | 2.50000i | 0.163898 | + | 0.0946264i | ||||
\(699\) | 36.0000 | + | 20.7846i | 1.36165 | + | 0.786146i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0000 | 0.868698 | 0.434349 | − | 0.900745i | \(-0.356978\pi\) | ||||
0.434349 | + | 0.900745i | \(0.356978\pi\) | |||||||
\(702\) | 10.3923 | 0.392232 | ||||||||
\(703\) | 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 | ||||
\(708\) | −24.2487 | −0.911322 | ||||||||
\(709\) | −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 | ||||||||
\(711\) | −9.00000 | + | 15.5885i | −0.337526 | + | 0.584613i | ||||
\(712\) | − | 45.0000i | − | 1.68645i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 18.0000 | − | 10.3923i | 0.673633 | − | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.00000 | + | 1.73205i | −0.0373718 | + | 0.0647298i | ||||
\(717\) | 6.92820 | + | 12.0000i | 0.258738 | + | 0.448148i | ||||
\(718\) | 20.7846 | − | 12.0000i | 0.775675 | − | 0.447836i | ||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | −38.9711 | + | 22.5000i | −1.45036 | + | 0.837363i | ||||
\(723\) | 19.0526 | 0.708572 | ||||||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.5000 | + | 6.06218i | 0.389692 | + | 0.224989i | ||||
\(727\) | −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 | ||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | + | 27.7128i | 0.591781 | + | 1.02500i | ||||
\(732\) | 6.06218 | − | 10.5000i | 0.224065 | − | 0.388091i | ||||
\(733\) | 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 | ||||||
\(738\) | −12.9904 | + | 7.50000i | −0.478183 | + | 0.276079i | ||||
\(739\) | 2.00000 | 0.0735712 | 0.0367856 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | − | 13.8564i | 0.881662 | − | 0.509028i | ||||
\(742\) | 5.19615 | + | 3.00000i | 0.190757 | + | 0.110133i | ||||
\(743\) | 25.1147 | + | 14.5000i | 0.921370 | + | 0.531953i | 0.884072 | − | 0.467351i | \(-0.154791\pi\) |
0.0372984 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | −23.3827 | − | 13.5000i | −0.855528 | − | 0.493939i | ||||
\(748\) | 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 | ||||||||
\(756\) | − | 15.5885i | − | 0.566947i | ||||||
\(757\) | 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 | ||||
\(759\) | −9.00000 | − | 5.19615i | −0.326679 | − | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.50000 | + | 12.9904i | −0.271875 | + | 0.470901i | −0.969342 | − | 0.245716i | \(-0.920977\pi\) |
0.697467 | + | 0.716617i | \(0.254310\pi\) | |||||||
\(762\) | −8.66025 | −0.313728 | ||||||||
\(763\) | −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 | ||||
\(768\) | −14.7224 | − | 25.5000i | −0.531250 | − | 0.920152i | ||||
\(769\) | 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 | ||||||||
\(771\) | −9.00000 | + | 5.19615i | −0.324127 | + | 0.187135i | ||||
\(772\) | −8.66025 | + | 5.00000i | −0.311689 | + | 0.179954i | ||||
\(773\) | − | 24.0000i | − | 0.863220i | −0.902060 | − | 0.431610i | \(-0.857946\pi\) | ||
0.902060 | − | 0.431610i | \(-0.142054\pi\) | |||||||
\(774\) | −24.0000 | −0.862662 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.00000 | + | 5.19615i | 0.107694 | + | 0.186531i | ||||
\(777\) | 20.7846 | 0.745644 | ||||||||
\(778\) | −28.5788 | − | 16.5000i | −1.02460 | − | 0.591554i | ||||
\(779\) | −20.0000 | + | 34.6410i |