Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(607,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.607");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.607 |
Dual form | 912.2.k.a.607.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843i | 0.784465i | 0.919866 | + | 0.392232i | \(0.128297\pi\) | ||||
−0.919866 | + | 0.392232i | \(0.871703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 4.24264i | −0.229416 | − | 0.973329i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843i | 0.617213i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.41421i | 0.294884i | 0.989071 | + | 0.147442i | \(0.0471040\pi\) | ||||
−0.989071 | + | 0.147442i | \(0.952896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07107i | 1.31306i | 0.754298 | + | 0.656532i | \(0.227977\pi\) | ||||
−0.754298 | + | 0.656532i | \(0.772023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.41421i | − | 0.246183i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.65685i | 0.956183i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3137i | 1.85996i | 0.367607 | + | 0.929981i | \(0.380177\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.82843i | − | 0.452911i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264i | 0.662589i | 0.943527 | + | 0.331295i | \(0.107485\pi\) | ||||
−0.943527 | + | 0.331295i | \(0.892515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.07107i | 1.03142i | 0.856763 | + | 0.515711i | \(0.172472\pi\) | ||||
−0.856763 | + | 0.515711i | \(0.827528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.89949i | 1.35980i | 0.733305 | + | 0.679900i | \(0.237977\pi\) | ||||
−0.733305 | + | 0.679900i | \(0.762023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.82843i | − | 0.381385i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | + | 4.24264i | 0.132453 | + | 0.561951i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.82843i | − | 0.356348i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.65685i | − | 0.701646i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | −0.244339 | −0.122169 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122169 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.41421i | − | 0.170251i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7279i | 1.39707i | 0.715575 | + | 0.698535i | \(0.246165\pi\) | ||||
−0.715575 | + | 0.698535i | \(0.753835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.07107i | − | 0.758098i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.89949i | − | 1.04934i | −0.851304 | − | 0.524672i | \(-0.824188\pi\) | ||
0.851304 | − | 0.524672i | \(-0.175812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | + | 8.48528i | 0.205196 | + | 0.870572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.82843i | − | 0.287183i | −0.989637 | − | 0.143592i | \(-0.954135\pi\) | ||
0.989637 | − | 0.143592i | \(-0.0458652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.41421i | 0.142134i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.65685i | − | 0.552052i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.0000 | 1.93347 | 0.966736 | − | 0.255774i | \(-0.0823304\pi\) | ||||
0.966736 | + | 0.255774i | \(0.0823304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.48528i | − | 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 11.3137i | − | 1.07385i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41421i | 0.133038i | 0.997785 | + | 0.0665190i | \(0.0211893\pi\) | ||||
−0.997785 | + | 0.0665190i | \(0.978811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.82843i | − | 0.263752i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82843i | 0.261488i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65685i | 0.518563i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.24264i | − | 0.382546i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.24264i | − | 0.370681i | −0.982674 | − | 0.185341i | \(-0.940661\pi\) | ||
0.982674 | − | 0.185341i | \(-0.0593388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | + | 2.82843i | −1.04053 | + | 0.245256i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82843i | 0.239904i | 0.992780 | + | 0.119952i | \(0.0382741\pi\) | ||||
−0.992780 | + | 0.119952i | \(0.961726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 7.07107i | − | 0.595491i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.1421i | − | 1.17444i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0000 | −1.14692 | −0.573462 | − | 0.819232i | \(-0.694400\pi\) | ||||
−0.573462 | + | 0.819232i | \(0.694400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00000 | 0.638470 | 0.319235 | − | 0.947676i | \(-0.396574\pi\) | ||||
0.319235 | + | 0.947676i | \(0.396574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.89949i | − | 0.785081i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.48528i | − | 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843i | 0.220193i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 4.24264i | −0.0764719 | − | 0.324443i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.07107i | − | 0.537603i | −0.963196 | − | 0.268802i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268802i | \(-0.0866276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.82843i | 0.213809i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 22.6274i | − | 1.66360i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.82843i | − | 0.206835i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843i | 0.205738i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7279i | 0.920960i | 0.887670 | + | 0.460480i | \(0.152323\pi\) | ||||
−0.887670 | + | 0.460480i | \(0.847677\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.65685i | 0.405096i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0000 | −0.997459 | −0.498729 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498729 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.3137i | − | 0.802008i | −0.916076 | − | 0.401004i | \(-0.868661\pi\) | ||
0.916076 | − | 0.401004i | \(-0.131339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | 0.141069 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.0000 | 1.40372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.48528i | − | 0.592638i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.41421i | 0.0982946i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | − | 1.41421i | 0.415029 | − | 0.0978232i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.9706i | − | 1.15204i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.65685i | − | 0.380521i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0000 | −0.796468 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.00000 | −0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 14.1421i | − | 0.922531i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.8701i | 1.73808i | 0.494742 | + | 0.869040i | \(0.335262\pi\) | ||||
−0.494742 | + | 0.869040i | \(0.664738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.82843i | − | 0.182195i | −0.995842 | − | 0.0910975i | \(-0.970963\pi\) | ||
0.995842 | − | 0.0910975i | \(-0.0290375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | 0.127775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | − | 2.82843i | 0.763542 | − | 0.179969i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 12.7279i | − | 0.806599i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24.0416i | − | 1.51749i | −0.651385 | − | 0.758747i | \(-0.725812\pi\) | ||
0.651385 | − | 0.758747i | \(-0.274188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.89949i | − | 0.617514i | −0.951141 | − | 0.308757i | \(-0.900087\pi\) | ||
0.951141 | − | 0.308757i | \(-0.0999129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.0000 | 1.98838 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.07107i | 0.437688i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.0416i | 1.48247i | 0.671245 | + | 0.741235i | \(0.265760\pi\) | ||||
−0.671245 | + | 0.741235i | \(0.734240\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 19.7990i | − | 1.21624i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.89949i | 0.605839i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.0416i | − | 1.46584i | −0.680313 | − | 0.732922i | \(-0.738156\pi\) | ||
0.680313 | − | 0.732922i | \(-0.261844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.3137i | − | 0.687259i | −0.939105 | − | 0.343629i | \(-0.888344\pi\) | ||
0.939105 | − | 0.343629i | \(-0.111656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | −0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.41421i | − | 0.0852803i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.41421i | − | 0.0843649i | −0.999110 | − | 0.0421825i | \(-0.986569\pi\) | ||
0.999110 | − | 0.0421825i | \(-0.0134311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.2843i | 1.68133i | 0.541559 | + | 0.840663i | \(0.317834\pi\) | ||||
−0.541559 | + | 0.840663i | \(0.682166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.00000 | − | 8.48528i | −0.118470 | − | 0.502625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82843i | 0.165805i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.6985i | 1.73500i | 0.497434 | + | 0.867502i | \(0.334276\pi\) | ||||
−0.497434 | + | 0.867502i | \(0.665724\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.41421i | − | 0.0820610i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.0000 | 0.916157 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.89949i | 0.561349i | 0.959803 | + | 0.280674i | \(0.0905581\pi\) | ||||
−0.959803 | + | 0.280674i | \(0.909442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0000 | 1.13047 | 0.565233 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565233 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.65685i | 0.318728i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.07107i | 0.397151i | 0.980086 | + | 0.198575i | \(0.0636315\pi\) | ||||
−0.980086 | + | 0.198575i | \(0.936369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0000 | −0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.0000 | −1.11629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | + | 8.48528i | 0.111283 | + | 0.472134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.82843i | − | 0.156893i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.48528i | 0.469237i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.0000 | 1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.3137i | 0.619987i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4558i | 1.38667i | 0.720616 | + | 0.693334i | \(0.243859\pi\) | ||||
−0.720616 | + | 0.693334i | \(0.756141\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 1.41421i | − | 0.0768095i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.48528i | 0.459504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.82843i | 0.152277i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 32.5269i | − | 1.74614i | −0.487598 | − | 0.873068i | \(-0.662127\pi\) | ||
0.487598 | − | 0.873068i | \(-0.337873\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.82843i | − | 0.150970i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0000 | 0.849192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 5.65685i | − | 0.299392i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.3848i | − | 0.970311i | −0.874428 | − | 0.485156i | \(-0.838763\pi\) | ||
0.874428 | − | 0.485156i | \(-0.161237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | + | 8.48528i | −0.894737 | + | 0.446594i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.00000 | −0.472377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.9706i | 0.885856i | 0.896557 | + | 0.442928i | \(0.146060\pi\) | ||||
−0.896557 | + | 0.442928i | \(0.853940\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.24264i | 0.220863i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.0000 | 1.45369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6274i | 1.17160i | 0.810454 | + | 0.585802i | \(0.199220\pi\) | ||||
−0.810454 | + | 0.585802i | \(0.800780\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0000 | −1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0000 | −0.717242 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.0000 | −1.63512 | −0.817562 | − | 0.575841i | \(-0.804675\pi\) | ||||
−0.817562 | + | 0.575841i | \(0.804675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0000 | −1.11544 | −0.557722 | − | 0.830028i | \(-0.688325\pi\) | ||||
−0.557722 | + | 0.830028i | \(0.688325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.82843i | − | 0.143040i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.24264i | 0.214013i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.0000 | 0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | 0.501886 | 0.250943 | − | 0.968002i | \(-0.419259\pi\) | ||||
0.250943 | + | 0.968002i | \(0.419259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | − | 2.82843i | 0.600751 | − | 0.141598i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9706i | 0.845364i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.0000 | −0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.4558i | − | 1.25871i | −0.777118 | − | 0.629355i | \(-0.783319\pi\) | ||
0.777118 | − | 0.629355i | \(-0.216681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.6274i | 1.11342i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 25.4558i | − | 1.24958i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.82843i | − | 0.138509i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.3848i | − | 0.898155i | −0.893493 | − | 0.449078i | \(-0.851753\pi\) | ||
0.893493 | − | 0.449078i | \(-0.148247\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1421i | 0.689246i | 0.938741 | + | 0.344623i | \(0.111993\pi\) | ||||
−0.938741 | + | 0.344623i | \(0.888007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.07107i | 0.343807i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.6274i | 1.09502i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.9411i | 1.63111i | 0.578682 | + | 0.815553i | \(0.303567\pi\) | ||||
−0.578682 | + | 0.815553i | \(0.696433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.1421i | 0.678064i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.00000 | − | 1.41421i | 0.287019 | − | 0.0676510i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 26.8701i | − | 1.27663i | −0.769773 | − | 0.638317i | \(-0.779631\pi\) | ||
0.769773 | − | 0.638317i | \(-0.220369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.7990i | 0.938562i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5563i | 0.734150i | 0.930191 | + | 0.367075i | \(0.119641\pi\) | ||||
−0.930191 | + | 0.367075i | \(0.880359\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.0000 | −0.750092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9706i | 0.788689i | 0.918963 | + | 0.394344i | \(0.129028\pi\) | ||||
−0.918963 | + | 0.394344i | \(0.870972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.0000 | 0.556487 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 24.0416i | − | 1.11251i | −0.831010 | − | 0.556257i | \(-0.812237\pi\) | ||
0.831010 | − | 0.556257i | \(-0.187763\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.65685i | 0.261209i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.00000 | −0.368621 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | + | 4.24264i | 0.0458831 | + | 0.194666i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.89949i | 0.453267i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 7.07107i | − | 0.323085i | −0.986866 | − | 0.161543i | \(-0.948353\pi\) | ||
0.986866 | − | 0.161543i | \(-0.0516469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.0000 | −1.45907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.65685i | 0.256865i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000 | 0.453143 | 0.226572 | − | 0.973995i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973995i | \(0.427248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.48528i | 0.383718i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.0416i | − | 1.08498i | −0.840061 | − | 0.542492i | \(-0.817481\pi\) | ||
0.840061 | − | 0.542492i | \(-0.182519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.1421i | − | 0.636930i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 2.82843i | − | 0.127128i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.6274i | 1.01498i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.4558i | 1.13956i | 0.821797 | + | 0.569780i | \(0.192972\pi\) | ||||
−0.821797 | + | 0.569780i | \(0.807028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.7279i | − | 0.567510i | −0.958897 | − | 0.283755i | \(-0.908420\pi\) | ||
0.958897 | − | 0.283755i | \(-0.0915802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | −0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 24.0416i | − | 1.06563i | −0.846233 | − | 0.532813i | \(-0.821135\pi\) | ||
0.846233 | − | 0.532813i | \(-0.178865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | + | 4.24264i | 0.0441511 | + | 0.187317i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.07107i | 0.310385i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.41421i | 0.0619578i | 0.999520 | + | 0.0309789i | \(0.00986247\pi\) | ||||
−0.999520 | + | 0.0309789i | \(0.990138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.0000 | 1.48672 | 0.743358 | − | 0.668894i | \(-0.233232\pi\) | ||||
0.743358 | + | 0.668894i | \(0.233232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.82843i | − | 0.123443i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.0000 | −1.72935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0000 | 0.863064 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.41421i | − | 0.0609145i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0000 | 0.515920 | 0.257960 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257960 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.48528i | − | 0.364138i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9706i | 0.726939i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | −0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.0000 | − | 7.07107i | 1.27804 | − | 0.301238i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.6274i | 0.962216i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.6274i | 0.960480i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.82843i | 0.119416i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.82843i | − | 0.118993i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.82843i | − | 0.118783i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 32.5269i | − | 1.36360i | −0.731539 | − | 0.681800i | \(-0.761198\pi\) | ||
0.731539 | − | 0.681800i | \(-0.238802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.2548i | 1.89386i | 0.321446 | + | 0.946928i | \(0.395831\pi\) | ||||
−0.321446 | + | 0.946928i | \(0.604169\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 12.7279i | − | 0.531717i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.41421i | − | 0.0589768i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | 1.49353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.0000 | −0.579821 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 5.65685i | − | 0.233882i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 35.3553i | − | 1.45927i | −0.683836 | − | 0.729636i | \(-0.739690\pi\) | ||
0.683836 | − | 0.729636i | \(-0.260310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | − | 25.4558i | −0.247226 | − | 1.04889i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0000 | 0.575883 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.0000 | −1.72473 | −0.862367 | − | 0.506284i | \(-0.831019\pi\) | ||||
−0.862367 | + | 0.506284i | \(0.831019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 11.3137i | − | 0.463817i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.3137i | 0.463039i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.0000 | 1.79779 | 0.898896 | − | 0.438163i | \(-0.144371\pi\) | ||||
0.898896 | + | 0.438163i | \(0.144371\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.2843i | 1.15374i | 0.816836 | + | 0.576870i | \(0.195726\pi\) | ||||
−0.816836 | + | 0.576870i | \(0.804274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.0000 | −0.731804 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0000 | −1.38002 | −0.690009 | − | 0.723801i | \(-0.742393\pi\) | ||||
−0.690009 | + | 0.723801i | \(0.742393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.0000 | −0.810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.0000 | −0.809113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0000 | 0.646234 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.48528i | 0.342160i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0000 | −1.36879 | −0.684394 | − | 0.729112i | \(-0.739933\pi\) | ||||
−0.684394 | + | 0.729112i | \(0.739933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4558i | 1.02316i | 0.859237 | + | 0.511578i | \(0.170939\pi\) | ||||
−0.859237 | + | 0.511578i | \(0.829061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.41421i | − | 0.0567504i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.0000 | −1.12180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | + | 1.41421i | −0.239617 | + | 0.0564782i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 22.6274i | − | 0.902214i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.1421i | − | 0.562990i | −0.959563 | − | 0.281495i | \(-0.909170\pi\) | ||
0.959563 | − | 0.281495i | \(-0.0908302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.0000 | 0.397464 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.0000 | −1.11115 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.82843i | − | 0.112066i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.0122i | 1.61988i | 0.586510 | + | 0.809942i | \(0.300502\pi\) | ||||
−0.586510 | + | 0.809942i | \(0.699498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.5980i | 1.56159i | 0.624786 | + | 0.780796i | \(0.285186\pi\) | ||||
−0.624786 | + | 0.780796i | \(0.714814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 7.07107i | − | 0.277992i | −0.990293 | − | 0.138996i | \(-0.955612\pi\) | ||
0.990293 | − | 0.138996i | \(-0.0443876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.3137i | − | 0.444102i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.9706i | 0.665129i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.48528i | 0.331547i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.00000 | 0.311636 | 0.155818 | − | 0.987786i | \(-0.450199\pi\) | ||||
0.155818 | + | 0.987786i | \(0.450199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.5980i | − | 1.54018i | −0.637934 | − | 0.770091i | \(-0.720211\pi\) | ||
0.637934 | − | 0.770091i | \(-0.279789\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.65685i | 0.219694i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | − | 5.65685i | 0.930680 | − | 0.219363i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0000 | −0.387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.3137i | − | 0.436761i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.2843i | 1.09028i | 0.838346 | + | 0.545139i | \(0.183523\pi\) | ||||
−0.838346 | + | 0.545139i | \(0.816477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.89949i | 0.380468i | 0.981739 | + | 0.190234i | \(0.0609248\pi\) | ||||
−0.981739 | + | 0.190234i | \(0.939075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.00000 | −0.307012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.0000 | −1.22445 | −0.612223 | − | 0.790685i | \(-0.709725\pi\) | ||||
−0.612223 | + | 0.790685i | \(0.709725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.0000 | −0.839352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.0000 | −1.06672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 16.9706i | − | 0.645591i | −0.946469 | − | 0.322795i | \(-0.895377\pi\) | ||
0.946469 | − | 0.322795i | \(-0.104623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.65685i | − | 0.214577i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.48528i | − | 0.321403i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.0000 | − | 11.3137i | 1.81035 | − | 0.426705i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.1421i | 0.532624i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.9706i | − | 0.638244i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | 0.150223 | 0.0751116 | − | 0.997175i | \(-0.476069\pi\) | ||||
0.0751116 | + | 0.997175i | \(0.476069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.48528i | 0.317776i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 26.8701i | − | 1.00348i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5269i | 1.21305i | 0.795065 | + | 0.606525i | \(0.207437\pi\) | ||||
−0.795065 | + | 0.606525i | \(0.792563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6274i | 0.842689i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.82843i | 0.105190i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 7.07107i | − | 0.262613i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2843i | 1.04901i | 0.851409 | + | 0.524503i | \(0.175749\pi\) | ||||
−0.851409 | + | 0.524503i | \(0.824251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −52.0000 | −1.92066 | −0.960332 | − | 0.278859i | \(-0.910044\pi\) | ||||
−0.960332 | + | 0.278859i | \(0.910044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | −0.0737711 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.82843i | − | 0.104186i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 36.7696i | − | 1.35259i | −0.736631 | − | 0.676295i | \(-0.763585\pi\) | ||
0.736631 | − | 0.676295i | \(-0.236415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | + | 2.82843i | −0.440831 | + | 0.103905i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | 1.02584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7279i | 0.465690i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 56.5685i | − | 2.06697i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0416i | 0.876126i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | 0.0725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | 0.652499 | 0.326250 | − | 0.945284i | \(-0.394215\pi\) | ||||
0.326250 | + | 0.945284i | \(0.394215\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.0000 | −0.868858 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.6274i | − | 0.817029i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0000 | 0.721218 | 0.360609 | − | 0.932717i | \(-0.382569\pi\) | ||||
0.360609 | + | 0.932717i | \(0.382569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.89949i | 0.356522i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.2132i | − | 0.762986i | −0.924372 | − | 0.381493i | \(-0.875410\pi\) | ||
0.924372 | − | 0.381493i | \(-0.124590\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.0000 | −1.14799 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.0000 | − | 4.24264i | 0.644917 | − | 0.152008i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 11.3137i | − | 0.404836i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.07107i | − | 0.252699i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0000 | −0.571064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.0000 | −1.49714 | −0.748569 | − | 0.663057i | \(-0.769259\pi\) | ||||
−0.748569 | + | 0.663057i | \(0.769259\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 24.0416i | − | 0.855905i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 22.6274i | − | 0.803523i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.7990i | 0.702198i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.07107i | 0.250470i | 0.992127 | + | 0.125235i |