Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 242x^{12} + 13297x^{8} + 201600x^{4} + 331776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.6 | ||
Root | \(1.85032 + 1.85032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.h.2591.12 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.517638i | − 0.231495i | −0.993279 | − | 0.115747i | \(-0.963074\pi\) | ||||
0.993279 | − | 0.115747i | \(-0.0369263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.63249 | 1.69826 | 0.849130 | − | 0.528185i | \(-0.177127\pi\) | ||||
0.849130 | + | 0.528185i | \(0.177127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.91559 | 0.531289 | 0.265645 | − | 0.964071i | \(-0.414415\pi\) | ||||
0.265645 | + | 0.964071i | \(0.414415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.29484i | 0.314045i | 0.987595 | + | 0.157022i | \(0.0501895\pi\) | ||||
−0.987595 | + | 0.157022i | \(0.949810\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.23349i | − 0.971229i | −0.874173 | − | 0.485615i | \(-0.838596\pi\) | ||||
0.874173 | − | 0.485615i | \(-0.161404\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.38134 | 0.913573 | 0.456786 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456786 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73205 | 0.946410 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.70064i | − 0.687191i | −0.939118 | − | 0.343595i | \(-0.888355\pi\) | ||||
0.939118 | − | 0.343595i | \(-0.111645\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 5.11174i | − 0.918096i | −0.888411 | − | 0.459048i | \(-0.848191\pi\) | ||||
0.888411 | − | 0.459048i | \(-0.151809\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.517638 | −0.0874968 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.18354 | 0.358972 | 0.179486 | − | 0.983761i | \(-0.442557\pi\) | ||||
0.179486 | + | 0.983761i | \(0.442557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.88816i | 0.294881i | 0.989071 | + | 0.147440i | \(0.0471035\pi\) | ||||
−0.989071 | + | 0.147440i | \(0.952897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37969i | 0.820395i | 0.911997 | + | 0.410198i | \(0.134540\pi\) | ||||
−0.911997 | + | 0.410198i | \(0.865460\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.32221 | −1.21392 | −0.606960 | − | 0.794732i | \(-0.707611\pi\) | ||||
−0.606960 | + | 0.794732i | \(0.707611\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 5.53748i | − 0.760632i | −0.924857 | − | 0.380316i | \(-0.875815\pi\) | ||||
0.924857 | − | 0.380316i | \(-0.124185\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.91559i | − 0.393138i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.54599 | −0.331459 | −0.165730 | − | 0.986171i | \(-0.552998\pi\) | ||||
−0.165730 | + | 0.986171i | \(0.552998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0617920 | −0.00791166 | −0.00395583 | − | 0.999992i | \(-0.501259\pi\) | ||||
−0.00395583 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.991583i | − 0.122991i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.31790i | 0.894024i | 0.894528 | + | 0.447012i | \(0.147512\pi\) | ||||
−0.894528 | + | 0.447012i | \(0.852488\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4036 | 1.59071 | 0.795357 | − | 0.606142i | \(-0.207284\pi\) | ||||
0.795357 | + | 0.606142i | \(0.207284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6132 | −1.71034 | −0.855172 | − | 0.518345i | \(-0.826548\pi\) | ||||
−0.855172 | + | 0.518345i | \(0.826548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.63249i | − 0.641882i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9185i | 1.90348i | 0.306911 | + | 0.951738i | \(0.400705\pi\) | ||||
−0.306911 | + | 0.951738i | \(0.599295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.59962 | 0.943931 | 0.471965 | − | 0.881617i | \(-0.343545\pi\) | ||||
0.471965 | + | 0.881617i | \(0.343545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.670259 | 0.0726998 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.33704i | − 0.141726i | −0.997486 | − | 0.0708632i | \(-0.977425\pi\) | ||||
0.997486 | − | 0.0708632i | \(-0.0225754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.91559i | − 0.200808i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.19142 | −0.224835 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.23349 | 0.531380 | 0.265690 | − | 0.964058i | \(-0.414400\pi\) | ||||
0.265690 | + | 0.964058i | \(0.414400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.51995i | − 0.648760i | −0.945927 | − | 0.324380i | \(-0.894844\pi\) | ||||
0.945927 | − | 0.324380i | \(-0.105156\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 3.04995i | − 0.300521i | −0.988646 | − | 0.150260i | \(-0.951989\pi\) | ||||
0.988646 | − | 0.150260i | \(-0.0480112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.705070 | 0.0681617 | 0.0340809 | − | 0.999419i | \(-0.489150\pi\) | ||||
0.0340809 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0155 | −1.05509 | −0.527546 | − | 0.849526i | \(-0.676888\pi\) | ||||
−0.527546 | + | 0.849526i | \(0.676888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.915903i | − 0.0861609i | −0.999072 | − | 0.0430805i | \(-0.986283\pi\) | ||||
0.999072 | − | 0.0430805i | \(-0.0137172\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.26795i | − 0.211487i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.29484 | 0.118698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.7249 | 1.88408 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.03768i | − 0.450584i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.71733i | − 0.329860i | −0.986305 | − | 0.164930i | \(-0.947260\pi\) | ||||
0.986305 | − | 0.164930i | \(-0.0527398\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.52897 | 0.745180 | 0.372590 | − | 0.927996i | \(-0.378470\pi\) | ||||
0.372590 | + | 0.927996i | \(0.378470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.23349 | −0.367090 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 6.85520i | − 0.585679i | −0.956162 | − | 0.292840i | \(-0.905400\pi\) | ||||
0.956162 | − | 0.292840i | \(-0.0946002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3600i | 1.38763i | 0.720152 | + | 0.693817i | \(0.244072\pi\) | ||||
−0.720152 | + | 0.693817i | \(0.755928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.7895 | 0.902267 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.91559 | −0.159081 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.34764i | 0.110403i | 0.998475 | + | 0.0552017i | \(0.0175802\pi\) | ||||
−0.998475 | + | 0.0552017i | \(0.982420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 16.5288i | − 1.34509i | −0.740055 | − | 0.672546i | \(-0.765201\pi\) | ||||
0.740055 | − | 0.672546i | \(-0.234799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.64603 | −0.212534 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9903 | −0.956927 | −0.478464 | − | 0.878107i | \(-0.658806\pi\) | ||||
−0.478464 | + | 0.878107i | \(0.658806\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4.38134i | − 0.345298i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3079i | 1.12068i | 0.828262 | + | 0.560340i | \(0.189330\pi\) | ||||
−0.828262 | + | 0.560340i | \(0.810670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.8378 | 1.22557 | 0.612784 | − | 0.790251i | \(-0.290050\pi\) | ||||
0.612784 | + | 0.790251i | \(0.290050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.33051 | −0.717732 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 10.8139i | − 0.822166i | −0.911598 | − | 0.411083i | \(-0.865151\pi\) | ||||
0.911598 | − | 0.411083i | \(-0.134849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.73205i | − 0.357709i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.7053 | 1.92131 | 0.960653 | − | 0.277750i | \(-0.0895887\pi\) | ||||
0.960653 | + | 0.277750i | \(0.0895887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.93821 | 0.144066 | 0.0720329 | − | 0.997402i | \(-0.477051\pi\) | ||||
0.0720329 | + | 0.997402i | \(0.477051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.13028i | − 0.0831001i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.29317i | 0.533330i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0780 | −1.30808 | −0.654038 | − | 0.756462i | \(-0.726926\pi\) | ||||
−0.654038 | + | 0.756462i | \(0.726926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.06467 | −0.364563 | −0.182282 | − | 0.983246i | \(-0.558348\pi\) | ||||
−0.182282 | + | 0.983246i | \(0.558348\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.12266i | 0.0799864i | 0.999200 | + | 0.0399932i | \(0.0127336\pi\) | ||||
−0.999200 | + | 0.0399932i | \(0.987266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 0.379692i | − 0.0269157i | −0.999909 | − | 0.0134578i | \(-0.995716\pi\) | ||||
0.999909 | − | 0.0134578i | \(-0.00428389\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.70064 | −0.259734 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.977383 | 0.0682634 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 23.8451i | − 1.64940i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 9.43175i | − 0.649309i | −0.945833 | − | 0.324654i | \(-0.894752\pi\) | ||||
0.945833 | − | 0.324654i | \(-0.105248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.78473 | 0.189917 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.11174 | −0.347008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.48038i | 0.166849i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.2490i | − 1.35597i | −0.735075 | − | 0.677986i | \(-0.762853\pi\) | ||||
0.735075 | − | 0.677986i | \(-0.237147\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.26008 | −0.349124 | −0.174562 | − | 0.984646i | \(-0.555851\pi\) | ||||
−0.174562 | + | 0.984646i | \(0.555851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.30241 | −0.350393 | −0.175196 | − | 0.984533i | \(-0.556056\pi\) | ||||
−0.175196 | + | 0.984533i | \(0.556056\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 27.5870i | − 1.80728i | −0.428291 | − | 0.903641i | \(-0.640884\pi\) | ||||
0.428291 | − | 0.903641i | \(-0.359116\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.30790i | 0.281016i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.6134 | 1.33337 | 0.666684 | − | 0.745341i | \(-0.267713\pi\) | ||||
0.666684 | + | 0.745341i | \(0.267713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.31078 | 0.599760 | 0.299880 | − | 0.953977i | \(-0.403053\pi\) | ||||
0.299880 | + | 0.953977i | \(0.403053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.517638i | 0.0330707i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 8.10963i | − 0.516004i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0783 | −0.636139 | −0.318070 | − | 0.948067i | \(-0.603035\pi\) | ||||
−0.318070 | + | 0.948067i | \(0.603035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6779 | 1.55148 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 27.9029i | − 1.74053i | −0.492581 | − | 0.870267i | \(-0.663946\pi\) | ||||
0.492581 | − | 0.870267i | \(-0.336054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.18354i | − 0.135679i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9891 | −0.677615 | −0.338807 | − | 0.940856i | \(-0.610024\pi\) | ||||
−0.338807 | + | 0.940856i | \(0.610024\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.86641 | −0.176082 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.2550i | 1.60079i | 0.599471 | + | 0.800396i | \(0.295378\pi\) | ||||
−0.599471 | + | 0.800396i | \(0.704622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 25.1517i | − 1.52786i | −0.645301 | − | 0.763928i | \(-0.723268\pi\) | ||||
0.645301 | − | 0.763928i | \(-0.276732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.6532 | 1.60725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.58585 | 0.215453 | 0.107726 | − | 0.994181i | \(-0.465643\pi\) | ||||
0.107726 | + | 0.994181i | \(0.465643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 5.70055i | − 0.340066i | −0.985438 | − | 0.170033i | \(-0.945613\pi\) | ||||
0.985438 | − | 0.170033i | \(-0.0543875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.86353i | 0.348551i | 0.984697 | + | 0.174275i | \(0.0557583\pi\) | ||||
−0.984697 | + | 0.174275i | \(0.944242\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.88816 | 0.111454 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3234 | 0.901376 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.50281i | 0.438319i | 0.975689 | + | 0.219159i | \(0.0703315\pi\) | ||||
−0.975689 | + | 0.219159i | \(0.929669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.31790i | 0.0767311i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.39286 | 0.485371 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.37969 | 0.310080 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0319859i | 0.00183151i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.5569i | 1.51568i | 0.652440 | + | 0.757841i | \(0.273746\pi\) | ||||
−0.652440 | + | 0.757841i | \(0.726254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.2656 | 1.88632 | 0.943160 | − | 0.332340i | \(-0.107838\pi\) | ||||
0.943160 | + | 0.332340i | \(0.107838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4825 | −1.83602 | −0.918009 | − | 0.396560i | \(-0.870204\pi\) | ||||
−0.918009 | + | 0.396560i | \(0.870204\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 25.7282i | − 1.44504i | −0.691350 | − | 0.722520i | \(-0.742984\pi\) | ||||
0.691350 | − | 0.722520i | \(-0.257016\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 20.8438i | − 1.16703i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.48170 | 0.305010 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.06467 | 0.502818 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.32221i | 0.458819i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0999i | 0.665071i | 0.943091 | + | 0.332535i | \(0.107904\pi\) | ||||
−0.943091 | + | 0.332535i | \(0.892096\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.78802 | 0.206962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.3305 | 1.27089 | 0.635447 | − | 0.772144i | \(-0.280816\pi\) | ||||
0.635447 | + | 0.772144i | \(0.280816\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 28.7918i | − 1.55917i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3071 | 0.714362 | 0.357181 | − | 0.934035i | \(-0.383738\pi\) | ||||
0.357181 | + | 0.934035i | \(0.383738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.9311 | 1.38806 | 0.694030 | − | 0.719947i | \(-0.255834\pi\) | ||||
0.694030 | + | 0.719947i | \(0.255834\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 12.3596i | − 0.657834i | −0.944359 | − | 0.328917i | \(-0.893316\pi\) | ||||
0.944359 | − | 0.328917i | \(-0.106684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 6.93821i | − 0.368242i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.55203 | −0.240247 | −0.120123 | − | 0.992759i | \(-0.538329\pi\) | ||||
−0.120123 | + | 0.992759i | \(0.538329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.07756 | 0.0567135 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.56434i | 0.395936i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 17.4696i | − 0.911905i | −0.890004 | − | 0.455953i | \(-0.849299\pi\) | ||||
0.890004 | − | 0.455953i | \(-0.150701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.53748 | −0.287492 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1714 | −0.889103 | −0.444551 | − | 0.895753i | \(-0.646637\pi\) | ||||
−0.444551 | + | 0.895753i | \(0.646637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.08890i | − 0.365097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.4049i | 0.585831i | 0.956138 | + | 0.292916i | \(0.0946255\pi\) | ||||
−0.956138 | + | 0.292916i | \(0.905374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0616 | −0.514124 | −0.257062 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257062 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.91559 | −0.148592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.01497i | − 0.304971i | −0.988306 | − | 0.152486i | \(-0.951272\pi\) | ||||
0.988306 | − | 0.152486i | \(-0.0487278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.67314i | 0.286903i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.75764 | 0.440645 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.1940 | 0.812756 | 0.406378 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406378 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2427i | 0.711247i | 0.934629 | + | 0.355623i | \(0.115731\pi\) | ||||
−0.934629 | + | 0.355623i | \(0.884269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9.79201i | − 0.487775i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2988 | 0.609627 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.9703 | −0.789678 | −0.394839 | − | 0.918750i | \(-0.629200\pi\) | ||||
−0.394839 | + | 0.918750i | \(0.629200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.54599i | 0.125280i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 4.45149i | − 0.218515i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.6846 | −1.15707 | −0.578534 | − | 0.815658i | \(-0.696375\pi\) | ||||
−0.578534 | + | 0.815658i | \(0.696375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4451 | −0.801487 | −0.400743 | − | 0.916190i | \(-0.631248\pi\) | ||||
−0.400743 | + | 0.916190i | \(0.631248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.12725i | 0.297215i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0617920i | 0.00299032i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.963144 | 0.0463930 | 0.0231965 | − | 0.999731i | \(-0.492616\pi\) | ||||
0.0231965 | + | 0.999731i | \(0.492616\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.16197 | −0.248068 | −0.124034 | − | 0.992278i | \(-0.539583\pi\) | ||||
−0.124034 | + | 0.992278i | \(0.539583\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 18.5484i | − 0.887289i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3700i | 0.542659i | 0.962487 | + | 0.271329i | \(0.0874632\pi\) | ||||
−0.962487 | + | 0.271329i | \(0.912537\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.2690 | −0.772965 | −0.386483 | − | 0.922297i | \(-0.626310\pi\) | ||||
−0.386483 | + | 0.922297i | \(0.626310\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.692105 | −0.0328089 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4105i | 1.15200i | 0.817449 | + | 0.576001i | \(0.195388\pi\) | ||||
−0.817449 | + | 0.576001i | \(0.804612\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6350i | 0.500784i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.991583 | −0.0464861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.5834 | −1.19674 | −0.598371 | − | 0.801219i | \(-0.704185\pi\) | ||||
−0.598371 | + | 0.801219i | \(0.704185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 37.2950i | − 1.73700i | −0.495690 | − | 0.868500i | \(-0.665085\pi\) | ||||
0.495690 | − | 0.868500i | \(-0.334915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.6876i | − 0.543168i | −0.962415 | − | 0.271584i | \(-0.912452\pi\) | ||||
0.962415 | − | 0.271584i | \(-0.0875475\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.2812 | 0.845952 | 0.422976 | − | 0.906141i | \(-0.360985\pi\) | ||||
0.422976 | + | 0.906141i | \(0.360985\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.31790 | 0.337909 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.3011i | 1.39324i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 20.0331i | − 0.919181i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.1230 | 1.10221 | 0.551104 | − | 0.834436i | \(-0.314207\pi\) | ||||
0.551104 | + | 0.834436i | \(0.314207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.18277 | 0.190718 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.70905i | − 0.123012i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.2209i | 0.463152i | 0.972817 | + | 0.231576i | \(0.0743882\pi\) | ||||
−0.972817 | + | 0.231576i | \(0.925612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.1633 | 1.54177 | 0.770883 | − | 0.636976i | \(-0.219815\pi\) | ||||
0.770883 | + | 0.636976i | \(0.219815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.79173 | 0.215809 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 13.4036i | − 0.601233i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9745i | 0.491286i | 0.969360 | + | 0.245643i | \(0.0789991\pi\) | ||||
−0.969360 | + | 0.245643i | \(0.921001\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.49370 | 0.334128 | 0.167064 | − | 0.985946i | \(-0.446571\pi\) | ||||
0.167064 | + | 0.985946i | \(0.446571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.37498 | −0.150184 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.1521i | 1.33647i | 0.743950 | + | 0.668235i | \(0.232950\pi\) | ||||
−0.743950 | + | 0.668235i | \(0.767050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6132i | 0.646449i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.57877 | −0.0695690 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −46.8748 | −2.06155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.48731i | 0.0651603i | 0.999469 | + | 0.0325801i | \(0.0103724\pi\) | ||||
−0.999469 | + | 0.0325801i | \(0.989628\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1372i | 1.14290i | 0.820636 | + | 0.571451i | \(0.193619\pi\) | ||||
−0.820636 | + | 0.571451i | \(0.806381\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.61889 | 0.288323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.80385 | −0.165385 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.61694i | 0.156667i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 0.364971i | − 0.0157791i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.63249 | −0.242608 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0794 | −0.648314 | −0.324157 | − | 0.946003i | \(-0.605081\pi\) | ||||
−0.324157 | + | 0.946003i | \(0.605081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.70204i | 0.244248i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.6481i | 1.35318i | 0.736362 | + | 0.676588i | \(0.236542\pi\) | ||||
−0.736362 | + | 0.676588i | \(0.763458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.6666 | −0.667420 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.9185 | 0.719447 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.8208i | 0.924577i | 0.886729 | + | 0.462289i | \(0.152972\pi\) | ||||
−0.886729 | + | 0.462289i | \(0.847028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.3053i | 0.435867i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4121 | 1.15528 | 0.577640 | − | 0.816291i | \(-0.303974\pi\) | ||||
0.577640 | + | 0.816291i | \(0.303974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.474106 | −0.0199458 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 19.8376i | − 0.831637i | −0.909448 | − | 0.415819i | \(-0.863495\pi\) | ||||
0.909448 | − | 0.415819i | \(-0.136505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0152i | 0.628367i | 0.949362 | + | 0.314184i | \(0.101731\pi\) | ||||
−0.949362 | + | 0.314184i | \(0.898269\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7327 | 0.864615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.72994 | −0.280171 | −0.140086 | − | 0.990139i | \(-0.544738\pi\) | ||||
−0.140086 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 8.59962i | − 0.356772i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 31.1898i | − 1.29175i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.5541 | −1.88022 | −0.940110 | − | 0.340870i | \(-0.889278\pi\) | ||||
−0.940110 | + | 0.340870i | \(0.889278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.6405 | −0.891682 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.9300i | 0.900556i | 0.892888 | + | 0.450278i | \(0.148675\pi\) | ||||
−0.892888 | + | 0.450278i | \(0.851325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 0.670259i | − 0.0274779i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.2008 | −0.621088 | −0.310544 | − | 0.950559i | \(-0.600511\pi\) | ||||
−0.310544 | + | 0.950559i | \(0.600511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2519 | 1.47874 | 0.739372 | − | 0.673297i | \(-0.235122\pi\) | ||||
0.739372 | + | 0.673297i | \(0.235122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 10.7280i | − 0.436156i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8693i | 0.644115i | 0.946720 | + | 0.322057i | \(0.104374\pi\) | ||||
−0.946720 | + | 0.322057i | \(0.895626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.9420 | −0.644943 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.91984 | 0.158321 | 0.0791603 | − | 0.996862i | \(-0.474776\pi\) | ||||
0.0791603 | + | 0.996862i | \(0.474776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.6851i | 1.91973i | 0.280460 | + | 0.959866i | \(0.409513\pi\) | ||||
−0.280460 | + | 0.959866i | \(0.590487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.7867i | 1.43839i | 0.694808 | + | 0.719195i | \(0.255489\pi\) | ||||
−0.694808 | + | 0.719195i | \(0.744511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.33704 | −0.0535675 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.0526 | 0.842102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.82734i | 0.112733i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 23.1743i | − 0.922555i | −0.887256 | − | 0.461277i | \(-0.847391\pi\) | ||||
0.887256 | − | 0.461277i | \(-0.152609\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.92423 | −0.0763608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.91559 | −0.0758985 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 28.2675i | − 1.11650i | −0.829673 | − | 0.558250i | \(-0.811473\pi\) | ||||
0.829673 | − | 0.558250i | \(-0.188527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6610i | 0.775355i | 0.921795 | + | 0.387678i | \(0.126723\pi\) | ||||
−0.921795 | + | 0.387678i | \(0.873277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3608 | −0.407324 | −0.203662 | − | 0.979041i | \(-0.565284\pi\) | ||||
−0.203662 | + | 0.979041i | \(0.565284\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.3402 | −0.562904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 33.9610i | − 1.32900i | −0.747290 | − | 0.664498i | \(-0.768645\pi\) | ||||
0.747290 | − | 0.664498i | \(-0.231355\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 4.41492i | − 0.172505i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0280540 | 0.00109283 | 0.000546414 | − | 1.00000i | \(-0.499826\pi\) | ||||
0.000546414 | 1.00000i | \(0.499826\pi\) | ||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.4472 | 0.678619 | 0.339310 | − | 0.940675i | \(-0.389807\pi\) | ||||
0.339310 | + | 0.940675i | \(0.389807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.19142i | 0.0849795i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 16.2138i | − 0.627799i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.348043 | −0.0134360 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.96765 | −0.230036 | −0.115018 | − | 0.993363i | \(-0.536693\pi\) | ||||
−0.115018 | + | 0.993363i | \(0.536693\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 46.7977i | − 1.79858i | −0.437352 | − | 0.899290i | \(-0.644084\pi\) | ||||
0.437352 | − | 0.899290i | \(-0.355916\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 5.23349i | − 0.200843i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.5620 | 1.24595 | 0.622976 | − | 0.782241i | \(-0.285924\pi\) | ||||
0.622976 | + | 0.782241i | \(0.285924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.54851 | −0.135582 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 10.6075i | − 0.404115i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5022i | 0.741899i | 0.928653 | + | 0.370950i | \(0.120968\pi\) | ||||
−0.928653 | + | 0.370950i | \(0.879032\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.46854 | 0.321230 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.44486 | −0.0926058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.54301i | 0.0960480i | 0.998846 | + | 0.0480240i | \(0.0152924\pi\) | ||||
−0.998846 | + | 0.0480240i | \(0.984708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 9.24400i | − 0.348644i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.51995 | −0.245208 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.9237 | −0.973584 | −0.486792 | − | 0.873518i | \(-0.661833\pi\) | ||||
−0.486792 | + | 0.873518i | \(0.661833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 22.3963i | − 0.838748i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5.58508i | − 0.208870i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.3623 | −0.647504 | −0.323752 | − | 0.946142i | \(-0.604944\pi\) | ||||
−0.323752 | + | 0.946142i | \(0.604944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.04995 | −0.113586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 17.5116i | − 0.650365i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 41.7746i | − 1.54933i | −0.632369 | − | 0.774667i | \(-0.717917\pi\) | ||||
0.632369 | − | 0.774667i | \(-0.282083\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.96584 | −0.257641 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.0630 | 1.77525 | 0.887624 | − | 0.460568i | \(-0.152354\pi\) | ||||
0.887624 | + | 0.460568i | \(0.152354\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.2180i | 1.51828i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.35707i | − 0.270634i | −0.990802 | − | 0.135317i | \(-0.956795\pi\) | ||||
0.990802 | − | 0.135317i | \(-0.0432053\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.38155 | −0.307489 | −0.153745 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153745 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.697592 | 0.0255578 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 0.705070i | − 0.0257627i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 43.2713i | − 1.57899i | −0.613756 | − | 0.789496i | \(-0.710342\pi\) | ||||
0.613756 | − | 0.789496i | \(-0.289658\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.55592 | −0.311382 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.5188 | −0.564039 | −0.282020 | − | 0.959409i | \(-0.591004\pi\) | ||||
−0.282020 | + | 0.959409i | \(0.591004\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 38.9572i | − 1.41220i | −0.708114 | − | 0.706098i | \(-0.750454\pi\) | ||||
0.708114 | − | 0.706098i | \(-0.249546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0155i | 0.398788i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.87707 | −0.176101 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4120 | 0.627894 | 0.313947 | − | 0.949440i | \(-0.398349\pi\) | ||||
0.313947 | + | 0.949440i | \(0.398349\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.6813i | 0.815791i | 0.913029 | + | 0.407895i | \(0.133737\pi\) | ||||
−0.913029 | + | 0.407895i | \(0.866263\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 24.1890i | − 0.868896i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.99350 | 0.286397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 75.4956 | 2.70144 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.20662i | 0.221524i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.8974i | 1.17267i | 0.810070 | + | 0.586333i | \(0.199429\pi\) | ||||
−0.810070 | + | 0.586333i | \(0.800571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.915903 | −0.0325658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.118368 | −0.00420338 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 0.904336i | − 0.0320332i | −0.999872 | − | 0.0160166i | \(-0.994902\pi\) | ||||
0.999872 | − | 0.0160166i | \(-0.00509847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 10.7759i | − 0.381225i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −82.3086 | −2.90461 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.26795 | −0.0799347 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 42.7876i | − 1.50433i | −0.658973 | − | 0.752167i | \(-0.729009\pi\) | ||||
0.658973 | − | 0.752167i | \(-0.270991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 50.2048i | − 1.76293i | −0.472251 | − | 0.881464i | \(-0.656558\pi\) | ||||
0.472251 | − | 0.881464i | \(-0.343442\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.40631 | 0.259432 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.7749 | 0.796792 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3031i | 0.638782i | 0.947623 | + | 0.319391i | \(0.103478\pi\) | ||||
−0.947623 | + | 0.319391i | \(0.896522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.1293i | 0.980527i | 0.871574 | + | 0.490264i | \(0.163100\pi\) | ||||
−0.871574 | + | 0.490264i | \(0.836900\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.1059 | 1.04688 | 0.523442 | − | 0.852062i | \(-0.324648\pi\) | ||||
0.523442 | + | 0.852062i | \(0.324648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.4049 | 0.673961 | 0.336980 | − | 0.941512i | \(-0.390594\pi\) | ||||
0.336980 | + | 0.941512i | \(0.390594\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.29484i | − 0.0448636i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.19826i | − 0.283713i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.3106 | −1.66787 | −0.833933 | − | 0.551865i | \(-0.813916\pi\) | ||||
−0.833933 | + | 0.551865i | \(0.813916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3053 | 0.527769 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.82983i | 0.166151i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 20.7249i | − 0.712117i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.56683 | 0.327947 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5511 | −0.532460 | −0.266230 | − | 0.963910i | \(-0.585778\pi\) | ||||
−0.266230 | + | 0.963910i | \(0.585778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.1766i | 1.74816i | 0.485784 | + | 0.874079i | \(0.338534\pi\) | ||||
−0.485784 | + | 0.874079i | \(0.661466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.42175i | 0.253227i | 0.991952 | + | 0.126613i | \(0.0404107\pi\) | ||||
−0.991952 | + | 0.126613i | \(0.959589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.1405 | 0.855791 | 0.427895 | − | 0.903828i | \(-0.359255\pi\) | ||||
0.427895 | + | 0.903828i | \(0.359255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.59769 | −0.190327 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 95.2931i | 3.23260i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0181i | 0.474985i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.03768 | −0.170305 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.2853 | −1.02266 | −0.511331 | − | 0.859384i | \(-0.670847\pi\) | ||||
−0.511331 | + | 0.859384i | \(0.670847\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 2.81414i | − 0.0948107i | −0.998876 | − | 0.0474054i | \(-0.984905\pi\) | ||||
0.998876 | − | 0.0474054i | \(-0.0150952\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 20.0928i | − 0.676176i | −0.941115 | − | 0.338088i | \(-0.890220\pi\) | ||||
0.941115 | − | 0.338088i | \(-0.109780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.25144 | 0.109173 | 0.0545864 | − | 0.998509i | \(-0.482616\pi\) | ||||
0.0545864 | + | 0.998509i | \(0.482616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.71733 | −0.124675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.2320i | 1.17899i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 13.3061i | − 0.444773i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.9167 | −0.630907 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.17016 | 0.238873 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1.00329i | − 0.0333505i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9282i | 0.960545i | 0.877119 | + | 0.480273i | \(0.159462\pi\) | ||||
−0.877119 | + | 0.480273i | \(0.840538\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.9111 | 0.527157 | 0.263578 | − | 0.964638i | \(-0.415097\pi\) | ||||
0.263578 | + | 0.964638i | \(0.415097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.4372 | 1.60304 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 8.52897i | − 0.281652i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 31.3628i | − 1.03456i | −0.855815 | − | 0.517282i | \(-0.826944\pi\) | ||||
0.855815 | − | 0.517282i | \(-0.173056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.6758 | 0.845129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3326 | 0.339734 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 38.5872i | − 1.26601i | −0.774150 | − | 0.633003i | \(-0.781822\pi\) | ||||
0.774150 | − | 0.633003i | \(-0.218178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.23349i | 0.138747i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.77522 | 0.123463 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.0676 | −1.63564 | −0.817818 | − | 0.575477i | \(-0.804816\pi\) | ||||
−0.817818 | + | 0.575477i | \(0.804816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.0005i | 0.619400i | 0.950834 | + | 0.309700i | \(0.100229\pi\) | ||||
−0.950834 | + | 0.309700i | \(0.899771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.27267i | 0.269395i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.5187 | −0.634274 | −0.317137 | − | 0.948380i | \(-0.602722\pi\) | ||||
−0.317137 | + | 0.948380i | \(0.602722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.9929 | −0.908687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6208i | 1.02430i | 0.858896 | + | 0.512150i | \(0.171151\pi\) | ||||
−0.858896 | + | 0.512150i | \(0.828849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.35785i | 0.302813i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.85520 | −0.221366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.87008 | 0.157099 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.62167i | 0.0843944i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7113i | 0.376609i | 0.982111 | + | 0.188305i | \(0.0602992\pi\) | ||||
−0.982111 | + | 0.188305i | \(0.939701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.5400 | −1.07635 | −0.538175 | − | 0.842833i | \(-0.680886\pi\) | ||||
−0.538175 | + | 0.842833i | \(0.680886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.3600 | 0.524476 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.2645i | 1.96002i | 0.198940 | + | 0.980012i | \(0.436250\pi\) | ||||
−0.198940 | + | 0.980012i | \(0.563750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 7.53088i | − 0.240688i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.5150 | −1.67497 | −0.837483 | − | 0.546463i | \(-0.815974\pi\) | ||||
−0.837483 | + | 0.546463i | \(0.815974\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.581133 | 0.0185164 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.5703i | 0.749491i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 6.80723i | − 0.216239i | −0.994138 | − | 0.108119i | \(-0.965517\pi\) | ||||
0.994138 | − | 0.108119i | \(-0.0344829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.196543 | −0.00623084 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.9576 | 0.347032 | 0.173516 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173516 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.h.h.2591.6 | ✓ | 16 | |
3.2 | odd | 2 | inner | 6048.2.h.h.2591.9 | yes | 16 | |
4.3 | odd | 2 | inner | 6048.2.h.h.2591.7 | yes | 16 | |
12.11 | even | 2 | inner | 6048.2.h.h.2591.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.h.2591.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6048.2.h.h.2591.7 | yes | 16 | 4.3 | odd | 2 | inner | |
6048.2.h.h.2591.9 | yes | 16 | 3.2 | odd | 2 | inner | |
6048.2.h.h.2591.12 | yes | 16 | 12.11 | even | 2 | inner |