Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6900,2,Mod(6349,6900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6900.6349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6900.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(55.0967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.158155776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 24x^{3} + 81x^{2} + 54x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6349.3 | ||
Root | \(-0.376763 + 0.376763i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6900.6349 |
Dual form | 6900.2.f.r.6349.4 |
$q$-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 \(\left(\mathbb{Z}/6900\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1201\) | \(3451\) | \(4601\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.20905i | 1.59087i | 0.606038 | + | 0.795436i | \(0.292758\pi\) | ||||
−0.606038 | + | 0.795436i | \(0.707242\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.75353 | 0.830219 | 0.415110 | − | 0.909771i | \(-0.363743\pi\) | ||||
0.415110 | + | 0.909771i | \(0.363743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.753525i | 0.208990i | 0.994525 | + | 0.104495i | \(0.0333227\pi\) | ||||
−0.994525 | + | 0.104495i | \(0.966677\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 4.96257i | − 1.20360i | −0.798646 | − | 0.601801i | \(-0.794450\pi\) | ||||
0.798646 | − | 0.601801i | \(-0.205550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.75353 | −1.09053 | −0.545267 | − | 0.838263i | \(-0.683572\pi\) | ||||
−0.545267 | + | 0.838263i | \(0.683572\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.20905 | 0.918490 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.96257 | −0.921527 | −0.460764 | − | 0.887523i | \(-0.652424\pi\) | ||||
−0.460764 | + | 0.887523i | \(0.652424\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.209050 | −0.0375464 | −0.0187732 | − | 0.999824i | \(-0.505976\pi\) | ||||
−0.0187732 | + | 0.999824i | \(0.505976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.75353i | − 0.479327i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.71610i | − 0.939721i | −0.882741 | − | 0.469861i | \(-0.844304\pi\) | ||||
0.882741 | − | 0.469861i | \(-0.155696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.753525 | 0.120661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.38067 | −1.46502 | −0.732508 | − | 0.680759i | \(-0.761650\pi\) | ||||
−0.732508 | + | 0.680759i | \(0.761650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 12.4181i | − 1.89374i | −0.321613 | − | 0.946871i | \(-0.604225\pi\) | ||||
0.321613 | − | 0.946871i | \(-0.395775\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.17162i | 1.04609i | 0.852305 | + | 0.523044i | \(0.175204\pi\) | ||||
−0.852305 | + | 0.523044i | \(0.824796\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.7161 | −1.53087 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.96257 | −0.694899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.38067i | 1.28853i | 0.764800 | + | 0.644267i | \(0.222838\pi\) | ||||
−0.764800 | + | 0.644267i | \(0.777162\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.75353i | 0.629620i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.96257 | 0.646072 | 0.323036 | − | 0.946387i | \(-0.395296\pi\) | ||||
0.323036 | + | 0.946387i | \(0.395296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17162 | −0.662159 | −0.331079 | − | 0.943603i | \(-0.607413\pi\) | ||||
−0.331079 | + | 0.943603i | \(0.607413\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.20905i | − 0.530290i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 0.209050i | − 0.0255395i | −0.999918 | − | 0.0127697i | \(-0.995935\pi\) | ||||
0.999918 | − | 0.0127697i | \(-0.00406485\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38067 | 1.11328 | 0.556641 | − | 0.830753i | \(-0.312090\pi\) | ||||
0.556641 | + | 0.830753i | \(0.312090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 10.2606i | − 1.20091i | −0.799659 | − | 0.600455i | \(-0.794986\pi\) | ||||
0.799659 | − | 0.600455i | \(-0.205014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.5897i | 1.32077i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.41810 | 0.272057 | 0.136029 | − | 0.990705i | \(-0.456566\pi\) | ||||
0.136029 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.45552i | − 0.598822i | −0.954124 | − | 0.299411i | \(-0.903210\pi\) | ||||
0.954124 | − | 0.299411i | \(-0.0967901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.96257i | 0.532044i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.91105 | −0.520570 | −0.260285 | − | 0.965532i | \(-0.583817\pi\) | ||||
−0.260285 | + | 0.965532i | \(0.583817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.17162 | −0.332477 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.209050i | 0.0216775i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3432i | 1.05020i | 0.851041 | + | 0.525099i | \(0.175972\pi\) | ||||
−0.851041 | + | 0.525099i | \(0.824028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.75353 | −0.276740 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.8877 | 1.48138 | 0.740692 | − | 0.671845i | \(-0.234498\pi\) | ||||
0.740692 | + | 0.671845i | \(0.234498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.9251i | − 1.76622i | −0.469168 | − | 0.883109i | \(-0.655446\pi\) | ||||
0.469168 | − | 0.883109i | \(-0.344554\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.4696i | − 1.59218i | −0.605179 | − | 0.796089i | \(-0.706898\pi\) | ||||
0.605179 | − | 0.796089i | \(-0.293102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.26058 | 0.599654 | 0.299827 | − | 0.953994i | \(-0.403071\pi\) | ||||
0.299827 | + | 0.953994i | \(0.403071\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.71610 | −0.542548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.38067i | 0.882460i | 0.897394 | + | 0.441230i | \(0.145458\pi\) | ||||
−0.897394 | + | 0.441230i | \(0.854542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 0.753525i | − 0.0696634i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.8877 | 1.91477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.41810 | −0.310736 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.38067i | 0.845827i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 22.0827i | − 1.95952i | −0.200175 | − | 0.979760i | \(-0.564151\pi\) | ||||
0.200175 | − | 0.979760i | \(-0.435849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4181 | −1.09335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.58190 | −0.138211 | −0.0691056 | − | 0.997609i | \(-0.522015\pi\) | ||||
−0.0691056 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 20.0078i | − 1.73490i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 4.91105i | − 0.419579i | −0.977747 | − | 0.209790i | \(-0.932722\pi\) | ||||
0.977747 | − | 0.209790i | \(-0.0672779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1342 | −1.19885 | −0.599424 | − | 0.800432i | \(-0.704603\pi\) | ||||
−0.599424 | + | 0.800432i | \(0.704603\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.17162 | 0.603960 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.07485i | 0.173508i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7161i | 0.883849i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.24647 | −0.265962 | −0.132981 | − | 0.991119i | \(-0.542455\pi\) | ||||
−0.132981 | + | 0.991119i | \(0.542455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.418100 | 0.0340245 | 0.0170122 | − | 0.999855i | \(-0.494585\pi\) | ||||
0.0170122 | + | 0.999855i | \(0.494585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.96257i | 0.401200i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 21.0452i | − 1.67959i | −0.542901 | − | 0.839797i | \(-0.682674\pi\) | ||||
0.542901 | − | 0.839797i | \(-0.317326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.38067 | 0.743936 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.20905 | 0.331720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.43220i | 0.582135i | 0.956703 | + | 0.291067i | \(0.0940104\pi\) | ||||
−0.956703 | + | 0.291067i | \(0.905990\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 19.1716i | − 1.48354i | −0.670652 | − | 0.741772i | \(-0.733985\pi\) | ||||
0.670652 | − | 0.741772i | \(-0.266015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4322 | 0.956323 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.75353 | 0.363511 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 4.96257i | − 0.373010i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8503 | −1.03522 | −0.517610 | − | 0.855617i | \(-0.673178\pi\) | ||||
−0.517610 | + | 0.855617i | \(0.673178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9110 | 0.959671 | 0.479835 | − | 0.877359i | \(-0.340696\pi\) | ||||
0.479835 | + | 0.877359i | \(0.340696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.17162i | 0.382297i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 13.6646i | − 0.999253i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.20905 | −0.306163 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.15752 | −0.590258 | −0.295129 | − | 0.955457i | \(-0.595363\pi\) | ||||
−0.295129 | + | 0.955457i | \(0.595363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.7613i | 1.20651i | 0.797549 | + | 0.603254i | \(0.206130\pi\) | ||||
−0.797549 | + | 0.603254i | \(0.793870\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 10.9110i | − 0.777380i | −0.921369 | − | 0.388690i | \(-0.872928\pi\) | ||||
0.921369 | − | 0.388690i | \(-0.127072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.49295 | 0.318497 | 0.159248 | − | 0.987239i | \(-0.449093\pi\) | ||||
0.159248 | + | 0.987239i | \(0.449093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.209050 | −0.0147452 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 20.8877i | − 1.46603i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.0890 | −0.905382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.71610 | 0.668884 | 0.334442 | − | 0.942416i | \(-0.391452\pi\) | ||||
0.334442 | + | 0.942416i | \(0.391452\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 9.38067i | − 0.642753i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 0.879901i | − 0.0597316i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2606 | −0.693345 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.73942 | 0.251541 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4322i | 1.30128i | 0.759388 | + | 0.650638i | \(0.225499\pi\) | ||||
−0.759388 | + | 0.650638i | \(0.774501\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 0.985900i | − 0.0654365i | −0.999465 | − | 0.0327182i | \(-0.989584\pi\) | ||||
0.999465 | − | 0.0327182i | \(-0.0104164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.08895 | −0.204124 | −0.102062 | − | 0.994778i | \(-0.532544\pi\) | ||||
−0.102062 | + | 0.994778i | \(0.532544\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.5897 | 0.762548 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 8.83620i | − 0.578879i | −0.957196 | − | 0.289439i | \(-0.906531\pi\) | ||||
0.957196 | − | 0.289439i | \(-0.0934688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.41810i | − 0.157072i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3807 | 1.38300 | 0.691500 | − | 0.722376i | \(-0.256950\pi\) | ||||
0.691500 | + | 0.722376i | \(0.256950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.2606 | 1.43393 | 0.716965 | − | 0.697109i | \(-0.245531\pi\) | ||||
0.716965 | + | 0.697109i | \(0.245531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.58190i | − 0.227911i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.45552 | −0.345730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.59600 | −0.416336 | −0.208168 | − | 0.978093i | \(-0.566750\pi\) | ||||
−0.208168 | + | 0.978093i | \(0.566750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.75353i | − 0.173113i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 18.1857i | − 1.13439i | −0.823582 | − | 0.567197i | \(-0.808028\pi\) | ||||
0.823582 | − | 0.567197i | \(-0.191972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.0593 | 1.49498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.96257 | 0.307176 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3807i | 0.948413i | 0.880414 | + | 0.474207i | \(0.157265\pi\) | ||||
−0.880414 | + | 0.474207i | \(0.842735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.91105i | 0.300551i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.544475 | −0.0331972 | −0.0165986 | − | 0.999862i | \(-0.505284\pi\) | ||||
−0.0165986 | + | 0.999862i | \(0.505284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2090 | −0.741647 | −0.370823 | − | 0.928703i | \(-0.620925\pi\) | ||||
−0.370823 | + | 0.928703i | \(0.620925\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.17162i | 0.191955i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 21.0141i | − 1.26261i | −0.775533 | − | 0.631307i | \(-0.782519\pi\) | ||||
0.775533 | − | 0.631307i | \(-0.217481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.209050 | 0.0125155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1857 | −1.44280 | −0.721400 | − | 0.692519i | \(-0.756501\pi\) | ||||
−0.721400 | + | 0.692519i | \(0.756501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 15.1201i | − 0.898797i | −0.893331 | − | 0.449398i | \(-0.851638\pi\) | ||||
0.893331 | − | 0.449398i | \(-0.148362\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 39.4837i | − 2.33065i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.62715 | −0.448656 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3432 | 0.606332 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 10.4696i | − 0.611642i | −0.952089 | − | 0.305821i | \(-0.901069\pi\) | ||||
0.952089 | − | 0.305821i | \(-0.0989309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.75353i | 0.159776i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.753525 | 0.0435775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.2684 | 3.01270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 14.8877i | − 0.855277i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 12.1575i | − 0.693867i | −0.937890 | − | 0.346933i | \(-0.887223\pi\) | ||||
0.937890 | − | 0.346933i | \(-0.112777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.9251 | −1.01973 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.4181 | −1.95167 | −0.975836 | − | 0.218506i | \(-0.929882\pi\) | ||||
−0.975836 | + | 0.218506i | \(0.929882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 29.5664i | − 1.67119i | −0.549345 | − | 0.835596i | \(-0.685123\pi\) | ||||
0.549345 | − | 0.835596i | \(-0.314877\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.66457i | 0.0934918i | 0.998907 | + | 0.0467459i | \(0.0148851\pi\) | ||||
−0.998907 | + | 0.0467459i | \(0.985115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6646 | −0.765069 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4696 | −0.919245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.5897i | 1.31257i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 6.26058i | − 0.346211i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.1857 | −1.66419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.12010 | 0.171496 | 0.0857481 | − | 0.996317i | \(-0.472672\pi\) | ||||
0.0857481 | + | 0.996317i | \(0.472672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.71610i | 0.313240i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 11.5819i | − 0.630906i | −0.948941 | − | 0.315453i | \(-0.897843\pi\) | ||||
0.948941 | − | 0.315453i | \(-0.102157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.38067 | 0.509488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.575624 | −0.0311718 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 15.6412i | − 0.844548i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3432i | 1.41418i | 0.707124 | + | 0.707090i | \(0.249992\pi\) | ||||
−0.707124 | + | 0.707090i | \(0.750008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.22315 | −0.493704 | −0.246852 | − | 0.969053i | \(-0.579396\pi\) | ||||
−0.246852 | + | 0.969053i | \(0.579396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.753525 | −0.0402202 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.1857i | 0.967928i | 0.875088 | + | 0.483964i | \(0.160804\pi\) | ||||
−0.875088 | + | 0.483964i | \(0.839196\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 20.8877i | − 1.10550i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.17162 | −0.378504 | −0.189252 | − | 0.981929i | \(-0.560606\pi\) | ||||
−0.189252 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.59600 | 0.189263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.41810i | 0.179404i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5664i | 0.916959i | 0.888705 | + | 0.458479i | \(0.151606\pi\) | ||||
−0.888705 | + | 0.458479i | \(0.848394\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.38067 | 0.488338 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −39.4837 | −2.04989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.6724i | 1.74349i | 0.489959 | + | 0.871745i | \(0.337012\pi\) | ||||
−0.489959 | + | 0.871745i | \(0.662988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.73942i | − 0.192590i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.4181 | −0.946074 | −0.473037 | − | 0.881043i | \(-0.656842\pi\) | ||||
−0.473037 | + | 0.881043i | \(0.656842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.0827 | −1.13133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.7847i | 1.06205i | 0.847357 | + | 0.531024i | \(0.178192\pi\) | ||||
−0.847357 | + | 0.531024i | \(0.821808\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4181i | 0.631247i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5212 | −1.14187 | −0.570934 | − | 0.820996i | \(-0.693419\pi\) | ||||
−0.570934 | + | 0.820996i | \(0.693419\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.96257 | −0.250968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.58190i | 0.0797963i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.4040i | − 0.773105i | −0.922267 | − | 0.386552i | \(-0.873666\pi\) | ||||
0.922267 | − | 0.386552i | \(-0.126334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.0078 | −1.00164 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5212 | −0.525401 | −0.262701 | − | 0.964877i | \(-0.584613\pi\) | ||||
−0.262701 | + | 0.964877i | \(0.584613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.157524i | − 0.00784684i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 15.7394i | − 0.780174i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0593 | 1.28855 | 0.644276 | − | 0.764793i | \(-0.277159\pi\) | ||||
0.644276 | + | 0.764793i | \(0.277159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.91105 | −0.242244 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.8877i | 1.02782i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.1342i | 0.692155i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.73942 | 0.182683 | 0.0913414 | − | 0.995820i | \(-0.470885\pi\) | ||||
0.0913414 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09677 | −0.150928 | −0.0754638 | − | 0.997149i | \(-0.524044\pi\) | ||||
−0.0754638 | + | 0.997149i | \(0.524044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 7.17162i | − 0.348696i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 21.7676i | − 1.05341i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.07485 | 0.100175 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1653 | −1.74202 | −0.871012 | − | 0.491262i | \(-0.836536\pi\) | ||||
−0.871012 | + | 0.491262i | \(0.836536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.6271i | 0.799050i | 0.916722 | + | 0.399525i | \(0.130825\pi\) | ||||
−0.916722 | + | 0.399525i | \(0.869175\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.75353i | 0.227392i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.7613 | −1.84998 | −0.924989 | − | 0.379994i | \(-0.875926\pi\) | ||||
−0.924989 | + | 0.379994i | \(0.875926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7161 | 0.510290 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 33.5149i | − 1.59234i | −0.605073 | − | 0.796170i | \(-0.706856\pi\) | ||||
0.605073 | − | 0.796170i | \(-0.293144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.24647i | 0.153553i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.9018 | 0.656068 | 0.328034 | − | 0.944666i | \(-0.393614\pi\) | ||||
0.328034 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8299 | −1.21628 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 0.418100i | − 0.0196440i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.28390i | − 0.106836i | −0.998572 | − | 0.0534182i | \(-0.982988\pi\) | ||||
0.998572 | − | 0.0534182i | \(-0.0170116\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.96257 | 0.231633 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.34325 | 0.388584 | 0.194292 | − | 0.980944i | \(-0.437759\pi\) | ||||
0.194292 | + | 0.980944i | \(0.437759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.6928i | 1.28699i | 0.765449 | + | 0.643496i | \(0.222517\pi\) | ||||
−0.765449 | + | 0.643496i | \(0.777483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.53037i | 0.348464i | 0.984705 | + | 0.174232i | \(0.0557443\pi\) | ||||
−0.984705 | + | 0.174232i | \(0.944256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.879901 | 0.0406300 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0452 | −0.969714 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 34.1935i | − 1.57222i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 9.38067i | − 0.429512i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1857 | 0.830927 | 0.415463 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415463 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.30722 | 0.196393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.20905i | − 0.191518i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 24.2606i | − 1.09935i | −0.835378 | − | 0.549676i | \(-0.814751\pi\) | ||||
0.835378 | − | 0.549676i | \(-0.185249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.43220 | 0.336096 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.8877 | 0.671874 | 0.335937 | − | 0.941885i | \(-0.390947\pi\) | ||||
0.335937 | + | 0.941885i | \(0.390947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.6271i | 1.10915i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.4837i | 1.77109i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.312101 | 0.0139716 | 0.00698578 | − | 0.999976i | \(-0.497776\pi\) | ||||
0.00698578 | + | 0.999976i | \(0.497776\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.1716 | −0.856525 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 20.8877i | − 0.931338i | −0.884959 | − | 0.465669i | \(-0.845814\pi\) | ||||
0.884959 | − | 0.465669i | \(-0.154186\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 12.4322i | − 0.552133i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.9251 | −1.23776 | −0.618880 | − | 0.785485i | \(-0.712413\pi\) | ||||
−0.618880 | + | 0.785485i | \(0.712413\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.1873 | 1.91049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.75353i | − 0.209873i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.7472i | 0.868483i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0360 | 1.40352 | 0.701762 | − | 0.712412i | \(-0.252397\pi\) | ||||
0.701762 | + | 0.712412i | \(0.252397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 38.8644i | − 1.69942i | −0.527249 | − | 0.849711i | \(-0.676777\pi\) | ||||
0.527249 | − | 0.849711i | \(-0.323223\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03743i | 0.0451909i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.96257 | −0.215357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.06857i | − 0.306174i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.8503i | 0.597685i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.5071 | −1.27096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.07485 | 0.175191 | 0.0875957 | − | 0.996156i | \(-0.472082\pi\) | ||||
0.0875957 | + | 0.996156i | \(0.472082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 12.9110i | − 0.554066i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.0000i | − 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.17162 | 0.220720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.5897 | 1.00496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1779i | 0.432808i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.63343i | 0.0692105i | 0.999401 | + | 0.0346052i | \(0.0110174\pi\) | ||||
−0.999401 | + | 0.0346052i | \(0.988983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.35735 | 0.395774 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6646 | −0.576919 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.2310i | 0.979069i | 0.871984 | + | 0.489534i | \(0.162833\pi\) | ||||
−0.871984 | + | 0.489534i | \(0.837167\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.20905i | 0.176763i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.3291 | −0.894164 | −0.447082 | − | 0.894493i | \(-0.647537\pi\) | ||||
−0.447082 | + | 0.894493i | \(0.647537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.18573 | −0.175167 | −0.0875836 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875836 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.15752i | 0.340785i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5678i | 0.439943i | 0.975506 | + | 0.219972i | \(0.0705965\pi\) | ||||
−0.975506 | + | 0.219972i | \(0.929404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.7613 | 0.696578 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.9626 | 0.952648 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.8299i | 1.06977i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4181i | 1.17294i | 0.809971 | + | 0.586470i | \(0.199483\pi\) | ||||
−0.809971 | + | 0.586470i | \(0.800517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.993723 | 0.0409457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.9110 | −0.448821 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 28.9937i | − 1.19063i | −0.803493 | − | 0.595315i | \(-0.797027\pi\) | ||||
0.803493 | − | 0.595315i | \(-0.202973\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.49295i | − 0.183884i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.10305 | 0.249364 | 0.124682 | − | 0.992197i | \(-0.460209\pi\) | ||||
0.124682 | + | 0.992197i | \(0.460209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3885 | −1.19878 | −0.599391 | − | 0.800456i | \(-0.704590\pi\) | ||||
−0.599391 | + | 0.800456i | \(0.704590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.209050i | 0.00851316i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.58972i | − 0.145702i | −0.997343 | − | 0.0728512i | \(-0.976790\pi\) | ||||
0.997343 | − | 0.0728512i | \(-0.0232098\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.8877 | −0.846413 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.40400 | −0.218622 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.4040i | 0.864499i | 0.901754 | + | 0.432250i | \(0.142280\pi\) | ||||
−0.901754 | + | 0.432250i | \(0.857720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2917i | 1.30002i | 0.759927 | + | 0.650008i | \(0.225234\pi\) | ||||
−0.759927 | + | 0.650008i | \(0.774766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.1046 | −1.89329 | −0.946647 | − | 0.322273i | \(-0.895553\pi\) | ||||
−0.946647 | + | 0.322273i | \(0.895553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 20.6709i | − 0.828160i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0890i | 0.522722i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.3666 | −1.13105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5149 | 0.936112 | 0.468056 | − | 0.883699i | \(-0.344954\pi\) | ||||
0.468056 | + | 0.883699i | \(0.344954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 9.71610i | − 0.386180i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8.07485i | − 0.319937i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.38067 | −0.371094 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.67867 | −0.263792 | −0.131896 | − | 0.991264i | \(-0.542106\pi\) | ||||
−0.131896 | + | 0.991264i | \(0.542106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27.1201i | − 1.06951i | −0.845006 | − | 0.534756i | \(-0.820403\pi\) | ||||
0.845006 | − | 0.534756i | \(-0.179597\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 27.7394i | − 1.09055i | −0.838257 | − | 0.545275i | \(-0.816425\pi\) | ||||
0.838257 | − | 0.545275i | \(-0.183575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6646 | 0.536381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.879901 | −0.0344860 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.75353i | 0.107754i | 0.998548 | + | 0.0538769i | \(0.0171579\pi\) | ||||
−0.998548 | + | 0.0538769i | \(0.982842\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2606i | 0.400303i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.5897 | −0.451472 | −0.225736 | − | 0.974189i | \(-0.572479\pi\) | ||||
−0.225736 | + | 0.974189i | \(0.572479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3432 | 1.10242 | 0.551212 | − | 0.834365i | \(-0.314165\pi\) | ||||
0.551212 | + | 0.834365i | \(0.314165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.73942i | − 0.145227i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.96257i | 0.192152i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.4322 | 0.751292 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2402 | −0.549737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.0360i | 1.85165i | 0.377949 | + | 0.925826i | \(0.376629\pi\) | ||||
−0.377949 | + | 0.925826i | \(0.623371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.51627i | 0.0967083i | 0.998830 | + | 0.0483541i | \(0.0153976\pi\) | ||||
−0.998830 | + | 0.0483541i | \(0.984602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.5353 | −1.67073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.985900 | −0.0377798 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.84248i | 0.147028i | 0.997294 | + | 0.0735141i | \(0.0234214\pi\) | ||||
−0.997294 | + | 0.0735141i | \(0.976579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.08895i | 0.117851i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.06857 | −0.269291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59600 | 0.0987565 | 0.0493783 | − | 0.998780i | \(-0.484276\pi\) | ||||
0.0493783 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 11.5897i | − 0.440257i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.5523i | 1.76329i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.83620 | −0.334216 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.5897 | 1.57082 | 0.785411 | − | 0.618974i | \(-0.212452\pi\) | ||||
0.785411 | + | 0.618974i | \(0.212452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.1716i | 1.02480i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 62.6632i | 2.35669i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 53.1716 | 1.99690 | 0.998451 | − | 0.0556356i | \(-0.0177185\pi\) | ||||
0.998451 | + | 0.0556356i | \(0.0177185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.41810 | −0.0906858 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.209050i | 0.00782898i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21.3807i | − 0.798476i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.3807 | −1.69241 | −0.846207 | − | 0.532855i | \(-0.821119\pi\) | ||||
−0.846207 | + | 0.532855i | \(0.821119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 75.4478 | 2.80982 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 22.2606i | − 0.827880i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 46.4026i | − 1.72098i | −0.509470 | − | 0.860489i | \(-0.670158\pi\) | ||||
0.509470 | − | 0.860489i | \(-0.329842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.6257 | −2.27931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.8051i | − 0.842324i | −0.906985 | − | 0.421162i | \(-0.861622\pi\) | ||||
0.906985 | − | 0.421162i | \(-0.138378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 0.575624i | − 0.0212034i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5241 | 0.607849 | 0.303924 | − | 0.952696i | \(-0.401703\pi\) | ||||
0.303924 | + | 0.952696i | \(0.401703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.58190 | −0.131584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 43.8503i | − 1.60871i | −0.594148 | − | 0.804356i | \(-0.702511\pi\) | ||||
0.594148 | − | 0.804356i | \(-0.297489\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.45552i | 0.199607i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 69.3215 | 2.53295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.73942 | 0.209435 | 0.104717 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104717 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.59600i | 0.240372i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.86580i | − 0.358579i | −0.983796 | − | 0.179289i | \(-0.942620\pi\) | ||||
0.983796 | − | 0.179289i | \(-0.0573798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.75353 | −0.0999466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.69418 | 0.170164 | 0.0850819 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850819 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.3511i | 0.953973i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.73942i | 0.135023i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.5431 | −1.64233 | −0.821163 | − | 0.570694i | \(-0.806674\pi\) | ||||
−0.821163 | + | 0.570694i | \(0.806674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1857 | −0.654943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 12.4929i | − 0.449340i | −0.974435 | − | 0.224670i | \(-0.927870\pi\) | ||||
0.974435 | − | 0.224670i | \(-0.0721304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 24.0593i | − 0.863124i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.5913 | 1.59765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8299 | 0.924267 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.96257i | − 0.177348i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.71610i | − 0.203757i | −0.994797 | − | 0.101878i | \(-0.967515\pi\) | ||||
0.994797 | − | 0.101878i | \(-0.0324853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.3807 | 0.547567 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.4837 | −1.40388 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 3.89695i | − 0.138385i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.48373i | − 0.335931i | −0.985793 | − | 0.167965i | \(-0.946280\pi\) | ||||
0.985793 | − | 0.167965i | \(-0.0537197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.5897 | 1.25907 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.91105 | 0.173523 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 28.2528i | − 0.997018i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.544475i | 0.0191664i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.0672 | −1.76027 | −0.880134 | − | 0.474725i | \(-0.842547\pi\) | ||||
−0.880134 | + | 0.474725i | \(0.842547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.14830 | −0.321240 | −0.160620 | − | 0.987016i | \(-0.551349\pi\) | ||||
−0.160620 | + | 0.987016i | \(0.551349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2090i | 0.428190i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.0297i | 2.06519i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.17162 | 0.110826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.91105 | −0.171397 | −0.0856984 | − | 0.996321i | \(-0.527312\pi\) | ||||
−0.0856984 | + | 0.996321i | \(0.527312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 23.7006i | − 0.826151i | −0.910697 | − | 0.413075i | \(-0.864455\pi\) | ||||
0.910697 | − | 0.413075i | \(-0.135545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.1405i | 0.456939i | 0.973551 | + | 0.228470i | \(0.0733721\pi\) | ||||
−0.973551 | + | 0.228470i | \(0.926628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.6412 | 1.58519 | 0.792593 | − | 0.609751i | \(-0.208731\pi\) | ||||
0.792593 | + | 0.609751i | \(0.208731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0141 | −0.728971 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 53.1794i | 1.84256i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.209050i | − 0.00722582i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.40400 | 0.186567 | 0.0932834 | − | 0.995640i | \(-0.470264\pi\) | ||||
0.0932834 | + | 0.995640i | \(0.470264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.37285 | −0.150788 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1857i | 0.833001i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 14.3870i | − 0.494341i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.1201 | −0.518920 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.71610 | −0.195945 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 53.0297i | 1.81570i | 0.419291 | + | 0.907852i | \(0.362279\pi\) | ||||
−0.419291 | + | 0.907852i | \(0.637721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 14.4463i | − 0.493476i | −0.969082 | − | 0.246738i | \(-0.920641\pi\) | ||||
0.969082 | − | 0.246738i | \(-0.0793587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8658 | −0.473095 | −0.236548 | − | 0.971620i | \(-0.576016\pi\) | ||||
−0.236548 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.4837 | −1.34560 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 52.5834i | − 1.78996i | −0.446105 | − | 0.894981i | \(-0.647189\pi\) | ||||
0.446105 | − | 0.894981i | \(-0.352811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.62715i | 0.259032i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.65830 | 0.225867 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.157524 | 0.00533751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 10.3432i | − 0.350066i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 25.3291i | − 0.855305i | −0.903943 | − | 0.427652i | \(-0.859341\pi\) | ||||
0.903943 | − | 0.427652i | \(-0.140659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.4696 | −0.353132 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2606 | 0.480451 | 0.240225 | − | 0.970717i | \(-0.422779\pi\) | ||||
0.240225 | + | 0.970717i | \(0.422779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 40.6320i | − 1.36738i | −0.729774 | − | 0.683688i | \(-0.760375\pi\) | ||||
0.729774 | − | 0.683688i | \(-0.239625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 19.9534i | − 0.669968i | −0.942224 | − | 0.334984i | \(-0.891269\pi\) | ||||
0.942224 | − | 0.334984i | \(-0.108731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 92.9471 | 3.11734 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.75353 | 0.0922466 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 34.0905i | − 1.14080i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 0.753525i | − 0.0251595i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.03743 | 0.0346001 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.5523 | 1.55088 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 52.2684i | − 1.73938i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 29.8814i | − 0.992197i | −0.868266 | − | 0.496099i | \(-0.834765\pi\) | ||||
0.868266 | − | 0.496099i | \(-0.165235\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.8877 | −0.493795 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8644 | 0.625005 | 0.312503 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312503 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 15.0219i | − 0.497153i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6.65830i | − 0.219876i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.2402 | −0.535715 | −0.267857 | − | 0.963459i | \(-0.586316\pi\) | ||||
−0.267857 | + | 0.963459i | \(0.586316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1575 | −0.400604 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.06857i | 0.232665i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.9251i | 0.588739i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.3340 | −0.962418 | −0.481209 | − | 0.876606i | \(-0.659802\pi\) | ||||
−0.481209 | + | 0.876606i | \(0.659802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.9393 | 1.66947 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.4181i | 1.12680i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 41.3573i | − 1.35109i | −0.737321 | − | 0.675543i | \(-0.763909\pi\) | ||||
0.737321 | − | 0.675543i | \(-0.236091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.5664 | −0.964863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4259 | 1.64384 | 0.821919 | − | 0.569604i | \(-0.192904\pi\) | ||||
0.821919 | + | 0.569604i | \(0.192904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.38067i | 0.305477i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.50705i | 0.178955i | 0.995989 | + | 0.0894775i | \(0.0285197\pi\) | ||||
−0.995989 | + | 0.0894775i | \(0.971480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73160 | 0.250978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.66457 | 0.0539775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 0.864400i | − 0.0280007i | −0.999902 | − | 0.0140003i | \(-0.995543\pi\) | ||||
0.999902 | − | 0.0140003i | \(-0.00445659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.6646i | 0.441713i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.6709 | 0.667497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9563 | −0.998590 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.4696i | 0.530726i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.7535i | 0.345810i | 0.984939 | + | 0.172905i | \(0.0553154\pi\) | ||||
−0.984939 | + | 0.172905i | \(0.944685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.5897 | 0.757811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1794 | 1.12896 | 0.564481 | − | 0.825446i | \(-0.309076\pi\) | ||||
0.564481 | + | 0.825446i | \(0.309076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 59.4915i | − 1.90721i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.9767i | 0.511139i | 0.966791 | + | 0.255570i | \(0.0822630\pi\) | ||||
−0.966791 | + | 0.255570i | \(0.917737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5227 | −0.432187 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.26058 | −0.199885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.2592i | 1.82628i | 0.407642 | + | 0.913142i | \(0.366351\pi\) | ||||
−0.407642 | + | 0.913142i | \(0.633649\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.1857i | 0.960822i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.4181 | −0.394873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8799 | 0.409144 | 0.204572 | − | 0.978852i | \(-0.434420\pi\) | ||||
0.204572 | + | 0.978852i | \(0.434420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 3.12010i | − 0.0990134i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 39.7754i | − 1.25970i | −0.776716 | − | 0.629851i | \(-0.783116\pi\) | ||||
0.776716 | − | 0.629851i | \(-0.216884\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.71610 | 0.180849 |
(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 | 6900.2.f.r.6349.3 | 6 | ||
5.2 | odd | 4 | 6900.2.a.x.1.1 | 3 | |||
5.3 | odd | 4 | 1380.2.a.j.1.3 | ✓ | 3 | ||
5.4 | even | 2 | inner | 6900.2.f.r.6349.4 | 6 | ||
15.8 | even | 4 | 4140.2.a.s.1.3 | 3 | |||
20.3 | even | 4 | 5520.2.a.bv.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.a.j.1.3 | ✓ | 3 | 5.3 | odd | 4 | ||
4140.2.a.s.1.3 | 3 | 15.8 | even | 4 | |||
5520.2.a.bv.1.1 | 3 | 20.3 | even | 4 | |||
6900.2.a.x.1.1 | 3 | 5.2 | odd | 4 | |||
6900.2.f.r.6349.3 | 6 | 1.1 | even | 1 | trivial | ||
6900.2.f.r.6349.4 | 6 | 5.4 | even | 2 | inner |