Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7500,2,Mod(1249,7500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7500.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7500.d (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: | \(59.8878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.11 | ||
Character | \(\chi\) | \(=\) | 7500.1249 |
Dual form | 7500.2.d.g.1249.14 |
$q$-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 \(\left(\mathbb{Z}/7500\mathbb{Z}\right)^\times\).
\(n\) | \(2501\) | \(3751\) | \(6877\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(7\) | 4.41540i | 1.66886i | 0.551111 | + | 0.834432i | \(0.314204\pi\) | ||||
−0.551111 | + | 0.834432i | \(0.685796\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.45181 | 1.34227 | 0.671135 | − | 0.741335i | \(-0.265807\pi\) | ||||
0.671135 | + | 0.741335i | \(0.265807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.74778i | 1.59415i | 0.603882 | + | 0.797074i | \(0.293620\pi\) | ||||
−0.603882 | + | 0.797074i | \(0.706380\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.57035i | 1.59355i | 0.604279 | + | 0.796773i | \(0.293461\pi\) | ||||
−0.604279 | + | 0.796773i | \(0.706539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.78315 | 0.638499 | 0.319250 | − | 0.947671i | \(-0.396569\pi\) | ||||
0.319250 | + | 0.947671i | \(0.396569\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41540 | 0.963519 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.31495i | − 0.274186i | −0.990558 | − | 0.137093i | \(-0.956224\pi\) | ||||
0.990558 | − | 0.137093i | \(-0.0437759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.84521 | 0.899732 | 0.449866 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449866 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.197136 | −0.0354066 | −0.0177033 | − | 0.999843i | \(-0.505635\pi\) | ||||
−0.0177033 | + | 0.999843i | \(0.505635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 4.45181i | − 0.774960i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.20866i | − 1.34950i | −0.738048 | − | 0.674748i | \(-0.764252\pi\) | ||||
0.738048 | − | 0.674748i | \(-0.235748\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.74778 | 0.920381 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.84984 | 1.22594 | 0.612970 | − | 0.790106i | \(-0.289975\pi\) | ||||
0.612970 | + | 0.790106i | \(0.289975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.412792i | 0.0629502i | 0.999505 | + | 0.0314751i | \(0.0100205\pi\) | ||||
−0.999505 | + | 0.0314751i | \(0.989980\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.79459i | 1.13696i | 0.822698 | + | 0.568479i | \(0.192468\pi\) | ||||
−0.822698 | + | 0.568479i | \(0.807532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.4958 | −1.78511 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.57035 | 0.920034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.315455i | 0.0433311i | 0.999765 | + | 0.0216655i | \(0.00689689\pi\) | ||||
−0.999765 | + | 0.0216655i | \(0.993103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.78315i | − 0.368638i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.51902 | −0.327948 | −0.163974 | − | 0.986465i | \(-0.552431\pi\) | ||||
−0.163974 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.33114 | 1.19473 | 0.597365 | − | 0.801970i | \(-0.296214\pi\) | ||||
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.41540i | − 0.556288i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9457i | 1.45940i | 0.683767 | + | 0.729700i | \(0.260340\pi\) | ||||
−0.683767 | + | 0.729700i | \(0.739660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.31495 | −0.158301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.509248 | 0.0604366 | 0.0302183 | − | 0.999543i | \(-0.490380\pi\) | ||||
0.0302183 | + | 0.999543i | \(0.490380\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.7708i | − 1.84584i | −0.384996 | − | 0.922918i | \(-0.625797\pi\) | ||||
0.384996 | − | 0.922918i | \(-0.374203\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.6565i | 2.24007i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.43153 | 0.386077 | 0.193039 | − | 0.981191i | \(-0.438166\pi\) | ||||
0.193039 | + | 0.981191i | \(0.438166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.37155i | 0.589604i | 0.955558 | + | 0.294802i | \(0.0952538\pi\) | ||||
−0.955558 | + | 0.294802i | \(0.904746\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 4.84521i | − 0.519461i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.3452 | −1.20258 | −0.601292 | − | 0.799029i | \(-0.705347\pi\) | ||||
−0.601292 | + | 0.799029i | \(0.705347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.3787 | −2.66042 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.197136i | 0.0204420i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 5.07960i | − 0.515755i | −0.966178 | − | 0.257878i | \(-0.916977\pi\) | ||||
0.966178 | − | 0.257878i | \(-0.0830232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.45181 | −0.447424 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1860 | −1.11305 | −0.556525 | − | 0.830831i | \(-0.687866\pi\) | ||||
−0.556525 | + | 0.830831i | \(0.687866\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.14567i | 0.309952i | 0.987918 | + | 0.154976i | \(0.0495301\pi\) | ||||
−0.987918 | + | 0.154976i | \(0.950470\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.74013i | − 0.748266i | −0.927375 | − | 0.374133i | \(-0.877940\pi\) | ||||
0.927375 | − | 0.374133i | \(-0.122060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3708 | 0.993347 | 0.496673 | − | 0.867937i | \(-0.334555\pi\) | ||||
0.496673 | + | 0.867937i | \(0.334555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.20866 | −0.779132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2263i | 0.962005i | 0.876719 | + | 0.481002i | \(0.159727\pi\) | ||||
−0.876719 | + | 0.481002i | \(0.840273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5.74778i | − 0.531382i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −29.0107 | −2.65941 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.81860 | 0.801691 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 7.84984i | − 0.707797i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 11.3127i | − 1.00384i | −0.864914 | − | 0.501920i | \(-0.832627\pi\) | ||||
0.864914 | − | 0.501920i | \(-0.167373\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.412792 | 0.0363443 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.45365 | −0.825969 | −0.412985 | − | 0.910738i | \(-0.635514\pi\) | ||||
−0.412985 | + | 0.910738i | \(0.635514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2887i | 1.06557i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.41023i | 0.718535i | 0.933235 | + | 0.359267i | \(0.116973\pi\) | ||||
−0.933235 | + | 0.359267i | \(0.883027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8216 | −1.00269 | −0.501346 | − | 0.865247i | \(-0.667162\pi\) | ||||
−0.501346 | + | 0.865247i | \(0.667162\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.79459 | 0.656422 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.5880i | 2.13978i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.4958i | 1.03063i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.6355 | −0.871294 | −0.435647 | − | 0.900118i | \(-0.643480\pi\) | ||||
−0.435647 | + | 0.900118i | \(0.643480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.41657 | 0.359415 | 0.179707 | − | 0.983720i | \(-0.442485\pi\) | ||||
0.179707 | + | 0.983720i | \(0.442485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 6.57035i | − 0.531182i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5289i | 1.07972i | 0.841754 | + | 0.539861i | \(0.181523\pi\) | ||||
−0.841754 | + | 0.539861i | \(0.818477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.315455 | 0.0250172 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.80602 | 0.457579 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.5583i | − 1.14029i | −0.821543 | − | 0.570146i | \(-0.806886\pi\) | ||||
0.821543 | − | 0.570146i | \(-0.193114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 9.96824i | − 0.771366i | −0.922631 | − | 0.385683i | \(-0.873966\pi\) | ||||
0.922631 | − | 0.385683i | \(-0.126034\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.0370 | −1.54131 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.78315 | −0.212833 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8750i | 0.826811i | 0.910547 | + | 0.413406i | \(0.135661\pi\) | ||||
−0.910547 | + | 0.413406i | \(0.864339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.51902i | 0.189341i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.1740 | 1.88159 | 0.940795 | − | 0.338975i | \(-0.110080\pi\) | ||||
0.940795 | + | 0.338975i | \(0.110080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.59173 | −0.564289 | −0.282145 | − | 0.959372i | \(-0.591046\pi\) | ||||
−0.282145 | + | 0.959372i | \(0.591046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 9.33114i | − 0.689777i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.2500i | 2.13897i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.41540 | −0.321173 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0120931 | −0.000875025 0 | −0.000437512 | − | 1.00000i | \(-0.500139\pi\) | ||||
−0.000437512 | 1.00000i | \(0.500139\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 12.7841i | − 0.920219i | −0.887862 | − | 0.460110i | \(-0.847810\pi\) | ||||
0.887862 | − | 0.460110i | \(-0.152190\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.86545i | 0.702885i | 0.936210 | + | 0.351442i | \(0.114309\pi\) | ||||
−0.936210 | + | 0.351442i | \(0.885691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.295640 | 0.0209573 | 0.0104787 | − | 0.999945i | \(-0.496664\pi\) | ||||
0.0104787 | + | 0.999945i | \(0.496664\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.9457 | 0.842585 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.3935i | 1.50153i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.31495i | 0.0913952i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.3901 | 0.857039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6477 | −0.870705 | −0.435352 | − | 0.900260i | \(-0.643376\pi\) | ||||
−0.435352 | + | 0.900260i | \(0.643376\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 0.509248i | − 0.0348931i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 0.870433i | − 0.0590888i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.7708 | −1.06569 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.7650 | −2.54035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 5.23980i | − 0.350883i | −0.984490 | − | 0.175442i | \(-0.943865\pi\) | ||||
0.984490 | − | 0.175442i | \(-0.0561353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.76897i | 0.515645i | 0.966192 | + | 0.257822i | \(0.0830049\pi\) | ||||
−0.966192 | + | 0.257822i | \(0.916995\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.99192 | 0.395958 | 0.197979 | − | 0.980206i | \(-0.436562\pi\) | ||||
0.197979 | + | 0.980206i | \(0.436562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.6565 | 1.29330 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.8631i | − 0.973714i | −0.873482 | − | 0.486857i | \(-0.838143\pi\) | ||||
0.873482 | − | 0.486857i | \(-0.161857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3.43153i | − 0.222902i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.2008 | 1.37136 | 0.685682 | − | 0.727902i | \(-0.259504\pi\) | ||||
0.685682 | + | 0.727902i | \(0.259504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0562 | 1.03427 | 0.517134 | − | 0.855905i | \(-0.326999\pi\) | ||||
0.517134 | + | 0.855905i | \(0.326999\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.9970i | 1.01786i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.37155 | 0.340408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1371 | −1.52352 | −0.761761 | − | 0.647858i | \(-0.775665\pi\) | ||||
−0.761761 | + | 0.647858i | \(0.775665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.85390i | − 0.368031i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.22940i | 0.263823i | 0.991262 | + | 0.131911i | \(0.0421114\pi\) | ||||
−0.991262 | + | 0.131911i | \(0.957889\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.2445 | 2.25213 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.84521 | −0.299911 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 8.38782i | − 0.517215i | −0.965982 | − | 0.258608i | \(-0.916736\pi\) | ||||
0.965982 | − | 0.258608i | \(-0.0832636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3452i | 0.694313i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.53526 | 0.337490 | 0.168745 | − | 0.985660i | \(-0.446028\pi\) | ||||
0.168745 | + | 0.985660i | \(0.446028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8497 | 0.962802 | 0.481401 | − | 0.876501i | \(-0.340128\pi\) | ||||
0.481401 | + | 0.876501i | \(0.340128\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.3787i | 1.53599i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 8.69243i | − 0.522277i | −0.965301 | − | 0.261139i | \(-0.915902\pi\) | ||||
0.965301 | − | 0.261139i | \(-0.0840980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.197136 | 0.0118022 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.7800 | 0.643081 | 0.321540 | − | 0.946896i | \(-0.395799\pi\) | ||||
0.321540 | + | 0.946896i | \(0.395799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.84520i | − 0.585236i | −0.956229 | − | 0.292618i | \(-0.905473\pi\) | ||||
0.956229 | − | 0.292618i | \(-0.0945265\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.6602i | 2.04593i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.1696 | −1.53939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.07960 | −0.297772 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9.77733i | − 0.571198i | −0.958349 | − | 0.285599i | \(-0.907808\pi\) | ||||
0.958349 | − | 0.285599i | \(-0.0921925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.45181i | 0.258320i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.55803 | 0.437092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.82264 | −0.105055 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.1860i | 0.642620i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.7301i | 1.86801i | 0.357265 | + | 0.934003i | \(0.383709\pi\) | ||||
−0.357265 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.14567 | 0.178951 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.6245 | −1.39633 | −0.698164 | − | 0.715938i | \(-0.745999\pi\) | ||||
−0.698164 | + | 0.715938i | \(0.745999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.5495i | 1.27457i | 0.770628 | + | 0.637285i | \(0.219943\pi\) | ||||
−0.770628 | + | 0.637285i | \(0.780057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.62435i | 0.0912324i | 0.998959 | + | 0.0456162i | \(0.0145251\pi\) | ||||
−0.998959 | + | 0.0456162i | \(0.985475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.5699 | 1.20768 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.74013 | −0.432012 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.2863i | 1.01748i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 10.3708i | − 0.573509i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.4162 | −1.89743 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.01314 | −0.495407 | −0.247703 | − | 0.968836i | \(-0.579676\pi\) | ||||
−0.247703 | + | 0.968836i | \(0.579676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.20866i | 0.449832i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.9681i | 1.46905i | 0.678583 | + | 0.734524i | \(0.262594\pi\) | ||||
−0.678583 | + | 0.734524i | \(0.737406\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.2263 | 0.555414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.877611 | −0.0475253 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 24.2660i | − 1.31024i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 26.2448i | − 1.40889i | −0.709757 | − | 0.704447i | \(-0.751195\pi\) | ||||
0.709757 | − | 0.704447i | \(-0.248805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.2310 | −0.975885 | −0.487943 | − | 0.872876i | \(-0.662252\pi\) | ||||
−0.487943 | + | 0.872876i | \(0.662252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.74778 | −0.306794 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 4.44962i | − 0.236829i | −0.992964 | − | 0.118415i | \(-0.962219\pi\) | ||||
0.992964 | − | 0.118415i | \(-0.0377812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.0107i | 1.53541i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3271 | 1.70616 | 0.853081 | − | 0.521779i | \(-0.174731\pi\) | ||||
0.853081 | + | 0.521779i | \(0.174731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2540 | −0.592318 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8.81860i | − 0.462857i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 5.74002i | − 0.299627i | −0.988714 | − | 0.149813i | \(-0.952133\pi\) | ||||
0.988714 | − | 0.149813i | \(-0.0478673\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.84984 | −0.408647 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.39286 | −0.0723137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.04186i | − 0.0539455i | −0.999636 | − | 0.0269727i | \(-0.991413\pi\) | ||||
0.999636 | − | 0.0269727i | \(-0.00858673\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.8492i | 1.43431i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.74934 | 0.243957 | 0.121979 | − | 0.992533i | \(-0.461076\pi\) | ||||
0.121979 | + | 0.992533i | \(0.461076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3127 | −0.579568 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 11.0200i | − 0.563095i | −0.959547 | − | 0.281548i | \(-0.909152\pi\) | ||||
0.959547 | − | 0.281548i | \(-0.0908477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 0.412792i | − 0.0209834i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.2111 | 1.68387 | 0.841934 | − | 0.539581i | \(-0.181417\pi\) | ||||
0.841934 | + | 0.539581i | \(0.181417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.63968 | 0.436927 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.45365i | 0.476873i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.74418i | 0.137726i | 0.997626 | + | 0.0688631i | \(0.0219372\pi\) | ||||
−0.997626 | + | 0.0688631i | \(0.978063\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.2887 | 0.615207 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.11503 | −0.105619 | −0.0528097 | − | 0.998605i | \(-0.516818\pi\) | ||||
−0.0528097 | + | 0.998605i | \(0.516818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.13309i | − 0.0564434i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 36.5434i | − 1.81139i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.57251 | 0.324990 | 0.162495 | − | 0.986709i | \(-0.448046\pi\) | ||||
0.162495 | + | 0.986709i | \(0.448046\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.41023 | 0.414846 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.1225i | − 0.547301i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.8216i | 0.578905i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.2434 | −1.72175 | −0.860876 | − | 0.508815i | \(-0.830084\pi\) | ||||
−0.860876 | + | 0.508815i | \(0.830084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.27329 | 0.305742 | 0.152871 | − | 0.988246i | \(-0.451148\pi\) | ||||
0.152871 | + | 0.988246i | \(0.451148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 7.79459i | − 0.378986i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.2007i | 1.99384i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.5880 | 1.23540 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6721 | −0.658561 | −0.329280 | − | 0.944232i | \(-0.606806\pi\) | ||||
−0.329280 | + | 0.944232i | \(0.606806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.77819i | 0.325739i | 0.986648 | + | 0.162870i | \(0.0520750\pi\) | ||||
−0.986648 | + | 0.162870i | \(0.947925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.65970i | − 0.175067i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9446 | 0.808723 | 0.404362 | − | 0.914599i | \(-0.367494\pi\) | ||||
0.404362 | + | 0.914599i | \(0.367494\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.4958 | 0.595036 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 23.8927i | − 1.13517i | −0.823313 | − | 0.567587i | \(-0.807877\pi\) | ||||
0.823313 | − | 0.567587i | \(-0.192123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.6355i | 0.503042i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.39281 | −0.301695 | −0.150848 | − | 0.988557i | \(-0.548200\pi\) | ||||
−0.150848 | + | 0.988557i | \(0.548200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.9460 | 1.64554 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.41657i | − 0.207508i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 5.89482i | − 0.275748i | −0.990450 | − | 0.137874i | \(-0.955973\pi\) | ||||
0.990450 | − | 0.137874i | \(-0.0440269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.57035 | −0.306678 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.6200 | −1.14667 | −0.573335 | − | 0.819321i | \(-0.694351\pi\) | ||||
−0.573335 | + | 0.819321i | \(0.694351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 29.8611i | − 1.38776i | −0.720090 | − | 0.693880i | \(-0.755900\pi\) | ||||
0.720090 | − | 0.693880i | \(-0.244100\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.1513i | 1.21014i | 0.796173 | + | 0.605069i | \(0.206855\pi\) | ||||
−0.796173 | + | 0.605069i | \(0.793145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52.7451 | −2.43554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.5289 | 0.623378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.83767i | 0.0844962i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 0.315455i | − 0.0144437i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.54690 | −0.0706798 | −0.0353399 | − | 0.999375i | \(-0.511251\pi\) | ||||
−0.0353399 | + | 0.999375i | \(0.511251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.1816 | 2.15130 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.80602i | − 0.264183i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.4789i | 0.565473i | 0.959198 | + | 0.282736i | \(0.0912422\pi\) | ||||
−0.959198 | + | 0.282736i | \(0.908758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.5583 | −0.658348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6969 | −0.798649 | −0.399325 | − | 0.916810i | \(-0.630755\pi\) | ||||
−0.399325 | + | 0.916810i | \(0.630755\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.8347i | 1.43376i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.24853i | 0.100860i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9281 | 1.38453 | 0.692267 | − | 0.721642i | \(-0.256612\pi\) | ||||
0.692267 | + | 0.721642i | \(0.256612\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.96824 | −0.445348 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 31.5535i | − 1.40690i | −0.710744 | − | 0.703450i | \(-0.751642\pi\) | ||||
0.710744 | − | 0.703450i | \(-0.248358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0370i | 0.889873i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.22535 | 0.320258 | 0.160129 | − | 0.987096i | \(-0.448809\pi\) | ||||
0.160129 | + | 0.987096i | \(0.448809\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 69.6345 | 3.08045 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.78315i | 0.122879i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.7000i | 1.52610i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8750 | 0.477360 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.48574 | −0.415578 | −0.207789 | − | 0.978174i | \(-0.566627\pi\) | ||||
−0.207789 | + | 0.978174i | \(0.566627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3551i | 0.890067i | 0.895514 | + | 0.445033i | \(0.146808\pi\) | ||||
−0.895514 | + | 0.445033i | \(0.853192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.29525i | − 0.0564220i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2709 | 0.924822 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.51902 | 0.109316 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.1192i | 1.95433i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 25.1740i | − 1.08634i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −55.6287 | −2.39610 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8749 | 1.32741 | 0.663707 | − | 0.747992i | \(-0.268982\pi\) | ||||
0.663707 | + | 0.747992i | \(0.268982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.59173i | 0.325792i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 15.3396i | − 0.655872i | −0.944700 | − | 0.327936i | \(-0.893647\pi\) | ||||
0.944700 | − | 0.327936i | \(-0.106353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.33114 | −0.398243 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4850 | 0.574478 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.1516i | 0.644310i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.6722i | 1.21488i | 0.794365 | + | 0.607441i | \(0.207804\pi\) | ||||
−0.794365 | + | 0.607441i | \(0.792196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.37264 | −0.100352 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 29.2500 | 1.23493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.34999i | − 0.309765i | −0.987933 | − | 0.154883i | \(-0.950500\pi\) | ||||
0.987933 | − | 0.154883i | \(-0.0494999\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.41540i | 0.185429i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.1279 | 1.30495 | 0.652474 | − | 0.757811i | \(-0.273731\pi\) | ||||
0.652474 | + | 0.757811i | \(0.273731\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9855 | 0.543426 | 0.271713 | − | 0.962378i | \(-0.412410\pi\) | ||||
0.271713 | + | 0.962378i | \(0.412410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.0120931i | 0 0.000505196i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 21.7895i | − 0.907109i | −0.891229 | − | 0.453554i | \(-0.850156\pi\) | ||||
0.891229 | − | 0.453554i | \(-0.149844\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.7841 | −0.531289 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.7176 | −0.983970 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.40434i | 0.0581620i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 26.6239i | − 1.09889i | −0.835531 | − | 0.549443i | \(-0.814840\pi\) | ||||
0.835531 | − | 0.549443i | \(-0.185160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.548659 | −0.0226071 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.86545 | 0.405811 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.23169i | 0.214840i | 0.994214 | + | 0.107420i | \(0.0342589\pi\) | ||||
−0.994214 | + | 0.107420i | \(0.965741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.295640i | − 0.0120997i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.5405 | −1.61558 | −0.807790 | − | 0.589471i | \(-0.799336\pi\) | ||||
−0.807790 | + | 0.589471i | \(0.799336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.5789 | −1.85920 | −0.929602 | − | 0.368565i | \(-0.879849\pi\) | ||||
−0.929602 | + | 0.368565i | \(0.879849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 11.9457i | − 0.486467i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.6524i | 0.757078i | 0.925585 | + | 0.378539i | \(0.123573\pi\) | ||||
−0.925585 | + | 0.378539i | \(0.876427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.3935 | 0.866909 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44.8016 | −1.81248 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7077i | 0.432482i | 0.976340 | + | 0.216241i | \(0.0693796\pi\) | ||||
−0.976340 | + | 0.216241i | \(0.930620\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7334i | 0.673662i | 0.941565 | + | 0.336831i | \(0.109355\pi\) | ||||
−0.941565 | + | 0.336831i | \(0.890645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.9329 | −0.921750 | −0.460875 | − | 0.887465i | \(-0.652464\pi\) | ||||
−0.460875 | + | 0.887465i | \(0.652464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.31495 | 0.0527671 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 50.0934i | − 2.00695i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 12.3901i | − 0.494812i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53.9338 | 2.15048 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.5167 | 0.577903 | 0.288951 | − | 0.957344i | \(-0.406693\pi\) | ||||
0.288951 | + | 0.957344i | \(0.406693\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.6477i | 0.502701i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 71.8229i | − 2.84573i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.509248 | −0.0201455 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.7526 | −1.25415 | −0.627075 | − | 0.778959i | \(-0.715748\pi\) | ||||
−0.627075 | + | 0.778959i | \(0.715748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.63816i | − 0.143475i | −0.997424 | − | 0.0717376i | \(-0.977146\pi\) | ||||
0.997424 | − | 0.0717376i | \(-0.0228544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 11.2444i | − 0.442065i | −0.975266 | − | 0.221032i | \(-0.929057\pi\) | ||||
0.975266 | − | 0.221032i | \(-0.0709426\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.2142 | −0.440195 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.870433 | −0.0341150 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.02226i | 0.0791372i | 0.999217 | + | 0.0395686i | \(0.0125984\pi\) | ||||
−0.999217 | + | 0.0395686i | \(0.987402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7708i | 0.615279i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.794810 | 0.0309614 | 0.0154807 | − | 0.999880i | \(-0.495072\pi\) | ||||
0.0154807 | + | 0.999880i | \(0.495072\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.9778 | 1.59385 | 0.796925 | − | 0.604078i | \(-0.206459\pi\) | ||||
0.796925 | + | 0.604078i | \(0.206459\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.7650i | 1.46667i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.37119i | − 0.246694i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.23980 | −0.202583 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.5404 | 1.60365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1014i | 1.35306i | 0.736416 | + | 0.676529i | \(0.236517\pi\) | ||||
−0.736416 | + | 0.676529i | \(0.763483\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.3867i | 1.47532i | 0.675173 | + | 0.737660i | \(0.264069\pi\) | ||||
−0.675173 | + | 0.737660i | \(0.735931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.4285 | 0.860726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.76897 | 0.297708 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 8.36485i | − 0.320072i | −0.987111 | − | 0.160036i | \(-0.948839\pi\) | ||||
0.987111 | − | 0.160036i | \(-0.0511610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 5.99192i | − 0.228606i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.81317 | −0.0690761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.83085 | 0.221816 | 0.110908 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110908 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 19.6565i | − 0.746689i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51.5763i | 1.95359i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.8631 | −0.562174 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.6649 | 1.91359 | 0.956793 | − | 0.290770i | \(-0.0939114\pi\) | ||||
0.956793 | + | 0.290770i | \(0.0939114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22.8460i | − 0.861652i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 49.3907i | − 1.85753i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.73196 | 0.365492 | 0.182746 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182746 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.43153 | −0.128692 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.259223i | 0.00970799i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21.2008i | − 0.791757i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.7362 | −0.698742 | −0.349371 | − | 0.936985i | \(-0.613605\pi\) | ||||
−0.349371 | + | 0.936985i | \(0.613605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8894 | −0.517269 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16.0562i | − 0.597135i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 37.9837i | − 1.40874i | −0.709834 | − | 0.704369i | \(-0.751230\pi\) | ||||
0.709834 | − | 0.704369i | \(-0.248770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.71219 | −0.100314 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.3618i | 0.973694i | 0.873487 | + | 0.486847i | \(0.161853\pi\) | ||||
−0.873487 | + | 0.486847i | \(0.838147\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.1800i | 1.95891i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0342 | 1.21518 | 0.607592 | − | 0.794249i | \(-0.292136\pi\) | ||||
0.607592 | + | 0.794249i | \(0.292136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.9970 | 0.587663 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 40.2017i | − 1.47486i | −0.675425 | − | 0.737428i | \(-0.736040\pi\) | ||||
0.675425 | − | 0.737428i | \(-0.263960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.37155i | − 0.196535i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.1758 | 1.24876 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5937 | 1.11638 | 0.558190 | − | 0.829713i | \(-0.311496\pi\) | ||||
0.558190 | + | 0.829713i | \(0.311496\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.1371i | 0.879606i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 24.4003i | − 0.886845i | −0.896313 | − | 0.443422i | \(-0.853764\pi\) | ||||
0.896313 | − | 0.443422i | \(-0.146236\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.85390 | −0.212483 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.3342 | 1.02711 | 0.513556 | − | 0.858056i | \(-0.328328\pi\) | ||||
0.513556 | + | 0.858056i | \(0.328328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45.7914i | 1.65776i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 14.4788i | − 0.522798i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.1214 | 1.48288 | 0.741438 | − | 0.671021i | \(-0.234144\pi\) | ||||
0.741438 | + | 0.671021i | \(0.234144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.22940 | 0.152318 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4.81707i | − 0.173258i | −0.996241 | − | 0.0866290i | \(-0.972391\pi\) | ||||
0.996241 | − | 0.0866290i | \(-0.0276095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 36.2445i | − 1.30027i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.8473 | 0.782762 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.26707 | 0.0811223 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.84521i | 0.173154i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 40.3180i | − 1.43718i | −0.695433 | − | 0.718591i | \(-0.744787\pi\) | ||||
0.695433 | − | 0.718591i | \(-0.255213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.38782 | −0.298614 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.1530 | −1.60546 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.6333i | 1.90457i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 30.1958i | − 1.06959i | −0.844981 | − | 0.534796i | \(-0.820389\pi\) | ||||
0.844981 | − | 0.534796i | \(-0.179611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.2132 | −1.81179 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.3452 | 0.400862 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 70.2087i | − 2.47761i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 5.53526i | − 0.194850i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.8803 | −0.382529 | −0.191265 | − | 0.981539i | \(-0.561259\pi\) | ||||
−0.191265 | + | 0.981539i | \(0.561259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.2580 | −1.65945 | −0.829727 | − | 0.558169i | \(-0.811504\pi\) | ||||
−0.829727 | + | 0.558169i | \(0.811504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 15.8497i | − 0.555874i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.14886i | 0.0401936i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.3787 | 0.886805 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8696 | 0.867956 | 0.433978 | − | 0.900923i | \(-0.357110\pi\) | ||||
0.433978 | + | 0.900923i | \(0.357110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.7590i | 0.793330i | 0.917963 | + | 0.396665i | \(0.129833\pi\) | ||||
−0.917963 | + | 0.396665i | \(0.870167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.8458i | 1.62899i | 0.580172 | + | 0.814494i | \(0.302985\pi\) | ||||
−0.580172 | + | 0.814494i | \(0.697015\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.8010 | 0.479328 | 0.239664 | − | 0.970856i | \(-0.422963\pi\) | ||||
0.239664 | + | 0.970856i | \(0.422963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.69243 | −0.301537 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 82.1015i | − 2.84465i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 0.197136i | − 0.00681401i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5887 | 0.365564 | 0.182782 | − | 0.983153i | \(-0.441490\pi\) | ||||
0.182782 | + | 0.983153i | \(0.441490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.52399 | −0.190482 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 10.7800i | − 0.371283i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.9377i | 1.33791i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.84520 | −0.337886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7940 | −0.370012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6497i | 0.775510i | 0.921762 | + | 0.387755i | \(0.126749\pi\) | ||||
−0.921762 | + | 0.387755i | \(0.873251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 39.4749i | − 1.34844i | −0.738533 | − | 0.674218i | \(-0.764481\pi\) | ||||
0.738533 | − | 0.674218i | \(-0.235519\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.3379 | −1.51279 | −0.756395 | − | 0.654115i | \(-0.773041\pi\) | ||||
−0.756395 | + | 0.654115i | \(0.773041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.6602 | 1.18122 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.03563i | 0.171415i | 0.996320 | + | 0.0857074i | \(0.0273150\pi\) | ||||
−0.996320 | + | 0.0857074i | \(0.972685\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.1696i | 0.888765i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.2765 | 0.518220 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −68.6613 | −2.32650 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.07960i | 0.171918i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.4943i | 0.590739i | 0.955383 | + | 0.295370i | \(0.0954428\pi\) | ||||
−0.955383 | + | 0.295370i | \(0.904557\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.77733 | −0.329781 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.2456 | −1.82758 | −0.913791 | − | 0.406185i | \(-0.866859\pi\) | ||||
−0.913791 | + | 0.406185i | \(0.866859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 30.3544i | − 1.02151i | −0.859727 | − | 0.510753i | \(-0.829367\pi\) | ||||
0.859727 | − | 0.510753i | \(-0.170633\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.6472i | 1.76772i | 0.467751 | + | 0.883860i | \(0.345065\pi\) | ||||
−0.467751 | + | 0.883860i | \(0.654935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.9501 | 1.67527 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.45181 | 0.149141 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.6935i | 0.725947i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7.55803i | − 0.252355i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.955163 | −0.0318565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.07265 | −0.0690500 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.82264i | 0.0606537i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.79799i | 0.292133i | 0.989275 | + | 0.146066i | \(0.0466613\pi\) | ||||
−0.989275 | + | 0.146066i | \(0.953339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1860 | 0.371017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.5174 | −1.04422 | −0.522110 | − | 0.852878i | \(-0.674855\pi\) | ||||
−0.522110 | + | 0.852878i | \(0.674855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9131i | 0.791409i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 41.7416i | − 1.37843i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.4799 | 1.10440 | 0.552200 | − | 0.833712i | \(-0.313789\pi\) | ||||
0.552200 | + | 0.833712i | \(0.313789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.7301 | 1.07849 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.92704i | 0.0963448i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 3.14567i | − 0.103317i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.87841 | 0.0616286 | 0.0308143 | − | 0.999525i | \(-0.490190\pi\) | ||||
0.0308143 | + | 0.999525i | \(0.490190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.7776 | −1.13979 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.6245i | 0.806170i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.28820i | − 0.0747523i | −0.999301 | − | 0.0373762i | \(-0.988100\pi\) | ||||
0.999301 | − | 0.0373762i | \(-0.0119000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.5495 | 0.735874 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.1381 | −1.96044 | −0.980222 | − | 0.197900i | \(-0.936588\pi\) | ||||
−0.980222 | + | 0.197900i | \(0.936588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 10.3221i | − 0.336135i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.2697i | 1.40608i | 0.711152 | + | 0.703039i | \(0.248174\pi\) | ||||
−0.711152 | + | 0.703039i | \(0.751826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 90.6473 | 2.94253 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62435 | 0.0526731 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.8553i | 1.12907i | 0.825407 | + | 0.564537i | \(0.190945\pi\) | ||||
−0.825407 | + | 0.564537i | \(0.809055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 21.5699i | − 0.697257i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −37.1345 | −1.19914 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9611 | −0.998746 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.74013i | 0.249422i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 34.9748i | − 1.12471i | −0.826895 | − | 0.562357i | \(-0.809895\pi\) | ||||
0.826895 | − | 0.562357i | \(-0.190105\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.2863 | 0.587441 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −59.4788 | −1.90877 | −0.954383 | − | 0.298586i | \(-0.903485\pi\) | ||||
−0.954383 | + | 0.298586i | \(0.903485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 52.1970i | − 1.67336i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.4162i | 0.493207i | 0.969117 | + | 0.246603i | \(0.0793145\pi\) | ||||
−0.969117 | + | 0.246603i | \(0.920686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.5065 | −1.61419 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3708 | −0.331116 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.7500i | 1.87383i | 0.349552 | + | 0.936917i | \(0.386334\pi\) | ||||
−0.349552 | + | 0.936917i | \(0.613666\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.4162i | 1.09548i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.542800 | 0.0172600 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.71246 | 0.0543982 | 0.0271991 | − | 0.999630i | \(-0.491341\pi\) | ||||
0.0271991 | + | 0.999630i | \(0.491341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.01314i | 0.286023i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7966i | 0.373603i | 0.982398 | + | 0.186802i | \(0.0598121\pi\) | ||||
−0.982398 | + | 0.186802i | \(0.940188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.20866 | 0.259711 |
(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 | 7500.2.d.g.1249.11 | 24 | ||
5.2 | odd | 4 | 7500.2.a.m.1.2 | 12 | |||
5.3 | odd | 4 | 7500.2.a.n.1.11 | 12 | |||
5.4 | even | 2 | inner | 7500.2.d.g.1249.14 | 24 | ||
25.2 | odd | 20 | 1500.2.m.d.601.1 | 24 | |||
25.9 | even | 10 | 1500.2.o.c.349.3 | 24 | |||
25.11 | even | 5 | 1500.2.o.c.649.3 | 24 | |||
25.12 | odd | 20 | 1500.2.m.d.901.1 | 24 | |||
25.13 | odd | 20 | 1500.2.m.c.901.6 | 24 | |||
25.14 | even | 10 | 300.2.o.a.229.4 | yes | 24 | ||
25.16 | even | 5 | 300.2.o.a.169.4 | ✓ | 24 | ||
25.23 | odd | 20 | 1500.2.m.c.601.6 | 24 | |||
75.14 | odd | 10 | 900.2.w.c.829.5 | 24 | |||
75.41 | odd | 10 | 900.2.w.c.469.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.4 | ✓ | 24 | 25.16 | even | 5 | ||
300.2.o.a.229.4 | yes | 24 | 25.14 | even | 10 | ||
900.2.w.c.469.5 | 24 | 75.41 | odd | 10 | |||
900.2.w.c.829.5 | 24 | 75.14 | odd | 10 | |||
1500.2.m.c.601.6 | 24 | 25.23 | odd | 20 | |||
1500.2.m.c.901.6 | 24 | 25.13 | odd | 20 | |||
1500.2.m.d.601.1 | 24 | 25.2 | odd | 20 | |||
1500.2.m.d.901.1 | 24 | 25.12 | odd | 20 | |||
1500.2.o.c.349.3 | 24 | 25.9 | even | 10 | |||
1500.2.o.c.649.3 | 24 | 25.11 | even | 5 | |||
7500.2.a.m.1.2 | 12 | 5.2 | odd | 4 | |||
7500.2.a.n.1.11 | 12 | 5.3 | odd | 4 | |||
7500.2.d.g.1249.11 | 24 | 1.1 | even | 1 | trivial | ||
7500.2.d.g.1249.14 | 24 | 5.4 | even | 2 | inner |