Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(1009,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2520.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.t (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.3 | ||
Root | \(1.45161 + 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.1009 |
Dual form | 2520.2.t.j.1009.4 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.311108 | − | 2.21432i | 0.139132 | − | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.80642 | 1.14768 | 0.573840 | − | 0.818967i | \(-0.305453\pi\) | ||||
0.573840 | + | 0.818967i | \(0.305453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.622216i | 0.172572i | 0.996270 | + | 0.0862858i | \(0.0274998\pi\) | ||||
−0.996270 | + | 0.0862858i | \(0.972500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.42864i | − | 1.07410i | −0.843550 | − | 0.537051i | \(-0.819538\pi\) | ||
0.843550 | − | 0.537051i | \(-0.180462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.622216 | −0.142746 | −0.0713730 | − | 0.997450i | \(-0.522738\pi\) | ||||
−0.0713730 | + | 0.997450i | \(0.522738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.62222i | − | 0.546770i | −0.961905 | − | 0.273385i | \(-0.911857\pi\) | ||
0.961905 | − | 0.273385i | \(-0.0881433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | − | 1.37778i | −0.961285 | − | 0.275557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.61285 | 1.78506 | 0.892531 | − | 0.450987i | \(-0.148928\pi\) | ||||
0.892531 | + | 0.450987i | \(0.148928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.622216 | −0.111753 | −0.0558766 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558766 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.21432 | − | 0.311108i | −0.374288 | − | 0.0525868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.24443i | 0.204583i | 0.994754 | + | 0.102292i | \(0.0326175\pi\) | ||||
−0.994754 | + | 0.102292i | \(0.967383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.62222 | −0.721869 | −0.360934 | − | 0.932591i | \(-0.617542\pi\) | ||||
−0.360934 | + | 0.932591i | \(0.617542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.85728i | − | 0.740728i | −0.928887 | − | 0.370364i | \(-0.879233\pi\) | ||
0.928887 | − | 0.370364i | \(-0.120767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6128i | 1.69391i | 0.531666 | + | 0.846954i | \(0.321566\pi\) | ||||
−0.531666 | + | 0.846954i | \(0.678434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 13.4795i | − | 1.85155i | −0.378074 | − | 0.925775i | \(-0.623413\pi\) | ||
0.378074 | − | 0.925775i | \(-0.376587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.18421 | − | 8.42864i | 0.159679 | − | 1.13652i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6128 | 1.51186 | 0.755932 | − | 0.654650i | \(-0.227184\pi\) | ||||
0.755932 | + | 0.654650i | \(0.227184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.10171 | −1.03732 | −0.518659 | − | 0.854981i | \(-0.673569\pi\) | ||||
−0.518659 | + | 0.854981i | \(0.673569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.37778 | + | 0.193576i | 0.170893 | + | 0.0240102i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.56199 | −0.304053 | −0.152026 | − | 0.988376i | \(-0.548580\pi\) | ||||
−0.152026 | + | 0.988376i | \(0.548580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9906i | 1.28636i | 0.765717 | + | 0.643178i | \(0.222385\pi\) | ||||
−0.765717 | + | 0.643178i | \(0.777615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.80642i | − | 0.433782i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.75557 | 0.760061 | 0.380030 | − | 0.924974i | \(-0.375914\pi\) | ||||
0.380030 | + | 0.924974i | \(0.375914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.6128i | − | 1.27468i | −0.770585 | − | 0.637338i | \(-0.780036\pi\) | ||
0.770585 | − | 0.637338i | \(-0.219964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.80642 | − | 1.37778i | −1.06366 | − | 0.149442i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.23506 | −0.872915 | −0.436457 | − | 0.899725i | \(-0.643767\pi\) | ||||
−0.436457 | + | 0.899725i | \(0.643767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.622216 | 0.0652259 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.193576 | + | 1.37778i | −0.0198605 | + | 0.141358i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.23506i | − | 0.430006i | −0.976613 | − | 0.215003i | \(-0.931024\pi\) | ||
0.976613 | − | 0.215003i | \(-0.0689761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.7239 | −1.86310 | −0.931550 | − | 0.363613i | \(-0.881543\pi\) | ||||
−0.931550 | + | 0.363613i | \(0.881543\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.857279i | − | 0.0844702i | −0.999108 | − | 0.0422351i | \(-0.986552\pi\) | ||
0.999108 | − | 0.0422351i | \(-0.0134479\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.0923i | − | 1.07234i | −0.844111 | − | 0.536169i | \(-0.819871\pi\) | ||
0.844111 | − | 0.536169i | \(-0.180129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.61285 | −0.537613 | −0.268807 | − | 0.963194i | \(-0.586629\pi\) | ||||
−0.268807 | + | 0.963194i | \(0.586629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.2351i | − | 1.52727i | −0.645650 | − | 0.763633i | \(-0.723414\pi\) | ||
0.645650 | − | 0.763633i | \(-0.276586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.80642 | − | 0.815792i | −0.541452 | − | 0.0760730i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.48886 | 0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.54617 | + | 10.2143i | −0.406622 | + | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.3461i | − | 1.36175i | −0.732400 | − | 0.680875i | \(-0.761600\pi\) | ||
0.732400 | − | 0.680875i | \(-0.238400\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.622216i | 0.0539529i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.0923i | − | 1.46030i | −0.683288 | − | 0.730149i | \(-0.739451\pi\) | ||
0.683288 | − | 0.730149i | \(-0.260549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4795 | 1.14332 | 0.571658 | − | 0.820492i | \(-0.306300\pi\) | ||||
0.571658 | + | 0.820492i | \(0.306300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.36842i | 0.198057i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.99063 | − | 21.2859i | 0.248358 | − | 1.76770i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.34614 | −0.765666 | −0.382833 | − | 0.923818i | \(-0.625051\pi\) | ||||
−0.382833 | + | 0.923818i | \(0.625051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.14272 | −0.581266 | −0.290633 | − | 0.956835i | \(-0.593866\pi\) | ||||
−0.290633 | + | 0.956835i | \(0.593866\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.193576 | + | 1.37778i | −0.0155484 | + | 0.110666i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.99063i | 0.557913i | 0.960304 | + | 0.278957i | \(0.0899886\pi\) | ||||
−0.960304 | + | 0.278957i | \(0.910011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.62222 | −0.206660 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.6128i | 1.22289i | 0.791286 | + | 0.611446i | \(0.209412\pi\) | ||||
−0.791286 | + | 0.611446i | \(0.790588\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.51114i | − | 0.116935i | −0.998289 | − | 0.0584677i | \(-0.981379\pi\) | ||
0.998289 | − | 0.0584677i | \(-0.0186215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6128 | 0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.53035i | 0.496493i | 0.968697 | + | 0.248247i | \(0.0798543\pi\) | ||||
−0.968697 | + | 0.248247i | \(0.920146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37778 | + | 4.80642i | −0.104151 | + | 0.363331i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.29529 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.85728 | −0.509698 | −0.254849 | − | 0.966981i | \(-0.582026\pi\) | ||||
−0.254849 | + | 0.966981i | \(0.582026\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.75557 | + | 0.387152i | 0.202593 | + | 0.0284640i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.8573i | − | 1.23273i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5620 | 0.764239 | 0.382119 | − | 0.924113i | \(-0.375194\pi\) | ||||
0.382119 | + | 0.924113i | \(0.375194\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.24443i | 0.377502i | 0.982025 | + | 0.188751i | \(0.0604440\pi\) | ||||
−0.982025 | + | 0.188751i | \(0.939556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.7462i | 1.26436i | 0.774820 | + | 0.632182i | \(0.217841\pi\) | ||||
−0.774820 | + | 0.632182i | \(0.782159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2351 | 1.43443 | 0.717213 | − | 0.696854i | \(-0.245418\pi\) | ||||
0.717213 | + | 0.696854i | \(0.245418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.61285i | − | 0.674690i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.43801 | + | 10.2351i | −0.100435 | + | 0.714848i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.36842 | −0.163827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3274 | 1.46824 | 0.734120 | − | 0.679020i | \(-0.237595\pi\) | ||||
0.734120 | + | 0.679020i | \(0.237595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7556 | − | 1.51114i | −0.733524 | − | 0.103059i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.622216i | 0.0422387i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.75557 | 0.185360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.71456i | − | 0.650535i | −0.945622 | − | 0.325267i | \(-0.894546\pi\) | ||
0.945622 | − | 0.325267i | \(-0.105454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 11.3461i | − | 0.753070i | −0.926402 | − | 0.376535i | \(-0.877115\pi\) | ||
0.926402 | − | 0.376535i | \(-0.122885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34614 | −0.0889555 | −0.0444778 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444778 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.3778i | − | 1.00743i | −0.863869 | − | 0.503716i | \(-0.831966\pi\) | ||
0.863869 | − | 0.503716i | \(-0.168034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.7146 | + | 3.61285i | 1.67743 | + | 0.235676i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.53972 | 0.487704 | 0.243852 | − | 0.969812i | \(-0.421589\pi\) | ||||
0.243852 | + | 0.969812i | \(0.421589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9813 | 1.54477 | 0.772385 | − | 0.635155i | \(-0.219064\pi\) | ||||
0.772385 | + | 0.635155i | \(0.219064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.311108 | + | 2.21432i | −0.0198759 | + | 0.141468i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.387152i | − | 0.0246339i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.1017 | −0.890092 | −0.445046 | − | 0.895508i | \(-0.646813\pi\) | ||||
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 9.98126i | − | 0.627517i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.0192i | 1.06163i | 0.847488 | + | 0.530815i | \(0.178114\pi\) | ||||
−0.847488 | + | 0.530815i | \(0.821886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.24443 | 0.0773252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.6035i | − | 0.777164i | −0.921414 | − | 0.388582i | \(-0.872965\pi\) | ||
0.921414 | − | 0.388582i | \(-0.127035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.8479 | − | 4.19358i | −1.83354 | − | 0.257609i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.76494 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8666 | −1.08532 | −0.542661 | − | 0.839952i | \(-0.682583\pi\) | ||||
−0.542661 | + | 0.839952i | \(0.682583\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2953 | − | 5.24443i | −1.10325 | − | 0.316251i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.24443i | 0.0747706i | 0.999301 | + | 0.0373853i | \(0.0119029\pi\) | ||||
−0.999301 | + | 0.0373853i | \(0.988097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.95899 | 0.534448 | 0.267224 | − | 0.963634i | \(-0.413894\pi\) | ||||
0.267224 | + | 0.963634i | \(0.413894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.5718i | 1.81731i | 0.417551 | + | 0.908654i | \(0.362889\pi\) | ||||
−0.417551 | + | 0.908654i | \(0.637111\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62222i | 0.272841i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.61285 | −0.153697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.67307i | 0.331424i | 0.986174 | + | 0.165712i | \(0.0529923\pi\) | ||||
−0.986174 | + | 0.165712i | \(0.947008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.61285 | − | 25.7146i | 0.210348 | − | 1.49716i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63158 | 0.0943569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85728 | −0.279969 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.52051 | + | 17.9398i | −0.144324 | + | 1.02723i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.85728i | 0.277220i | 0.990347 | + | 0.138610i | \(0.0442634\pi\) | ||||
−0.990347 | + | 0.138610i | \(0.955737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.5718 | 1.96039 | 0.980195 | − | 0.198037i | \(-0.0634567\pi\) | ||||
0.980195 | + | 0.198037i | \(0.0634567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.33677i | − | 0.358176i | −0.983833 | − | 0.179088i | \(-0.942685\pi\) | ||
0.983833 | − | 0.179088i | \(-0.0573146\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.9684i | 0.896872i | 0.893815 | + | 0.448436i | \(0.148019\pi\) | ||||
−0.893815 | + | 0.448436i | \(0.851981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.5906 | 2.04868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.75557i | 0.153324i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.857279 | − | 2.99063i | 0.0475533 | − | 0.165890i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6128 | 0.640237 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.6128 | −1.51774 | −0.758870 | − | 0.651243i | \(-0.774248\pi\) | ||||
−0.758870 | + | 0.651243i | \(0.774248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.36842 | −0.128257 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 11.8666i | − | 0.637035i | −0.947917 | − | 0.318517i | \(-0.896815\pi\) | ||
0.947917 | − | 0.318517i | \(-0.103185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8163 | −1.16780 | −0.583899 | − | 0.811826i | \(-0.698474\pi\) | ||||
−0.583899 | + | 0.811826i | \(0.698474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.79706i | 0.148872i | 0.997226 | + | 0.0744361i | \(0.0237157\pi\) | ||||
−0.997226 | + | 0.0744361i | \(0.976284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.797056 | + | 5.67307i | −0.0423033 | + | 0.301095i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.0509 | −0.688798 | −0.344399 | − | 0.938823i | \(-0.611917\pi\) | ||||
−0.344399 | + | 0.938823i | \(0.611917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6128 | −0.979624 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.3368 | + | 3.41927i | 1.27384 | + | 0.178973i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.4889i | 0.547514i | 0.961799 | + | 0.273757i | \(0.0882664\pi\) | ||||
−0.961799 | + | 0.273757i | \(0.911734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.4795 | −0.699820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1847i | 1.56290i | 0.623966 | + | 0.781452i | \(0.285521\pi\) | ||||
−0.623966 | + | 0.781452i | \(0.714479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.98126i | 0.308051i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.8573 | 0.660434 | 0.330217 | − | 0.943905i | \(-0.392878\pi\) | ||||
0.330217 | + | 0.943905i | \(0.392878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.4701i | 1.25037i | 0.780479 | + | 0.625183i | \(0.214975\pi\) | ||||
−0.780479 | + | 0.625183i | \(0.785025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.42864 | − | 1.18421i | −0.429563 | − | 0.0603528i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.61285 | −0.0817746 | −0.0408873 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408873 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.6128 | −0.587287 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.10171 | − | 14.9590i | 0.105749 | − | 0.752668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.2163i | − | 1.11501i | −0.830175 | − | 0.557503i | \(-0.811760\pi\) | ||
0.830175 | − | 0.557503i | \(-0.188240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.9813 | −0.997817 | −0.498908 | − | 0.866655i | \(-0.666266\pi\) | ||||
−0.498908 | + | 0.866655i | \(0.666266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.387152i | − | 0.0192854i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.73683i | 0.234796i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.73329 | 0.283493 | 0.141747 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141747 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.6128i | − | 0.571431i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.7146 | − | 3.61285i | −1.26228 | − | 0.177348i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.3684 | 1.28818 | 0.644091 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644091 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3274 | −0.941960 | −0.470980 | − | 0.882144i | \(-0.656100\pi\) | ||||
−0.470980 | + | 0.882144i | \(0.656100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.10171 | + | 21.2859i | −0.295976 | + | 1.03252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.10171i | 0.392069i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.9491 | 1.29809 | 0.649047 | − | 0.760748i | \(-0.275168\pi\) | ||||
0.649047 | + | 0.760748i | \(0.275168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.13335i | − | 0.102522i | −0.998685 | − | 0.0512612i | \(-0.983676\pi\) | ||
0.998685 | − | 0.0512612i | \(-0.0163241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63158i | 0.0780492i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5205 | 0.502116 | 0.251058 | − | 0.967972i | \(-0.419221\pi\) | ||||
0.251058 | + | 0.967972i | \(0.419221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.88892i | 0.327303i | 0.986518 | + | 0.163651i | \(0.0523272\pi\) | ||||
−0.986518 | + | 0.163651i | \(0.947673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.56199 | + | 18.2351i | −0.121450 | + | 0.864425i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.9180 | 1.88385 | 0.941923 | − | 0.335829i | \(-0.109016\pi\) | ||||
0.941923 | + | 0.335829i | \(0.109016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.5941 | −0.828474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.193576 | − | 1.37778i | 0.00907499 | − | 0.0645915i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.47013i | 0.396216i | 0.980180 | + | 0.198108i | \(0.0634796\pi\) | ||||
−0.980180 | + | 0.198108i | \(0.936520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.1146 | −1.86832 | −0.934162 | − | 0.356849i | \(-0.883851\pi\) | ||||
−0.934162 | + | 0.356849i | \(0.883851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.5941i | 1.56125i | 0.624999 | + | 0.780625i | \(0.285099\pi\) | ||||
−0.624999 | + | 0.780625i | \(0.714901\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.3461i | 0.525037i | 0.964927 | + | 0.262518i | \(0.0845530\pi\) | ||||
−0.964927 | + | 0.262518i | \(0.915447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 18.4889i | − | 0.850119i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.99063 | + | 0.857279i | 0.137220 | + | 0.0393347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.2864 | 1.65797 | 0.828984 | − | 0.559273i | \(-0.188919\pi\) | ||||
0.828984 | + | 0.559273i | \(0.188919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.774305 | −0.0353053 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.37778 | − | 1.31756i | −0.425823 | − | 0.0598274i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.8385i | 1.75994i | 0.475027 | + | 0.879971i | \(0.342438\pi\) | ||||
−0.475027 | + | 0.879971i | \(0.657562\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.7467 | 1.29732 | 0.648660 | − | 0.761079i | \(-0.275330\pi\) | ||||
0.648660 | + | 0.761079i | \(0.275330\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 42.5718i | − | 1.91734i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.56199i | 0.114921i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.63158 | 0.252104 | 0.126052 | − | 0.992024i | \(-0.459769\pi\) | ||||
0.126052 | + | 0.992024i | \(0.459769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9590i | 1.55874i | 0.626561 | + | 0.779372i | \(0.284462\pi\) | ||||
−0.626561 | + | 0.779372i | \(0.715538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.82516 | + | 41.4608i | −0.259216 | + | 1.84498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.9906 | −0.487151 | −0.243576 | − | 0.969882i | \(-0.578320\pi\) | ||||
−0.243576 | + | 0.969882i | \(0.578320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9906 | 0.486197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.89829 | − | 0.266706i | −0.0836486 | − | 0.0117525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2034i | 1.94406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.90766 | −0.302630 | −0.151315 | − | 0.988486i | \(-0.548351\pi\) | ||||
−0.151315 | + | 0.988486i | \(0.548351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7146i | 1.64914i | 0.565758 | + | 0.824571i | \(0.308584\pi\) | ||||
−0.565758 | + | 0.824571i | \(0.691416\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.75557i | 0.120034i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.1240 | 0.701043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.87601i | − | 0.124574i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.5620 | − | 3.45091i | −1.06191 | − | 0.149196i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.80642 | −0.163954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.12399 | −0.134311 | −0.0671553 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671553 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.74620 | + | 12.4286i | −0.0747990 | + | 0.532384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.51114i | 0.235639i | 0.993035 | + | 0.117820i | \(0.0375905\pi\) | ||||
−0.993035 | + | 0.117820i | \(0.962410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.98126 | −0.254810 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.75557i | − | 0.287276i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.7052i | 1.55525i | 0.628729 | + | 0.777624i | \(0.283575\pi\) | ||||
−0.628729 | + | 0.777624i | \(0.716425\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.02227 | 0.127829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4924i | 1.15867i | 0.815091 | + | 0.579333i | \(0.196687\pi\) | ||||
−0.815091 | + | 0.579333i | \(0.803313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.9496 | − | 5.05086i | −1.51241 | − | 0.212491i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2444 | 0.974457 | 0.487229 | − | 0.873274i | \(-0.338008\pi\) | ||||
0.487229 | + | 0.873274i | \(0.338008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.5111 | −1.06761 | −0.533804 | − | 0.845608i | \(-0.679238\pi\) | ||||
−0.533804 | + | 0.845608i | \(0.679238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.61285 | + | 12.6035i | −0.150666 | + | 0.525601i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 26.0701i | − | 1.08531i | −0.839955 | − | 0.542656i | \(-0.817419\pi\) | ||
0.839955 | − | 0.542656i | \(-0.182581\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6128 | −0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 51.3087i | − | 2.12499i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.2667i | − | 0.506301i | −0.967427 | − | 0.253151i | \(-0.918533\pi\) | ||
0.967427 | − | 0.253151i | \(-0.0814668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.387152 | 0.0159523 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.9175i | 0.612588i | 0.951937 | + | 0.306294i | \(0.0990891\pi\) | ||||
−0.951937 | + | 0.306294i | \(0.900911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37778 | + | 9.80642i | −0.0564837 | + | 0.402024i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.5620 | −1.08529 | −0.542647 | − | 0.839961i | \(-0.682578\pi\) | ||||
−0.542647 | + | 0.839961i | \(0.682578\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.7146 | 1.61999 | 0.809995 | − | 0.586436i | \(-0.199470\pi\) | ||||
0.809995 | + | 0.586436i | \(0.199470\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.08541 | − | 7.72546i | 0.0441283 | − | 0.314084i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.28544i | − | 0.255118i | −0.991831 | − | 0.127559i | \(-0.959286\pi\) | ||
0.991831 | − | 0.127559i | \(-0.0407143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.22570 | −0.292320 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 45.7146i | − | 1.84639i | −0.384328 | − | 0.923197i | \(-0.625567\pi\) | ||
0.384328 | − | 0.923197i | \(-0.374433\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.88892i | 0.196821i | 0.995146 | + | 0.0984103i | \(0.0313758\pi\) | ||||
−0.995146 | + | 0.0984103i | \(0.968624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.2351 | −0.491769 | −0.245884 | − | 0.969299i | \(-0.579078\pi\) | ||||
−0.245884 | + | 0.969299i | \(0.579078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.23506i | 0.329931i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.51114 | 0.219743 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.24443 | 0.0495400 | 0.0247700 | − | 0.999693i | \(-0.492115\pi\) | ||||
0.0247700 | + | 0.999693i | \(0.492115\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −33.9813 | − | 4.77430i | −1.34851 | − | 0.189462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.622216i | − | 0.0246531i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.1847 | 1.90318 | 0.951590 | − | 0.307369i | \(-0.0994487\pi\) | ||||
0.951590 | + | 0.307369i | \(0.0994487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.85728i | 0.191552i | 0.995403 | + | 0.0957762i | \(0.0305333\pi\) | ||||
−0.995403 | + | 0.0957762i | \(0.969467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.203420i | 0.00799728i | 0.999992 | + | 0.00399864i | \(0.00127281\pi\) | ||||
−0.999992 | + | 0.00399864i | \(0.998727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.2034 | 1.73514 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.3145i | 1.06890i | 0.845200 | + | 0.534449i | \(0.179481\pi\) | ||||
−0.845200 | + | 0.534449i | \(0.820519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.24443 | − | 8.85728i | 0.0486240 | − | 0.346083i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3176 | 1.29787 | 0.648934 | − | 0.760845i | \(-0.275215\pi\) | ||||
0.648934 | + | 0.760845i | \(0.275215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5906 | 0.567508 | 0.283754 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283754 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.37778 | + | 0.193576i | 0.0534282 | + | 0.00750656i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 25.2070i | − | 0.976017i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.8385 | −1.19051 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.53341i | 0.174750i | 0.996175 | + | 0.0873751i | \(0.0278479\pi\) | ||||
−0.996175 | + | 0.0873751i | \(0.972152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 27.2672i | − | 1.04796i | −0.851730 | − | 0.523981i | \(-0.824446\pi\) | ||
0.851730 | − | 0.523981i | \(-0.175554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.23506 | −0.162527 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.5812i | 1.13189i | 0.824442 | + | 0.565947i | \(0.191489\pi\) | ||||
−0.824442 | + | 0.565947i | \(0.808511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8479 | − | 5.31756i | −1.44609 | − | 0.203174i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.38715 | 0.319525 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.99063 | 0.113769 | 0.0568845 | − | 0.998381i | \(-0.481883\pi\) | ||||
0.0568845 | + | 0.998381i | \(0.481883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.19358 | − | 29.8479i | 0.159071 | − | 1.13220i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4701i | 0.775361i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.0420 | 1.55013 | 0.775067 | − | 0.631879i | \(-0.217716\pi\) | ||||
0.775067 | + | 0.631879i | \(0.217716\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.774305i | − | 0.0292035i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7239i | 0.704186i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.4291 | 1.55590 | 0.777952 | − | 0.628324i | \(-0.216259\pi\) | ||||
0.777952 | + | 0.628324i | \(0.216259\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.63158i | 0.0611033i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.24443 | + | 0.736833i | 0.196131 | + | 0.0275560i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.9590 | −0.707051 | −0.353525 | − | 0.935425i | \(-0.615017\pi\) | ||||
−0.353525 | + | 0.935425i | \(0.615017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.857279 | −0.0319267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −46.2034 | − | 13.2444i | −1.71595 | − | 0.491886i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 41.7975i | − | 1.55018i | −0.631848 | − | 0.775092i | \(-0.717703\pi\) | ||
0.631848 | − | 0.775092i | \(-0.282297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.5111 | −0.795618 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3145i | 0.565654i | 0.959171 | + | 0.282827i | \(0.0912722\pi\) | ||||
−0.959171 | + | 0.282827i | \(0.908728\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.7368 | 1.20424 | 0.602122 | − | 0.798404i | \(-0.294322\pi\) | ||||
0.602122 | + | 0.798404i | \(0.294322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3778i | 1.37126i | 0.727951 | + | 0.685629i | \(0.240473\pi\) | ||||
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.90766 | + | 20.6953i | −0.106528 | + | 0.758219i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.0923 | −0.405305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.3497 | 0.742570 | 0.371285 | − | 0.928519i | \(-0.378917\pi\) | ||||
0.371285 | + | 0.928519i | \(0.378917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.22216 | + | 15.8163i | −0.0808725 | + | 0.575613i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.95899i | 0.252929i | 0.991971 | + | 0.126464i | \(0.0403629\pi\) | ||||
−0.991971 | + | 0.126464i | \(0.959637\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.6419 | −1.76327 | −0.881634 | − | 0.471934i | \(-0.843556\pi\) | ||||
−0.881634 | + | 0.471934i | \(0.843556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.61285i | 0.203199i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.22570i | 0.260905i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6923 | 0.890426 | 0.445213 | − | 0.895425i | \(-0.353128\pi\) | ||||
0.445213 | + | 0.895425i | \(0.353128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 36.0415i | − | 1.29632i | −0.761503 | − | 0.648161i | \(-0.775538\pi\) | ||
0.761503 | − | 0.648161i | \(-0.224462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.99063 | + | 0.857279i | 0.107427 | + | 0.0307944i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.87601 | 0.103044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.75203 | −0.348955 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.4795 | + | 2.17484i | 0.552487 | + | 0.0776234i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.2034i | 1.14793i | 0.818881 | + | 0.573964i | \(0.194595\pi\) | ||||
−0.818881 | + | 0.573964i | \(0.805405\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2351 | −0.577252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 5.04101i | − | 0.179012i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 17.5526i | − | 0.621746i | −0.950451 | − | 0.310873i | \(-0.899379\pi\) | ||
0.950451 | − | 0.310873i | \(-0.100621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.4291 | 1.81943 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.8350i | 1.47633i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.815792 | + | 5.80642i | −0.0287529 | + | 0.204650i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.1659 | 1.62311 | 0.811554 | − | 0.584277i | \(-0.198622\pi\) | ||||
0.811554 | + | 0.584277i | \(0.198622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.5205 | 0.650343 | 0.325171 | − | 0.945655i | \(-0.394578\pi\) | ||||
0.325171 | + | 0.945655i | \(0.394578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.5718 | + | 4.85728i | 1.21100 | + | 0.170143i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.02227i | 0.105736i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.0607 | −1.50283 | −0.751414 | − | 0.659831i | \(-0.770628\pi\) | ||||
−0.751414 | + | 0.659831i | \(0.770628\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5718i | 0.507942i | 0.967212 | + | 0.253971i | \(0.0817368\pi\) | ||||
−0.967212 | + | 0.253971i | \(0.918263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 55.8292i | − | 1.94137i | −0.240354 | − | 0.970685i | \(-0.577264\pi\) | ||
0.240354 | − | 0.970685i | \(-0.422736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.3087 | 1.29578 | 0.647892 | − | 0.761732i | \(-0.275651\pi\) | ||||
0.647892 | + | 0.761732i | \(0.275651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.42864i | 0.153443i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.34614 | − | 0.470127i | −0.115798 | − | 0.0162694i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.0420 | −1.76216 | −0.881082 | − | 0.472963i | \(-0.843184\pi\) | ||||
−0.881082 | + | 0.472963i | \(0.843184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.4068 | 2.18644 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.92396 | − | 27.9289i | 0.134988 | − | 0.960783i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.48886i | − | 0.119879i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.26317 | 0.111860 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4197i | 0.904595i | 0.891867 | + | 0.452297i | \(0.149395\pi\) | ||||
−0.891867 | + | 0.452297i | \(0.850605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.161933i | − | 0.00553154i | −0.999996 | − | 0.00276577i | \(-0.999120\pi\) | ||
0.999996 | − | 0.00276577i | \(-0.000880372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.3403 | −1.75171 | −0.875854 | − | 0.482575i | \(-0.839701\pi\) | ||||
−0.875854 | + | 0.482575i | \(0.839701\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.8702i | − | 0.438106i | −0.975713 | − | 0.219053i | \(-0.929703\pi\) | ||
0.975713 | − | 0.219053i | \(-0.0702968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.4603 | + | 2.03164i | 0.491664 | + | 0.0690779i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.7146 | 0.872307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2143 | + | 4.54617i | 0.345307 | + | 0.153689i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.2257i | 1.45963i | 0.683646 | + | 0.729814i | \(0.260393\pi\) | ||||
−0.683646 | + | 0.729814i | \(0.739607\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.5018 | 0.555959 | 0.277979 | − | 0.960587i | \(-0.410335\pi\) | ||||
0.277979 | + | 0.960587i | \(0.410335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.1847i | − | 1.55424i | −0.629353 | − | 0.777119i | \(-0.716680\pi\) | ||
0.629353 | − | 0.777119i | \(-0.283320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 37.3274i | − | 1.25333i | −0.779288 | − | 0.626666i | \(-0.784419\pi\) | ||
0.779288 | − | 0.626666i | \(-0.215581\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.3461 | −0.514693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.22570i | − | 0.241799i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.95851 | + | 13.9398i | −0.0654659 | + | 0.465955i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.98126 | −0.199486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.6958 | −1.98876 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.13335 | + | 15.1842i | −0.0709151 | + | 0.504740i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.6735i | − | 0.819272i | −0.912249 | − | 0.409636i | \(-0.865656\pi\) | ||
0.912249 | − | 0.409636i | \(-0.134344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4380 | −0.975325 | −0.487662 | − | 0.873032i | \(-0.662150\pi\) | ||||
−0.487662 | + | 0.873032i | \(0.662150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 44.2034i | − | 1.46292i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.00000i | − | 0.132092i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0197 | −1.32013 | −0.660064 | − | 0.751209i | \(-0.729471\pi\) | ||||
−0.660064 | + | 0.751209i | \(0.729471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.59411i | − | 0.0524708i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.71456 | − | 5.98126i | 0.0563743 | − | 0.196663i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4572 | −0.736797 | −0.368399 | − | 0.929668i | \(-0.620094\pi\) | ||||
−0.368399 | + | 0.929668i | \(0.620094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.622216 | 0.0203923 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.3274 | − | 5.24443i | −1.22074 | − | 0.171511i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.8292i | 1.10515i | 0.833463 | + | 0.552575i | \(0.186355\pi\) | ||||
−0.833463 | + | 0.552575i | \(0.813645\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.8479 | −1.55980 | −0.779899 | − | 0.625906i | \(-0.784729\pi\) | ||||
−0.779899 | + | 0.625906i | \(0.784729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.1204i | 0.394696i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.8069i | 1.45603i | 0.685562 | + | 0.728014i | \(0.259557\pi\) | ||||
−0.685562 | + | 0.728014i | \(0.740443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.83854 | −0.221989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 15.7017i | − | 0.508626i | −0.967122 | − | 0.254313i | \(-0.918151\pi\) | ||
0.967122 | − | 0.254313i | \(-0.0818494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.28592 | − | 23.3876i | 0.106330 | − | 0.756806i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.0923 | −0.551941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6128 | −0.987511 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6128 | + | 1.63158i | 0.373831 | + | 0.0525225i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.9590i | 1.51010i | 0.655668 | + | 0.755050i | \(0.272387\pi\) | ||||
−0.655668 | + | 0.755050i | \(0.727613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.7556 | 0.601895 | 0.300947 | − | 0.953641i | \(-0.402697\pi\) | ||||
0.300947 | + | 0.953641i | \(0.402697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.4795i | − | 0.432133i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.8292i | 1.21026i | 0.796126 | + | 0.605131i | \(0.206879\pi\) | ||||
−0.796126 | + | 0.605131i | \(0.793121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.3461 | −1.00183 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.6316i | 0.562360i | 0.959655 | + | 0.281180i | \(0.0907258\pi\) | ||||
−0.959655 | + | 0.281180i | \(0.909274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.2958 | + | 5.52098i | 1.25207 | + | 0.175913i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7368 | −0.405008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1240 | −1.17928 | −0.589641 | − | 0.807665i | \(-0.700731\pi\) | ||||
−0.589641 | + | 0.807665i | \(0.700731\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.29529 | − | 44.8069i | 0.199574 | − | 1.42047i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.4197i | − | 1.34345i | −0.740802 | − | 0.671723i | \(-0.765554\pi\) | ||
0.740802 | − | 0.671723i | \(-0.234446\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2520.2.t.j.1009.3 | 6 | ||
3.2 | odd | 2 | 840.2.t.e.169.5 | yes | 6 | ||
4.3 | odd | 2 | 5040.2.t.ba.1009.3 | 6 | |||
5.4 | even | 2 | inner | 2520.2.t.j.1009.4 | 6 | ||
12.11 | even | 2 | 1680.2.t.i.1009.2 | 6 | |||
15.2 | even | 4 | 4200.2.a.bq.1.1 | 3 | |||
15.8 | even | 4 | 4200.2.a.bo.1.1 | 3 | |||
15.14 | odd | 2 | 840.2.t.e.169.2 | ✓ | 6 | ||
20.19 | odd | 2 | 5040.2.t.ba.1009.4 | 6 | |||
60.23 | odd | 4 | 8400.2.a.dk.1.3 | 3 | |||
60.47 | odd | 4 | 8400.2.a.dh.1.3 | 3 | |||
60.59 | even | 2 | 1680.2.t.i.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.2 | ✓ | 6 | 15.14 | odd | 2 | ||
840.2.t.e.169.5 | yes | 6 | 3.2 | odd | 2 | ||
1680.2.t.i.1009.2 | 6 | 12.11 | even | 2 | |||
1680.2.t.i.1009.5 | 6 | 60.59 | even | 2 | |||
2520.2.t.j.1009.3 | 6 | 1.1 | even | 1 | trivial | ||
2520.2.t.j.1009.4 | 6 | 5.4 | even | 2 | inner | ||
4200.2.a.bo.1.1 | 3 | 15.8 | even | 4 | |||
4200.2.a.bq.1.1 | 3 | 15.2 | even | 4 | |||
5040.2.t.ba.1009.3 | 6 | 4.3 | odd | 2 | |||
5040.2.t.ba.1009.4 | 6 | 20.19 | odd | 2 | |||
8400.2.a.dh.1.3 | 3 | 60.47 | odd | 4 | |||
8400.2.a.dk.1.3 | 3 | 60.23 | odd | 4 |