Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(289,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("960.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.289 |
Dual form | 960.2.d.e.289.1 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18890 | + | 0.456850i | −0.978906 | + | 0.204310i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.913701i | 0.345346i | 0.984979 | + | 0.172673i | \(0.0552404\pi\) | ||||
−0.984979 | + | 0.172673i | \(0.944760\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.58258i | − | 1.08019i | −0.841605 | − | 0.540094i | \(-0.818389\pi\) | ||
0.841605 | − | 0.540094i | \(-0.181611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.913701 | −0.253415 | −0.126707 | − | 0.991940i | \(-0.540441\pi\) | ||||
−0.126707 | + | 0.991940i | \(0.540441\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.18890 | − | 0.456850i | 0.565172 | − | 0.117958i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.58258i | 0.868902i | 0.900695 | + | 0.434451i | \(0.143058\pi\) | ||||
−0.900695 | + | 0.434451i | \(0.856942\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.913701i | − | 0.199386i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.58258 | − | 2.00000i | 0.916515 | − | 0.400000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.84190i | 1.45620i | 0.685468 | + | 0.728102i | \(0.259598\pi\) | ||||
−0.685468 | + | 0.728102i | \(0.740402\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29150 | 0.950382 | 0.475191 | − | 0.879883i | \(-0.342379\pi\) | ||||
0.475191 | + | 0.879883i | \(0.342379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.58258i | 0.623646i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.417424 | − | 2.00000i | −0.0705576 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.84190 | 1.28920 | 0.644601 | − | 0.764520i | \(-0.277024\pi\) | ||||
0.644601 | + | 0.764520i | \(0.277024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.913701 | 0.146309 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16515 | 1.09268 | 0.546338 | − | 0.837565i | \(-0.316022\pi\) | ||||
0.546338 | + | 0.837565i | \(0.316022\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.18890 | + | 0.456850i | −0.326302 | + | 0.0681032i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.92820i | − | 1.01058i | −0.862949 | − | 0.505291i | \(-0.831385\pi\) | ||
0.862949 | − | 0.505291i | \(-0.168615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.16515 | 0.880736 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.58258i | − | 0.501661i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.55040 | −0.350325 | −0.175162 | − | 0.984540i | \(-0.556045\pi\) | ||||
−0.175162 | + | 0.984540i | \(0.556045\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.63670 | + | 7.84190i | 0.220693 | + | 1.05740i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000i | 0.529813i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 7.58258i | − | 0.987167i | −0.869698 | − | 0.493584i | \(-0.835687\pi\) | ||
0.869698 | − | 0.493584i | \(-0.164313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5830i | 1.35501i | 0.735516 | + | 0.677507i | \(0.236940\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.913701i | 0.115115i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | − | 0.417424i | 0.248069 | − | 0.0517751i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1652 | 1.85272 | 0.926359 | − | 0.376642i | \(-0.122921\pi\) | ||||
0.926359 | + | 0.376642i | \(0.122921\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.0000i | − | 1.40449i | −0.711934 | − | 0.702247i | \(-0.752180\pi\) | ||
0.711934 | − | 0.702247i | \(-0.247820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.58258 | + | 2.00000i | −0.529150 | + | 0.230940i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.27340 | 0.373039 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1652 | −1.22553 | −0.612767 | − | 0.790263i | \(-0.709944\pi\) | ||||
−0.612767 | + | 0.790263i | \(0.709944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.63670 | − | 7.84190i | −0.177525 | − | 0.850574i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.84190i | − | 0.840740i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.834849i | − | 0.0875159i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.29150 | −0.548703 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.82740 | + | 8.75560i | 0.187487 | + | 0.898306i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.16515i | − | 0.727511i | −0.931494 | − | 0.363755i | \(-0.881494\pi\) | ||
0.931494 | − | 0.363755i | \(-0.118506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.58258i | − | 0.360062i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.5975i | − | 1.65151i | −0.564026 | − | 0.825757i | \(-0.690748\pi\) | ||
0.564026 | − | 0.825757i | \(-0.309252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5975i | 1.63540i | 0.575644 | + | 0.817701i | \(0.304751\pi\) | ||||
−0.575644 | + | 0.817701i | \(0.695249\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.417424 | + | 2.00000i | 0.0407364 | + | 0.195180i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.75560i | 0.838635i | 0.907840 | + | 0.419317i | \(0.137731\pi\) | ||||
−0.907840 | + | 0.419317i | \(0.862269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.84190 | −0.744321 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.41742i | 0.415556i | 0.978176 | + | 0.207778i | \(0.0666232\pi\) | ||||
−0.978176 | + | 0.207778i | \(0.933377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.913701 | −0.0844716 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.27340 | −0.300072 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83485 | −0.166804 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.00000 | −0.541002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.11710 | + | 6.47135i | −0.815459 | + | 0.578815i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.7701i | − | 1.31064i | −0.755354 | − | 0.655318i | \(-0.772535\pi\) | ||
0.755354 | − | 0.655318i | \(-0.227465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.16515 | −0.630856 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5826i | 1.36146i | 0.732536 | + | 0.680728i | \(0.238336\pi\) | ||||
−0.732536 | + | 0.680728i | \(0.761664\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.65480 | 0.316912 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.18890 | − | 0.456850i | 0.188391 | − | 0.0393194i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5826i | 1.67305i | 0.547927 | + | 0.836526i | \(0.315417\pi\) | ||||
−0.547927 | + | 0.836526i | \(0.684583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.1652i | 0.947016i | 0.880790 | + | 0.473508i | \(0.157012\pi\) | ||||
−0.880790 | + | 0.473508i | \(0.842988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.27340i | 0.273736i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.58258 | − | 17.1652i | −0.297517 | − | 1.42549i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.16515 | −0.508493 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 11.4967i | − | 0.941847i | −0.882174 | − | 0.470923i | \(-0.843921\pi\) | ||
0.882174 | − | 0.470923i | \(-0.156079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8745 | −1.29185 | −0.645925 | − | 0.763401i | \(-0.723528\pi\) | ||||
−0.645925 | + | 0.763401i | \(0.723528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.58258i | 0.289634i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5826 | + | 2.41742i | −0.930335 | + | 0.194172i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6983 | 1.73171 | 0.865857 | − | 0.500292i | \(-0.166774\pi\) | ||||
0.865857 | + | 0.500292i | \(0.166774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.55040 | 0.202260 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.63670 | − | 7.84190i | −0.127417 | − | 0.610491i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 22.6120i | − | 1.74977i | −0.484331 | − | 0.874885i | \(-0.660937\pi\) | ||
0.484331 | − | 0.874885i | \(-0.339063\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1652 | −0.935781 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.00000i | − | 0.305888i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3060 | −0.859580 | −0.429790 | − | 0.902929i | \(-0.641412\pi\) | ||||
−0.429790 | + | 0.902929i | \(0.641412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82740 | + | 4.18710i | 0.138139 | + | 0.316515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.58258i | 0.569941i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.58258i | 0.566748i | 0.959009 | + | 0.283374i | \(0.0914538\pi\) | ||||
−0.959009 | + | 0.283374i | \(0.908546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.75560i | − | 0.650799i | −0.945577 | − | 0.325399i | \(-0.894501\pi\) | ||
0.945577 | − | 0.325399i | \(-0.105499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.5830i | − | 0.782318i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.1652 | + | 3.58258i | −1.26201 | + | 0.263396i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8348 | 0.938577 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 0.913701i | − | 0.0664619i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8564 | 1.00261 | 0.501307 | − | 0.865269i | \(-0.332853\pi\) | ||||
0.501307 | + | 0.865269i | \(0.332853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.16515i | − | 0.227833i | −0.993490 | − | 0.113916i | \(-0.963660\pi\) | ||
0.993490 | − | 0.113916i | \(-0.0363396\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | + | 0.417424i | −0.143223 | + | 0.0298924i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5438 | 1.81992 | 0.909961 | − | 0.414695i | \(-0.136112\pi\) | ||||
0.909961 | + | 0.414695i | \(0.136112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.63670 | 0.116023 | 0.0580113 | − | 0.998316i | \(-0.481524\pi\) | ||||
0.0580113 | + | 0.998316i | \(0.481524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1652 | −1.06967 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.16515 | −0.502895 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.1334 | + | 2.74110i | −0.917277 | + | 0.191447i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.3303 | −0.991248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1652i | 0.768641i | 0.923200 | + | 0.384320i | \(0.125564\pi\) | ||||
−0.923200 | + | 0.384320i | \(0.874436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | −0.474713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.6838 | + | 3.27340i | −1.06963 | + | 0.223244i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.83485i | 0.328211i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0000i | 0.810885i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.27340i | − | 0.220193i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.913701i | 0.0611859i | 0.999532 | + | 0.0305930i | \(0.00973956\pi\) | ||||
−0.999532 | + | 0.0305930i | \(0.990260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.58258 | − | 2.00000i | 0.305505 | − | 0.133333i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.16515 | −0.210078 | −0.105039 | − | 0.994468i | \(-0.533497\pi\) | ||||
−0.105039 | + | 0.994468i | \(0.533497\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 22.6120i | − | 1.49424i | −0.664687 | − | 0.747122i | \(-0.731435\pi\) | ||
0.664687 | − | 0.747122i | \(-0.268565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.27340 | −0.215374 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.5826i | − | 1.28290i | −0.767166 | − | 0.641449i | \(-0.778334\pi\) | ||
0.767166 | − | 0.641449i | \(-0.221666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.16515 | + | 15.1652i | 0.206472 | + | 0.989265i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.29150 | 0.343720 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.1660 | −1.36912 | −0.684558 | − | 0.728959i | \(-0.740005\pi\) | ||||
−0.684558 | + | 0.728959i | \(0.740005\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.4949 | + | 2.81655i | −0.862158 | + | 0.179943i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65480i | 0.232549i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1652 | 0.707563 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5826i | 0.731086i | 0.930795 | + | 0.365543i | \(0.119117\pi\) | ||||
−0.930795 | + | 0.365543i | \(0.880883\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.63670 | + | 7.84190i | 0.102494 | + | 0.491079i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.74773i | − | 0.171399i | −0.996321 | − | 0.0856993i | \(-0.972688\pi\) | ||
0.996321 | − | 0.0856993i | \(-0.0273124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.16515i | 0.445221i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.84190i | 0.485402i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.75560i | − | 0.539894i | −0.962875 | − | 0.269947i | \(-0.912994\pi\) | ||
0.962875 | − | 0.269947i | \(-0.0870061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.58258 | − | 1.16515i | 0.342935 | − | 0.0715747i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000 | 0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.66930i | 0.589548i | 0.955567 | + | 0.294774i | \(0.0952444\pi\) | ||||
−0.955567 | + | 0.294774i | \(0.904756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.0761 | −1.58401 | −0.792006 | − | 0.610514i | \(-0.790963\pi\) | ||||
−0.792006 | + | 0.610514i | \(0.790963\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.834849i | 0.0505273i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.16515 | − | 16.4174i | −0.432075 | − | 0.990008i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7701 | 0.887450 | 0.443725 | − | 0.896163i | \(-0.353657\pi\) | ||||
0.443725 | + | 0.896163i | \(0.353657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.29150 | 0.316794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.33030 | −0.258324 | −0.129162 | − | 0.991623i | \(-0.541229\pi\) | ||||
−0.129162 | + | 0.991623i | \(0.541229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.16515 | −0.425924 | −0.212962 | − | 0.977060i | \(-0.568311\pi\) | ||||
−0.212962 | + | 0.977060i | \(0.568311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.82740 | − | 8.75560i | −0.108246 | − | 0.518637i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.48220i | 0.323604i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.16515 | 0.245009 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.16515i | 0.420029i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.37780 | −0.255754 | −0.127877 | − | 0.991790i | \(-0.540816\pi\) | ||||
−0.127877 | + | 0.991790i | \(0.540816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | + | 16.5975i | 0.201688 | + | 0.966344i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.58258i | 0.207882i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.54680i | 0.377351i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.5975i | 0.953502i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.83485 | − | 23.1652i | −0.276843 | − | 1.32643i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 16.5975i | − | 0.944199i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.5112 | 0.992970 | 0.496485 | − | 0.868045i | \(-0.334624\pi\) | ||||
0.496485 | + | 0.868045i | \(0.334624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.1652i | − | 1.08328i | −0.840611 | − | 0.541639i | \(-0.817804\pi\) | ||
0.840611 | − | 0.541639i | \(-0.182196\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.417424 | − | 2.00000i | −0.0235192 | − | 0.112687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.93180 | −0.164666 | −0.0823332 | − | 0.996605i | \(-0.526237\pi\) | ||||
−0.0823332 | + | 0.996605i | \(0.526237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0942 | 1.57297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3303 | 0.797359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.18710 | + | 1.82740i | −0.232259 | + | 0.101366i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.75560i | − | 0.484186i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.33030 | 0.349001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.3303i | − | 1.44724i | −0.690196 | − | 0.723622i | \(-0.742476\pi\) | ||
0.690196 | − | 0.723622i | \(-0.257524\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.84190 | 0.429734 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.1950 | + | 6.92820i | −1.81364 | + | 0.378528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.3303i | 0.562727i | 0.959601 | + | 0.281364i | \(0.0907867\pi\) | ||||
−0.959601 | + | 0.281364i | \(0.909213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.41742i | − | 0.239922i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 18.9572i | − | 1.02659i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0290i | 0.649505i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.1652 | 1.02884 | 0.514420 | − | 0.857539i | \(-0.328007\pi\) | ||||
0.514420 | + | 0.857539i | \(0.328007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.27340i | − | 0.175221i | −0.996155 | − | 0.0876106i | \(-0.972077\pi\) | ||
0.996155 | − | 0.0876106i | \(-0.0279231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.913701 | 0.0487697 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.9129i | 1.80500i | 0.430689 | + | 0.902500i | \(0.358270\pi\) | ||||
−0.430689 | + | 0.902500i | \(0.641730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1652 | + | 3.16515i | −0.804883 | + | 0.167989i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.27340 | 0.173247 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92820 | 0.365657 | 0.182828 | − | 0.983145i | \(-0.441475\pi\) | ||||
0.182828 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.83485 | 0.0963046 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.48220 | + | 26.2668i | 0.286952 | + | 1.37487i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 35.9361i | − | 1.87585i | −0.346838 | − | 0.937925i | \(-0.612745\pi\) | ||
0.346838 | − | 0.937925i | \(-0.387255\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.33030i | − | 0.120983i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.01450 | −0.311419 | −0.155710 | − | 0.987803i | \(-0.549766\pi\) | ||||
−0.155710 | + | 0.987803i | \(0.549766\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.11710 | − | 6.47135i | 0.470805 | − | 0.334179i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.16515i | − | 0.369024i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.83485i | 0.248349i | 0.992260 | + | 0.124175i | \(0.0396283\pi\) | ||||
−0.992260 | + | 0.124175i | \(0.960372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.7701i | 0.756696i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9934i | 1.17491i | 0.809257 | + | 0.587454i | \(0.199870\pi\) | ||||
−0.809257 | + | 0.587454i | \(0.800130\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.16515 | + | 1.49545i | −0.365170 | + | 0.0762154i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.16515 | 0.364225 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.4249i | 0.934180i | 0.884210 | + | 0.467090i | \(0.154698\pi\) | ||||
−0.884210 | + | 0.467090i | \(0.845302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 15.5826i | − | 0.786037i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.5826 | − | 2.41742i | 0.582783 | − | 0.121634i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.84190 | −0.393574 | −0.196787 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196787 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.65480 | −0.182969 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.83485 | −0.240841 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.18890 | + | 0.456850i | −0.108767 | + | 0.0227011i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 28.0942i | − | 1.39258i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8348 | 0.931323 | 0.465662 | − | 0.884963i | \(-0.345816\pi\) | ||||
0.465662 | + | 0.884963i | \(0.345816\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 19.5826i | − | 0.965937i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.92820 | 0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.4394 | − | 5.10080i | 1.19968 | − | 0.250389i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 11.1652i | − | 0.546760i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10.7477i | − | 0.525061i | −0.964924 | − | 0.262530i | \(-0.915443\pi\) | ||
0.964924 | − | 0.262530i | \(-0.0845570\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9572i | 0.923918i | 0.886901 | + | 0.461959i | \(0.152853\pi\) | ||||
−0.886901 | + | 0.461959i | \(0.847147\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.92820i | − | 0.336861i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.16515 | + | 16.4174i | 0.347561 | + | 0.796362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.66970 | −0.467949 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 3.27340i | − | 0.158041i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1298 | 0.825114 | 0.412557 | − | 0.910932i | \(-0.364636\pi\) | ||||
0.412557 | + | 0.910932i | \(0.364636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.3303i | 1.84204i | 0.389519 | + | 0.921018i | \(0.372641\pi\) | ||||
−0.389519 | + | 0.921018i | \(0.627359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58258 | + | 17.1652i | 0.171771 | + | 0.823006i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.01810 | −0.0963187 | −0.0481594 | − | 0.998840i | \(-0.515336\pi\) | ||||
−0.0481594 | + | 0.998840i | \(0.515336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.16515 | 0.293579 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8348 | −0.609802 | −0.304901 | − | 0.952384i | \(-0.598623\pi\) | ||||
−0.304901 | + | 0.952384i | \(0.598623\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.37780 | − | 0.913701i | 0.207528 | − | 0.0433136i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.4967i | 0.543776i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.33030 | 0.393131 | 0.196566 | − | 0.980491i | \(-0.437021\pi\) | ||||
0.196566 | + | 0.980491i | \(0.437021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 21.4955i | − | 1.01218i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.8745 | 0.745849 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.381401 | + | 1.82740i | 0.0178803 | + | 0.0856699i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1652i | 1.08362i | 0.840501 | + | 0.541810i | \(0.182261\pi\) | ||||
−0.840501 | + | 0.541810i | \(0.817739\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.58258i | − | 0.167220i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 25.3531i | − | 1.18081i | −0.807106 | − | 0.590406i | \(-0.798968\pi\) | ||
0.807106 | − | 0.590406i | \(-0.201032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.5909i | − | 1.83995i | −0.391982 | − | 0.919973i | \(-0.628210\pi\) | ||
0.391982 | − | 0.919973i | \(-0.371790\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.5826 | − | 2.41742i | 0.537129 | − | 0.112105i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1652 | 0.886857 | 0.443429 | − | 0.896310i | \(-0.353762\pi\) | ||||
0.443429 | + | 0.896310i | \(0.353762\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8564i | 0.639829i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.6983 | −0.999805 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.6697i | − | 1.18029i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | − | 18.3303i | −0.367065 | − | 0.841052i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.55040 | −0.116775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.7490 | 1.45065 | 0.725325 | − | 0.688407i | \(-0.241690\pi\) | ||||
0.725325 | + | 0.688407i | \(0.241690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.16515 | −0.326703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.27340 | + | 15.6838i | 0.148637 | + | 0.712165i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2523i | 0.917720i | 0.888509 | + | 0.458860i | \(0.151742\pi\) | ||||
−0.888509 | + | 0.458860i | \(0.848258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.7477i | 0.665556i | 0.943005 | + | 0.332778i | \(0.107986\pi\) | ||||
−0.943005 | + | 0.332778i | \(0.892014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.0942 | −1.26530 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.63670 | + | 7.84190i | 0.0735642 | + | 0.352467i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.33030i | 0.283953i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3303i | − | 0.820577i | −0.911956 | − | 0.410289i | \(-0.865428\pi\) | ||
0.911956 | − | 0.410289i | \(-0.134572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.6120i | 1.01023i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.2378i | 0.634832i | 0.948286 | + | 0.317416i | \(0.102815\pi\) | ||||
−0.948286 | + | 0.317416i | \(0.897185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.58258 | + | 36.3303i | 0.337420 | + | 1.61668i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1652 | 0.540273 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.22330i | − | 0.364492i | −0.983253 | − | 0.182246i | \(-0.941663\pi\) | ||
0.983253 | − | 0.182246i | \(-0.0583367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.9644 | 0.485037 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000i | 0.176604i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.58258 | − | 36.3303i | −0.334128 | − | 1.60090i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.8208 | −1.09162 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.3060 | 0.496279 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.6606 | 1.69375 | 0.846876 | − | 0.531791i | \(-0.178481\pi\) | ||||
0.846876 | + | 0.531791i | \(0.178481\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3303 | −0.801528 | −0.400764 | − | 0.916181i | \(-0.631255\pi\) | ||||
−0.400764 | + | 0.916181i | \(0.631255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.82740 | − | 4.18710i | −0.0797543 | − | 0.182740i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.9572i | 0.825789i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 7.58258i | − | 0.329056i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.48220 | −0.237461 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.75560 | + | 1.82740i | −0.378538 | + | 0.0790054i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7.58258i | − | 0.327212i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 22.0871i | − | 0.951360i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0652i | 0.690697i | 0.938474 | + | 0.345349i | \(0.112239\pi\) | ||||
−0.938474 | + | 0.345349i | \(0.887761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.75560i | 0.375739i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | − | 19.1652i | −0.171341 | − | 0.820945i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.4955 | −1.26113 | −0.630567 | − | 0.776135i | \(-0.717178\pi\) | ||||
−0.630567 | + | 0.776135i | \(0.717178\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.5830i | 0.451672i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.3676 | 1.33631 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.83485i | − | 0.205599i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.1652 | − | 3.58258i | 0.728620 | − | 0.152072i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.0616 | 0.850038 | 0.425019 | − | 0.905185i | \(-0.360267\pi\) | ||||
0.425019 | + | 0.905185i | \(0.360267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.54680 | −0.276900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8348 | −0.541888 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4955 | 1.07451 | 0.537253 | − | 0.843421i | \(-0.319462\pi\) | ||||
0.537253 | + | 0.843421i | \(0.319462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.01810 | − | 9.66930i | −0.0849022 | − | 0.406791i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.913701i | 0.0383718i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.330303 | −0.0138470 | −0.00692351 | − | 0.999976i | \(-0.502204\pi\) | ||||
−0.00692351 | + | 0.999976i | \(0.502204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.0000i | − | 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8564 | −0.578860 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.16515i | 0.131767i | 0.997827 | + | 0.0658835i | \(0.0209866\pi\) | ||||
−0.997827 | + | 0.0658835i | \(0.979013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.16515i | 0.131539i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 10.2016i | − | 0.423234i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.13701i | 0.378416i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | − | 0.417424i | 0.0826898 | − | 0.0172584i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.3303 | −1.74716 | −0.873579 | − | 0.486682i | \(-0.838207\pi\) | ||||
−0.873579 | + | 0.486682i | \(0.838207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.1660i | − | 0.872130i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5438 | −1.05073 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.91288i | − | 0.407073i | −0.979067 | − | 0.203537i | \(-0.934756\pi\) | ||
0.979067 | − | 0.203537i | \(-0.0652436\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.16515 | − | 1.49545i | 0.293743 | − | 0.0613076i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.63670 | −0.0669857 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.0942 | −1.14790 | −0.573949 | − | 0.818891i | \(-0.694589\pi\) | ||||
−0.573949 | + | 0.818891i | \(0.694589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.16515 | −0.210691 | −0.105345 | − | 0.994436i | \(-0.533595\pi\) | ||||
−0.105345 | + | 0.994436i | \(0.533595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.1652 | 0.617573 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.01630 | − | 0.838251i | 0.163286 | − | 0.0340798i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.28790i | − | 0.376984i | −0.982075 | − | 0.188492i | \(-0.939640\pi\) | ||
0.982075 | − | 0.188492i | \(-0.0603600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.16515 | 0.290347 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.33030i | 0.256097i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.1515 | −0.611964 | −0.305982 | − | 0.952037i | \(-0.598985\pi\) | ||||
−0.305982 | + | 0.952037i | \(0.598985\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.1334 | − | 2.74110i | 0.529590 | − | 0.110532i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.41742i | − | 0.177839i | −0.996039 | − | 0.0889194i | \(-0.971659\pi\) | ||
0.996039 | − | 0.0889194i | \(-0.0283414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 9.49545i | − | 0.381655i | −0.981624 | − | 0.190827i | \(-0.938883\pi\) | ||
0.981624 | − | 0.190827i | \(-0.0611170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.82740i | − | 0.0732133i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.0000 | − | 18.3303i | 0.680000 | − | 0.733212i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3303 | 0.572297 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.0942i | 1.12019i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.63670 | −0.0651560 | −0.0325780 | − | 0.999469i | \(-0.510372\pi\) | ||||
−0.0325780 | + | 0.999469i | \(0.510372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 11.1652i | − | 0.443775i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.74773 | + | 32.3303i | 0.267775 | + | 1.28299i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.63310 | −0.223192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.92820 | 0.274075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.3303 | 1.27697 | 0.638485 | − | 0.769634i | \(-0.279561\pi\) | ||||
0.638485 | + | 0.769634i | \(0.279561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.3303 | −0.722877 | −0.361438 | − | 0.932396i | \(-0.617714\pi\) | ||||
−0.361438 | + | 0.932396i | \(0.617714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.6838 | − | 3.27340i | 0.617549 | − | 0.128890i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6054i | 1.79293i | 0.443110 | + | 0.896467i | \(0.353875\pi\) | ||||
−0.443110 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1652 | −1.06633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.83485i | − | 0.189493i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.5438 | 0.999607 | 0.499803 | − | 0.866139i | \(-0.333406\pi\) | ||||
0.499803 | + | 0.866139i | \(0.333406\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.11890 | − | 34.1087i | −0.278159 | − | 1.33274i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 12.0000i | − | 0.468165i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.4174i | 0.639532i | 0.947497 | + | 0.319766i | \(0.103604\pi\) | ||||
−0.947497 | + | 0.319766i | \(0.896396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.6054i | 1.77385i | 0.461918 | + | 0.886923i | \(0.347161\pi\) | ||||
−0.461918 | + | 0.886923i | \(0.652839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.27340i | 0.127128i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | + | 1.66970i | −0.310227 | + | 0.0647481i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 0.913701i | − | 0.0353257i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.9144 | 1.46367 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0000i | 1.54189i | 0.636904 | + | 0.770943i | \(0.280215\pi\) | ||||
−0.636904 | + | 0.770943i | \(0.719785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.58258 | + | 2.00000i | −0.176383 | + | 0.0769800i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.3350 | −0.896837 | −0.448419 | − | 0.893824i | \(-0.648013\pi\) | ||||
−0.448419 | + | 0.893824i | \(0.648013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.54680 | 0.251243 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.16515 | 0.121289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.4955 | 1.89389 | 0.946945 | − | 0.321394i | \(-0.104151\pi\) | ||||
0.946945 | + | 0.321394i | \(0.104151\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.94630 | − | 42.8643i | −0.341821 | − | 1.63776i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.6120i | 0.862702i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.33030 | 0.0887775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6606i | 1.24247i | 0.783625 | + | 0.621234i | \(0.213368\pi\) | ||||
−0.783625 | + | 0.621234i | \(0.786632\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.27340 | 0.124346 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.10080 | − | 24.4394i | −0.193484 | − | 0.927040i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.4955i | 0.814198i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.5826i | 0.740681i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 40.6555i | − | 1.53554i | −0.640727 | − | 0.767769i | \(-0.721367\pi\) | ||
0.640727 | − | 0.767769i | \(-0.278633\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.3676i | − | 1.18305i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.16515 | − | 15.1652i | −0.119206 | − | 0.571153i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.1652 | 0.570344 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.10080i | 0.191565i | 0.995402 | + | 0.0957823i | \(0.0305353\pi\) | ||||
−0.995402 | + | 0.0957823i | \(0.969465\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.29150 | −0.198447 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.49545 | − | 7.16515i | −0.0559268 | − | 0.267961i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.1660 | 0.790459 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −52.1522 | −1.94495 | −0.972475 | − | 0.233008i | \(-0.925143\pi\) | ||||
−0.972475 | + | 0.233008i | \(0.925143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.1652 | −0.564780 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000 | 0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.6838 | + | 35.9361i | 0.582482 | + | 1.33463i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.1443i | 0.858375i | 0.903215 | + | 0.429187i | \(0.141200\pi\) | ||||
−0.903215 | + | 0.429187i | \(0.858800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.6697i | 0.949428i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5909 | 1.46232 | 0.731162 | − | 0.682204i | \(-0.238978\pi\) | ||||
0.731162 | + | 0.682204i | \(0.238978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.4949 | − | 2.81655i | 0.497767 | − | 0.103890i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 54.3303i | − | 2.00128i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 20.0000i | − | 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.65480i | − | 0.134263i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 26.6482i | − | 0.977628i | −0.872388 | − | 0.488814i | \(-0.837430\pi\) | ||
0.872388 | − | 0.488814i | \(-0.162570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.25227 | + | 25.1652i | 0.192428 | + | 0.921980i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.1652 | −0.408512 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.65480i | 0.133544i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4213 | −0.818165 | −0.409083 | − | 0.912497i | \(-0.634151\pi\) | ||||
−0.409083 | + | 0.912497i | \(0.634151\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 11.5826i | − | 0.422093i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 34.7477 | − | 7.25227i | 1.26460 | − | 0.263937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.9427 | −0.470411 | −0.235205 | − | 0.971946i | \(-0.575576\pi\) | ||||
−0.235205 | + | 0.971946i | \(0.575576\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0000 | −0.797499 | −0.398750 | − | 0.917060i | \(-0.630556\pi\) | ||||
−0.398750 | + | 0.917060i | \(0.630556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.00000 | −0.289619 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.63670 | − | 7.84190i | −0.0591750 | − | 0.283525i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92820i | 0.250163i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.4955 | −1.13576 | −0.567878 | − | 0.823113i | \(-0.692235\pi\) | ||||
−0.567878 | + | 0.823113i | \(0.692235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.74773i | 0.0989570i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5794 | 0.524385 | 0.262192 | − | 0.965016i | \(-0.415554\pi\) | ||||
0.262192 | + | 0.965016i | \(0.415554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.2487 | − | 10.5830i | 0.871039 | − | 0.380153i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.16515i | − | 0.257048i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.0000i | − | 0.859889i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 24.8208i | − | 0.888159i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 7.84190i | − | 0.280247i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.4955 | + | 9.91288i | −1.69519 | + | 0.353806i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0000 | −1.28326 | −0.641631 | − | 0.767014i | \(-0.721742\pi\) | ||||
−0.641631 | + | 0.767014i | \(0.721742\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.75560i | 0.311708i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.03620 | −0.143511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.66970i | − | 0.343381i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.58258 | + | 1.16515i | −0.197994 | + | 0.0413237i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.6084 | −0.942518 | −0.471259 | − | 0.881995i | \(-0.656200\pi\) | ||||
−0.471259 | + | 0.881995i | \(0.656200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.8208 | 0.878097 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.9909 | −1.51712 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.66930i | − | 0.340376i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.1652i | 0.672979i | 0.941687 | + | 0.336490i | \(0.109240\pi\) | ||||
−0.941687 | + | 0.336490i | \(0.890760\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.0761 | 0.914529 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.75560 | + | 1.82740i | −0.306695 | + | 0.0640111i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 28.6606i | − | 1.00271i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 0.834849i | − | 0.0291720i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 9.66930i | − | 0.337461i | −0.985662 | − | 0.168731i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168731i | \(-0.0539668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.7701i | 0.514854i | 0.966298 | + | 0.257427i | \(0.0828746\pi\) | ||||
−0.966298 | + | 0.257427i | \(0.917125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.16515 | + | 16.4174i | 0.249459 | + | 0.571581i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16.0652i | − | 0.557968i | −0.960296 | − | 0.278984i | \(-0.910002\pi\) | ||
0.960296 | − | 0.278984i | \(-0.0899976\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.7701 | −0.512369 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.0871i | 0.765273i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.3303 | + | 49.4955i | 0.357495 | + | 1.71286i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.29150 | −0.182901 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.4750 | −0.465209 | −0.232604 | − | 0.972571i | \(-0.574725\pi\) | ||||
−0.232604 | + | 0.972571i | \(0.574725\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.4955 | −1.12053 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.33030 | 0.149144 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.6283 | − | 5.55765i | 0.916042 | − | 0.191189i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.67650i | − | 0.0576053i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.16515 | 0.245907 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5257 | 0.805505 | 0.402753 | − | 0.915309i | \(-0.368054\pi\) | ||||
0.402753 | + | 0.915309i | \(0.368054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.82740 | + | 8.75560i | 0.0624958 | + | 0.299435i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.4174i | 0.697446i | 0.937226 | + | 0.348723i | \(0.113385\pi\) | ||||
−0.937226 | + | 0.348723i | \(0.886615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.1652i | 1.47278i | 0.676559 | + | 0.736388i | \(0.263470\pi\) | ||||
−0.676559 | + | 0.736388i | \(0.736530\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 5.48220i | − | 0.186833i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.20880i | 0.0751885i | 0.999293 | + | 0.0375942i | \(0.0119694\pi\) | ||||
−0.999293 | + | 0.0375942i | \(0.988031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.7477 | − | 5.16515i | 0.841448 | − | 0.175620i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.16515 | −0.141456 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.9572i | 0.643079i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.8564 | −0.469506 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.16515i | − | 0.242504i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.91288 | − | 8.33030i | −0.199892 | − | 0.281616i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.8933 | −1.85362 | −0.926808 | − | 0.375536i | \(-0.877459\pi\) | ||||
−0.926808 | + | 0.375536i | \(0.877459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.37780 | 0.147660 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.330303 | −0.0111282 | −0.00556409 | − | 0.999985i | \(-0.501771\pi\) | ||||
−0.00556409 | + | 0.999985i | \(0.501771\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.33030 | −0.0784209 | −0.0392105 | − | 0.999231i | \(-0.512484\pi\) | ||||
−0.0392105 | + | 0.999231i | \(0.512484\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.46410 | − | 16.5975i | −0.116445 | − | 0.557919i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.3024i | 0.513805i | 0.966437 | + | 0.256902i | \(0.0827018\pi\) | ||||
−0.966437 | + | 0.256902i | \(0.917298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4955 | 0.452623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.58258i | − | 0.120021i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.7128 | −0.927374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.46410 | − | 16.5975i | −0.115792 | − | 0.554794i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.4955i | 1.38395i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.13701i | − | 0.304398i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 6.54680i | − | 0.217864i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.00000 | + | 19.1652i | 0.132964 | + | 0.637071i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.4955 | −1.24502 | −0.622508 | − | 0.782613i | \(-0.713886\pi\) | ||||
−0.622508 | + | 0.782613i | \(0.713886\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 16.5975i | − | 0.550505i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.0224 | −1.16034 | −0.580172 | − | 0.814494i | \(-0.697015\pi\) | ||||
−0.580172 | + | 0.814494i | \(0.697015\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.0000i | 1.32381i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.83485 | + | 23.1652i | 0.159835 | + | 0.765816i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.2378 | −0.470174 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.5873 | −1.43781 | −0.718907 | − | 0.695107i | \(-0.755357\pi\) | ||||
−0.718907 | + | 0.695107i | \(0.755357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | −0.131804 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.33030 | −0.208364 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.9361 | − | 15.6838i | 1.18157 | − | 0.515680i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.5975i | 0.545134i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.6606 | −1.39965 | −0.699825 | − | 0.714315i | \(-0.746738\pi\) | ||||
−0.699825 | + | 0.714315i | \(0.746738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 24.6606i | − | 0.808219i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5112 | −0.573291 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.0942 | + | 5.86360i | −0.918779 | + | 0.191760i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.3303i | − | 0.729499i | −0.931106 | − | 0.364750i | \(-0.881155\pi\) | ||
0.931106 | − | 0.364750i | \(-0.118845\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.1652i | 0.625431i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 44.3103i | − | 1.44448i | −0.691645 | − | 0.722238i | \(-0.743114\pi\) | ||
0.691645 | − | 0.722238i | \(-0.256886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.417424 | + | 2.00000i | 0.0135788 | + | 0.0650600i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.0000 | −1.68977 | −0.844886 | − | 0.534946i | \(-0.820332\pi\) | ||||
−0.844886 | + | 0.534946i | \(0.820332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.9644i | 0.355920i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.93180 | 0.0950702 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56.2432i | − | 1.82190i | −0.412522 | − | 0.910948i | \(-0.635352\pi\) | ||
0.412522 | − | 0.910948i | \(-0.364648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.3303 | + | 6.33030i | −0.981466 | + | 0.204844i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.0942 | −0.908157 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.8926 | −0.577782 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.00000 | −0.0967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.44600 | + | 6.92820i | 0.0465484 | + | 0.223027i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.1153i | 0.357444i | 0.983900 | + | 0.178722i | \(0.0571963\pi\) | ||||
−0.983900 | + | 0.178722i | \(0.942804\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3303 | −0.460356 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.9129i | 1.60178i | 0.598811 | + | 0.800890i | \(0.295640\pi\) | ||||
−0.598811 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2016 | −0.327048 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.18710 | − | 1.82740i | 0.134095 | − | 0.0585237i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 34.7477i | − | 1.11168i | −0.831290 | − | 0.555839i | \(-0.812397\pi\) | ||
0.831290 | − | 0.555839i | \(-0.187603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.16515i | 0.228999i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.75560i | 0.279545i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 50.7062i | − | 1.61728i | −0.588306 | − | 0.808639i | \(-0.700205\pi\) | ||
0.588306 | − | 0.808639i | \(-0.299795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −55.9129 | + | 11.6697i | −1.78153 | + | 0.371827i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.33030 | −0.201496 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5873 | 1.38460 | 0.692298 | − | 0.721611i | \(-0.256598\pi\) | ||||
0.692298 | + | 0.721611i | \(0.256598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.3303i | 0.835567i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.58258 | + | 0.747727i | −0.113575 | + | 0.0237045i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2095 | −1.24178 | −0.620889 | − | 0.783899i | \(-0.713228\pi\) | ||||
−0.620889 | + | 0.783899i | \(0.713228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.84190 | −0.248107 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))