Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(49,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, 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("2400.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.40680 + 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.49 |
Dual form | 2400.2.d.f.49.5 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.62721i | − 1.37096i | −0.728093 | − | 0.685479i | \(-0.759593\pi\) | ||||
0.728093 | − | 0.685479i | \(-0.240407\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.20555i | 1.87104i | 0.353269 | + | 0.935522i | \(0.385070\pi\) | ||||
−0.353269 | + | 0.935522i | \(0.614930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.578337 | −0.160402 | −0.0802009 | − | 0.996779i | \(-0.525556\pi\) | ||||
−0.0802009 | + | 0.996779i | \(0.525556\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.42166i | − 0.344804i | −0.985027 | − | 0.172402i | \(-0.944847\pi\) | ||||
0.985027 | − | 0.172402i | \(-0.0551528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.62721i | 1.29097i | 0.763772 | + | 0.645486i | \(0.223345\pi\) | ||||
−0.763772 | + | 0.645486i | \(0.776655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 3.62721i | − 0.791523i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.62721i | 1.17336i | 0.809821 | + | 0.586678i | \(0.199564\pi\) | ||||
−0.809821 | + | 0.586678i | \(0.800436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.57834 | 0.463083 | 0.231542 | − | 0.972825i | \(-0.425623\pi\) | ||||
0.231542 | + | 0.972825i | \(0.425623\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.20555i | 1.08025i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.83276 | 1.28770 | 0.643849 | − | 0.765152i | \(-0.277336\pi\) | ||||
0.643849 | + | 0.765152i | \(0.277336\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.578337 | −0.0926081 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.25443 | 0.820603 | 0.410302 | − | 0.911950i | \(-0.365423\pi\) | ||||
0.410302 | + | 0.911950i | \(0.365423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.25443 | 1.10629 | 0.553145 | − | 0.833085i | \(-0.313428\pi\) | ||||
0.553145 | + | 0.833085i | \(0.313428\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.78389i | 0.989532i | 0.869026 | + | 0.494766i | \(0.164746\pi\) | ||||
−0.869026 | + | 0.494766i | \(0.835254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.15667 | −0.879525 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 1.42166i | − 0.199073i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.62721i | 0.745343i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.20555i | 0.287138i | 0.989640 | + | 0.143569i | \(0.0458579\pi\) | ||||
−0.989640 | + | 0.143569i | \(0.954142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 12.4111i | − 1.58908i | −0.607213 | − | 0.794539i | \(-0.707712\pi\) | ||||
0.607213 | − | 0.794539i | \(-0.292288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.62721i | − 0.456986i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.62721i | 0.677437i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.41110 | −0.998214 | −0.499107 | − | 0.866540i | \(-0.666339\pi\) | ||||
−0.499107 | + | 0.866540i | \(0.666339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.00000i | − 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.5089 | 2.56512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.42166 | 0.609985 | 0.304992 | − | 0.952355i | \(-0.401346\pi\) | ||||
0.304992 | + | 0.952355i | \(0.401346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.25443 | −0.357220 | −0.178610 | − | 0.983920i | \(-0.557160\pi\) | ||||
−0.178610 | + | 0.983920i | \(0.557160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000i | 0.214423i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2544 | 1.40497 | 0.702483 | − | 0.711700i | \(-0.252075\pi\) | ||||
0.702483 | + | 0.711700i | \(0.252075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09775i | 0.219904i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.57834 | 0.267361 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 4.84333i | − 0.491765i | −0.969300 | − | 0.245883i | \(-0.920922\pi\) | ||||
0.969300 | − | 0.245883i | \(-0.0790778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.20555i | 0.623681i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.47054i | − 0.243429i | −0.992565 | − | 0.121715i | \(-0.961161\pi\) | ||||
0.992565 | − | 0.121715i | \(-0.0388393\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.0978 | 1.36288 | 0.681441 | − | 0.731873i | \(-0.261354\pi\) | ||||
0.681441 | + | 0.731873i | \(0.261354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.25443i | 0.694848i | 0.937708 | + | 0.347424i | \(0.112944\pi\) | ||||
−0.937708 | + | 0.347424i | \(0.887056\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.83276 | 0.743453 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 9.08719i | − 0.854851i | −0.904051 | − | 0.427425i | \(-0.859421\pi\) | ||||
0.904051 | − | 0.427425i | \(-0.140579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.578337 | −0.0534673 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.15667 | −0.472712 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.5089 | −2.50080 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.25443 | 0.473776 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.4705i | − 0.929110i | −0.885544 | − | 0.464555i | \(-0.846214\pi\) | ||||
0.885544 | − | 0.464555i | \(-0.153786\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.25443 | 0.638717 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 13.4600i | − 1.17600i | −0.808860 | − | 0.588002i | \(-0.799915\pi\) | ||||
0.808860 | − | 0.588002i | \(-0.200085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4111 | 1.76987 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5783i | 0.903768i | 0.892077 | + | 0.451884i | \(0.149248\pi\) | ||||
−0.892077 | + | 0.451884i | \(0.850752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4705i | 1.05774i | 0.848704 | + | 0.528869i | \(0.177384\pi\) | ||||
−0.848704 | + | 0.528869i | \(0.822616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.78389i | 0.571306i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.58890i | − 0.300119i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.15667 | −0.507794 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6761 | −1.03157 | −0.515783 | − | 0.856719i | \(-0.672499\pi\) | ||||
−0.515783 | + | 0.856719i | \(0.672499\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 1.42166i | − 0.114935i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.32391 | 0.105660 | 0.0528298 | − | 0.998604i | \(-0.483176\pi\) | ||||
0.0528298 | + | 0.998604i | \(0.483176\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.4111 | 1.60862 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.2544 | −1.19482 | −0.597409 | − | 0.801936i | \(-0.703803\pi\) | ||||
−0.597409 | + | 0.801936i | \(0.703803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7839i | 0.834482i | 0.908796 | + | 0.417241i | \(0.137003\pi\) | ||||
−0.908796 | + | 0.417241i | \(0.862997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6655 | −0.974271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.62721i | 0.430324i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.6655 | 1.03897 | 0.519485 | − | 0.854479i | \(-0.326124\pi\) | ||||
0.519485 | + | 0.854479i | \(0.326124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.20555i | 0.165779i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.04888i | 0.676345i | 0.941084 | + | 0.338172i | \(0.109809\pi\) | ||||
−0.941084 | + | 0.338172i | \(0.890191\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.2544i | 1.72849i | 0.503073 | + | 0.864244i | \(0.332203\pi\) | ||||
−0.503073 | + | 0.864244i | \(0.667797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 12.4111i | − 0.917455i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.82220 | 0.645143 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 3.62721i | − 0.263841i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.6655i | 1.84745i | 0.383062 | + | 0.923723i | \(0.374869\pi\) | ||||
−0.383062 | + | 0.923723i | \(0.625131\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1567 | −1.07987 | −0.539934 | − | 0.841707i | \(-0.681551\pi\) | ||||
−0.539934 | + | 0.841707i | \(0.681551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.6761 | −1.46569 | −0.732845 | − | 0.680396i | \(-0.761808\pi\) | ||||
−0.732845 | + | 0.680396i | \(0.761808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.25443 | 0.509161 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.62721i | 0.391118i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.9200 | −2.41546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2.03831i | − 0.140323i | −0.997536 | − | 0.0701616i | \(-0.977648\pi\) | ||||
0.997536 | − | 0.0701616i | \(-0.0223515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.41110 | −0.576319 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 9.35218i | − 0.634867i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.00000i | − 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.822200i | 0.0553072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.21611i | 0.483227i | 0.970373 | + | 0.241613i | \(0.0776766\pi\) | ||||
−0.970373 | + | 0.241613i | \(0.922323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.15667 | 0.0767712 | 0.0383856 | − | 0.999263i | \(-0.487778\pi\) | ||||
0.0383856 | + | 0.999263i | \(0.487778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0978i | 0.931606i | 0.884889 | + | 0.465803i | \(0.154234\pi\) | ||||
−0.884889 | + | 0.465803i | \(0.845766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.5089 | 1.48097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.5783i | − 0.955059i | −0.878616 | − | 0.477529i | \(-0.841532\pi\) | ||||
0.878616 | − | 0.477529i | \(-0.158468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.42166 | 0.352175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2544 | 1.24547 | 0.622733 | − | 0.782435i | \(-0.286022\pi\) | ||||
0.622733 | + | 0.782435i | \(0.286022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6655 | −0.880274 | −0.440137 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440137 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.25443i | − 0.207074i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.25443 | −0.206241 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 7.14663i | − 0.451091i | −0.974233 | − | 0.225546i | \(-0.927584\pi\) | ||||
0.974233 | − | 0.225546i | \(-0.0724165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.9200 | −2.19540 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.73501i | − 0.482497i | −0.970463 | − | 0.241248i | \(-0.922443\pi\) | ||||
0.970463 | − | 0.241248i | \(-0.0775568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 28.4111i | − 1.76538i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000i | 0.123797i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.7839i | 1.15826i | 0.815234 | + | 0.579132i | \(0.196608\pi\) | ||||
−0.815234 | + | 0.579132i | \(0.803392\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2544 | 0.811158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.50885i | 0.518794i | 0.965771 | + | 0.259397i | \(0.0835238\pi\) | ||||
−0.965771 | + | 0.259397i | \(0.916476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9894 | −1.88247 | −0.941237 | − | 0.337746i | \(-0.890335\pi\) | ||||
−0.941237 | + | 0.337746i | \(0.890335\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.09775i | 0.126962i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.51941 | −0.571966 | −0.285983 | − | 0.958235i | \(-0.592320\pi\) | ||||
−0.285983 | + | 0.958235i | \(0.592320\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.57834 | 0.154361 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6655 | 0.815217 | 0.407608 | − | 0.913157i | \(-0.366363\pi\) | ||||
0.407608 | + | 0.913157i | \(0.366363\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 19.0589i | − 1.12501i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9789 | 0.881110 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.84333i | − 0.283921i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.31335 | −0.251989 | −0.125994 | − | 0.992031i | \(-0.540212\pi\) | ||||
−0.125994 | + | 0.992031i | \(0.540212\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.20555i | 0.360083i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3.25443i | − 0.188208i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 26.3133i | − 1.51668i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000i | 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5678 | 1.45923 | 0.729615 | − | 0.683858i | \(-0.239699\pi\) | ||||
0.729615 | + | 0.683858i | \(0.239699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 2.47054i | − 0.140544i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0766 | 1.13844 | 0.569221 | − | 0.822185i | \(-0.307245\pi\) | ||||
0.569221 | + | 0.822185i | \(0.307245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.15667i | 0.404519i | 0.979332 | + | 0.202260i | \(0.0648285\pi\) | ||||
−0.979332 | + | 0.202260i | \(0.935172\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.1744 | −1.35777 | −0.678884 | − | 0.734245i | \(-0.737536\pi\) | ||||
−0.678884 | + | 0.734245i | \(0.737536\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.4111 | −0.694888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0978 | 0.786860 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.25443i | 0.401171i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.6066 | 1.35661 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 27.1950i | − 1.49477i | −0.664390 | − | 0.747386i | \(-0.731309\pi\) | ||||
0.664390 | − | 0.747386i | \(-0.268691\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.83276 | 0.429233 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 22.8222i | − 1.24320i | −0.783333 | − | 0.621602i | \(-0.786482\pi\) | ||||
0.783333 | − | 0.621602i | \(-0.213518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 9.08719i | − 0.493548i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.05892i | − 0.165166i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.6655 | −1.27043 | −0.635216 | − | 0.772335i | \(-0.719089\pi\) | ||||
−0.635216 | + | 0.772335i | \(0.719089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 34.9200i | − 1.86922i | −0.355671 | − | 0.934611i | \(-0.615748\pi\) | ||||
0.355671 | − | 0.934611i | \(-0.384252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.578337 | −0.0308694 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.9305i | − 0.847896i | −0.905687 | − | 0.423948i | \(-0.860644\pi\) | ||||
0.905687 | − | 0.423948i | \(-0.139356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.15667 | −0.272920 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.41110 | 0.443921 | 0.221960 | − | 0.975056i | \(-0.428754\pi\) | ||||
0.221960 | + | 0.975056i | \(0.428754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6655 | −0.666607 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.5089 | −1.44384 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 24.4494i | − 1.27625i | −0.769933 | − | 0.638124i | \(-0.779711\pi\) | ||||
0.769933 | − | 0.638124i | \(-0.220289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.25443 | 0.273534 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.25443i | 0.376631i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.167237 | −0.00865920 | −0.00432960 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432960 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.15667i | − 0.0595718i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 7.72496i | − 0.396805i | −0.980121 | − | 0.198402i | \(-0.936425\pi\) | ||||
0.980121 | − | 0.198402i | \(-0.0635753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 10.4705i | − 0.536422i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.62721i | 0.0831467i | 0.999135 | + | 0.0415734i | \(0.0132370\pi\) | ||||
−0.999135 | + | 0.0415734i | \(0.986763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.25443 | 0.368763 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3133i | 0.624312i | 0.950031 | + | 0.312156i | \(0.101051\pi\) | ||||
−0.950031 | + | 0.312156i | \(0.898949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 13.4600i | − 0.678966i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0872 | 0.957959 | 0.478979 | − | 0.877826i | \(-0.341007\pi\) | ||||
0.478979 | + | 0.877826i | \(0.341007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.4111 | 1.02183 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4111 | −0.719656 | −0.359828 | − | 0.933019i | \(-0.617165\pi\) | ||||
−0.359828 | + | 0.933019i | \(0.617165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.49115 | −0.0742794 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.6066i | 2.40934i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.31335 | 0.411069 | 0.205534 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205534 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5783i | 0.521791i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4705i | 0.610685i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.36222i | 0.359668i | 0.983697 | + | 0.179834i | \(0.0575561\pi\) | ||||
−0.983697 | + | 0.179834i | \(0.942444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0978i | 1.46687i | 0.679757 | + | 0.733437i | \(0.262085\pi\) | ||||
−0.679757 | + | 0.733437i | \(0.737915\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.78389i | 0.329844i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.0177 | −2.17856 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3.58890i | − 0.173274i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.41110 | −0.405148 | −0.202574 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202574 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 4.31335i | − 0.207286i | −0.994615 | − | 0.103643i | \(-0.966950\pi\) | ||||
0.994615 | − | 0.103643i | \(-0.0330500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.6655 | −1.51477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.83276 | 0.469292 | 0.234646 | − | 0.972081i | \(-0.424607\pi\) | ||||
0.234646 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.15667 | −0.293175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3522 | −1.01447 | −0.507236 | − | 0.861807i | \(-0.669333\pi\) | ||||
−0.507236 | + | 0.861807i | \(0.669333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.00000i | 0.0945968i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.3133 | 0.958646 | 0.479323 | − | 0.877639i | \(-0.340882\pi\) | ||||
0.479323 | + | 0.877639i | \(0.340882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.6066i | 1.53539i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6761 | −0.595575 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.35218i | 0.156808i | 0.996922 | + | 0.0784041i | \(0.0249825\pi\) | ||||
−0.996922 | + | 0.0784041i | \(0.975018\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1.42166i | − 0.0663575i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 28.5089i | − 1.32779i | −0.747826 | − | 0.663895i | \(-0.768902\pi\) | ||||
0.747826 | − | 0.663895i | \(-0.231098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.6272i | − 1.09805i | −0.835806 | − | 0.549025i | \(-0.814999\pi\) | ||||
0.835806 | − | 0.549025i | \(-0.185001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.5678 | −1.36823 | −0.684117 | − | 0.729373i | \(-0.739812\pi\) | ||||
−0.684117 | + | 0.729373i | \(0.739812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 14.5089i | − 0.669957i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32391 | 0.0610026 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.0177i | 2.06992i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.0978 | −1.00967 | −0.504836 | − | 0.863215i | \(-0.668447\pi\) | ||||
−0.504836 | + | 0.863215i | \(0.668447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.52998 | −0.206549 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.4111 | 0.928737 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.03831i | 0.182993i | 0.995805 | + | 0.0914967i | \(0.0291651\pi\) | ||||
−0.995805 | + | 0.0914967i | \(0.970835\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.2544 | −0.689829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2056i | 0.821605i | 0.911724 | + | 0.410802i | \(0.134751\pi\) | ||||
−0.911724 | + | 0.410802i | \(0.865249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.84333 | 0.128057 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.5089i | 1.36851i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 0.0594386i | − 0.00266084i | −0.999999 | − | 0.00133042i | \(-0.999577\pi\) | ||||
0.999999 | − | 0.00133042i | \(-0.000423486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7839i | 0.481789i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.03831i | − 0.0908839i | −0.998967 | − | 0.0454419i | \(-0.985530\pi\) | ||||
0.998967 | − | 0.0454419i | \(-0.0144696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6655 | −0.562496 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 40.7044i | − 1.80419i | −0.431539 | − | 0.902094i | \(-0.642029\pi\) | ||||
0.431539 | − | 0.902094i | \(-0.357971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.7633 | −0.962751 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.62721i | 0.248448i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.0978 | −1.85146 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6655 | 0.599850 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0000 | 0.438108 | 0.219054 | − | 0.975713i | \(-0.429703\pi\) | ||||
0.219054 | + | 0.975713i | \(0.429703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3311 | −1.54492 | −0.772460 | − | 0.635064i | \(-0.780974\pi\) | ||||
−0.772460 | + | 0.635064i | \(0.780974\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.66553i | − 0.159673i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.66553 | −0.376762 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.20555i | 0.0957127i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.03883 | −0.131626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.04888i | 0.390488i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 38.2056i | − 1.64563i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.05892i | − 0.131513i | −0.997836 | − | 0.0657567i | \(-0.979054\pi\) | ||||
0.997836 | − | 0.0657567i | \(-0.0209461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.2544i | 0.997943i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0766 | −1.37150 | −0.685749 | − | 0.727838i | \(-0.740525\pi\) | ||||
−0.685749 | + | 0.727838i | \(0.740525\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 12.4111i | − 0.529693i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2544 | −0.479455 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 19.6655i | − 0.836263i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.6655 | 1.42645 | 0.713227 | − | 0.700933i | \(-0.247233\pi\) | ||||
0.713227 | + | 0.700933i | \(0.247233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.19550 | −0.177451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.82220 | 0.372474 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.35218 | 0.225567 | 0.112784 | − | 0.993620i | \(-0.464023\pi\) | ||||
0.112784 | + | 0.993620i | \(0.464023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 3.62721i | − 0.152329i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.58890 | −0.234299 | −0.117149 | − | 0.993114i | \(-0.537376\pi\) | ||||
−0.117149 | + | 0.993114i | \(0.537376\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 10.3728i | − 0.434088i | −0.976162 | − | 0.217044i | \(-0.930359\pi\) | ||||
0.976162 | − | 0.217044i | \(-0.0696414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 21.6655i | − 0.901948i | −0.892537 | − | 0.450974i | \(-0.851077\pi\) | ||||
0.892537 | − | 0.450974i | \(-0.148923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.6655i | 1.06662i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8045i | 0.489733i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 12.4111i | − 0.514015i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.90225 | 0.0785142 | 0.0392571 | − | 0.999229i | \(-0.487501\pi\) | ||||
0.0392571 | + | 0.999229i | \(0.487501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.5089i | 0.597827i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.1567 | −0.623462 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.57834i | − 0.105880i | −0.998598 | − | 0.0529398i | \(-0.983141\pi\) | ||||
0.998598 | − | 0.0529398i | \(-0.0168591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6761 | −0.846216 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.7244 | 1.09193 | 0.545966 | − | 0.837808i | \(-0.316163\pi\) | ||||
0.545966 | + | 0.837808i | \(0.316163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3311 | 1.35960 | 0.679801 | − | 0.733397i | \(-0.262066\pi\) | ||||
0.679801 | + | 0.733397i | \(0.262066\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 21.9406i | − 0.890540i | −0.895396 | − | 0.445270i | \(-0.853108\pi\) | ||||
0.895396 | − | 0.445270i | \(-0.146892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.25443 | 0.293964 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 3.92337i | − 0.158723i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.42166 | −0.138200 | −0.0690998 | − | 0.997610i | \(-0.522013\pi\) | ||||
−0.0690998 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 19.7350i | − 0.794502i | −0.917710 | − | 0.397251i | \(-0.869964\pi\) | ||||
0.917710 | − | 0.397251i | \(-0.130036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4705i | 0.822780i | 0.911459 | + | 0.411390i | \(0.134957\pi\) | ||||
−0.911459 | + | 0.411390i | \(0.865043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.62721i | 0.225812i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 48.0766i | − 1.92615i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −34.9200 | −1.39457 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 11.1355i | − 0.444003i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.08719 | −0.0432803 | −0.0216402 | − | 0.999766i | \(-0.506889\pi\) | ||||
−0.0216402 | + | 0.999766i | \(0.506889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 2.03831i | − 0.0810157i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.56063 | 0.141077 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.41110 | −0.332738 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.9789 | −1.10510 | −0.552550 | − | 0.833480i | \(-0.686345\pi\) | ||||
−0.552550 | + | 0.833480i | \(0.686345\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.94108 | 0.194857 | 0.0974285 | − | 0.995243i | \(-0.468938\pi\) | ||||
0.0974285 | + | 0.995243i | \(0.468938\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 49.3694i | − 1.94091i | −0.241282 | − | 0.970455i | \(-0.577568\pi\) | ||||
0.241282 | − | 0.970455i | \(-0.422432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6867 | −0.537248 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 9.35218i | − 0.366541i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.1744 | −1.57214 | −0.786072 | − | 0.618134i | \(-0.787889\pi\) | ||||
−0.786072 | + | 0.618134i | \(0.787889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 6.00000i | − 0.234082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 21.1255i | − 0.822933i | −0.911425 | − | 0.411466i | \(-0.865017\pi\) | ||||
0.911425 | − | 0.411466i | \(-0.134983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 10.9200i | − 0.424737i | −0.977190 | − | 0.212368i | \(-0.931882\pi\) | ||||
0.977190 | − | 0.212368i | \(-0.0681177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.822200i | 0.0319316i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2544 | −0.435773 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.21611i | 0.278991i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 77.0177 | 2.97324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 18.0000i | − 0.693849i | −0.937893 | − | 0.346925i | \(-0.887226\pi\) | ||||
0.937893 | − | 0.346925i | \(-0.112774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.4877 | 1.17174 | 0.585869 | − | 0.810406i | \(-0.300753\pi\) | ||||
0.585869 | + | 0.810406i | \(0.300753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5678 | −0.674189 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.15667 | 0.0443239 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.2544 | −1.34897 | −0.674487 | − | 0.738287i | \(-0.735635\pi\) | ||||
−0.674487 | + | 0.738287i | \(0.735635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0978i | 0.537863i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.15667 | 0.0440658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1361i | 1.07035i | 0.844742 | + | 0.535173i | \(0.179754\pi\) | ||||
−0.844742 | + | 0.535173i | \(0.820246\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.5089 | 0.855041 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 7.47002i | − 0.282947i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 14.5783i | − 0.551403i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 34.8222i | − 1.31522i | −0.753360 | − | 0.657608i | \(-0.771568\pi\) | ||||
0.753360 | − | 0.657608i | \(-0.228432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.0766i | 1.66238i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.25443 | 0.272831 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.58890i | 0.285007i | 0.989794 | + | 0.142504i | \(0.0455152\pi\) | ||||
−0.989794 | + | 0.142504i | \(0.954485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.42166 | 0.203328 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.5089i | 0.543361i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.2544 | 0.719070 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.66553 | −0.136701 | −0.0683505 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683505 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.96117 | −0.333731 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.6655 | −0.508226 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 36.1149i | − 1.33943i | −0.742619 | − | 0.669714i | \(-0.766416\pi\) | ||||
0.742619 | − | 0.669714i | \(-0.233584\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 10.3133i | − 0.381453i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0071 | 1.25608 | 0.628041 | − | 0.778180i | \(-0.283857\pi\) | ||||
0.628041 | + | 0.778180i | \(0.283857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.8222i | 0.914338i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 52.0172i | − 1.91348i | −0.290939 | − | 0.956742i | \(-0.593968\pi\) | ||||
0.290939 | − | 0.956742i | \(-0.406032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 3.25443i | − 0.119554i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.3139i | 0.855303i | 0.903944 | + | 0.427651i | \(0.140659\pi\) | ||||
−0.903944 | + | 0.427651i | \(0.859341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.25443 | −0.119073 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 51.1355i | − 1.86845i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.1083 | −0.405348 | −0.202674 | − | 0.979246i | \(-0.564963\pi\) | ||||
−0.202674 | + | 0.979246i | \(0.564963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 7.14663i | − 0.260438i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3239 | −0.484266 | −0.242133 | − | 0.970243i | \(-0.577847\pi\) | ||||
−0.242133 | + | 0.970243i | \(0.577847\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.9200 | −1.26751 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1355 | −0.621163 | −0.310582 | − | 0.950547i | \(-0.600524\pi\) | ||||
−0.310582 | + | 0.950547i | \(0.600524\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.3133 | 0.952607 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.27555i | − 0.0460575i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.47002 | −0.197254 | −0.0986270 | − | 0.995124i | \(-0.531445\pi\) | ||||
−0.0986270 | + | 0.995124i | \(0.531445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 7.73501i | − 0.278570i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.15667 | −0.113538 | −0.0567688 | − | 0.998387i | \(-0.518080\pi\) | ||||
−0.0567688 | + | 0.998387i | \(0.518080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 28.4111i | − 1.01924i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.5678i | 1.05938i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 52.1955i | − 1.86770i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1355 | 1.10986 | 0.554931 | − | 0.831896i | \(-0.312745\pi\) | ||||
0.554931 | + | 0.831896i | \(0.312745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.7839i | 0.668724i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.9612 | −1.17196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.17780i | 0.254891i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0000 | 0.354218 | 0.177109 | − | 0.984191i | \(-0.443325\pi\) | ||||
0.177109 | + | 0.984191i | \(0.443325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.64440 | 0.341194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.2544 | 0.468322 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.2333 | 1.31393 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.50885i | 0.299526i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.0388 | −1.02095 | −0.510475 | − | 0.859892i | \(-0.670531\pi\) | ||||
−0.510475 | + | 0.859892i | \(0.670531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.58838i | 0.0908904i | 0.998967 | + | 0.0454452i | \(0.0144706\pi\) | ||||
−0.998967 | + | 0.0454452i | \(0.985529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.9894 | −1.08685 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.8222i | 1.42819i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.09775i | 0.0733014i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.1955i | 1.33303i | 0.745491 | + | 0.666516i | \(0.232215\pi\) | ||||
−0.745491 | + | 0.666516i | \(0.767785\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.3517i | 0.639699i | 0.947468 | + | 0.319849i | \(0.103632\pi\) | ||||
−0.947468 | + | 0.319849i | \(0.896368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 24.7456i | − 0.859449i | −0.902960 | − | 0.429725i | \(-0.858611\pi\) | ||||
0.902960 | − | 0.429725i | \(-0.141389\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.51941 | −0.330225 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.75272i | 0.303264i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.57834 | 0.0891204 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.4288 | −1.84457 | −0.922284 | − | 0.386514i | \(-0.873679\pi\) | ||||
−0.922284 | + | 0.386514i | \(0.873679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.6655 | 0.470666 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 99.7805i | 3.42850i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.0000 | 0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.0766i | 1.51093i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0661 | −0.995203 | −0.497602 | − | 0.867406i | \(-0.665786\pi\) | ||||
−0.497602 | + | 0.867406i | \(0.665786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.2439i | 0.349924i | 0.984575 | + | 0.174962i | \(0.0559802\pi\) | ||||
−0.984575 | + | 0.174962i | \(0.944020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9794i | 0.374612i | 0.982302 | + | 0.187306i | \(0.0599756\pi\) | ||||
−0.982302 | + | 0.187306i | \(0.940024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 19.0589i | − 0.649526i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 38.8605i | − 1.32283i | −0.750021 | − | 0.661414i | \(-0.769957\pi\) | ||||
0.750021 | − | 0.661414i | \(-0.230043\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.9789 | 0.508709 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.6444i | 1.14131i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31335 | −0.0783848 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 4.84333i | − 0.163922i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3416 | 0.754423 | 0.377211 | − | 0.926127i | \(-0.376883\pi\) | ||||
0.377211 | + | 0.926127i | \(0.376883\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.31335 | −0.145486 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.88112 | 0.332903 | 0.166452 | − | 0.986050i | \(-0.446769\pi\) | ||||
0.166452 | + | 0.986050i | \(0.446769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6277 | −0.357652 | −0.178826 | − | 0.983881i | \(-0.557230\pi\) | ||||
−0.178826 | + | 0.983881i | \(0.557230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6061i | 0.389694i | 0.980834 | + | 0.194847i | \(0.0624211\pi\) | ||||
−0.980834 | + | 0.194847i | \(0.937579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.9789 | −1.27377 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.20555i | 0.207894i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.1744 | −1.27746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.25443i | − 0.108662i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.15667i | 0.171985i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.84333i | 0.0947249i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 26.3133i | − 0.875653i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.195504 | 0.00649159 | 0.00324580 | − | 0.999995i | \(-0.498967\pi\) | ||||
0.00324580 | + | 0.999995i | \(0.498967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000i | 0.0663358i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.88112 | 0.261113 | 0.130557 | − | 0.991441i | \(-0.458324\pi\) | ||||
0.130557 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 20.1955i | − 0.668374i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.8222 | −1.61225 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.75614 | 0.321825 | 0.160913 | − | 0.986969i | \(-0.448556\pi\) | ||||
0.160913 | + | 0.986969i | \(0.448556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.5678 | 0.842487 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.86445 | 0.160115 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.47054i | − 0.0811431i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.82220 | −0.223829 | −0.111915 | − | 0.993718i | \(-0.535698\pi\) | ||||
−0.111915 | + | 0.993718i | \(0.535698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 34.6449i | − 1.13544i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.0766 | 0.657279 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 57.5266i | − 1.87931i | −0.342123 | − | 0.939655i | \(-0.611146\pi\) | ||||
0.342123 | − | 0.939655i | \(-0.388854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.15667i | 0.233549i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.508852i | 0.0165881i | 0.999966 | + | 0.00829405i | \(0.00264011\pi\) | ||||
−0.999966 | + | 0.00829405i | \(0.997360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.5678i | 0.962859i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.68665 | 0.0548088 | 0.0274044 | − | 0.999624i | \(-0.491276\pi\) | ||||
0.0274044 | + | 0.999624i | \(0.491276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.47002i | 0.112642i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.1744 | −0.783908 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.22616i | 0.298865i | 0.988772 | + | 0.149432i | \(0.0477446\pi\) | ||||
−0.988772 | + | 0.149432i | \(0.952255\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.4111 | −0.401194 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.3699 | 1.23903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3522 | −0.785554 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.0978 | 0.454294 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2338i | 0.393413i | 0.980462 | + | 0.196707i | \(0.0630246\pi\) | ||||
−0.980462 | + | 0.196707i | \(0.936975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.2444i | 1.06686i | 0.845843 | + | 0.533431i | \(0.179098\pi\) | ||||
−0.845843 | + | 0.533431i | \(0.820902\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.2333 | 1.45011 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 7.93051i | − 0.253720i | −0.991921 | − | 0.126860i | \(-0.959510\pi\) | ||||
0.991921 | − | 0.126860i | \(-0.0404898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82.2510i | 2.62875i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.25443i | 0.231616i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 41.8993i | − 1.33638i | −0.743990 | − | 0.668191i | \(-0.767069\pi\) | ||||
0.743990 | − | 0.668191i | \(-0.232931\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.6066 | 0.783237 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.8222i | 1.29807i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.1849 | 1.11769 | 0.558843 | − | 0.829273i | \(-0.311245\pi\) | ||||
0.558843 | + | 0.829273i | \(0.311245\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 27.1950i | − 0.863007i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.04836 | −0.254894 | −0.127447 | − | 0.991845i | \(-0.540678\pi\) | ||||
−0.127447 | + | 0.991845i | \(0.540678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.83276 | 0.247818 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))