Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.7 | ||
Character | \(\chi\) | \(=\) | 950.293 |
Dual form | 950.2.q.f.107.7 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 0.258819i | 0.683013 | − | 0.183013i | ||||
\(3\) | 0.313773 | + | 1.17102i | 0.181157 | + | 0.676088i | 0.995421 | + | 0.0955921i | \(0.0304744\pi\) |
−0.814263 | + | 0.580495i | \(0.802859\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.606164 | + | 1.04991i | 0.247465 | + | 0.428622i | ||||
\(7\) | −1.88504 | + | 1.88504i | −0.712476 | + | 0.712476i | −0.967053 | − | 0.254576i | \(-0.918064\pi\) |
0.254576 | + | 0.967053i | \(0.418064\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.32525 | − | 0.765131i | 0.441749 | − | 0.255044i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.08711 | 1.53382 | 0.766911 | − | 0.641753i | \(-0.221793\pi\) | ||||
0.766911 | + | 0.641753i | \(0.221793\pi\) | |||||||
\(12\) | 0.857245 | + | 0.857245i | 0.247465 | + | 0.247465i | ||||
\(13\) | 1.59907 | + | 0.428469i | 0.443502 | + | 0.118836i | 0.473657 | − | 0.880709i | \(-0.342934\pi\) |
−0.0301554 | + | 0.999545i | \(0.509600\pi\) | |||||||
\(14\) | −1.33292 | + | 2.30869i | −0.356238 | + | 0.617023i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −2.07389 | − | 7.73985i | −0.502991 | − | 1.87719i | −0.479648 | − | 0.877461i | \(-0.659236\pi\) |
−0.0233430 | − | 0.999728i | \(-0.507431\pi\) | |||||||
\(18\) | 1.08206 | − | 1.08206i | 0.255044 | − | 0.255044i | ||||
\(19\) | 1.52448 | + | 4.08362i | 0.349739 | + | 0.936847i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.79888 | − | 1.61594i | −0.610767 | − | 0.352626i | ||||
\(22\) | 4.91377 | − | 1.31664i | 1.04762 | − | 0.280709i | ||||
\(23\) | −2.16907 | + | 8.09508i | −0.452282 | + | 1.68794i | 0.243675 | + | 0.969857i | \(0.421647\pi\) |
−0.695957 | + | 0.718083i | \(0.745020\pi\) | |||||||
\(24\) | 1.04991 | + | 0.606164i | 0.214311 | + | 0.123733i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.65548 | 0.324666 | ||||||||
\(27\) | 3.88354 | + | 3.88354i | 0.747388 | + | 0.747388i | ||||
\(28\) | −0.689971 | + | 2.57501i | −0.130392 | + | 0.486630i | ||||
\(29\) | −0.858351 | − | 1.48671i | −0.159392 | − | 0.276075i | 0.775258 | − | 0.631645i | \(-0.217620\pi\) |
−0.934649 | + | 0.355570i | \(0.884287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.07909i | 1.27144i | 0.771919 | + | 0.635721i | \(0.219297\pi\) | ||||
−0.771919 | + | 0.635721i | \(0.780703\pi\) | |||||||
\(32\) | 0.258819 | − | 0.965926i | 0.0457532 | − | 0.170753i | ||||
\(33\) | 1.59620 | + | 5.95710i | 0.277863 | + | 1.03700i | ||||
\(34\) | −4.00644 | − | 6.93936i | −0.687099 | − | 1.19009i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.765131 | − | 1.32525i | 0.127522 | − | 0.220874i | ||||
\(37\) | 0.618567 | + | 0.618567i | 0.101692 | + | 0.101692i | 0.756122 | − | 0.654430i | \(-0.227092\pi\) |
−0.654430 | + | 0.756122i | \(0.727092\pi\) | |||||||
\(38\) | 2.52945 | + | 3.54991i | 0.410331 | + | 0.575872i | ||||
\(39\) | 2.00698i | 0.321374i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.93587 | + | 2.84972i | 0.770853 | + | 0.445052i | 0.833179 | − | 0.553004i | \(-0.186519\pi\) |
−0.0623260 | + | 0.998056i | \(0.519852\pi\) | |||||||
\(42\) | −3.12175 | − | 0.836470i | −0.481697 | − | 0.129070i | ||||
\(43\) | 4.23321 | − | 1.13429i | 0.645559 | − | 0.172977i | 0.0788388 | − | 0.996887i | \(-0.474879\pi\) |
0.566720 | + | 0.823910i | \(0.308212\pi\) | |||||||
\(44\) | 4.40557 | − | 2.54356i | 0.664164 | − | 0.383456i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.38064i | 1.23566i | ||||||||
\(47\) | −9.97760 | − | 2.67349i | −1.45538 | − | 0.389968i | −0.557490 | − | 0.830184i | \(-0.688235\pi\) |
−0.897892 | + | 0.440215i | \(0.854902\pi\) | |||||||
\(48\) | 1.17102 | + | 0.313773i | 0.169022 | + | 0.0452893i | ||||
\(49\) | − | 0.106718i | − | 0.0152455i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.41277 | − | 4.85711i | 1.17802 | − | 0.680132i | ||||
\(52\) | 1.59907 | − | 0.428469i | 0.221751 | − | 0.0594180i | ||||
\(53\) | 6.22361 | + | 1.66761i | 0.854878 | + | 0.229064i | 0.659538 | − | 0.751672i | \(-0.270752\pi\) |
0.195340 | + | 0.980735i | \(0.437419\pi\) | |||||||
\(54\) | 4.75635 | + | 2.74608i | 0.647257 | + | 0.373694i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.66584i | 0.356238i | ||||||||
\(57\) | −4.30366 | + | 3.06652i | −0.570033 | + | 0.406171i | ||||
\(58\) | −1.21389 | − | 1.21389i | −0.159392 | − | 0.159392i | ||||
\(59\) | 7.18753 | − | 12.4492i | 0.935736 | − | 1.62074i | 0.162420 | − | 0.986722i | \(-0.448070\pi\) |
0.773316 | − | 0.634021i | \(-0.218597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.82198 | − | 4.88781i | −0.361318 | − | 0.625820i | 0.626860 | − | 0.779132i | \(-0.284340\pi\) |
−0.988178 | + | 0.153311i | \(0.951006\pi\) | |||||||
\(62\) | 1.83220 | + | 6.83787i | 0.232690 | + | 0.868411i | ||||
\(63\) | −1.05584 | + | 3.94044i | −0.133023 | + | 0.496448i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.08362 | + | 5.34099i | 0.379568 | + | 0.657430i | ||||
\(67\) | 0.363940 | − | 1.35824i | 0.0444624 | − | 0.165936i | −0.940125 | − | 0.340830i | \(-0.889292\pi\) |
0.984587 | + | 0.174895i | \(0.0559584\pi\) | |||||||
\(68\) | −5.66596 | − | 5.66596i | −0.687099 | − | 0.687099i | ||||
\(69\) | −10.1601 | −1.22313 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2313 | − | 7.63907i | −1.57026 | − | 0.906591i | −0.996136 | − | 0.0878239i | \(-0.972009\pi\) |
−0.574126 | − | 0.818767i | \(-0.694658\pi\) | |||||||
\(72\) | 0.396061 | − | 1.47812i | 0.0466763 | − | 0.174198i | ||||
\(73\) | −1.99861 | + | 0.535526i | −0.233920 | + | 0.0626786i | −0.373874 | − | 0.927479i | \(-0.621971\pi\) |
0.139955 | + | 0.990158i | \(0.455304\pi\) | |||||||
\(74\) | 0.757586 | + | 0.437393i | 0.0880676 | + | 0.0508459i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.36205 | + | 2.77428i | 0.385653 | + | 0.318232i | ||||
\(77\) | −9.58939 | + | 9.58939i | −1.09281 | + | 1.09281i | ||||
\(78\) | 0.519445 | + | 1.93859i | 0.0588155 | + | 0.219503i | ||||
\(79\) | 2.01507 | − | 3.49020i | 0.226713 | − | 0.392678i | −0.730119 | − | 0.683320i | \(-0.760536\pi\) |
0.956832 | + | 0.290642i | \(0.0938688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.03375 | + | 1.79051i | −0.114861 | + | 0.198946i | ||||
\(82\) | 5.50524 | + | 1.47513i | 0.607952 | + | 0.162900i | ||||
\(83\) | −3.12063 | − | 3.12063i | −0.342534 | − | 0.342534i | 0.514785 | − | 0.857319i | \(-0.327872\pi\) |
−0.857319 | + | 0.514785i | \(0.827872\pi\) | |||||||
\(84\) | −3.23187 | −0.352626 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.79539 | − | 2.19127i | 0.409268 | − | 0.236291i | ||||
\(87\) | 1.47163 | − | 1.47163i | 0.157776 | − | 0.157776i | ||||
\(88\) | 3.59713 | − | 3.59713i | 0.383456 | − | 0.383456i | ||||
\(89\) | −5.26392 | − | 9.11738i | −0.557974 | − | 0.966440i | −0.997665 | − | 0.0682908i | \(-0.978245\pi\) |
0.439691 | − | 0.898149i | \(-0.355088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.82198 | + | 2.20662i | −0.400652 | + | 0.231317i | ||||
\(92\) | 2.16907 | + | 8.09508i | 0.226141 | + | 0.843970i | ||||
\(93\) | −8.28974 | + | 2.22123i | −0.859606 | + | 0.230331i | ||||
\(94\) | −10.3296 | −1.06541 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.21233 | 0.123733 | ||||||||
\(97\) | −10.0259 | + | 2.68643i | −1.01798 | + | 0.272766i | −0.728958 | − | 0.684558i | \(-0.759995\pi\) |
−0.289017 | + | 0.957324i | \(0.593329\pi\) | |||||||
\(98\) | −0.0276208 | − | 0.103082i | −0.00279012 | − | 0.0104129i | ||||
\(99\) | 6.74168 | − | 3.89231i | 0.677564 | − | 0.391192i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.30520 | − | 5.72477i | −0.328879 | − | 0.569636i | 0.653410 | − | 0.757004i | \(-0.273338\pi\) |
−0.982290 | + | 0.187368i | \(0.940004\pi\) | |||||||
\(102\) | 6.86900 | − | 6.86900i | 0.680132 | − | 0.680132i | ||||
\(103\) | 6.38060 | − | 6.38060i | 0.628699 | − | 0.628699i | −0.319041 | − | 0.947741i | \(-0.603361\pi\) |
0.947741 | + | 0.319041i | \(0.103361\pi\) | |||||||
\(104\) | 1.43369 | − | 0.827739i | 0.140584 | − | 0.0811665i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.44315 | 0.625814 | ||||||||
\(107\) | −6.54875 | − | 6.54875i | −0.633092 | − | 0.633092i | 0.315750 | − | 0.948842i | \(-0.397744\pi\) |
−0.948842 | + | 0.315750i | \(0.897744\pi\) | |||||||
\(108\) | 5.30502 | + | 1.42148i | 0.510476 | + | 0.136782i | ||||
\(109\) | 2.10586 | − | 3.64745i | 0.201705 | − | 0.349363i | −0.747373 | − | 0.664404i | \(-0.768685\pi\) |
0.949078 | + | 0.315042i | \(0.102019\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.530263 | + | 0.918442i | −0.0503303 | + | 0.0871747i | ||||
\(112\) | 0.689971 | + | 2.57501i | 0.0651961 | + | 0.243315i | ||||
\(113\) | −6.93263 | + | 6.93263i | −0.652167 | + | 0.652167i | −0.953515 | − | 0.301347i | \(-0.902564\pi\) |
0.301347 | + | 0.953515i | \(0.402564\pi\) | |||||||
\(114\) | −3.36334 | + | 4.07590i | −0.315005 | + | 0.381743i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.48671 | − | 0.858351i | −0.138037 | − | 0.0796958i | ||||
\(117\) | 2.44700 | − | 0.655670i | 0.226225 | − | 0.0606168i | ||||
\(118\) | 3.72054 | − | 13.8852i | 0.342503 | − | 1.27824i | ||||
\(119\) | 18.4992 | + | 10.6805i | 1.69582 | + | 0.979083i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.8787 | 1.35261 | ||||||||
\(122\) | −3.99088 | − | 3.99088i | −0.361318 | − | 0.361318i | ||||
\(123\) | −1.78833 | + | 6.67416i | −0.161249 | + | 0.601788i | ||||
\(124\) | 3.53954 | + | 6.13067i | 0.317860 | + | 0.550550i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.07944i | 0.363425i | ||||||||
\(127\) | 3.06175 | − | 11.4266i | 0.271687 | − | 1.01395i | −0.686343 | − | 0.727278i | \(-0.740785\pi\) |
0.958029 | − | 0.286670i | \(-0.0925483\pi\) | |||||||
\(128\) | −0.258819 | − | 0.965926i | −0.0228766 | − | 0.0853766i | ||||
\(129\) | 2.65654 | + | 4.60126i | 0.233895 | + | 0.405118i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.90308 | + | 5.02829i | −0.253644 | + | 0.439324i | −0.964526 | − | 0.263987i | \(-0.914962\pi\) |
0.710883 | + | 0.703311i | \(0.248296\pi\) | |||||||
\(132\) | 4.36090 | + | 4.36090i | 0.379568 | + | 0.379568i | ||||
\(133\) | −10.5715 | − | 4.82408i | −0.916662 | − | 0.418301i | ||||
\(134\) | − | 1.40616i | − | 0.121474i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.93936 | − | 4.00644i | −0.595045 | − | 0.343549i | ||||
\(137\) | 16.5912 | + | 4.44559i | 1.41748 | + | 0.379812i | 0.884588 | − | 0.466373i | \(-0.154439\pi\) |
0.532890 | + | 0.846185i | \(0.321106\pi\) | |||||||
\(138\) | −9.81388 | + | 2.62962i | −0.835413 | + | 0.223848i | ||||
\(139\) | −11.7743 | + | 6.79791i | −0.998686 | + | 0.576591i | −0.907859 | − | 0.419275i | \(-0.862284\pi\) |
−0.0908265 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 12.5228i | − | 1.05461i | ||||||
\(142\) | −14.7576 | − | 3.95427i | −1.23843 | − | 0.331835i | ||||
\(143\) | 8.13464 | + | 2.17967i | 0.680253 | + | 0.182273i | ||||
\(144\) | − | 1.53026i | − | 0.127522i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.79190 | + | 1.03456i | −0.148299 | + | 0.0856205i | ||||
\(147\) | 0.124969 | − | 0.0334854i | 0.0103073 | − | 0.00276183i | ||||
\(148\) | 0.844978 | + | 0.226411i | 0.0694567 | + | 0.0186109i | ||||
\(149\) | −8.23647 | − | 4.75533i | −0.674758 | − | 0.389572i | 0.123119 | − | 0.992392i | \(-0.460710\pi\) |
−0.797877 | + | 0.602820i | \(0.794044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.21129i | 0.505468i | 0.967536 | + | 0.252734i | \(0.0813297\pi\) | ||||
−0.967536 | + | 0.252734i | \(0.918670\pi\) | |||||||
\(152\) | 3.96552 | + | 1.80959i | 0.321647 | + | 0.146777i | ||||
\(153\) | −8.67041 | − | 8.67041i | −0.700961 | − | 0.700961i | ||||
\(154\) | −6.78072 | + | 11.7446i | −0.546406 | + | 0.946403i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00349 | + | 1.73810i | 0.0803435 | + | 0.139159i | ||||
\(157\) | 3.70862 | + | 13.8408i | 0.295980 | + | 1.10461i | 0.940436 | + | 0.339971i | \(0.110417\pi\) |
−0.644456 | + | 0.764641i | \(0.722916\pi\) | |||||||
\(158\) | 1.04308 | − | 3.89281i | 0.0829826 | − | 0.309695i | ||||
\(159\) | 7.81121i | 0.619469i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.1707 | − | 19.3483i | −0.880377 | − | 1.52486i | ||||
\(162\) | −0.535110 | + | 1.99706i | −0.0420422 | + | 0.156904i | ||||
\(163\) | −1.78065 | − | 1.78065i | −0.139471 | − | 0.139471i | 0.633924 | − | 0.773395i | \(-0.281443\pi\) |
−0.773395 | + | 0.633924i | \(0.781443\pi\) | |||||||
\(164\) | 5.69945 | 0.445052 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.82198 | − | 2.20662i | −0.296643 | − | 0.171267i | ||||
\(167\) | −3.47427 | + | 12.9661i | −0.268847 | + | 1.00335i | 0.691006 | + | 0.722849i | \(0.257168\pi\) |
−0.959853 | + | 0.280502i | \(0.909499\pi\) | |||||||
\(168\) | −3.12175 | + | 0.836470i | −0.240848 | + | 0.0645351i | ||||
\(169\) | −8.88490 | − | 5.12970i | −0.683454 | − | 0.394592i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.14482 | + | 4.24538i | 0.393434 | + | 0.324652i | ||||
\(172\) | 3.09893 | − | 3.09893i | 0.236291 | − | 0.236291i | ||||
\(173\) | −2.67657 | − | 9.98909i | −0.203496 | − | 0.759457i | −0.989903 | − | 0.141748i | \(-0.954728\pi\) |
0.786407 | − | 0.617709i | \(-0.211939\pi\) | |||||||
\(174\) | 1.04060 | − | 1.80237i | 0.0788878 | − | 0.136638i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.54356 | − | 4.40557i | 0.191728 | − | 0.332082i | ||||
\(177\) | 16.8334 | + | 4.51051i | 1.26528 | + | 0.339031i | ||||
\(178\) | −7.44431 | − | 7.44431i | −0.557974 | − | 0.557974i | ||||
\(179\) | 15.2968 | 1.14333 | 0.571666 | − | 0.820486i | \(-0.306297\pi\) | ||||
0.571666 | + | 0.820486i | \(0.306297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.3780 | + | 7.72382i | −0.994382 | + | 0.574107i | −0.906581 | − | 0.422031i | \(-0.861317\pi\) |
−0.0878009 | + | 0.996138i | \(0.527984\pi\) | |||||||
\(182\) | −3.12063 | + | 3.12063i | −0.231317 | + | 0.231317i | ||||
\(183\) | 4.83826 | − | 4.83826i | 0.357654 | − | 0.357654i | ||||
\(184\) | 4.19032 | + | 7.25785i | 0.308914 | + | 0.535056i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.43238 | + | 4.29108i | −0.544968 | + | 0.314638i | ||||
\(187\) | −10.5501 | − | 39.3735i | −0.771499 | − | 2.87927i | ||||
\(188\) | −9.97760 | + | 2.67349i | −0.727691 | + | 0.194984i | ||||
\(189\) | −14.6412 | −1.06499 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.4216 | −1.04351 | −0.521755 | − | 0.853095i | \(-0.674723\pi\) | ||||
−0.521755 | + | 0.853095i | \(0.674723\pi\) | |||||||
\(192\) | 1.17102 | − | 0.313773i | 0.0845109 | − | 0.0226446i | ||||
\(193\) | −1.98826 | − | 7.42030i | −0.143118 | − | 0.534125i | −0.999832 | − | 0.0183327i | \(-0.994164\pi\) |
0.856714 | − | 0.515793i | \(-0.172502\pi\) | |||||||
\(194\) | −8.98897 | + | 5.18979i | −0.645371 | + | 0.372605i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0533592 | − | 0.0924208i | −0.00381137 | − | 0.00660149i | ||||
\(197\) | 15.0397 | − | 15.0397i | 1.07153 | − | 1.07153i | 0.0742953 | − | 0.997236i | \(-0.476329\pi\) |
0.997236 | − | 0.0742953i | \(-0.0236708\pi\) | |||||||
\(198\) | 5.50456 | − | 5.50456i | 0.391192 | − | 0.391192i | ||||
\(199\) | −3.99272 | + | 2.30520i | −0.283036 | + | 0.163411i | −0.634797 | − | 0.772679i | \(-0.718916\pi\) |
0.351761 | + | 0.936090i | \(0.385583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.70472 | 0.120242 | ||||||||
\(202\) | −4.67426 | − | 4.67426i | −0.328879 | − | 0.328879i | ||||
\(203\) | 4.42052 | + | 1.18447i | 0.310259 | + | 0.0831338i | ||||
\(204\) | 4.85711 | − | 8.41277i | 0.340066 | − | 0.589012i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.51177 | − | 7.81461i | 0.314350 | − | 0.544470i | ||||
\(207\) | 3.31925 | + | 12.3876i | 0.230704 | + | 0.860997i | ||||
\(208\) | 1.17060 | − | 1.17060i | 0.0811665 | − | 0.0811665i | ||||
\(209\) | 7.75519 | + | 20.7738i | 0.536437 | + | 1.43696i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.99020 | − | 1.14904i | −0.137011 | − | 0.0791032i | 0.429928 | − | 0.902863i | \(-0.358539\pi\) |
−0.566939 | + | 0.823760i | \(0.691872\pi\) | |||||||
\(212\) | 6.22361 | − | 1.66761i | 0.427439 | − | 0.114532i | ||||
\(213\) | 4.79387 | − | 17.8910i | 0.328471 | − | 1.22587i | ||||
\(214\) | −8.02055 | − | 4.63067i | −0.548274 | − | 0.316546i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.49216 | 0.373694 | ||||||||
\(217\) | −13.3443 | − | 13.3443i | −0.905872 | − | 0.905872i | ||||
\(218\) | 1.09007 | − | 4.06820i | 0.0738290 | − | 0.275534i | ||||
\(219\) | −1.25422 | − | 2.17237i | −0.0847524 | − | 0.146795i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.2651i | − | 0.892310i | ||||||
\(222\) | −0.274484 | + | 1.02439i | −0.0184222 | + | 0.0687525i | ||||
\(223\) | −5.34017 | − | 19.9298i | −0.357604 | − | 1.33460i | −0.877176 | − | 0.480169i | \(-0.840575\pi\) |
0.519572 | − | 0.854427i | \(-0.326091\pi\) | |||||||
\(224\) | 1.33292 | + | 2.30869i | 0.0890596 | + | 0.154256i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.90211 | + | 8.49071i | −0.326084 | + | 0.564794i | ||||
\(227\) | −2.31642 | − | 2.31642i | −0.153746 | − | 0.153746i | 0.626043 | − | 0.779789i | \(-0.284674\pi\) |
−0.779789 | + | 0.626043i | \(0.784674\pi\) | |||||||
\(228\) | −2.19381 | + | 4.80751i | −0.145289 | + | 0.318385i | ||||
\(229\) | − | 7.45517i | − | 0.492651i | −0.969187 | − | 0.246326i | \(-0.920777\pi\) | ||
0.969187 | − | 0.246326i | \(-0.0792233\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.2382 | − | 8.22045i | −0.936807 | − | 0.540866i | ||||
\(232\) | −1.65821 | − | 0.444315i | −0.108867 | − | 0.0291707i | ||||
\(233\) | 10.8912 | − | 2.91830i | 0.713509 | − | 0.191184i | 0.116236 | − | 0.993222i | \(-0.462917\pi\) |
0.597274 | + | 0.802037i | \(0.296251\pi\) | |||||||
\(234\) | 2.19392 | − | 1.26666i | 0.143421 | − | 0.0828040i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 14.3751i | − | 0.935736i | ||||||
\(237\) | 4.71936 | + | 1.26455i | 0.306555 | + | 0.0821412i | ||||
\(238\) | 20.6332 | + | 5.52865i | 1.33745 | + | 0.358369i | ||||
\(239\) | 13.3826i | 0.865650i | 0.901478 | + | 0.432825i | \(0.142483\pi\) | ||||
−0.901478 | + | 0.432825i | \(0.857517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.2007 | + | 9.35347i | −1.04358 | + | 0.602510i | −0.920845 | − | 0.389929i | \(-0.872499\pi\) |
−0.122734 | + | 0.992440i | \(0.539166\pi\) | |||||||
\(242\) | 14.3717 | − | 3.85089i | 0.923850 | − | 0.247545i | ||||
\(243\) | 13.4940 | + | 3.61570i | 0.865639 | + | 0.231947i | ||||
\(244\) | −4.88781 | − | 2.82198i | −0.312910 | − | 0.180659i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.90959i | 0.440540i | ||||||||
\(247\) | 0.688037 | + | 7.18318i | 0.0437788 | + | 0.457055i | ||||
\(248\) | 5.00567 | + | 5.00567i | 0.317860 | + | 0.317860i | ||||
\(249\) | 2.67515 | − | 4.63349i | 0.169531 | − | 0.293636i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.16442 | + | 15.8732i | 0.578453 | + | 1.00191i | 0.995657 | + | 0.0930973i | \(0.0296768\pi\) |
−0.417204 | + | 0.908813i | \(0.636990\pi\) | |||||||
\(252\) | 1.05584 | + | 3.94044i | 0.0665115 | + | 0.248224i | ||||
\(253\) | −11.0343 | + | 41.1806i | −0.693720 | + | 2.58900i | ||||
\(254\) | − | 11.8297i | − | 0.742262i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.399675 | + | 1.49161i | −0.0249310 | + | 0.0930438i | −0.977270 | − | 0.211997i | \(-0.932003\pi\) |
0.952339 | + | 0.305041i | \(0.0986700\pi\) | |||||||
\(258\) | 3.75691 | + | 3.75691i | 0.233895 | + | 0.233895i | ||||
\(259\) | −2.33204 | −0.144906 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.27505 | − | 1.31350i | −0.140822 | − | 0.0813037i | ||||
\(262\) | −1.50275 | + | 5.60833i | −0.0928400 | + | 0.346484i | ||||
\(263\) | 1.08181 | − | 0.289870i | 0.0667072 | − | 0.0178741i | −0.225311 | − | 0.974287i | \(-0.572340\pi\) |
0.292018 | + | 0.956413i | \(0.405673\pi\) | |||||||
\(264\) | 5.34099 | + | 3.08362i | 0.328715 | + | 0.189784i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.4598 | − | 1.92361i | −0.702646 | − | 0.117944i | ||||
\(267\) | 9.02493 | − | 9.02493i | 0.552317 | − | 0.552317i | ||||
\(268\) | −0.363940 | − | 1.35824i | −0.0222312 | − | 0.0829680i | ||||
\(269\) | −1.94303 | + | 3.36542i | −0.118468 | + | 0.205193i | −0.919161 | − | 0.393882i | \(-0.871132\pi\) |
0.800693 | + | 0.599076i | \(0.204465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.49369 | − | 2.58714i | 0.0907350 | − | 0.157158i | −0.817086 | − | 0.576516i | \(-0.804412\pi\) |
0.907821 | + | 0.419359i | \(0.137745\pi\) | |||||||
\(272\) | −7.73985 | − | 2.07389i | −0.469297 | − | 0.125748i | ||||
\(273\) | −3.78323 | − | 3.78323i | −0.228971 | − | 0.228971i | ||||
\(274\) | 17.1764 | 1.03767 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.79888 | + | 5.08004i | −0.529631 | + | 0.305782i | ||||
\(277\) | −15.9817 | + | 15.9817i | −0.960248 | + | 0.960248i | −0.999240 | − | 0.0389918i | \(-0.987585\pi\) |
0.0389918 | + | 0.999240i | \(0.487585\pi\) | |||||||
\(278\) | −9.61370 | + | 9.61370i | −0.576591 | + | 0.576591i | ||||
\(279\) | 5.41643 | + | 9.38154i | 0.324273 | + | 0.561658i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6331 | − | 11.9125i | 1.23087 | − | 0.710641i | 0.263655 | − | 0.964617i | \(-0.415072\pi\) |
0.967210 | + | 0.253976i | \(0.0817385\pi\) | |||||||
\(282\) | −3.24114 | − | 12.0961i | −0.193007 | − | 0.720313i | ||||
\(283\) | 8.49923 | − | 2.27736i | 0.505227 | − | 0.135375i | 0.00280196 | − | 0.999996i | \(-0.499108\pi\) |
0.502425 | + | 0.864621i | \(0.332441\pi\) | |||||||
\(284\) | −15.2781 | −0.906591 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.42160 | 0.497980 | ||||||||
\(287\) | −14.6761 | + | 3.93245i | −0.866304 | + | 0.232125i | ||||
\(288\) | −0.396061 | − | 1.47812i | −0.0233381 | − | 0.0870991i | ||||
\(289\) | −40.8818 | + | 23.6031i | −2.40481 | + | 1.38842i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.29172 | − | 10.8976i | −0.368827 | − | 0.638827i | ||||
\(292\) | −1.46308 | + | 1.46308i | −0.0856205 | + | 0.0856205i | ||||
\(293\) | −13.9858 | + | 13.9858i | −0.817062 | + | 0.817062i | −0.985681 | − | 0.168619i | \(-0.946069\pi\) |
0.168619 | + | 0.985681i | \(0.446069\pi\) | |||||||
\(294\) | 0.112044 | − | 0.0646888i | 0.00653456 | − | 0.00377273i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.874785 | 0.0508459 | ||||||||
\(297\) | 19.7560 | + | 19.7560i | 1.14636 | + | 1.14636i | ||||
\(298\) | −9.18659 | − | 2.46154i | −0.532165 | − | 0.142593i | ||||
\(299\) | −6.93698 | + | 12.0152i | −0.401176 | + | 0.694857i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.84159 | + | 10.1179i | −0.336703 | + | 0.583188i | ||||
\(302\) | 1.60760 | + | 5.99964i | 0.0925070 | + | 0.345241i | ||||
\(303\) | 5.66673 | − | 5.66673i | 0.325545 | − | 0.325545i | ||||
\(304\) | 4.29876 | + | 0.721575i | 0.246551 | + | 0.0413852i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.6190 | − | 6.13091i | −0.607050 | − | 0.350481i | ||||
\(307\) | 11.9567 | − | 3.20378i | 0.682404 | − | 0.182849i | 0.0990679 | − | 0.995081i | \(-0.468414\pi\) |
0.583336 | + | 0.812231i | \(0.301747\pi\) | |||||||
\(308\) | −3.50996 | + | 13.0993i | −0.199999 | + | 0.746405i | ||||
\(309\) | 9.47386 | + | 5.46974i | 0.538949 | + | 0.311162i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.9658 | −0.735224 | −0.367612 | − | 0.929979i | \(-0.619825\pi\) | ||||
−0.367612 | + | 0.929979i | \(0.619825\pi\) | |||||||
\(312\) | 1.41915 | + | 1.41915i | 0.0803435 | + | 0.0803435i | ||||
\(313\) | −1.08434 | + | 4.04681i | −0.0612904 | + | 0.228739i | −0.989776 | − | 0.142629i | \(-0.954444\pi\) |
0.928486 | + | 0.371368i | \(0.121111\pi\) | |||||||
\(314\) | 7.16450 | + | 12.4093i | 0.404316 | + | 0.700296i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 4.03013i | − | 0.226713i | ||||||
\(317\) | 2.18344 | − | 8.14871i | 0.122634 | − | 0.457677i | −0.877110 | − | 0.480290i | \(-0.840532\pi\) |
0.999744 | + | 0.0226121i | \(0.00719827\pi\) | |||||||
\(318\) | 2.02169 | + | 7.54505i | 0.113371 | + | 0.423105i | ||||
\(319\) | −4.36653 | − | 7.56304i | −0.244479 | − | 0.423449i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.61389 | − | 9.72353i | 0.313337 | − | 0.542715i | ||||
\(322\) | −15.7978 | − | 15.7978i | −0.880377 | − | 0.880377i | ||||
\(323\) | 28.4450 | − | 20.2682i | 1.58272 | − | 1.12775i | ||||
\(324\) | 2.06751i | 0.114861i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.18084 | − | 1.25911i | −0.120786 | − | 0.0697356i | ||||
\(327\) | 4.93199 | + | 1.32152i | 0.272740 | + | 0.0730804i | ||||
\(328\) | 5.50524 | − | 1.47513i | 0.303976 | − | 0.0814502i | ||||
\(329\) | 23.8477 | − | 13.7685i | 1.31477 | − | 0.759082i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9.62608i | − | 0.529097i | −0.964372 | − | 0.264549i | \(-0.914777\pi\) | ||
0.964372 | − | 0.264549i | \(-0.0852230\pi\) | |||||||
\(332\) | −4.26287 | − | 1.14223i | −0.233955 | − | 0.0626881i | ||||
\(333\) | 1.29304 | + | 0.346469i | 0.0708580 | + | 0.0189864i | ||||
\(334\) | 13.4235i | 0.734504i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.79888 | + | 1.61594i | −0.152692 | + | 0.0881566i | ||||
\(337\) | 3.54986 | − | 0.951182i | 0.193373 | − | 0.0518142i | −0.160833 | − | 0.986982i | \(-0.551418\pi\) |
0.354206 | + | 0.935168i | \(0.384751\pi\) | |||||||
\(338\) | −9.90981 | − | 2.65533i | −0.539023 | − | 0.144431i | ||||
\(339\) | −10.2935 | − | 5.94296i | −0.559067 | − | 0.322778i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.0121i | 1.95016i | ||||||||
\(342\) | 6.06830 | + | 2.76915i | 0.328136 | + | 0.149738i | ||||
\(343\) | −12.9941 | − | 12.9941i | −0.701614 | − | 0.701614i | ||||
\(344\) | 2.19127 | − | 3.79539i | 0.118145 | − | 0.204634i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.17073 | − | 8.95597i | −0.277980 | − | 0.481476i | ||||
\(347\) | 0.111421 | + | 0.415829i | 0.00598139 | + | 0.0223228i | 0.968852 | − | 0.247640i | \(-0.0796551\pi\) |
−0.962871 | + | 0.269963i | \(0.912988\pi\) | |||||||
\(348\) | 0.538655 | − | 2.01029i | 0.0288749 | − | 0.107763i | ||||
\(349\) | − | 11.4552i | − | 0.613181i | −0.951841 | − | 0.306591i | \(-0.900812\pi\) | ||
0.951841 | − | 0.306591i | \(-0.0991882\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.54607 | + | 7.87403i | 0.242652 | + | 0.420285i | ||||
\(352\) | 1.31664 | − | 4.91377i | 0.0701772 | − | 0.261905i | ||||
\(353\) | −21.7675 | − | 21.7675i | −1.15857 | − | 1.15857i | −0.984784 | − | 0.173784i | \(-0.944400\pi\) |
−0.173784 | − | 0.984784i | \(-0.555600\pi\) | |||||||
\(354\) | 17.4273 | 0.926249 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.11738 | − | 5.26392i | −0.483220 | − | 0.278987i | ||||
\(357\) | −6.70254 | + | 25.0142i | −0.354736 | + | 1.32389i | ||||
\(358\) | 14.7755 | − | 3.95909i | 0.780911 | − | 0.209244i | ||||
\(359\) | 32.2397 | + | 18.6136i | 1.70154 | + | 0.982387i | 0.944201 | + | 0.329371i | \(0.106837\pi\) |
0.757344 | + | 0.653016i | \(0.226497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3519 | + | 12.4508i | −0.755365 | + | 0.655304i | ||||
\(362\) | −10.9231 | + | 10.9231i | −0.574107 | + | 0.574107i | ||||
\(363\) | 4.66854 | + | 17.4232i | 0.245035 | + | 0.914483i | ||||
\(364\) | −2.20662 | + | 3.82198i | −0.115658 | + | 0.200326i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.42116 | − | 5.92563i | 0.178827 | − | 0.309738i | ||||
\(367\) | −0.905122 | − | 0.242527i | −0.0472470 | − | 0.0126598i | 0.235118 | − | 0.971967i | \(-0.424452\pi\) |
−0.282365 | + | 0.959307i | \(0.591119\pi\) | |||||||
\(368\) | 5.92601 | + | 5.92601i | 0.308914 | + | 0.308914i | ||||
\(369\) | 8.72165 | 0.454031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.8752 | + | 8.58821i | −0.772283 | + | 0.445878i | ||||
\(372\) | −6.06851 | + | 6.06851i | −0.314638 | + | 0.314638i | ||||
\(373\) | 18.3157 | − | 18.3157i | 0.948349 | − | 0.948349i | −0.0503814 | − | 0.998730i | \(-0.516044\pi\) |
0.998730 | + | 0.0503814i | \(0.0160437\pi\) | |||||||
\(374\) | −20.3812 | − | 35.3013i | −1.05389 | − | 1.82539i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.94567 | + | 5.16478i | −0.461338 | + | 0.266353i | ||||
\(377\) | −0.735553 | − | 2.74512i | −0.0378829 | − | 0.141381i | ||||
\(378\) | −14.1423 | + | 3.78943i | −0.727404 | + | 0.194907i | ||||
\(379\) | −32.8155 | −1.68562 | −0.842810 | − | 0.538211i | \(-0.819100\pi\) | ||||
−0.842810 | + | 0.538211i | \(0.819100\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.3415 | 0.734736 | ||||||||
\(382\) | −13.9302 | + | 3.73259i | −0.712731 | + | 0.190976i | ||||
\(383\) | −2.80563 | − | 10.4707i | −0.143361 | − | 0.535030i | −0.999823 | − | 0.0188199i | \(-0.994009\pi\) |
0.856462 | − | 0.516210i | \(-0.172658\pi\) | |||||||
\(384\) | 1.04991 | − | 0.606164i | 0.0535778 | − | 0.0309332i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.84103 | − | 6.65286i | −0.195503 | − | 0.338622i | ||||
\(387\) | 4.74217 | − | 4.74217i | 0.241058 | − | 0.241058i | ||||
\(388\) | −7.33947 | + | 7.33947i | −0.372605 | + | 0.372605i | ||||
\(389\) | 18.7610 | − | 10.8317i | 0.951220 | − | 0.549187i | 0.0577605 | − | 0.998330i | \(-0.481604\pi\) |
0.893460 | + | 0.449143i | \(0.148271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 67.1530 | 3.39608 | ||||||||
\(392\) | −0.0754613 | − | 0.0754613i | −0.00381137 | − | 0.00381137i | ||||
\(393\) | −6.79913 | − | 1.82182i | −0.342971 | − | 0.0918987i | ||||
\(394\) | 10.6346 | − | 18.4198i | 0.535766 | − | 0.927974i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.89231 | − | 6.74168i | 0.195596 | − | 0.338782i | ||||
\(397\) | 6.43427 | + | 24.0130i | 0.322927 | + | 1.20518i | 0.916380 | + | 0.400310i | \(0.131098\pi\) |
−0.593453 | + | 0.804869i | \(0.702236\pi\) | |||||||
\(398\) | −3.26004 | + | 3.26004i | −0.163411 | + | 0.163411i | ||||
\(399\) | 2.33204 | − | 13.8930i | 0.116748 | − | 0.695522i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.2666 | + | 14.5877i | 1.26175 | + | 0.728473i | 0.973413 | − | 0.229056i | \(-0.0735638\pi\) |
0.288339 | + | 0.957529i | \(0.406897\pi\) | |||||||
\(402\) | 1.64664 | − | 0.441215i | 0.0821268 | − | 0.0220058i | ||||
\(403\) | −3.03317 | + | 11.3199i | −0.151093 | + | 0.563887i | ||||
\(404\) | −5.72477 | − | 3.30520i | −0.284818 | − | 0.164440i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.57646 | 0.227126 | ||||||||
\(407\) | 3.14672 | + | 3.14672i | 0.155977 | + | 0.155977i | ||||
\(408\) | 2.51423 | − | 9.38323i | 0.124473 | − | 0.464539i | ||||
\(409\) | −6.42063 | − | 11.1209i | −0.317480 | − | 0.549891i | 0.662482 | − | 0.749078i | \(-0.269503\pi\) |
−0.979962 | + | 0.199187i | \(0.936170\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.8234i | 1.02714i | ||||||||
\(412\) | 2.33546 | − | 8.71606i | 0.115060 | − | 0.429410i | ||||
\(413\) | 9.91837 | + | 37.0158i | 0.488051 | + | 1.82143i | ||||
\(414\) | 6.41229 | + | 11.1064i | 0.315147 | + | 0.545850i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.827739 | − | 1.43369i | 0.0405832 | − | 0.0702922i | ||||
\(417\) | −11.6549 | − | 11.6549i | −0.570745 | − | 0.570745i | ||||
\(418\) | 12.8676 | + | 18.0588i | 0.629375 | + | 0.883285i | ||||
\(419\) | − | 17.7916i | − | 0.869177i | −0.900629 | − | 0.434588i | \(-0.856894\pi\) | ||
0.900629 | − | 0.434588i | \(-0.143106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5157 | + | 17.0409i | 1.43851 | + | 0.830522i | 0.997746 | − | 0.0671023i | \(-0.0213754\pi\) |
0.440761 | + | 0.897625i | \(0.354709\pi\) | |||||||
\(422\) | −2.21978 | − | 0.594787i | −0.108057 | − | 0.0289538i | ||||
\(423\) | −15.2683 | + | 4.09114i | −0.742372 | + | 0.198918i | ||||
\(424\) | 5.57993 | − | 3.22158i | 0.270985 | − | 0.156454i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 18.5221i | − | 0.897399i | ||||||
\(427\) | 14.5332 | + | 3.89417i | 0.703313 | + | 0.188452i | ||||
\(428\) | −8.94576 | − | 2.39701i | −0.432410 | − | 0.115864i | ||||
\(429\) | 10.2097i | 0.492931i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0591 | − | 12.1585i | 1.01438 | − | 0.585652i | 0.101908 | − | 0.994794i | \(-0.467505\pi\) |
0.912471 | + | 0.409142i | \(0.134172\pi\) | |||||||
\(432\) | 5.30502 | − | 1.42148i | 0.255238 | − | 0.0683908i | ||||
\(433\) | −24.8949 | − | 6.67057i | −1.19637 | − | 0.320567i | −0.394971 | − | 0.918694i | \(-0.629245\pi\) |
−0.801402 | + | 0.598126i | \(0.795912\pi\) | |||||||
\(434\) | −16.3434 | − | 9.43587i | −0.784508 | − | 0.452936i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 4.21171i | − | 0.201705i | ||||||
\(437\) | −36.3639 | + | 3.48310i | −1.73952 | + | 0.166619i | ||||
\(438\) | −1.77374 | − | 1.77374i | −0.0847524 | − | 0.0847524i | ||||
\(439\) | 0.512599 | − | 0.887848i | 0.0244650 | − | 0.0423747i | −0.853534 | − | 0.521038i | \(-0.825545\pi\) |
0.877999 | + | 0.478663i | \(0.158878\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0816536 | − | 0.141428i | −0.00388827 | − | 0.00673468i | ||||
\(442\) | −3.43327 | − | 12.8131i | −0.163304 | − | 0.609459i | ||||
\(443\) | −2.14710 | + | 8.01308i | −0.102012 | + | 0.380713i | −0.997989 | − | 0.0633869i | \(-0.979810\pi\) |
0.895977 | + | 0.444100i | \(0.146476\pi\) | |||||||
\(444\) | 1.06053i | 0.0503303i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.3164 | − | 17.8685i | −0.488496 | − | 0.846100i | ||||
\(447\) | 2.98419 | − | 11.1372i | 0.141147 | − | 0.526769i | ||||
\(448\) | 1.88504 | + | 1.88504i | 0.0890596 | + | 0.0890596i | ||||
\(449\) | −19.6032 | −0.925134 | −0.462567 | − | 0.886584i | \(-0.653072\pi\) | ||||
−0.462567 | + | 0.886584i | \(0.653072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.1093 | + | 14.4969i | 1.18235 | + | 0.682631i | ||||
\(452\) | −2.53752 | + | 9.47015i | −0.119355 | + | 0.445439i | ||||
\(453\) | −7.27353 | + | 1.94894i | −0.341740 | + | 0.0915691i | ||||
\(454\) | −2.83702 | − | 1.63795i | −0.133148 | − | 0.0768729i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.874785 | + | 5.21150i | −0.0409656 | + | 0.244051i | ||||
\(457\) | 19.5026 | − | 19.5026i | 0.912293 | − | 0.912293i | −0.0841597 | − | 0.996452i | \(-0.526821\pi\) |
0.996452 | + | 0.0841597i | \(0.0268206\pi\) | |||||||
\(458\) | −1.92954 | − | 7.20114i | −0.0901615 | − | 0.336487i | ||||
\(459\) | 22.0040 | − | 38.1121i | 1.02706 | − | 1.77892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.84973 | − | 6.66792i | 0.179300 | − | 0.310556i | −0.762341 | − | 0.647175i | \(-0.775950\pi\) |
0.941641 | + | 0.336619i | \(0.109284\pi\) | |||||||
\(462\) | −15.8807 | − | 4.25522i | −0.738837 | − | 0.197971i | ||||
\(463\) | 12.6250 | + | 12.6250i | 0.586735 | + | 0.586735i | 0.936746 | − | 0.350010i | \(-0.113822\pi\) |
−0.350010 | + | 0.936746i | \(0.613822\pi\) | |||||||
\(464\) | −1.71670 | −0.0796958 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.76483 | − | 5.63773i | 0.452347 | − | 0.261163i | ||||
\(467\) | −10.9349 | + | 10.9349i | −0.506008 | + | 0.506008i | −0.913299 | − | 0.407291i | \(-0.866474\pi\) |
0.407291 | + | 0.913299i | \(0.366474\pi\) | |||||||
\(468\) | 1.79133 | − | 1.79133i | 0.0828040 | − | 0.0828040i | ||||
\(469\) | 1.87430 | + | 3.24638i | 0.0865470 | + | 0.149904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.0441 | + | 8.68572i | −0.693196 | + | 0.400217i | ||||
\(472\) | −3.72054 | − | 13.8852i | −0.171252 | − | 0.639120i | ||||
\(473\) | 21.5348 | − | 5.77024i | 0.990172 | − | 0.265316i | ||||
\(474\) | 4.88584 | 0.224414 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.3611 | 0.979083 | ||||||||
\(477\) | 9.52375 | − | 2.55188i | 0.436063 | − | 0.116843i | ||||
\(478\) | 3.46368 | + | 12.9266i | 0.158425 | + | 0.591250i | ||||
\(479\) | −2.12792 | + | 1.22856i | −0.0972272 | + | 0.0561341i | −0.547825 | − | 0.836593i | \(-0.684544\pi\) |
0.450598 | + | 0.892727i | \(0.351211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.724094 | + | 1.25417i | 0.0330158 | + | 0.0571851i | ||||
\(482\) | −13.2278 | + | 13.2278i | −0.602510 | + | 0.602510i | ||||
\(483\) | 19.1521 | − | 19.1521i | 0.871451 | − | 0.871451i | ||||
\(484\) | 12.8853 | − | 7.43936i | 0.585697 | − | 0.338153i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.9700 | 0.633692 | ||||||||
\(487\) | −7.28307 | − | 7.28307i | −0.330027 | − | 0.330027i | 0.522569 | − | 0.852597i | \(-0.324974\pi\) |
−0.852597 | + | 0.522569i | \(0.824974\pi\) | |||||||
\(488\) | −5.45165 | − | 1.46076i | −0.246785 | − | 0.0661257i | ||||
\(489\) | 1.52645 | − | 2.64389i | 0.0690286 | − | 0.119561i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.4517 | + | 18.1028i | −0.471678 | + | 0.816970i | −0.999475 | − | 0.0324007i | \(-0.989685\pi\) |
0.527797 | + | 0.849370i | \(0.323018\pi\) | |||||||
\(492\) | 1.78833 | + | 6.67416i | 0.0806244 | + | 0.300894i | ||||
\(493\) | −9.72676 | + | 9.72676i | −0.438071 | + | 0.438071i | ||||
\(494\) | 2.52374 | + | 6.76035i | 0.113548 | + | 0.304162i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.13067 | + | 3.53954i | 0.275275 | + | 0.158930i | ||||
\(497\) | 39.3413 | − | 10.5415i | 1.76470 | − | 0.472850i | ||||
\(498\) | 1.38476 | − | 5.16799i | 0.0620525 | − | 0.231583i | ||||
\(499\) | 24.1791 | + | 13.9598i | 1.08241 | + | 0.624927i | 0.931544 | − | 0.363628i | \(-0.118462\pi\) |
0.150861 | + | 0.988555i | \(0.451795\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.2737 | −0.727057 | ||||||||
\(502\) | 12.9604 | + | 12.9604i | 0.578453 | + | 0.578453i | ||||
\(503\) | −0.198659 | + | 0.741405i | −0.00885777 | + | 0.0330576i | −0.970213 | − | 0.242252i | \(-0.922114\pi\) |
0.961356 | + | 0.275310i | \(0.0887805\pi\) | |||||||
\(504\) | 2.03972 | + | 3.53290i | 0.0908564 | + | 0.157368i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 42.6333i | 1.89528i | ||||||||
\(507\) | 3.21912 | − | 12.0139i | 0.142966 | − | 0.533558i | ||||
\(508\) | −3.06175 | − | 11.4266i | −0.135843 | − | 0.506974i | ||||
\(509\) | −9.55337 | − | 16.5469i | −0.423446 | − | 0.733430i | 0.572828 | − | 0.819676i | \(-0.305846\pi\) |
−0.996274 | + | 0.0862459i | \(0.972513\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.75796 | − | 4.77694i | 0.122005 | − | 0.211319i | ||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −9.93855 | + | 21.7793i | −0.438798 | + | 0.961580i | ||||
\(514\) | 1.54422i | 0.0681128i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.60126 | + | 2.65654i | 0.202559 | + | 0.116948i | ||||
\(517\) | −50.7572 | − | 13.6003i | −2.23230 | − | 0.598142i | ||||
\(518\) | −2.25258 | + | 0.603576i | −0.0989726 | + | 0.0265196i | ||||
\(519\) | 10.8576 | − | 6.26862i | 0.476594 | − | 0.275162i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.6777i | − | 0.730665i | −0.930877 | − | 0.365332i | \(-0.880955\pi\) | ||
0.930877 | − | 0.365332i | \(-0.119045\pi\) | |||||||
\(522\) | −2.53749 | − | 0.679919i | −0.111063 | − | 0.0297592i | ||||
\(523\) | 7.84835 | + | 2.10296i | 0.343185 | + | 0.0919560i | 0.426295 | − | 0.904584i | \(-0.359819\pi\) |
−0.0831101 | + | 0.996540i | \(0.526485\pi\) | |||||||
\(524\) | 5.80617i | 0.253644i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.969923 | − | 0.559985i | 0.0422907 | − | 0.0244165i | ||||
\(527\) | 54.7910 | − | 14.6812i | 2.38674 | − | 0.639524i | ||||
\(528\) | 5.95710 | + | 1.59620i | 0.259250 | + | 0.0694657i | ||||
\(529\) | −40.9068 | − | 23.6176i | −1.77856 | − | 1.02685i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 21.9976i | − | 0.954615i | ||||||
\(532\) | −11.5672 | + | 1.10796i | −0.501502 | + | 0.0480361i | ||||
\(533\) | 6.67177 | + | 6.67177i | 0.288986 | + | 0.288986i | ||||
\(534\) | 6.38159 | − | 11.0532i | 0.276158 | − | 0.478321i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.703079 | − | 1.21777i | −0.0303684 | − | 0.0525996i | ||||
\(537\) | 4.79971 | + | 17.9128i | 0.207123 | + | 0.772993i | ||||
\(538\) | −1.00578 | + | 3.75364i | −0.0433624 | + | 0.161831i | ||||
\(539\) | − | 0.542888i | − | 0.0233839i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.51329 | − | 4.35315i | −0.108055 | − | 0.187157i | 0.806927 | − | 0.590651i | \(-0.201129\pi\) |
−0.914982 | + | 0.403494i | \(0.867796\pi\) | |||||||
\(542\) | 0.773189 | − | 2.88558i | 0.0332113 | − | 0.123946i | ||||
\(543\) | −13.2424 | − | 13.2424i | −0.568286 | − | 0.568286i | ||||
\(544\) | −8.01288 | −0.343549 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.63349 | − | 2.67515i | −0.198295 | − | 0.114486i | ||||
\(547\) | −11.0124 | + | 41.0987i | −0.470855 | + | 1.75725i | 0.165854 | + | 0.986150i | \(0.446962\pi\) |
−0.636709 | + | 0.771104i | \(0.719705\pi\) | |||||||
\(548\) | 16.5912 | − | 4.44559i | 0.708739 | − | 0.189906i | ||||
\(549\) | −7.47964 | − | 4.31837i | −0.319223 | − | 0.184304i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.76261 | − | 5.77163i | 0.202894 | − | 0.245880i | ||||
\(552\) | −7.18426 | + | 7.18426i | −0.305782 | + | 0.305782i | ||||
\(553\) | 2.78067 | + | 10.3776i | 0.118246 | + | 0.441301i | ||||
\(554\) | −11.3008 | + | 19.5735i | −0.480124 | + | 0.831599i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.79791 | + | 11.7743i | −0.288296 | + | 0.499343i | ||||
\(557\) | 36.1697 | + | 9.69165i | 1.53256 | + | 0.410648i | 0.923853 | − | 0.382747i | \(-0.125022\pi\) |
0.608707 | + | 0.793395i | \(0.291688\pi\) | |||||||
\(558\) | 7.65999 | + | 7.65999i | 0.324273 | + | 0.324273i | ||||
\(559\) | 7.25520 | 0.306862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 42.7967 | − | 24.7087i | 1.80688 | − | 1.04320i | ||||
\(562\) | 16.8468 | − | 16.8468i | 0.710641 | − | 0.710641i | ||||
\(563\) | 2.95561 | − | 2.95561i | 0.124564 | − | 0.124564i | −0.642076 | − | 0.766641i | \(-0.721927\pi\) |
0.766641 | + | 0.642076i | \(0.221927\pi\) | |||||||
\(564\) | −6.26141 | − | 10.8451i | −0.263653 | − | 0.456660i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.62020 | − | 4.39952i | 0.320301 | − | 0.184926i | ||||
\(567\) | −1.42652 | − | 5.32384i | −0.0599082 | − | 0.223580i | ||||
\(568\) | −14.7576 | + | 3.95427i | −0.619213 | + | 0.165918i | ||||
\(569\) | 8.11963 | 0.340393 | 0.170196 | − | 0.985410i | \(-0.445560\pi\) | ||||
0.170196 | + | 0.985410i | \(0.445560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.5277 | −1.27754 | −0.638772 | − | 0.769396i | \(-0.720557\pi\) | ||||
−0.638772 | + | 0.769396i | \(0.720557\pi\) | |||||||
\(572\) | 8.13464 | − | 2.17967i | 0.340126 | − | 0.0911366i | ||||
\(573\) | −4.52511 | − | 16.8880i | −0.189039 | − | 0.705504i | ||||
\(574\) | −13.1582 | + | 7.59692i | −0.549214 | + | 0.317089i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.765131 | − | 1.32525i | −0.0318805 | − | 0.0552186i | ||||
\(577\) | 3.75441 | − | 3.75441i | 0.156298 | − | 0.156298i | −0.624626 | − | 0.780924i | \(-0.714749\pi\) |
0.780924 | + | 0.624626i | \(0.214749\pi\) | |||||||
\(578\) | −33.3798 | + | 33.3798i | −1.38842 | + | 1.38842i | ||||
\(579\) | 8.06545 | − | 4.65659i | 0.335188 | − | 0.193521i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.7650 | 0.488095 | ||||||||
\(582\) | −8.89783 | − | 8.89783i | −0.368827 | − | 0.368827i | ||||
\(583\) | 31.6602 | + | 8.48332i | 1.31123 | + | 0.351343i | ||||
\(584\) | −1.03456 | + | 1.79190i | −0.0428102 | + | 0.0741495i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.88949 | + | 17.1291i | −0.408531 | + | 0.707596i | ||||
\(587\) | −0.526737 | − | 1.96581i | −0.0217407 | − | 0.0811376i | 0.954203 | − | 0.299159i | \(-0.0967063\pi\) |
−0.975944 | + | 0.218022i | \(0.930040\pi\) | |||||||
\(588\) | 0.0914838 | − | 0.0914838i | 0.00377273 | − | 0.00377273i | ||||
\(589\) | −28.9083 | + | 10.7919i | −1.19115 | + | 0.444673i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.3308 | + | 12.8927i | 0.918565 | + | 0.530334i | ||||
\(592\) | 0.844978 | − | 0.226411i | 0.0347284 | − | 0.00930544i | ||||
\(593\) | −3.63727 | + | 13.5745i | −0.149365 | + | 0.557437i | 0.850157 | + | 0.526529i | \(0.176507\pi\) |
−0.999522 | + | 0.0309085i | \(0.990160\pi\) | |||||||
\(594\) | 24.1961 | + | 13.9696i | 0.992778 | + | 0.573180i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.51066 | −0.389572 | ||||||||
\(597\) | −3.95224 | − | 3.95224i | −0.161754 | − | 0.161754i | ||||
\(598\) | −3.59085 | + | 13.4012i | −0.146841 | + | 0.548017i | ||||
\(599\) | 20.6686 | + | 35.7990i | 0.844495 | + | 1.46271i | 0.886059 | + | 0.463573i | \(0.153433\pi\) |
−0.0415632 | + | 0.999136i | \(0.513234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.7390i | 1.70257i | 0.524704 | + | 0.851285i | \(0.324176\pi\) | ||||
−0.524704 | + | 0.851285i | \(0.675824\pi\) | |||||||
\(602\) | −3.02383 | + | 11.2851i | −0.123242 | + | 0.459945i | ||||
\(603\) | −0.556925 | − | 2.07847i | −0.0226797 | − | 0.0846419i | ||||
\(604\) | 3.10564 | + | 5.37913i | 0.126367 | + | 0.218874i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.00698 | − | 6.94029i | 0.162772 | − | 0.281930i | ||||
\(607\) | −16.1858 | − | 16.1858i | −0.656963 | − | 0.656963i | 0.297697 | − | 0.954660i | \(-0.403781\pi\) |
−0.954660 | + | 0.297697i | \(0.903781\pi\) | |||||||
\(608\) | 4.33904 | − | 0.415613i | 0.175971 | − | 0.0168553i | ||||
\(609\) | 5.54816i | 0.224823i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.8094 | − | 8.55019i | −0.599122 | − | 0.345903i | ||||
\(612\) | −11.8440 | − | 3.17359i | −0.478765 | − | 0.128285i | ||||
\(613\) | −19.2434 | + | 5.15626i | −0.777235 | + | 0.208260i | −0.625566 | − | 0.780172i | \(-0.715132\pi\) |
−0.151670 | + | 0.988431i | \(0.548465\pi\) | |||||||
\(614\) | 10.7201 | − | 6.18923i | 0.432627 | − | 0.249777i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.5614i | 0.546406i | ||||||||
\(617\) | −14.9980 | − | 4.01870i | −0.603796 | − | 0.161787i | −0.0560454 | − | 0.998428i | \(-0.517849\pi\) |
−0.547751 | + | 0.836642i | \(0.684516\pi\) | |||||||
\(618\) | 10.5667 | + | 2.83134i | 0.425056 | + | 0.113893i | ||||
\(619\) | 32.8578i | 1.32067i | 0.750973 | + | 0.660333i | \(0.229585\pi\) | ||||
−0.750973 | + | 0.660333i | \(0.770415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −39.8613 | + | 23.0139i | −1.59958 | + | 0.923516i | ||||
\(622\) | −12.5240 | + | 3.35580i | −0.502168 | + | 0.134555i | ||||
\(623\) | 27.1093 | + | 7.26390i | 1.08611 | + | 0.291022i | ||||
\(624\) | 1.73810 | + | 1.00349i | 0.0695795 | + | 0.0401718i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.18956i | 0.167449i | ||||||||
\(627\) | −21.8932 | + | 15.5997i | −0.874329 | + | 0.622994i | ||||
\(628\) | 10.1321 | + | 10.1321i | 0.404316 | + | 0.404316i | ||||
\(629\) | 3.50477 | − | 6.07045i | 0.139744 | − | 0.242045i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1438 | + | 27.9620i | 0.642676 | + | 1.11315i | 0.984833 | + | 0.173505i | \(0.0555093\pi\) |
−0.342157 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(632\) | −1.04308 | − | 3.89281i | −0.0414913 | − | 0.154848i | ||||
\(633\) | 0.721077 | − | 2.69110i | 0.0286602 | − | 0.106961i | ||||
\(634\) | − | 8.43617i | − | 0.335043i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.90560 | + | 6.76470i | 0.154867 | + | 0.268238i | ||||
\(637\) | 0.0457255 | − | 0.170650i | 0.00181171 | − | 0.00676140i | ||||
\(638\) | −6.17520 | − | 6.17520i | −0.244479 | − | 0.244479i | ||||
\(639\) | −23.3796 | −0.924882 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.07111 | − | 2.92781i | −0.200297 | − | 0.115642i | 0.396497 | − | 0.918036i | \(-0.370226\pi\) |
−0.596794 | + | 0.802394i | \(0.703559\pi\) | |||||||
\(642\) | 2.90596 | − | 10.8452i | 0.114689 | − | 0.428026i | ||||
\(643\) | −10.6783 | + | 2.86125i | −0.421113 | + | 0.112837i | −0.463151 | − | 0.886279i | \(-0.653281\pi\) |
0.0420388 | + | 0.999116i | \(0.486615\pi\) | |||||||
\(644\) | −19.3483 | − | 11.1707i | −0.762429 | − | 0.440189i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.2300 | − | 26.9397i | 0.874627 | − | 1.05993i | ||||
\(647\) | −24.0362 | + | 24.0362i | −0.944960 | + | 0.944960i | −0.998562 | − | 0.0536023i | \(-0.982930\pi\) |
0.0536023 | + | 0.998562i | \(0.482930\pi\) | |||||||
\(648\) | 0.535110 | + | 1.99706i | 0.0210211 | + | 0.0784518i | ||||
\(649\) | 36.5637 | − | 63.3303i | 1.43525 | − | 2.48593i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.4394 | − | 19.8135i | 0.448344 | − | 0.776554i | ||||
\(652\) | −2.43241 | − | 0.651763i | −0.0952606 | − | 0.0255250i | ||||
\(653\) | 2.19175 | + | 2.19175i | 0.0857697 | + | 0.0857697i | 0.748690 | − | 0.662920i | \(-0.230683\pi\) |
−0.662920 | + | 0.748690i | \(0.730683\pi\) | |||||||
\(654\) | 5.10598 | 0.199659 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.93587 | − | 2.84972i | 0.192713 | − | 0.111263i | ||||
\(657\) | −2.23890 | + | 2.23890i | −0.0873479 | + | 0.0873479i | ||||
\(658\) | 19.4716 | − | 19.4716i | 0.759082 | − | 0.759082i | ||||
\(659\) | 2.00998 | + | 3.48139i | 0.0782978 | + | 0.135616i | 0.902516 | − | 0.430657i | \(-0.141718\pi\) |
−0.824218 | + | 0.566273i | \(0.808385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.46361 | + | 5.46382i | −0.368092 | + | 0.212518i | −0.672624 | − | 0.739984i | \(-0.734833\pi\) |
0.304533 | + | 0.952502i | \(0.401500\pi\) | |||||||
\(662\) | −2.49141 | − | 9.29808i | −0.0968315 | − | 0.361380i | ||||
\(663\) | 15.5337 | − | 4.16225i | 0.603280 | − | 0.161648i | ||||
\(664\) | −4.41324 | −0.171267 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.33865 | 0.0518717 | ||||||||
\(667\) | 13.8968 | − | 3.72364i | 0.538087 | − | 0.144180i | ||||
\(668\) | 3.47427 | + | 12.9661i | 0.134424 | + | 0.501675i | ||||
\(669\) | 21.6625 | − | 12.5069i | 0.837521 | − | 0.483543i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.3557 | − | 24.8649i | −0.554197 | − | 0.959897i | ||||
\(672\) | −2.28528 | + | 2.28528i | −0.0881566 | + | 0.0881566i | ||||
\(673\) | 7.33331 | − | 7.33331i | 0.282679 | − | 0.282679i | −0.551498 | − | 0.834176i | \(-0.685944\pi\) |
0.834176 | + | 0.551498i | \(0.185944\pi\) | |||||||
\(674\) | 3.18272 | − | 1.83754i | 0.122594 | − | 0.0707795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.2594 | −0.394592 | ||||||||
\(677\) | 20.7086 | + | 20.7086i | 0.795895 | + | 0.795895i | 0.982445 | − | 0.186550i | \(-0.0597307\pi\) |
−0.186550 | + | 0.982445i | \(0.559731\pi\) | |||||||
\(678\) | −11.4809 | − | 3.07630i | −0.440922 | − | 0.118145i | ||||
\(679\) | 13.8352 | − | 23.9632i | 0.530944 | − | 0.919623i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.98573 | − | 3.43939i | 0.0760935 | − | 0.131798i | ||||
\(682\) | 9.32062 | + | 34.7850i | 0.356905 | + | 1.33199i | ||||
\(683\) | 24.6294 | − | 24.6294i | 0.942417 | − | 0.942417i | −0.0560135 | − | 0.998430i | \(-0.517839\pi\) |
0.998430 | + | 0.0560135i | \(0.0178390\pi\) | |||||||
\(684\) | 6.57823 | + | 1.10420i | 0.251525 | + | 0.0422201i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.9144 | − | 9.18820i | −0.607616 | − | 0.350807i | ||||
\(687\) | 8.73014 | − | 2.33923i | 0.333075 | − | 0.0892473i | ||||
\(688\) | 1.13429 | − | 4.23321i | 0.0432442 | − | 0.161390i | ||||
\(689\) | 9.23745 | + | 5.33325i | 0.351919 | + | 0.203180i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0871 | −0.954359 | −0.477179 | − | 0.878806i | \(-0.658341\pi\) | ||||
−0.477179 | + | 0.878806i | \(0.658341\pi\) | |||||||
\(692\) | −7.31252 | − | 7.31252i | −0.277980 | − | 0.277980i | ||||
\(693\) | −5.37116 | + | 20.0454i | −0.204034 | + | 0.761464i | ||||
\(694\) | 0.215249 | + | 0.372822i | 0.00817073 | + | 0.0141521i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 2.08120i | − | 0.0788878i | ||||||
\(697\) | 11.8200 | − | 44.1128i | 0.447714 | − | 1.67089i | ||||
\(698\) | −2.96482 | − | 11.0648i | −0.112220 | − | 0.418810i | ||||
\(699\) | 6.83477 | + | 11.8382i | 0.258515 | + | 0.447761i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.67140 | + | 9.82316i | −0.214206 | + | 0.371016i | −0.953027 | − | 0.302887i | \(-0.902050\pi\) |
0.738821 | + | 0.673902i | \(0.235383\pi\) | |||||||
\(702\) | 6.42912 | + | 6.42912i | 0.242652 | + | 0.242652i | ||||
\(703\) | −1.58300 | + | 3.46898i | −0.0597040 | + | 0.130835i | ||||
\(704\) | − | 5.08711i | − | 0.191728i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.6597 | − | 15.3920i | −1.00335 | − | 0.579284i | ||||
\(707\) | 17.0218 | + | 4.56098i | 0.640171 | + | 0.171533i | ||||
\(708\) | 16.8334 | − | 4.51051i | 0.632640 | − | 0.169515i | ||||
\(709\) | −23.3759 | + | 13.4961i | −0.877901 | + | 0.506856i | −0.869966 | − | 0.493112i | \(-0.835859\pi\) |
−0.00793506 | + | 0.999969i | \(0.502526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.16716i | − | 0.231287i | ||||||
\(712\) | −10.1691 | − | 2.72481i | −0.381104 | − | 0.102116i | ||||
\(713\) | −57.3057 | − | 15.3550i | −2.14612 | − | 0.575050i | ||||
\(714\) | 25.8966i | 0.969156i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.2474 | − | 7.64838i | 0.495078 | − | 0.285833i | ||||
\(717\) | −15.6713 | + | 4.19911i | −0.585255 | + | 0.156819i | ||||
\(718\) | 35.9587 | + | 9.63510i | 1.34197 | + | 0.359579i | ||||
\(719\) | 5.21897 | + | 3.01318i | 0.194635 | + | 0.112372i | 0.594151 | − | 0.804354i | \(-0.297488\pi\) |
−0.399516 | + | 0.916726i | \(0.630822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0553i | 0.895867i | ||||||||
\(722\) | −10.6404 | + | 15.7411i | −0.395995 | + | 0.585822i | ||||
\(723\) | −16.0364 | − | 16.0364i | −0.596401 | − | 0.596401i | ||||
\(724\) | −7.72382 | + | 13.3780i | −0.287053 | + | 0.497191i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.01893 | + | 15.6213i | 0.334724 | + | 0.579759i | ||||
\(727\) | −0.343444 | − | 1.28175i | −0.0127376 | − | 0.0475375i | 0.959265 | − | 0.282509i | \(-0.0911668\pi\) |
−0.972002 | + | 0.234972i | \(0.924500\pi\) | |||||||
\(728\) | −1.14223 | + | 4.26287i | −0.0423339 | + | 0.157992i | ||||
\(729\) | 23.1387i | 0.856989i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5584 | − | 30.4120i | −0.649421 | − | 1.12483i | ||||
\(732\) | 1.77092 | − | 6.60918i | 0.0654553 | − | 0.244282i | ||||
\(733\) | 23.2056 | + | 23.2056i | 0.857120 | + | 0.857120i | 0.990998 | − | 0.133878i | \(-0.0427430\pi\) |
−0.133878 | + | 0.990998i | \(0.542743\pi\) | |||||||
\(734\) | −0.937051 | −0.0345872 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.25785 | + | 4.19032i | 0.267528 | + | 0.154457i | ||||
\(737\) | 1.85141 | − | 6.90954i | 0.0681974 | − | 0.254516i | ||||
\(738\) | 8.42447 | − | 2.25733i | 0.310109 | − | 0.0830935i | ||||
\(739\) | 1.10497 | + | 0.637953i | 0.0406469 | + | 0.0234675i | 0.520186 | − | 0.854053i | \(-0.325863\pi\) |
−0.479539 | + | 0.877521i | \(0.659196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.19575 | + | 3.05960i | −0.301078 | + | 0.112397i | ||||
\(742\) | −12.1456 | + | 12.1456i | −0.445878 | + | 0.445878i | ||||
\(743\) | 0.0708104 | + | 0.264268i | 0.00259778 | + | 0.00969505i | 0.967213 | − | 0.253968i | \(-0.0817359\pi\) |
−0.964615 | + | 0.263663i | \(0.915069\pi\) | |||||||
\(744\) | −4.29108 | + | 7.43238i | −0.157319 | + | 0.272484i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.9511 | − | 22.4320i | 0.474174 | − | 0.821294i | ||||
\(747\) | −6.52331 | − | 1.74791i | −0.238675 | − | 0.0639528i | ||||
\(748\) | −28.8234 | − | 28.8234i | −1.05389 | − | 1.05389i | ||||
\(749\) | 24.6893 | 0.902126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.25436 | − | 4.76566i | 0.301206 | − | 0.173901i | −0.341779 | − | 0.939780i | \(-0.611029\pi\) |
0.642984 | + | 0.765879i | \(0.277696\pi\) | |||||||
\(752\) | −7.30411 | + | 7.30411i | −0.266353 | + | 0.266353i | ||||
\(753\) | −15.7123 | + | 15.7123i | −0.572588 | + | 0.572588i | ||||
\(754\) | −1.42098 | − | 2.46121i | −0.0517490 | − | 0.0896320i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.6797 | + | 7.32062i | −0.461156 | + | 0.266248i | ||||
\(757\) | 6.68168 | + | 24.9364i | 0.242850 | + | 0.906328i | 0.974452 | + | 0.224596i | \(0.0721063\pi\) |
−0.731602 | + | 0.681732i | \(0.761227\pi\) | |||||||
\(758\) | −31.6974 | + | 8.49328i | −1.15130 | + | 0.308490i | ||||
\(759\) | −51.6855 | −1.87606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.4904 | 1.21403 | 0.607014 | − | 0.794691i | \(-0.292367\pi\) | ||||
0.607014 | + | 0.794691i | \(0.292367\pi\) | |||||||
\(762\) | 13.8528 | − | 3.71185i | 0.501834 | − | 0.134466i | ||||
\(763\) | 2.90596 | + | 10.8452i | 0.105203 | + | 0.392622i | ||||
\(764\) | −12.4895 | + | 7.21080i | −0.451853 | + | 0.260878i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.42005 | − | 9.38781i | −0.195835 | − | 0.339195i | ||||
\(767\) | 16.8274 | − | 16.8274i | 0.607603 | − | 0.607603i | ||||
\(768\) | 0.857245 | − | 0.857245i | 0.0309332 | − | 0.0309332i | ||||
\(769\) | −40.9858 | + | 23.6631i | −1.47798 | + | 0.853315i | −0.999690 | − | 0.0248847i | \(-0.992078\pi\) |
−0.478294 | + | 0.878200i | \(0.658745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.87210 | −0.0674222 | ||||||||
\(772\) | −5.43204 | − | 5.43204i | −0.195503 | − | 0.195503i | ||||
\(773\) | 31.0899 | + | 8.33051i | 1.11823 | + | 0.299628i | 0.770165 | − | 0.637845i | \(-0.220174\pi\) |
0.348060 | + | 0.937472i | \(0.386840\pi\) | |||||||
\(774\) | 3.35322 | − | 5.80795i | 0.120529 | − | 0.208763i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.18979 | + | 8.98897i | −0.186302 | + | 0.322685i | ||||
\(777\) | −0.731732 | − | 2.73086i | −0.0262507 | − | 0.0979691i | ||||
\(778\) | 15.3183 | − | 15.3183i | 0.549187 | − | 0.549187i | ||||
\(779\) | −4.11258 | + | 24.5005i | −0.147348 | + | 0.877823i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67.3089 | − | 38.8608i | −2.40850 | − | 1.39055i | ||||
\(782\) | 64.8649 | − | 17.3805i | 2.31956 | − | 0.621525i | ||||
\(783\) | 2.44025 | − | 9.10713i | 0.0872074 | − | 0.325462i | ||||
\(784\) | −0.0924208 | − | 0.0533592i | −0.00330074 | − | 0.00190569i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.03898 | −0.251072 | ||||||||
\(787\) | −20.9433 | − | 20.9433i | −0.746547 | − | 0.746547i | 0.227282 | − | 0.973829i | \(-0.427016\pi\) |
−0.973829 | + | 0.227282i | \(0.927016\pi\) | |||||||
\(788\) | 5.50490 | − | 20.5446i | 0.196104 | − | 0.731870i | ||||
\(789\) | 0.678886 | + | 1.17586i | 0.0241690 | + | 0.0418619i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 26.1365i | − | 0.929308i | ||||||
\(792\) | 2.01481 | − | 7.51937i | 0.0715931 | − | 0.267189i | ||||
\(793\) | −2.41826 | − | 9.02508i | −0.0858751 | − | 0.320490i | ||||
\(794\) | 12.4300 | + | 21.5295i | 0.441126 | + | 0.764053i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.30520 | + | 3.99272i | −0.0817056 | + | 0.141518i | ||||
\(797\) | −21.1881 | − | 21.1881i | −0.750521 | − | 0.750521i | 0.224056 | − | 0.974576i | \(-0.428070\pi\) |
−0.974576 | + | 0.224056i | \(0.928070\pi\) | |||||||
\(798\) | −1.34321 | − | 14.0232i | −0.0475490 | − | 0.496417i | ||||
\(799\) | 82.7696i | 2.92818i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.9520 | − | 8.05518i | −0.492969 | − | 0.284616i | ||||
\(802\) | 28.1812 | + | 7.55113i | 0.995112 | + | 0.266640i | ||||
\(803\) | −10.1672 | + | 2.72428i | −0.358791 | + | 0.0961377i | ||||
\(804\) | 1.47633 | − | 0.852362i | 0.0520663 | − | 0.0300605i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.7193i | 0.412794i | ||||||||
\(807\) | −4.55064 | − | 1.21934i | −0.160190 | − | 0.0429228i | ||||
\(808\) | −6.38515 | − | 1.71090i | −0.224629 | − | 0.0601891i | ||||
\(809\) | 17.3630i | 0.610451i | 0.952280 | + | 0.305226i | \(0.0987319\pi\) | ||||
−0.952280 | + | 0.305226i | \(0.901268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.18151 | + | 4.14625i | −0.252177 | + | 0.145594i | −0.620761 | − | 0.784000i | \(-0.713176\pi\) |
0.368584 | + | 0.929595i | \(0.379843\pi\) | |||||||
\(812\) | 4.42052 | − | 1.18447i | 0.155130 | − | 0.0415669i | ||||
\(813\) | 3.49827 | + | 0.937358i | 0.122690 | + | 0.0328746i | ||||
\(814\) | 3.85393 | + | 2.22507i | 0.135080 | + | 0.0779885i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 9.71423i | − | 0.340066i | ||||||
\(817\) | 11.0854 | + | 15.5576i | 0.387830 | + | 0.544293i | ||||
\(818\) | −9.08015 | − | 9.08015i | −0.317480 | − | 0.317480i | ||||
\(819\) | −3.37671 | + | 5.84864i | −0.117992 | + | 0.204368i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.91289 | + | 11.9735i | 0.241261 | + | 0.417877i | 0.961074 | − | 0.276292i | \(-0.0891055\pi\) |
−0.719812 | + | 0.694169i | \(0.755772\pi\) | |||||||
\(822\) | 5.38951 | + | 20.1139i | 0.187981 | + | 0.701553i | ||||
\(823\) | −0.304420 | + | 1.13611i | −0.0106114 | + | 0.0396023i | −0.971029 | − | 0.238963i | \(-0.923192\pi\) |
0.960417 | + | 0.278566i | \(0.0898590\pi\) | |||||||
\(824\) | − | 9.02353i | − | 0.314350i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.1608 | + | 33.1875i | 0.666690 | + | 1.15474i | ||||
\(827\) | −8.41337 | + | 31.3991i | −0.292562 | + | 1.09185i | 0.650573 | + | 0.759444i | \(0.274529\pi\) |
−0.943135 | + | 0.332411i | \(0.892138\pi\) | |||||||
\(828\) | 9.06835 | + | 9.06835i | 0.315147 | + | 0.315147i | ||||
\(829\) | −23.1927 | −0.805516 | −0.402758 | − | 0.915307i | \(-0.631948\pi\) | ||||
−0.402758 | + | 0.915307i | \(0.631948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.7295 | − | 13.7002i | −0.823167 | − | 0.475256i | ||||
\(832\) | 0.428469 | − | 1.59907i | 0.0148545 | − | 0.0554377i | ||||
\(833\) | −0.825984 | + | 0.221322i | −0.0286186 | + | 0.00766834i | ||||
\(834\) | −14.2743 | − | 8.24129i | −0.494280 | − | 0.285373i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.1031 | + | 14.1131i | 0.591523 | + | 0.488111i | ||||
\(837\) | −27.4919 | + | 27.4919i | −0.950261 | + | 0.950261i | ||||
\(838\) | −4.60480 | − | 17.1854i | −0.159070 | − | 0.593659i | ||||
\(839\) | 25.4002 | − | 43.9944i | 0.876912 | − | 1.51886i | 0.0222001 | − | 0.999754i | \(-0.492933\pi\) |
0.854712 | − | 0.519103i | \(-0.173734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0265 | − | 22.5625i | 0.449189 | − | 0.778017i | ||||
\(842\) | 32.9205 | + | 8.82102i | 1.13451 | + | 0.303992i | ||||
\(843\) | 20.4239 | + | 20.4239i | 0.703435 | + | 0.703435i | ||||
\(844\) | −2.29808 | −0.0791032 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.6892 | + | 7.90348i | −0.470645 | + | 0.271727i | ||||
\(847\) | −28.0469 | + | 28.0469i | −0.963703 | + | 0.963703i | ||||
\(848\) | 4.55600 | − | 4.55600i | 0.156454 | − | 0.156454i | ||||
\(849\) | 5.33366 | + | 9.23817i | 0.183051 | + | 0.317053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.34906 | + | 3.66563i | −0.217643 | + | 0.125656i | ||||
\(852\) | −4.79387 | − | 17.8910i | −0.164235 | − | 0.612935i | ||||
\(853\) | 35.0879 | − | 9.40178i | 1.20139 | − | 0.321911i | 0.398010 | − | 0.917381i | \(-0.369701\pi\) |
0.803377 | + | 0.595470i | \(0.203034\pi\) | |||||||
\(854\) | 15.0459 | 0.514861 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.26134 | −0.316546 | ||||||||
\(857\) | 15.7194 | − | 4.21201i | 0.536966 | − | 0.143880i | 0.0198628 | − | 0.999803i | \(-0.493677\pi\) |
0.517103 | + | 0.855923i | \(0.327010\pi\) | |||||||
\(858\) | 2.64247 | + | 9.86185i | 0.0902126 | + | 0.336678i | ||||
\(859\) | 26.5596 | − | 15.3342i | 0.906201 | − | 0.523196i | 0.0269944 | − | 0.999636i | \(-0.491406\pi\) |
0.879207 | + | 0.476440i | \(0.158073\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.20995 | − | 15.9521i | −0.313874 | − | 0.543646i | ||||
\(862\) | 17.1947 | − | 17.1947i | 0.585652 | − | 0.585652i | ||||
\(863\) | −7.66348 | + | 7.66348i | −0.260868 | + | 0.260868i | −0.825407 | − | 0.564539i | \(-0.809054\pi\) |
0.564539 | + | 0.825407i | \(0.309054\pi\) | |||||||
\(864\) | 4.75635 | − | 2.74608i | 0.161814 | − | 0.0934235i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.7731 | −0.875806 | ||||||||
\(867\) | −40.4673 | − | 40.4673i | −1.37434 | − | 1.37434i | ||||
\(868\) | −18.2287 | − | 4.88436i | −0.618722 | − | 0.165786i | ||||
\(869\) | 10.2509 | − | 17.7550i | 0.347737 | − | 0.602298i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.16393 | − | 2.01599i | 0.0394383 | − | 0.0683092i | ||||
\(872\) | −1.09007 | − | 4.06820i | −0.0369145 | − | 0.137767i | ||||
\(873\) | −11.2313 | + | 11.2313i | −0.380122 | + | 0.380122i | ||||
\(874\) | −34.2234 | + | 12.7761i | −1.15762 | + | 0.432158i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.17237 | − | 1.25422i | −0.0733977 | − | 0.0423762i | ||||
\(877\) | 13.5051 | − | 3.61868i | 0.456035 | − | 0.122194i | −0.0234870 | − | 0.999724i | \(-0.507477\pi\) |
0.479522 | + | 0.877530i | \(0.340810\pi\) | |||||||
\(878\) | 0.265341 | − | 0.990266i | 0.00895482 | − | 0.0334198i | ||||
\(879\) | −20.7661 | − | 11.9893i | −0.700422 | − | 0.404389i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.2524 | 0.817085 | 0.408542 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(882\) | −0.115476 | − | 0.115476i | −0.00388827 | − | 0.00388827i | ||||
\(883\) | 1.87920 | − | 7.01327i | 0.0632401 | − | 0.236015i | −0.927070 | − | 0.374888i | \(-0.877681\pi\) |
0.990310 | + | 0.138873i | \(0.0443479\pi\) | |||||||
\(884\) | −6.63257 | − | 11.4879i | −0.223077 | − | 0.386382i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.29575i | 0.278701i | ||||||||
\(887\) | 4.01762 | − | 14.9940i | 0.134899 | − | 0.503449i | −0.865100 | − | 0.501600i | \(-0.832745\pi\) |
0.999998 | − | 0.00184854i | \(-0.000588408\pi\) | |||||||
\(888\) | 0.274484 | + | 1.02439i | 0.00921109 | + | 0.0343763i | ||||
\(889\) | 15.7681 | + | 27.3111i | 0.528844 | + | 0.915985i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.25882 | + | 9.10854i | −0.176177 | + | 0.305148i | ||||
\(892\) | −14.5896 | − | 14.5896i | −0.488496 | − | 0.488496i | ||||
\(893\) | −4.29310 | − | 44.8204i | −0.143663 | − | 1.49986i | ||||
\(894\) | − | 11.5300i | − | 0.385622i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.30869 | + | 1.33292i | 0.0771278 | + | 0.0445298i | ||||
\(897\) | −16.2467 | − | 4.35328i | −0.542460 | − | 0.145352i | ||||
\(898\) | −18.9353 | + | 5.07369i | −0.631878 | + | 0.169311i | ||||
\(899\) | 10.5245 | − | 6.07634i | 0.351013 | − | 0.202657i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 51.6282i | − | 1.71998i | ||||||
\(902\) | 28.0058 | + | 7.50413i | 0.932491 | + | 0.249860i | ||||
\(903\) | −13.6812 | − | 3.66587i | −0.455282 | − | 0.121992i | ||||
\(904\) | 9.80423i | 0.326084i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.52127 | + | 3.76506i | −0.216655 | + | 0.125086i | ||||
\(907\) | 32.3118 | − | 8.65791i | 1.07289 | − | 0.287481i | 0.321213 | − | 0.947007i | \(-0.395909\pi\) |
0.751682 | + | 0.659526i | \(0.229243\pi\) | |||||||
\(908\) | −3.16428 | − | 0.847867i | −0.105010 | − | 0.0281375i | ||||
\(909\) | −8.76040 | − | 5.05782i | −0.290564 | − | 0.167757i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.3197i | 0.739486i | 0.929134 | + | 0.369743i | \(0.120554\pi\) | ||||
−0.929134 | + | 0.369743i | \(0.879446\pi\) | |||||||
\(912\) | 0.503858 | + | 5.26034i | 0.0166844 | + | 0.174187i | ||||
\(913\) | −15.8750 | − | 15.8750i | −0.525386 | − | 0.525386i | ||||
\(914\) | 13.7904 | − | 23.8857i | 0.456146 | − | 0.790069i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.72758 | − | 6.45636i | −0.123163 | − | 0.213324i | ||||
\(917\) | −4.00609 | − | 14.9509i | −0.132293 | − | 0.493723i | ||||
\(918\) | 11.3901 | − | 42.5085i | 0.375930 | − | 1.40299i | ||||
\(919\) | − | 50.0242i | − | 1.65015i | −0.565027 | − | 0.825073i | \(-0.691134\pi\) | ||
0.565027 | − | 0.825073i | \(-0.308866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.50337 | + | 12.9962i | 0.247245 | + | 0.428240i | ||||
\(922\) | 1.99276 | − | 7.43710i | 0.0656282 | − | 0.244928i | ||||
\(923\) | −17.8846 | − | 17.8846i | −0.588678 | − | 0.588678i | ||||
\(924\) | −16.4409 | −0.540866 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.4625 | + | 8.92725i | 0.508128 | + | 0.293368i | ||||
\(927\) | 3.57387 | − | 13.3379i | 0.117381 | − | 0.438073i | ||||
\(928\) | −1.65821 | + | 0.444315i | −0.0544333 | + | 0.0145854i | ||||
\(929\) | 11.8563 | + | 6.84526i | 0.388994 | + | 0.224586i | 0.681724 | − | 0.731609i | \(-0.261230\pi\) |
−0.292730 | + | 0.956195i | \(0.594564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.435798 | − | 0.162690i | 0.0142827 | − | 0.00533194i | ||||
\(932\) | 7.97295 | − | 7.97295i | 0.261163 | − | 0.261163i | ||||
\(933\) | −4.06833 | − | 15.1832i | −0.133191 | − | 0.497076i | ||||
\(934\) | −7.73216 | + | 13.3925i | −0.253004 | + | 0.438216i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.26666 | − | 2.19392i | 0.0414020 | − | 0.0717104i | ||||
\(937\) | 4.32476 | + | 1.15881i | 0.141284 | + | 0.0378568i | 0.328768 | − | 0.944411i | \(-0.393367\pi\) |
−0.187484 | + | 0.982268i | \(0.560033\pi\) | |||||||
\(938\) | 2.65066 | + | 2.65066i | 0.0865470 | + | 0.0865470i | ||||
\(939\) | −5.07912 | −0.165751 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3527 | + | 16.9468i | −0.956871 | + | 0.552450i | −0.895209 | − | 0.445648i | \(-0.852973\pi\) |
−0.0616622 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(942\) | −12.2835 | + | 12.2835i | −0.400217 | + | 0.400217i | ||||
\(943\) | −33.7750 | + | 33.7750i | −1.09986 | + | 1.09986i | ||||
\(944\) | −7.18753 | − | 12.4492i | −0.233934 | − | 0.405186i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3076 | − | 11.1472i | 0.627744 | − | 0.362428i | ||||
\(947\) | −13.1384 | − | 49.0334i | −0.426942 | − | 1.59337i | −0.759645 | − | 0.650338i | \(-0.774627\pi\) |
0.332703 | − | 0.943032i | \(-0.392039\pi\) | |||||||
\(948\) | 4.71936 | − | 1.26455i | 0.153278 | − | 0.0410706i | ||||
\(949\) | −3.42537 | −0.111192 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2274 | 0.331646 | ||||||||
\(952\) | 20.6332 | − | 5.52865i | 0.668726 | − | 0.179185i | ||||
\(953\) | 2.55499 | + | 9.53536i | 0.0827643 | + | 0.308881i | 0.994881 | − | 0.101049i | \(-0.0322199\pi\) |
−0.912117 | + | 0.409930i | \(0.865553\pi\) | |||||||
\(954\) | 8.53876 | − | 4.92986i | 0.276453 | − | 0.159610i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.69131 | + | 11.5897i | 0.216413 | + | 0.374837i | ||||
\(957\) | 7.48636 | − | 7.48636i | 0.242000 | − | 0.242000i | ||||
\(958\) | −1.73744 | + | 1.73744i | −0.0561341 | + | 0.0561341i | ||||
\(959\) | −39.6550 | + | 22.8948i | −1.28053 | + | 0.739313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1135 | −0.616563 | ||||||||
\(962\) | 1.02402 | + | 1.02402i | 0.0330158 | + | 0.0330158i | ||||
\(963\) | −13.6894 | − | 3.66806i | −0.441134 | − | 0.118201i | ||||
\(964\) | −9.35347 | + | 16.2007i | −0.301255 | + | 0.521789i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.5426 | − | 23.4564i | 0.435726 | − | 0.754699i | ||||
\(967\) | −5.63481 | − | 21.0294i | −0.181203 | − | 0.676260i | −0.995411 | − | 0.0956872i | \(-0.969495\pi\) |
0.814208 | − | 0.580573i | \(-0.197172\pi\) | |||||||
\(968\) | 10.5208 | − | 10.5208i | 0.338153 | − | 0.338153i | ||||
\(969\) | 32.6597 | + | 26.9500i | 1.04918 | + | 0.865759i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.8347 | − | 9.14215i | −0.508159 | − | 0.293386i | 0.223918 | − | 0.974608i | \(-0.428115\pi\) |
−0.732077 | + | 0.681222i | \(0.761449\pi\) | |||||||
\(972\) | 13.4940 | − | 3.61570i | 0.432819 | − | 0.115974i | ||||
\(973\) | 9.38072 | − | 35.0093i | 0.300732 | − | 1.12235i | ||||
\(974\) | −8.91990 | − | 5.14991i | −0.285812 | − | 0.165014i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.64396 | −0.180659 | ||||||||
\(977\) | 2.79812 | + | 2.79812i | 0.0895197 | + | 0.0895197i | 0.750449 | − | 0.660929i | \(-0.229838\pi\) |
−0.660929 | + | 0.750449i | \(0.729838\pi\) | |||||||
\(978\) | 0.790150 | − | 2.94888i | 0.0252662 | − | 0.0942948i | ||||
\(979\) | −26.7781 | − | 46.3811i | −0.855833 | − | 1.48235i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.44503i | − | 0.205774i | ||||||
\(982\) | −5.41019 | + | 20.1911i | −0.172646 | + | 0.644324i | ||||
\(983\) | −1.59078 | − | 5.93687i | −0.0507380 | − | 0.189357i | 0.935906 | − | 0.352251i | \(-0.114584\pi\) |
−0.986644 | + | 0.162894i | \(0.947917\pi\) | |||||||
\(984\) | 3.45480 | + | 5.98388i | 0.110135 | + | 0.190759i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.87786 | + | 11.9128i | −0.219036 | + | 0.379381i | ||||
\(987\) | 23.6060 | + | 23.6060i | 0.751386 | + | 0.751386i | ||||
\(988\) | 4.18745 | + | 5.87680i | 0.133221 | + | 0.186966i | ||||
\(989\) | 36.7285i | 1.16790i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.11089 | − | 1.79607i | −0.0988205 | − | 0.0570541i | 0.449775 | − | 0.893142i | \(-0.351504\pi\) |
−0.548596 | + | 0.836088i | \(0.684837\pi\) | |||||||
\(992\) | 6.83787 | + | 1.83220i | 0.217103 | + | 0.0581725i | ||||
\(993\) | 11.2723 | − | 3.02041i | 0.357716 | − | 0.0958498i | ||||
\(994\) | 35.2725 | − | 20.3646i | 1.11877 | − | 0.645925i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 5.35029i | − | 0.169531i | ||||||
\(997\) | −19.0140 | − | 5.09479i | −0.602180 | − | 0.161354i | −0.0551662 | − | 0.998477i | \(-0.517569\pi\) |
−0.547014 | + | 0.837124i | \(0.684236\pi\) | |||||||
\(998\) | 26.9683 | + | 7.22613i | 0.853666 | + | 0.228739i | ||||
\(999\) | 4.80446i | 0.152006i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 950.2.q.f.293.7 | yes | 32 | |
5.2 | odd | 4 | inner | 950.2.q.f.407.7 | yes | 32 | |
5.3 | odd | 4 | inner | 950.2.q.f.407.2 | yes | 32 | |
5.4 | even | 2 | inner | 950.2.q.f.293.2 | yes | 32 | |
19.12 | odd | 6 | inner | 950.2.q.f.943.7 | yes | 32 | |
95.12 | even | 12 | inner | 950.2.q.f.107.7 | yes | 32 | |
95.69 | odd | 6 | inner | 950.2.q.f.943.2 | yes | 32 | |
95.88 | even | 12 | inner | 950.2.q.f.107.2 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.q.f.107.2 | ✓ | 32 | 95.88 | even | 12 | inner | |
950.2.q.f.107.7 | yes | 32 | 95.12 | even | 12 | inner | |
950.2.q.f.293.2 | yes | 32 | 5.4 | even | 2 | inner | |
950.2.q.f.293.7 | yes | 32 | 1.1 | even | 1 | trivial | |
950.2.q.f.407.2 | yes | 32 | 5.3 | odd | 4 | inner | |
950.2.q.f.407.7 | yes | 32 | 5.2 | odd | 4 | inner | |
950.2.q.f.943.2 | yes | 32 | 95.69 | odd | 6 | inner | |
950.2.q.f.943.7 | yes | 32 | 19.12 | odd | 6 | inner |