Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (of order \(4\), degree \(2\), 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: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.8 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.3.f.b.93.8 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.74954 | − | 1.74954i | 0.583178 | − | 0.583178i | −0.352597 | − | 0.935775i | \(-0.614701\pi\) |
0.935775 | + | 0.352597i | \(0.114701\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −3.63965 | + | 3.42826i | −0.727929 | + | 0.685652i | ||||
\(6\) | 3.49907 | 0.583178 | ||||||||
\(7\) | 4.68530 | + | 4.68530i | 0.669329 | + | 0.669329i | 0.957561 | − | 0.288232i | \(-0.0930673\pi\) |
−0.288232 | + | 0.957561i | \(0.593067\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.87825i | 0.319806i | ||||||||
\(10\) | −7.06791 | − | 0.211383i | −0.706791 | − | 0.0211383i | ||||
\(11\) | 7.34415 | 0.667650 | 0.333825 | − | 0.942635i | \(-0.391660\pi\) | ||||
0.333825 | + | 0.942635i | \(0.391660\pi\) | |||||||
\(12\) | 3.49907 | + | 3.49907i | 0.291589 | + | 0.291589i | ||||
\(13\) | −0.802148 | + | 0.802148i | −0.0617037 | + | 0.0617037i | −0.737285 | − | 0.675582i | \(-0.763893\pi\) |
0.675582 | + | 0.737285i | \(0.263893\pi\) | |||||||
\(14\) | 9.37061i | 0.669329i | ||||||||
\(15\) | −0.369822 | + | 12.3656i | −0.0246548 | + | 0.824370i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 2.03445 | + | 2.03445i | 0.119674 | + | 0.119674i | 0.764407 | − | 0.644734i | \(-0.223032\pi\) |
−0.644734 | + | 0.764407i | \(0.723032\pi\) | |||||||
\(18\) | −2.87825 | + | 2.87825i | −0.159903 | + | 0.159903i | ||||
\(19\) | 12.6979i | 0.668313i | 0.942518 | + | 0.334156i | \(0.108451\pi\) | ||||
−0.942518 | + | 0.334156i | \(0.891549\pi\) | |||||||
\(20\) | −6.85652 | − | 7.27929i | −0.342826 | − | 0.363965i | ||||
\(21\) | 16.3942 | 0.780677 | ||||||||
\(22\) | 7.34415 | + | 7.34415i | 0.333825 | + | 0.333825i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 6.99814i | 0.291589i | ||||||||
\(25\) | 1.49404 | − | 24.9553i | 0.0597614 | − | 0.998213i | ||||
\(26\) | −1.60430 | −0.0617037 | ||||||||
\(27\) | 20.7814 | + | 20.7814i | 0.769682 | + | 0.769682i | ||||
\(28\) | −9.37061 | + | 9.37061i | −0.334665 | + | 0.334665i | ||||
\(29\) | − | 18.2947i | − | 0.630851i | −0.948950 | − | 0.315426i | \(-0.897853\pi\) | ||
0.948950 | − | 0.315426i | \(-0.102147\pi\) | |||||||
\(30\) | −12.7354 | + | 11.9957i | −0.424512 | + | 0.399858i | ||||
\(31\) | 32.9458 | 1.06277 | 0.531384 | − | 0.847131i | \(-0.321672\pi\) | ||||
0.531384 | + | 0.847131i | \(0.321672\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 12.8489 | − | 12.8489i | 0.389359 | − | 0.389359i | ||||
\(34\) | 4.06891i | 0.119674i | ||||||||
\(35\) | −33.1153 | − | 0.990394i | −0.946151 | − | 0.0282970i | ||||
\(36\) | −5.75651 | −0.159903 | ||||||||
\(37\) | −22.1338 | − | 22.1338i | −0.598212 | − | 0.598212i | 0.341625 | − | 0.939836i | \(-0.389023\pi\) |
−0.939836 | + | 0.341625i | \(0.889023\pi\) | |||||||
\(38\) | −12.6979 | + | 12.6979i | −0.334156 | + | 0.334156i | ||||
\(39\) | 2.80677i | 0.0719686i | ||||||||
\(40\) | 0.422766 | − | 14.1358i | 0.0105691 | − | 0.353395i | ||||
\(41\) | −16.8120 | −0.410049 | −0.205024 | − | 0.978757i | \(-0.565727\pi\) | ||||
−0.205024 | + | 0.978757i | \(0.565727\pi\) | |||||||
\(42\) | 16.3942 | + | 16.3942i | 0.390338 | + | 0.390338i | ||||
\(43\) | 15.6643 | − | 15.6643i | 0.364285 | − | 0.364285i | −0.501103 | − | 0.865388i | \(-0.667072\pi\) |
0.865388 | + | 0.501103i | \(0.167072\pi\) | |||||||
\(44\) | 14.6883i | 0.333825i | ||||||||
\(45\) | −9.86741 | − | 10.4758i | −0.219276 | − | 0.232796i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −53.7739 | − | 53.7739i | −1.14412 | − | 1.14412i | −0.987688 | − | 0.156437i | \(-0.949999\pi\) |
−0.156437 | − | 0.987688i | \(-0.550001\pi\) | |||||||
\(48\) | −6.99814 | + | 6.99814i | −0.145795 | + | 0.145795i | ||||
\(49\) | − | 5.09584i | − | 0.103997i | ||||||
\(50\) | 26.4494 | − | 23.4613i | 0.528987 | − | 0.469226i | ||||
\(51\) | 7.11869 | 0.139582 | ||||||||
\(52\) | −1.60430 | − | 1.60430i | −0.0308519 | − | 0.0308519i | ||||
\(53\) | −15.1999 | + | 15.1999i | −0.286790 | + | 0.286790i | −0.835809 | − | 0.549020i | \(-0.815001\pi\) |
0.549020 | + | 0.835809i | \(0.315001\pi\) | |||||||
\(54\) | 41.5628i | 0.769682i | ||||||||
\(55\) | −26.7301 | + | 25.1777i | −0.486002 | + | 0.457776i | ||||
\(56\) | −18.7412 | −0.334665 | ||||||||
\(57\) | 22.2155 | + | 22.2155i | 0.389745 | + | 0.389745i | ||||
\(58\) | 18.2947 | − | 18.2947i | 0.315426 | − | 0.315426i | ||||
\(59\) | 8.32600i | 0.141119i | 0.997508 | + | 0.0705593i | \(0.0224784\pi\) | ||||
−0.997508 | + | 0.0705593i | \(0.977522\pi\) | |||||||
\(60\) | −24.7311 | − | 0.739644i | −0.412185 | − | 0.0123274i | ||||
\(61\) | 16.1313 | 0.264448 | 0.132224 | − | 0.991220i | \(-0.457788\pi\) | ||||
0.132224 | + | 0.991220i | \(0.457788\pi\) | |||||||
\(62\) | 32.9458 | + | 32.9458i | 0.531384 | + | 0.531384i | ||||
\(63\) | −13.4855 | + | 13.4855i | −0.214055 | + | 0.214055i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0.169561 | − | 5.66951i | 0.00260862 | − | 0.0872233i | ||||
\(66\) | 25.6977 | 0.389359 | ||||||||
\(67\) | 21.8813 | + | 21.8813i | 0.326587 | + | 0.326587i | 0.851287 | − | 0.524700i | \(-0.175823\pi\) |
−0.524700 | + | 0.851287i | \(0.675823\pi\) | |||||||
\(68\) | −4.06891 | + | 4.06891i | −0.0598368 | + | 0.0598368i | ||||
\(69\) | − | 11.8659i | − | 0.171970i | ||||||
\(70\) | −32.1249 | − | 34.1057i | −0.458927 | − | 0.487224i | ||||
\(71\) | −105.543 | −1.48652 | −0.743258 | − | 0.669005i | \(-0.766721\pi\) | ||||
−0.743258 | + | 0.669005i | \(0.766721\pi\) | |||||||
\(72\) | −5.75651 | − | 5.75651i | −0.0799515 | − | 0.0799515i | ||||
\(73\) | 63.5112 | − | 63.5112i | 0.870017 | − | 0.870017i | −0.122457 | − | 0.992474i | \(-0.539077\pi\) |
0.992474 | + | 0.122457i | \(0.0390773\pi\) | |||||||
\(74\) | − | 44.2677i | − | 0.598212i | ||||||
\(75\) | −41.0463 | − | 46.2741i | −0.547285 | − | 0.616988i | ||||
\(76\) | −25.3959 | −0.334156 | ||||||||
\(77\) | 34.4096 | + | 34.4096i | 0.446878 | + | 0.446878i | ||||
\(78\) | −2.80677 | + | 2.80677i | −0.0359843 | + | 0.0359843i | ||||
\(79\) | − | 19.7472i | − | 0.249964i | −0.992159 | − | 0.124982i | \(-0.960113\pi\) | ||
0.992159 | − | 0.124982i | \(-0.0398874\pi\) | |||||||
\(80\) | 14.5586 | − | 13.7130i | 0.181982 | − | 0.171413i | ||||
\(81\) | 46.8114 | 0.577918 | ||||||||
\(82\) | −16.8120 | − | 16.8120i | −0.205024 | − | 0.205024i | ||||
\(83\) | 105.262 | − | 105.262i | 1.26822 | − | 1.26822i | 0.321214 | − | 0.947007i | \(-0.395909\pi\) |
0.947007 | − | 0.321214i | \(-0.104091\pi\) | |||||||
\(84\) | 32.7884i | 0.390338i | ||||||||
\(85\) | −14.3793 | − | 0.430049i | −0.169169 | − | 0.00505940i | ||||
\(86\) | 31.3285 | 0.364285 | ||||||||
\(87\) | −32.0072 | − | 32.0072i | −0.367899 | − | 0.367899i | ||||
\(88\) | −14.6883 | + | 14.6883i | −0.166913 | + | 0.166913i | ||||
\(89\) | − | 131.803i | − | 1.48093i | −0.672092 | − | 0.740467i | \(-0.734604\pi\) | ||
0.672092 | − | 0.740467i | \(-0.265396\pi\) | |||||||
\(90\) | 0.608414 | − | 20.3432i | 0.00676015 | − | 0.226036i | ||||
\(91\) | −7.51662 | −0.0826002 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 57.6398 | − | 57.6398i | 0.619783 | − | 0.619783i | ||||
\(94\) | − | 107.548i | − | 1.14412i | ||||||
\(95\) | −43.5319 | − | 46.2160i | −0.458230 | − | 0.486484i | ||||
\(96\) | −13.9963 | −0.145795 | ||||||||
\(97\) | 101.232 | + | 101.232i | 1.04362 | + | 1.04362i | 0.999004 | + | 0.0446199i | \(0.0142077\pi\) |
0.0446199 | + | 0.999004i | \(0.485792\pi\) | |||||||
\(98\) | 5.09584 | − | 5.09584i | 0.0519984 | − | 0.0519984i | ||||
\(99\) | 21.1383i | 0.213519i | ||||||||
\(100\) | 49.9106 | + | 2.98807i | 0.499106 | + | 0.0298807i | ||||
\(101\) | −33.1423 | −0.328141 | −0.164071 | − | 0.986449i | \(-0.552463\pi\) | ||||
−0.164071 | + | 0.986449i | \(0.552463\pi\) | |||||||
\(102\) | 7.11869 | + | 7.11869i | 0.0697911 | + | 0.0697911i | ||||
\(103\) | 63.5710 | − | 63.5710i | 0.617194 | − | 0.617194i | −0.327616 | − | 0.944811i | \(-0.606245\pi\) |
0.944811 | + | 0.327616i | \(0.106245\pi\) | |||||||
\(104\) | − | 3.20859i | − | 0.0308519i | ||||||
\(105\) | −59.6691 | + | 56.2037i | −0.568277 | + | 0.535273i | ||||
\(106\) | −30.3997 | −0.286790 | ||||||||
\(107\) | 49.0182 | + | 49.0182i | 0.458114 | + | 0.458114i | 0.898036 | − | 0.439922i | \(-0.144994\pi\) |
−0.439922 | + | 0.898036i | \(0.644994\pi\) | |||||||
\(108\) | −41.5628 | + | 41.5628i | −0.384841 | + | 0.384841i | ||||
\(109\) | 192.423i | 1.76534i | 0.469989 | + | 0.882672i | \(0.344258\pi\) | ||||
−0.469989 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(110\) | −51.9078 | − | 1.55243i | −0.471889 | − | 0.0141130i | ||||
\(111\) | −77.4478 | −0.697728 | ||||||||
\(112\) | −18.7412 | − | 18.7412i | −0.167332 | − | 0.167332i | ||||
\(113\) | 68.6393 | − | 68.6393i | 0.607428 | − | 0.607428i | −0.334845 | − | 0.942273i | \(-0.608684\pi\) |
0.942273 | + | 0.334845i | \(0.108684\pi\) | |||||||
\(114\) | 44.4310i | 0.389745i | ||||||||
\(115\) | −0.716834 | + | 23.9684i | −0.00623334 | + | 0.208421i | ||||
\(116\) | 36.5894 | 0.315426 | ||||||||
\(117\) | −2.30879 | − | 2.30879i | −0.0197332 | − | 0.0197332i | ||||
\(118\) | −8.32600 | + | 8.32600i | −0.0705593 | + | 0.0705593i | ||||
\(119\) | 19.0641i | 0.160202i | ||||||||
\(120\) | −23.9915 | − | 25.4707i | −0.199929 | − | 0.212256i | ||||
\(121\) | −67.0634 | −0.554243 | ||||||||
\(122\) | 16.1313 | + | 16.1313i | 0.132224 | + | 0.132224i | ||||
\(123\) | −29.4132 | + | 29.4132i | −0.239131 | + | 0.239131i | ||||
\(124\) | 65.8916i | 0.531384i | ||||||||
\(125\) | 80.1156 | + | 95.9504i | 0.640925 | + | 0.767604i | ||||
\(126\) | −26.9710 | −0.214055 | ||||||||
\(127\) | 39.6115 | + | 39.6115i | 0.311901 | + | 0.311901i | 0.845646 | − | 0.533744i | \(-0.179216\pi\) |
−0.533744 | + | 0.845646i | \(0.679216\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | − | 54.8103i | − | 0.424886i | ||||||
\(130\) | 5.83907 | − | 5.49995i | 0.0449159 | − | 0.0423073i | ||||
\(131\) | −151.732 | −1.15826 | −0.579130 | − | 0.815236i | \(-0.696607\pi\) | ||||
−0.579130 | + | 0.815236i | \(0.696607\pi\) | |||||||
\(132\) | 25.6977 | + | 25.6977i | 0.194680 | + | 0.194680i | ||||
\(133\) | −59.4937 | + | 59.4937i | −0.447321 | + | 0.447321i | ||||
\(134\) | 43.7626i | 0.326587i | ||||||||
\(135\) | −146.881 | − | 4.39284i | −1.08801 | − | 0.0325395i | ||||
\(136\) | −8.13781 | −0.0598368 | ||||||||
\(137\) | 115.031 | + | 115.031i | 0.839642 | + | 0.839642i | 0.988812 | − | 0.149169i | \(-0.0476600\pi\) |
−0.149169 | + | 0.988812i | \(0.547660\pi\) | |||||||
\(138\) | 11.8659 | − | 11.8659i | 0.0859850 | − | 0.0859850i | ||||
\(139\) | − | 8.87351i | − | 0.0638382i | −0.999490 | − | 0.0319191i | \(-0.989838\pi\) | ||
0.999490 | − | 0.0319191i | \(-0.0101619\pi\) | |||||||
\(140\) | 1.98079 | − | 66.2306i | 0.0141485 | − | 0.473076i | ||||
\(141\) | −188.159 | −1.33446 | ||||||||
\(142\) | −105.543 | − | 105.543i | −0.743258 | − | 0.743258i | ||||
\(143\) | −5.89110 | + | 5.89110i | −0.0411965 | + | 0.0411965i | ||||
\(144\) | − | 11.5130i | − | 0.0799515i | ||||||
\(145\) | 62.7190 | + | 66.5862i | 0.432545 | + | 0.459215i | ||||
\(146\) | 127.022 | 0.870017 | ||||||||
\(147\) | −8.91535 | − | 8.91535i | −0.0606487 | − | 0.0606487i | ||||
\(148\) | 44.2677 | − | 44.2677i | 0.299106 | − | 0.299106i | ||||
\(149\) | 98.3865i | 0.660312i | 0.943926 | + | 0.330156i | \(0.107101\pi\) | ||||
−0.943926 | + | 0.330156i | \(0.892899\pi\) | |||||||
\(150\) | 5.22773 | − | 87.3204i | 0.0348516 | − | 0.582136i | ||||
\(151\) | −74.3468 | −0.492363 | −0.246181 | − | 0.969224i | \(-0.579176\pi\) | ||||
−0.246181 | + | 0.969224i | \(0.579176\pi\) | |||||||
\(152\) | −25.3959 | − | 25.3959i | −0.167078 | − | 0.167078i | ||||
\(153\) | −5.85567 | + | 5.85567i | −0.0382724 | + | 0.0382724i | ||||
\(154\) | 68.8192i | 0.446878i | ||||||||
\(155\) | −119.911 | + | 112.947i | −0.773620 | + | 0.728689i | ||||
\(156\) | −5.61355 | −0.0359843 | ||||||||
\(157\) | 102.456 | + | 102.456i | 0.652587 | + | 0.652587i | 0.953615 | − | 0.301028i | \(-0.0973298\pi\) |
−0.301028 | + | 0.953615i | \(0.597330\pi\) | |||||||
\(158\) | 19.7472 | − | 19.7472i | 0.124982 | − | 0.124982i | ||||
\(159\) | 53.1853i | 0.334499i | ||||||||
\(160\) | 28.2716 | + | 0.845532i | 0.176698 | + | 0.00528457i | ||||
\(161\) | 31.7773 | 0.197374 | ||||||||
\(162\) | 46.8114 | + | 46.8114i | 0.288959 | + | 0.288959i | ||||
\(163\) | 69.6921 | − | 69.6921i | 0.427559 | − | 0.427559i | −0.460237 | − | 0.887796i | \(-0.652236\pi\) |
0.887796 | + | 0.460237i | \(0.152236\pi\) | |||||||
\(164\) | − | 33.6240i | − | 0.205024i | ||||||
\(165\) | −2.71603 | + | 90.8145i | −0.0164608 | + | 0.550391i | ||||
\(166\) | 210.525 | 1.26822 | ||||||||
\(167\) | −134.667 | − | 134.667i | −0.806391 | − | 0.806391i | 0.177695 | − | 0.984086i | \(-0.443136\pi\) |
−0.984086 | + | 0.177695i | \(0.943136\pi\) | |||||||
\(168\) | −32.7884 | + | 32.7884i | −0.195169 | + | 0.195169i | ||||
\(169\) | 167.713i | 0.992385i | ||||||||
\(170\) | −13.9493 | − | 14.8094i | −0.0820546 | − | 0.0871140i | ||||
\(171\) | −36.5479 | −0.213730 | ||||||||
\(172\) | 31.3285 | + | 31.3285i | 0.182143 | + | 0.182143i | ||||
\(173\) | −54.9807 | + | 54.9807i | −0.317808 | + | 0.317808i | −0.847925 | − | 0.530117i | \(-0.822148\pi\) |
0.530117 | + | 0.847925i | \(0.322148\pi\) | |||||||
\(174\) | − | 64.0144i | − | 0.367899i | ||||||
\(175\) | 123.923 | − | 109.923i | 0.708133 | − | 0.628133i | ||||
\(176\) | −29.3766 | −0.166913 | ||||||||
\(177\) | 14.5666 | + | 14.5666i | 0.0822974 | + | 0.0822974i | ||||
\(178\) | 131.803 | − | 131.803i | 0.740467 | − | 0.740467i | ||||
\(179\) | 151.781i | 0.847941i | 0.905676 | + | 0.423970i | \(0.139364\pi\) | ||||
−0.905676 | + | 0.423970i | \(0.860636\pi\) | |||||||
\(180\) | 20.9516 | − | 19.7348i | 0.116398 | − | 0.109638i | ||||
\(181\) | −13.6959 | −0.0756682 | −0.0378341 | − | 0.999284i | \(-0.512046\pi\) | ||||
−0.0378341 | + | 0.999284i | \(0.512046\pi\) | |||||||
\(182\) | −7.51662 | − | 7.51662i | −0.0413001 | − | 0.0413001i | ||||
\(183\) | 28.2223 | − | 28.2223i | 0.154220 | − | 0.154220i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | 156.440 | + | 4.67871i | 0.845621 | + | 0.0252903i | ||||
\(186\) | 115.280 | 0.619783 | ||||||||
\(187\) | 14.9413 | + | 14.9413i | 0.0799002 | + | 0.0799002i | ||||
\(188\) | 107.548 | − | 107.548i | 0.572062 | − | 0.572062i | ||||
\(189\) | 194.735i | 1.03034i | ||||||||
\(190\) | 2.68413 | − | 89.7479i | 0.0141270 | − | 0.472357i | ||||
\(191\) | −222.336 | −1.16406 | −0.582032 | − | 0.813166i | \(-0.697742\pi\) | ||||
−0.582032 | + | 0.813166i | \(0.697742\pi\) | |||||||
\(192\) | −13.9963 | − | 13.9963i | −0.0728973 | − | 0.0728973i | ||||
\(193\) | 107.725 | − | 107.725i | 0.558158 | − | 0.558158i | −0.370625 | − | 0.928783i | \(-0.620856\pi\) |
0.928783 | + | 0.370625i | \(0.120856\pi\) | |||||||
\(194\) | 202.463i | 1.04362i | ||||||||
\(195\) | −9.62236 | − | 10.2157i | −0.0493454 | − | 0.0523880i | ||||
\(196\) | 10.1917 | 0.0519984 | ||||||||
\(197\) | −5.03748 | − | 5.03748i | −0.0255709 | − | 0.0255709i | 0.694206 | − | 0.719777i | \(-0.255756\pi\) |
−0.719777 | + | 0.694206i | \(0.755756\pi\) | |||||||
\(198\) | −21.1383 | + | 21.1383i | −0.106759 | + | 0.106759i | ||||
\(199\) | 127.303i | 0.639711i | 0.947466 | + | 0.319856i | \(0.103634\pi\) | ||||
−0.947466 | + | 0.319856i | \(0.896366\pi\) | |||||||
\(200\) | 46.9226 | + | 52.8987i | 0.234613 | + | 0.264494i | ||||
\(201\) | 76.5642 | 0.380916 | ||||||||
\(202\) | −33.1423 | − | 33.1423i | −0.164071 | − | 0.164071i | ||||
\(203\) | 85.7162 | − | 85.7162i | 0.422247 | − | 0.422247i | ||||
\(204\) | 14.2374i | 0.0697911i | ||||||||
\(205\) | 61.1897 | − | 57.6359i | 0.298486 | − | 0.281151i | ||||
\(206\) | 127.142 | 0.617194 | ||||||||
\(207\) | 9.76063 | + | 9.76063i | 0.0471528 | + | 0.0471528i | ||||
\(208\) | 3.20859 | − | 3.20859i | 0.0154259 | − | 0.0154259i | ||||
\(209\) | 93.2556i | 0.446199i | ||||||||
\(210\) | −115.873 | − | 3.46546i | −0.551775 | − | 0.0165022i | ||||
\(211\) | 9.59463 | 0.0454722 | 0.0227361 | − | 0.999742i | \(-0.492762\pi\) | ||||
0.0227361 | + | 0.999742i | \(0.492762\pi\) | |||||||
\(212\) | −30.3997 | − | 30.3997i | −0.143395 | − | 0.143395i | ||||
\(213\) | −184.651 | + | 184.651i | −0.866904 | + | 0.866904i | ||||
\(214\) | 98.0363i | 0.458114i | ||||||||
\(215\) | −3.31116 | + | 110.714i | −0.0154007 | + | 0.514947i | ||||
\(216\) | −83.1257 | −0.384841 | ||||||||
\(217\) | 154.361 | + | 154.361i | 0.711342 | + | 0.711342i | ||||
\(218\) | −192.423 | + | 192.423i | −0.882672 | + | 0.882672i | ||||
\(219\) | − | 222.230i | − | 1.01475i | ||||||
\(220\) | −50.3554 | − | 53.4602i | −0.228888 | − | 0.243001i | ||||
\(221\) | −3.26387 | −0.0147686 | ||||||||
\(222\) | −77.4478 | − | 77.4478i | −0.348864 | − | 0.348864i | ||||
\(223\) | 231.304 | − | 231.304i | 1.03724 | − | 1.03724i | 0.0379566 | − | 0.999279i | \(-0.487915\pi\) |
0.999279 | − | 0.0379566i | \(-0.0120849\pi\) | |||||||
\(224\) | − | 37.4824i | − | 0.167332i | ||||||
\(225\) | 71.8277 | + | 4.30021i | 0.319234 | + | 0.0191121i | ||||
\(226\) | 137.279 | 0.607428 | ||||||||
\(227\) | −295.186 | − | 295.186i | −1.30038 | − | 1.30038i | −0.928134 | − | 0.372247i | \(-0.878588\pi\) |
−0.372247 | − | 0.928134i | \(-0.621412\pi\) | |||||||
\(228\) | −44.4310 | + | 44.4310i | −0.194873 | + | 0.194873i | ||||
\(229\) | − | 441.791i | − | 1.92922i | −0.263687 | − | 0.964608i | \(-0.584939\pi\) | ||
0.263687 | − | 0.964608i | \(-0.415061\pi\) | |||||||
\(230\) | −24.6853 | + | 23.2516i | −0.107327 | + | 0.101094i | ||||
\(231\) | 120.402 | 0.521219 | ||||||||
\(232\) | 36.5894 | + | 36.5894i | 0.157713 | + | 0.157713i | ||||
\(233\) | −142.357 | + | 142.357i | −0.610974 | + | 0.610974i | −0.943200 | − | 0.332226i | \(-0.892200\pi\) |
0.332226 | + | 0.943200i | \(0.392200\pi\) | |||||||
\(234\) | − | 4.61757i | − | 0.0197332i | ||||||
\(235\) | 380.069 | + | 11.3669i | 1.61731 | + | 0.0483697i | ||||
\(236\) | −16.6520 | −0.0705593 | ||||||||
\(237\) | −34.5484 | − | 34.5484i | −0.145774 | − | 0.145774i | ||||
\(238\) | −19.0641 | + | 19.0641i | −0.0801011 | + | 0.0801011i | ||||
\(239\) | 103.472i | 0.432938i | 0.976289 | + | 0.216469i | \(0.0694541\pi\) | ||||
−0.976289 | + | 0.216469i | \(0.930546\pi\) | |||||||
\(240\) | 1.47929 | − | 49.4622i | 0.00616370 | − | 0.206093i | ||||
\(241\) | 11.4659 | 0.0475762 | 0.0237881 | − | 0.999717i | \(-0.492427\pi\) | ||||
0.0237881 | + | 0.999717i | \(0.492427\pi\) | |||||||
\(242\) | −67.0634 | − | 67.0634i | −0.277122 | − | 0.277122i | ||||
\(243\) | −105.135 | + | 105.135i | −0.432653 | + | 0.432653i | ||||
\(244\) | 32.2626i | 0.132224i | ||||||||
\(245\) | 17.4699 | + | 18.5471i | 0.0713056 | + | 0.0757023i | ||||
\(246\) | −58.8263 | −0.239131 | ||||||||
\(247\) | −10.1856 | − | 10.1856i | −0.0412374 | − | 0.0412374i | ||||
\(248\) | −65.8916 | + | 65.8916i | −0.265692 | + | 0.265692i | ||||
\(249\) | − | 368.320i | − | 1.47920i | ||||||
\(250\) | −15.8348 | + | 176.066i | −0.0633393 | + | 0.704264i | ||||
\(251\) | 46.6849 | 0.185996 | 0.0929978 | − | 0.995666i | \(-0.470355\pi\) | ||||
0.0929978 | + | 0.995666i | \(0.470355\pi\) | |||||||
\(252\) | −26.9710 | − | 26.9710i | −0.107028 | − | 0.107028i | ||||
\(253\) | 24.9052 | − | 24.9052i | 0.0984397 | − | 0.0984397i | ||||
\(254\) | 79.2229i | 0.311901i | ||||||||
\(255\) | −25.9095 | + | 24.4047i | −0.101606 | + | 0.0957049i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −309.876 | − | 309.876i | −1.20574 | − | 1.20574i | −0.972393 | − | 0.233351i | \(-0.925031\pi\) |
−0.233351 | − | 0.972393i | \(-0.574969\pi\) | |||||||
\(258\) | 54.8103 | − | 54.8103i | 0.212443 | − | 0.212443i | ||||
\(259\) | − | 207.407i | − | 0.800801i | ||||||
\(260\) | 11.3390 | + | 0.339121i | 0.0436116 | + | 0.00130431i | ||||
\(261\) | 52.6567 | 0.201750 | ||||||||
\(262\) | −151.732 | − | 151.732i | −0.579130 | − | 0.579130i | ||||
\(263\) | −45.9507 | + | 45.9507i | −0.174718 | + | 0.174718i | −0.789048 | − | 0.614331i | \(-0.789426\pi\) |
0.614331 | + | 0.789048i | \(0.289426\pi\) | |||||||
\(264\) | 51.3954i | 0.194680i | ||||||||
\(265\) | 3.21299 | − | 107.431i | 0.0121245 | − | 0.405401i | ||||
\(266\) | −118.987 | −0.447321 | ||||||||
\(267\) | −230.594 | − | 230.594i | −0.863649 | − | 0.863649i | ||||
\(268\) | −43.7626 | + | 43.7626i | −0.163293 | + | 0.163293i | ||||
\(269\) | − | 138.967i | − | 0.516606i | −0.966064 | − | 0.258303i | \(-0.916837\pi\) | ||
0.966064 | − | 0.258303i | \(-0.0831632\pi\) | |||||||
\(270\) | −142.488 | − | 151.274i | −0.527735 | − | 0.560274i | ||||
\(271\) | −373.516 | −1.37829 | −0.689143 | − | 0.724625i | \(-0.742013\pi\) | ||||
−0.689143 | + | 0.724625i | \(0.742013\pi\) | |||||||
\(272\) | −8.13781 | − | 8.13781i | −0.0299184 | − | 0.0299184i | ||||
\(273\) | −13.1506 | + | 13.1506i | −0.0481707 | + | 0.0481707i | ||||
\(274\) | 230.062i | 0.839642i | ||||||||
\(275\) | 10.9724 | − | 183.276i | 0.0398997 | − | 0.666457i | ||||
\(276\) | 23.7318 | 0.0859850 | ||||||||
\(277\) | 329.820 | + | 329.820i | 1.19069 | + | 1.19069i | 0.976875 | + | 0.213813i | \(0.0685882\pi\) |
0.213813 | + | 0.976875i | \(0.431412\pi\) | |||||||
\(278\) | 8.87351 | − | 8.87351i | 0.0319191 | − | 0.0319191i | ||||
\(279\) | 94.8264i | 0.339880i | ||||||||
\(280\) | 68.2114 | − | 64.2498i | 0.243612 | − | 0.229464i | ||||
\(281\) | 433.168 | 1.54152 | 0.770761 | − | 0.637124i | \(-0.219876\pi\) | ||||
0.770761 | + | 0.637124i | \(0.219876\pi\) | |||||||
\(282\) | −188.159 | − | 188.159i | −0.667229 | − | 0.667229i | ||||
\(283\) | −112.199 | + | 112.199i | −0.396462 | + | 0.396462i | −0.876983 | − | 0.480521i | \(-0.840448\pi\) |
0.480521 | + | 0.876983i | \(0.340448\pi\) | |||||||
\(284\) | − | 211.085i | − | 0.743258i | ||||||
\(285\) | −157.017 | − | 4.69598i | −0.550937 | − | 0.0164771i | ||||
\(286\) | −11.7822 | −0.0411965 | ||||||||
\(287\) | −78.7693 | − | 78.7693i | −0.274457 | − | 0.274457i | ||||
\(288\) | 11.5130 | − | 11.5130i | 0.0399757 | − | 0.0399757i | ||||
\(289\) | − | 280.722i | − | 0.971356i | ||||||
\(290\) | −3.86719 | + | 129.305i | −0.0133351 | + | 0.445880i | ||||
\(291\) | 354.216 | 1.21724 | ||||||||
\(292\) | 127.022 | + | 127.022i | 0.435008 | + | 0.435008i | ||||
\(293\) | −157.692 | + | 157.692i | −0.538196 | + | 0.538196i | −0.922999 | − | 0.384803i | \(-0.874270\pi\) |
0.384803 | + | 0.922999i | \(0.374270\pi\) | |||||||
\(294\) | − | 17.8307i | − | 0.0606487i | ||||||
\(295\) | −28.5437 | − | 30.3037i | −0.0967584 | − | 0.102724i | ||||
\(296\) | 88.5353 | 0.299106 | ||||||||
\(297\) | 152.622 | + | 152.622i | 0.513879 | + | 0.513879i | ||||
\(298\) | −98.3865 | + | 98.3865i | −0.330156 | + | 0.330156i | ||||
\(299\) | 5.44044i | 0.0181954i | ||||||||
\(300\) | 92.5481 | − | 82.0927i | 0.308494 | − | 0.273642i | ||||
\(301\) | 146.784 | 0.487653 | ||||||||
\(302\) | −74.3468 | − | 74.3468i | −0.246181 | − | 0.246181i | ||||
\(303\) | −57.9836 | + | 57.9836i | −0.191365 | + | 0.191365i | ||||
\(304\) | − | 50.7918i | − | 0.167078i | ||||||
\(305\) | −58.7122 | + | 55.3023i | −0.192499 | + | 0.181319i | ||||
\(306\) | −11.7113 | −0.0382724 | ||||||||
\(307\) | 157.847 | + | 157.847i | 0.514159 | + | 0.514159i | 0.915798 | − | 0.401639i | \(-0.131559\pi\) |
−0.401639 | + | 0.915798i | \(0.631559\pi\) | |||||||
\(308\) | −68.8192 | + | 68.8192i | −0.223439 | + | 0.223439i | ||||
\(309\) | − | 222.440i | − | 0.719869i | ||||||
\(310\) | −232.858 | − | 6.96418i | −0.751155 | − | 0.0224651i | ||||
\(311\) | −543.283 | −1.74689 | −0.873445 | − | 0.486923i | \(-0.838119\pi\) | ||||
−0.873445 | + | 0.486923i | \(0.838119\pi\) | |||||||
\(312\) | −5.61355 | − | 5.61355i | −0.0179921 | − | 0.0179921i | ||||
\(313\) | 30.7142 | − | 30.7142i | 0.0981286 | − | 0.0981286i | −0.656338 | − | 0.754467i | \(-0.727896\pi\) |
0.754467 | + | 0.656338i | \(0.227896\pi\) | |||||||
\(314\) | 204.912i | 0.652587i | ||||||||
\(315\) | 2.85060 | − | 95.3142i | 0.00904954 | − | 0.302585i | ||||
\(316\) | 39.4944 | 0.124982 | ||||||||
\(317\) | −370.911 | − | 370.911i | −1.17007 | − | 1.17007i | −0.982193 | − | 0.187873i | \(-0.939841\pi\) |
−0.187873 | − | 0.982193i | \(-0.560159\pi\) | |||||||
\(318\) | −53.1853 | + | 53.1853i | −0.167250 | + | 0.167250i | ||||
\(319\) | − | 134.359i | − | 0.421188i | ||||||
\(320\) | 27.4261 | + | 29.1172i | 0.0857066 | + | 0.0909911i | ||||
\(321\) | 171.518 | 0.534324 | ||||||||
\(322\) | 31.7773 | + | 31.7773i | 0.0986872 | + | 0.0986872i | ||||
\(323\) | −25.8334 | + | 25.8334i | −0.0799794 | + | 0.0799794i | ||||
\(324\) | 93.6228i | 0.288959i | ||||||||
\(325\) | 18.8194 | + | 21.2163i | 0.0579059 | + | 0.0652809i | ||||
\(326\) | 139.384 | 0.427559 | ||||||||
\(327\) | 336.650 | + | 336.650i | 1.02951 | + | 1.02951i | ||||
\(328\) | 33.6240 | − | 33.6240i | 0.102512 | − | 0.102512i | ||||
\(329\) | − | 503.894i | − | 1.53159i | ||||||
\(330\) | −93.5305 | + | 88.0985i | −0.283426 | + | 0.266965i | ||||
\(331\) | −334.223 | −1.00974 | −0.504869 | − | 0.863196i | \(-0.668459\pi\) | ||||
−0.504869 | + | 0.863196i | \(0.668459\pi\) | |||||||
\(332\) | 210.525 | + | 210.525i | 0.634110 | + | 0.634110i | ||||
\(333\) | 63.7068 | − | 63.7068i | 0.191312 | − | 0.191312i | ||||
\(334\) | − | 269.335i | − | 0.806391i | ||||||
\(335\) | −154.655 | − | 4.62533i | −0.461657 | − | 0.0138070i | ||||
\(336\) | −65.5768 | −0.195169 | ||||||||
\(337\) | −280.330 | − | 280.330i | −0.831841 | − | 0.831841i | 0.155927 | − | 0.987769i | \(-0.450163\pi\) |
−0.987769 | + | 0.155927i | \(0.950163\pi\) | |||||||
\(338\) | −167.713 | + | 167.713i | −0.496193 | + | 0.496193i | ||||
\(339\) | − | 240.174i | − | 0.708477i | ||||||
\(340\) | 0.860097 | − | 28.7586i | 0.00252970 | − | 0.0845843i | ||||
\(341\) | 241.959 | 0.709557 | ||||||||
\(342\) | −36.5479 | − | 36.5479i | −0.106865 | − | 0.106865i | ||||
\(343\) | 253.455 | − | 253.455i | 0.738937 | − | 0.738937i | ||||
\(344\) | 62.6570i | 0.182143i | ||||||||
\(345\) | 40.6795 | + | 43.1878i | 0.117912 | + | 0.125182i | ||||
\(346\) | −109.961 | −0.317808 | ||||||||
\(347\) | 433.965 | + | 433.965i | 1.25062 | + | 1.25062i | 0.955443 | + | 0.295176i | \(0.0953782\pi\) |
0.295176 | + | 0.955443i | \(0.404622\pi\) | |||||||
\(348\) | 64.0144 | − | 64.0144i | 0.183949 | − | 0.183949i | ||||
\(349\) | − | 221.072i | − | 0.633443i | −0.948519 | − | 0.316721i | \(-0.897418\pi\) | ||
0.948519 | − | 0.316721i | \(-0.102582\pi\) | |||||||
\(350\) | 233.847 | + | 14.0000i | 0.668133 | + | 0.0400001i | ||||
\(351\) | −33.3396 | −0.0949845 | ||||||||
\(352\) | −29.3766 | − | 29.3766i | −0.0834563 | − | 0.0834563i | ||||
\(353\) | −10.4152 | + | 10.4152i | −0.0295049 | + | 0.0295049i | −0.721705 | − | 0.692200i | \(-0.756641\pi\) |
0.692200 | + | 0.721705i | \(0.256641\pi\) | |||||||
\(354\) | 29.1333i | 0.0822974i | ||||||||
\(355\) | 384.138 | − | 361.828i | 1.08208 | − | 1.01923i | ||||
\(356\) | 263.606 | 0.740467 | ||||||||
\(357\) | 33.3532 | + | 33.3532i | 0.0934265 | + | 0.0934265i | ||||
\(358\) | −151.781 | + | 151.781i | −0.423970 | + | 0.423970i | ||||
\(359\) | 92.8731i | 0.258699i | 0.991599 | + | 0.129350i | \(0.0412890\pi\) | ||||
−0.991599 | + | 0.129350i | \(0.958711\pi\) | |||||||
\(360\) | 40.6865 | + | 1.21683i | 0.113018 | + | 0.00338008i | ||||
\(361\) | 199.762 | 0.553358 | ||||||||
\(362\) | −13.6959 | − | 13.6959i | −0.0378341 | − | 0.0378341i | ||||
\(363\) | −117.330 | + | 117.330i | −0.323223 | + | 0.323223i | ||||
\(364\) | − | 15.0332i | − | 0.0413001i | ||||||
\(365\) | −13.4252 | + | 448.892i | −0.0367814 | + | 1.22984i | ||||
\(366\) | 56.4446 | 0.154220 | ||||||||
\(367\) | −42.3293 | − | 42.3293i | −0.115339 | − | 0.115339i | 0.647082 | − | 0.762421i | \(-0.275989\pi\) |
−0.762421 | + | 0.647082i | \(0.775989\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 48.3892i | − | 0.131136i | ||||||
\(370\) | 151.761 | + | 161.119i | 0.410165 | + | 0.435456i | ||||
\(371\) | −142.432 | −0.383913 | ||||||||
\(372\) | 115.280 | + | 115.280i | 0.309892 | + | 0.309892i | ||||
\(373\) | −99.0976 | + | 99.0976i | −0.265677 | + | 0.265677i | −0.827356 | − | 0.561678i | \(-0.810156\pi\) |
0.561678 | + | 0.827356i | \(0.310156\pi\) | |||||||
\(374\) | 29.8827i | 0.0799002i | ||||||||
\(375\) | 308.034 | + | 27.7036i | 0.821423 | + | 0.0738763i | ||||
\(376\) | 215.095 | 0.572062 | ||||||||
\(377\) | 14.6751 | + | 14.6751i | 0.0389259 | + | 0.0389259i | ||||
\(378\) | −194.735 | + | 194.735i | −0.515171 | + | 0.515171i | ||||
\(379\) | 267.871i | 0.706784i | 0.935475 | + | 0.353392i | \(0.114972\pi\) | ||||
−0.935475 | + | 0.353392i | \(0.885028\pi\) | |||||||
\(380\) | 92.4320 | − | 87.0637i | 0.243242 | − | 0.229115i | ||||
\(381\) | 138.603 | 0.363788 | ||||||||
\(382\) | −222.336 | − | 222.336i | −0.582032 | − | 0.582032i | ||||
\(383\) | 193.931 | − | 193.931i | 0.506347 | − | 0.506347i | −0.407056 | − | 0.913403i | \(-0.633445\pi\) |
0.913403 | + | 0.407056i | \(0.133445\pi\) | |||||||
\(384\) | − | 27.9926i | − | 0.0728973i | ||||||
\(385\) | −243.204 | − | 7.27360i | −0.631698 | − | 0.0188925i | ||||
\(386\) | 215.449 | 0.558158 | ||||||||
\(387\) | 45.0857 | + | 45.0857i | 0.116501 | + | 0.116501i | ||||
\(388\) | −202.463 | + | 202.463i | −0.521812 | + | 0.521812i | ||||
\(389\) | 582.596i | 1.49768i | 0.662753 | + | 0.748838i | \(0.269388\pi\) | ||||
−0.662753 | + | 0.748838i | \(0.730612\pi\) | |||||||
\(390\) | 0.593304 | − | 19.8380i | 0.00152129 | − | 0.0508667i | ||||
\(391\) | 13.7983 | 0.0352898 | ||||||||
\(392\) | 10.1917 | + | 10.1917i | 0.0259992 | + | 0.0259992i | ||||
\(393\) | −265.460 | + | 265.460i | −0.675472 | + | 0.675472i | ||||
\(394\) | − | 10.0750i | − | 0.0255709i | ||||||
\(395\) | 67.6985 | + | 71.8728i | 0.171389 | + | 0.181956i | ||||
\(396\) | −42.2767 | −0.106759 | ||||||||
\(397\) | 325.494 | + | 325.494i | 0.819885 | + | 0.819885i | 0.986091 | − | 0.166206i | \(-0.0531518\pi\) |
−0.166206 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(398\) | −127.303 | + | 127.303i | −0.319856 | + | 0.319856i | ||||
\(399\) | 208.173i | 0.521736i | ||||||||
\(400\) | −5.97614 | + | 99.8213i | −0.0149404 | + | 0.249553i | ||||
\(401\) | 101.242 | 0.252474 | 0.126237 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126237 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(402\) | 76.5642 | + | 76.5642i | 0.190458 | + | 0.190458i | ||||
\(403\) | −26.4274 | + | 26.4274i | −0.0655767 | + | 0.0655767i | ||||
\(404\) | − | 66.2845i | − | 0.164071i | ||||||
\(405\) | −170.377 | + | 160.482i | −0.420683 | + | 0.396251i | ||||
\(406\) | 171.432 | 0.422247 | ||||||||
\(407\) | −162.554 | − | 162.554i | −0.399396 | − | 0.399396i | ||||
\(408\) | −14.2374 | + | 14.2374i | −0.0348956 | + | 0.0348956i | ||||
\(409\) | − | 348.881i | − | 0.853011i | −0.904485 | − | 0.426505i | \(-0.859745\pi\) | ||
0.904485 | − | 0.426505i | \(-0.140255\pi\) | |||||||
\(410\) | 118.826 | + | 3.55377i | 0.289819 | + | 0.00866773i | ||||
\(411\) | 402.501 | 0.979322 | ||||||||
\(412\) | 127.142 | + | 127.142i | 0.308597 | + | 0.308597i | ||||
\(413\) | −39.0098 | + | 39.0098i | −0.0944548 | + | 0.0944548i | ||||
\(414\) | 19.5213i | 0.0471528i | ||||||||
\(415\) | −22.2507 | + | 743.984i | −0.0536161 | + | 1.79273i | ||||
\(416\) | 6.41719 | 0.0154259 | ||||||||
\(417\) | −15.5245 | − | 15.5245i | −0.0372291 | − | 0.0372291i | ||||
\(418\) | −93.2556 | + | 93.2556i | −0.223100 | + | 0.223100i | ||||
\(419\) | 120.421i | 0.287401i | 0.989621 | + | 0.143700i | \(0.0459002\pi\) | ||||
−0.989621 | + | 0.143700i | \(0.954100\pi\) | |||||||
\(420\) | −112.407 | − | 119.338i | −0.267636 | − | 0.284139i | ||||
\(421\) | −703.519 | −1.67107 | −0.835534 | − | 0.549439i | \(-0.814841\pi\) | ||||
−0.835534 | + | 0.549439i | \(0.814841\pi\) | |||||||
\(422\) | 9.59463 | + | 9.59463i | 0.0227361 | + | 0.0227361i | ||||
\(423\) | 154.775 | − | 154.775i | 0.365898 | − | 0.365898i | ||||
\(424\) | − | 60.7994i | − | 0.143395i | ||||||
\(425\) | 53.8100 | − | 47.7309i | 0.126612 | − | 0.112308i | ||||
\(426\) | −369.301 | −0.866904 | ||||||||
\(427\) | 75.5801 | + | 75.5801i | 0.177002 | + | 0.177002i | ||||
\(428\) | −98.0363 | + | 98.0363i | −0.229057 | + | 0.229057i | ||||
\(429\) | 20.6134i | 0.0480498i | ||||||||
\(430\) | −114.025 | + | 107.402i | −0.265174 | + | 0.249773i | ||||
\(431\) | −309.307 | −0.717650 | −0.358825 | − | 0.933405i | \(-0.616823\pi\) | ||||
−0.358825 | + | 0.933405i | \(0.616823\pi\) | |||||||
\(432\) | −83.1257 | − | 83.1257i | −0.192421 | − | 0.192421i | ||||
\(433\) | −88.2644 | + | 88.2644i | −0.203844 | + | 0.203844i | −0.801645 | − | 0.597801i | \(-0.796041\pi\) |
0.597801 | + | 0.801645i | \(0.296041\pi\) | |||||||
\(434\) | 308.722i | 0.711342i | ||||||||
\(435\) | 226.224 | + | 6.76578i | 0.520055 | + | 0.0155535i | ||||
\(436\) | −384.845 | −0.882672 | ||||||||
\(437\) | 43.0608 | + | 43.0608i | 0.0985373 | + | 0.0985373i | ||||
\(438\) | 222.230 | − | 222.230i | 0.507375 | − | 0.507375i | ||||
\(439\) | 231.130i | 0.526492i | 0.964729 | + | 0.263246i | \(0.0847931\pi\) | ||||
−0.964729 | + | 0.263246i | \(0.915207\pi\) | |||||||
\(440\) | 3.10486 | − | 103.816i | 0.00705649 | − | 0.235945i | ||||
\(441\) | 14.6671 | 0.0332588 | ||||||||
\(442\) | −3.26387 | − | 3.26387i | −0.00738431 | − | 0.00738431i | ||||
\(443\) | −572.899 | + | 572.899i | −1.29322 | + | 1.29322i | −0.360444 | + | 0.932781i | \(0.617375\pi\) |
−0.932781 | + | 0.360444i | \(0.882625\pi\) | |||||||
\(444\) | − | 154.896i | − | 0.348864i | ||||||
\(445\) | 451.856 | + | 479.717i | 1.01541 | + | 1.07802i | ||||
\(446\) | 462.607 | 1.03724 | ||||||||
\(447\) | 172.131 | + | 172.131i | 0.385080 | + | 0.385080i | ||||
\(448\) | 37.4824 | − | 37.4824i | 0.0836662 | − | 0.0836662i | ||||
\(449\) | − | 58.7939i | − | 0.130944i | −0.997854 | − | 0.0654721i | \(-0.979145\pi\) | ||
0.997854 | − | 0.0654721i | \(-0.0208553\pi\) | |||||||
\(450\) | 67.5275 | + | 76.1279i | 0.150061 | + | 0.169173i | ||||
\(451\) | −123.470 | −0.273769 | ||||||||
\(452\) | 137.279 | + | 137.279i | 0.303714 | + | 0.303714i | ||||
\(453\) | −130.072 | + | 130.072i | −0.287135 | + | 0.287135i | ||||
\(454\) | − | 590.373i | − | 1.30038i | ||||||
\(455\) | 27.3578 | − | 25.7689i | 0.0601271 | − | 0.0566350i | ||||
\(456\) | −88.8620 | −0.194873 | ||||||||
\(457\) | −146.469 | − | 146.469i | −0.320501 | − | 0.320501i | 0.528458 | − | 0.848959i | \(-0.322770\pi\) |
−0.848959 | + | 0.528458i | \(0.822770\pi\) | |||||||
\(458\) | 441.791 | − | 441.791i | 0.964608 | − | 0.964608i | ||||
\(459\) | 84.5576i | 0.184221i | ||||||||
\(460\) | −47.9369 | − | 1.43367i | −0.104211 | − | 0.00311667i | ||||
\(461\) | 532.088 | 1.15420 | 0.577102 | − | 0.816672i | \(-0.304183\pi\) | ||||
0.577102 | + | 0.816672i | \(0.304183\pi\) | |||||||
\(462\) | 120.402 | + | 120.402i | 0.260609 | + | 0.260609i | ||||
\(463\) | −97.3256 | + | 97.3256i | −0.210206 | + | 0.210206i | −0.804355 | − | 0.594149i | \(-0.797489\pi\) |
0.594149 | + | 0.804355i | \(0.297489\pi\) | |||||||
\(464\) | 73.1788i | 0.157713i | ||||||||
\(465\) | −12.1841 | + | 407.393i | −0.0262023 | + | 0.876114i | ||||
\(466\) | −284.714 | −0.610974 | ||||||||
\(467\) | −648.867 | − | 648.867i | −1.38944 | − | 1.38944i | −0.826501 | − | 0.562935i | \(-0.809672\pi\) |
−0.562935 | − | 0.826501i | \(-0.690328\pi\) | |||||||
\(468\) | 4.61757 | − | 4.61757i | 0.00986661 | − | 0.00986661i | ||||
\(469\) | 205.041i | 0.437188i | ||||||||
\(470\) | 368.702 | + | 391.436i | 0.784472 | + | 0.832842i | ||||
\(471\) | 358.501 | 0.761149 | ||||||||
\(472\) | −16.6520 | − | 16.6520i | −0.0352797 | − | 0.0352797i | ||||
\(473\) | 115.041 | − | 115.041i | 0.243215 | − | 0.243215i | ||||
\(474\) | − | 69.0968i | − | 0.145774i | ||||||
\(475\) | 316.881 | + | 18.9712i | 0.667118 | + | 0.0399393i | ||||
\(476\) | −38.1281 | −0.0801011 | ||||||||
\(477\) | −43.7490 | − | 43.7490i | −0.0917170 | − | 0.0917170i | ||||
\(478\) | −103.472 | + | 103.472i | −0.216469 | + | 0.216469i | ||||
\(479\) | − | 67.3465i | − | 0.140598i | −0.997526 | − | 0.0702991i | \(-0.977605\pi\) | ||
0.997526 | − | 0.0702991i | \(-0.0223954\pi\) | |||||||
\(480\) | 50.9415 | − | 47.9829i | 0.106128 | − | 0.0999644i | ||||
\(481\) | 35.5092 | 0.0738238 | ||||||||
\(482\) | 11.4659 | + | 11.4659i | 0.0237881 | + | 0.0237881i | ||||
\(483\) | 55.5955 | − | 55.5955i | 0.115104 | − | 0.115104i | ||||
\(484\) | − | 134.127i | − | 0.277122i | ||||||
\(485\) | −715.495 | − | 21.3986i | −1.47525 | − | 0.0441209i | ||||
\(486\) | −210.269 | −0.432653 | ||||||||
\(487\) | 74.4495 | + | 74.4495i | 0.152874 | + | 0.152874i | 0.779400 | − | 0.626526i | \(-0.215524\pi\) |
−0.626526 | + | 0.779400i | \(0.715524\pi\) | |||||||
\(488\) | −32.2626 | + | 32.2626i | −0.0661119 | + | 0.0661119i | ||||
\(489\) | − | 243.858i | − | 0.498687i | ||||||
\(490\) | −1.07717 | + | 36.0169i | −0.00219831 | + | 0.0735039i | ||||
\(491\) | 767.159 | 1.56244 | 0.781221 | − | 0.624255i | \(-0.214597\pi\) | ||||
0.781221 | + | 0.624255i | \(0.214597\pi\) | |||||||
\(492\) | −58.8263 | − | 58.8263i | −0.119566 | − | 0.119566i | ||||
\(493\) | 37.2197 | − | 37.2197i | 0.0754963 | − | 0.0754963i | ||||
\(494\) | − | 20.3713i | − | 0.0412374i | ||||||
\(495\) | −72.4678 | − | 76.9360i | −0.146399 | − | 0.155426i | ||||
\(496\) | −131.783 | −0.265692 | ||||||||
\(497\) | −494.500 | − | 494.500i | −0.994969 | − | 0.994969i | ||||
\(498\) | 368.320 | − | 368.320i | 0.739599 | − | 0.739599i | ||||
\(499\) | − | 530.092i | − | 1.06231i | −0.847275 | − | 0.531154i | \(-0.821759\pi\) | ||
0.847275 | − | 0.531154i | \(-0.178241\pi\) | |||||||
\(500\) | −191.901 | + | 160.231i | −0.383802 | + | 0.320462i | ||||
\(501\) | −471.210 | −0.940539 | ||||||||
\(502\) | 46.6849 | + | 46.6849i | 0.0929978 | + | 0.0929978i | ||||
\(503\) | −145.546 | + | 145.546i | −0.289355 | + | 0.289355i | −0.836825 | − | 0.547470i | \(-0.815591\pi\) |
0.547470 | + | 0.836825i | \(0.315591\pi\) | |||||||
\(504\) | − | 53.9420i | − | 0.107028i | ||||||
\(505\) | 120.626 | − | 113.620i | 0.238864 | − | 0.224991i | ||||
\(506\) | 49.8105 | 0.0984397 | ||||||||
\(507\) | 293.420 | + | 293.420i | 0.578738 | + | 0.578738i | ||||
\(508\) | −79.2229 | + | 79.2229i | −0.155951 | + | 0.155951i | ||||
\(509\) | − | 771.820i | − | 1.51635i | −0.652054 | − | 0.758173i | \(-0.726092\pi\) | ||
0.652054 | − | 0.758173i | \(-0.273908\pi\) | |||||||
\(510\) | −50.3143 | − | 1.50477i | −0.0986554 | − | 0.00295053i | ||||
\(511\) | 595.139 | 1.16466 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −263.881 | + | 263.881i | −0.514388 | + | 0.514388i | ||||
\(514\) | − | 619.752i | − | 1.20574i | ||||||
\(515\) | −13.4378 | + | 449.314i | −0.0260929 | + | 0.872455i | ||||
\(516\) | 109.621 | 0.212443 | ||||||||
\(517\) | −394.923 | − | 394.923i | −0.763875 | − | 0.763875i | ||||
\(518\) | 207.407 | − | 207.407i | 0.400400 | − | 0.400400i | ||||
\(519\) | 192.381i | 0.370677i | ||||||||
\(520\) | 10.9999 | + | 11.6781i | 0.0211537 | + | 0.0224580i | ||||
\(521\) | −61.1677 | −0.117404 | −0.0587022 | − | 0.998276i | \(-0.518696\pi\) | ||||
−0.0587022 | + | 0.998276i | \(0.518696\pi\) | |||||||
\(522\) | 52.6567 | + | 52.6567i | 0.100875 | + | 0.100875i | ||||
\(523\) | 471.652 | − | 471.652i | 0.901819 | − | 0.901819i | −0.0937741 | − | 0.995593i | \(-0.529893\pi\) |
0.995593 | + | 0.0937741i | \(0.0298932\pi\) | |||||||
\(524\) | − | 303.464i | − | 0.579130i | ||||||
\(525\) | 24.4935 | − | 409.123i | 0.0466543 | − | 0.779281i | ||||
\(526\) | −91.9014 | −0.174718 | ||||||||
\(527\) | 67.0267 | + | 67.0267i | 0.127185 | + | 0.127185i | ||||
\(528\) | −51.3954 | + | 51.3954i | −0.0973398 | + | 0.0973398i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 110.644 | − | 104.218i | 0.208763 | − | 0.196638i | ||||
\(531\) | −23.9643 | −0.0451306 | ||||||||
\(532\) | −118.987 | − | 118.987i | −0.223661 | − | 0.223661i | ||||
\(533\) | 13.4857 | − | 13.4857i | 0.0253015 | − | 0.0253015i | ||||
\(534\) | − | 461.189i | − | 0.863649i | ||||||
\(535\) | −346.456 | − | 10.3616i | −0.647581 | − | 0.0193675i | ||||
\(536\) | −87.5252 | −0.163293 | ||||||||
\(537\) | 265.547 | + | 265.547i | 0.494501 | + | 0.494501i | ||||
\(538\) | 138.967 | − | 138.967i | 0.258303 | − | 0.258303i | ||||
\(539\) | − | 37.4246i | − | 0.0694335i | ||||||
\(540\) | 8.78568 | − | 293.762i | 0.0162698 | − | 0.544004i | ||||
\(541\) | −721.465 | −1.33358 | −0.666789 | − | 0.745247i | \(-0.732332\pi\) | ||||
−0.666789 | + | 0.745247i | \(0.732332\pi\) | |||||||
\(542\) | −373.516 | − | 373.516i | −0.689143 | − | 0.689143i | ||||
\(543\) | −23.9615 | + | 23.9615i | −0.0441280 | + | 0.0441280i | ||||
\(544\) | − | 16.2756i | − | 0.0299184i | ||||||
\(545\) | −659.675 | − | 700.350i | −1.21041 | − | 1.28505i | ||||
\(546\) | −26.3012 | −0.0481707 | ||||||||
\(547\) | −574.163 | − | 574.163i | −1.04966 | − | 1.04966i | −0.998701 | − | 0.0509573i | \(-0.983773\pi\) |
−0.0509573 | − | 0.998701i | \(-0.516227\pi\) | |||||||
\(548\) | −230.062 | + | 230.062i | −0.419821 | + | 0.419821i | ||||
\(549\) | 46.4300i | 0.0845719i | ||||||||
\(550\) | 194.248 | − | 172.303i | 0.353178 | − | 0.313279i | ||||
\(551\) | 232.305 | 0.421606 | ||||||||
\(552\) | 23.7318 | + | 23.7318i | 0.0429925 | + | 0.0429925i | ||||
\(553\) | 92.5216 | − | 92.5216i | 0.167308 | − | 0.167308i | ||||
\(554\) | 659.641i | 1.19069i | ||||||||
\(555\) | 281.883 | − | 265.511i | 0.507897 | − | 0.478399i | ||||
\(556\) | 17.7470 | 0.0319191 | ||||||||
\(557\) | −337.658 | − | 337.658i | −0.606209 | − | 0.606209i | 0.335744 | − | 0.941953i | \(-0.391012\pi\) |
−0.941953 | + | 0.335744i | \(0.891012\pi\) | |||||||
\(558\) | −94.8264 | + | 94.8264i | −0.169940 | + | 0.169940i | ||||
\(559\) | 25.1301i | 0.0449555i | ||||||||
\(560\) | 132.461 | + | 3.96157i | 0.236538 | + | 0.00707424i | ||||
\(561\) | 52.2808 | 0.0931921 | ||||||||
\(562\) | 433.168 | + | 433.168i | 0.770761 | + | 0.770761i | ||||
\(563\) | −42.8665 | + | 42.8665i | −0.0761394 | + | 0.0761394i | −0.744151 | − | 0.668012i | \(-0.767146\pi\) |
0.668012 | + | 0.744151i | \(0.267146\pi\) | |||||||
\(564\) | − | 376.317i | − | 0.667229i | ||||||
\(565\) | −14.5092 | + | 485.136i | −0.0256800 | + | 0.858648i | ||||
\(566\) | −224.398 | −0.396462 | ||||||||
\(567\) | 219.326 | + | 219.326i | 0.386818 | + | 0.386818i | ||||
\(568\) | 211.085 | − | 211.085i | 0.371629 | − | 0.371629i | ||||
\(569\) | 428.539i | 0.753145i | 0.926387 | + | 0.376572i | \(0.122897\pi\) | ||||
−0.926387 | + | 0.376572i | \(0.877103\pi\) | |||||||
\(570\) | −152.321 | − | 161.713i | −0.267230 | − | 0.283707i | ||||
\(571\) | −1067.35 | −1.86926 | −0.934628 | − | 0.355626i | \(-0.884268\pi\) | ||||
−0.934628 | + | 0.355626i | \(0.884268\pi\) | |||||||
\(572\) | −11.7822 | − | 11.7822i | −0.0205983 | − | 0.0205983i | ||||
\(573\) | −388.985 | + | 388.985i | −0.678857 | + | 0.678857i | ||||
\(574\) | − | 157.539i | − | 0.274457i | ||||||
\(575\) | −79.5611 | − | 89.6941i | −0.138367 | − | 0.155990i | ||||
\(576\) | 23.0260 | 0.0399757 | ||||||||
\(577\) | −308.950 | − | 308.950i | −0.535442 | − | 0.535442i | 0.386745 | − | 0.922187i | \(-0.373599\pi\) |
−0.922187 | + | 0.386745i | \(0.873599\pi\) | |||||||
\(578\) | 280.722 | − | 280.722i | 0.485678 | − | 0.485678i | ||||
\(579\) | − | 376.936i | − | 0.651011i | ||||||
\(580\) | −133.172 | + | 125.438i | −0.229607 | + | 0.216272i | ||||
\(581\) | 986.372 | 1.69771 | ||||||||
\(582\) | 354.216 | + | 354.216i | 0.608619 | + | 0.608619i | ||||
\(583\) | −111.630 | + | 111.630i | −0.191475 | + | 0.191475i | ||||
\(584\) | 254.045i | 0.435008i | ||||||||
\(585\) | 16.3183 | + | 0.488038i | 0.0278945 | + | 0.000834253i | ||||
\(586\) | −315.383 | −0.538196 | ||||||||
\(587\) | 348.585 | + | 348.585i | 0.593842 | + | 0.593842i | 0.938667 | − | 0.344825i | \(-0.112062\pi\) |
−0.344825 | + | 0.938667i | \(0.612062\pi\) | |||||||
\(588\) | 17.8307 | − | 17.8307i | 0.0303243 | − | 0.0303243i | ||||
\(589\) | 418.344i | 0.710261i | ||||||||
\(590\) | 1.75997 | − | 58.8474i | 0.00298301 | − | 0.0997414i | ||||
\(591\) | −17.6265 | −0.0298248 | ||||||||
\(592\) | 88.5353 | + | 88.5353i | 0.149553 | + | 0.149553i | ||||
\(593\) | 483.268 | − | 483.268i | 0.814954 | − | 0.814954i | −0.170418 | − | 0.985372i | \(-0.554512\pi\) |
0.985372 | + | 0.170418i | \(0.0545118\pi\) | |||||||
\(594\) | 305.244i | 0.513879i | ||||||||
\(595\) | −65.3566 | − | 69.3864i | −0.109843 | − | 0.116616i | ||||
\(596\) | −196.773 | −0.330156 | ||||||||
\(597\) | 222.720 | + | 222.720i | 0.373066 | + | 0.373066i | ||||
\(598\) | −5.44044 | + | 5.44044i | −0.00909772 | + | 0.00909772i | ||||
\(599\) | 879.264i | 1.46789i | 0.679211 | + | 0.733943i | \(0.262322\pi\) | ||||
−0.679211 | + | 0.733943i | \(0.737678\pi\) | |||||||
\(600\) | 174.641 | + | 10.4555i | 0.291068 | + | 0.0174258i | ||||
\(601\) | −462.938 | −0.770279 | −0.385139 | − | 0.922858i | \(-0.625847\pi\) | ||||
−0.385139 | + | 0.922858i | \(0.625847\pi\) | |||||||
\(602\) | 146.784 | + | 146.784i | 0.243827 | + | 0.243827i | ||||
\(603\) | −62.9799 | + | 62.9799i | −0.104444 | + | 0.104444i | ||||
\(604\) | − | 148.694i | − | 0.246181i | ||||||
\(605\) | 244.087 | − | 229.911i | 0.403450 | − | 0.380018i | ||||
\(606\) | −115.967 | −0.191365 | ||||||||
\(607\) | 523.602 | + | 523.602i | 0.862606 | + | 0.862606i | 0.991640 | − | 0.129034i | \(-0.0411877\pi\) |
−0.129034 | + | 0.991640i | \(0.541188\pi\) | |||||||
\(608\) | 50.7918 | − | 50.7918i | 0.0835391 | − | 0.0835391i | ||||
\(609\) | − | 299.927i | − | 0.492491i | ||||||
\(610\) | −114.015 | − | 3.40988i | −0.186909 | − | 0.00558997i | ||||
\(611\) | 86.2692 | 0.141194 | ||||||||
\(612\) | −11.7113 | − | 11.7113i | −0.0191362 | − | 0.0191362i | ||||
\(613\) | −625.075 | + | 625.075i | −1.01970 | + | 1.01970i | −0.0198960 | + | 0.999802i | \(0.506334\pi\) |
−0.999802 | + | 0.0198960i | \(0.993666\pi\) | |||||||
\(614\) | 315.694i | 0.514159i | ||||||||
\(615\) | 6.21744 | − | 207.890i | 0.0101097 | − | 0.338032i | ||||
\(616\) | −137.638 | −0.223439 | ||||||||
\(617\) | −267.604 | − | 267.604i | −0.433719 | − | 0.433719i | 0.456173 | − | 0.889891i | \(-0.349220\pi\) |
−0.889891 | + | 0.456173i | \(0.849220\pi\) | |||||||
\(618\) | 222.440 | − | 222.440i | 0.359934 | − | 0.359934i | ||||
\(619\) | 1088.11i | 1.75785i | 0.476960 | + | 0.878925i | \(0.341739\pi\) | ||||
−0.476960 | + | 0.878925i | \(0.658261\pi\) | |||||||
\(620\) | −225.894 | − | 239.822i | −0.364345 | − | 0.386810i | ||||
\(621\) | 140.946 | 0.226967 | ||||||||
\(622\) | −543.283 | − | 543.283i | −0.873445 | − | 0.873445i | ||||
\(623\) | 617.538 | − | 617.538i | 0.991233 | − | 0.991233i | ||||
\(624\) | − | 11.2271i | − | 0.0179921i | ||||||
\(625\) | −620.536 | − | 74.5682i | −0.992857 | − | 0.119309i | ||||
\(626\) | 61.4285 | 0.0981286 | ||||||||
\(627\) | 163.154 | + | 163.154i | 0.260214 | + | 0.260214i | ||||
\(628\) | −204.912 | + | 204.912i | −0.326293 | + | 0.326293i | ||||
\(629\) | − | 90.0605i | − | 0.143180i | ||||||
\(630\) | 98.1648 | − | 92.4636i | 0.155817 | − | 0.146768i | ||||
\(631\) | 742.234 | 1.17628 | 0.588141 | − | 0.808759i | \(-0.299860\pi\) | ||||
0.588141 | + | 0.808759i | \(0.299860\pi\) | |||||||
\(632\) | 39.4944 | + | 39.4944i | 0.0624911 | + | 0.0624911i | ||||
\(633\) | 16.7861 | − | 16.7861i | 0.0265184 | − | 0.0265184i | ||||
\(634\) | − | 741.822i | − | 1.17007i | ||||||
\(635\) | −279.970 | − | 8.37319i | −0.440898 | − | 0.0131861i | ||||
\(636\) | −106.371 | −0.167250 | ||||||||
\(637\) | 4.08762 | + | 4.08762i | 0.00641699 | + | 0.00641699i | ||||
\(638\) | 134.359 | − | 134.359i | 0.210594 | − | 0.210594i | ||||
\(639\) | − | 303.779i | − | 0.475397i | ||||||
\(640\) | −1.69106 | + | 56.5433i | −0.00264229 | + | 0.0883488i | ||||
\(641\) | 799.585 | 1.24740 | 0.623702 | − | 0.781663i | \(-0.285628\pi\) | ||||
0.623702 | + | 0.781663i | \(0.285628\pi\) | |||||||
\(642\) | 171.518 | + | 171.518i | 0.267162 | + | 0.267162i | ||||
\(643\) | −647.571 | + | 647.571i | −1.00711 | + | 1.00711i | −0.00713404 | + | 0.999975i | \(0.502271\pi\) |
−0.999975 | + | 0.00713404i | \(0.997729\pi\) | |||||||
\(644\) | 63.5546i | 0.0986872i | ||||||||
\(645\) | 187.904 | + | 199.490i | 0.291324 | + | 0.309287i | ||||
\(646\) | −51.6667 | −0.0799794 | ||||||||
\(647\) | −710.350 | − | 710.350i | −1.09791 | − | 1.09791i | −0.994654 | − | 0.103259i | \(-0.967073\pi\) |
−0.103259 | − | 0.994654i | \(-0.532927\pi\) | |||||||
\(648\) | −93.6228 | + | 93.6228i | −0.144480 | + | 0.144480i | ||||
\(649\) | 61.1474i | 0.0942179i | ||||||||
\(650\) | −2.39688 | + | 40.0357i | −0.00368750 | + | 0.0615934i | ||||
\(651\) | 540.120 | 0.829678 | ||||||||
\(652\) | 139.384 | + | 139.384i | 0.213780 | + | 0.213780i | ||||
\(653\) | 816.226 | − | 816.226i | 1.24996 | − | 1.24996i | 0.294228 | − | 0.955735i | \(-0.404938\pi\) |
0.955735 | − | 0.294228i | \(-0.0950624\pi\) | |||||||
\(654\) | 673.300i | 1.02951i | ||||||||
\(655\) | 552.250 | − | 520.177i | 0.843130 | − | 0.794163i | ||||
\(656\) | 67.2480 | 0.102512 | ||||||||
\(657\) | 182.801 | + | 182.801i | 0.278237 | + | 0.278237i | ||||
\(658\) | 503.894 | − | 503.894i | 0.765796 | − | 0.765796i | ||||
\(659\) | 1221.53i | 1.85361i | 0.375542 | + | 0.926805i | \(0.377457\pi\) | ||||
−0.375542 | + | 0.926805i | \(0.622543\pi\) | |||||||
\(660\) | −181.629 | − | 5.43206i | −0.275195 | − | 0.00823039i | ||||
\(661\) | 269.209 | 0.407275 | 0.203638 | − | 0.979046i | \(-0.434724\pi\) | ||||
0.203638 | + | 0.979046i | \(0.434724\pi\) | |||||||
\(662\) | −334.223 | − | 334.223i | −0.504869 | − | 0.504869i | ||||
\(663\) | −5.71025 | + | 5.71025i | −0.00861274 | + | 0.00861274i | ||||
\(664\) | 421.049i | 0.634110i | ||||||||
\(665\) | 12.5760 | − | 420.496i | 0.0189112 | − | 0.632325i | ||||
\(666\) | 127.414 | 0.191312 | ||||||||
\(667\) | −62.0403 | − | 62.0403i | −0.0930139 | − | 0.0930139i | ||||
\(668\) | 269.335 | − | 269.335i | 0.403195 | − | 0.403195i | ||||
\(669\) | − | 809.348i | − | 1.20979i | ||||||
\(670\) | −150.030 | − | 159.280i | −0.223925 | − | 0.237732i | ||||
\(671\) | 118.471 | 0.176558 | ||||||||
\(672\) | −65.5768 | − | 65.5768i | −0.0975846 | − | 0.0975846i | ||||
\(673\) | −19.4524 | + | 19.4524i | −0.0289041 | + | 0.0289041i | −0.721411 | − | 0.692507i | \(-0.756506\pi\) |
0.692507 | + | 0.721411i | \(0.256506\pi\) | |||||||
\(674\) | − | 560.661i | − | 0.831841i | ||||||
\(675\) | 549.655 | − | 487.559i | 0.814304 | − | 0.722309i | ||||
\(676\) | −335.426 | −0.496193 | ||||||||
\(677\) | 173.259 | + | 173.259i | 0.255922 | + | 0.255922i | 0.823393 | − | 0.567471i | \(-0.192078\pi\) |
−0.567471 | + | 0.823393i | \(0.692078\pi\) | |||||||
\(678\) | 240.174 | − | 240.174i | 0.354239 | − | 0.354239i | ||||
\(679\) | 948.601i | 1.39706i | ||||||||
\(680\) | 29.6187 | − | 27.8986i | 0.0435570 | − | 0.0410273i | ||||
\(681\) | −1032.88 | −1.51671 | ||||||||
\(682\) | 241.959 | + | 241.959i | 0.354779 | + | 0.354779i | ||||
\(683\) | 155.847 | − | 155.847i | 0.228181 | − | 0.228181i | −0.583752 | − | 0.811932i | \(-0.698416\pi\) |
0.811932 | + | 0.583752i | \(0.198416\pi\) | |||||||
\(684\) | − | 73.0958i | − | 0.106865i | ||||||
\(685\) | −813.028 | − | 24.3156i | −1.18690 | − | 0.0354972i | ||||
\(686\) | 506.911 | 0.738937 | ||||||||
\(687\) | −772.928 | − | 772.928i | −1.12508 | − | 1.12508i | ||||
\(688\) | −62.6570 | + | 62.6570i | −0.0910713 | + | 0.0910713i | ||||
\(689\) | − | 24.3851i | − | 0.0353920i | ||||||
\(690\) | −2.50825 | + | 83.8673i | −0.00363515 | + | 0.121547i | ||||
\(691\) | −834.701 | −1.20796 | −0.603981 | − | 0.796999i | \(-0.706420\pi\) | ||||
−0.603981 | + | 0.796999i | \(0.706420\pi\) | |||||||
\(692\) | −109.961 | − | 109.961i | −0.158904 | − | 0.158904i | ||||
\(693\) | −99.0395 | + | 99.0395i | −0.142914 | + | 0.142914i | ||||
\(694\) | 867.929i | 1.25062i | ||||||||
\(695\) | 30.4207 | + | 32.2964i | 0.0437708 | + | 0.0464697i | ||||
\(696\) | 128.029 | 0.183949 | ||||||||
\(697\) | −34.2032 | − | 34.2032i | −0.0490720 | − | 0.0490720i | ||||
\(698\) | 221.072 | − | 221.072i | 0.316721 | − | 0.316721i | ||||
\(699\) | 498.117i | 0.712613i | ||||||||
\(700\) | 219.847 | + | 247.847i | 0.314066 | + | 0.354066i | ||||
\(701\) | −1081.67 | −1.54304 | −0.771520 | − | 0.636205i | \(-0.780503\pi\) | ||||
−0.771520 | + | 0.636205i | \(0.780503\pi\) | |||||||
\(702\) | −33.3396 | − | 33.3396i | −0.0474923 | − | 0.0474923i | ||||
\(703\) | 281.054 | − | 281.054i | 0.399792 | − | 0.399792i | ||||
\(704\) | − | 58.7532i | − | 0.0834563i | ||||||
\(705\) | 684.830 | − | 645.057i | 0.971390 | − | 0.914974i | ||||
\(706\) | −20.8305 | −0.0295049 | ||||||||
\(707\) | −155.282 | − | 155.282i | −0.219635 | − | 0.219635i | ||||
\(708\) | −29.1333 | + | 29.1333i | −0.0411487 | + | 0.0411487i | ||||
\(709\) | 736.698i | 1.03907i | 0.854450 | + | 0.519533i | \(0.173894\pi\) | ||||
−0.854450 | + | 0.519533i | \(0.826106\pi\) | |||||||
\(710\) | 745.966 | + | 22.3099i | 1.05066 | + | 0.0314224i | ||||
\(711\) | 56.8374 | 0.0799401 | ||||||||
\(712\) | 263.606 | + | 263.606i | 0.370234 | + | 0.370234i | ||||
\(713\) | 111.725 | − | 111.725i | 0.156697 | − | 0.156697i | ||||
\(714\) | 66.7065i | 0.0934265i | ||||||||
\(715\) | 1.24528 | − | 41.6378i | 0.00174165 | − | 0.0582346i | ||||
\(716\) | −303.563 | −0.423970 | ||||||||
\(717\) | 181.028 | + | 181.028i | 0.252480 | + | 0.252480i | ||||
\(718\) | −92.8731 | + | 92.8731i | −0.129350 | + | 0.129350i | ||||
\(719\) | − | 158.393i | − | 0.220297i | −0.993915 | − | 0.110148i | \(-0.964867\pi\) | ||
0.993915 | − | 0.110148i | \(-0.0351326\pi\) | |||||||
\(720\) | 39.4696 | + | 41.9033i | 0.0548189 | + | 0.0581990i | ||||
\(721\) | 595.699 | 0.826213 | ||||||||
\(722\) | 199.762 | + | 199.762i | 0.276679 | + | 0.276679i | ||||
\(723\) | 20.0599 | − | 20.0599i | 0.0277454 | − | 0.0277454i | ||||
\(724\) | − | 27.3919i | − | 0.0378341i | ||||||
\(725\) | −456.550 | − | 27.3329i | −0.629724 | − | 0.0377006i | ||||
\(726\) | −234.660 | −0.323223 | ||||||||
\(727\) | −470.451 | − | 470.451i | −0.647112 | − | 0.647112i | 0.305182 | − | 0.952294i | \(-0.401283\pi\) |
−0.952294 | + | 0.305182i | \(0.901283\pi\) | |||||||
\(728\) | 15.0332 | − | 15.0332i | 0.0206501 | − | 0.0206501i | ||||
\(729\) | 789.176i | 1.08255i | ||||||||
\(730\) | −462.317 | + | 435.466i | −0.633311 | + | 0.596529i | ||||
\(731\) | 63.7364 | 0.0871907 | ||||||||
\(732\) | 56.4446 | + | 56.4446i | 0.0771101 | + | 0.0771101i | ||||
\(733\) | −83.7227 | + | 83.7227i | −0.114219 | + | 0.114219i | −0.761906 | − | 0.647687i | \(-0.775736\pi\) |
0.647687 | + | 0.761906i | \(0.275736\pi\) | |||||||
\(734\) | − | 84.6586i | − | 0.115339i | ||||||
\(735\) | 63.0129 | + | 1.88455i | 0.0857318 | + | 0.00256402i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 160.700 | + | 160.700i | 0.218046 | + | 0.218046i | ||||
\(738\) | 48.3892 | − | 48.3892i | 0.0655680 | − | 0.0655680i | ||||
\(739\) | 786.751i | 1.06462i | 0.846551 | + | 0.532308i | \(0.178675\pi\) | ||||
−0.846551 | + | 0.532308i | \(0.821325\pi\) | |||||||
\(740\) | −9.35743 | + | 312.880i | −0.0126452 | + | 0.422810i | ||||
\(741\) | −35.6402 | −0.0480975 | ||||||||
\(742\) | −142.432 | − | 142.432i | −0.191957 | − | 0.191957i | ||||
\(743\) | 434.532 | − | 434.532i | 0.584834 | − | 0.584834i | −0.351394 | − | 0.936228i | \(-0.614292\pi\) |
0.936228 | + | 0.351394i | \(0.114292\pi\) | |||||||
\(744\) | 230.559i | 0.309892i | ||||||||
\(745\) | −337.295 | − | 358.092i | −0.452745 | − | 0.480661i | ||||
\(746\) | −198.195 | −0.265677 | ||||||||
\(747\) | 302.972 | + | 302.972i | 0.405585 | + | 0.405585i | ||||
\(748\) | −29.8827 | + | 29.8827i | −0.0399501 | + | 0.0399501i | ||||
\(749\) | 459.330i | 0.613258i | ||||||||
\(750\) | 280.330 | + | 335.737i | 0.373774 | + | 0.447650i | ||||
\(751\) | −36.0488 | −0.0480010 | −0.0240005 | − | 0.999712i | \(-0.507640\pi\) | ||||
−0.0240005 | + | 0.999712i | \(0.507640\pi\) | |||||||
\(752\) | 215.095 | + | 215.095i | 0.286031 | + | 0.286031i | ||||
\(753\) | 81.6769 | − | 81.6769i | 0.108469 | − | 0.108469i | ||||
\(754\) | 29.3501i | 0.0389259i | ||||||||
\(755\) | 270.596 | − | 254.880i | 0.358405 | − | 0.337590i | ||||
\(756\) | −389.469 | −0.515171 | ||||||||
\(757\) | 991.601 | + | 991.601i | 1.30991 | + | 1.30991i | 0.921478 | + | 0.388431i | \(0.126983\pi\) |
0.388431 | + | 0.921478i | \(0.373017\pi\) | |||||||
\(758\) | −267.871 | + | 267.871i | −0.353392 | + | 0.353392i | ||||
\(759\) | − | 87.1452i | − | 0.114816i | ||||||
\(760\) | 179.496 | + | 5.36826i | 0.236179 | + | 0.00706350i | ||||
\(761\) | 1444.95 | 1.89875 | 0.949375 | − | 0.314145i | \(-0.101718\pi\) | ||||
0.949375 | + | 0.314145i | \(0.101718\pi\) | |||||||
\(762\) | 138.603 | + | 138.603i | 0.181894 | + | 0.181894i | ||||
\(763\) | −901.559 | + | 901.559i | −1.18160 | + | 1.18160i | ||||
\(764\) | − | 444.673i | − | 0.582032i | ||||||
\(765\) | 1.23779 | − | 41.3873i | 0.00161802 | − | 0.0541011i | ||||
\(766\) | 387.862 | 0.506347 | ||||||||
\(767\) | −6.67869 | − | 6.67869i | −0.00870755 | − | 0.00870755i | ||||
\(768\) | 27.9926 | − | 27.9926i | 0.0364486 | − | 0.0364486i | ||||
\(769\) | − | 630.455i | − | 0.819838i | −0.912122 | − | 0.409919i | \(-0.865557\pi\) | ||
0.912122 | − | 0.409919i | \(-0.134443\pi\) | |||||||
\(770\) | −235.930 | − | 250.477i | −0.306403 | − | 0.325295i | ||||
\(771\) | −1084.28 | −1.40633 | ||||||||
\(772\) | 215.449 | + | 215.449i | 0.279079 | + | 0.279079i | ||||
\(773\) | −333.366 | + | 333.366i | −0.431262 | + | 0.431262i | −0.889058 | − | 0.457795i | \(-0.848639\pi\) |
0.457795 | + | 0.889058i | \(0.348639\pi\) | |||||||
\(774\) | 90.1714i | 0.116501i | ||||||||
\(775\) | 49.2222 | − | 822.173i | 0.0635125 | − | 1.06087i | ||||
\(776\) | −404.926 | −0.521812 | ||||||||
\(777\) | −362.867 | − | 362.867i | −0.467010 | − | 0.467010i | ||||
\(778\) | −582.596 | + | 582.596i | −0.748838 | + | 0.748838i | ||||
\(779\) | − | 213.478i | − | 0.274041i | ||||||
\(780\) | 20.4313 | − | 19.2447i | 0.0261940 | − | 0.0246727i | ||||
\(781\) | −775.122 | −0.992473 | ||||||||
\(782\) | 13.7983 | + | 13.7983i | 0.0176449 | + | 0.0176449i | ||||
\(783\) | 380.190 | − | 380.190i | 0.485555 | − | 0.485555i | ||||
\(784\) | 20.3834i | 0.0259992i | ||||||||
\(785\) | −724.151 | − | 21.6575i | −0.922485 | − | 0.0275892i | ||||
\(786\) | −530.921 | −0.675472 | ||||||||
\(787\) | 478.649 | + | 478.649i | 0.608194 | + | 0.608194i | 0.942474 | − | 0.334280i | \(-0.108493\pi\) |
−0.334280 | + | 0.942474i | \(0.608493\pi\) | |||||||
\(788\) | 10.0750 | − | 10.0750i | 0.0127855 | − | 0.0127855i | ||||
\(789\) | 160.785i | 0.203783i | ||||||||
\(790\) | −4.17422 | + | 139.571i | −0.00528382 | + | 0.176673i | ||||
\(791\) | 643.192 | 0.813138 | ||||||||
\(792\) | −42.2767 | − | 42.2767i | −0.0533796 | − | 0.0533796i | ||||
\(793\) | −12.9397 | + | 12.9397i | −0.0163174 | + | 0.0163174i | ||||
\(794\) | 650.988i | 0.819885i | ||||||||
\(795\) | −182.333 | − | 193.576i | −0.229350 | − | 0.243492i | ||||
\(796\) | −254.605 | −0.319856 | ||||||||
\(797\) | 285.605 | + | 285.605i | 0.358350 | + | 0.358350i | 0.863204 | − | 0.504855i | \(-0.168454\pi\) |
−0.504855 | + | 0.863204i | \(0.668454\pi\) | |||||||
\(798\) | −208.173 | + | 208.173i | −0.260868 | + | 0.260868i | ||||
\(799\) | − | 218.801i | − | 0.273843i | ||||||
\(800\) | −105.797 | + | 93.8451i | −0.132247 | + | 0.117306i | ||||
\(801\) | 379.363 | 0.473612 | ||||||||
\(802\) | 101.242 | + | 101.242i | 0.126237 | + | 0.126237i | ||||
\(803\) | 466.436 | − | 466.436i | 0.580867 | − | 0.580867i | ||||
\(804\) | 153.128i | 0.190458i | ||||||||
\(805\) | −115.658 | + | 108.941i | −0.143675 | + | 0.135330i | ||||
\(806\) | −52.8549 | −0.0655767 | ||||||||
\(807\) | −243.127 | − | 243.127i | −0.301273 | − | 0.301273i | ||||
\(808\) | 66.2845 | − | 66.2845i | 0.0820353 | − | 0.0820353i | ||||
\(809\) | − | 1404.45i | − | 1.73603i | −0.496539 | − | 0.868014i | \(-0.665396\pi\) | ||
0.496539 | − | 0.868014i | \(-0.334604\pi\) | |||||||
\(810\) | −330.858 | − | 9.89513i | −0.408467 | − | 0.0122162i | ||||
\(811\) | −700.599 | −0.863871 | −0.431935 | − | 0.901905i | \(-0.642169\pi\) | ||||
−0.431935 | + | 0.901905i | \(0.642169\pi\) | |||||||
\(812\) | 171.432 | + | 171.432i | 0.211124 | + | 0.211124i | ||||
\(813\) | −653.479 | + | 653.479i | −0.803787 | + | 0.803787i | ||||
\(814\) | − | 325.108i | − | 0.399396i | ||||||
\(815\) | −14.7317 | + | 492.578i | −0.0180757 | + | 0.604390i | ||||
\(816\) | −28.4748 | −0.0348956 | ||||||||
\(817\) | 198.904 | + | 198.904i | 0.243456 | + | 0.243456i | ||||
\(818\) | 348.881 | − | 348.881i | 0.426505 | − | 0.426505i | ||||
\(819\) | − | 21.6347i | − | 0.0264160i | ||||||
\(820\) | 115.272 | + | 122.379i | 0.140575 | + | 0.149243i | ||||
\(821\) | −599.235 | −0.729884 | −0.364942 | − | 0.931030i | \(-0.618911\pi\) | ||||
−0.364942 | + | 0.931030i | \(0.618911\pi\) | |||||||
\(822\) | 402.501 | + | 402.501i | 0.489661 | + | 0.489661i | ||||
\(823\) | 328.958 | − | 328.958i | 0.399705 | − | 0.399705i | −0.478424 | − | 0.878129i | \(-0.658792\pi\) |
0.878129 | + | 0.478424i | \(0.158792\pi\) | |||||||
\(824\) | 254.284i | 0.308597i | ||||||||
\(825\) | −301.451 | − | 339.844i | −0.365395 | − | 0.411932i | ||||
\(826\) | −78.0197 | −0.0944548 | ||||||||
\(827\) | 405.815 | + | 405.815i | 0.490708 | + | 0.490708i | 0.908529 | − | 0.417821i | \(-0.137206\pi\) |
−0.417821 | + | 0.908529i | \(0.637206\pi\) | |||||||
\(828\) | −19.5213 | + | 19.5213i | −0.0235764 | + | 0.0235764i | ||||
\(829\) | 731.100i | 0.881906i | 0.897530 | + | 0.440953i | \(0.145359\pi\) | ||||
−0.897530 | + | 0.440953i | \(0.854641\pi\) | |||||||
\(830\) | −766.235 | + | 721.734i | −0.923175 | + | 0.869559i | ||||
\(831\) | 1154.06 | 1.38877 | ||||||||
\(832\) | 6.41719 | + | 6.41719i | 0.00771297 | + | 0.00771297i | ||||
\(833\) | 10.3672 | − | 10.3672i | 0.0124457 | − | 0.0124457i | ||||
\(834\) | − | 31.0490i | − | 0.0372291i | ||||||
\(835\) | 951.816 | + | 28.4664i | 1.13990 | + | 0.0340915i | ||||
\(836\) | −186.511 | −0.223100 | ||||||||
\(837\) | 684.661 | + | 684.661i | 0.817994 | + | 0.817994i | ||||
\(838\) | −120.421 | + | 120.421i | −0.143700 | + | 0.143700i | ||||
\(839\) | 1144.06i | 1.36360i | 0.731539 | + | 0.681800i | \(0.238803\pi\) | ||||
−0.731539 | + | 0.681800i | \(0.761197\pi\) | |||||||
\(840\) | 6.93091 | − | 231.746i | 0.00825109 | − | 0.275888i | ||||
\(841\) | 506.304 | 0.602027 | ||||||||
\(842\) | −703.519 | − | 703.519i | −0.835534 | − | 0.835534i | ||||
\(843\) | 757.842 | − | 757.842i | 0.898983 | − | 0.898983i | ||||
\(844\) | 19.1893i | 0.0227361i | ||||||||
\(845\) | −574.965 | − | 610.416i | −0.680431 | − | 0.722386i | ||||
\(846\) | 309.550 | 0.365898 | ||||||||
\(847\) | −314.213 | − | 314.213i | −0.370971 | − | 0.370971i | ||||
\(848\) | 60.7994 | − | 60.7994i | 0.0716974 | − | 0.0716974i | ||||
\(849\) | 392.591i | 0.462416i | ||||||||
\(850\) | 101.541 | + | 6.07909i | 0.119460 | + | 0.00715187i | ||||
\(851\) | −150.119 | −0.176403 | ||||||||
\(852\) | −369.301 | − | 369.301i | −0.433452 | − | 0.433452i | ||||
\(853\) | 672.838 | − | 672.838i | 0.788790 | − | 0.788790i | −0.192506 | − | 0.981296i | \(-0.561662\pi\) |
0.981296 | + | 0.192506i | \(0.0616615\pi\) | |||||||
\(854\) | 151.160i | 0.177002i | ||||||||
\(855\) | 133.021 | − | 125.296i | 0.155581 | − | 0.146545i | ||||
\(856\) | −196.073 | −0.229057 | ||||||||
\(857\) | 1132.64 | + | 1132.64i | 1.32163 | + | 1.32163i | 0.912453 | + | 0.409182i | \(0.134186\pi\) |
0.409182 | + | 0.912453i | \(0.365814\pi\) | |||||||
\(858\) | −20.6134 | + | 20.6134i | −0.0240249 | + | 0.0240249i | ||||
\(859\) | − | 26.7642i | − | 0.0311574i | −0.999879 | − | 0.0155787i | \(-0.995041\pi\) | ||
0.999879 | − | 0.0155787i | \(-0.00495906\pi\) | |||||||
\(860\) | −221.427 | − | 6.62231i | −0.257473 | − | 0.00770037i | ||||
\(861\) | −275.619 | −0.320115 | ||||||||
\(862\) | −309.307 | − | 309.307i | −0.358825 | − | 0.358825i | ||||
\(863\) | 151.057 | − | 151.057i | 0.175037 | − | 0.175037i | −0.614151 | − | 0.789188i | \(-0.710502\pi\) |
0.789188 | + | 0.614151i | \(0.210502\pi\) | |||||||
\(864\) | − | 166.251i | − | 0.192421i | ||||||
\(865\) | 11.6220 | − | 388.599i | 0.0134358 | − | 0.449247i | ||||
\(866\) | −176.529 | −0.203844 | ||||||||
\(867\) | −491.133 | − | 491.133i | −0.566474 | − | 0.566474i | ||||
\(868\) | −308.722 | + | 308.722i | −0.355671 | + | 0.355671i | ||||
\(869\) | − | 145.026i | − | 0.166889i | ||||||
\(870\) | 219.458 | + | 232.990i | 0.252251 | + | 0.267804i | ||||
\(871\) | −35.1041 | −0.0403032 | ||||||||
\(872\) | −384.845 | − | 384.845i | −0.441336 | − | 0.441336i | ||||
\(873\) | −291.370 | + | 291.370i | −0.333757 | + | 0.333757i | ||||
\(874\) | 86.1216i | 0.0985373i | ||||||||
\(875\) | −74.1910 | + | 824.923i | −0.0847897 | + | 0.942769i | ||||
\(876\) | 444.461 | 0.507375 | ||||||||
\(877\) | 217.435 | + | 217.435i | 0.247930 | + | 0.247930i | 0.820121 | − | 0.572191i | \(-0.193906\pi\) |
−0.572191 | + | 0.820121i | \(0.693906\pi\) | |||||||
\(878\) | −231.130 | + | 231.130i | −0.263246 | + | 0.263246i | ||||
\(879\) | 551.774i | 0.627729i | ||||||||
\(880\) | 106.920 | − | 100.711i | 0.121501 | − | 0.114444i | ||||
\(881\) | −238.193 | −0.270367 | −0.135183 | − | 0.990821i | \(-0.543162\pi\) | ||||
−0.135183 | + | 0.990821i | \(0.543162\pi\) | |||||||
\(882\) | 14.6671 | + | 14.6671i | 0.0166294 | + | 0.0166294i | ||||
\(883\) | −38.7342 | + | 38.7342i | −0.0438666 | + | 0.0438666i | −0.728700 | − | 0.684833i | \(-0.759875\pi\) |
0.684833 | + | 0.728700i | \(0.259875\pi\) | |||||||
\(884\) | − | 6.52773i | − | 0.00738431i | ||||||
\(885\) | −102.956 | − | 3.07914i | −0.116334 | − | 0.00347925i | ||||
\(886\) | −1145.80 | −1.29322 | ||||||||
\(887\) | 664.555 | + | 664.555i | 0.749217 | + | 0.749217i | 0.974332 | − | 0.225115i | \(-0.0722759\pi\) |
−0.225115 | + | 0.974332i | \(0.572276\pi\) | |||||||
\(888\) | 154.896 | − | 154.896i | 0.174432 | − | 0.174432i | ||||
\(889\) | 371.184i | 0.417529i | ||||||||
\(890\) | −27.8609 | + | 931.573i | −0.0313044 | + | 1.04671i | ||||
\(891\) | 343.790 | 0.385847 | ||||||||
\(892\) | 462.607 | + | 462.607i | 0.518618 | + | 0.518618i | ||||
\(893\) | 682.817 | − | 682.817i | 0.764633 | − | 0.764633i | ||||
\(894\) | 344.261i | 0.385080i | ||||||||
\(895\) | −520.347 | − | 552.431i | −0.581393 | − | 0.617241i | ||||
\(896\) | 74.9649 | 0.0836662 | ||||||||
\(897\) | 9.51823 | + | 9.51823i | 0.0106112 | + | 0.0106112i | ||||
\(898\) | 58.7939 | − | 58.7939i | 0.0654721 | − | 0.0654721i | ||||
\(899\) | − | 602.733i | − | 0.670449i | ||||||
\(900\) | −8.60042 | + | 143.655i | −0.00955603 | + | 0.159617i | ||||
\(901\) | −61.8468 | −0.0686424 | ||||||||
\(902\) | −123.470 | − | 123.470i | −0.136885 | − | 0.136885i | ||||
\(903\) | 256.803 | − | 256.803i | 0.284389 | − | 0.284389i | ||||
\(904\) | 274.557i | 0.303714i | ||||||||
\(905\) | 49.8484 | − | 46.9533i | 0.0550811 | − | 0.0518821i | ||||
\(906\) | −260.145 | −0.287135 | ||||||||
\(907\) | −439.664 | − | 439.664i | −0.484746 | − | 0.484746i | 0.421898 | − | 0.906643i | \(-0.361364\pi\) |
−0.906643 | + | 0.421898i | \(0.861364\pi\) | |||||||
\(908\) | 590.373 | − | 590.373i | 0.650190 | − | 0.650190i | ||||
\(909\) | − | 95.3919i | − | 0.104942i | ||||||
\(910\) | 53.1268 | + | 1.58889i | 0.0583811 | + | 0.00174603i | ||||
\(911\) | 636.924 | 0.699148 | 0.349574 | − | 0.936909i | \(-0.386326\pi\) | ||||
0.349574 | + | 0.936909i | \(0.386326\pi\) | |||||||
\(912\) | −88.8620 | − | 88.8620i | −0.0974364 | − | 0.0974364i | ||||
\(913\) | 773.063 | − | 773.063i | 0.846728 | − | 0.846728i | ||||
\(914\) | − | 292.938i | − | 0.320501i | ||||||
\(915\) | −5.96571 | + | 199.472i | −0.00651990 | + | 0.218003i | ||||
\(916\) | 883.581 | 0.964608 | ||||||||
\(917\) | −710.910 | − | 710.910i | −0.775257 | − | 0.775257i | ||||
\(918\) | −84.5576 | + | 84.5576i | −0.0921107 | + | 0.0921107i | ||||
\(919\) | − | 863.041i | − | 0.939109i | −0.882903 | − | 0.469555i | \(-0.844414\pi\) | ||
0.882903 | − | 0.469555i | \(-0.155586\pi\) | |||||||
\(920\) | −46.5032 | − | 49.3706i | −0.0505470 | − | 0.0536636i | ||||
\(921\) | 552.317 | 0.599693 | ||||||||
\(922\) | 532.088 | + | 532.088i | 0.577102 | + | 0.577102i | ||||
\(923\) | 84.6609 | − | 84.6609i | 0.0917236 | − | 0.0917236i | ||||
\(924\) | 240.803i | 0.260609i | ||||||||
\(925\) | −585.425 | + | 519.288i | −0.632892 | + | 0.561392i | ||||
\(926\) | −194.651 | −0.210206 | ||||||||
\(927\) | 182.974 | + | 182.974i | 0.197382 | + | 0.197382i | ||||
\(928\) | −73.1788 | + | 73.1788i | −0.0788564 | + | 0.0788564i | ||||
\(929\) | − | 1277.97i | − | 1.37564i | −0.725881 | − | 0.687821i | \(-0.758568\pi\) | ||
0.725881 | − | 0.687821i | \(-0.241432\pi\) | |||||||
\(930\) | −419.577 | + | 395.209i | −0.451158 | + | 0.424956i | ||||
\(931\) | 64.7067 | 0.0695023 | ||||||||
\(932\) | −284.714 | − | 284.714i | −0.305487 | − | 0.305487i | ||||
\(933\) | −950.493 | + | 950.493i | −1.01875 | + | 1.01875i | ||||
\(934\) | − | 1297.73i | − | 1.38944i | ||||||
\(935\) | −105.604 | − | 3.15834i | −0.112945 | − | 0.00337791i | ||||
\(936\) | 9.23515 | 0.00986661 | ||||||||
\(937\) | 1058.24 | + | 1058.24i | 1.12939 | + | 1.12939i | 0.990276 | + | 0.139116i | \(0.0444261\pi\) |
0.139116 | + | 0.990276i | \(0.455574\pi\) | |||||||
\(938\) | −205.041 | + | 205.041i | −0.218594 | + | 0.218594i | ||||
\(939\) | − | 107.471i | − | 0.114453i | ||||||
\(940\) | −22.7338 | + | 760.137i | −0.0241848 | + | 0.808657i | ||||
\(941\) | 812.669 | 0.863623 | 0.431812 | − | 0.901964i | \(-0.357875\pi\) | ||||
0.431812 | + | 0.901964i | \(0.357875\pi\) | |||||||
\(942\) | 358.501 | + | 358.501i | 0.380575 | + | 0.380575i | ||||
\(943\) | −57.0122 | + | 57.0122i | −0.0604584 | + | 0.0604584i | ||||
\(944\) | − | 33.3040i | − | 0.0352797i | ||||||
\(945\) | −667.601 | − | 708.765i | −0.706456 | − | 0.750016i | ||||
\(946\) | 230.081 | 0.243215 | ||||||||
\(947\) | 332.856 | + | 332.856i | 0.351485 | + | 0.351485i | 0.860662 | − | 0.509177i | \(-0.170050\pi\) |
−0.509177 | + | 0.860662i | \(0.670050\pi\) | |||||||
\(948\) | 69.0968 | − | 69.0968i | 0.0728869 | − | 0.0728869i | ||||
\(949\) | 101.891i | 0.107367i | ||||||||
\(950\) | 297.910 | + | 335.852i | 0.313589 | + | 0.353529i | ||||
\(951\) | −1297.84 | −1.36472 | ||||||||
\(952\) | −38.1281 | − | 38.1281i | −0.0400506 | − | 0.0400506i | ||||
\(953\) | 54.2554 | − | 54.2554i | 0.0569312 | − | 0.0569312i | −0.678068 | − | 0.734999i | \(-0.737183\pi\) |
0.734999 | + | 0.678068i | \(0.237183\pi\) | |||||||
\(954\) | − | 87.4980i | − | 0.0917170i | ||||||
\(955\) | 809.225 | − | 762.227i | 0.847356 | − | 0.798144i | ||||
\(956\) | −206.945 | −0.216469 | ||||||||
\(957\) | −235.066 | − | 235.066i | −0.245628 | − | 0.245628i | ||||
\(958\) | 67.3465 | − | 67.3465i | 0.0702991 | − | 0.0702991i | ||||
\(959\) | 1077.91i | 1.12399i | ||||||||
\(960\) | 98.9244 | + | 2.95858i | 0.103046 | + | 0.00308185i | ||||
\(961\) | 124.426 | 0.129476 | ||||||||
\(962\) | 35.5092 | + | 35.5092i | 0.0369119 | + | 0.0369119i | ||||
\(963\) | −141.087 | + | 141.087i | −0.146508 | + | 0.146508i | ||||
\(964\) | 22.9317i | 0.0237881i | ||||||||
\(965\) | −22.7711 | + | 761.387i | −0.0235970 | + | 0.789002i | ||||
\(966\) | 111.191 | 0.115104 | ||||||||
\(967\) | −1089.02 | − | 1089.02i | −1.12619 | − | 1.12619i | −0.990792 | − | 0.135395i | \(-0.956770\pi\) |
−0.135395 | − | 0.990792i | \(-0.543230\pi\) | |||||||
\(968\) | 134.127 | − | 134.127i | 0.138561 | − | 0.138561i | ||||
\(969\) | 90.3927i | 0.0932846i | ||||||||
\(970\) | −694.096 | − | 736.894i | −0.715563 | − | 0.759684i | ||||
\(971\) | 781.891 | 0.805243 | 0.402621 | − | 0.915367i | \(-0.368099\pi\) | ||||
0.402621 | + | 0.915367i | \(0.368099\pi\) | |||||||
\(972\) | −210.269 | − | 210.269i | −0.216326 | − | 0.216326i | ||||
\(973\) | 41.5751 | − | 41.5751i | 0.0427288 | − | 0.0427288i | ||||
\(974\) | 148.899i | 0.152874i | ||||||||
\(975\) | 70.0439 | + | 4.19342i | 0.0718399 | + | 0.00430094i | ||||
\(976\) | −64.5252 | −0.0661119 | ||||||||
\(977\) | 92.3138 | + | 92.3138i | 0.0944870 | + | 0.0944870i | 0.752770 | − | 0.658283i | \(-0.228717\pi\) |
−0.658283 | + | 0.752770i | \(0.728717\pi\) | |||||||
\(978\) | 243.858 | − | 243.858i | 0.249343 | − | 0.249343i | ||||
\(979\) | − | 967.983i | − | 0.988746i | ||||||
\(980\) | −37.0941 | + | 34.9398i | −0.0378511 | + | 0.0356528i | ||||
\(981\) | −553.841 | −0.564568 | ||||||||
\(982\) | 767.159 | + | 767.159i | 0.781221 | + | 0.781221i | ||||
\(983\) | −458.204 | + | 458.204i | −0.466128 | + | 0.466128i | −0.900658 | − | 0.434529i | \(-0.856915\pi\) |
0.434529 | + | 0.900658i | \(0.356915\pi\) | |||||||
\(984\) | − | 117.653i | − | 0.119566i | ||||||
\(985\) | 35.6044 | + | 1.06484i | 0.0361466 | + | 0.00108105i | ||||
\(986\) | 74.4394 | 0.0754963 | ||||||||
\(987\) | −881.580 | − | 881.580i | −0.893191 | − | 0.893191i | ||||
\(988\) | 20.3713 | − | 20.3713i | 0.0206187 | − | 0.0206187i | ||||
\(989\) | − | 106.240i | − | 0.107422i | ||||||
\(990\) | 4.46828 | − | 149.404i | 0.00451342 | − | 0.150913i | ||||
\(991\) | 988.103 | 0.997077 | 0.498538 | − | 0.866868i | \(-0.333870\pi\) | ||||
0.498538 | + | 0.866868i | \(0.333870\pi\) | |||||||
\(992\) | −131.783 | − | 131.783i | −0.132846 | − | 0.132846i | ||||
\(993\) | −584.735 | + | 584.735i | −0.588857 | + | 0.588857i | ||||
\(994\) | − | 988.999i | − | 0.994969i | ||||||
\(995\) | −436.426 | − | 463.336i | −0.438620 | − | 0.465664i | ||||
\(996\) | 736.641 | 0.739599 | ||||||||
\(997\) | −105.423 | − | 105.423i | −0.105741 | − | 0.105741i | 0.652257 | − | 0.757998i | \(-0.273822\pi\) |
−0.757998 | + | 0.652257i | \(0.773822\pi\) | |||||||
\(998\) | 530.092 | − | 530.092i | 0.531154 | − | 0.531154i | ||||
\(999\) | − | 919.945i | − | 0.920866i |
(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 | 230.3.f.b.47.8 | ✓ | 24 | |
5.3 | odd | 4 | inner | 230.3.f.b.93.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.b.47.8 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.f.b.93.8 | yes | 24 | 5.3 | odd | 4 | inner |