Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,3,Mod(229,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.h (of order \(6\), 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: | \(11.2806829445\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.8 | ||
Character | \(\chi\) | \(=\) | 414.229 |
Dual form | 414.3.h.a.367.8 |
$q$-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 \(\left(\mathbb{Z}/414\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(235\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.353553 | − | 0.612372i | ||||
\(3\) | −1.45535 | + | 2.62335i | −0.485116 | + | 0.874450i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 6.63175 | + | 3.82884i | 1.32635 | + | 0.765769i | 0.984733 | − | 0.174070i | \(-0.0556920\pi\) |
0.341617 | + | 0.939839i | \(0.389025\pi\) | |||||||
\(6\) | 4.24202 | − | 0.0725559i | 0.707003 | − | 0.0120926i | ||||
\(7\) | 9.09135 | − | 5.24889i | 1.29876 | − | 0.749842i | 0.318573 | − | 0.947898i | \(-0.396796\pi\) |
0.980191 | + | 0.198057i | \(0.0634630\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −4.76392 | − | 7.63578i | −0.529324 | − | 0.848420i | ||||
\(10\) | − | 10.8296i | − | 1.08296i | ||||||
\(11\) | 6.63227 | − | 3.82914i | 0.602934 | − | 0.348104i | −0.167261 | − | 0.985913i | \(-0.553492\pi\) |
0.770195 | + | 0.637809i | \(0.220159\pi\) | |||||||
\(12\) | −3.08842 | − | 5.14409i | −0.257369 | − | 0.428674i | ||||
\(13\) | 3.25235 | − | 5.63323i | 0.250181 | − | 0.433326i | −0.713395 | − | 0.700762i | \(-0.752843\pi\) |
0.963575 | + | 0.267437i | \(0.0861766\pi\) | |||||||
\(14\) | −12.8571 | − | 7.42305i | −0.918365 | − | 0.530218i | ||||
\(15\) | −19.6959 | + | 11.8251i | −1.31306 | + | 0.788339i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.48310i | 0.204888i | 0.994739 | + | 0.102444i | \(0.0326663\pi\) | ||||
−0.994739 | + | 0.102444i | \(0.967334\pi\) | |||||||
\(18\) | −5.98328 | + | 11.2339i | −0.332405 | + | 0.624105i | ||||
\(19\) | − | 17.2685i | − | 0.908869i | −0.890780 | − | 0.454434i | \(-0.849841\pi\) | ||
0.890780 | − | 0.454434i | \(-0.150159\pi\) | |||||||
\(20\) | −13.2635 | + | 7.65769i | −0.663175 | + | 0.382884i | ||||
\(21\) | 0.538586 | + | 31.4887i | 0.0256470 | + | 1.49946i | ||||
\(22\) | −9.37945 | − | 5.41523i | −0.426339 | − | 0.246147i | ||||
\(23\) | 7.98151 | − | 21.5707i | 0.347022 | − | 0.937857i | ||||
\(24\) | −4.11635 | + | 7.41995i | −0.171515 | + | 0.309165i | ||||
\(25\) | 16.8201 | + | 29.1333i | 0.672804 | + | 1.16533i | ||||
\(26\) | −9.19903 | −0.353809 | ||||||||
\(27\) | 26.9645 | − | 1.38469i | 0.998684 | − | 0.0512847i | ||||
\(28\) | 20.9956i | 0.749842i | ||||||||
\(29\) | −2.15172 | − | 3.72690i | −0.0741974 | − | 0.128514i | 0.826540 | − | 0.562879i | \(-0.190306\pi\) |
−0.900737 | + | 0.434365i | \(0.856973\pi\) | |||||||
\(30\) | 28.4098 | + | 15.7609i | 0.946994 | + | 0.525362i | ||||
\(31\) | −15.8006 | + | 27.3675i | −0.509697 | + | 0.882821i | 0.490240 | + | 0.871588i | \(0.336909\pi\) |
−0.999937 | + | 0.0112335i | \(0.996424\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0.392907 | + | 22.9715i | 0.0119063 | + | 0.696106i | ||||
\(34\) | 4.26591 | − | 2.46292i | 0.125468 | − | 0.0724390i | ||||
\(35\) | 80.3887 | 2.29682 | ||||||||
\(36\) | 17.9895 | − | 0.615567i | 0.499708 | − | 0.0170991i | ||||
\(37\) | − | 12.3638i | − | 0.334157i | −0.985944 | − | 0.167078i | \(-0.946567\pi\) | ||
0.985944 | − | 0.167078i | \(-0.0534333\pi\) | |||||||
\(38\) | −21.1495 | + | 12.2107i | −0.556566 | + | 0.321334i | ||||
\(39\) | 10.0446 | + | 16.7304i | 0.257555 | + | 0.428984i | ||||
\(40\) | 18.7574 | + | 10.8296i | 0.468936 | + | 0.270740i | ||||
\(41\) | 31.3416 | − | 54.2853i | 0.764430 | − | 1.32403i | −0.176118 | − | 0.984369i | \(-0.556354\pi\) |
0.940547 | − | 0.339662i | \(-0.110313\pi\) | |||||||
\(42\) | 38.1848 | − | 22.9255i | 0.909163 | − | 0.545846i | ||||
\(43\) | −11.5760 | + | 6.68344i | −0.269210 | + | 0.155429i | −0.628529 | − | 0.777786i | \(-0.716343\pi\) |
0.359318 | + | 0.933215i | \(0.383009\pi\) | |||||||
\(44\) | 15.3166i | 0.348104i | ||||||||
\(45\) | −2.35691 | − | 68.8789i | −0.0523758 | − | 1.53064i | ||||
\(46\) | −32.0624 | + | 5.47749i | −0.697009 | + | 0.119076i | ||||
\(47\) | 38.7644 | + | 67.1419i | 0.824775 | + | 1.42855i | 0.902091 | + | 0.431545i | \(0.142031\pi\) |
−0.0773169 | + | 0.997007i | \(0.524635\pi\) | |||||||
\(48\) | 11.9982 | − | 0.205219i | 0.249963 | − | 0.00427540i | ||||
\(49\) | 30.6017 | − | 53.0037i | 0.624525 | − | 1.08171i | ||||
\(50\) | 23.7872 | − | 41.2006i | 0.475744 | − | 0.824013i | ||||
\(51\) | −9.13739 | − | 5.06913i | −0.179165 | − | 0.0993947i | ||||
\(52\) | 6.50470 | + | 11.2665i | 0.125090 | + | 0.216663i | ||||
\(53\) | 9.96736i | 0.188063i | 0.995569 | + | 0.0940317i | \(0.0299755\pi\) | ||||
−0.995569 | + | 0.0940317i | \(0.970024\pi\) | |||||||
\(54\) | −20.7626 | − | 32.0455i | −0.384493 | − | 0.593435i | ||||
\(55\) | 58.6448 | 1.06627 | ||||||||
\(56\) | 25.7142 | − | 14.8461i | 0.459182 | − | 0.265109i | ||||
\(57\) | 45.3013 | + | 25.1317i | 0.794760 | + | 0.440907i | ||||
\(58\) | −3.04300 | + | 5.27063i | −0.0524655 | + | 0.0908729i | ||||
\(59\) | 6.49183 | − | 11.2442i | 0.110031 | − | 0.190579i | −0.805752 | − | 0.592254i | \(-0.798238\pi\) |
0.915783 | + | 0.401674i | \(0.131572\pi\) | |||||||
\(60\) | −0.785751 | − | 45.9394i | −0.0130959 | − | 0.765657i | ||||
\(61\) | −71.9662 | + | 41.5497i | −1.17977 | + | 0.681142i | −0.955962 | − | 0.293490i | \(-0.905183\pi\) |
−0.223811 | + | 0.974633i | \(0.571850\pi\) | |||||||
\(62\) | 44.6909 | 0.720820 | ||||||||
\(63\) | −83.3898 | − | 44.4142i | −1.32365 | − | 0.704988i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 43.1375 | − | 24.9055i | 0.663655 | − | 0.383161i | ||||
\(66\) | 27.8564 | − | 16.7245i | 0.422067 | − | 0.253402i | ||||
\(67\) | 80.1858 | + | 46.2953i | 1.19680 | + | 0.690974i | 0.959841 | − | 0.280545i | \(-0.0905151\pi\) |
0.236962 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(68\) | −6.03291 | − | 3.48310i | −0.0887193 | − | 0.0512221i | ||||
\(69\) | 44.9716 | + | 52.3312i | 0.651763 | + | 0.758423i | ||||
\(70\) | −56.8434 | − | 98.4557i | −0.812049 | − | 1.40651i | ||||
\(71\) | 22.5625 | 0.317782 | 0.158891 | − | 0.987296i | \(-0.449208\pi\) | ||||
0.158891 | + | 0.987296i | \(0.449208\pi\) | |||||||
\(72\) | −13.4744 | − | 21.5972i | −0.187144 | − | 0.299962i | ||||
\(73\) | −143.920 | −1.97150 | −0.985750 | − | 0.168214i | \(-0.946200\pi\) | ||||
−0.985750 | + | 0.168214i | \(0.946200\pi\) | |||||||
\(74\) | −15.1425 | + | 8.74253i | −0.204629 | + | 0.118142i | ||||
\(75\) | −100.906 | + | 1.72590i | −1.34541 | + | 0.0230120i | ||||
\(76\) | 29.9099 | + | 17.2685i | 0.393552 | + | 0.227217i | ||||
\(77\) | 40.1975 | − | 69.6242i | 0.522046 | − | 0.904210i | ||||
\(78\) | 13.3878 | − | 24.1323i | 0.171639 | − | 0.309388i | ||||
\(79\) | −28.0019 | + | 16.1669i | −0.354455 | + | 0.204645i | −0.666646 | − | 0.745375i | \(-0.732271\pi\) |
0.312191 | + | 0.950019i | \(0.398937\pi\) | |||||||
\(80\) | − | 30.6308i | − | 0.382884i | ||||||
\(81\) | −35.6102 | + | 72.7524i | −0.439632 | + | 0.898178i | ||||
\(82\) | −88.6475 | −1.08107 | ||||||||
\(83\) | 33.5092 | − | 19.3466i | 0.403726 | − | 0.233091i | −0.284365 | − | 0.958716i | \(-0.591783\pi\) |
0.688090 | + | 0.725625i | \(0.258449\pi\) | |||||||
\(84\) | −55.0787 | − | 30.5559i | −0.655699 | − | 0.363761i | ||||
\(85\) | −13.3363 | + | 23.0991i | −0.156897 | + | 0.271754i | ||||
\(86\) | 16.3710 | + | 9.45180i | 0.190361 | + | 0.109905i | ||||
\(87\) | 12.9085 | − | 0.220787i | 0.148373 | − | 0.00253778i | ||||
\(88\) | 18.7589 | − | 10.8305i | 0.213169 | − | 0.123073i | ||||
\(89\) | 130.470i | 1.46595i | 0.680253 | + | 0.732977i | \(0.261870\pi\) | ||||
−0.680253 | + | 0.732977i | \(0.738130\pi\) | |||||||
\(90\) | −82.6925 | + | 51.5913i | −0.918805 | + | 0.573237i | ||||
\(91\) | − | 68.2849i | − | 0.750384i | ||||||
\(92\) | 29.3801 | + | 35.3951i | 0.319348 | + | 0.384729i | ||||
\(93\) | −48.7990 | − | 81.2797i | −0.524720 | − | 0.873975i | ||||
\(94\) | 54.8211 | − | 94.9530i | 0.583204 | − | 1.01014i | ||||
\(95\) | 66.1184 | − | 114.520i | 0.695983 | − | 1.20548i | ||||
\(96\) | −8.73538 | − | 14.5497i | −0.0909936 | − | 0.151559i | ||||
\(97\) | −163.119 | + | 94.1767i | −1.68164 | + | 0.970894i | −0.721065 | + | 0.692868i | \(0.756347\pi\) |
−0.960573 | + | 0.278027i | \(0.910320\pi\) | |||||||
\(98\) | −86.5547 | −0.883212 | ||||||||
\(99\) | −60.8341 | − | 32.4008i | −0.614486 | − | 0.327281i | ||||
\(100\) | −67.2804 | −0.672804 | ||||||||
\(101\) | 51.2428 | + | 88.7552i | 0.507355 | + | 0.878764i | 0.999964 | + | 0.00851330i | \(0.00270990\pi\) |
−0.492609 | + | 0.870251i | \(0.663957\pi\) | |||||||
\(102\) | 0.252719 | + | 14.7754i | 0.00247764 | + | 0.144857i | ||||
\(103\) | 49.7088 | + | 28.6994i | 0.482609 | + | 0.278635i | 0.721503 | − | 0.692411i | \(-0.243451\pi\) |
−0.238894 | + | 0.971046i | \(0.576785\pi\) | |||||||
\(104\) | 9.19903 | − | 15.9332i | 0.0884522 | − | 0.153204i | ||||
\(105\) | −116.994 | + | 210.888i | −1.11423 | + | 2.00845i | ||||
\(106\) | 12.2075 | − | 7.04799i | 0.115165 | − | 0.0664905i | ||||
\(107\) | 41.1977i | 0.385026i | 0.981294 | + | 0.192513i | \(0.0616637\pi\) | ||||
−0.981294 | + | 0.192513i | \(0.938336\pi\) | |||||||
\(108\) | −24.5661 | + | 48.0885i | −0.227464 | + | 0.445264i | ||||
\(109\) | − | 162.732i | − | 1.49295i | −0.665414 | − | 0.746475i | \(-0.731745\pi\) | ||
0.665414 | − | 0.746475i | \(-0.268255\pi\) | |||||||
\(110\) | −41.4681 | − | 71.8249i | −0.376983 | − | 0.652954i | ||||
\(111\) | 32.4346 | + | 17.9937i | 0.292203 | + | 0.162105i | ||||
\(112\) | −36.3654 | − | 20.9956i | −0.324691 | − | 0.187460i | ||||
\(113\) | 82.8422 | + | 47.8290i | 0.733117 | + | 0.423265i | 0.819561 | − | 0.572991i | \(-0.194217\pi\) |
−0.0864444 | + | 0.996257i | \(0.527550\pi\) | |||||||
\(114\) | −1.25293 | − | 73.2534i | −0.0109906 | − | 0.642573i | ||||
\(115\) | 135.522 | − | 112.492i | 1.17845 | − | 0.978188i | ||||
\(116\) | 8.60690 | 0.0741974 | ||||||||
\(117\) | −58.5080 | + | 2.00204i | −0.500069 | + | 0.0171114i | ||||
\(118\) | −18.3617 | −0.155607 | ||||||||
\(119\) | 18.2824 | + | 31.6661i | 0.153634 | + | 0.266102i | ||||
\(120\) | −55.7084 | + | 33.4464i | −0.464237 | + | 0.278720i | ||||
\(121\) | −31.1753 | + | 53.9972i | −0.257647 | + | 0.446258i | ||||
\(122\) | 101.776 | + | 58.7601i | 0.834226 | + | 0.481640i | ||||
\(123\) | 96.7962 | + | 161.224i | 0.786961 | + | 1.31076i | ||||
\(124\) | −31.6012 | − | 54.7349i | −0.254848 | − | 0.441411i | ||||
\(125\) | 66.1638i | 0.529311i | ||||||||
\(126\) | 4.56939 | + | 133.537i | 0.0362650 | + | 1.05982i | ||||
\(127\) | 117.112 | 0.922142 | 0.461071 | − | 0.887363i | \(-0.347465\pi\) | ||||
0.461071 | + | 0.887363i | \(0.347465\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −0.685784 | − | 40.0947i | −0.00531615 | − | 0.310812i | ||||
\(130\) | −61.0057 | − | 35.2217i | −0.469275 | − | 0.270936i | ||||
\(131\) | −38.5045 | + | 66.6918i | −0.293928 | + | 0.509097i | −0.974735 | − | 0.223365i | \(-0.928296\pi\) |
0.680807 | + | 0.732463i | \(0.261629\pi\) | |||||||
\(132\) | −40.1807 | − | 22.2910i | −0.304399 | − | 0.168871i | ||||
\(133\) | −90.6405 | − | 156.994i | −0.681508 | − | 1.18041i | ||||
\(134\) | − | 130.943i | − | 0.977185i | ||||||
\(135\) | 184.123 | + | 94.0598i | 1.36388 | + | 0.696740i | ||||
\(136\) | 9.85170i | 0.0724390i | ||||||||
\(137\) | 65.6420 | − | 37.8984i | 0.479139 | − | 0.276631i | −0.240919 | − | 0.970545i | \(-0.577449\pi\) |
0.720057 | + | 0.693914i | \(0.244115\pi\) | |||||||
\(138\) | 32.2926 | − | 92.0825i | 0.234005 | − | 0.667264i | ||||
\(139\) | −48.2767 | + | 83.6178i | −0.347315 | + | 0.601567i | −0.985771 | − | 0.168091i | \(-0.946240\pi\) |
0.638457 | + | 0.769658i | \(0.279573\pi\) | |||||||
\(140\) | −80.3887 | + | 139.237i | −0.574205 | + | 0.994553i | ||||
\(141\) | −232.552 | + | 3.97760i | −1.64931 | + | 0.0282099i | ||||
\(142\) | −15.9541 | − | 27.6333i | −0.112353 | − | 0.194601i | ||||
\(143\) | − | 49.8149i | − | 0.348356i | ||||||
\(144\) | −16.9233 | + | 31.7742i | −0.117523 | + | 0.220654i | ||||
\(145\) | − | 32.9545i | − | 0.227272i | ||||||
\(146\) | 101.766 | + | 176.265i | 0.697031 | + | 1.20729i | ||||
\(147\) | 94.5111 | + | 157.418i | 0.642933 | + | 1.07087i | ||||
\(148\) | 21.4147 | + | 12.3638i | 0.144694 | + | 0.0835392i | ||||
\(149\) | −234.918 | − | 135.630i | −1.57663 | − | 0.910266i | −0.995325 | − | 0.0965789i | \(-0.969210\pi\) |
−0.581302 | − | 0.813688i | \(-0.697457\pi\) | |||||||
\(150\) | 73.4650 | + | 122.363i | 0.489766 | + | 0.815756i | ||||
\(151\) | 29.5767 | + | 51.2283i | 0.195872 | + | 0.339260i | 0.947186 | − | 0.320685i | \(-0.103913\pi\) |
−0.751314 | + | 0.659945i | \(0.770580\pi\) | |||||||
\(152\) | − | 48.8427i | − | 0.321334i | ||||||
\(153\) | 26.5962 | − | 16.5932i | 0.173831 | − | 0.108452i | ||||
\(154\) | −113.696 | −0.738284 | ||||||||
\(155\) | −209.571 | + | 120.996i | −1.35207 | + | 0.780620i | ||||
\(156\) | −39.0225 | + | 0.667444i | −0.250144 | + | 0.00427849i | ||||
\(157\) | −229.038 | − | 132.235i | −1.45884 | − | 0.842263i | −0.459889 | − | 0.887977i | \(-0.652111\pi\) |
−0.998955 | + | 0.0457132i | \(0.985444\pi\) | |||||||
\(158\) | 39.6007 | + | 22.8635i | 0.250637 | + | 0.144706i | ||||
\(159\) | −26.1479 | − | 14.5060i | −0.164452 | − | 0.0912327i | ||||
\(160\) | −37.5149 | + | 21.6592i | −0.234468 | + | 0.135370i | ||||
\(161\) | −40.6597 | − | 238.001i | −0.252545 | − | 1.47827i | ||||
\(162\) | 114.283 | − | 7.83030i | 0.705453 | − | 0.0483352i | ||||
\(163\) | −245.228 | −1.50447 | −0.752233 | − | 0.658897i | \(-0.771023\pi\) | ||||
−0.752233 | + | 0.658897i | \(0.771023\pi\) | |||||||
\(164\) | 62.6833 | + | 108.571i | 0.382215 | + | 0.662016i | ||||
\(165\) | −85.3487 | + | 153.846i | −0.517265 | + | 0.932398i | ||||
\(166\) | −47.3892 | − | 27.3602i | −0.285477 | − | 0.164820i | ||||
\(167\) | 124.487 | − | 215.617i | 0.745430 | − | 1.29112i | −0.204564 | − | 0.978853i | \(-0.565578\pi\) |
0.949994 | − | 0.312269i | \(-0.101089\pi\) | |||||||
\(168\) | 1.52335 | + | 89.0636i | 0.00906757 | + | 0.530141i | ||||
\(169\) | 63.3445 | + | 109.716i | 0.374819 | + | 0.649206i | ||||
\(170\) | 37.7206 | 0.221886 | ||||||||
\(171\) | −131.858 | + | 82.2657i | −0.771102 | + | 0.481086i | ||||
\(172\) | − | 26.7337i | − | 0.155429i | ||||||
\(173\) | −67.0262 | − | 116.093i | −0.387435 | − | 0.671057i | 0.604669 | − | 0.796477i | \(-0.293305\pi\) |
−0.992104 | + | 0.125420i | \(0.959972\pi\) | |||||||
\(174\) | −9.39806 | − | 15.6534i | −0.0540119 | − | 0.0899623i | ||||
\(175\) | 305.835 | + | 176.574i | 1.74763 | + | 1.00899i | ||||
\(176\) | −26.5291 | − | 15.3166i | −0.150733 | − | 0.0870260i | ||||
\(177\) | 20.0495 | + | 33.3945i | 0.113274 | + | 0.188670i | ||||
\(178\) | 159.792 | − | 92.2562i | 0.897710 | − | 0.518293i | ||||
\(179\) | 72.9875 | 0.407751 | 0.203876 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203876 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(180\) | 121.659 | + | 64.7966i | 0.675881 | + | 0.359981i | ||||
\(181\) | 190.552i | 1.05277i | 0.850246 | + | 0.526386i | \(0.176453\pi\) | ||||
−0.850246 | + | 0.526386i | \(0.823547\pi\) | |||||||
\(182\) | −83.6316 | + | 48.2847i | −0.459514 | + | 0.265301i | ||||
\(183\) | −4.26339 | − | 249.262i | −0.0232972 | − | 1.36209i | ||||
\(184\) | 22.5751 | − | 61.0112i | 0.122691 | − | 0.331583i | ||||
\(185\) | 47.3391 | − | 81.9937i | 0.255887 | − | 0.443209i | ||||
\(186\) | −65.0408 | + | 117.240i | −0.349682 | + | 0.630321i | ||||
\(187\) | 13.3373 | + | 23.1009i | 0.0713225 | + | 0.123534i | ||||
\(188\) | −155.058 | −0.824775 | ||||||||
\(189\) | 237.875 | − | 154.122i | 1.25860 | − | 0.815462i | ||||
\(190\) | −187.011 | −0.984269 | ||||||||
\(191\) | −151.421 | + | 87.4229i | −0.792780 | + | 0.457711i | −0.840940 | − | 0.541128i | \(-0.817997\pi\) |
0.0481606 | + | 0.998840i | \(0.484664\pi\) | |||||||
\(192\) | −11.6428 | + | 20.9868i | −0.0606396 | + | 0.109306i | ||||
\(193\) | 125.690 | − | 217.702i | 0.651246 | − | 1.12799i | −0.331575 | − | 0.943429i | \(-0.607580\pi\) |
0.982821 | − | 0.184562i | \(-0.0590866\pi\) | |||||||
\(194\) | 230.685 | + | 133.186i | 1.18910 | + | 0.686526i | ||||
\(195\) | 2.55554 | + | 149.411i | 0.0131053 | + | 0.766210i | ||||
\(196\) | 61.2034 | + | 106.007i | 0.312262 | + | 0.540854i | ||||
\(197\) | −275.079 | −1.39634 | −0.698169 | − | 0.715933i | \(-0.746002\pi\) | ||||
−0.698169 | + | 0.715933i | \(0.746002\pi\) | |||||||
\(198\) | 3.33344 | + | 97.4171i | 0.0168355 | + | 0.492006i | ||||
\(199\) | − | 81.7222i | − | 0.410664i | −0.978692 | − | 0.205332i | \(-0.934173\pi\) | ||
0.978692 | − | 0.205332i | \(-0.0658275\pi\) | |||||||
\(200\) | 47.5744 | + | 82.4013i | 0.237872 | + | 0.412006i | ||||
\(201\) | −238.147 | + | 142.979i | −1.18481 | + | 0.711341i | ||||
\(202\) | 72.4683 | − | 125.519i | 0.358754 | − | 0.621380i | ||||
\(203\) | −39.1241 | − | 22.5883i | −0.192730 | − | 0.111273i | ||||
\(204\) | 17.9174 | − | 10.7573i | 0.0878303 | − | 0.0527318i | ||||
\(205\) | 415.700 | − | 240.004i | 2.02780 | − | 1.17075i | ||||
\(206\) | − | 81.1741i | − | 0.394049i | ||||||
\(207\) | −202.732 | + | 41.8160i | −0.979383 | + | 0.202010i | ||||
\(208\) | −26.0188 | −0.125090 | ||||||||
\(209\) | −66.1236 | − | 114.529i | −0.316381 | − | 0.547988i | ||||
\(210\) | 341.011 | − | 5.83267i | 1.62386 | − | 0.0277746i | ||||
\(211\) | 124.496 | − | 215.634i | 0.590029 | − | 1.02196i | −0.404199 | − | 0.914671i | \(-0.632450\pi\) |
0.994228 | − | 0.107289i | \(-0.0342170\pi\) | |||||||
\(212\) | −17.2640 | − | 9.96736i | −0.0814339 | − | 0.0470159i | ||||
\(213\) | −32.8363 | + | 59.1893i | −0.154161 | + | 0.277884i | ||||
\(214\) | 50.4567 | − | 29.1312i | 0.235779 | − | 0.136127i | ||||
\(215\) | −102.359 | −0.476090 | ||||||||
\(216\) | 76.2670 | − | 3.91649i | 0.353088 | − | 0.0181319i | ||||
\(217\) | 331.743i | 1.52877i | ||||||||
\(218\) | −199.305 | + | 115.069i | −0.914241 | + | 0.527837i | ||||
\(219\) | 209.453 | − | 377.551i | 0.956408 | − | 1.72398i | ||||
\(220\) | −58.6448 | + | 101.576i | −0.266567 | + | 0.461708i | ||||
\(221\) | 19.6211 | + | 11.3283i | 0.0887834 | + | 0.0512591i | ||||
\(222\) | −0.897067 | − | 52.4475i | −0.00404084 | − | 0.236250i | ||||
\(223\) | 20.0472 | + | 34.7228i | 0.0898979 | + | 0.155708i | 0.907468 | − | 0.420122i | \(-0.138013\pi\) |
−0.817570 | + | 0.575829i | \(0.804679\pi\) | |||||||
\(224\) | 59.3844i | 0.265109i | ||||||||
\(225\) | 142.326 | − | 267.223i | 0.632558 | − | 1.18766i | ||||
\(226\) | − | 135.281i | − | 0.598588i | ||||||
\(227\) | −247.073 | + | 142.648i | −1.08843 | + | 0.628405i | −0.933158 | − | 0.359467i | \(-0.882958\pi\) |
−0.155271 | + | 0.987872i | \(0.549625\pi\) | |||||||
\(228\) | −88.8307 | + | 53.3325i | −0.389608 | + | 0.233914i | ||||
\(229\) | −163.806 | − | 94.5737i | −0.715312 | − | 0.412986i | 0.0977127 | − | 0.995215i | \(-0.468847\pi\) |
−0.813025 | + | 0.582229i | \(0.802181\pi\) | |||||||
\(230\) | −233.602 | − | 86.4366i | −1.01566 | − | 0.375811i | ||||
\(231\) | 124.147 | + | 206.780i | 0.537433 | + | 0.895150i | ||||
\(232\) | −6.08599 | − | 10.5413i | −0.0262327 | − | 0.0454364i | ||||
\(233\) | −166.369 | −0.714032 | −0.357016 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357016 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(234\) | 43.8234 | + | 70.2418i | 0.187280 | + | 0.300178i | ||||
\(235\) | 593.691i | 2.52635i | ||||||||
\(236\) | 12.9837 | + | 22.4884i | 0.0550155 | + | 0.0952896i | ||||
\(237\) | −1.65888 | − | 96.9874i | −0.00699949 | − | 0.409229i | ||||
\(238\) | 25.8552 | − | 44.7826i | 0.108636 | − | 0.188162i | ||||
\(239\) | 218.361 | − | 378.213i | 0.913646 | − | 1.58248i | 0.104775 | − | 0.994496i | \(-0.466588\pi\) |
0.808871 | − | 0.587986i | \(-0.200079\pi\) | |||||||
\(240\) | 80.3551 | + | 44.5784i | 0.334813 | + | 0.185744i | ||||
\(241\) | −127.316 | + | 73.5057i | −0.528281 | + | 0.305003i | −0.740316 | − | 0.672259i | \(-0.765324\pi\) |
0.212035 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(242\) | 88.1771 | 0.364368 | ||||||||
\(243\) | −139.030 | − | 199.298i | −0.572138 | − | 0.820157i | ||||
\(244\) | − | 166.199i | − | 0.681142i | ||||||
\(245\) | 405.886 | − | 234.338i | 1.65668 | − | 0.956483i | ||||
\(246\) | 129.013 | − | 232.553i | 0.524443 | − | 0.945339i | ||||
\(247\) | −97.2775 | − | 56.1632i | −0.393836 | − | 0.227381i | ||||
\(248\) | −44.6909 | + | 77.4068i | −0.180205 | + | 0.312124i | ||||
\(249\) | 1.98514 | + | 116.062i | 0.00797245 | + | 0.466114i | ||||
\(250\) | 81.0338 | − | 46.7849i | 0.324135 | − | 0.187140i | ||||
\(251\) | 250.806i | 0.999226i | 0.866249 | + | 0.499613i | \(0.166524\pi\) | ||||
−0.866249 | + | 0.499613i | \(0.833476\pi\) | |||||||
\(252\) | 160.317 | − | 100.021i | 0.636180 | − | 0.396909i | ||||
\(253\) | −29.6618 | − | 173.625i | −0.117240 | − | 0.686266i | ||||
\(254\) | −82.8107 | − | 143.432i | −0.326026 | − | 0.564694i | ||||
\(255\) | −41.1880 | − | 68.6029i | −0.161522 | − | 0.269031i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.52776 | + | 14.7705i | −0.0331820 | + | 0.0574728i | −0.882139 | − | 0.470988i | \(-0.843897\pi\) |
0.848958 | + | 0.528461i | \(0.177231\pi\) | |||||||
\(258\) | −48.6209 | + | 29.1912i | −0.188453 | + | 0.113144i | ||||
\(259\) | −64.8963 | − | 112.404i | −0.250565 | − | 0.433991i | ||||
\(260\) | 99.6219i | 0.383161i | ||||||||
\(261\) | −18.2071 | + | 34.1847i | −0.0697590 | + | 0.130976i | ||||
\(262\) | 108.907 | 0.415676 | ||||||||
\(263\) | 147.843 | − | 85.3572i | 0.562141 | − | 0.324552i | −0.191864 | − | 0.981422i | \(-0.561453\pi\) |
0.754004 | + | 0.656870i | \(0.228120\pi\) | |||||||
\(264\) | 1.11131 | + | 64.9732i | 0.00420950 | + | 0.246111i | ||||
\(265\) | −38.1635 | + | 66.1011i | −0.144013 | + | 0.249438i | ||||
\(266\) | −128.185 | + | 222.023i | −0.481899 | + | 0.834673i | ||||
\(267\) | −342.268 | − | 189.879i | −1.28190 | − | 0.711159i | ||||
\(268\) | −160.372 | + | 92.5906i | −0.598401 | + | 0.345487i | ||||
\(269\) | 253.889 | 0.943824 | 0.471912 | − | 0.881646i | \(-0.343564\pi\) | ||||
0.471912 | + | 0.881646i | \(0.343564\pi\) | |||||||
\(270\) | −14.9956 | − | 292.015i | −0.0555393 | − | 1.08154i | ||||
\(271\) | 347.620 | 1.28273 | 0.641365 | − | 0.767236i | \(-0.278368\pi\) | ||||
0.641365 | + | 0.767236i | \(0.278368\pi\) | |||||||
\(272\) | 12.0658 | − | 6.96620i | 0.0443596 | − | 0.0256110i | ||||
\(273\) | 179.135 | + | 99.3784i | 0.656173 | + | 0.364023i | ||||
\(274\) | −92.8318 | − | 53.5965i | −0.338802 | − | 0.195607i | ||||
\(275\) | 223.111 | + | 128.813i | 0.811312 | + | 0.468411i | ||||
\(276\) | −135.612 | + | 25.5619i | −0.491347 | + | 0.0926157i | ||||
\(277\) | −41.6944 | − | 72.2168i | −0.150521 | − | 0.260710i | 0.780898 | − | 0.624659i | \(-0.214762\pi\) |
−0.931419 | + | 0.363948i | \(0.881429\pi\) | |||||||
\(278\) | 136.547 | 0.491177 | ||||||||
\(279\) | 284.245 | − | 9.72633i | 1.01880 | − | 0.0348614i | ||||
\(280\) | 227.374 | 0.812049 | ||||||||
\(281\) | 417.189 | − | 240.864i | 1.48466 | − | 0.857167i | 0.484809 | − | 0.874620i | \(-0.338889\pi\) |
0.999848 | + | 0.0174527i | \(0.00555565\pi\) | |||||||
\(282\) | 169.311 | + | 282.005i | 0.600393 | + | 1.00002i | ||||
\(283\) | −248.658 | − | 143.563i | −0.878651 | − | 0.507290i | −0.00843793 | − | 0.999964i | \(-0.502686\pi\) |
−0.870214 | + | 0.492675i | \(0.836019\pi\) | |||||||
\(284\) | −22.5625 | + | 39.0794i | −0.0794454 | + | 0.137603i | ||||
\(285\) | 204.202 | + | 340.119i | 0.716497 | + | 1.19340i | ||||
\(286\) | −61.0105 | + | 35.2244i | −0.213323 | + | 0.123162i | ||||
\(287\) | − | 658.035i | − | 2.29281i | ||||||
\(288\) | 50.8819 | − | 1.74109i | 0.176673 | − | 0.00604544i | ||||
\(289\) | 276.868 | 0.958021 | ||||||||
\(290\) | −40.3608 | + | 23.3023i | −0.139175 | + | 0.0803528i | ||||
\(291\) | −9.66343 | − | 564.978i | −0.0332077 | − | 1.94150i | ||||
\(292\) | 143.920 | − | 249.276i | 0.492875 | − | 0.853685i | ||||
\(293\) | 263.762 | + | 152.283i | 0.900213 | + | 0.519738i | 0.877269 | − | 0.479999i | \(-0.159363\pi\) |
0.0229434 | + | 0.999737i | \(0.492696\pi\) | |||||||
\(294\) | 125.967 | − | 227.063i | 0.428460 | − | 0.772324i | ||||
\(295\) | 86.1044 | − | 49.7124i | 0.291879 | − | 0.168517i | ||||
\(296\) | − | 34.9701i | − | 0.118142i | ||||||
\(297\) | 173.534 | − | 112.434i | 0.584288 | − | 0.378567i | ||||
\(298\) | 383.619i | 1.28731i | ||||||||
\(299\) | −95.5542 | − | 115.117i | −0.319579 | − | 0.385007i | ||||
\(300\) | 97.9164 | − | 176.500i | 0.326388 | − | 0.588333i | ||||
\(301\) | −70.1612 | + | 121.523i | −0.233094 | + | 0.403730i | ||||
\(302\) | 41.8277 | − | 72.4478i | 0.138502 | − | 0.239893i | ||||
\(303\) | −307.412 | + | 5.25800i | −1.01456 | + | 0.0173531i | ||||
\(304\) | −59.8199 | + | 34.5370i | −0.196776 | + | 0.113609i | ||||
\(305\) | −636.349 | −2.08639 | ||||||||
\(306\) | −39.1288 | − | 20.8404i | −0.127872 | − | 0.0681058i | ||||
\(307\) | 5.06144 | 0.0164868 | 0.00824339 | − | 0.999966i | \(-0.497376\pi\) | ||||
0.00824339 | + | 0.999966i | \(0.497376\pi\) | |||||||
\(308\) | 80.3951 | + | 139.248i | 0.261023 | + | 0.452105i | ||||
\(309\) | −147.632 | + | 88.6358i | −0.477774 | + | 0.286847i | ||||
\(310\) | 296.379 | + | 171.114i | 0.956060 | + | 0.551982i | ||||
\(311\) | 17.2716 | − | 29.9153i | 0.0555357 | − | 0.0961906i | −0.836921 | − | 0.547324i | \(-0.815647\pi\) |
0.892457 | + | 0.451133i | \(0.148980\pi\) | |||||||
\(312\) | 28.4105 | + | 47.3206i | 0.0910593 | + | 0.151669i | ||||
\(313\) | −196.003 | + | 113.162i | −0.626207 | + | 0.361541i | −0.779282 | − | 0.626674i | \(-0.784416\pi\) |
0.153075 | + | 0.988215i | \(0.451083\pi\) | |||||||
\(314\) | 374.018i | 1.19114i | ||||||||
\(315\) | −382.965 | − | 613.831i | −1.21576 | − | 1.94867i | ||||
\(316\) | − | 64.6677i | − | 0.204645i | ||||||
\(317\) | −97.7364 | − | 169.284i | −0.308317 | − | 0.534020i | 0.669678 | − | 0.742652i | \(-0.266432\pi\) |
−0.977994 | + | 0.208632i | \(0.933099\pi\) | |||||||
\(318\) | 0.723191 | + | 42.2818i | 0.00227418 | + | 0.132961i | ||||
\(319\) | −28.5416 | − | 16.4785i | −0.0894722 | − | 0.0516568i | ||||
\(320\) | 53.0540 | + | 30.6308i | 0.165794 | + | 0.0957211i | ||||
\(321\) | −108.076 | − | 59.9571i | −0.336685 | − | 0.186782i | ||||
\(322\) | −262.740 | + | 218.090i | −0.815961 | + | 0.677297i | ||||
\(323\) | 60.1480 | 0.186217 | ||||||||
\(324\) | −90.4007 | − | 134.431i | −0.279014 | − | 0.414911i | ||||
\(325\) | 218.819 | 0.673290 | ||||||||
\(326\) | 173.402 | + | 300.342i | 0.531909 | + | 0.921294i | ||||
\(327\) | 426.902 | + | 236.831i | 1.30551 | + | 0.724255i | ||||
\(328\) | 88.6475 | − | 153.542i | 0.270267 | − | 0.468116i | ||||
\(329\) | 704.841 | + | 406.940i | 2.14237 | + | 1.23690i | ||||
\(330\) | 248.772 | − | 4.25502i | 0.753856 | − | 0.0128940i | ||||
\(331\) | 268.758 | + | 465.503i | 0.811959 | + | 1.40635i | 0.911491 | + | 0.411319i | \(0.134932\pi\) |
−0.0995328 | + | 0.995034i | \(0.531735\pi\) | |||||||
\(332\) | 77.3862i | 0.233091i | ||||||||
\(333\) | −94.4073 | + | 58.9001i | −0.283505 | + | 0.176877i | ||||
\(334\) | −352.102 | −1.05420 | ||||||||
\(335\) | 354.515 | + | 614.038i | 1.05825 | + | 1.83295i | ||||
\(336\) | 108.003 | − | 64.8432i | 0.321438 | − | 0.192986i | ||||
\(337\) | −183.887 | − | 106.167i | −0.545658 | − | 0.315036i | 0.201711 | − | 0.979445i | \(-0.435350\pi\) |
−0.747369 | + | 0.664409i | \(0.768683\pi\) | |||||||
\(338\) | 89.5826 | − | 155.162i | 0.265037 | − | 0.459058i | ||||
\(339\) | −246.036 | + | 147.716i | −0.725771 | + | 0.435741i | ||||
\(340\) | −26.6725 | − | 46.1981i | −0.0784485 | − | 0.135877i | ||||
\(341\) | 242.011i | 0.709710i | ||||||||
\(342\) | 193.993 | + | 103.322i | 0.567230 | + | 0.302112i | ||||
\(343\) | − | 128.109i | − | 0.373496i | ||||||
\(344\) | −32.7420 | + | 18.9036i | −0.0951803 | + | 0.0549524i | ||||
\(345\) | 97.8726 | + | 519.237i | 0.283689 | + | 1.50503i | ||||
\(346\) | −94.7894 | + | 164.180i | −0.273958 | + | 0.474509i | ||||
\(347\) | −60.1946 | + | 104.260i | −0.173471 | + | 0.300461i | −0.939631 | − | 0.342189i | \(-0.888832\pi\) |
0.766160 | + | 0.642650i | \(0.222165\pi\) | |||||||
\(348\) | −12.5260 | + | 22.5789i | −0.0359944 | + | 0.0648819i | ||||
\(349\) | 292.697 | + | 506.967i | 0.838674 | + | 1.45263i | 0.891003 | + | 0.453997i | \(0.150002\pi\) |
−0.0523291 | + | 0.998630i | \(0.516664\pi\) | |||||||
\(350\) | − | 499.426i | − | 1.42693i | ||||||
\(351\) | 79.8976 | − | 156.401i | 0.227628 | − | 0.445586i | ||||
\(352\) | 43.3218i | 0.123073i | ||||||||
\(353\) | 151.198 | + | 261.882i | 0.428323 | + | 0.741876i | 0.996724 | − | 0.0808747i | \(-0.0257714\pi\) |
−0.568402 | + | 0.822751i | \(0.692438\pi\) | |||||||
\(354\) | 26.7226 | − | 48.1690i | 0.0754877 | − | 0.136071i | ||||
\(355\) | 149.629 | + | 86.3882i | 0.421490 | + | 0.243347i | ||||
\(356\) | −225.981 | − | 130.470i | −0.634777 | − | 0.366489i | ||||
\(357\) | −109.678 | + | 1.87595i | −0.307223 | + | 0.00525476i | ||||
\(358\) | −51.6100 | − | 89.3911i | −0.144162 | − | 0.249696i | ||||
\(359\) | 513.802i | 1.43120i | 0.698509 | + | 0.715602i | \(0.253847\pi\) | ||||
−0.698509 | + | 0.715602i | \(0.746153\pi\) | |||||||
\(360\) | −6.66635 | − | 194.819i | −0.0185176 | − | 0.541164i | ||||
\(361\) | 62.7986 | 0.173957 | ||||||||
\(362\) | 233.377 | − | 134.740i | 0.644689 | − | 0.372211i | ||||
\(363\) | −96.2825 | − | 160.368i | −0.265241 | − | 0.441786i | ||||
\(364\) | 118.273 | + | 68.2849i | 0.324926 | + | 0.187596i | ||||
\(365\) | −954.439 | − | 551.046i | −2.61490 | − | 1.50971i | ||||
\(366\) | −302.267 | + | 181.476i | −0.825867 | + | 0.495837i | ||||
\(367\) | −515.596 | + | 297.680i | −1.40489 | + | 0.811116i | −0.994890 | − | 0.100967i | \(-0.967806\pi\) |
−0.410005 | + | 0.912083i | \(0.634473\pi\) | |||||||
\(368\) | −90.6861 | + | 15.4927i | −0.246430 | + | 0.0420997i | ||||
\(369\) | −563.819 | + | 19.2929i | −1.52797 | + | 0.0522842i | ||||
\(370\) | −133.895 | −0.361879 | ||||||||
\(371\) | 52.3176 | + | 90.6167i | 0.141018 | + | 0.244250i | ||||
\(372\) | 189.580 | − | 3.24258i | 0.509622 | − | 0.00871662i | ||||
\(373\) | −161.998 | − | 93.5294i | −0.434310 | − | 0.250749i | 0.266871 | − | 0.963732i | \(-0.414010\pi\) |
−0.701181 | + | 0.712983i | \(0.747344\pi\) | |||||||
\(374\) | 18.8618 | − | 32.6696i | 0.0504326 | − | 0.0873518i | ||||
\(375\) | −173.571 | − | 96.2915i | −0.462856 | − | 0.256777i | ||||
\(376\) | 109.642 | + | 189.906i | 0.291602 | + | 0.505069i | ||||
\(377\) | −27.9926 | −0.0742510 | ||||||||
\(378\) | −356.964 | − | 182.356i | −0.944348 | − | 0.482422i | ||||
\(379\) | − | 511.096i | − | 1.34854i | −0.738486 | − | 0.674269i | \(-0.764459\pi\) | ||
0.738486 | − | 0.674269i | \(-0.235541\pi\) | |||||||
\(380\) | 132.237 | + | 229.041i | 0.347992 | + | 0.602739i | ||||
\(381\) | −170.439 | + | 307.226i | −0.447346 | + | 0.806366i | ||||
\(382\) | 214.141 | + | 123.635i | 0.560580 | + | 0.323651i | ||||
\(383\) | 321.814 | + | 185.800i | 0.840246 | + | 0.485116i | 0.857348 | − | 0.514737i | \(-0.172111\pi\) |
−0.0171018 | + | 0.999854i | \(0.505444\pi\) | |||||||
\(384\) | 33.9362 | − | 0.580447i | 0.0883754 | − | 0.00151158i | ||||
\(385\) | 533.160 | − | 307.820i | 1.38483 | − | 0.799533i | ||||
\(386\) | −355.506 | −0.921001 | ||||||||
\(387\) | 106.181 | + | 56.5528i | 0.274368 | + | 0.146131i | ||||
\(388\) | − | 376.707i | − | 0.970894i | ||||||
\(389\) | −537.537 | + | 310.347i | −1.38184 | + | 0.797807i | −0.992378 | − | 0.123234i | \(-0.960673\pi\) |
−0.389465 | + | 0.921041i | \(0.627340\pi\) | |||||||
\(390\) | 181.183 | − | 108.779i | 0.464573 | − | 0.278922i | ||||
\(391\) | 75.1330 | + | 27.8004i | 0.192156 | + | 0.0711008i | ||||
\(392\) | 86.5547 | − | 149.917i | 0.220803 | − | 0.382442i | ||||
\(393\) | −118.918 | − | 198.071i | −0.302591 | − | 0.503996i | ||||
\(394\) | 194.510 | + | 336.901i | 0.493680 | + | 0.855079i | ||||
\(395\) | −247.603 | −0.626842 | ||||||||
\(396\) | 116.954 | − | 72.9669i | 0.295338 | − | 0.184260i | ||||
\(397\) | 76.3556 | 0.192332 | 0.0961658 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961658 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(398\) | −100.089 | + | 57.7863i | −0.251480 | + | 0.145192i | ||||
\(399\) | 543.764 | − | 9.30058i | 1.36282 | − | 0.0233097i | ||||
\(400\) | 67.2804 | − | 116.533i | 0.168201 | − | 0.291333i | ||||
\(401\) | −510.500 | − | 294.737i | −1.27307 | − | 0.735005i | −0.297503 | − | 0.954721i | \(-0.596154\pi\) |
−0.975564 | + | 0.219716i | \(0.929487\pi\) | |||||||
\(402\) | 343.509 | + | 190.568i | 0.854499 | + | 0.474049i | ||||
\(403\) | 102.778 | + | 178.017i | 0.255033 | + | 0.441730i | ||||
\(404\) | −204.971 | −0.507355 | ||||||||
\(405\) | −514.716 | + | 346.130i | −1.27090 | + | 0.854642i | ||||
\(406\) | 63.8894i | 0.157363i | ||||||||
\(407\) | −47.3428 | − | 82.0001i | −0.116321 | − | 0.201475i | ||||
\(408\) | −25.8444 | − | 14.3377i | −0.0633442 | − | 0.0351413i | ||||
\(409\) | 21.6653 | − | 37.5254i | 0.0529714 | − | 0.0917492i | −0.838324 | − | 0.545173i | \(-0.816464\pi\) |
0.891295 | + | 0.453423i | \(0.149797\pi\) | |||||||
\(410\) | −587.888 | − | 339.417i | −1.43387 | − | 0.827847i | ||||
\(411\) | 3.88874 | + | 227.357i | 0.00946165 | + | 0.553181i | ||||
\(412\) | −99.4175 | + | 57.3987i | −0.241305 | + | 0.139317i | ||||
\(413\) | − | 136.300i | − | 0.330023i | ||||||
\(414\) | 194.567 | + | 218.727i | 0.469970 | + | 0.528326i | ||||
\(415\) | 296.300 | 0.713975 | ||||||||
\(416\) | 18.3981 | + | 31.8664i | 0.0442261 | + | 0.0766019i | ||||
\(417\) | −149.099 | − | 248.340i | −0.357552 | − | 0.595539i | ||||
\(418\) | −93.5129 | + | 161.969i | −0.223715 | + | 0.387486i | ||||
\(419\) | 222.516 | + | 128.470i | 0.531065 | + | 0.306611i | 0.741450 | − | 0.671008i | \(-0.234138\pi\) |
−0.210385 | + | 0.977619i | \(0.567472\pi\) | |||||||
\(420\) | −248.275 | − | 413.527i | −0.591130 | − | 0.984588i | ||||
\(421\) | 474.348 | − | 273.865i | 1.12672 | − | 0.650510i | 0.183609 | − | 0.982999i | \(-0.441222\pi\) |
0.943107 | + | 0.332489i | \(0.107889\pi\) | |||||||
\(422\) | −352.128 | −0.834427 | ||||||||
\(423\) | 328.010 | − | 615.855i | 0.775438 | − | 1.45592i | ||||
\(424\) | 28.1920i | 0.0664905i | ||||||||
\(425\) | −101.474 | + | 58.5861i | −0.238763 | + | 0.137850i | ||||
\(426\) | 95.7105 | − | 1.63704i | 0.224673 | − | 0.00384282i | ||||
\(427\) | −436.180 | + | 755.485i | −1.02150 | + | 1.76929i | ||||
\(428\) | −71.3566 | − | 41.1977i | −0.166721 | − | 0.0962564i | ||||
\(429\) | 130.682 | + | 72.4980i | 0.304619 | + | 0.168993i | ||||
\(430\) | 72.3790 | + | 125.364i | 0.168323 | + | 0.291544i | ||||
\(431\) | 38.3961i | 0.0890860i | 0.999007 | + | 0.0445430i | \(0.0141832\pi\) | ||||
−0.999007 | + | 0.0445430i | \(0.985817\pi\) | |||||||
\(432\) | −58.7256 | − | 90.6383i | −0.135939 | − | 0.209811i | ||||
\(433\) | 290.174i | 0.670147i | 0.942192 | + | 0.335074i | \(0.108761\pi\) | ||||
−0.942192 | + | 0.335074i | \(0.891239\pi\) | |||||||
\(434\) | 406.300 | − | 234.577i | 0.936175 | − | 0.540501i | ||||
\(435\) | 86.4510 | + | 47.9603i | 0.198738 | + | 0.110253i | ||||
\(436\) | 281.859 | + | 162.732i | 0.646466 | + | 0.373237i | ||||
\(437\) | −372.494 | − | 137.829i | −0.852389 | − | 0.315397i | ||||
\(438\) | −610.510 | + | 10.4422i | −1.39386 | + | 0.0238407i | ||||
\(439\) | −280.532 | − | 485.895i | −0.639025 | − | 1.10682i | −0.985647 | − | 0.168819i | \(-0.946005\pi\) |
0.346622 | − | 0.938005i | \(-0.387329\pi\) | |||||||
\(440\) | 165.873 | 0.376983 | ||||||||
\(441\) | −550.509 | + | 18.8374i | −1.24832 | + | 0.0427152i | ||||
\(442\) | − | 32.0412i | − | 0.0724913i | ||||||
\(443\) | −367.576 | − | 636.661i | −0.829744 | − | 1.43716i | −0.898239 | − | 0.439507i | \(-0.855153\pi\) |
0.0684957 | − | 0.997651i | \(-0.478180\pi\) | |||||||
\(444\) | −63.6005 | + | 38.1847i | −0.143244 | + | 0.0860015i | ||||
\(445\) | −499.549 | + | 865.244i | −1.12258 | + | 1.94437i | ||||
\(446\) | 28.3511 | − | 49.1055i | 0.0635674 | − | 0.110102i | ||||
\(447\) | 697.691 | − | 418.882i | 1.56083 | − | 0.937096i | ||||
\(448\) | 72.7308 | − | 41.9911i | 0.162345 | − | 0.0937302i | ||||
\(449\) | 198.440 | 0.441960 | 0.220980 | − | 0.975278i | \(-0.429074\pi\) | ||||
0.220980 | + | 0.975278i | \(0.429074\pi\) | |||||||
\(450\) | −427.919 | + | 14.6426i | −0.950932 | + | 0.0325391i | ||||
\(451\) | − | 480.046i | − | 1.06440i | ||||||
\(452\) | −165.684 | + | 95.6580i | −0.366559 | + | 0.211633i | ||||
\(453\) | −177.434 | + | 3.03485i | −0.391687 | + | 0.00669944i | ||||
\(454\) | 349.414 | + | 201.735i | 0.769635 | + | 0.444349i | ||||
\(455\) | 261.452 | − | 452.849i | 0.574620 | − | 0.995272i | ||||
\(456\) | 128.131 | + | 71.0832i | 0.280990 | + | 0.155884i | ||||
\(457\) | −179.844 | + | 103.833i | −0.393531 | + | 0.227205i | −0.683689 | − | 0.729774i | \(-0.739626\pi\) |
0.290158 | + | 0.956979i | \(0.406292\pi\) | |||||||
\(458\) | 267.495i | 0.584050i | ||||||||
\(459\) | 4.82301 | + | 93.9200i | 0.0105076 | + | 0.204619i | ||||
\(460\) | 59.3190 | + | 347.223i | 0.128954 | + | 0.754833i | ||||
\(461\) | 115.273 | + | 199.658i | 0.250049 | + | 0.433098i | 0.963539 | − | 0.267567i | \(-0.0862198\pi\) |
−0.713490 | + | 0.700666i | \(0.752886\pi\) | |||||||
\(462\) | 165.467 | − | 298.264i | 0.358154 | − | 0.645592i | ||||
\(463\) | 19.9279 | − | 34.5162i | 0.0430408 | − | 0.0745489i | −0.843702 | − | 0.536811i | \(-0.819629\pi\) |
0.886743 | + | 0.462262i | \(0.152962\pi\) | |||||||
\(464\) | −8.60690 | + | 14.9076i | −0.0185493 | + | 0.0321284i | ||||
\(465\) | −12.4153 | − | 725.870i | −0.0266997 | − | 1.56101i | ||||
\(466\) | 117.641 | + | 203.760i | 0.252448 | + | 0.437254i | ||||
\(467\) | 40.0347i | 0.0857273i | 0.999081 | + | 0.0428637i | \(0.0136481\pi\) | ||||
−0.999081 | + | 0.0428637i | \(0.986352\pi\) | |||||||
\(468\) | 55.0404 | − | 103.341i | 0.117608 | − | 0.220814i | ||||
\(469\) | 971.996 | 2.07249 | ||||||||
\(470\) | 727.121 | − | 419.803i | 1.54706 | − | 0.893198i | ||||
\(471\) | 680.230 | − | 408.399i | 1.44423 | − | 0.867089i | ||||
\(472\) | 18.3617 | − | 31.8033i | 0.0389018 | − | 0.0673799i | ||||
\(473\) | −51.1837 | + | 88.6527i | −0.108211 | + | 0.187426i | ||||
\(474\) | −117.612 | + | 70.6121i | −0.248126 | + | 0.148971i | ||||
\(475\) | 503.088 | − | 290.458i | 1.05913 | − | 0.611490i | ||||
\(476\) | −73.1297 | −0.153634 | ||||||||
\(477\) | 76.1086 | − | 47.4837i | 0.159557 | − | 0.0995465i | ||||
\(478\) | −617.619 | −1.29209 | ||||||||
\(479\) | −414.763 | + | 239.463i | −0.865893 | + | 0.499924i | −0.865981 | − | 0.500076i | \(-0.833305\pi\) |
8.80271e−5 | 1.00000i | \(0.499972\pi\) | ||||||||
\(480\) | −2.22244 | − | 129.936i | −0.00463008 | − | 0.270701i | ||||
\(481\) | −69.6482 | − | 40.2114i | −0.144799 | − | 0.0835996i | ||||
\(482\) | 180.052 | + | 103.953i | 0.373551 | + | 0.215670i | ||||
\(483\) | 683.533 | + | 239.710i | 1.41518 | + | 0.496294i | ||||
\(484\) | −62.3506 | − | 107.994i | −0.128824 | − | 0.223129i | ||||
\(485\) | −1442.35 | −2.97392 | ||||||||
\(486\) | −145.781 | + | 311.201i | −0.299960 | + | 0.640331i | ||||
\(487\) | −350.275 | −0.719251 | −0.359626 | − | 0.933097i | \(-0.617096\pi\) | ||||
−0.359626 | + | 0.933097i | \(0.617096\pi\) | |||||||
\(488\) | −203.551 | + | 117.520i | −0.417113 | + | 0.240820i | ||||
\(489\) | 356.893 | − | 643.319i | 0.729842 | − | 1.31558i | ||||
\(490\) | −574.010 | − | 331.405i | −1.17145 | − | 0.676336i | ||||
\(491\) | −438.771 | + | 759.975i | −0.893628 | + | 1.54781i | −0.0581352 | + | 0.998309i | \(0.518515\pi\) |
−0.835493 | + | 0.549501i | \(0.814818\pi\) | |||||||
\(492\) | −376.045 | + | 6.43190i | −0.764318 | + | 0.0130730i | ||||
\(493\) | 12.9812 | − | 7.49467i | 0.0263309 | − | 0.0152022i | ||||
\(494\) | 158.854i | 0.321566i | ||||||||
\(495\) | −279.379 | − | 447.799i | −0.564402 | − | 0.904644i | ||||
\(496\) | 126.405 | 0.254848 | ||||||||
\(497\) | 205.123 | − | 118.428i | 0.412723 | − | 0.238286i | ||||
\(498\) | 140.743 | − | 84.4998i | 0.282617 | − | 0.169678i | ||||
\(499\) | 140.869 | − | 243.993i | 0.282303 | − | 0.488964i | −0.689648 | − | 0.724145i | \(-0.742235\pi\) |
0.971952 | + | 0.235181i | \(0.0755682\pi\) | |||||||
\(500\) | −114.599 | − | 66.1638i | −0.229198 | − | 0.132328i | ||||
\(501\) | 384.468 | + | 640.371i | 0.767401 | + | 1.27819i | ||||
\(502\) | 307.173 | − | 177.346i | 0.611898 | − | 0.353280i | ||||
\(503\) | − | 939.291i | − | 1.86738i | −0.358084 | − | 0.933689i | \(-0.616570\pi\) | ||
0.358084 | − | 0.933689i | \(-0.383430\pi\) | |||||||
\(504\) | −235.862 | − | 125.622i | −0.467980 | − | 0.249251i | ||||
\(505\) | 784.803i | 1.55407i | ||||||||
\(506\) | −191.672 | + | 159.100i | −0.378799 | + | 0.314426i | ||||
\(507\) | −380.011 | + | 6.49974i | −0.749529 | + | 0.0128200i | ||||
\(508\) | −117.112 | + | 202.844i | −0.230535 | + | 0.399299i | ||||
\(509\) | −128.475 | + | 222.525i | −0.252406 | + | 0.437181i | −0.964188 | − | 0.265220i | \(-0.914555\pi\) |
0.711781 | + | 0.702401i | \(0.247889\pi\) | |||||||
\(510\) | −54.8967 | + | 98.9543i | −0.107641 | + | 0.194028i | ||||
\(511\) | −1308.42 | + | 755.418i | −2.56051 | + | 1.47831i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −23.9115 | − | 465.636i | −0.0466111 | − | 0.907673i | ||||
\(514\) | 24.1202 | 0.0469264 | ||||||||
\(515\) | 219.771 | + | 380.654i | 0.426739 | + | 0.739134i | ||||
\(516\) | 70.1319 | + | 38.9069i | 0.135915 | + | 0.0754010i | ||||
\(517\) | 514.192 | + | 296.869i | 0.994569 | + | 0.574215i | ||||
\(518\) | −91.7772 | + | 158.963i | −0.177176 | + | 0.306878i | ||||
\(519\) | 402.098 | − | 6.87752i | 0.774756 | − | 0.0132515i | ||||
\(520\) | 122.011 | − | 70.4433i | 0.234637 | − | 0.135468i | ||||
\(521\) | 937.471i | 1.79937i | 0.436542 | + | 0.899684i | \(0.356203\pi\) | ||||
−0.436542 | + | 0.899684i | \(0.643797\pi\) | |||||||
\(522\) | 54.7419 | − | 1.87317i | 0.104870 | − | 0.00358844i | ||||
\(523\) | − | 850.415i | − | 1.62603i | −0.582241 | − | 0.813016i | \(-0.697824\pi\) | ||
0.582241 | − | 0.813016i | \(-0.302176\pi\) | |||||||
\(524\) | −77.0090 | − | 133.384i | −0.146964 | − | 0.254549i | ||||
\(525\) | −908.310 | + | 545.334i | −1.73012 | + | 1.03873i | ||||
\(526\) | −209.082 | − | 120.713i | −0.397493 | − | 0.229493i | ||||
\(527\) | −95.3236 | − | 55.0351i | −0.180880 | − | 0.104431i | ||||
\(528\) | 78.7898 | − | 47.3041i | 0.149223 | − | 0.0895911i | ||||
\(529\) | −401.591 | − | 344.334i | −0.759151 | − | 0.650914i | ||||
\(530\) | 107.943 | 0.203665 | ||||||||
\(531\) | −116.785 | + | 3.99615i | −0.219933 | + | 0.00752571i | ||||
\(532\) | 362.562 | 0.681508 | ||||||||
\(533\) | −203.868 | − | 353.109i | −0.382491 | − | 0.662494i | ||||
\(534\) | 9.46636 | + | 553.456i | 0.0177273 | + | 1.03643i | ||||
\(535\) | −157.740 | + | 273.213i | −0.294841 | + | 0.510679i | ||||
\(536\) | 226.800 | + | 130.943i | 0.423134 | + | 0.244296i | ||||
\(537\) | −106.222 | + | 191.472i | −0.197807 | + | 0.356558i | ||||
\(538\) | −179.526 | − | 310.949i | −0.333692 | − | 0.577972i | ||||
\(539\) | − | 468.714i | − | 0.869599i | ||||||
\(540\) | −347.040 | + | 224.851i | −0.642666 | + | 0.416391i | ||||
\(541\) | −236.028 | −0.436282 | −0.218141 | − | 0.975917i | \(-0.569999\pi\) | ||||
−0.218141 | + | 0.975917i | \(0.569999\pi\) | |||||||
\(542\) | −245.804 | − | 425.746i | −0.453514 | − | 0.785508i | ||||
\(543\) | −499.884 | − | 277.319i | −0.920596 | − | 0.510717i | ||||
\(544\) | −17.0636 | − | 9.85170i | −0.0313670 | − | 0.0181097i | ||||
\(545\) | 623.074 | − | 1079.20i | 1.14325 | − | 1.98017i | ||||
\(546\) | −4.95447 | − | 289.666i | −0.00907412 | − | 0.530524i | ||||
\(547\) | −230.034 | − | 398.431i | −0.420538 | − | 0.728393i | 0.575454 | − | 0.817834i | \(-0.304825\pi\) |
−0.995992 | + | 0.0894410i | \(0.971492\pi\) | |||||||
\(548\) | 151.594i | 0.276631i | ||||||||
\(549\) | 660.105 | + | 351.578i | 1.20238 | + | 0.640398i | ||||
\(550\) | − | 364.339i | − | 0.662434i | ||||||
\(551\) | −64.3579 | + | 37.1571i | −0.116802 | + | 0.0674357i | ||||
\(552\) | 127.199 | + | 148.015i | 0.230433 | + | 0.268143i | ||||
\(553\) | −169.717 | + | 293.958i | −0.306902 | + | 0.531570i | ||||
\(554\) | −58.9648 | + | 102.130i | −0.106435 | + | 0.184350i | ||||
\(555\) | 146.203 | + | 243.516i | 0.263429 | + | 0.438768i | ||||
\(556\) | −96.5535 | − | 167.236i | −0.173657 | − | 0.300783i | ||||
\(557\) | − | 897.717i | − | 1.61170i | −0.592120 | − | 0.805850i | \(-0.701709\pi\) | ||
0.592120 | − | 0.805850i | \(-0.298291\pi\) | |||||||
\(558\) | −212.904 | − | 341.249i | −0.381548 | − | 0.611558i | ||||
\(559\) | 86.9475i | 0.155541i | ||||||||
\(560\) | −160.777 | − | 278.475i | −0.287103 | − | 0.497276i | ||||
\(561\) | −80.0121 | + | 1.36853i | −0.142624 | + | 0.00243945i | ||||
\(562\) | −589.994 | − | 340.633i | −1.04981 | − | 0.606109i | ||||
\(563\) | 555.151 | + | 320.517i | 0.986059 | + | 0.569302i | 0.904094 | − | 0.427334i | \(-0.140547\pi\) |
0.0819652 | + | 0.996635i | \(0.473880\pi\) | |||||||
\(564\) | 225.663 | − | 406.770i | 0.400112 | − | 0.721224i | ||||
\(565\) | 366.259 | + | 634.380i | 0.648247 | + | 1.12280i | ||||
\(566\) | 406.057i | 0.717416i | ||||||||
\(567\) | 58.1248 | + | 848.331i | 0.102513 | + | 1.49618i | ||||
\(568\) | 63.8164 | 0.112353 | ||||||||
\(569\) | −194.287 | + | 112.171i | −0.341453 | + | 0.197138i | −0.660914 | − | 0.750461i | \(-0.729831\pi\) |
0.319461 | + | 0.947599i | \(0.396498\pi\) | |||||||
\(570\) | 272.167 | − | 490.595i | 0.477485 | − | 0.860694i | ||||
\(571\) | 5.21105 | + | 3.00860i | 0.00912619 | + | 0.00526901i | 0.504556 | − | 0.863379i | \(-0.331656\pi\) |
−0.495430 | + | 0.868648i | \(0.664989\pi\) | |||||||
\(572\) | 86.2819 | + | 49.8149i | 0.150842 | + | 0.0870889i | ||||
\(573\) | −8.97042 | − | 524.461i | −0.0156552 | − | 0.915289i | ||||
\(574\) | −805.925 | + | 465.301i | −1.40405 | + | 0.810629i | ||||
\(575\) | 762.675 | − | 130.294i | 1.32639 | − | 0.226598i | ||||
\(576\) | −38.1113 | − | 61.0862i | −0.0661655 | − | 0.106052i | ||||
\(577\) | 698.191 | 1.21004 | 0.605018 | − | 0.796211i | \(-0.293166\pi\) | ||||
0.605018 | + | 0.796211i | \(0.293166\pi\) | |||||||
\(578\) | −195.775 | − | 339.093i | −0.338711 | − | 0.586666i | ||||
\(579\) | 388.185 | + | 646.563i | 0.670441 | + | 1.11669i | ||||
\(580\) | 57.0788 | + | 32.9545i | 0.0984117 | + | 0.0568180i | ||||
\(581\) | 203.096 | − | 351.773i | 0.349563 | − | 0.605460i | ||||
\(582\) | −685.121 | + | 411.335i | −1.17718 | + | 0.706761i | ||||
\(583\) | 38.1665 | + | 66.1063i | 0.0654656 | + | 0.113390i | ||||
\(584\) | −407.066 | −0.697031 | ||||||||
\(585\) | −395.676 | − | 210.741i | −0.676370 | − | 0.360241i | ||||
\(586\) | − | 430.722i | − | 0.735020i | ||||||
\(587\) | 312.223 | + | 540.787i | 0.531897 | + | 0.921272i | 0.999307 | + | 0.0372316i | \(0.0118539\pi\) |
−0.467410 | + | 0.884041i | \(0.654813\pi\) | |||||||
\(588\) | −367.167 | + | 6.28005i | −0.624434 | + | 0.0106804i | ||||
\(589\) | 472.595 | + | 272.853i | 0.802369 | + | 0.463248i | ||||
\(590\) | −121.770 | − | 70.3039i | −0.206390 | − | 0.119159i | ||||
\(591\) | 400.336 | − | 721.627i | 0.677387 | − | 1.22103i | ||||
\(592\) | −42.8295 | + | 24.7276i | −0.0723471 | + | 0.0417696i | ||||
\(593\) | −739.749 | −1.24747 | −0.623734 | − | 0.781636i | \(-0.714385\pi\) | ||||
−0.623734 | + | 0.781636i | \(0.714385\pi\) | |||||||
\(594\) | −260.410 | − | 133.031i | −0.438401 | − | 0.223958i | ||||
\(595\) | 280.002i | 0.470592i | ||||||||
\(596\) | 469.835 | − | 271.259i | 0.788314 | − | 0.455133i | ||||
\(597\) | 214.386 | + | 118.934i | 0.359105 | + | 0.199220i | ||||
\(598\) | −73.4221 | + | 198.430i | −0.122779 | + | 0.331822i | ||||
\(599\) | −294.003 | + | 509.228i | −0.490822 | + | 0.850130i | −0.999944 | − | 0.0105650i | \(-0.996637\pi\) |
0.509122 | + | 0.860695i | \(0.329970\pi\) | |||||||
\(600\) | −285.405 | + | 4.88159i | −0.475674 | + | 0.00813598i | ||||
\(601\) | −155.793 | − | 269.842i | −0.259224 | − | 0.448988i | 0.706811 | − | 0.707403i | \(-0.250133\pi\) |
−0.966034 | + | 0.258414i | \(0.916800\pi\) | |||||||
\(602\) | 198.446 | 0.329644 | ||||||||
\(603\) | −28.4978 | − | 832.828i | −0.0472601 | − | 1.38114i | ||||
\(604\) | −118.307 | −0.195872 | ||||||||
\(605\) | −413.494 | + | 238.731i | −0.683461 | + | 0.394596i | ||||
\(606\) | 223.813 | + | 372.783i | 0.369328 | + | 0.615154i | ||||
\(607\) | 129.619 | − | 224.507i | 0.213541 | − | 0.369863i | −0.739280 | − | 0.673399i | \(-0.764834\pi\) |
0.952820 | + | 0.303536i | \(0.0981671\pi\) | |||||||
\(608\) | 84.5981 | + | 48.8427i | 0.139142 | + | 0.0803334i | ||||
\(609\) | 116.196 | − | 69.7623i | 0.190799 | − | 0.114552i | ||||
\(610\) | 449.967 | + | 779.365i | 0.737650 | + | 1.27765i | ||||
\(611\) | 504.301 | 0.825371 | ||||||||
\(612\) | 2.14408 | + | 62.6592i | 0.00350340 | + | 0.102384i | ||||
\(613\) | 630.497i | 1.02854i | 0.857628 | + | 0.514271i | \(0.171938\pi\) | ||||
−0.857628 | + | 0.514271i | \(0.828062\pi\) | |||||||
\(614\) | −3.57898 | − | 6.19897i | −0.00582895 | − | 0.0100960i | ||||
\(615\) | 24.6267 | + | 1439.82i | 0.0400435 | + | 2.34116i | ||||
\(616\) | 113.696 | − | 196.927i | 0.184571 | − | 0.319686i | ||||
\(617\) | 439.884 | + | 253.967i | 0.712940 | + | 0.411616i | 0.812149 | − | 0.583451i | \(-0.198298\pi\) |
−0.0992086 | + | 0.995067i | \(0.531631\pi\) | |||||||
\(618\) | 212.948 | + | 118.137i | 0.344576 | + | 0.191160i | ||||
\(619\) | 193.814 | − | 111.898i | 0.313108 | − | 0.180773i | −0.335208 | − | 0.942144i | \(-0.608807\pi\) |
0.648316 | + | 0.761371i | \(0.275473\pi\) | |||||||
\(620\) | − | 483.984i | − | 0.780620i | ||||||
\(621\) | 185.348 | − | 592.695i | 0.298468 | − | 0.954420i | ||||
\(622\) | −48.8514 | −0.0785393 | ||||||||
\(623\) | 684.823 | + | 1186.15i | 1.09923 | + | 1.90393i | ||||
\(624\) | 37.8664 | − | 68.2564i | 0.0606834 | − | 0.109385i | ||||
\(625\) | 167.171 | − | 289.549i | 0.267474 | − | 0.463279i | ||||
\(626\) | 277.190 | + | 160.036i | 0.442795 | + | 0.255648i | ||||
\(627\) | 396.684 | − | 6.78491i | 0.632669 | − | 0.0108212i | ||||
\(628\) | 458.077 | − | 264.471i | 0.729422 | − | 0.421132i | ||||
\(629\) | 43.0644 | 0.0684649 | ||||||||
\(630\) | −480.989 | + | 903.078i | −0.763474 | + | 1.43346i | ||||
\(631\) | 220.250i | 0.349048i | 0.984653 | + | 0.174524i | \(0.0558387\pi\) | ||||
−0.984653 | + | 0.174524i | \(0.944161\pi\) | |||||||
\(632\) | −79.2014 | + | 45.7270i | −0.125319 | + | 0.0723528i | ||||
\(633\) | 384.497 | + | 640.419i | 0.607420 | + | 1.01172i | ||||
\(634\) | −138.220 | + | 239.404i | −0.218013 | + | 0.377609i | ||||
\(635\) | 776.658 | + | 448.404i | 1.22308 | + | 0.706147i | ||||
\(636\) | 51.2730 | − | 30.7834i | 0.0806179 | − | 0.0484016i | ||||
\(637\) | −199.055 | − | 344.773i | −0.312488 | − | 0.541245i | ||||
\(638\) | 46.6083i | 0.0730538i | ||||||||
\(639\) | −107.486 | − | 172.282i | −0.168209 | − | 0.269612i | ||||
\(640\) | − | 86.6368i | − | 0.135370i | ||||||
\(641\) | 88.5671 | − | 51.1342i | 0.138170 | − | 0.0797726i | −0.429321 | − | 0.903152i | \(-0.641247\pi\) |
0.567492 | + | 0.823379i | \(0.307914\pi\) | |||||||
\(642\) | 2.98914 | + | 174.762i | 0.00465598 | + | 0.272214i | ||||
\(643\) | −402.394 | − | 232.322i | −0.625806 | − | 0.361310i | 0.153320 | − | 0.988177i | \(-0.451004\pi\) |
−0.779126 | + | 0.626867i | \(0.784337\pi\) | |||||||
\(644\) | 452.889 | + | 167.576i | 0.703244 | + | 0.260212i | ||||
\(645\) | 148.969 | − | 268.524i | 0.230959 | − | 0.416317i | ||||
\(646\) | −42.5310 | − | 73.6659i | −0.0658375 | − | 0.114034i | ||||
\(647\) | −579.636 | −0.895883 | −0.447941 | − | 0.894063i | \(-0.647843\pi\) | ||||
−0.447941 | + | 0.894063i | \(0.647843\pi\) | |||||||
\(648\) | −100.721 | + | 205.775i | −0.155433 | + | 0.317554i | ||||
\(649\) | − | 99.4326i | − | 0.153209i | ||||||
\(650\) | −154.729 | − | 267.998i | −0.238044 | − | 0.412304i | ||||
\(651\) | −870.277 | − | 482.801i | −1.33683 | − | 0.741631i | ||||
\(652\) | 245.228 | − | 424.748i | 0.376117 | − | 0.651453i | ||||
\(653\) | −354.331 | + | 613.720i | −0.542621 | + | 0.939846i | 0.456132 | + | 0.889912i | \(0.349235\pi\) |
−0.998753 | + | 0.0499342i | \(0.984099\pi\) | |||||||
\(654\) | −11.8071 | − | 690.310i | −0.0180537 | − | 1.05552i | ||||
\(655\) | −510.705 | + | 294.856i | −0.779702 | + | 0.450161i | ||||
\(656\) | −250.733 | −0.382215 | ||||||||
\(657\) | 685.621 | + | 1098.94i | 1.04356 | + | 1.67266i | ||||
\(658\) | − | 1151.00i | − | 1.74924i | ||||||
\(659\) | 615.794 | − | 355.529i | 0.934437 | − | 0.539498i | 0.0462250 | − | 0.998931i | \(-0.485281\pi\) |
0.888212 | + | 0.459433i | \(0.151948\pi\) | |||||||
\(660\) | −181.120 | − | 301.674i | −0.274424 | − | 0.457082i | ||||
\(661\) | 617.516 | + | 356.523i | 0.934214 | + | 0.539369i | 0.888142 | − | 0.459569i | \(-0.151996\pi\) |
0.0460723 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(662\) | 380.082 | − | 658.321i | 0.574141 | − | 0.994442i | ||||
\(663\) | −58.2736 | + | 34.9865i | −0.0878938 | + | 0.0527699i | ||||
\(664\) | 94.7784 | − | 54.7203i | 0.142739 | − | 0.0824101i | ||||
\(665\) | − | 1388.19i | − | 2.08751i | ||||||
\(666\) | 138.894 | + | 73.9762i | 0.208549 | + | 0.111075i | ||||
\(667\) | −97.5658 | + | 16.6680i | −0.146276 | + | 0.0249895i | ||||
\(668\) | 248.974 | + | 431.235i | 0.372715 | + | 0.645561i | ||||
\(669\) | −120.266 | + | 2.05704i | −0.179770 | + | 0.00307479i | ||||
\(670\) | 501.360 | − | 868.380i | 0.748298 | − | 1.29609i | ||||
\(671\) | −318.200 | + | 551.138i | −0.474217 | + | 0.821368i | ||||
\(672\) | −155.786 | − | 86.4251i | −0.231824 | − | 0.128609i | ||||
\(673\) | −356.416 | − | 617.331i | −0.529593 | − | 0.917282i | −0.999404 | − | 0.0345154i | \(-0.989011\pi\) |
0.469811 | − | 0.882767i | \(-0.344322\pi\) | |||||||
\(674\) | 300.286i | 0.445528i | ||||||||
\(675\) | 493.885 | + | 762.272i | 0.731682 | + | 1.12929i | ||||
\(676\) | −253.378 | −0.374819 | ||||||||
\(677\) | −332.520 | + | 191.981i | −0.491167 | + | 0.283575i | −0.725058 | − | 0.688687i | \(-0.758187\pi\) |
0.233892 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(678\) | 354.889 | + | 196.881i | 0.523435 | + | 0.290385i | ||||
\(679\) | −988.647 | + | 1712.39i | −1.45603 | + | 2.52192i | ||||
\(680\) | −37.7206 | + | 65.3340i | −0.0554715 | + | 0.0960795i | ||||
\(681\) | −14.6370 | − | 855.762i | −0.0214934 | − | 1.25663i | ||||
\(682\) | 296.402 | − | 171.128i | 0.434607 | − | 0.250920i | ||||
\(683\) | 113.984 | 0.166887 | 0.0834437 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834437 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(684\) | −10.6299 | − | 310.651i | −0.0155408 | − | 0.454169i | ||||
\(685\) | 580.428 | 0.847341 | ||||||||
\(686\) | −156.901 | + | 90.5868i | −0.228719 | + | 0.132051i | ||||
\(687\) | 486.495 | − | 292.084i | 0.708145 | − | 0.425158i | ||||
\(688\) | 46.3042 | + | 26.7337i | 0.0673026 | + | 0.0388572i | ||||
\(689\) | 56.1485 | + | 32.4173i | 0.0814927 | + | 0.0470498i | ||||
\(690\) | 566.726 | − | 487.025i | 0.821342 | − | 0.705833i | ||||
\(691\) | −99.1654 | − | 171.759i | −0.143510 | − | 0.248567i | 0.785306 | − | 0.619108i | \(-0.212506\pi\) |
−0.928816 | + | 0.370541i | \(0.879172\pi\) | |||||||
\(692\) | 268.105 | 0.387435 | ||||||||
\(693\) | −723.132 | + | 24.7443i | −1.04348 | + | 0.0357060i | ||||
\(694\) | 170.256 | 0.245326 | ||||||||
\(695\) | −640.319 | + | 369.688i | −0.921322 | + | 0.531925i | ||||
\(696\) | 36.5106 | − | 0.624481i | 0.0524578 | − | 0.000897242i | ||||
\(697\) | 189.081 | + | 109.166i | 0.271279 | + | 0.156623i | ||||
\(698\) | 413.937 | − | 716.959i | 0.593032 | − | 1.02716i | ||||
\(699\) | 242.126 | − | 436.445i | 0.346389 | − | 0.624385i | ||||
\(700\) | −611.669 | + | 353.147i | −0.873813 | + | 0.504496i | ||||
\(701\) | 728.334i | 1.03899i | 0.854473 | + | 0.519497i | \(0.173881\pi\) | ||||
−0.854473 | + | 0.519497i | \(0.826119\pi\) | |||||||
\(702\) | −248.047 | + | 12.7378i | −0.353343 | + | 0.0181450i | ||||
\(703\) | −213.505 | −0.303705 | ||||||||
\(704\) | 53.0582 | − | 30.6332i | 0.0753667 | − | 0.0435130i | ||||
\(705\) | −1557.46 | − | 864.028i | −2.20916 | − | 1.22557i | ||||
\(706\) | 213.826 | − | 370.358i | 0.302870 | − | 0.524586i | ||||
\(707\) | 931.732 | + | 537.936i | 1.31787 | + | 0.760871i | ||||
\(708\) | −77.8905 | + | 1.33225i | −0.110015 | + | 0.00188170i | ||||
\(709\) | 707.456 | − | 408.450i | 0.997823 | − | 0.576093i | 0.0902195 | − | 0.995922i | \(-0.471243\pi\) |
0.907603 | + | 0.419829i | \(0.137910\pi\) | |||||||
\(710\) | − | 244.343i | − | 0.344145i | ||||||
\(711\) | 256.846 | + | 136.799i | 0.361246 | + | 0.192403i | ||||
\(712\) | 369.025i | 0.518293i | ||||||||
\(713\) | 464.223 | + | 559.264i | 0.651084 | + | 0.784381i | ||||
\(714\) | 79.8520 | + | 133.002i | 0.111837 | + | 0.186277i | ||||
\(715\) | 190.733 | − | 330.360i | 0.266760 | − | 0.462042i | ||||
\(716\) | −72.9875 | + | 126.418i | −0.101938 | + | 0.176562i | ||||
\(717\) | 674.393 | + | 1123.27i | 0.940576 | + | 1.56663i | ||||
\(718\) | 629.276 | − | 363.313i | 0.876429 | − | 0.506007i | ||||
\(719\) | 748.935 | 1.04163 | 0.520817 | − | 0.853668i | \(-0.325627\pi\) | ||||
0.520817 | + | 0.853668i | \(0.325627\pi\) | |||||||
\(720\) | −233.890 | + | 145.922i | −0.324847 | + | 0.202670i | ||||
\(721\) | 602.559 | 0.835727 | ||||||||
\(722\) | −44.4054 | − | 76.9123i | −0.0615033 | − | 0.106527i | ||||
\(723\) | −7.54239 | − | 440.970i | −0.0104321 | − | 0.609917i | ||||
\(724\) | −330.045 | − | 190.552i | −0.455864 | − | 0.263193i | ||||
\(725\) | 72.3844 | − | 125.373i | 0.0998405 | − | 0.172929i | ||||
\(726\) | −128.328 | + | 231.319i | −0.176761 | + | 0.318621i | ||||
\(727\) | −486.795 | + | 281.051i | −0.669594 | + | 0.386590i | −0.795923 | − | 0.605398i | \(-0.793014\pi\) |
0.126329 | + | 0.991988i | \(0.459681\pi\) | |||||||
\(728\) | − | 193.139i | − | 0.265301i | ||||||
\(729\) | 725.165 | − | 74.6747i | 0.994740 | − | 0.102434i | ||||
\(730\) | 1558.59i | 2.13506i | ||||||||
\(731\) | −23.2791 | − | 40.3206i | −0.0318455 | − | 0.0551581i | ||||
\(732\) | 435.997 | + | 241.877i | 0.595625 | + | 0.330433i | ||||
\(733\) | −26.1085 | − | 15.0738i | −0.0356188 | − | 0.0205645i | 0.482085 | − | 0.876125i | \(-0.339880\pi\) |
−0.517704 | + | 0.855560i | \(0.673213\pi\) | |||||||
\(734\) | 729.163 | + | 420.983i | 0.993411 | + | 0.573546i | ||||
\(735\) | 24.0453 | + | 1405.82i | 0.0327148 | + | 1.91269i | ||||
\(736\) | 83.0994 | + | 100.112i | 0.112907 | + | 0.136022i | ||||
\(737\) | 709.085 | 0.962124 | ||||||||
\(738\) | 422.309 | + | 676.893i | 0.572235 | + | 0.917199i | ||||
\(739\) | −279.108 | −0.377683 | −0.188841 | − | 0.982008i | \(-0.560473\pi\) | ||||
−0.188841 | + | 0.982008i | \(0.560473\pi\) | |||||||
\(740\) | 94.6782 | + | 163.987i | 0.127943 | + | 0.221605i | ||||
\(741\) | 288.909 | − | 173.456i | 0.389890 | − | 0.234083i | ||||
\(742\) | 73.9883 | − | 128.151i | 0.0997146 | − | 0.172711i | ||||
\(743\) | −192.900 | − | 111.371i | −0.259623 | − | 0.149893i | 0.364540 | − | 0.931188i | \(-0.381226\pi\) |
−0.624162 | + | 0.781295i | \(0.714560\pi\) | |||||||
\(744\) | −138.024 | − | 229.894i | −0.185517 | − | 0.308997i | ||||
\(745\) | −1038.61 | − | 1798.93i | −1.39411 | − | 2.41466i | ||||
\(746\) | 264.541i | 0.354613i | ||||||||
\(747\) | −307.361 | − | 163.704i | −0.411461 | − | 0.219148i | ||||
\(748\) | −53.3492 | −0.0713225 | ||||||||
\(749\) | 216.242 | + | 374.543i | 0.288708 | + | 0.500057i | ||||
\(750\) | 4.80057 | + | 280.668i | 0.00640077 | + | 0.374224i | ||||
\(751\) | −514.990 | − | 297.330i | −0.685739 | − | 0.395912i | 0.116275 | − | 0.993217i | \(-0.462905\pi\) |
−0.802014 | + | 0.597306i | \(0.796238\pi\) | |||||||
\(752\) | 155.058 | − | 268.568i | 0.206194 | − | 0.357138i | ||||
\(753\) | −657.951 | − | 365.010i | −0.873773 | − | 0.484741i | ||||
\(754\) | 19.7938 | + | 34.2838i | 0.0262517 | + | 0.0454693i | ||||
\(755\) | 452.978i | 0.599971i | ||||||||
\(756\) | 29.0723 | + | 566.134i | 0.0384554 | + | 0.748855i | ||||
\(757\) | − | 862.654i | − | 1.13957i | −0.821794 | − | 0.569785i | \(-0.807027\pi\) | ||
0.821794 | − | 0.569785i | \(-0.192973\pi\) | |||||||
\(758\) | −625.962 | + | 361.399i | −0.825807 | + | 0.476780i | ||||
\(759\) | 498.648 | + | 174.872i | 0.656980 | + | 0.230398i | ||||
\(760\) | 187.011 | − | 323.913i | 0.246067 | − | 0.426201i | ||||
\(761\) | 252.015 | − | 436.502i | 0.331163 | − | 0.573590i | −0.651578 | − | 0.758582i | \(-0.725892\pi\) |
0.982740 | + | 0.184992i | \(0.0592258\pi\) | |||||||
\(762\) | 496.791 | − | 8.49716i | 0.651957 | − | 0.0111511i | ||||
\(763\) | −854.160 | − | 1479.45i | −1.11948 | − | 1.93899i | ||||
\(764\) | − | 349.692i | − | 0.457711i | ||||||
\(765\) | 239.912 | − | 8.20936i | 0.313611 | − | 0.0107312i | ||||
\(766\) | − | 525.520i | − | 0.686058i | ||||||
\(767\) | −42.2274 | − | 73.1400i | −0.0550553 | − | 0.0953585i | ||||
\(768\) | −24.7074 | − | 41.1527i | −0.0321711 | − | 0.0535842i | ||||
\(769\) | −163.182 | − | 94.2131i | −0.212200 | − | 0.122514i | 0.390133 | − | 0.920758i | \(-0.372429\pi\) |
−0.602333 | + | 0.798245i | \(0.705762\pi\) | |||||||
\(770\) | −754.002 | − | 435.323i | −0.979224 | − | 0.565355i | ||||
\(771\) | −26.3373 | − | 43.8676i | −0.0341600 | − | 0.0568970i | ||||
\(772\) | 251.381 | + | 435.404i | 0.325623 | + | 0.563995i | ||||
\(773\) | 766.217i | 0.991224i | 0.868544 | + | 0.495612i | \(0.165056\pi\) | ||||
−0.868544 | + | 0.495612i | \(0.834944\pi\) | |||||||
\(774\) | −5.81822 | − | 170.033i | −0.00751708 | − | 0.219681i | ||||
\(775\) | −1063.07 | −1.37170 | ||||||||
\(776\) | −461.370 | + | 266.372i | −0.594549 | + | 0.343263i | ||||
\(777\) | 389.321 | − | 6.65897i | 0.501056 | − | 0.00857011i | ||||
\(778\) | 760.192 | + | 438.897i | 0.977110 | + | 0.564135i | ||||
\(779\) | −937.426 | − | 541.223i | −1.20337 | − | 0.694766i | ||||
\(780\) | −261.343 | − | 144.985i | −0.335055 | − | 0.185878i | ||||
\(781\) | 149.641 | − | 86.3950i | 0.191601 | − | 0.110621i | ||||
\(782\) | −19.0786 | − | 111.677i | −0.0243972 | − | 0.142809i | ||||
\(783\) | −63.1807 | − | 97.5143i | −0.0806905 | − | 0.124539i | ||||
\(784\) | −244.814 | −0.312262 | ||||||||
\(785\) | −1012.62 | − | 1753.90i | −1.28996 | − | 2.23427i | ||||
\(786\) | −158.498 | + | 285.702i | −0.201651 | + | 0.363488i | ||||
\(787\) | 7.74621 | + | 4.47228i | 0.00984271 | + | 0.00568269i | 0.504913 | − | 0.863170i | \(-0.331524\pi\) |
−0.495071 | + | 0.868853i | \(0.664858\pi\) | |||||||
\(788\) | 275.079 | − | 476.450i | 0.349085 | − | 0.604632i | ||||
\(789\) | 8.75846 | + | 512.068i | 0.0111007 | + | 0.649009i | ||||
\(790\) | 175.081 | + | 303.250i | 0.221622 | + | 0.383861i | ||||
\(791\) | 1004.20 | 1.26953 | ||||||||
\(792\) | −172.065 | − | 91.6434i | −0.217254 | − | 0.115711i | ||||
\(793\) | 540.536i | 0.681635i | ||||||||
\(794\) | −53.9916 | − | 93.5162i | −0.0679995 | − | 0.117779i | ||||
\(795\) | −117.865 | − | 196.316i | −0.148258 | − | 0.246939i | ||||
\(796\) | 141.547 | + | 81.7222i | 0.177823 | + | 0.102666i | ||||
\(797\) | −934.987 | − | 539.815i | −1.17313 | − | 0.677309i | −0.218717 | − | 0.975788i | \(-0.570187\pi\) |
−0.954416 | + | 0.298480i | \(0.903520\pi\) | |||||||
\(798\) | −395.890 | − | 659.395i | −0.496102 | − | 0.826310i | ||||
\(799\) | −233.862 | + | 135.020i | −0.292694 | + | 0.168987i | ||||
\(800\) | −190.298 | −0.237872 | ||||||||
\(801\) | 996.239 | − | 621.548i | 1.24374 | − | 0.775965i | ||||
\(802\) | 833.642i | 1.03945i | ||||||||
\(803\) | −954.514 | + | 551.089i | −1.18868 | + | 0.686287i | ||||
\(804\) | −9.50067 | − | 555.462i | −0.0118168 | − | 0.690873i | ||||
\(805\) | 641.623 | − | 1734.04i | 0.797048 | − | 2.15409i | ||||
\(806\) | 145.350 | − | 251.754i | 0.180335 | − | 0.312350i | ||||
\(807\) | −369.497 | + | 666.039i | −0.457865 | + | 0.825327i | ||||
\(808\) | 144.937 | + | 251.038i | 0.179377 | + | 0.310690i | ||||
\(809\) | −25.4712 | −0.0314848 | −0.0157424 | − | 0.999876i | \(-0.505011\pi\) | ||||
−0.0157424 | + | 0.999876i | \(0.505011\pi\) | |||||||
\(810\) | 787.880 | + | 385.645i | 0.972691 | + | 0.476104i | ||||
\(811\) | 1106.58 | 1.36447 | 0.682234 | − | 0.731134i | \(-0.261008\pi\) | ||||
0.682234 | + | 0.731134i | \(0.261008\pi\) | |||||||
\(812\) | 78.2483 | − | 45.1767i | 0.0963649 | − | 0.0556363i | ||||
\(813\) | −505.908 | + | 911.928i | −0.622273 | + | 1.12168i | ||||
\(814\) | −66.9528 | + | 115.966i | −0.0822516 | + | 0.142464i | ||||
\(815\) | −1626.29 | − | 938.940i | −1.99545 | − | 1.15207i | ||||
\(816\) | 0.714799 | + | 41.7911i | 0.000875979 | + | 0.0512146i | ||||
\(817\) | 115.413 | + | 199.901i | 0.141264 | + | 0.244677i | ||||
\(818\) | −61.2787 | −0.0749129 | ||||||||
\(819\) | −521.408 | + | 325.304i | −0.636640 | + | 0.397196i | ||||
\(820\) | 960.018i | 1.17075i | ||||||||
\(821\) | 579.638 | + | 1003.96i | 0.706015 | + | 1.22285i | 0.966324 | + | 0.257328i | \(0.0828422\pi\) |
−0.260309 | + | 0.965525i | \(0.583825\pi\) | |||||||
\(822\) | 275.705 | − | 165.529i | 0.335407 | − | 0.201373i | ||||
\(823\) | 610.556 | − | 1057.51i | 0.741866 | − | 1.28495i | −0.209778 | − | 0.977749i | \(-0.567274\pi\) |
0.951645 | − | 0.307201i | \(-0.0993925\pi\) | |||||||
\(824\) | 140.598 | + | 81.1741i | 0.170628 | + | 0.0985122i | ||||
\(825\) | −662.626 | + | 397.830i | −0.803183 | + | 0.482218i | ||||
\(826\) | −166.932 | + | 96.3784i | −0.202097 | + | 0.116681i | ||||
\(827\) | − | 521.081i | − | 0.630086i | −0.949077 | − | 0.315043i | \(-0.897981\pi\) | ||
0.949077 | − | 0.315043i | \(-0.102019\pi\) | |||||||
\(828\) | 130.305 | − | 392.959i | 0.157373 | − | 0.474588i | ||||
\(829\) | −471.748 | −0.569056 | −0.284528 | − | 0.958668i | \(-0.591837\pi\) | ||||
−0.284528 | + | 0.958668i | \(0.591837\pi\) | |||||||
\(830\) | −209.516 | − | 362.892i | −0.252428 | − | 0.437219i | ||||
\(831\) | 250.130 | − | 4.27824i | 0.300998 | − | 0.00514830i | ||||
\(832\) | 26.0188 | − | 45.0659i | 0.0312726 | − | 0.0541657i | ||||
\(833\) | 184.617 | + | 106.589i | 0.221630 | + | 0.127958i | ||||
\(834\) | −198.724 | + | 358.211i | −0.238278 | + | 0.429510i | ||||
\(835\) | 1651.13 | − | 953.281i | 1.97740 | − | 1.14165i | ||||
\(836\) | 264.494 | 0.316381 | ||||||||
\(837\) | −388.160 | + | 759.828i | −0.463751 | + | 0.907799i | ||||
\(838\) | − | 363.368i | − | 0.433613i | ||||||
\(839\) | 523.877 | − | 302.461i | 0.624407 | − | 0.360501i | −0.154176 | − | 0.988043i | \(-0.549272\pi\) |
0.778583 | + | 0.627542i | \(0.215939\pi\) | |||||||
\(840\) | −330.908 | + | 596.480i | −0.393938 | + | 0.710096i | ||||
\(841\) | 411.240 | − | 712.289i | 0.488989 | − | 0.846955i | ||||
\(842\) | −670.829 | − | 387.303i | −0.796709 | − | 0.459980i | ||||
\(843\) | 24.7149 | + | 1444.97i | 0.0293178 | + | 1.71408i | ||||
\(844\) | 248.992 | + | 431.267i | 0.295014 | + | 0.510980i | ||||
\(845\) | 970.144i | 1.14810i | ||||||||
\(846\) | −986.203 | + | 33.7461i | −1.16573 | + | 0.0398890i | ||||
\(847\) | 654.543i | 0.772778i | ||||||||
\(848\) | 34.5280 | − | 19.9347i | 0.0407169 | − | 0.0235079i | ||||
\(849\) | 738.501 | − | 443.383i | 0.869848 | − | 0.522242i | ||||
\(850\) | 143.506 | + | 82.8532i | 0.168831 | + | 0.0974744i | ||||
\(851\) | −266.696 | − | 98.6818i | −0.313391 | − | 0.115960i | ||||
\(852\) | −69.6825 | − | 116.063i | −0.0817870 | − | 0.136225i | ||||
\(853\) | −521.919 | − | 903.990i | −0.611863 | − | 1.05978i | −0.990926 | − | 0.134406i | \(-0.957087\pi\) |
0.379064 | − | 0.925371i | \(-0.376246\pi\) | |||||||
\(854\) | 1233.70 | 1.44462 | ||||||||
\(855\) | −1189.44 | + | 40.7003i | −1.39115 | + | 0.0476027i | ||||
\(856\) | 116.525i | 0.136127i | ||||||||
\(857\) | −768.101 | − | 1330.39i | −0.896267 | − | 1.55238i | −0.832228 | − | 0.554433i | \(-0.812935\pi\) |
−0.0640391 | − | 0.997947i | \(-0.520398\pi\) | |||||||
\(858\) | −3.61436 | − | 211.316i | −0.00421254 | − | 0.246289i | ||||
\(859\) | −363.977 | + | 630.427i | −0.423722 | + | 0.733908i | −0.996300 | − | 0.0859420i | \(-0.972610\pi\) |
0.572578 | + | 0.819850i | \(0.305943\pi\) | |||||||
\(860\) | 102.359 | − | 177.292i | 0.119022 | − | 0.206153i | ||||
\(861\) | 1726.26 | + | 957.671i | 2.00494 | + | 1.11228i | ||||
\(862\) | 47.0254 | − | 27.1501i | 0.0545538 | − | 0.0314967i | ||||
\(863\) | 256.074 | 0.296726 | 0.148363 | − | 0.988933i | \(-0.452600\pi\) | ||||
0.148363 | + | 0.988933i | \(0.452600\pi\) | |||||||
\(864\) | −69.4835 | + | 136.015i | −0.0804207 | + | 0.157425i | ||||
\(865\) | − | 1026.53i | − | 1.18674i | ||||||
\(866\) | 355.389 | − | 205.184i | 0.410380 | − | 0.236933i | ||||
\(867\) | −402.940 | + | 726.321i | −0.464752 | + | 0.837741i | ||||
\(868\) | −574.595 | − | 331.743i | −0.661976 | − | 0.382192i | ||||
\(869\) | −123.811 | + | 214.447i | −0.142475 | + | 0.246774i | ||||
\(870\) | −2.39104 | − | 139.793i | −0.00274832 | − | 0.160682i | ||||
\(871\) | 521.584 | − | 301.137i | 0.598834 | − | 0.345737i | ||||
\(872\) | − | 460.274i | − | 0.527837i | ||||||
\(873\) | 1496.20 | + | 796.890i | 1.71386 | + | 0.912817i | ||||
\(874\) | 94.5880 | + | 553.670i | 0.108224 | + | 0.633489i | ||||
\(875\) | 347.287 | + | 601.518i | 0.396899 | + | 0.687450i | ||||
\(876\) | 444.485 | + | 740.335i | 0.507402 | + | 0.845131i | ||||
\(877\) | −197.018 | + | 341.245i | −0.224650 | + | 0.389105i | −0.956214 | − | 0.292667i | \(-0.905457\pi\) |
0.731564 | + | 0.681772i | \(0.238791\pi\) | |||||||
\(878\) | −396.732 | + | 687.160i | −0.451859 | + | 0.782642i | ||||
\(879\) | −783.358 | + | 470.315i | −0.891193 | + | 0.535057i | ||||
\(880\) | −117.290 | − | 203.152i | −0.133284 | − | 0.230854i | ||||
\(881\) | − | 31.9176i | − | 0.0362289i | −0.999836 | − | 0.0181144i | \(-0.994234\pi\) | ||
0.999836 | − | 0.0181144i | \(-0.00576632\pi\) | |||||||
\(882\) | 412.339 | + | 660.913i | 0.467505 | + | 0.749334i | ||||
\(883\) | −751.469 | −0.851041 | −0.425521 | − | 0.904949i | \(-0.639909\pi\) | ||||
−0.425521 | + | 0.904949i | \(0.639909\pi\) | |||||||
\(884\) | −39.2423 | + | 22.6565i | −0.0443917 | + | 0.0256296i | ||||
\(885\) | 5.10096 | + | 298.231i | 0.00576380 | + | 0.336984i | ||||
\(886\) | −519.832 | + | 900.375i | −0.586717 | + | 1.01622i | ||||
\(887\) | 216.650 | − | 375.249i | 0.244250 | − | 0.423054i | −0.717670 | − | 0.696383i | \(-0.754791\pi\) |
0.961921 | + | 0.273329i | \(0.0881248\pi\) | |||||||
\(888\) | 91.7388 | + | 50.8938i | 0.103310 | + | 0.0573128i | ||||
\(889\) | 1064.71 | − | 614.708i | 1.19764 | − | 0.691460i | ||||
\(890\) | 1412.94 | 1.58757 | ||||||||
\(891\) | 42.4029 | + | 618.870i | 0.0475902 | + | 0.694580i | ||||
\(892\) | −80.1890 | −0.0898979 | ||||||||
\(893\) | 1159.44 | − | 669.403i | 1.29837 | − | 0.749612i | ||||
\(894\) | −1006.37 | − | 558.299i | −1.12569 | − | 0.624496i | ||||
\(895\) | 484.035 | + | 279.458i | 0.540821 | + | 0.312243i | ||||
\(896\) | −102.857 | − | 59.3844i | −0.114796 | − | 0.0662773i | ||||
\(897\) | 441.057 | − | 83.1363i | 0.491703 | − | 0.0926826i | ||||
\(898\) | −140.318 | − | 243.039i | −0.156257 | − | 0.270644i | ||||
\(899\) | 135.994 | 0.151273 | ||||||||
\(900\) | 320.518 | + | 513.738i | 0.356131 | + | 0.570820i | ||||
\(901\) | −34.7173 | −0.0385320 | ||||||||
\(902\) | −587.934 | + | 339.444i | −0.651812 | + | 0.376324i | ||||
\(903\) | −216.688 | − | 360.916i | −0.239964 | − | 0.399685i | ||||
\(904\) | 234.313 | + | 135.281i | 0.259196 | + | 0.149647i | ||||
\(905\) | −729.593 | + | 1263.69i | −0.806180 | + | 1.39635i | ||||
\(906\) | 129.182 | + | 215.166i | 0.142585 | + | 0.237490i | ||||
\(907\) | 153.502 | − | 88.6244i | 0.169241 | − | 0.0977116i | −0.412987 | − | 0.910737i | \(-0.635514\pi\) |
0.582228 | + | 0.813026i | \(0.302181\pi\) | |||||||
\(908\) | − | 570.591i | − | 0.628405i | ||||||
\(909\) | 433.598 | − | 814.101i | 0.477006 | − | 0.895601i | ||||
\(910\) | −739.499 | −0.812636 | ||||||||
\(911\) | 1297.37 | − | 749.038i | 1.42412 | − | 0.822215i | 0.427470 | − | 0.904030i | \(-0.359405\pi\) |
0.996648 | + | 0.0818149i | \(0.0260716\pi\) | |||||||
\(912\) | −3.54383 | − | 207.192i | −0.00388577 | − | 0.227184i | ||||
\(913\) | 148.162 | − | 256.623i | 0.162280 | − | 0.281077i | ||||
\(914\) | 254.337 | + | 146.842i | 0.278269 | + | 0.160658i | ||||
\(915\) | 926.110 | − | 1669.37i | 1.01214 | − | 1.82444i | ||||
\(916\) | 327.613 | − | 189.147i | 0.357656 | − | 0.206493i | ||||
\(917\) | 808.424i | 0.881596i | ||||||||
\(918\) | 111.618 | − | 72.3184i | 0.121588 | − | 0.0787782i | ||||
\(919\) | − | 1430.42i | − | 1.55649i | −0.627958 | − | 0.778247i | \(-0.716109\pi\) | ||
0.627958 | − | 0.778247i | \(-0.283891\pi\) | |||||||
\(920\) | 383.315 | − | 318.174i | 0.416647 | − | 0.345842i | ||||
\(921\) | −7.36616 | + | 13.2779i | −0.00799801 | + | 0.0144169i | ||||
\(922\) | 163.020 | − | 282.360i | 0.176812 | − | 0.306247i | ||||
\(923\) | 73.3811 | − | 127.100i | 0.0795028 | − | 0.137703i | ||||
\(924\) | −482.300 | + | 8.24929i | −0.521969 | + | 0.00892781i | ||||
\(925\) | 360.198 | − | 207.960i | 0.389403 | − | 0.224822i | ||||
\(926\) | −56.3646 | −0.0608690 | ||||||||
\(927\) | −17.6664 | − | 516.286i | −0.0190576 | − | 0.556943i | ||||
\(928\) | 24.3440 | 0.0262327 | ||||||||
\(929\) | −481.859 | − | 834.604i | −0.518686 | − | 0.898390i | −0.999764 | − | 0.0217124i | \(-0.993088\pi\) |
0.481079 | − | 0.876677i | \(-0.340245\pi\) | |||||||
\(930\) | −880.227 | + | 528.474i | −0.946481 | + | 0.568251i | ||||
\(931\) | −915.295 | − | 528.446i | −0.983131 | − | 0.567611i | ||||
\(932\) | 166.369 | − | 288.160i | 0.178508 | − | 0.309185i | ||||
\(933\) | 53.3420 | + | 88.8466i | 0.0571726 | + | 0.0952268i | ||||
\(934\) | 49.0323 | − | 28.3088i | 0.0524971 | − | 0.0303092i | ||||
\(935\) | 204.266i | 0.218466i | ||||||||
\(936\) | −165.486 | + | 5.66262i | −0.176801 | + | 0.00604981i | ||||
\(937\) | − | 1440.44i | − | 1.53729i | −0.639678 | − | 0.768643i | \(-0.720932\pi\) | ||
0.639678 | − | 0.768643i | \(-0.279068\pi\) | |||||||
\(938\) | −687.305 | − | 1190.45i | −0.732734 | − | 1.26913i | ||||
\(939\) | −11.6115 | − | 678.874i | −0.0123658 | − | 0.722976i | ||||
\(940\) | −1028.30 | − | 593.691i | −1.09394 | − | 0.631587i | ||||
\(941\) | −47.2306 | − | 27.2686i | −0.0501919 | − | 0.0289783i | 0.474694 | − | 0.880151i | \(-0.342559\pi\) |
−0.524886 | + | 0.851173i | \(0.675892\pi\) | |||||||
\(942\) | −981.180 | − | 544.327i | −1.04159 | − | 0.577842i | ||||
\(943\) | −920.819 | − | 1109.34i | −0.976478 | − | 1.17639i | ||||
\(944\) | −51.9346 | −0.0550155 | ||||||||
\(945\) | 2167.64 | − | 111.313i | 2.29380 | − | 0.117792i | ||||
\(946\) | 144.769 | 0.153033 | ||||||||
\(947\) | 666.309 | + | 1154.08i | 0.703600 | + | 1.21867i | 0.967194 | + | 0.254037i | \(0.0817586\pi\) |
−0.263594 | + | 0.964634i | \(0.584908\pi\) | |||||||
\(948\) | 169.646 | + | 94.1141i | 0.178951 | + | 0.0992765i | ||||
\(949\) | −468.077 | + | 810.733i | −0.493231 | + | 0.854302i | ||||
\(950\) | −711.474 | − | 410.769i | −0.748920 | − | 0.432389i | ||||
\(951\) | 586.333 | − | 10.0287i | 0.616543 | − | 0.0105454i | ||||
\(952\) | 51.7105 | + | 89.5652i | 0.0543178 | + | 0.0940811i | ||||
\(953\) | 1672.44i | 1.75492i | 0.479647 | + | 0.877462i | \(0.340765\pi\) | ||||
−0.479647 | + | 0.877462i | \(0.659235\pi\) | |||||||
\(954\) | −111.972 | − | 59.6375i | −0.117371 | − | 0.0625131i | ||||
\(955\) | −1338.91 | −1.40200 | ||||||||
\(956\) | 436.723 | + | 756.426i | 0.456823 | + | 0.791241i | ||||
\(957\) | 84.7670 | − | 50.8927i | 0.0885757 | − | 0.0531794i | ||||
\(958\) | 586.563 | + | 338.653i | 0.612279 | + | 0.353499i | ||||
\(959\) | 397.849 | − | 689.095i | 0.414859 | − | 0.718556i | ||||
\(960\) | −157.567 | + | 94.6007i | −0.164133 | + | 0.0985424i | ||||
\(961\) | −18.8183 | − | 32.5942i | −0.0195820 | − | 0.0339170i | ||||
\(962\) | 113.735i | 0.118228i | ||||||||
\(963\) | 314.577 | − | 196.263i | 0.326663 | − | 0.203803i | ||||
\(964\) | − | 294.023i | − | 0.305003i | ||||||
\(965\) | 1667.10 | − | 962.498i | 1.72756 | − | 0.997407i | ||||
\(966\) | −189.748 | − | 1006.65i | −0.196426 | − | 1.04209i | ||||
\(967\) | −176.151 | + | 305.103i | −0.182162 | + | 0.315514i | −0.942617 | − | 0.333877i | \(-0.891643\pi\) |
0.760454 | + | 0.649391i | \(0.224976\pi\) | |||||||
\(968\) | −88.1771 | + | 152.727i | −0.0910920 | + | 0.157776i | ||||
\(969\) | −87.5363 | + | 157.789i | −0.0903367 | + | 0.162837i | ||||
\(970\) | 1019.90 | + | 1766.51i | 1.05144 | + | 1.82115i | ||||
\(971\) | 603.889i | 0.621924i | 0.950422 | + | 0.310962i | \(0.100651\pi\) | ||||
−0.950422 | + | 0.310962i | \(0.899349\pi\) | |||||||
\(972\) | 484.224 | − | 41.5082i | 0.498173 | − | 0.0427039i | ||||
\(973\) | 1013.60i | 1.04172i | ||||||||
\(974\) | 247.682 | + | 428.998i | 0.254294 | + | 0.440450i | ||||
\(975\) | −318.458 | + | 574.039i | −0.326624 | + | 0.588758i | ||||
\(976\) | 287.865 | + | 166.199i | 0.294943 | + | 0.170286i | ||||
\(977\) | 1160.04 | + | 669.752i | 1.18735 | + | 0.685519i | 0.957704 | − | 0.287755i | \(-0.0929088\pi\) |
0.229649 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(978\) | −1040.26 | + | 17.7927i | −1.06366 | + | 0.0181930i | ||||
\(979\) | 499.588 | + | 865.312i | 0.510305 | + | 0.883874i | ||||
\(980\) | 937.354i | 0.956483i | ||||||||
\(981\) | −1242.58 | + | 775.239i | −1.26665 | + | 0.790254i | ||||
\(982\) | 1241.03 | 1.26378 | ||||||||
\(983\) | −801.040 | + | 462.481i | −0.814894 | + | 0.470479i | −0.848652 | − | 0.528951i | \(-0.822586\pi\) |
0.0337588 | + | 0.999430i | \(0.489252\pi\) | |||||||
\(984\) | 273.781 | + | 456.011i | 0.278233 | + | 0.463425i | ||||
\(985\) | −1824.25 | − | 1053.23i | −1.85203 | − | 1.06927i | ||||
\(986\) | −18.3581 | − | 10.5991i | −0.0186188 | − | 0.0107496i | ||||
\(987\) | −2093.34 | + | 1256.80i | −2.12091 | + | 1.27336i | ||||
\(988\) | 194.555 | − | 112.326i | 0.196918 | − | 0.113691i | ||||
\(989\) | 51.7721 | + | 303.047i | 0.0523480 | + | 0.306418i | ||||
\(990\) | −350.888 | + | 658.809i | −0.354433 | + | 0.665464i | ||||
\(991\) | −1715.82 | −1.73141 | −0.865703 | − | 0.500559i | \(-0.833128\pi\) | ||||
−0.865703 | + | 0.500559i | \(0.833128\pi\) | |||||||
\(992\) | −89.3817 | − | 154.814i | −0.0901025 | − | 0.156062i | ||||
\(993\) | −1612.31 | + | 27.5771i | −1.62368 | + | 0.0277715i | ||||
\(994\) | −290.088 | − | 167.483i | −0.291839 | − | 0.168494i | ||||
\(995\) | 312.902 | − | 541.962i | 0.314474 | − | 0.544685i | ||||
\(996\) | −203.011 | − | 112.624i | −0.203826 | − | 0.113076i | ||||
\(997\) | 132.368 | + | 229.268i | 0.132766 | + | 0.229957i | 0.924742 | − | 0.380595i | \(-0.124281\pi\) |
−0.791976 | + | 0.610552i | \(0.790947\pi\) | |||||||
\(998\) | −398.439 | −0.399237 | ||||||||
\(999\) | −17.1200 | − | 333.384i | −0.0171372 | − | 0.333717i |
(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 | 414.3.h.a.229.8 | yes | 96 | |
3.2 | odd | 2 | 1242.3.h.a.91.27 | 96 | |||
9.2 | odd | 6 | 1242.3.h.a.505.28 | 96 | |||
9.7 | even | 3 | inner | 414.3.h.a.367.7 | yes | 96 | |
23.22 | odd | 2 | inner | 414.3.h.a.229.7 | ✓ | 96 | |
69.68 | even | 2 | 1242.3.h.a.91.28 | 96 | |||
207.137 | even | 6 | 1242.3.h.a.505.27 | 96 | |||
207.160 | odd | 6 | inner | 414.3.h.a.367.8 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.3.h.a.229.7 | ✓ | 96 | 23.22 | odd | 2 | inner | |
414.3.h.a.229.8 | yes | 96 | 1.1 | even | 1 | trivial | |
414.3.h.a.367.7 | yes | 96 | 9.7 | even | 3 | inner | |
414.3.h.a.367.8 | yes | 96 | 207.160 | odd | 6 | inner | |
1242.3.h.a.91.27 | 96 | 3.2 | odd | 2 | |||
1242.3.h.a.91.28 | 96 | 69.68 | even | 2 | |||
1242.3.h.a.505.27 | 96 | 207.137 | even | 6 | |||
1242.3.h.a.505.28 | 96 | 9.2 | odd | 6 |