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 | 47.10 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.3.f.b.93.10 |
$q$-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 | ||||
\(3\) | 2.20008 | − | 2.20008i | 0.733360 | − | 0.733360i | −0.237924 | − | 0.971284i | \(-0.576467\pi\) |
0.971284 | + | 0.237924i | \(0.0764669\pi\) | |||||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 0.183624 | − | 4.99663i | 0.0367249 | − | 0.999325i | ||||
\(6\) | 4.40016 | 0.733360 | ||||||||
\(7\) | −8.35722 | − | 8.35722i | −1.19389 | − | 1.19389i | −0.975966 | − | 0.217922i | \(-0.930072\pi\) |
−0.217922 | − | 0.975966i | \(-0.569928\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 0.680698i | − | 0.0756331i | ||||||
\(10\) | 5.18025 | − | 4.81300i | 0.518025 | − | 0.481300i | ||||
\(11\) | 4.85484 | 0.441349 | 0.220675 | − | 0.975347i | \(-0.429174\pi\) | ||||
0.220675 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(12\) | 4.40016 | + | 4.40016i | 0.366680 | + | 0.366680i | ||||
\(13\) | 17.1820 | − | 17.1820i | 1.32169 | − | 1.32169i | 0.409290 | − | 0.912404i | \(-0.365776\pi\) |
0.912404 | − | 0.409290i | \(-0.134224\pi\) | |||||||
\(14\) | − | 16.7144i | − | 1.19389i | ||||||
\(15\) | −10.5890 | − | 11.3970i | −0.705932 | − | 0.759798i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −9.16287 | − | 9.16287i | −0.538992 | − | 0.538992i | 0.384241 | − | 0.923233i | \(-0.374463\pi\) |
−0.923233 | + | 0.384241i | \(0.874463\pi\) | |||||||
\(18\) | 0.680698 | − | 0.680698i | 0.0378166 | − | 0.0378166i | ||||
\(19\) | 28.3432i | 1.49175i | 0.666087 | + | 0.745874i | \(0.267968\pi\) | ||||
−0.666087 | + | 0.745874i | \(0.732032\pi\) | |||||||
\(20\) | 9.99325 | + | 0.367249i | 0.499663 | + | 0.0183624i | ||||
\(21\) | −36.7731 | −1.75110 | ||||||||
\(22\) | 4.85484 | + | 4.85484i | 0.220675 | + | 0.220675i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 8.80032i | 0.366680i | ||||||||
\(25\) | −24.9326 | − | 1.83501i | −0.997303 | − | 0.0734002i | ||||
\(26\) | 34.3641 | 1.32169 | ||||||||
\(27\) | 18.3031 | + | 18.3031i | 0.677893 | + | 0.677893i | ||||
\(28\) | 16.7144 | − | 16.7144i | 0.596944 | − | 0.596944i | ||||
\(29\) | 16.7951i | 0.579140i | 0.957157 | + | 0.289570i | \(0.0935124\pi\) | ||||
−0.957157 | + | 0.289570i | \(0.906488\pi\) | |||||||
\(30\) | 0.807977 | − | 21.9860i | 0.0269326 | − | 0.732865i | ||||
\(31\) | 49.9685 | 1.61189 | 0.805944 | − | 0.591991i | \(-0.201658\pi\) | ||||
0.805944 | + | 0.591991i | \(0.201658\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 10.6810 | − | 10.6810i | 0.323668 | − | 0.323668i | ||||
\(34\) | − | 18.3257i | − | 0.538992i | ||||||
\(35\) | −43.2925 | + | 40.2233i | −1.23693 | + | 1.14924i | ||||
\(36\) | 1.36140 | 0.0378166 | ||||||||
\(37\) | −15.0634 | − | 15.0634i | −0.407118 | − | 0.407118i | 0.473614 | − | 0.880732i | \(-0.342949\pi\) |
−0.880732 | + | 0.473614i | \(0.842949\pi\) | |||||||
\(38\) | −28.3432 | + | 28.3432i | −0.745874 | + | 0.745874i | ||||
\(39\) | − | 75.6037i | − | 1.93856i | ||||||
\(40\) | 9.62601 | + | 10.3605i | 0.240650 | + | 0.259013i | ||||
\(41\) | 43.9441 | 1.07181 | 0.535903 | − | 0.844279i | \(-0.319971\pi\) | ||||
0.535903 | + | 0.844279i | \(0.319971\pi\) | |||||||
\(42\) | −36.7731 | − | 36.7731i | −0.875550 | − | 0.875550i | ||||
\(43\) | −5.23091 | + | 5.23091i | −0.121649 | + | 0.121649i | −0.765310 | − | 0.643661i | \(-0.777415\pi\) |
0.643661 | + | 0.765310i | \(0.277415\pi\) | |||||||
\(44\) | 9.70969i | 0.220675i | ||||||||
\(45\) | −3.40119 | − | 0.124993i | −0.0755821 | − | 0.00277762i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 20.2706 | + | 20.2706i | 0.431289 | + | 0.431289i | 0.889067 | − | 0.457778i | \(-0.151354\pi\) |
−0.457778 | + | 0.889067i | \(0.651354\pi\) | |||||||
\(48\) | −8.80032 | + | 8.80032i | −0.183340 | + | 0.183340i | ||||
\(49\) | 90.6862i | 1.85074i | ||||||||
\(50\) | −23.0976 | − | 26.7676i | −0.461951 | − | 0.535351i | ||||
\(51\) | −40.3181 | −0.790550 | ||||||||
\(52\) | 34.3641 | + | 34.3641i | 0.660847 | + | 0.660847i | ||||
\(53\) | −34.0517 | + | 34.0517i | −0.642484 | + | 0.642484i | −0.951165 | − | 0.308681i | \(-0.900112\pi\) |
0.308681 | + | 0.951165i | \(0.400112\pi\) | |||||||
\(54\) | 36.6062i | 0.677893i | ||||||||
\(55\) | 0.891468 | − | 24.2578i | 0.0162085 | − | 0.441052i | ||||
\(56\) | 33.4289 | 0.596944 | ||||||||
\(57\) | 62.3573 | + | 62.3573i | 1.09399 | + | 1.09399i | ||||
\(58\) | −16.7951 | + | 16.7951i | −0.289570 | + | 0.289570i | ||||
\(59\) | − | 67.5325i | − | 1.14462i | −0.820038 | − | 0.572310i | \(-0.806048\pi\) | ||
0.820038 | − | 0.572310i | \(-0.193952\pi\) | |||||||
\(60\) | 22.7939 | − | 21.1780i | 0.379899 | − | 0.352966i | ||||
\(61\) | −10.1955 | −0.167139 | −0.0835697 | − | 0.996502i | \(-0.526632\pi\) | ||||
−0.0835697 | + | 0.996502i | \(0.526632\pi\) | |||||||
\(62\) | 49.9685 | + | 49.9685i | 0.805944 | + | 0.805944i | ||||
\(63\) | −5.68874 | + | 5.68874i | −0.0902975 | + | 0.0902975i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −82.6971 | − | 89.0072i | −1.27226 | − | 1.36934i | ||||
\(66\) | 21.3621 | 0.323668 | ||||||||
\(67\) | 18.0435 | + | 18.0435i | 0.269305 | + | 0.269305i | 0.828820 | − | 0.559515i | \(-0.189013\pi\) |
−0.559515 | + | 0.828820i | \(0.689013\pi\) | |||||||
\(68\) | 18.3257 | − | 18.3257i | 0.269496 | − | 0.269496i | ||||
\(69\) | − | 14.9217i | − | 0.216256i | ||||||
\(70\) | −83.5158 | − | 3.06918i | −1.19308 | − | 0.0438454i | ||||
\(71\) | 21.4957 | 0.302757 | 0.151378 | − | 0.988476i | \(-0.451629\pi\) | ||||
0.151378 | + | 0.988476i | \(0.451629\pi\) | |||||||
\(72\) | 1.36140 | + | 1.36140i | 0.0189083 | + | 0.0189083i | ||||
\(73\) | −21.4816 | + | 21.4816i | −0.294269 | + | 0.294269i | −0.838764 | − | 0.544495i | \(-0.816721\pi\) |
0.544495 | + | 0.838764i | \(0.316721\pi\) | |||||||
\(74\) | − | 30.1268i | − | 0.407118i | ||||||
\(75\) | −58.8908 | + | 50.8165i | −0.785210 | + | 0.677553i | ||||
\(76\) | −56.6864 | −0.745874 | ||||||||
\(77\) | −40.5730 | − | 40.5730i | −0.526922 | − | 0.526922i | ||||
\(78\) | 75.6037 | − | 75.6037i | 0.969278 | − | 0.969278i | ||||
\(79\) | 113.271i | 1.43381i | 0.697172 | + | 0.716904i | \(0.254442\pi\) | ||||
−0.697172 | + | 0.716904i | \(0.745558\pi\) | |||||||
\(80\) | −0.734498 | + | 19.9865i | −0.00918122 | + | 0.249831i | ||||
\(81\) | 86.6629 | 1.06991 | ||||||||
\(82\) | 43.9441 | + | 43.9441i | 0.535903 | + | 0.535903i | ||||
\(83\) | −45.6403 | + | 45.6403i | −0.549883 | + | 0.549883i | −0.926407 | − | 0.376524i | \(-0.877119\pi\) |
0.376524 | + | 0.926407i | \(0.377119\pi\) | |||||||
\(84\) | − | 73.5462i | − | 0.875550i | ||||||
\(85\) | −47.4660 | + | 44.1009i | −0.558423 | + | 0.518834i | ||||
\(86\) | −10.4618 | −0.121649 | ||||||||
\(87\) | 36.9505 | + | 36.9505i | 0.424718 | + | 0.424718i | ||||
\(88\) | −9.70969 | + | 9.70969i | −0.110337 | + | 0.110337i | ||||
\(89\) | 64.2133i | 0.721498i | 0.932663 | + | 0.360749i | \(0.117479\pi\) | ||||
−0.932663 | + | 0.360749i | \(0.882521\pi\) | |||||||
\(90\) | −3.27620 | − | 3.52619i | −0.0364022 | − | 0.0391799i | ||||
\(91\) | −287.188 | −3.15591 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 109.935 | − | 109.935i | 1.18209 | − | 1.18209i | ||||
\(94\) | 40.5412i | 0.431289i | ||||||||
\(95\) | 141.621 | + | 5.20451i | 1.49074 | + | 0.0547843i | ||||
\(96\) | −17.6006 | −0.183340 | ||||||||
\(97\) | −98.3956 | − | 98.3956i | −1.01439 | − | 1.01439i | −0.999895 | − | 0.0144922i | \(-0.995387\pi\) |
−0.0144922 | − | 0.999895i | \(-0.504613\pi\) | |||||||
\(98\) | −90.6862 | + | 90.6862i | −0.925370 | + | 0.925370i | ||||
\(99\) | − | 3.30468i | − | 0.0333806i | ||||||
\(100\) | 3.67001 | − | 49.8651i | 0.0367001 | − | 0.498651i | ||||
\(101\) | −133.352 | −1.32032 | −0.660159 | − | 0.751126i | \(-0.729511\pi\) | ||||
−0.660159 | + | 0.751126i | \(0.729511\pi\) | |||||||
\(102\) | −40.3181 | − | 40.3181i | −0.395275 | − | 0.395275i | ||||
\(103\) | 95.9912 | − | 95.9912i | 0.931953 | − | 0.931953i | −0.0658749 | − | 0.997828i | \(-0.520984\pi\) |
0.997828 | + | 0.0658749i | \(0.0209838\pi\) | |||||||
\(104\) | 68.7281i | 0.660847i | ||||||||
\(105\) | −6.75244 | + | 183.741i | −0.0643089 | + | 1.74992i | ||||
\(106\) | −68.1033 | −0.642484 | ||||||||
\(107\) | 93.8519 | + | 93.8519i | 0.877120 | + | 0.877120i | 0.993236 | − | 0.116116i | \(-0.0370443\pi\) |
−0.116116 | + | 0.993236i | \(0.537044\pi\) | |||||||
\(108\) | −36.6062 | + | 36.6062i | −0.338947 | + | 0.338947i | ||||
\(109\) | − | 201.194i | − | 1.84582i | −0.385021 | − | 0.922908i | \(-0.625806\pi\) | ||
0.385021 | − | 0.922908i | \(-0.374194\pi\) | |||||||
\(110\) | 25.1493 | − | 23.3664i | 0.228630 | − | 0.212422i | ||||
\(111\) | −66.2812 | −0.597128 | ||||||||
\(112\) | 33.4289 | + | 33.4289i | 0.298472 | + | 0.298472i | ||||
\(113\) | 52.4333 | − | 52.4333i | 0.464012 | − | 0.464012i | −0.435956 | − | 0.899968i | \(-0.643590\pi\) |
0.899968 | + | 0.435956i | \(0.143590\pi\) | |||||||
\(114\) | 124.715i | 1.09399i | ||||||||
\(115\) | −16.3217 | − | 17.5671i | −0.141928 | − | 0.152757i | ||||
\(116\) | −33.5901 | −0.289570 | ||||||||
\(117\) | −11.6958 | − | 11.6958i | −0.0999639 | − | 0.0999639i | ||||
\(118\) | 67.5325 | − | 67.5325i | 0.572310 | − | 0.572310i | ||||
\(119\) | 153.152i | 1.28699i | ||||||||
\(120\) | 43.9719 | + | 1.61595i | 0.366433 | + | 0.0134663i | ||||
\(121\) | −97.4305 | −0.805211 | ||||||||
\(122\) | −10.1955 | − | 10.1955i | −0.0835697 | − | 0.0835697i | ||||
\(123\) | 96.6804 | − | 96.6804i | 0.786020 | − | 0.786020i | ||||
\(124\) | 99.9371i | 0.805944i | ||||||||
\(125\) | −13.7471 | + | 124.242i | −0.109977 | + | 0.993934i | ||||
\(126\) | −11.3775 | −0.0902975 | ||||||||
\(127\) | −41.9177 | − | 41.9177i | −0.330061 | − | 0.330061i | 0.522549 | − | 0.852609i | \(-0.324981\pi\) |
−0.852609 | + | 0.522549i | \(0.824981\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 23.0168i | 0.178425i | ||||||||
\(130\) | 6.31008 | − | 171.704i | 0.0485391 | − | 1.32080i | ||||
\(131\) | 222.893 | 1.70147 | 0.850737 | − | 0.525591i | \(-0.176156\pi\) | ||||
0.850737 | + | 0.525591i | \(0.176156\pi\) | |||||||
\(132\) | 21.3621 | + | 21.3621i | 0.161834 | + | 0.161834i | ||||
\(133\) | 236.871 | − | 236.871i | 1.78098 | − | 1.78098i | ||||
\(134\) | 36.0869i | 0.269305i | ||||||||
\(135\) | 94.8148 | − | 88.0930i | 0.702332 | − | 0.652541i | ||||
\(136\) | 36.6515 | 0.269496 | ||||||||
\(137\) | −0.0309506 | − | 0.0309506i | −0.000225917 | − | 0.000225917i | 0.706994 | − | 0.707220i | \(-0.250051\pi\) |
−0.707220 | + | 0.706994i | \(0.750051\pi\) | |||||||
\(138\) | 14.9217 | − | 14.9217i | 0.108128 | − | 0.108128i | ||||
\(139\) | − | 40.4927i | − | 0.291314i | −0.989335 | − | 0.145657i | \(-0.953470\pi\) | ||
0.989335 | − | 0.145657i | \(-0.0465297\pi\) | |||||||
\(140\) | −80.4466 | − | 86.5850i | −0.574619 | − | 0.618464i | ||||
\(141\) | 89.1938 | 0.632580 | ||||||||
\(142\) | 21.4957 | + | 21.4957i | 0.151378 | + | 0.151378i | ||||
\(143\) | 83.4161 | − | 83.4161i | 0.583329 | − | 0.583329i | ||||
\(144\) | 2.72279i | 0.0189083i | ||||||||
\(145\) | 83.9187 | + | 3.08399i | 0.578750 | + | 0.0212689i | ||||
\(146\) | −42.9632 | −0.294269 | ||||||||
\(147\) | 199.517 | + | 199.517i | 1.35726 | + | 1.35726i | ||||
\(148\) | 30.1268 | − | 30.1268i | 0.203559 | − | 0.203559i | ||||
\(149\) | − | 52.8325i | − | 0.354581i | −0.984159 | − | 0.177290i | \(-0.943267\pi\) | ||
0.984159 | − | 0.177290i | \(-0.0567332\pi\) | |||||||
\(150\) | −109.707 | − | 8.07432i | −0.731382 | − | 0.0538288i | ||||
\(151\) | −180.168 | −1.19317 | −0.596583 | − | 0.802551i | \(-0.703475\pi\) | ||||
−0.596583 | + | 0.802551i | \(0.703475\pi\) | |||||||
\(152\) | −56.6864 | − | 56.6864i | −0.372937 | − | 0.372937i | ||||
\(153\) | −6.23715 | + | 6.23715i | −0.0407657 | + | 0.0407657i | ||||
\(154\) | − | 81.1460i | − | 0.526922i | ||||||
\(155\) | 9.17545 | − | 249.674i | 0.0591964 | − | 1.61080i | ||||
\(156\) | 151.207 | 0.969278 | ||||||||
\(157\) | 111.835 | + | 111.835i | 0.712323 | + | 0.712323i | 0.967021 | − | 0.254698i | \(-0.0819759\pi\) |
−0.254698 | + | 0.967021i | \(0.581976\pi\) | |||||||
\(158\) | −113.271 | + | 113.271i | −0.716904 | + | 0.716904i | ||||
\(159\) | 149.833i | 0.942344i | ||||||||
\(160\) | −20.7210 | + | 19.2520i | −0.129506 | + | 0.120325i | ||||
\(161\) | −56.6814 | −0.352059 | ||||||||
\(162\) | 86.6629 | + | 86.6629i | 0.534956 | + | 0.534956i | ||||
\(163\) | 5.10164 | − | 5.10164i | 0.0312984 | − | 0.0312984i | −0.691284 | − | 0.722583i | \(-0.742955\pi\) |
0.722583 | + | 0.691284i | \(0.242955\pi\) | |||||||
\(164\) | 87.8881i | 0.535903i | ||||||||
\(165\) | −51.4079 | − | 55.3305i | −0.311563 | − | 0.335336i | ||||
\(166\) | −91.2805 | −0.549883 | ||||||||
\(167\) | 73.6717 | + | 73.6717i | 0.441148 | + | 0.441148i | 0.892398 | − | 0.451250i | \(-0.149022\pi\) |
−0.451250 | + | 0.892398i | \(0.649022\pi\) | |||||||
\(168\) | 73.5462 | − | 73.5462i | 0.437775 | − | 0.437775i | ||||
\(169\) | − | 421.444i | − | 2.49375i | ||||||
\(170\) | −91.5669 | − | 3.36505i | −0.538629 | − | 0.0197944i | ||||
\(171\) | 19.2932 | 0.112826 | ||||||||
\(172\) | −10.4618 | − | 10.4618i | −0.0608245 | − | 0.0608245i | ||||
\(173\) | −88.0277 | + | 88.0277i | −0.508831 | + | 0.508831i | −0.914168 | − | 0.405337i | \(-0.867154\pi\) |
0.405337 | + | 0.914168i | \(0.367154\pi\) | |||||||
\(174\) | 73.9010i | 0.424718i | ||||||||
\(175\) | 193.031 | + | 223.702i | 1.10304 | + | 1.27830i | ||||
\(176\) | −19.4194 | −0.110337 | ||||||||
\(177\) | −148.577 | − | 148.577i | −0.839418 | − | 0.839418i | ||||
\(178\) | −64.2133 | + | 64.2133i | −0.360749 | + | 0.360749i | ||||
\(179\) | 322.864i | 1.80371i | 0.432038 | + | 0.901856i | \(0.357795\pi\) | ||||
−0.432038 | + | 0.901856i | \(0.642205\pi\) | |||||||
\(180\) | 0.249986 | − | 6.80239i | 0.00138881 | − | 0.0377910i | ||||
\(181\) | 114.556 | 0.632904 | 0.316452 | − | 0.948609i | \(-0.397508\pi\) | ||||
0.316452 | + | 0.948609i | \(0.397508\pi\) | |||||||
\(182\) | −287.188 | − | 287.188i | −1.57796 | − | 1.57796i | ||||
\(183\) | −22.4309 | + | 22.4309i | −0.122573 | + | 0.122573i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −78.0321 | + | 72.5001i | −0.421795 | + | 0.391892i | ||||
\(186\) | 219.870 | 1.18209 | ||||||||
\(187\) | −44.4843 | − | 44.4843i | −0.237884 | − | 0.237884i | ||||
\(188\) | −40.5412 | + | 40.5412i | −0.215644 | + | 0.215644i | ||||
\(189\) | − | 305.926i | − | 1.61866i | ||||||
\(190\) | 136.416 | + | 146.825i | 0.717979 | + | 0.772763i | ||||
\(191\) | 228.537 | 1.19653 | 0.598265 | − | 0.801298i | \(-0.295857\pi\) | ||||
0.598265 | + | 0.801298i | \(0.295857\pi\) | |||||||
\(192\) | −17.6006 | − | 17.6006i | −0.0916700 | − | 0.0916700i | ||||
\(193\) | 44.2681 | − | 44.2681i | 0.229368 | − | 0.229368i | −0.583061 | − | 0.812429i | \(-0.698145\pi\) |
0.812429 | + | 0.583061i | \(0.198145\pi\) | |||||||
\(194\) | − | 196.791i | − | 1.01439i | ||||||
\(195\) | −377.763 | − | 13.8827i | −1.93725 | − | 0.0711932i | ||||
\(196\) | −181.372 | −0.925370 | ||||||||
\(197\) | 108.253 | + | 108.253i | 0.549507 | + | 0.549507i | 0.926298 | − | 0.376791i | \(-0.122973\pi\) |
−0.376791 | + | 0.926298i | \(0.622973\pi\) | |||||||
\(198\) | 3.30468 | − | 3.30468i | 0.0166903 | − | 0.0166903i | ||||
\(199\) | − | 54.1132i | − | 0.271925i | −0.990714 | − | 0.135963i | \(-0.956587\pi\) | ||
0.990714 | − | 0.135963i | \(-0.0434127\pi\) | |||||||
\(200\) | 53.5351 | − | 46.1951i | 0.267676 | − | 0.230976i | ||||
\(201\) | 79.3941 | 0.394995 | ||||||||
\(202\) | −133.352 | − | 133.352i | −0.660159 | − | 0.660159i | ||||
\(203\) | 140.360 | − | 140.360i | 0.691429 | − | 0.691429i | ||||
\(204\) | − | 80.6361i | − | 0.395275i | ||||||
\(205\) | 8.06921 | − | 219.572i | 0.0393620 | − | 1.07108i | ||||
\(206\) | 191.982 | 0.931953 | ||||||||
\(207\) | −2.30836 | − | 2.30836i | −0.0111515 | − | 0.0111515i | ||||
\(208\) | −68.7281 | + | 68.7281i | −0.330424 | + | 0.330424i | ||||
\(209\) | 137.602i | 0.658382i | ||||||||
\(210\) | −190.494 | + | 176.989i | −0.907114 | + | 0.842805i | ||||
\(211\) | −318.790 | −1.51085 | −0.755426 | − | 0.655234i | \(-0.772570\pi\) | ||||
−0.755426 | + | 0.655234i | \(0.772570\pi\) | |||||||
\(212\) | −68.1033 | − | 68.1033i | −0.321242 | − | 0.321242i | ||||
\(213\) | 47.2923 | − | 47.2923i | 0.222029 | − | 0.222029i | ||||
\(214\) | 187.704i | 0.877120i | ||||||||
\(215\) | 25.1764 | + | 27.0974i | 0.117099 | + | 0.126035i | ||||
\(216\) | −73.2125 | −0.338947 | ||||||||
\(217\) | −417.598 | − | 417.598i | −1.92442 | − | 1.92442i | ||||
\(218\) | 201.194 | − | 201.194i | 0.922908 | − | 0.922908i | ||||
\(219\) | 94.5225i | 0.431610i | ||||||||
\(220\) | 48.5157 | + | 1.78294i | 0.220526 | + | 0.00810425i | ||||
\(221\) | −314.873 | −1.42477 | ||||||||
\(222\) | −66.2812 | − | 66.2812i | −0.298564 | − | 0.298564i | ||||
\(223\) | −115.343 | + | 115.343i | −0.517235 | + | 0.517235i | −0.916734 | − | 0.399499i | \(-0.869184\pi\) |
0.399499 | + | 0.916734i | \(0.369184\pi\) | |||||||
\(224\) | 66.8578i | 0.298472i | ||||||||
\(225\) | −1.24908 | + | 16.9715i | −0.00555149 | + | 0.0754291i | ||||
\(226\) | 104.867 | 0.464012 | ||||||||
\(227\) | 57.9945 | + | 57.9945i | 0.255482 | + | 0.255482i | 0.823214 | − | 0.567732i | \(-0.192179\pi\) |
−0.567732 | + | 0.823214i | \(0.692179\pi\) | |||||||
\(228\) | −124.715 | + | 124.715i | −0.546994 | + | 0.546994i | ||||
\(229\) | − | 320.751i | − | 1.40066i | −0.713820 | − | 0.700329i | \(-0.753037\pi\) | ||
0.713820 | − | 0.700329i | \(-0.246963\pi\) | |||||||
\(230\) | 1.24540 | − | 33.8888i | 0.00541479 | − | 0.147342i | ||||
\(231\) | −178.528 | −0.772847 | ||||||||
\(232\) | −33.5901 | − | 33.5901i | −0.144785 | − | 0.144785i | ||||
\(233\) | 111.290 | − | 111.290i | 0.477638 | − | 0.477638i | −0.426738 | − | 0.904375i | \(-0.640337\pi\) |
0.904375 | + | 0.426738i | \(0.140337\pi\) | |||||||
\(234\) | − | 23.3915i | − | 0.0999639i | ||||||
\(235\) | 105.007 | − | 97.5624i | 0.446837 | − | 0.415159i | ||||
\(236\) | 135.065 | 0.572310 | ||||||||
\(237\) | 249.205 | + | 249.205i | 1.05150 | + | 1.05150i | ||||
\(238\) | −153.152 | + | 153.152i | −0.643497 | + | 0.643497i | ||||
\(239\) | 249.659i | 1.04460i | 0.852762 | + | 0.522300i | \(0.174926\pi\) | ||||
−0.852762 | + | 0.522300i | \(0.825074\pi\) | |||||||
\(240\) | 42.3559 | + | 45.5879i | 0.176483 | + | 0.189949i | ||||
\(241\) | 105.175 | 0.436411 | 0.218206 | − | 0.975903i | \(-0.429980\pi\) | ||||
0.218206 | + | 0.975903i | \(0.429980\pi\) | |||||||
\(242\) | −97.4305 | − | 97.4305i | −0.402605 | − | 0.402605i | ||||
\(243\) | 25.9372 | − | 25.9372i | 0.106737 | − | 0.106737i | ||||
\(244\) | − | 20.3910i | − | 0.0835697i | ||||||
\(245\) | 453.125 | + | 16.6522i | 1.84949 | + | 0.0679682i | ||||
\(246\) | 193.361 | 0.786020 | ||||||||
\(247\) | 486.994 | + | 486.994i | 1.97164 | + | 1.97164i | ||||
\(248\) | −99.9371 | + | 99.9371i | −0.402972 | + | 0.402972i | ||||
\(249\) | 200.824i | 0.806524i | ||||||||
\(250\) | −137.989 | + | 110.495i | −0.551955 | + | 0.441979i | ||||
\(251\) | −114.474 | −0.456071 | −0.228036 | − | 0.973653i | \(-0.573230\pi\) | ||||
−0.228036 | + | 0.973653i | \(0.573230\pi\) | |||||||
\(252\) | −11.3775 | − | 11.3775i | −0.0451487 | − | 0.0451487i | ||||
\(253\) | 16.4636 | − | 16.4636i | 0.0650734 | − | 0.0650734i | ||||
\(254\) | − | 83.8355i | − | 0.330061i | ||||||
\(255\) | −7.40339 | + | 201.454i | −0.0290329 | + | 0.790017i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −159.057 | − | 159.057i | −0.618901 | − | 0.618901i | 0.326349 | − | 0.945249i | \(-0.394182\pi\) |
−0.945249 | + | 0.326349i | \(0.894182\pi\) | |||||||
\(258\) | −23.0168 | + | 23.0168i | −0.0892126 | + | 0.0892126i | ||||
\(259\) | 251.776i | 0.972108i | ||||||||
\(260\) | 178.014 | − | 165.394i | 0.684671 | − | 0.636132i | ||||
\(261\) | 11.4324 | 0.0438022 | ||||||||
\(262\) | 222.893 | + | 222.893i | 0.850737 | + | 0.850737i | ||||
\(263\) | −41.8699 | + | 41.8699i | −0.159201 | + | 0.159201i | −0.782213 | − | 0.623012i | \(-0.785909\pi\) |
0.623012 | + | 0.782213i | \(0.285909\pi\) | |||||||
\(264\) | 42.7242i | 0.161834i | ||||||||
\(265\) | 163.891 | + | 176.396i | 0.618455 | + | 0.665646i | ||||
\(266\) | 473.741 | 1.78098 | ||||||||
\(267\) | 141.274 | + | 141.274i | 0.529117 | + | 0.529117i | ||||
\(268\) | −36.0869 | + | 36.0869i | −0.134653 | + | 0.134653i | ||||
\(269\) | 354.532i | 1.31796i | 0.752160 | + | 0.658981i | \(0.229012\pi\) | ||||
−0.752160 | + | 0.658981i | \(0.770988\pi\) | |||||||
\(270\) | 182.908 | + | 6.72180i | 0.677436 | + | 0.0248956i | ||||
\(271\) | −179.845 | −0.663636 | −0.331818 | − | 0.943343i | \(-0.607662\pi\) | ||||
−0.331818 | + | 0.943343i | \(0.607662\pi\) | |||||||
\(272\) | 36.6515 | + | 36.6515i | 0.134748 | + | 0.134748i | ||||
\(273\) | −631.836 | + | 631.836i | −2.31442 | + | 2.31442i | ||||
\(274\) | − | 0.0619011i | − | 0.000225917i | ||||||
\(275\) | −121.044 | − | 8.90867i | −0.440159 | − | 0.0323952i | ||||
\(276\) | 29.8433 | 0.108128 | ||||||||
\(277\) | −308.660 | − | 308.660i | −1.11429 | − | 1.11429i | −0.992563 | − | 0.121732i | \(-0.961155\pi\) |
−0.121732 | − | 0.992563i | \(-0.538845\pi\) | |||||||
\(278\) | 40.4927 | − | 40.4927i | 0.145657 | − | 0.145657i | ||||
\(279\) | − | 34.0135i | − | 0.121912i | ||||||
\(280\) | 6.13836 | − | 167.032i | 0.0219227 | − | 0.596542i | ||||
\(281\) | 156.370 | 0.556478 | 0.278239 | − | 0.960512i | \(-0.410249\pi\) | ||||
0.278239 | + | 0.960512i | \(0.410249\pi\) | |||||||
\(282\) | 89.1938 | + | 89.1938i | 0.316290 | + | 0.316290i | ||||
\(283\) | −125.940 | + | 125.940i | −0.445016 | + | 0.445016i | −0.893694 | − | 0.448678i | \(-0.851895\pi\) |
0.448678 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(284\) | 42.9914i | 0.151378i | ||||||||
\(285\) | 323.027 | − | 300.126i | 1.13343 | − | 1.05307i | ||||
\(286\) | 166.832 | 0.583329 | ||||||||
\(287\) | −367.250 | − | 367.250i | −1.27962 | − | 1.27962i | ||||
\(288\) | −2.72279 | + | 2.72279i | −0.00945414 | + | 0.00945414i | ||||
\(289\) | − | 121.084i | − | 0.418975i | ||||||
\(290\) | 80.8347 | + | 87.0027i | 0.278740 | + | 0.300009i | ||||
\(291\) | −432.956 | −1.48782 | ||||||||
\(292\) | −42.9632 | − | 42.9632i | −0.147134 | − | 0.147134i | ||||
\(293\) | −150.158 | + | 150.158i | −0.512485 | + | 0.512485i | −0.915287 | − | 0.402802i | \(-0.868036\pi\) |
0.402802 | + | 0.915287i | \(0.368036\pi\) | |||||||
\(294\) | 399.034i | 1.35726i | ||||||||
\(295\) | −337.435 | − | 12.4006i | −1.14385 | − | 0.0420360i | ||||
\(296\) | 60.2535 | 0.203559 | ||||||||
\(297\) | 88.8588 | + | 88.8588i | 0.299188 | + | 0.299188i | ||||
\(298\) | 52.8325 | − | 52.8325i | 0.177290 | − | 0.177290i | ||||
\(299\) | − | 116.534i | − | 0.389746i | ||||||
\(300\) | −101.633 | − | 117.782i | −0.338776 | − | 0.392605i | ||||
\(301\) | 87.4317 | 0.290471 | ||||||||
\(302\) | −180.168 | − | 180.168i | −0.596583 | − | 0.596583i | ||||
\(303\) | −293.385 | + | 293.385i | −0.968268 | + | 0.968268i | ||||
\(304\) | − | 113.373i | − | 0.372937i | ||||||
\(305\) | −1.87214 | + | 50.9431i | −0.00613818 | + | 0.167027i | ||||
\(306\) | −12.4743 | −0.0407657 | ||||||||
\(307\) | −159.257 | − | 159.257i | −0.518753 | − | 0.518753i | 0.398441 | − | 0.917194i | \(-0.369551\pi\) |
−0.917194 | + | 0.398441i | \(0.869551\pi\) | |||||||
\(308\) | 81.1460 | − | 81.1460i | 0.263461 | − | 0.263461i | ||||
\(309\) | − | 422.376i | − | 1.36691i | ||||||
\(310\) | 258.850 | − | 240.499i | 0.834999 | − | 0.775802i | ||||
\(311\) | −153.824 | −0.494610 | −0.247305 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247305 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(312\) | 151.207 | + | 151.207i | 0.484639 | + | 0.484639i | ||||
\(313\) | −330.942 | + | 330.942i | −1.05732 | + | 1.05732i | −0.0590683 | + | 0.998254i | \(0.518813\pi\) |
−0.998254 | + | 0.0590683i | \(0.981187\pi\) | |||||||
\(314\) | 223.669i | 0.712323i | ||||||||
\(315\) | 27.3799 | + | 29.4691i | 0.0869204 | + | 0.0935528i | ||||
\(316\) | −226.542 | −0.716904 | ||||||||
\(317\) | 372.744 | + | 372.744i | 1.17585 | + | 1.17585i | 0.980792 | + | 0.195056i | \(0.0624889\pi\) |
0.195056 | + | 0.980792i | \(0.437511\pi\) | |||||||
\(318\) | −149.833 | + | 149.833i | −0.471172 | + | 0.471172i | ||||
\(319\) | 81.5374i | 0.255603i | ||||||||
\(320\) | −39.9730 | − | 1.46900i | −0.124916 | − | 0.00459061i | ||||
\(321\) | 412.963 | 1.28649 | ||||||||
\(322\) | −56.6814 | − | 56.6814i | −0.176029 | − | 0.176029i | ||||
\(323\) | 259.705 | − | 259.705i | 0.804041 | − | 0.804041i | ||||
\(324\) | 173.326i | 0.534956i | ||||||||
\(325\) | −459.921 | + | 396.863i | −1.41514 | + | 1.22112i | ||||
\(326\) | 10.2033 | 0.0312984 | ||||||||
\(327\) | −442.643 | − | 442.643i | −1.35365 | − | 1.35365i | ||||
\(328\) | −87.8881 | + | 87.8881i | −0.267952 | + | 0.267952i | ||||
\(329\) | − | 338.811i | − | 1.02982i | ||||||
\(330\) | 3.92260 | − | 106.738i | 0.0118867 | − | 0.323450i | ||||
\(331\) | −286.269 | −0.864861 | −0.432430 | − | 0.901667i | \(-0.642344\pi\) | ||||
−0.432430 | + | 0.901667i | \(0.642344\pi\) | |||||||
\(332\) | −91.2805 | − | 91.2805i | −0.274941 | − | 0.274941i | ||||
\(333\) | −10.2536 | + | 10.2536i | −0.0307916 | + | 0.0307916i | ||||
\(334\) | 147.343i | 0.441148i | ||||||||
\(335\) | 93.4697 | − | 86.8432i | 0.279014 | − | 0.259234i | ||||
\(336\) | 147.092 | 0.437775 | ||||||||
\(337\) | −41.4913 | − | 41.4913i | −0.123120 | − | 0.123120i | 0.642862 | − | 0.765982i | \(-0.277747\pi\) |
−0.765982 | + | 0.642862i | \(0.777747\pi\) | |||||||
\(338\) | 421.444 | − | 421.444i | 1.24688 | − | 1.24688i | ||||
\(339\) | − | 230.715i | − | 0.680575i | ||||||
\(340\) | −88.2018 | − | 94.9319i | −0.259417 | − | 0.279212i | ||||
\(341\) | 242.589 | 0.711406 | ||||||||
\(342\) | 19.2932 | + | 19.2932i | 0.0564128 | + | 0.0564128i | ||||
\(343\) | 348.381 | − | 348.381i | 1.01569 | − | 1.01569i | ||||
\(344\) | − | 20.9236i | − | 0.0608245i | ||||||
\(345\) | −74.5580 | − | 2.73998i | −0.216110 | − | 0.00794198i | ||||
\(346\) | −176.055 | −0.508831 | ||||||||
\(347\) | −393.288 | − | 393.288i | −1.13339 | − | 1.13339i | −0.989609 | − | 0.143785i | \(-0.954073\pi\) |
−0.143785 | − | 0.989609i | \(-0.545927\pi\) | |||||||
\(348\) | −73.9010 | + | 73.9010i | −0.212359 | + | 0.212359i | ||||
\(349\) | 61.6981i | 0.176785i | 0.996086 | + | 0.0883927i | \(0.0281730\pi\) | ||||
−0.996086 | + | 0.0883927i | \(0.971827\pi\) | |||||||
\(350\) | −30.6711 | + | 416.734i | −0.0876317 | + | 1.19067i | ||||
\(351\) | 628.970 | 1.79194 | ||||||||
\(352\) | −19.4194 | − | 19.4194i | −0.0551687 | − | 0.0551687i | ||||
\(353\) | −148.629 | + | 148.629i | −0.421045 | + | 0.421045i | −0.885563 | − | 0.464519i | \(-0.846227\pi\) |
0.464519 | + | 0.885563i | \(0.346227\pi\) | |||||||
\(354\) | − | 297.154i | − | 0.839418i | ||||||
\(355\) | 3.94714 | − | 107.406i | 0.0111187 | − | 0.302552i | ||||
\(356\) | −128.427 | −0.360749 | ||||||||
\(357\) | 336.947 | + | 336.947i | 0.943829 | + | 0.943829i | ||||
\(358\) | −322.864 | + | 322.864i | −0.901856 | + | 0.901856i | ||||
\(359\) | 133.489i | 0.371836i | 0.982565 | + | 0.185918i | \(0.0595259\pi\) | ||||
−0.982565 | + | 0.185918i | \(0.940474\pi\) | |||||||
\(360\) | 7.05237 | − | 6.55240i | 0.0195899 | − | 0.0182011i | ||||
\(361\) | −442.338 | −1.22531 | ||||||||
\(362\) | 114.556 | + | 114.556i | 0.316452 | + | 0.316452i | ||||
\(363\) | −214.355 | + | 214.355i | −0.590509 | + | 0.590509i | ||||
\(364\) | − | 574.376i | − | 1.57796i | ||||||
\(365\) | 103.391 | + | 111.280i | 0.283263 | + | 0.304877i | ||||
\(366\) | −44.8618 | −0.122573 | ||||||||
\(367\) | 159.240 | + | 159.240i | 0.433895 | + | 0.433895i | 0.889951 | − | 0.456056i | \(-0.150738\pi\) |
−0.456056 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 29.9126i | − | 0.0810641i | ||||||
\(370\) | −150.532 | − | 5.53201i | −0.406844 | − | 0.0149514i | ||||
\(371\) | 569.154 | 1.53411 | ||||||||
\(372\) | 219.870 | + | 219.870i | 0.591047 | + | 0.591047i | ||||
\(373\) | −340.134 | + | 340.134i | −0.911888 | + | 0.911888i | −0.996421 | − | 0.0845323i | \(-0.973060\pi\) |
0.0845323 | + | 0.996421i | \(0.473060\pi\) | |||||||
\(374\) | − | 88.9686i | − | 0.237884i | ||||||
\(375\) | 243.097 | + | 303.586i | 0.648259 | + | 0.809564i | ||||
\(376\) | −81.0823 | −0.215644 | ||||||||
\(377\) | 288.573 | + | 288.573i | 0.765447 | + | 0.765447i | ||||
\(378\) | 305.926 | − | 305.926i | 0.809329 | − | 0.809329i | ||||
\(379\) | 578.294i | 1.52584i | 0.646492 | + | 0.762921i | \(0.276235\pi\) | ||||
−0.646492 | + | 0.762921i | \(0.723765\pi\) | |||||||
\(380\) | −10.4090 | + | 283.241i | −0.0273922 | + | 0.745371i | ||||
\(381\) | −184.445 | −0.484107 | ||||||||
\(382\) | 228.537 | + | 228.537i | 0.598265 | + | 0.598265i | ||||
\(383\) | 41.1217 | − | 41.1217i | 0.107367 | − | 0.107367i | −0.651382 | − | 0.758750i | \(-0.725811\pi\) |
0.758750 | + | 0.651382i | \(0.225811\pi\) | |||||||
\(384\) | − | 35.2013i | − | 0.0916700i | ||||||
\(385\) | −210.178 | + | 195.278i | −0.545918 | + | 0.507215i | ||||
\(386\) | 88.5361 | 0.229368 | ||||||||
\(387\) | 3.56067 | + | 3.56067i | 0.00920070 | + | 0.00920070i | ||||
\(388\) | 196.791 | − | 196.791i | 0.507194 | − | 0.507194i | ||||
\(389\) | − | 539.251i | − | 1.38625i | −0.720818 | − | 0.693124i | \(-0.756234\pi\) | ||
0.720818 | − | 0.693124i | \(-0.243766\pi\) | |||||||
\(390\) | −363.881 | − | 391.646i | −0.933027 | − | 1.00422i | ||||
\(391\) | −62.1456 | −0.158940 | ||||||||
\(392\) | −181.372 | − | 181.372i | −0.462685 | − | 0.462685i | ||||
\(393\) | 490.383 | − | 490.383i | 1.24779 | − | 1.24779i | ||||
\(394\) | 216.506i | 0.549507i | ||||||||
\(395\) | 565.972 | + | 20.7993i | 1.43284 | + | 0.0526565i | ||||
\(396\) | 6.60936 | 0.0166903 | ||||||||
\(397\) | −122.141 | − | 122.141i | −0.307659 | − | 0.307659i | 0.536342 | − | 0.844001i | \(-0.319806\pi\) |
−0.844001 | + | 0.536342i | \(0.819806\pi\) | |||||||
\(398\) | 54.1132 | − | 54.1132i | 0.135963 | − | 0.135963i | ||||
\(399\) | − | 1042.27i | − | 2.61220i | ||||||
\(400\) | 99.7303 | + | 7.34002i | 0.249326 | + | 0.0183501i | ||||
\(401\) | −190.196 | −0.474305 | −0.237152 | − | 0.971472i | \(-0.576214\pi\) | ||||
−0.237152 | + | 0.971472i | \(0.576214\pi\) | |||||||
\(402\) | 79.3941 | + | 79.3941i | 0.197498 | + | 0.197498i | ||||
\(403\) | 858.561 | − | 858.561i | 2.13042 | − | 2.13042i | ||||
\(404\) | − | 266.704i | − | 0.660159i | ||||||
\(405\) | 15.9134 | − | 433.022i | 0.0392924 | − | 1.06919i | ||||
\(406\) | 280.720 | 0.691429 | ||||||||
\(407\) | −73.1303 | − | 73.1303i | −0.179681 | − | 0.179681i | ||||
\(408\) | 80.6361 | − | 80.6361i | 0.197638 | − | 0.197638i | ||||
\(409\) | − | 350.710i | − | 0.857482i | −0.903427 | − | 0.428741i | \(-0.858957\pi\) | ||
0.903427 | − | 0.428741i | \(-0.141043\pi\) | |||||||
\(410\) | 227.641 | − | 211.503i | 0.555223 | − | 0.515861i | ||||
\(411\) | −0.136187 | −0.000331356 | ||||||||
\(412\) | 191.982 | + | 191.982i | 0.465976 | + | 0.465976i | ||||
\(413\) | −564.384 | + | 564.384i | −1.36655 | + | 1.36655i | ||||
\(414\) | − | 4.61672i | − | 0.0111515i | ||||||
\(415\) | 219.667 | + | 236.428i | 0.529317 | + | 0.569706i | ||||
\(416\) | −137.456 | −0.330424 | ||||||||
\(417\) | −89.0872 | − | 89.0872i | −0.213638 | − | 0.213638i | ||||
\(418\) | −137.602 | + | 137.602i | −0.329191 | + | 0.329191i | ||||
\(419\) | − | 747.433i | − | 1.78385i | −0.452183 | − | 0.891925i | \(-0.649355\pi\) | ||
0.452183 | − | 0.891925i | \(-0.350645\pi\) | |||||||
\(420\) | −367.483 | − | 13.5049i | −0.874959 | − | 0.0321545i | ||||
\(421\) | 283.686 | 0.673839 | 0.336919 | − | 0.941534i | \(-0.390615\pi\) | ||||
0.336919 | + | 0.941534i | \(0.390615\pi\) | |||||||
\(422\) | −318.790 | − | 318.790i | −0.755426 | − | 0.755426i | ||||
\(423\) | 13.7981 | − | 13.7981i | 0.0326197 | − | 0.0326197i | ||||
\(424\) | − | 136.207i | − | 0.321242i | ||||||
\(425\) | 211.640 | + | 245.268i | 0.497976 | + | 0.577101i | ||||
\(426\) | 94.5845 | 0.222029 | ||||||||
\(427\) | 85.2060 | + | 85.2060i | 0.199546 | + | 0.199546i | ||||
\(428\) | −187.704 | + | 187.704i | −0.438560 | + | 0.438560i | ||||
\(429\) | − | 367.044i | − | 0.855580i | ||||||
\(430\) | −1.92105 | + | 52.2738i | −0.00446755 | + | 0.121567i | ||||
\(431\) | −47.3290 | −0.109812 | −0.0549061 | − | 0.998492i | \(-0.517486\pi\) | ||||
−0.0549061 | + | 0.998492i | \(0.517486\pi\) | |||||||
\(432\) | −73.2125 | − | 73.2125i | −0.169473 | − | 0.169473i | ||||
\(433\) | −160.083 | + | 160.083i | −0.369706 | + | 0.369706i | −0.867370 | − | 0.497664i | \(-0.834191\pi\) |
0.497664 | + | 0.867370i | \(0.334191\pi\) | |||||||
\(434\) | − | 835.196i | − | 1.92442i | ||||||
\(435\) | 191.413 | − | 177.843i | 0.440029 | − | 0.408834i | ||||
\(436\) | 402.388 | 0.922908 | ||||||||
\(437\) | 96.1165 | + | 96.1165i | 0.219946 | + | 0.219946i | ||||
\(438\) | −94.5225 | + | 94.5225i | −0.215805 | + | 0.215805i | ||||
\(439\) | − | 298.531i | − | 0.680026i | −0.940421 | − | 0.340013i | \(-0.889569\pi\) | ||
0.940421 | − | 0.340013i | \(-0.110431\pi\) | |||||||
\(440\) | 46.7327 | + | 50.2986i | 0.106211 | + | 0.114315i | ||||
\(441\) | 61.7299 | 0.139977 | ||||||||
\(442\) | −314.873 | − | 314.873i | −0.712383 | − | 0.712383i | ||||
\(443\) | −215.423 | + | 215.423i | −0.486282 | + | 0.486282i | −0.907131 | − | 0.420849i | \(-0.861732\pi\) |
0.420849 | + | 0.907131i | \(0.361732\pi\) | |||||||
\(444\) | − | 132.562i | − | 0.298564i | ||||||
\(445\) | 320.850 | + | 11.7911i | 0.721011 | + | 0.0264969i | ||||
\(446\) | −230.687 | −0.517235 | ||||||||
\(447\) | −116.236 | − | 116.236i | −0.260035 | − | 0.260035i | ||||
\(448\) | −66.8578 | + | 66.8578i | −0.149236 | + | 0.149236i | ||||
\(449\) | − | 143.978i | − | 0.320664i | −0.987063 | − | 0.160332i | \(-0.948744\pi\) | ||
0.987063 | − | 0.160332i | \(-0.0512564\pi\) | |||||||
\(450\) | −18.2206 | + | 15.7225i | −0.0404903 | + | 0.0349388i | ||||
\(451\) | 213.342 | 0.473041 | ||||||||
\(452\) | 104.867 | + | 104.867i | 0.232006 | + | 0.232006i | ||||
\(453\) | −396.384 | + | 396.384i | −0.875020 | + | 0.875020i | ||||
\(454\) | 115.989i | 0.255482i | ||||||||
\(455\) | −52.7347 | + | 1434.97i | −0.115901 | + | 3.15378i | ||||
\(456\) | −249.429 | −0.546994 | ||||||||
\(457\) | 275.771 | + | 275.771i | 0.603437 | + | 0.603437i | 0.941223 | − | 0.337786i | \(-0.109678\pi\) |
−0.337786 | + | 0.941223i | \(0.609678\pi\) | |||||||
\(458\) | 320.751 | − | 320.751i | 0.700329 | − | 0.700329i | ||||
\(459\) | − | 335.418i | − | 0.730759i | ||||||
\(460\) | 35.1342 | − | 32.6434i | 0.0763786 | − | 0.0709639i | ||||
\(461\) | 52.7338 | 0.114390 | 0.0571950 | − | 0.998363i | \(-0.481784\pi\) | ||||
0.0571950 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(462\) | −178.528 | − | 178.528i | −0.386423 | − | 0.386423i | ||||
\(463\) | −192.059 | + | 192.059i | −0.414814 | + | 0.414814i | −0.883412 | − | 0.468598i | \(-0.844759\pi\) |
0.468598 | + | 0.883412i | \(0.344759\pi\) | |||||||
\(464\) | − | 67.1803i | − | 0.144785i | ||||||
\(465\) | −529.116 | − | 569.490i | −1.13788 | − | 1.22471i | ||||
\(466\) | 222.579 | 0.477638 | ||||||||
\(467\) | 73.1687 | + | 73.1687i | 0.156678 | + | 0.156678i | 0.781093 | − | 0.624415i | \(-0.214662\pi\) |
−0.624415 | + | 0.781093i | \(0.714662\pi\) | |||||||
\(468\) | 23.3915 | − | 23.3915i | 0.0499819 | − | 0.0499819i | ||||
\(469\) | − | 301.586i | − | 0.643041i | ||||||
\(470\) | 202.569 | + | 7.44435i | 0.430998 | + | 0.0158390i | ||||
\(471\) | 492.091 | 1.04478 | ||||||||
\(472\) | 135.065 | + | 135.065i | 0.286155 | + | 0.286155i | ||||
\(473\) | −25.3953 | + | 25.3953i | −0.0536898 | + | 0.0536898i | ||||
\(474\) | 498.410i | 1.05150i | ||||||||
\(475\) | 52.0100 | − | 706.669i | 0.109495 | − | 1.48772i | ||||
\(476\) | −306.304 | −0.643497 | ||||||||
\(477\) | 23.1789 | + | 23.1789i | 0.0485931 | + | 0.0485931i | ||||
\(478\) | −249.659 | + | 249.659i | −0.522300 | + | 0.522300i | ||||
\(479\) | 99.9056i | 0.208571i | 0.994547 | + | 0.104286i | \(0.0332556\pi\) | ||||
−0.994547 | + | 0.104286i | \(0.966744\pi\) | |||||||
\(480\) | −3.23191 | + | 87.9438i | −0.00673314 | + | 0.183216i | ||||
\(481\) | −517.639 | −1.07617 | ||||||||
\(482\) | 105.175 | + | 105.175i | 0.218206 | + | 0.218206i | ||||
\(483\) | −124.704 | + | 124.704i | −0.258186 | + | 0.258186i | ||||
\(484\) | − | 194.861i | − | 0.402605i | ||||||
\(485\) | −509.714 | + | 473.578i | −1.05096 | + | 0.976450i | ||||
\(486\) | 51.8744 | 0.106737 | ||||||||
\(487\) | 186.182 | + | 186.182i | 0.382304 | + | 0.382304i | 0.871932 | − | 0.489628i | \(-0.162867\pi\) |
−0.489628 | + | 0.871932i | \(0.662867\pi\) | |||||||
\(488\) | 20.3910 | − | 20.3910i | 0.0417848 | − | 0.0417848i | ||||
\(489\) | − | 22.4480i | − | 0.0459060i | ||||||
\(490\) | 436.473 | + | 469.777i | 0.890761 | + | 0.958730i | ||||
\(491\) | 593.353 | 1.20846 | 0.604229 | − | 0.796811i | \(-0.293481\pi\) | ||||
0.604229 | + | 0.796811i | \(0.293481\pi\) | |||||||
\(492\) | 193.361 | + | 193.361i | 0.393010 | + | 0.393010i | ||||
\(493\) | 153.891 | − | 153.891i | 0.312152 | − | 0.312152i | ||||
\(494\) | 973.988i | 1.97164i | ||||||||
\(495\) | −16.5123 | − | 0.606820i | −0.0333581 | − | 0.00122590i | ||||
\(496\) | −199.874 | −0.402972 | ||||||||
\(497\) | −179.644 | − | 179.644i | −0.361458 | − | 0.361458i | ||||
\(498\) | −200.824 | + | 200.824i | −0.403262 | + | 0.403262i | ||||
\(499\) | 757.209i | 1.51745i | 0.651410 | + | 0.758726i | \(0.274178\pi\) | ||||
−0.651410 | + | 0.758726i | \(0.725822\pi\) | |||||||
\(500\) | −248.484 | − | 27.4941i | −0.496967 | − | 0.0549883i | ||||
\(501\) | 324.167 | 0.647041 | ||||||||
\(502\) | −114.474 | − | 114.474i | −0.228036 | − | 0.228036i | ||||
\(503\) | 243.599 | − | 243.599i | 0.484293 | − | 0.484293i | −0.422207 | − | 0.906500i | \(-0.638744\pi\) |
0.906500 | + | 0.422207i | \(0.138744\pi\) | |||||||
\(504\) | − | 22.7550i | − | 0.0451487i | ||||||
\(505\) | −24.4867 | + | 666.311i | −0.0484885 | + | 1.31943i | ||||
\(506\) | 32.9271 | 0.0650734 | ||||||||
\(507\) | −927.211 | − | 927.211i | −1.82882 | − | 1.82882i | ||||
\(508\) | 83.8355 | − | 83.8355i | 0.165030 | − | 0.165030i | ||||
\(509\) | 955.807i | 1.87781i | 0.344172 | + | 0.938906i | \(0.388160\pi\) | ||||
−0.344172 | + | 0.938906i | \(0.611840\pi\) | |||||||
\(510\) | −208.858 | + | 194.051i | −0.409525 | + | 0.380492i | ||||
\(511\) | 359.053 | 0.702648 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −518.770 | + | 518.770i | −1.01125 | + | 1.01125i | ||||
\(514\) | − | 318.115i | − | 0.618901i | ||||||
\(515\) | −462.006 | − | 497.258i | −0.897098 | − | 0.965550i | ||||
\(516\) | −46.0337 | −0.0892126 | ||||||||
\(517\) | 98.4105 | + | 98.4105i | 0.190349 | + | 0.190349i | ||||
\(518\) | −251.776 | + | 251.776i | −0.486054 | + | 0.486054i | ||||
\(519\) | 387.336i | 0.746312i | ||||||||
\(520\) | 343.409 | + | 12.6202i | 0.660401 | + | 0.0242695i | ||||
\(521\) | −383.665 | −0.736402 | −0.368201 | − | 0.929746i | \(-0.620026\pi\) | ||||
−0.368201 | + | 0.929746i | \(0.620026\pi\) | |||||||
\(522\) | 11.4324 | + | 11.4324i | 0.0219011 | + | 0.0219011i | ||||
\(523\) | 233.552 | − | 233.552i | 0.446563 | − | 0.446563i | −0.447647 | − | 0.894210i | \(-0.647738\pi\) |
0.894210 | + | 0.447647i | \(0.147738\pi\) | |||||||
\(524\) | 445.786i | 0.850737i | ||||||||
\(525\) | 916.847 | + | 67.4788i | 1.74638 | + | 0.128531i | ||||
\(526\) | −83.7398 | −0.159201 | ||||||||
\(527\) | −457.855 | − | 457.855i | −0.868796 | − | 0.868796i | ||||
\(528\) | −42.7242 | + | 42.7242i | −0.0809170 | + | 0.0809170i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −12.5054 | + | 340.287i | −0.0235952 | + | 0.642051i | ||||
\(531\) | −45.9693 | −0.0865711 | ||||||||
\(532\) | 473.741 | + | 473.741i | 0.890491 | + | 0.890491i | ||||
\(533\) | 755.048 | − | 755.048i | 1.41660 | − | 1.41660i | ||||
\(534\) | 282.549i | 0.529117i | ||||||||
\(535\) | 486.176 | − | 451.709i | 0.908741 | − | 0.844316i | ||||
\(536\) | −72.1738 | −0.134653 | ||||||||
\(537\) | 710.327 | + | 710.327i | 1.32277 | + | 1.32277i | ||||
\(538\) | −354.532 | + | 354.532i | −0.658981 | + | 0.658981i | ||||
\(539\) | 440.267i | 0.816823i | ||||||||
\(540\) | 176.186 | + | 189.630i | 0.326270 | + | 0.351166i | ||||
\(541\) | 99.6220 | 0.184144 | 0.0920721 | − | 0.995752i | \(-0.470651\pi\) | ||||
0.0920721 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(542\) | −179.845 | − | 179.845i | −0.331818 | − | 0.331818i | ||||
\(543\) | 252.031 | − | 252.031i | 0.464146 | − | 0.464146i | ||||
\(544\) | 73.3029i | 0.134748i | ||||||||
\(545\) | −1005.29 | − | 36.9441i | −1.84457 | − | 0.0677874i | ||||
\(546\) | −1263.67 | −2.31442 | ||||||||
\(547\) | −171.342 | − | 171.342i | −0.313240 | − | 0.313240i | 0.532924 | − | 0.846163i | \(-0.321093\pi\) |
−0.846163 | + | 0.532924i | \(0.821093\pi\) | |||||||
\(548\) | 0.0619011 | − | 0.0619011i | 0.000112958 | − | 0.000112958i | ||||
\(549\) | 6.94006i | 0.0126413i | ||||||||
\(550\) | −112.135 | − | 129.952i | −0.203882 | − | 0.236277i | ||||
\(551\) | −476.026 | −0.863932 | ||||||||
\(552\) | 29.8433 | + | 29.8433i | 0.0540640 | + | 0.0540640i | ||||
\(553\) | 946.629 | − | 946.629i | 1.71181 | − | 1.71181i | ||||
\(554\) | − | 617.319i | − | 1.11429i | ||||||
\(555\) | −12.1709 | + | 331.183i | −0.0219295 | + | 0.596726i | ||||
\(556\) | 80.9854 | 0.145657 | ||||||||
\(557\) | −236.687 | − | 236.687i | −0.424932 | − | 0.424932i | 0.461966 | − | 0.886898i | \(-0.347144\pi\) |
−0.886898 | + | 0.461966i | \(0.847144\pi\) | |||||||
\(558\) | 34.0135 | − | 34.0135i | 0.0609561 | − | 0.0609561i | ||||
\(559\) | 179.755i | 0.321566i | ||||||||
\(560\) | 173.170 | − | 160.893i | 0.309232 | − | 0.287309i | ||||
\(561\) | −195.738 | −0.348909 | ||||||||
\(562\) | 156.370 | + | 156.370i | 0.278239 | + | 0.278239i | ||||
\(563\) | −627.002 | + | 627.002i | −1.11368 | + | 1.11368i | −0.121032 | + | 0.992649i | \(0.538620\pi\) |
−0.992649 | + | 0.121032i | \(0.961380\pi\) | |||||||
\(564\) | 178.388i | 0.316290i | ||||||||
\(565\) | −252.362 | − | 271.618i | −0.446658 | − | 0.480739i | ||||
\(566\) | −251.879 | −0.445016 | ||||||||
\(567\) | −724.261 | − | 724.261i | −1.27736 | − | 1.27736i | ||||
\(568\) | −42.9914 | + | 42.9914i | −0.0756891 | + | 0.0756891i | ||||
\(569\) | 694.665i | 1.22085i | 0.792073 | + | 0.610426i | \(0.209002\pi\) | ||||
−0.792073 | + | 0.610426i | \(0.790998\pi\) | |||||||
\(570\) | 623.153 | + | 22.9007i | 1.09325 | + | 0.0401766i | ||||
\(571\) | −1107.18 | −1.93902 | −0.969512 | − | 0.245043i | \(-0.921198\pi\) | ||||
−0.969512 | + | 0.245043i | \(0.921198\pi\) | |||||||
\(572\) | 166.832 | + | 166.832i | 0.291665 | + | 0.291665i | ||||
\(573\) | 502.800 | − | 502.800i | 0.877487 | − | 0.877487i | ||||
\(574\) | − | 734.500i | − | 1.27962i | ||||||
\(575\) | −90.7732 | + | 78.3276i | −0.157867 | + | 0.136222i | ||||
\(576\) | −5.44558 | −0.00945414 | ||||||||
\(577\) | 82.5531 | + | 82.5531i | 0.143073 | + | 0.143073i | 0.775015 | − | 0.631942i | \(-0.217742\pi\) |
−0.631942 | + | 0.775015i | \(0.717742\pi\) | |||||||
\(578\) | 121.084 | − | 121.084i | 0.209487 | − | 0.209487i | ||||
\(579\) | − | 194.787i | − | 0.336419i | ||||||
\(580\) | −6.16797 | + | 167.837i | −0.0106344 | + | 0.289375i | ||||
\(581\) | 762.851 | 1.31300 | ||||||||
\(582\) | −432.956 | − | 432.956i | −0.743911 | − | 0.743911i | ||||
\(583\) | −165.315 | + | 165.315i | −0.283560 | + | 0.283560i | ||||
\(584\) | − | 85.9265i | − | 0.147134i | ||||||
\(585\) | −60.5870 | + | 56.2918i | −0.103568 | + | 0.0962253i | ||||
\(586\) | −300.316 | −0.512485 | ||||||||
\(587\) | 569.570 | + | 569.570i | 0.970306 | + | 0.970306i | 0.999572 | − | 0.0292653i | \(-0.00931676\pi\) |
−0.0292653 | + | 0.999572i | \(0.509317\pi\) | |||||||
\(588\) | −399.034 | + | 399.034i | −0.678629 | + | 0.678629i | ||||
\(589\) | 1416.27i | 2.40453i | ||||||||
\(590\) | −325.034 | − | 349.836i | −0.550906 | − | 0.592942i | ||||
\(591\) | 476.330 | 0.805972 | ||||||||
\(592\) | 60.2535 | + | 60.2535i | 0.101780 | + | 0.101780i | ||||
\(593\) | −713.467 | + | 713.467i | −1.20315 | + | 1.20315i | −0.229945 | + | 0.973204i | \(0.573855\pi\) |
−0.973204 | + | 0.229945i | \(0.926145\pi\) | |||||||
\(594\) | 177.718i | 0.299188i | ||||||||
\(595\) | 765.244 | + | 28.1225i | 1.28613 | + | 0.0472647i | ||||
\(596\) | 105.665 | 0.177290 | ||||||||
\(597\) | −119.053 | − | 119.053i | −0.199419 | − | 0.199419i | ||||
\(598\) | 116.534 | − | 116.534i | 0.194873 | − | 0.194873i | ||||
\(599\) | − | 128.311i | − | 0.214209i | −0.994248 | − | 0.107104i | \(-0.965842\pi\) | ||
0.994248 | − | 0.107104i | \(-0.0341579\pi\) | |||||||
\(600\) | 16.1486 | − | 219.414i | 0.0269144 | − | 0.365691i | ||||
\(601\) | 845.916 | 1.40751 | 0.703757 | − | 0.710440i | \(-0.251504\pi\) | ||||
0.703757 | + | 0.710440i | \(0.251504\pi\) | |||||||
\(602\) | 87.4317 | + | 87.4317i | 0.145235 | + | 0.145235i | ||||
\(603\) | 12.2821 | − | 12.2821i | 0.0203684 | − | 0.0203684i | ||||
\(604\) | − | 360.336i | − | 0.596583i | ||||||
\(605\) | −17.8906 | + | 486.824i | −0.0295713 | + | 0.804668i | ||||
\(606\) | −586.771 | −0.968268 | ||||||||
\(607\) | −693.618 | − | 693.618i | −1.14270 | − | 1.14270i | −0.987955 | − | 0.154745i | \(-0.950545\pi\) |
−0.154745 | − | 0.987955i | \(-0.549455\pi\) | |||||||
\(608\) | 113.373 | − | 113.373i | 0.186469 | − | 0.186469i | ||||
\(609\) | − | 617.607i | − | 1.01413i | ||||||
\(610\) | −52.8153 | + | 49.0710i | −0.0865824 | + | 0.0804442i | ||||
\(611\) | 696.579 | 1.14006 | ||||||||
\(612\) | −12.4743 | − | 12.4743i | −0.0203828 | − | 0.0203828i | ||||
\(613\) | 83.2281 | − | 83.2281i | 0.135772 | − | 0.135772i | −0.635955 | − | 0.771726i | \(-0.719393\pi\) |
0.771726 | + | 0.635955i | \(0.219393\pi\) | |||||||
\(614\) | − | 318.514i | − | 0.518753i | ||||||
\(615\) | −465.323 | − | 500.829i | −0.756623 | − | 0.814356i | ||||
\(616\) | 162.292 | 0.263461 | ||||||||
\(617\) | −309.635 | − | 309.635i | −0.501840 | − | 0.501840i | 0.410169 | − | 0.912009i | \(-0.365470\pi\) |
−0.912009 | + | 0.410169i | \(0.865470\pi\) | |||||||
\(618\) | 422.376 | − | 422.376i | 0.683457 | − | 0.683457i | ||||
\(619\) | 965.745i | 1.56017i | 0.625674 | + | 0.780085i | \(0.284824\pi\) | ||||
−0.625674 | + | 0.780085i | \(0.715176\pi\) | |||||||
\(620\) | 499.348 | + | 18.3509i | 0.805401 | + | 0.0295982i | ||||
\(621\) | 124.138 | 0.199900 | ||||||||
\(622\) | −153.824 | − | 153.824i | −0.247305 | − | 0.247305i | ||||
\(623\) | 536.645 | − | 536.645i | 0.861388 | − | 0.861388i | ||||
\(624\) | 302.415i | 0.484639i | ||||||||
\(625\) | 618.266 | + | 91.5028i | 0.989225 | + | 0.146404i | ||||
\(626\) | −661.884 | −1.05732 | ||||||||
\(627\) | 302.735 | + | 302.735i | 0.482831 | + | 0.482831i | ||||
\(628\) | −223.669 | + | 223.669i | −0.356162 | + | 0.356162i | ||||
\(629\) | 276.047i | 0.438867i | ||||||||
\(630\) | −2.08918 | + | 56.8490i | −0.00331617 | + | 0.0902366i | ||||
\(631\) | −36.9891 | −0.0586199 | −0.0293099 | − | 0.999570i | \(-0.509331\pi\) | ||||
−0.0293099 | + | 0.999570i | \(0.509331\pi\) | |||||||
\(632\) | −226.542 | − | 226.542i | −0.358452 | − | 0.358452i | ||||
\(633\) | −701.363 | + | 701.363i | −1.10800 | + | 1.10800i | ||||
\(634\) | 745.488i | 1.17585i | ||||||||
\(635\) | −217.144 | + | 201.750i | −0.341960 | + | 0.317717i | ||||
\(636\) | −299.665 | −0.471172 | ||||||||
\(637\) | 1558.17 | + | 1558.17i | 2.44611 | + | 2.44611i | ||||
\(638\) | −81.5374 | + | 81.5374i | −0.127802 | + | 0.127802i | ||||
\(639\) | − | 14.6321i | − | 0.0228984i | ||||||
\(640\) | −38.5040 | − | 41.4420i | −0.0601625 | − | 0.0647531i | ||||
\(641\) | −343.983 | −0.536635 | −0.268317 | − | 0.963331i | \(-0.586468\pi\) | ||||
−0.268317 | + | 0.963331i | \(0.586468\pi\) | |||||||
\(642\) | 412.963 | + | 412.963i | 0.643245 | + | 0.643245i | ||||
\(643\) | 307.618 | − | 307.618i | 0.478411 | − | 0.478411i | −0.426212 | − | 0.904623i | \(-0.640152\pi\) |
0.904623 | + | 0.426212i | \(0.140152\pi\) | |||||||
\(644\) | − | 113.363i | − | 0.176029i | ||||||
\(645\) | 115.007 | + | 4.22645i | 0.178305 | + | 0.00655264i | ||||
\(646\) | 519.410 | 0.804041 | ||||||||
\(647\) | −169.670 | − | 169.670i | −0.262241 | − | 0.262241i | 0.563723 | − | 0.825964i | \(-0.309369\pi\) |
−0.825964 | + | 0.563723i | \(0.809369\pi\) | |||||||
\(648\) | −173.326 | + | 173.326i | −0.267478 | + | 0.267478i | ||||
\(649\) | − | 327.860i | − | 0.505177i | ||||||
\(650\) | −856.784 | − | 63.0583i | −1.31813 | − | 0.0970127i | ||||
\(651\) | −1837.50 | −2.82258 | ||||||||
\(652\) | 10.2033 | + | 10.2033i | 0.0156492 | + | 0.0156492i | ||||
\(653\) | 417.861 | − | 417.861i | 0.639909 | − | 0.639909i | −0.310624 | − | 0.950533i | \(-0.600538\pi\) |
0.950533 | + | 0.310624i | \(0.100538\pi\) | |||||||
\(654\) | − | 885.285i | − | 1.35365i | ||||||
\(655\) | 40.9286 | − | 1113.71i | 0.0624865 | − | 1.70033i | ||||
\(656\) | −175.776 | −0.267952 | ||||||||
\(657\) | 14.6225 | + | 14.6225i | 0.0222565 | + | 0.0222565i | ||||
\(658\) | 338.811 | − | 338.811i | 0.514911 | − | 0.514911i | ||||
\(659\) | 483.607i | 0.733849i | 0.930251 | + | 0.366925i | \(0.119589\pi\) | ||||
−0.930251 | + | 0.366925i | \(0.880411\pi\) | |||||||
\(660\) | 110.661 | − | 102.816i | 0.167668 | − | 0.155781i | ||||
\(661\) | 692.421 | 1.04754 | 0.523768 | − | 0.851861i | \(-0.324526\pi\) | ||||
0.523768 | + | 0.851861i | \(0.324526\pi\) | |||||||
\(662\) | −286.269 | − | 286.269i | −0.432430 | − | 0.432430i | ||||
\(663\) | −692.746 | + | 692.746i | −1.04487 | + | 1.04487i | ||||
\(664\) | − | 182.561i | − | 0.274941i | ||||||
\(665\) | −1140.06 | − | 1227.05i | −1.71437 | − | 1.84519i | ||||
\(666\) | −20.5072 | −0.0307916 | ||||||||
\(667\) | 56.9549 | + | 56.9549i | 0.0853896 | + | 0.0853896i | ||||
\(668\) | −147.343 | + | 147.343i | −0.220574 | + | 0.220574i | ||||
\(669\) | 507.529i | 0.758639i | ||||||||
\(670\) | 180.313 | + | 6.62644i | 0.269124 | + | 0.00989021i | ||||
\(671\) | −49.4976 | −0.0737669 | ||||||||
\(672\) | 147.092 | + | 147.092i | 0.218887 | + | 0.218887i | ||||
\(673\) | −225.899 | + | 225.899i | −0.335660 | + | 0.335660i | −0.854731 | − | 0.519071i | \(-0.826278\pi\) |
0.519071 | + | 0.854731i | \(0.326278\pi\) | |||||||
\(674\) | − | 82.9826i | − | 0.123120i | ||||||
\(675\) | −422.757 | − | 489.930i | −0.626307 | − | 0.725822i | ||||
\(676\) | 842.888 | 1.24688 | ||||||||
\(677\) | −384.203 | − | 384.203i | −0.567508 | − | 0.567508i | 0.363922 | − | 0.931429i | \(-0.381437\pi\) |
−0.931429 | + | 0.363922i | \(0.881437\pi\) | |||||||
\(678\) | 230.715 | − | 230.715i | 0.340288 | − | 0.340288i | ||||
\(679\) | 1644.63i | 2.42213i | ||||||||
\(680\) | 6.73011 | − | 183.134i | 0.00989722 | − | 0.269314i | ||||
\(681\) | 255.185 | 0.374721 | ||||||||
\(682\) | 242.589 | + | 242.589i | 0.355703 | + | 0.355703i | ||||
\(683\) | 902.944 | − | 902.944i | 1.32203 | − | 1.32203i | 0.409893 | − | 0.912133i | \(-0.365566\pi\) |
0.912133 | − | 0.409893i | \(-0.134434\pi\) | |||||||
\(684\) | 38.5864i | 0.0564128i | ||||||||
\(685\) | −0.160332 | + | 0.148965i | −0.000234061 | + | 0.000217467i | ||||
\(686\) | 696.762 | 1.01569 | ||||||||
\(687\) | −705.677 | − | 705.677i | −1.02719 | − | 1.02719i | ||||
\(688\) | 20.9236 | − | 20.9236i | 0.0304123 | − | 0.0304123i | ||||
\(689\) | 1170.15i | 1.69834i | ||||||||
\(690\) | −71.8180 | − | 77.2980i | −0.104084 | − | 0.112026i | ||||
\(691\) | 621.287 | 0.899113 | 0.449557 | − | 0.893252i | \(-0.351582\pi\) | ||||
0.449557 | + | 0.893252i | \(0.351582\pi\) | |||||||
\(692\) | −176.055 | − | 176.055i | −0.254415 | − | 0.254415i | ||||
\(693\) | −27.6180 | + | 27.6180i | −0.0398527 | + | 0.0398527i | ||||
\(694\) | − | 786.575i | − | 1.13339i | ||||||
\(695\) | −202.327 | − | 7.43545i | −0.291118 | − | 0.0106985i | ||||
\(696\) | −147.802 | −0.212359 | ||||||||
\(697\) | −402.654 | − | 402.654i | −0.577695 | − | 0.577695i | ||||
\(698\) | −61.6981 | + | 61.6981i | −0.0883927 | + | 0.0883927i | ||||
\(699\) | − | 489.692i | − | 0.700561i | ||||||
\(700\) | −447.405 | + | 386.063i | −0.639150 | + | 0.551518i | ||||
\(701\) | 754.563 | 1.07641 | 0.538205 | − | 0.842814i | \(-0.319103\pi\) | ||||
0.538205 | + | 0.842814i | \(0.319103\pi\) | |||||||
\(702\) | 628.970 | + | 628.970i | 0.895968 | + | 0.895968i | ||||
\(703\) | 426.945 | − | 426.945i | 0.607318 | − | 0.607318i | ||||
\(704\) | − | 38.8387i | − | 0.0551687i | ||||||
\(705\) | 16.3782 | − | 445.668i | 0.0232314 | − | 0.632153i | ||||
\(706\) | −297.258 | −0.421045 | ||||||||
\(707\) | 1114.45 | + | 1114.45i | 1.57631 | + | 1.57631i | ||||
\(708\) | 297.154 | − | 297.154i | 0.419709 | − | 0.419709i | ||||
\(709\) | − | 789.221i | − | 1.11315i | −0.830798 | − | 0.556574i | \(-0.812116\pi\) | ||
0.830798 | − | 0.556574i | \(-0.187884\pi\) | |||||||
\(710\) | 111.353 | − | 103.459i | 0.156835 | − | 0.145717i | ||||
\(711\) | 77.1033 | 0.108443 | ||||||||
\(712\) | −128.427 | − | 128.427i | −0.180374 | − | 0.180374i | ||||
\(713\) | 169.452 | − | 169.452i | 0.237660 | − | 0.237660i | ||||
\(714\) | 673.894i | 0.943829i | ||||||||
\(715\) | −401.482 | − | 432.116i | −0.561513 | − | 0.604358i | ||||
\(716\) | −645.729 | −0.901856 | ||||||||
\(717\) | 549.270 | + | 549.270i | 0.766067 | + | 0.766067i | ||||
\(718\) | −133.489 | + | 133.489i | −0.185918 | + | 0.185918i | ||||
\(719\) | − | 904.423i | − | 1.25789i | −0.777450 | − | 0.628945i | \(-0.783487\pi\) | ||
0.777450 | − | 0.628945i | \(-0.216513\pi\) | |||||||
\(720\) | 13.6048 | + | 0.499971i | 0.0188955 | + | 0.000694404i | ||||
\(721\) | −1604.44 | −2.22530 | ||||||||
\(722\) | −442.338 | − | 442.338i | −0.612657 | − | 0.612657i | ||||
\(723\) | 231.394 | − | 231.394i | 0.320046 | − | 0.320046i | ||||
\(724\) | 229.111i | 0.316452i | ||||||||
\(725\) | 30.8191 | − | 418.744i | 0.0425090 | − | 0.577578i | ||||
\(726\) | −428.710 | −0.590509 | ||||||||
\(727\) | −80.8538 | − | 80.8538i | −0.111216 | − | 0.111216i | 0.649309 | − | 0.760525i | \(-0.275058\pi\) |
−0.760525 | + | 0.649309i | \(0.775058\pi\) | |||||||
\(728\) | 574.376 | − | 574.376i | 0.788978 | − | 0.788978i | ||||
\(729\) | 665.839i | 0.913359i | ||||||||
\(730\) | −7.88910 | + | 214.671i | −0.0108070 | + | 0.294070i | ||||
\(731\) | 95.8603 | 0.131136 | ||||||||
\(732\) | −44.8618 | − | 44.8618i | −0.0612866 | − | 0.0612866i | ||||
\(733\) | 3.67038 | − | 3.67038i | 0.00500735 | − | 0.00500735i | −0.704599 | − | 0.709606i | \(-0.748873\pi\) |
0.709606 | + | 0.704599i | \(0.248873\pi\) | |||||||
\(734\) | 318.479i | 0.433895i | ||||||||
\(735\) | 1033.55 | − | 960.275i | 1.40619 | − | 1.30650i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 87.5982 | + | 87.5982i | 0.118858 | + | 0.118858i | ||||
\(738\) | 29.9126 | − | 29.9126i | 0.0405320 | − | 0.0405320i | ||||
\(739\) | 13.1697i | 0.0178209i | 0.999960 | + | 0.00891047i | \(0.00283633\pi\) | ||||
−0.999960 | + | 0.00891047i | \(0.997164\pi\) | |||||||
\(740\) | −145.000 | − | 156.064i | −0.195946 | − | 0.210898i | ||||
\(741\) | 2142.85 | 2.89184 | ||||||||
\(742\) | 569.154 | + | 569.154i | 0.767054 | + | 0.767054i | ||||
\(743\) | −519.149 | + | 519.149i | −0.698720 | + | 0.698720i | −0.964134 | − | 0.265414i | \(-0.914491\pi\) |
0.265414 | + | 0.964134i | \(0.414491\pi\) | |||||||
\(744\) | 439.739i | 0.591047i | ||||||||
\(745\) | −263.985 | − | 9.70135i | −0.354342 | − | 0.0130219i | ||||
\(746\) | −680.269 | −0.911888 | ||||||||
\(747\) | 31.0672 | + | 31.0672i | 0.0415893 | + | 0.0415893i | ||||
\(748\) | 88.9686 | − | 88.9686i | 0.118942 | − | 0.118942i | ||||
\(749\) | − | 1568.68i | − | 2.09437i | ||||||
\(750\) | −60.4893 | + | 546.684i | −0.0806524 | + | 0.728911i | ||||
\(751\) | 1.54655 | 0.00205932 | 0.00102966 | − | 0.999999i | \(-0.499672\pi\) | ||||
0.00102966 | + | 0.999999i | \(0.499672\pi\) | |||||||
\(752\) | −81.0823 | − | 81.0823i | −0.107822 | − | 0.107822i | ||||
\(753\) | −251.852 | + | 251.852i | −0.334464 | + | 0.334464i | ||||
\(754\) | 577.147i | 0.765447i | ||||||||
\(755\) | −33.0833 | + | 900.233i | −0.0438189 | + | 1.19236i | ||||
\(756\) | 611.853 | 0.809329 | ||||||||
\(757\) | −354.268 | − | 354.268i | −0.467989 | − | 0.467989i | 0.433273 | − | 0.901263i | \(-0.357358\pi\) |
−0.901263 | + | 0.433273i | \(0.857358\pi\) | |||||||
\(758\) | −578.294 | + | 578.294i | −0.762921 | + | 0.762921i | ||||
\(759\) | − | 72.4423i | − | 0.0954445i | ||||||
\(760\) | −293.650 | + | 272.832i | −0.386382 | + | 0.358990i | ||||
\(761\) | 409.762 | 0.538452 | 0.269226 | − | 0.963077i | \(-0.413232\pi\) | ||||
0.269226 | + | 0.963077i | \(0.413232\pi\) | |||||||
\(762\) | −184.445 | − | 184.445i | −0.242053 | − | 0.242053i | ||||
\(763\) | −1681.42 | + | 1681.42i | −2.20370 | + | 2.20370i | ||||
\(764\) | 457.075i | 0.598265i | ||||||||
\(765\) | 30.0194 | + | 32.3100i | 0.0392410 | + | 0.0422353i | ||||
\(766\) | 82.2434 | 0.107367 | ||||||||
\(767\) | −1160.35 | − | 1160.35i | −1.51284 | − | 1.51284i | ||||
\(768\) | 35.2013 | − | 35.2013i | 0.0458350 | − | 0.0458350i | ||||
\(769\) | − | 386.028i | − | 0.501987i | −0.967989 | − | 0.250994i | \(-0.919243\pi\) | ||
0.967989 | − | 0.250994i | \(-0.0807573\pi\) | |||||||
\(770\) | −405.456 | − | 14.9004i | −0.526566 | − | 0.0193512i | ||||
\(771\) | −699.878 | −0.907753 | ||||||||
\(772\) | 88.5361 | + | 88.5361i | 0.114684 | + | 0.114684i | ||||
\(773\) | 1008.36 | − | 1008.36i | 1.30448 | − | 1.30448i | 0.379135 | − | 0.925341i | \(-0.376222\pi\) |
0.925341 | − | 0.379135i | \(-0.123778\pi\) | |||||||
\(774\) | 7.12134i | 0.00920070i | ||||||||
\(775\) | −1245.84 | − | 91.6926i | −1.60754 | − | 0.118313i | ||||
\(776\) | 393.582 | 0.507194 | ||||||||
\(777\) | 553.927 | + | 553.927i | 0.712905 | + | 0.712905i | ||||
\(778\) | 539.251 | − | 539.251i | 0.693124 | − | 0.693124i | ||||
\(779\) | 1245.52i | 1.59887i | ||||||||
\(780\) | 27.7654 | − | 755.526i | 0.0355966 | − | 0.968624i | ||||
\(781\) | 104.358 | 0.133621 | ||||||||
\(782\) | −62.1456 | − | 62.1456i | −0.0794701 | − | 0.0794701i | ||||
\(783\) | −307.402 | + | 307.402i | −0.392595 | + | 0.392595i | ||||
\(784\) | − | 362.745i | − | 0.462685i | ||||||
\(785\) | 579.332 | − | 538.261i | 0.738003 | − | 0.685683i | ||||
\(786\) | 980.765 | 1.24779 | ||||||||
\(787\) | 358.581 | + | 358.581i | 0.455630 | + | 0.455630i | 0.897218 | − | 0.441588i | \(-0.145585\pi\) |
−0.441588 | + | 0.897218i | \(0.645585\pi\) | |||||||
\(788\) | −216.506 | + | 216.506i | −0.274753 | + | 0.274753i | ||||
\(789\) | 184.234i | 0.233503i | ||||||||
\(790\) | 545.173 | + | 586.772i | 0.690092 | + | 0.742749i | ||||
\(791\) | −876.394 | −1.10796 | ||||||||
\(792\) | 6.60936 | + | 6.60936i | 0.00834516 | + | 0.00834516i | ||||
\(793\) | −175.179 | + | 175.179i | −0.220907 | + | 0.220907i | ||||
\(794\) | − | 244.281i | − | 0.307659i | ||||||
\(795\) | 748.658 | + | 27.5129i | 0.941708 | + | 0.0346075i | ||||
\(796\) | 108.226 | 0.135963 | ||||||||
\(797\) | −362.026 | − | 362.026i | −0.454236 | − | 0.454236i | 0.442522 | − | 0.896758i | \(-0.354084\pi\) |
−0.896758 | + | 0.442522i | \(0.854084\pi\) | |||||||
\(798\) | 1042.27 | − | 1042.27i | 1.30610 | − | 1.30610i | ||||
\(799\) | − | 371.473i | − | 0.464923i | ||||||
\(800\) | 92.3902 | + | 107.070i | 0.115488 | + | 0.133838i | ||||
\(801\) | 43.7099 | 0.0545691 | ||||||||
\(802\) | −190.196 | − | 190.196i | −0.237152 | − | 0.237152i | ||||
\(803\) | −104.290 | + | 104.290i | −0.129875 | + | 0.129875i | ||||
\(804\) | 158.788i | 0.197498i | ||||||||
\(805\) | −10.4081 | + | 283.216i | −0.0129293 | + | 0.351821i | ||||
\(806\) | 1717.12 | 2.13042 | ||||||||
\(807\) | 779.997 | + | 779.997i | 0.966540 | + | 0.966540i | ||||
\(808\) | 266.704 | − | 266.704i | 0.330080 | − | 0.330080i | ||||
\(809\) | − | 676.712i | − | 0.836479i | −0.908337 | − | 0.418240i | \(-0.862647\pi\) | ||
0.908337 | − | 0.418240i | \(-0.137353\pi\) | |||||||
\(810\) | 448.936 | − | 417.109i | 0.554242 | − | 0.514949i | ||||
\(811\) | −597.480 | −0.736720 | −0.368360 | − | 0.929683i | \(-0.620081\pi\) | ||||
−0.368360 | + | 0.929683i | \(0.620081\pi\) | |||||||
\(812\) | 280.720 | + | 280.720i | 0.345714 | + | 0.345714i | ||||
\(813\) | −395.674 | + | 395.674i | −0.486684 | + | 0.486684i | ||||
\(814\) | − | 146.261i | − | 0.179681i | ||||||
\(815\) | −24.5542 | − | 26.4278i | −0.0301278 | − | 0.0324267i | ||||
\(816\) | 161.272 | 0.197638 | ||||||||
\(817\) | −148.261 | − | 148.261i | −0.181470 | − | 0.181470i | ||||
\(818\) | 350.710 | − | 350.710i | 0.428741 | − | 0.428741i | ||||
\(819\) | 195.488i | 0.238691i | ||||||||
\(820\) | 439.144 | + | 16.1384i | 0.535542 | + | 0.0196810i | ||||
\(821\) | −731.016 | −0.890397 | −0.445199 | − | 0.895432i | \(-0.646867\pi\) | ||||
−0.445199 | + | 0.895432i | \(0.646867\pi\) | |||||||
\(822\) | −0.136187 | − | 0.136187i | −0.000165678 | − | 0.000165678i | ||||
\(823\) | −346.050 | + | 346.050i | −0.420474 | + | 0.420474i | −0.885367 | − | 0.464893i | \(-0.846093\pi\) |
0.464893 | + | 0.885367i | \(0.346093\pi\) | |||||||
\(824\) | 383.965i | 0.465976i | ||||||||
\(825\) | −285.905 | + | 246.706i | −0.346552 | + | 0.299038i | ||||
\(826\) | −1128.77 | −1.36655 | ||||||||
\(827\) | 209.168 | + | 209.168i | 0.252924 | + | 0.252924i | 0.822168 | − | 0.569245i | \(-0.192764\pi\) |
−0.569245 | + | 0.822168i | \(0.692764\pi\) | |||||||
\(828\) | 4.61672 | − | 4.61672i | 0.00557575 | − | 0.00557575i | ||||
\(829\) | − | 1158.20i | − | 1.39710i | −0.715561 | − | 0.698550i | \(-0.753829\pi\) | ||
0.715561 | − | 0.698550i | \(-0.246171\pi\) | |||||||
\(830\) | −16.7613 | + | 456.095i | −0.0201944 | + | 0.549512i | ||||
\(831\) | −1358.15 | −1.63436 | ||||||||
\(832\) | −137.456 | − | 137.456i | −0.165212 | − | 0.165212i | ||||
\(833\) | 830.946 | − | 830.946i | 0.997534 | − | 0.997534i | ||||
\(834\) | − | 178.174i | − | 0.213638i | ||||||
\(835\) | 381.638 | − | 354.582i | 0.457052 | − | 0.424649i | ||||
\(836\) | −275.204 | −0.329191 | ||||||||
\(837\) | 914.581 | + | 914.581i | 1.09269 | + | 1.09269i | ||||
\(838\) | 747.433 | − | 747.433i | 0.891925 | − | 0.891925i | ||||
\(839\) | − | 150.216i | − | 0.179042i | −0.995985 | − | 0.0895210i | \(-0.971466\pi\) | ||
0.995985 | − | 0.0895210i | \(-0.0285336\pi\) | |||||||
\(840\) | −353.978 | − | 380.988i | −0.421402 | − | 0.453557i | ||||
\(841\) | 558.926 | 0.664596 | ||||||||
\(842\) | 283.686 | + | 283.686i | 0.336919 | + | 0.336919i | ||||
\(843\) | 344.027 | − | 344.027i | 0.408099 | − | 0.408099i | ||||
\(844\) | − | 637.579i | − | 0.755426i | ||||||
\(845\) | −2105.80 | − | 77.3875i | −2.49207 | − | 0.0915828i | ||||
\(846\) | 27.5963 | 0.0326197 | ||||||||
\(847\) | 814.248 | + | 814.248i | 0.961332 | + | 0.961332i | ||||
\(848\) | 136.207 | − | 136.207i | 0.160621 | − | 0.160621i | ||||
\(849\) | 554.154i | 0.652714i | ||||||||
\(850\) | −33.6278 | + | 456.908i | −0.0395622 | + | 0.537538i | ||||
\(851\) | −102.165 | −0.120053 | ||||||||
\(852\) | 94.5845 | + | 94.5845i | 0.111015 | + | 0.111015i | ||||
\(853\) | −16.8839 | + | 16.8839i | −0.0197936 | + | 0.0197936i | −0.716934 | − | 0.697141i | \(-0.754455\pi\) |
0.697141 | + | 0.716934i | \(0.254455\pi\) | |||||||
\(854\) | 170.412i | 0.199546i | ||||||||
\(855\) | 3.54270 | − | 96.4008i | 0.00414351 | − | 0.112749i | ||||
\(856\) | −375.407 | −0.438560 | ||||||||
\(857\) | −943.212 | − | 943.212i | −1.10060 | − | 1.10060i | −0.994338 | − | 0.106259i | \(-0.966113\pi\) |
−0.106259 | − | 0.994338i | \(-0.533887\pi\) | |||||||
\(858\) | 367.044 | − | 367.044i | 0.427790 | − | 0.427790i | ||||
\(859\) | − | 1298.04i | − | 1.51110i | −0.655088 | − | 0.755552i | \(-0.727369\pi\) | ||
0.655088 | − | 0.755552i | \(-0.272631\pi\) | |||||||
\(860\) | −54.1949 | + | 50.3528i | −0.0630173 | + | 0.0585497i | ||||
\(861\) | −1615.96 | −1.87684 | ||||||||
\(862\) | −47.3290 | − | 47.3290i | −0.0549061 | − | 0.0549061i | ||||
\(863\) | 512.914 | − | 512.914i | 0.594338 | − | 0.594338i | −0.344462 | − | 0.938800i | \(-0.611939\pi\) |
0.938800 | + | 0.344462i | \(0.111939\pi\) | |||||||
\(864\) | − | 146.425i | − | 0.169473i | ||||||
\(865\) | 423.678 | + | 456.006i | 0.489801 | + | 0.527174i | ||||
\(866\) | −320.166 | −0.369706 | ||||||||
\(867\) | −266.394 | − | 266.394i | −0.307259 | − | 0.307259i | ||||
\(868\) | 835.196 | − | 835.196i | 0.962208 | − | 0.962208i | ||||
\(869\) | 549.912i | 0.632810i | ||||||||
\(870\) | 369.256 | + | 13.5700i | 0.424432 | + | 0.0155977i | ||||
\(871\) | 620.047 | 0.711879 | ||||||||
\(872\) | 402.388 | + | 402.388i | 0.461454 | + | 0.461454i | ||||
\(873\) | −66.9777 | + | 66.9777i | −0.0767213 | + | 0.0767213i | ||||
\(874\) | 192.233i | 0.219946i | ||||||||
\(875\) | 1153.20 | − | 923.428i | 1.31795 | − | 1.05535i | ||||
\(876\) | −189.045 | −0.215805 | ||||||||
\(877\) | −172.303 | − | 172.303i | −0.196469 | − | 0.196469i | 0.602015 | − | 0.798484i | \(-0.294365\pi\) |
−0.798484 | + | 0.602015i | \(0.794365\pi\) | |||||||
\(878\) | 298.531 | − | 298.531i | 0.340013 | − | 0.340013i | ||||
\(879\) | 660.719i | 0.751671i | ||||||||
\(880\) | −3.56587 | + | 97.0314i | −0.00405213 | + | 0.110263i | ||||
\(881\) | 723.223 | 0.820911 | 0.410456 | − | 0.911881i | \(-0.365370\pi\) | ||||
0.410456 | + | 0.911881i | \(0.365370\pi\) | |||||||
\(882\) | 61.7299 | + | 61.7299i | 0.0699886 | + | 0.0699886i | ||||
\(883\) | 1050.94 | − | 1050.94i | 1.19020 | − | 1.19020i | 0.213186 | − | 0.977012i | \(-0.431616\pi\) |
0.977012 | − | 0.213186i | \(-0.0683841\pi\) | |||||||
\(884\) | − | 629.747i | − | 0.712383i | ||||||
\(885\) | −769.666 | + | 715.101i | −0.869679 | + | 0.808024i | ||||
\(886\) | −430.846 | −0.486282 | ||||||||
\(887\) | −379.967 | − | 379.967i | −0.428373 | − | 0.428373i | 0.459701 | − | 0.888074i | \(-0.347957\pi\) |
−0.888074 | + | 0.459701i | \(0.847957\pi\) | |||||||
\(888\) | 132.562 | − | 132.562i | 0.149282 | − | 0.149282i | ||||
\(889\) | 700.631i | 0.788112i | ||||||||
\(890\) | 309.059 | + | 332.641i | 0.347257 | + | 0.373754i | ||||
\(891\) | 420.735 | 0.472205 | ||||||||
\(892\) | −230.687 | − | 230.687i | −0.258617 | − | 0.258617i | ||||
\(893\) | −574.534 | + | 574.534i | −0.643375 | + | 0.643375i | ||||
\(894\) | − | 232.472i | − | 0.260035i | ||||||
\(895\) | 1613.23 | + | 59.2858i | 1.80249 | + | 0.0662411i | ||||
\(896\) | −133.716 | −0.149236 | ||||||||
\(897\) | −256.384 | − | 256.384i | −0.285824 | − | 0.285824i | ||||
\(898\) | 143.978 | − | 143.978i | 0.160332 | − | 0.160332i | ||||
\(899\) | 839.225i | 0.933510i | ||||||||
\(900\) | −33.9431 | − | 2.49817i | −0.0377145 | − | 0.00277574i | ||||
\(901\) | 624.022 | 0.692588 | ||||||||
\(902\) | 213.342 | + | 213.342i | 0.236521 | + | 0.236521i | ||||
\(903\) | 192.357 | − | 192.357i | 0.213020 | − | 0.213020i | ||||
\(904\) | 209.733i | 0.232006i | ||||||||
\(905\) | 21.0352 | − | 572.392i | 0.0232433 | − | 0.632477i | ||||
\(906\) | −792.768 | −0.875020 | ||||||||
\(907\) | 651.343 | + | 651.343i | 0.718129 | + | 0.718129i | 0.968222 | − | 0.250093i | \(-0.0804612\pi\) |
−0.250093 | + | 0.968222i | \(0.580461\pi\) | |||||||
\(908\) | −115.989 | + | 115.989i | −0.127741 | + | 0.127741i | ||||
\(909\) | 90.7725i | 0.0998598i | ||||||||
\(910\) | −1487.71 | + | 1382.24i | −1.63484 | + | 1.51894i | ||||
\(911\) | 1182.01 | 1.29749 | 0.648744 | − | 0.761007i | \(-0.275295\pi\) | ||||
0.648744 | + | 0.761007i | \(0.275295\pi\) | |||||||
\(912\) | −249.429 | − | 249.429i | −0.273497 | − | 0.273497i | ||||
\(913\) | −221.576 | + | 221.576i | −0.242690 | + | 0.242690i | ||||
\(914\) | 551.542i | 0.603437i | ||||||||
\(915\) | 107.960 | + | 116.198i | 0.117989 | + | 0.126992i | ||||
\(916\) | 641.502 | 0.700329 | ||||||||
\(917\) | −1862.77 | − | 1862.77i | −2.03137 | − | 2.03137i | ||||
\(918\) | 335.418 | − | 335.418i | 0.365379 | − | 0.365379i | ||||
\(919\) | − | 1262.29i | − | 1.37355i | −0.726871 | − | 0.686774i | \(-0.759026\pi\) | ||
0.726871 | − | 0.686774i | \(-0.240974\pi\) | |||||||
\(920\) | 67.7775 | + | 2.49080i | 0.0736712 | + | 0.00270740i | ||||
\(921\) | −700.757 | −0.760865 | ||||||||
\(922\) | 52.7338 | + | 52.7338i | 0.0571950 | + | 0.0571950i | ||||
\(923\) | 369.340 | − | 369.340i | 0.400152 | − | 0.400152i | ||||
\(924\) | − | 357.055i | − | 0.386423i | ||||||
\(925\) | 347.927 | + | 403.210i | 0.376138 | + | 0.435903i | ||||
\(926\) | −384.118 | −0.414814 | ||||||||
\(927\) | −65.3410 | − | 65.3410i | −0.0704865 | − | 0.0704865i | ||||
\(928\) | 67.1803 | − | 67.1803i | 0.0723925 | − | 0.0723925i | ||||
\(929\) | 1396.75i | 1.50350i | 0.659448 | + | 0.751750i | \(0.270790\pi\) | ||||
−0.659448 | + | 0.751750i | \(0.729210\pi\) | |||||||
\(930\) | 40.3734 | − | 1098.61i | 0.0434123 | − | 1.18130i | ||||
\(931\) | −2570.34 | −2.76084 | ||||||||
\(932\) | 222.579 | + | 222.579i | 0.238819 | + | 0.238819i | ||||
\(933\) | −338.424 | + | 338.424i | −0.362727 | + | 0.362727i | ||||
\(934\) | 146.337i | 0.156678i | ||||||||
\(935\) | −230.440 | + | 214.103i | −0.246460 | + | 0.228987i | ||||
\(936\) | 46.7831 | 0.0499819 | ||||||||
\(937\) | 326.849 | + | 326.849i | 0.348825 | + | 0.348825i | 0.859672 | − | 0.510847i | \(-0.170668\pi\) |
−0.510847 | + | 0.859672i | \(0.670668\pi\) | |||||||
\(938\) | 301.586 | − | 301.586i | 0.321521 | − | 0.321521i | ||||
\(939\) | 1456.20i | 1.55080i | ||||||||
\(940\) | 195.125 | + | 210.013i | 0.207580 | + | 0.223419i | ||||
\(941\) | −415.375 | −0.441418 | −0.220709 | − | 0.975340i | \(-0.570837\pi\) | ||||
−0.220709 | + | 0.975340i | \(0.570837\pi\) | |||||||
\(942\) | 492.091 | + | 492.091i | 0.522389 | + | 0.522389i | ||||
\(943\) | 149.022 | − | 149.022i | 0.158029 | − | 0.158029i | ||||
\(944\) | 270.130i | 0.286155i | ||||||||
\(945\) | −1528.60 | − | 56.1756i | −1.61757 | − | 0.0594451i | ||||
\(946\) | −50.7905 | −0.0536898 | ||||||||
\(947\) | 368.863 | + | 368.863i | 0.389507 | + | 0.389507i | 0.874512 | − | 0.485005i | \(-0.161182\pi\) |
−0.485005 | + | 0.874512i | \(0.661182\pi\) | |||||||
\(948\) | −498.410 | + | 498.410i | −0.525749 | + | 0.525749i | ||||
\(949\) | 738.196i | 0.777867i | ||||||||
\(950\) | 758.679 | − | 654.659i | 0.798610 | − | 0.689115i | ||||
\(951\) | 1640.13 | 1.72464 | ||||||||
\(952\) | −306.304 | − | 306.304i | −0.321748 | − | 0.321748i | ||||
\(953\) | −1064.52 | + | 1064.52i | −1.11702 | + | 1.11702i | −0.124847 | + | 0.992176i | \(0.539844\pi\) |
−0.992176 | + | 0.124847i | \(0.960156\pi\) | |||||||
\(954\) | 46.3578i | 0.0485931i | ||||||||
\(955\) | 41.9651 | − | 1141.92i | 0.0439425 | − | 1.19572i | ||||
\(956\) | −499.319 | −0.522300 | ||||||||
\(957\) | 179.389 | + | 179.389i | 0.187449 | + | 0.187449i | ||||
\(958\) | −99.9056 | + | 99.9056i | −0.104286 | + | 0.104286i | ||||
\(959\) | 0.517321i | 0.000539438i | ||||||||
\(960\) | −91.1757 | + | 84.7119i | −0.0949747 | + | 0.0882416i | ||||
\(961\) | 1535.86 | 1.59819 | ||||||||
\(962\) | −517.639 | − | 517.639i | −0.538086 | − | 0.538086i | ||||
\(963\) | 63.8848 | − | 63.8848i | 0.0663393 | − | 0.0663393i | ||||
\(964\) | 210.350i | 0.218206i | ||||||||
\(965\) | −213.062 | − | 229.320i | −0.220790 | − | 0.237637i | ||||
\(966\) | −249.407 | −0.258186 | ||||||||
\(967\) | −55.8496 | − | 55.8496i | −0.0577555 | − | 0.0577555i | 0.677639 | − | 0.735395i | \(-0.263003\pi\) |
−0.735395 | + | 0.677639i | \(0.763003\pi\) | |||||||
\(968\) | 194.861 | − | 194.861i | 0.201303 | − | 0.201303i | ||||
\(969\) | − | 1142.74i | − | 1.17930i | ||||||
\(970\) | −983.292 | − | 36.1357i | −1.01370 | − | 0.0372533i | ||||
\(971\) | −50.5920 | −0.0521030 | −0.0260515 | − | 0.999661i | \(-0.508293\pi\) | ||||
−0.0260515 | + | 0.999661i | \(0.508293\pi\) | |||||||
\(972\) | 51.8744 | + | 51.8744i | 0.0533687 | + | 0.0533687i | ||||
\(973\) | −338.406 | + | 338.406i | −0.347797 | + | 0.347797i | ||||
\(974\) | 372.364i | 0.382304i | ||||||||
\(975\) | −138.733 | + | 1884.99i | −0.142290 | + | 1.93333i | ||||
\(976\) | 40.7820 | 0.0417848 | ||||||||
\(977\) | 1144.04 | + | 1144.04i | 1.17097 | + | 1.17097i | 0.981979 | + | 0.188992i | \(0.0605220\pi\) |
0.188992 | + | 0.981979i | \(0.439478\pi\) | |||||||
\(978\) | 22.4480 | − | 22.4480i | 0.0229530 | − | 0.0229530i | ||||
\(979\) | 311.746i | 0.318433i | ||||||||
\(980\) | −33.3044 | + | 906.251i | −0.0339841 | + | 0.924745i | ||||
\(981\) | −136.952 | −0.139605 | ||||||||
\(982\) | 593.353 | + | 593.353i | 0.604229 | + | 0.604229i | ||||
\(983\) | −525.511 | + | 525.511i | −0.534599 | + | 0.534599i | −0.921938 | − | 0.387339i | \(-0.873394\pi\) |
0.387339 | + | 0.921938i | \(0.373394\pi\) | |||||||
\(984\) | 386.722i | 0.393010i | ||||||||
\(985\) | 560.777 | − | 521.021i | 0.569317 | − | 0.528955i | ||||
\(986\) | 307.782 | 0.312152 | ||||||||
\(987\) | −745.412 | − | 745.412i | −0.755230 | − | 0.755230i | ||||
\(988\) | −973.988 | + | 973.988i | −0.985818 | + | 0.985818i | ||||
\(989\) | 35.4778i | 0.0358724i | ||||||||
\(990\) | −15.9054 | − | 17.1191i | −0.0160661 | − | 0.0172920i | ||||
\(991\) | −584.279 | −0.589585 | −0.294793 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294793 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(992\) | −199.874 | − | 199.874i | −0.201486 | − | 0.201486i | ||||
\(993\) | −629.814 | + | 629.814i | −0.634254 | + | 0.634254i | ||||
\(994\) | − | 359.289i | − | 0.361458i | ||||||
\(995\) | −270.383 | − | 9.93650i | −0.271742 | − | 0.00998643i | ||||
\(996\) | −401.649 | −0.403262 | ||||||||
\(997\) | −730.044 | − | 730.044i | −0.732240 | − | 0.732240i | 0.238823 | − | 0.971063i | \(-0.423238\pi\) |
−0.971063 | + | 0.238823i | \(0.923238\pi\) | |||||||
\(998\) | −757.209 | + | 757.209i | −0.758726 | + | 0.758726i | ||||
\(999\) | − | 551.414i | − | 0.551966i |
(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.47.10 | ✓ | 24 | |
5.3 | odd | 4 | inner | 230.3.f.b.93.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.f.b.47.10 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.f.b.93.10 | yes | 24 | 5.3 | odd | 4 | inner |