Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.15 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.15 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 2.64969 | − | 4.24018i | 0.529939 | − | 0.848036i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −5.13413 | − | 5.13413i | −0.733448 | − | 0.733448i | 0.237853 | − | 0.971301i | \(-0.423556\pi\) |
−0.971301 | + | 0.237853i | \(0.923556\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 6.88987 | − | 1.59048i | 0.688987 | − | 0.159048i | ||||
\(11\) | −18.8487 | −1.71351 | −0.856757 | − | 0.515720i | \(-0.827524\pi\) | ||||
−0.856757 | + | 0.515720i | \(0.827524\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | −4.85169 | + | 4.85169i | −0.373207 | + | 0.373207i | −0.868644 | − | 0.495437i | \(-0.835008\pi\) |
0.495437 | + | 0.868644i | \(0.335008\pi\) | |||||||
\(14\) | − | 10.2683i | − | 0.733448i | ||||||
\(15\) | −1.94794 | − | 8.43834i | −0.129862 | − | 0.562556i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −8.28144 | − | 8.28144i | −0.487144 | − | 0.487144i | 0.420260 | − | 0.907404i | \(-0.361939\pi\) |
−0.907404 | + | 0.420260i | \(0.861939\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 2.00840i | − | 0.105705i | −0.998602 | − | 0.0528526i | \(-0.983169\pi\) | ||
0.998602 | − | 0.0528526i | \(-0.0168313\pi\) | |||||||
\(20\) | 8.48036 | + | 5.29939i | 0.424018 | + | 0.264969i | ||||
\(21\) | −12.5760 | −0.598858 | ||||||||
\(22\) | −18.8487 | − | 18.8487i | −0.856757 | − | 0.856757i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −10.9582 | − | 22.4704i | −0.438329 | − | 0.898814i | ||||
\(26\) | −9.70339 | −0.373207 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 10.2683 | − | 10.2683i | 0.366724 | − | 0.366724i | ||||
\(29\) | 15.3053i | 0.527770i | 0.964554 | + | 0.263885i | \(0.0850040\pi\) | ||||
−0.964554 | + | 0.263885i | \(0.914996\pi\) | |||||||
\(30\) | 6.49040 | − | 10.3863i | 0.216347 | − | 0.346209i | ||||
\(31\) | −18.0217 | −0.581345 | −0.290673 | − | 0.956823i | \(-0.593879\pi\) | ||||
−0.290673 | + | 0.956823i | \(0.593879\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −23.0848 | + | 23.0848i | −0.699539 | + | 0.699539i | ||||
\(34\) | − | 16.5629i | − | 0.487144i | ||||||
\(35\) | −35.3735 | + | 8.16576i | −1.01067 | + | 0.233307i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 7.99013 | + | 7.99013i | 0.215950 | + | 0.215950i | 0.806789 | − | 0.590840i | \(-0.201203\pi\) |
−0.590840 | + | 0.806789i | \(0.701203\pi\) | |||||||
\(38\) | 2.00840 | − | 2.00840i | 0.0528526 | − | 0.0528526i | ||||
\(39\) | 11.8842i | 0.304722i | ||||||||
\(40\) | 3.18097 | + | 13.7797i | 0.0795242 | + | 0.344494i | ||||
\(41\) | −8.60556 | −0.209892 | −0.104946 | − | 0.994478i | \(-0.533467\pi\) | ||||
−0.104946 | + | 0.994478i | \(0.533467\pi\) | |||||||
\(42\) | −12.5760 | − | 12.5760i | −0.299429 | − | 0.299429i | ||||
\(43\) | −18.9595 | + | 18.9595i | −0.440920 | + | 0.440920i | −0.892321 | − | 0.451401i | \(-0.850924\pi\) |
0.451401 | + | 0.892321i | \(0.350924\pi\) | |||||||
\(44\) | − | 37.6973i | − | 0.856757i | ||||||
\(45\) | −12.7205 | − | 7.94908i | −0.282679 | − | 0.176646i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | 21.2643 | + | 21.2643i | 0.452431 | + | 0.452431i | 0.896161 | − | 0.443729i | \(-0.146345\pi\) |
−0.443729 | + | 0.896161i | \(0.646345\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | 3.71868i | 0.0758913i | ||||||||
\(50\) | 11.5121 | − | 33.4286i | 0.230243 | − | 0.668572i | ||||
\(51\) | −20.2853 | −0.397751 | ||||||||
\(52\) | −9.70339 | − | 9.70339i | −0.186604 | − | 0.186604i | ||||
\(53\) | 30.6997 | − | 30.6997i | 0.579240 | − | 0.579240i | −0.355454 | − | 0.934694i | \(-0.615674\pi\) |
0.934694 | + | 0.355454i | \(0.115674\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | −49.9432 | + | 79.9217i | −0.908058 | + | 1.45312i | ||||
\(56\) | 20.5365 | 0.366724 | ||||||||
\(57\) | −2.45978 | − | 2.45978i | −0.0431539 | − | 0.0431539i | ||||
\(58\) | −15.3053 | + | 15.3053i | −0.263885 | + | 0.263885i | ||||
\(59\) | − | 37.0580i | − | 0.628102i | −0.949406 | − | 0.314051i | \(-0.898314\pi\) | ||
0.949406 | − | 0.314051i | \(-0.101686\pi\) | |||||||
\(60\) | 16.8767 | − | 3.89587i | 0.281278 | − | 0.0649312i | ||||
\(61\) | 65.9013 | 1.08035 | 0.540175 | − | 0.841553i | \(-0.318358\pi\) | ||||
0.540175 | + | 0.841553i | \(0.318358\pi\) | |||||||
\(62\) | −18.0217 | − | 18.0217i | −0.290673 | − | 0.290673i | ||||
\(63\) | −15.4024 | + | 15.4024i | −0.244483 | + | 0.244483i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 7.71654 | + | 33.4276i | 0.118716 | + | 0.514270i | ||||
\(66\) | −46.1696 | −0.699539 | ||||||||
\(67\) | −70.4656 | − | 70.4656i | −1.05173 | − | 1.05173i | −0.998587 | − | 0.0531382i | \(-0.983078\pi\) |
−0.0531382 | − | 0.998587i | \(-0.516922\pi\) | |||||||
\(68\) | 16.5629 | − | 16.5629i | 0.243572 | − | 0.243572i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −43.5393 | − | 27.2078i | −0.621990 | − | 0.388683i | ||||
\(71\) | −8.38441 | −0.118090 | −0.0590452 | − | 0.998255i | \(-0.518806\pi\) | ||||
−0.0590452 | + | 0.998255i | \(0.518806\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 78.9935 | − | 78.9935i | 1.08210 | − | 1.08210i | 0.0857895 | − | 0.996313i | \(-0.472659\pi\) |
0.996313 | − | 0.0857895i | \(-0.0273412\pi\) | |||||||
\(74\) | 15.9803i | 0.215950i | ||||||||
\(75\) | −40.9415 | − | 14.0994i | −0.545887 | − | 0.187992i | ||||
\(76\) | 4.01680 | 0.0528526 | ||||||||
\(77\) | 96.7715 | + | 96.7715i | 1.25677 | + | 1.25677i | ||||
\(78\) | −11.8842 | + | 11.8842i | −0.152361 | + | 0.152361i | ||||
\(79\) | − | 103.875i | − | 1.31488i | −0.753508 | − | 0.657439i | \(-0.771640\pi\) | ||
0.753508 | − | 0.657439i | \(-0.228360\pi\) | |||||||
\(80\) | −10.5988 | + | 16.9607i | −0.132485 | + | 0.212009i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −8.60556 | − | 8.60556i | −0.104946 | − | 0.104946i | ||||
\(83\) | 37.7965 | − | 37.7965i | 0.455380 | − | 0.455380i | −0.441756 | − | 0.897135i | \(-0.645644\pi\) |
0.897135 | + | 0.441756i | \(0.145644\pi\) | |||||||
\(84\) | − | 25.1520i | − | 0.299429i | ||||||
\(85\) | −57.0581 | + | 13.1715i | −0.671272 | + | 0.154959i | ||||
\(86\) | −37.9191 | −0.440920 | ||||||||
\(87\) | 18.7451 | + | 18.7451i | 0.215461 | + | 0.215461i | ||||
\(88\) | 37.6973 | − | 37.6973i | 0.428379 | − | 0.428379i | ||||
\(89\) | − | 140.211i | − | 1.57541i | −0.616055 | − | 0.787703i | \(-0.711270\pi\) | ||
0.616055 | − | 0.787703i | \(-0.288730\pi\) | |||||||
\(90\) | −4.77145 | − | 20.6696i | −0.0530161 | − | 0.229662i | ||||
\(91\) | 49.8185 | 0.547456 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −22.0720 | + | 22.0720i | −0.237333 | + | 0.237333i | ||||
\(94\) | 42.5286i | 0.452431i | ||||||||
\(95\) | −8.51597 | − | 5.32164i | −0.0896418 | − | 0.0560173i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 105.406 | + | 105.406i | 1.08666 | + | 1.08666i | 0.995870 | + | 0.0907920i | \(0.0289398\pi\) |
0.0907920 | + | 0.995870i | \(0.471060\pi\) | |||||||
\(98\) | −3.71868 | + | 3.71868i | −0.0379457 | + | 0.0379457i | ||||
\(99\) | 56.5460i | 0.571171i | ||||||||
\(100\) | 44.9407 | − | 21.9165i | 0.449407 | − | 0.219165i | ||||
\(101\) | −166.271 | −1.64624 | −0.823122 | − | 0.567865i | \(-0.807770\pi\) | ||||
−0.823122 | + | 0.567865i | \(0.807770\pi\) | |||||||
\(102\) | −20.2853 | − | 20.2853i | −0.198876 | − | 0.198876i | ||||
\(103\) | −10.8622 | + | 10.8622i | −0.105458 | + | 0.105458i | −0.757867 | − | 0.652409i | \(-0.773759\pi\) |
0.652409 | + | 0.757867i | \(0.273759\pi\) | |||||||
\(104\) | − | 19.4068i | − | 0.186604i | ||||||
\(105\) | −33.3226 | + | 53.3245i | −0.317358 | + | 0.507853i | ||||
\(106\) | 61.3995 | 0.579240 | ||||||||
\(107\) | 18.6728 | + | 18.6728i | 0.174512 | + | 0.174512i | 0.788959 | − | 0.614446i | \(-0.210621\pi\) |
−0.614446 | + | 0.788959i | \(0.710621\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 102.811i | − | 0.943220i | −0.881807 | − | 0.471610i | \(-0.843673\pi\) | ||
0.881807 | − | 0.471610i | \(-0.156327\pi\) | |||||||
\(110\) | −129.865 | + | 29.9785i | −1.18059 | + | 0.272532i | ||||
\(111\) | 19.5718 | 0.176322 | ||||||||
\(112\) | 20.5365 | + | 20.5365i | 0.183362 | + | 0.183362i | ||||
\(113\) | 18.3180 | − | 18.3180i | 0.162106 | − | 0.162106i | −0.621393 | − | 0.783499i | \(-0.713433\pi\) |
0.783499 | + | 0.621393i | \(0.213433\pi\) | |||||||
\(114\) | − | 4.91955i | − | 0.0431539i | ||||||
\(115\) | 5.39359 | + | 23.3647i | 0.0469008 | + | 0.203171i | ||||
\(116\) | −30.6107 | −0.263885 | ||||||||
\(117\) | 14.5551 | + | 14.5551i | 0.124402 | + | 0.124402i | ||||
\(118\) | 37.0580 | − | 37.0580i | 0.314051 | − | 0.314051i | ||||
\(119\) | 85.0361i | 0.714589i | ||||||||
\(120\) | 20.7725 | + | 12.9808i | 0.173105 | + | 0.108173i | ||||
\(121\) | 234.272 | 1.93613 | ||||||||
\(122\) | 65.9013 | + | 65.9013i | 0.540175 | + | 0.540175i | ||||
\(123\) | −10.5396 | + | 10.5396i | −0.0856880 | + | 0.0856880i | ||||
\(124\) | − | 36.0434i | − | 0.290673i | ||||||
\(125\) | −124.314 | − | 13.0747i | −0.994515 | − | 0.104598i | ||||
\(126\) | −30.8048 | −0.244483 | ||||||||
\(127\) | −71.1197 | − | 71.1197i | −0.559998 | − | 0.559998i | 0.369309 | − | 0.929307i | \(-0.379594\pi\) |
−0.929307 | + | 0.369309i | \(0.879594\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 46.4412i | 0.360009i | ||||||||
\(130\) | −25.7110 | + | 41.1441i | −0.197777 | + | 0.316493i | ||||
\(131\) | −135.743 | −1.03621 | −0.518103 | − | 0.855318i | \(-0.673362\pi\) | ||||
−0.518103 | + | 0.855318i | \(0.673362\pi\) | |||||||
\(132\) | −46.1696 | − | 46.1696i | −0.349770 | − | 0.349770i | ||||
\(133\) | −10.3114 | + | 10.3114i | −0.0775292 | + | 0.0775292i | ||||
\(134\) | − | 140.931i | − | 1.05173i | ||||||
\(135\) | −25.3150 | + | 5.84381i | −0.187519 | + | 0.0432875i | ||||
\(136\) | 33.1258 | 0.243572 | ||||||||
\(137\) | −60.5881 | − | 60.5881i | −0.442249 | − | 0.442249i | 0.450518 | − | 0.892767i | \(-0.351239\pi\) |
−0.892767 | + | 0.450518i | \(0.851239\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | 227.197i | 1.63451i | 0.576276 | + | 0.817255i | \(0.304506\pi\) | ||||
−0.576276 | + | 0.817255i | \(0.695494\pi\) | |||||||
\(140\) | −16.3315 | − | 70.7471i | −0.116654 | − | 0.505336i | ||||
\(141\) | 52.0866 | 0.369409 | ||||||||
\(142\) | −8.38441 | − | 8.38441i | −0.0590452 | − | 0.0590452i | ||||
\(143\) | 91.4479 | − | 91.4479i | 0.639496 | − | 0.639496i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 64.8973 | + | 40.5545i | 0.447568 | + | 0.279686i | ||||
\(146\) | 157.987 | 1.08210 | ||||||||
\(147\) | 4.55443 | + | 4.55443i | 0.0309825 | + | 0.0309825i | ||||
\(148\) | −15.9803 | + | 15.9803i | −0.107975 | + | 0.107975i | ||||
\(149\) | − | 140.232i | − | 0.941152i | −0.882359 | − | 0.470576i | \(-0.844046\pi\) | ||
0.882359 | − | 0.470576i | \(-0.155954\pi\) | |||||||
\(150\) | −26.8421 | − | 55.0409i | −0.178947 | − | 0.366939i | ||||
\(151\) | 214.851 | 1.42285 | 0.711427 | − | 0.702760i | \(-0.248049\pi\) | ||||
0.711427 | + | 0.702760i | \(0.248049\pi\) | |||||||
\(152\) | 4.01680 | + | 4.01680i | 0.0264263 | + | 0.0264263i | ||||
\(153\) | −24.8443 | + | 24.8443i | −0.162381 | + | 0.162381i | ||||
\(154\) | 193.543i | 1.25677i | ||||||||
\(155\) | −47.7520 | + | 76.4153i | −0.308078 | + | 0.493002i | ||||
\(156\) | −23.7683 | −0.152361 | ||||||||
\(157\) | 119.482 | + | 119.482i | 0.761034 | + | 0.761034i | 0.976509 | − | 0.215475i | \(-0.0691301\pi\) |
−0.215475 | + | 0.976509i | \(0.569130\pi\) | |||||||
\(158\) | 103.875 | − | 103.875i | 0.657439 | − | 0.657439i | ||||
\(159\) | − | 75.1987i | − | 0.472948i | ||||||
\(160\) | −27.5595 | + | 6.36194i | −0.172247 | + | 0.0397621i | ||||
\(161\) | 34.8214 | 0.216282 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 22.6345 | − | 22.6345i | 0.138862 | − | 0.138862i | −0.634259 | − | 0.773121i | \(-0.718695\pi\) |
0.773121 | + | 0.634259i | \(0.218695\pi\) | |||||||
\(164\) | − | 17.2111i | − | 0.104946i | ||||||
\(165\) | 36.7160 | + | 159.051i | 0.222521 | + | 0.963948i | ||||
\(166\) | 75.5930 | 0.455380 | ||||||||
\(167\) | −51.9716 | − | 51.9716i | −0.311207 | − | 0.311207i | 0.534170 | − | 0.845377i | \(-0.320624\pi\) |
−0.845377 | + | 0.534170i | \(0.820624\pi\) | |||||||
\(168\) | 25.1520 | − | 25.1520i | 0.149714 | − | 0.149714i | ||||
\(169\) | 121.922i | 0.721433i | ||||||||
\(170\) | −70.2296 | − | 43.8866i | −0.413115 | − | 0.258156i | ||||
\(171\) | −6.02519 | −0.0352351 | ||||||||
\(172\) | −37.9191 | − | 37.9191i | −0.220460 | − | 0.220460i | ||||
\(173\) | −182.504 | + | 182.504i | −1.05494 | + | 1.05494i | −0.0565364 | + | 0.998401i | \(0.518006\pi\) |
−0.998401 | + | 0.0565364i | \(0.981994\pi\) | |||||||
\(174\) | 37.4903i | 0.215461i | ||||||||
\(175\) | −59.1048 | + | 171.627i | −0.337742 | + | 0.980725i | ||||
\(176\) | 75.3946 | 0.428379 | ||||||||
\(177\) | −45.3866 | − | 45.3866i | −0.256422 | − | 0.256422i | ||||
\(178\) | 140.211 | − | 140.211i | 0.787703 | − | 0.787703i | ||||
\(179\) | − | 23.8205i | − | 0.133076i | −0.997784 | − | 0.0665378i | \(-0.978805\pi\) | ||
0.997784 | − | 0.0665378i | \(-0.0211953\pi\) | |||||||
\(180\) | 15.8982 | − | 25.4411i | 0.0883232 | − | 0.141339i | ||||
\(181\) | 210.981 | 1.16564 | 0.582820 | − | 0.812601i | \(-0.301949\pi\) | ||||
0.582820 | + | 0.812601i | \(0.301949\pi\) | |||||||
\(182\) | 49.8185 | + | 49.8185i | 0.273728 | + | 0.273728i | ||||
\(183\) | 80.7123 | − | 80.7123i | 0.441051 | − | 0.441051i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 55.0510 | − | 12.7082i | 0.297573 | − | 0.0686929i | ||||
\(186\) | −44.1440 | −0.237333 | ||||||||
\(187\) | 156.094 | + | 156.094i | 0.834728 | + | 0.834728i | ||||
\(188\) | −42.5286 | + | 42.5286i | −0.226216 | + | 0.226216i | ||||
\(189\) | 37.7280i | 0.199619i | ||||||||
\(190\) | −3.19432 | − | 13.8376i | −0.0168122 | − | 0.0728295i | ||||
\(191\) | 107.185 | 0.561180 | 0.280590 | − | 0.959828i | \(-0.409470\pi\) | ||||
0.280590 | + | 0.959828i | \(0.409470\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −204.925 | + | 204.925i | −1.06179 | + | 1.06179i | −0.0638266 | + | 0.997961i | \(0.520330\pi\) |
−0.997961 | + | 0.0638266i | \(0.979670\pi\) | |||||||
\(194\) | 210.812i | 1.08666i | ||||||||
\(195\) | 50.3910 | + | 31.4894i | 0.258415 | + | 0.161484i | ||||
\(196\) | −7.43735 | −0.0379457 | ||||||||
\(197\) | −184.161 | − | 184.161i | −0.934829 | − | 0.934829i | 0.0631740 | − | 0.998003i | \(-0.479878\pi\) |
−0.998003 | + | 0.0631740i | \(0.979878\pi\) | |||||||
\(198\) | −56.5460 | + | 56.5460i | −0.285586 | + | 0.285586i | ||||
\(199\) | − | 104.404i | − | 0.524644i | −0.964980 | − | 0.262322i | \(-0.915512\pi\) | ||
0.964980 | − | 0.262322i | \(-0.0844882\pi\) | |||||||
\(200\) | 66.8572 | + | 23.0243i | 0.334286 | + | 0.115121i | ||||
\(201\) | −172.605 | −0.858730 | ||||||||
\(202\) | −166.271 | − | 166.271i | −0.823122 | − | 0.823122i | ||||
\(203\) | 78.5796 | − | 78.5796i | 0.387092 | − | 0.387092i | ||||
\(204\) | − | 40.5706i | − | 0.198876i | ||||||
\(205\) | −22.8021 | + | 36.4891i | −0.111230 | + | 0.177996i | ||||
\(206\) | −21.7244 | −0.105458 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | 19.4068 | − | 19.4068i | 0.0933018 | − | 0.0933018i | ||||
\(209\) | 37.8556i | 0.181127i | ||||||||
\(210\) | −86.6471 | + | 20.0019i | −0.412605 | + | 0.0952473i | ||||
\(211\) | 129.297 | 0.612783 | 0.306391 | − | 0.951906i | \(-0.400878\pi\) | ||||
0.306391 | + | 0.951906i | \(0.400878\pi\) | |||||||
\(212\) | 61.3995 | + | 61.3995i | 0.289620 | + | 0.289620i | ||||
\(213\) | −10.2688 | + | 10.2688i | −0.0482102 | + | 0.0482102i | ||||
\(214\) | 37.3457i | 0.174512i | ||||||||
\(215\) | 30.1548 | + | 130.629i | 0.140255 | + | 0.607576i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 92.5259 | + | 92.5259i | 0.426387 | + | 0.426387i | ||||
\(218\) | 102.811 | − | 102.811i | 0.471610 | − | 0.471610i | ||||
\(219\) | − | 193.494i | − | 0.883533i | ||||||
\(220\) | −159.843 | − | 99.8864i | −0.726561 | − | 0.454029i | ||||
\(221\) | 80.3580 | 0.363611 | ||||||||
\(222\) | 19.5718 | + | 19.5718i | 0.0881610 | + | 0.0881610i | ||||
\(223\) | −18.4366 | + | 18.4366i | −0.0826755 | + | 0.0826755i | −0.747235 | − | 0.664560i | \(-0.768619\pi\) |
0.664560 | + | 0.747235i | \(0.268619\pi\) | |||||||
\(224\) | 41.0731i | 0.183362i | ||||||||
\(225\) | −67.4111 | + | 32.8747i | −0.299605 | + | 0.146110i | ||||
\(226\) | 36.6359 | 0.162106 | ||||||||
\(227\) | −118.408 | − | 118.408i | −0.521621 | − | 0.521621i | 0.396439 | − | 0.918061i | \(-0.370246\pi\) |
−0.918061 | + | 0.396439i | \(0.870246\pi\) | |||||||
\(228\) | 4.91955 | − | 4.91955i | 0.0215770 | − | 0.0215770i | ||||
\(229\) | 39.8738i | 0.174122i | 0.996203 | + | 0.0870608i | \(0.0277474\pi\) | ||||
−0.996203 | + | 0.0870608i | \(0.972253\pi\) | |||||||
\(230\) | −17.9711 | + | 28.7583i | −0.0781352 | + | 0.125036i | ||||
\(231\) | 237.041 | 1.02615 | ||||||||
\(232\) | −30.6107 | − | 30.6107i | −0.131943 | − | 0.131943i | ||||
\(233\) | 103.054 | − | 103.054i | 0.442294 | − | 0.442294i | −0.450489 | − | 0.892782i | \(-0.648750\pi\) |
0.892782 | + | 0.450489i | \(0.148750\pi\) | |||||||
\(234\) | 29.1102i | 0.124402i | ||||||||
\(235\) | 146.508 | − | 33.8205i | 0.623439 | − | 0.143917i | ||||
\(236\) | 74.1160 | 0.314051 | ||||||||
\(237\) | −127.221 | − | 127.221i | −0.536797 | − | 0.536797i | ||||
\(238\) | −85.0361 | + | 85.0361i | −0.357294 | + | 0.357294i | ||||
\(239\) | 395.064i | 1.65299i | 0.562947 | + | 0.826493i | \(0.309668\pi\) | ||||
−0.562947 | + | 0.826493i | \(0.690332\pi\) | |||||||
\(240\) | 7.79175 | + | 33.7534i | 0.0324656 | + | 0.140639i | ||||
\(241\) | 267.186 | 1.10865 | 0.554327 | − | 0.832299i | \(-0.312976\pi\) | ||||
0.554327 | + | 0.832299i | \(0.312976\pi\) | |||||||
\(242\) | 234.272 | + | 234.272i | 0.968066 | + | 0.968066i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 131.803i | 0.540175i | ||||||||
\(245\) | 15.7679 | + | 9.85336i | 0.0643586 | + | 0.0402178i | ||||
\(246\) | −21.0792 | −0.0856880 | ||||||||
\(247\) | 9.74413 | + | 9.74413i | 0.0394499 | + | 0.0394499i | ||||
\(248\) | 36.0434 | − | 36.0434i | 0.145336 | − | 0.145336i | ||||
\(249\) | − | 92.5822i | − | 0.371816i | ||||||
\(250\) | −111.240 | − | 137.389i | −0.444958 | − | 0.549556i | ||||
\(251\) | −335.484 | −1.33659 | −0.668294 | − | 0.743897i | \(-0.732975\pi\) | ||||
−0.668294 | + | 0.743897i | \(0.732975\pi\) | |||||||
\(252\) | −30.8048 | − | 30.8048i | −0.122241 | − | 0.122241i | ||||
\(253\) | 63.9189 | − | 63.9189i | 0.252644 | − | 0.252644i | ||||
\(254\) | − | 142.239i | − | 0.559998i | ||||||
\(255\) | −53.7499 | + | 86.0133i | −0.210784 | + | 0.337307i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 63.0112 | + | 63.0112i | 0.245180 | + | 0.245180i | 0.818989 | − | 0.573809i | \(-0.194535\pi\) |
−0.573809 | + | 0.818989i | \(0.694535\pi\) | |||||||
\(258\) | −46.4412 | + | 46.4412i | −0.180005 | + | 0.180005i | ||||
\(259\) | − | 82.0448i | − | 0.316775i | ||||||
\(260\) | −66.8551 | + | 15.4331i | −0.257135 | + | 0.0593580i | ||||
\(261\) | 45.9160 | 0.175923 | ||||||||
\(262\) | −135.743 | − | 135.743i | −0.518103 | − | 0.518103i | ||||
\(263\) | −142.414 | + | 142.414i | −0.541497 | + | 0.541497i | −0.923968 | − | 0.382471i | \(-0.875073\pi\) |
0.382471 | + | 0.923968i | \(0.375073\pi\) | |||||||
\(264\) | − | 92.3392i | − | 0.349770i | ||||||
\(265\) | −48.8274 | − | 211.517i | −0.184255 | − | 0.798179i | ||||
\(266\) | −20.6228 | −0.0775292 | ||||||||
\(267\) | −171.723 | − | 171.723i | −0.643157 | − | 0.643157i | ||||
\(268\) | 140.931 | − | 140.931i | 0.525863 | − | 0.525863i | ||||
\(269\) | − | 207.123i | − | 0.769973i | −0.922922 | − | 0.384987i | \(-0.874206\pi\) | ||
0.922922 | − | 0.384987i | \(-0.125794\pi\) | |||||||
\(270\) | −31.1588 | − | 19.4712i | −0.115403 | − | 0.0721156i | ||||
\(271\) | −380.296 | −1.40331 | −0.701654 | − | 0.712518i | \(-0.747555\pi\) | ||||
−0.701654 | + | 0.712518i | \(0.747555\pi\) | |||||||
\(272\) | 33.1258 | + | 33.1258i | 0.121786 | + | 0.121786i | ||||
\(273\) | 61.0149 | − | 61.0149i | 0.223498 | − | 0.223498i | ||||
\(274\) | − | 121.176i | − | 0.442249i | ||||||
\(275\) | 206.548 | + | 423.536i | 0.751084 | + | 1.54013i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 202.941 | + | 202.941i | 0.732639 | + | 0.732639i | 0.971142 | − | 0.238502i | \(-0.0766565\pi\) |
−0.238502 | + | 0.971142i | \(0.576657\pi\) | |||||||
\(278\) | −227.197 | + | 227.197i | −0.817255 | + | 0.817255i | ||||
\(279\) | 54.0651i | 0.193782i | ||||||||
\(280\) | 54.4156 | − | 87.0786i | 0.194341 | − | 0.310995i | ||||
\(281\) | −215.868 | −0.768215 | −0.384108 | − | 0.923288i | \(-0.625491\pi\) | ||||
−0.384108 | + | 0.923288i | \(0.625491\pi\) | |||||||
\(282\) | 52.0866 | + | 52.0866i | 0.184704 | + | 0.184704i | ||||
\(283\) | −281.977 | + | 281.977i | −0.996383 | + | 0.996383i | −0.999993 | − | 0.00361003i | \(-0.998851\pi\) |
0.00361003 | + | 0.999993i | \(0.498851\pi\) | |||||||
\(284\) | − | 16.7688i | − | 0.0590452i | ||||||
\(285\) | −16.9475 | + | 3.91223i | −0.0594651 | + | 0.0137271i | ||||
\(286\) | 182.896 | 0.639496 | ||||||||
\(287\) | 44.1821 | + | 44.1821i | 0.153945 | + | 0.153945i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 151.835i | − | 0.525382i | ||||||
\(290\) | 24.3429 | + | 105.452i | 0.0839410 | + | 0.363627i | ||||
\(291\) | 258.191 | 0.887256 | ||||||||
\(292\) | 157.987 | + | 157.987i | 0.541051 | + | 0.541051i | ||||
\(293\) | −268.608 | + | 268.608i | −0.916752 | + | 0.916752i | −0.996792 | − | 0.0800393i | \(-0.974495\pi\) |
0.0800393 | + | 0.996792i | \(0.474495\pi\) | |||||||
\(294\) | 9.10886i | 0.0309825i | ||||||||
\(295\) | −157.133 | − | 98.1924i | −0.532653 | − | 0.332856i | ||||
\(296\) | −31.9605 | −0.107975 | ||||||||
\(297\) | 69.2544 | + | 69.2544i | 0.233180 | + | 0.233180i | ||||
\(298\) | 140.232 | − | 140.232i | 0.470576 | − | 0.470576i | ||||
\(299\) | − | 32.9058i | − | 0.110053i | ||||||
\(300\) | 28.1988 | − | 81.8830i | 0.0939961 | − | 0.272943i | ||||
\(301\) | 194.682 | 0.646783 | ||||||||
\(302\) | 214.851 | + | 214.851i | 0.711427 | + | 0.711427i | ||||
\(303\) | −203.639 | + | 203.639i | −0.672076 | + | 0.672076i | ||||
\(304\) | 8.03359i | 0.0264263i | ||||||||
\(305\) | 174.618 | − | 279.433i | 0.572519 | − | 0.916175i | ||||
\(306\) | −49.6886 | −0.162381 | ||||||||
\(307\) | 242.905 | + | 242.905i | 0.791222 | + | 0.791222i | 0.981693 | − | 0.190471i | \(-0.0610014\pi\) |
−0.190471 | + | 0.981693i | \(0.561001\pi\) | |||||||
\(308\) | −193.543 | + | 193.543i | −0.628387 | + | 0.628387i | ||||
\(309\) | 26.6069i | 0.0861064i | ||||||||
\(310\) | −124.167 | + | 28.6632i | −0.400540 | + | 0.0924621i | ||||
\(311\) | −207.359 | −0.666749 | −0.333374 | − | 0.942795i | \(-0.608187\pi\) | ||||
−0.333374 | + | 0.942795i | \(0.608187\pi\) | |||||||
\(312\) | −23.7683 | − | 23.7683i | −0.0761806 | − | 0.0761806i | ||||
\(313\) | −281.476 | + | 281.476i | −0.899286 | + | 0.899286i | −0.995373 | − | 0.0960873i | \(-0.969367\pi\) |
0.0960873 | + | 0.995373i | \(0.469367\pi\) | |||||||
\(314\) | 238.965i | 0.761034i | ||||||||
\(315\) | 24.4973 | + | 106.121i | 0.0777691 | + | 0.336891i | ||||
\(316\) | 207.751 | 0.657439 | ||||||||
\(317\) | 244.685 | + | 244.685i | 0.771877 | + | 0.771877i | 0.978435 | − | 0.206557i | \(-0.0662260\pi\) |
−0.206557 | + | 0.978435i | \(0.566226\pi\) | |||||||
\(318\) | 75.1987 | − | 75.1987i | 0.236474 | − | 0.236474i | ||||
\(319\) | − | 288.485i | − | 0.904342i | ||||||
\(320\) | −33.9214 | − | 21.1976i | −0.106004 | − | 0.0662424i | ||||
\(321\) | 45.7389 | 0.142489 | ||||||||
\(322\) | 34.8214 | + | 34.8214i | 0.108141 | + | 0.108141i | ||||
\(323\) | −16.6324 | + | 16.6324i | −0.0514936 | + | 0.0514936i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 162.185 | + | 55.8533i | 0.499032 | + | 0.171856i | ||||
\(326\) | 45.2690 | 0.138862 | ||||||||
\(327\) | −125.917 | − | 125.917i | −0.385068 | − | 0.385068i | ||||
\(328\) | 17.2111 | − | 17.2111i | 0.0524729 | − | 0.0524729i | ||||
\(329\) | − | 218.347i | − | 0.663670i | ||||||
\(330\) | −122.335 | + | 195.767i | −0.370713 | + | 0.593234i | ||||
\(331\) | 638.751 | 1.92976 | 0.964881 | − | 0.262688i | \(-0.0846089\pi\) | ||||
0.964881 | + | 0.262688i | \(0.0846089\pi\) | |||||||
\(332\) | 75.5930 | + | 75.5930i | 0.227690 | + | 0.227690i | ||||
\(333\) | 23.9704 | − | 23.9704i | 0.0719832 | − | 0.0719832i | ||||
\(334\) | − | 103.943i | − | 0.311207i | ||||||
\(335\) | −485.499 | + | 112.074i | −1.44925 | + | 0.334550i | ||||
\(336\) | 50.3040 | 0.149714 | ||||||||
\(337\) | 245.749 | + | 245.749i | 0.729225 | + | 0.729225i | 0.970465 | − | 0.241240i | \(-0.0775542\pi\) |
−0.241240 | + | 0.970465i | \(0.577554\pi\) | |||||||
\(338\) | −121.922 | + | 121.922i | −0.360716 | + | 0.360716i | ||||
\(339\) | − | 44.8696i | − | 0.132359i | ||||||
\(340\) | −26.3430 | − | 114.116i | −0.0774794 | − | 0.335636i | ||||
\(341\) | 339.685 | 0.996144 | ||||||||
\(342\) | −6.02519 | − | 6.02519i | −0.0176175 | − | 0.0176175i | ||||
\(343\) | −232.480 | + | 232.480i | −0.677785 | + | 0.677785i | ||||
\(344\) | − | 75.8382i | − | 0.220460i | ||||||
\(345\) | 35.2216 | + | 22.0100i | 0.102092 | + | 0.0637972i | ||||
\(346\) | −365.008 | −1.05494 | ||||||||
\(347\) | 151.497 | + | 151.497i | 0.436591 | + | 0.436591i | 0.890863 | − | 0.454272i | \(-0.150100\pi\) |
−0.454272 | + | 0.890863i | \(0.650100\pi\) | |||||||
\(348\) | −37.4903 | + | 37.4903i | −0.107731 | + | 0.107731i | ||||
\(349\) | − | 247.408i | − | 0.708904i | −0.935074 | − | 0.354452i | \(-0.884667\pi\) | ||
0.935074 | − | 0.354452i | \(-0.115333\pi\) | |||||||
\(350\) | −230.732 | + | 112.522i | −0.659233 | + | 0.321492i | ||||
\(351\) | 35.6525 | 0.101574 | ||||||||
\(352\) | 75.3946 | + | 75.3946i | 0.214189 | + | 0.214189i | ||||
\(353\) | −304.079 | + | 304.079i | −0.861415 | + | 0.861415i | −0.991503 | − | 0.130088i | \(-0.958474\pi\) |
0.130088 | + | 0.991503i | \(0.458474\pi\) | |||||||
\(354\) | − | 90.7732i | − | 0.256422i | ||||||
\(355\) | −22.2161 | + | 35.5514i | −0.0625807 | + | 0.100145i | ||||
\(356\) | 280.422 | 0.787703 | ||||||||
\(357\) | 104.147 | + | 104.147i | 0.291730 | + | 0.291730i | ||||
\(358\) | 23.8205 | − | 23.8205i | 0.0665378 | − | 0.0665378i | ||||
\(359\) | − | 257.894i | − | 0.718369i | −0.933267 | − | 0.359184i | \(-0.883055\pi\) | ||
0.933267 | − | 0.359184i | \(-0.116945\pi\) | |||||||
\(360\) | 41.3392 | − | 9.54290i | 0.114831 | − | 0.0265081i | ||||
\(361\) | 356.966 | 0.988826 | ||||||||
\(362\) | 210.981 | + | 210.981i | 0.582820 | + | 0.582820i | ||||
\(363\) | 286.923 | − | 286.923i | 0.790422 | − | 0.790422i | ||||
\(364\) | 99.6370i | 0.273728i | ||||||||
\(365\) | −125.638 | − | 544.255i | −0.344213 | − | 1.49111i | ||||
\(366\) | 161.425 | 0.441051 | ||||||||
\(367\) | −293.848 | − | 293.848i | −0.800675 | − | 0.800675i | 0.182526 | − | 0.983201i | \(-0.441573\pi\) |
−0.983201 | + | 0.182526i | \(0.941573\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | 25.8167i | 0.0699639i | ||||||||
\(370\) | 67.7592 | + | 42.3428i | 0.183133 | + | 0.114440i | ||||
\(371\) | −315.233 | −0.849685 | ||||||||
\(372\) | −44.1440 | − | 44.1440i | −0.118667 | − | 0.118667i | ||||
\(373\) | 414.362 | − | 414.362i | 1.11089 | − | 1.11089i | 0.117861 | − | 0.993030i | \(-0.462396\pi\) |
0.993030 | − | 0.117861i | \(-0.0376037\pi\) | |||||||
\(374\) | 312.188i | 0.834728i | ||||||||
\(375\) | −168.267 | + | 136.240i | −0.448711 | + | 0.363307i | ||||
\(376\) | −85.0571 | −0.226216 | ||||||||
\(377\) | −74.2568 | − | 74.2568i | −0.196968 | − | 0.196968i | ||||
\(378\) | −37.7280 | + | 37.7280i | −0.0998096 | + | 0.0998096i | ||||
\(379\) | − | 308.141i | − | 0.813036i | −0.913643 | − | 0.406518i | \(-0.866743\pi\) | ||
0.913643 | − | 0.406518i | \(-0.133257\pi\) | |||||||
\(380\) | 10.6433 | − | 17.0319i | 0.0280086 | − | 0.0448209i | ||||
\(381\) | −174.207 | −0.457236 | ||||||||
\(382\) | 107.185 | + | 107.185i | 0.280590 | + | 0.280590i | ||||
\(383\) | 206.195 | − | 206.195i | 0.538368 | − | 0.538368i | −0.384682 | − | 0.923049i | \(-0.625689\pi\) |
0.923049 | + | 0.384682i | \(0.125689\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 666.744 | − | 153.914i | 1.73180 | − | 0.399776i | ||||
\(386\) | −409.850 | −1.06179 | ||||||||
\(387\) | 56.8786 | + | 56.8786i | 0.146973 | + | 0.146973i | ||||
\(388\) | −210.812 | + | 210.812i | −0.543331 | + | 0.543331i | ||||
\(389\) | − | 474.840i | − | 1.22067i | −0.792144 | − | 0.610334i | \(-0.791035\pi\) | ||
0.792144 | − | 0.610334i | \(-0.208965\pi\) | |||||||
\(390\) | 18.9016 | + | 81.8804i | 0.0484656 | + | 0.209950i | ||||
\(391\) | 56.1675 | 0.143651 | ||||||||
\(392\) | −7.43735 | − | 7.43735i | −0.0189728 | − | 0.0189728i | ||||
\(393\) | −166.251 | + | 166.251i | −0.423029 | + | 0.423029i | ||||
\(394\) | − | 368.322i | − | 0.934829i | ||||||
\(395\) | −440.450 | − | 275.238i | −1.11506 | − | 0.696805i | ||||
\(396\) | −113.092 | −0.285586 | ||||||||
\(397\) | −240.297 | − | 240.297i | −0.605281 | − | 0.605281i | 0.336428 | − | 0.941709i | \(-0.390781\pi\) |
−0.941709 | + | 0.336428i | \(0.890781\pi\) | |||||||
\(398\) | 104.404 | − | 104.404i | 0.262322 | − | 0.262322i | ||||
\(399\) | 25.2576i | 0.0633023i | ||||||||
\(400\) | 43.8329 | + | 89.8814i | 0.109582 | + | 0.224704i | ||||
\(401\) | 201.562 | 0.502648 | 0.251324 | − | 0.967903i | \(-0.419134\pi\) | ||||
0.251324 | + | 0.967903i | \(0.419134\pi\) | |||||||
\(402\) | −172.605 | − | 172.605i | −0.429365 | − | 0.429365i | ||||
\(403\) | 87.4358 | − | 87.4358i | 0.216962 | − | 0.216962i | ||||
\(404\) | − | 332.541i | − | 0.823122i | ||||||
\(405\) | −23.8473 | + | 38.1616i | −0.0588821 | + | 0.0942262i | ||||
\(406\) | 157.159 | 0.387092 | ||||||||
\(407\) | −150.603 | − | 150.603i | −0.370033 | − | 0.370033i | ||||
\(408\) | 40.5706 | − | 40.5706i | 0.0994378 | − | 0.0994378i | ||||
\(409\) | − | 675.609i | − | 1.65186i | −0.563775 | − | 0.825928i | \(-0.690651\pi\) | ||
0.563775 | − | 0.825928i | \(-0.309349\pi\) | |||||||
\(410\) | −59.2912 | + | 13.6870i | −0.144613 | + | 0.0333830i | ||||
\(411\) | −148.410 | −0.361095 | ||||||||
\(412\) | −21.7244 | − | 21.7244i | −0.0527292 | − | 0.0527292i | ||||
\(413\) | −190.261 | + | 190.261i | −0.460680 | + | 0.460680i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | −60.1148 | − | 260.413i | −0.144855 | − | 0.627502i | ||||
\(416\) | 38.8135 | 0.0933018 | ||||||||
\(417\) | 278.258 | + | 278.258i | 0.667286 | + | 0.667286i | ||||
\(418\) | −37.8556 | + | 37.8556i | −0.0905637 | + | 0.0905637i | ||||
\(419\) | − | 384.622i | − | 0.917952i | −0.888449 | − | 0.458976i | \(-0.848216\pi\) | ||
0.888449 | − | 0.458976i | \(-0.151784\pi\) | |||||||
\(420\) | −106.649 | − | 66.6452i | −0.253926 | − | 0.158679i | ||||
\(421\) | −454.018 | −1.07843 | −0.539214 | − | 0.842169i | \(-0.681279\pi\) | ||||
−0.539214 | + | 0.842169i | \(0.681279\pi\) | |||||||
\(422\) | 129.297 | + | 129.297i | 0.306391 | + | 0.306391i | ||||
\(423\) | 63.7928 | − | 63.7928i | 0.150810 | − | 0.150810i | ||||
\(424\) | 122.799i | 0.289620i | ||||||||
\(425\) | −95.3370 | + | 276.837i | −0.224322 | + | 0.651381i | ||||
\(426\) | −20.5375 | −0.0482102 | ||||||||
\(427\) | −338.346 | − | 338.346i | −0.792380 | − | 0.792380i | ||||
\(428\) | −37.3457 | + | 37.3457i | −0.0872562 | + | 0.0872562i | ||||
\(429\) | − | 224.001i | − | 0.522146i | ||||||
\(430\) | −100.474 | + | 160.784i | −0.233660 | + | 0.373916i | ||||
\(431\) | −241.139 | −0.559487 | −0.279743 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279743 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −278.432 | + | 278.432i | −0.643031 | + | 0.643031i | −0.951299 | − | 0.308269i | \(-0.900250\pi\) |
0.308269 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(434\) | 185.052i | 0.426387i | ||||||||
\(435\) | 129.152 | − | 29.8138i | 0.296900 | − | 0.0685375i | ||||
\(436\) | 205.622 | 0.471610 | ||||||||
\(437\) | 6.81081 | + | 6.81081i | 0.0155854 | + | 0.0155854i | ||||
\(438\) | 193.494 | − | 193.494i | 0.441767 | − | 0.441767i | ||||
\(439\) | − | 439.356i | − | 1.00081i | −0.865791 | − | 0.500406i | \(-0.833184\pi\) | ||
0.865791 | − | 0.500406i | \(-0.166816\pi\) | |||||||
\(440\) | −59.9570 | − | 259.730i | −0.136266 | − | 0.590295i | ||||
\(441\) | 11.1560 | 0.0252971 | ||||||||
\(442\) | 80.3580 | + | 80.3580i | 0.181805 | + | 0.181805i | ||||
\(443\) | −261.606 | + | 261.606i | −0.590532 | + | 0.590532i | −0.937775 | − | 0.347243i | \(-0.887118\pi\) |
0.347243 | + | 0.937775i | \(0.387118\pi\) | |||||||
\(444\) | 39.1435i | 0.0881610i | ||||||||
\(445\) | −594.520 | − | 371.517i | −1.33600 | − | 0.834869i | ||||
\(446\) | −36.8733 | −0.0826755 | ||||||||
\(447\) | −171.748 | − | 171.748i | −0.384224 | − | 0.384224i | ||||
\(448\) | −41.0731 | + | 41.0731i | −0.0916810 | + | 0.0916810i | ||||
\(449\) | − | 876.612i | − | 1.95237i | −0.216948 | − | 0.976183i | \(-0.569610\pi\) | ||
0.216948 | − | 0.976183i | \(-0.430390\pi\) | |||||||
\(450\) | −100.286 | − | 34.5364i | −0.222857 | − | 0.0767475i | ||||
\(451\) | 162.203 | 0.359653 | ||||||||
\(452\) | 36.6359 | + | 36.6359i | 0.0810529 | + | 0.0810529i | ||||
\(453\) | 263.138 | − | 263.138i | 0.580878 | − | 0.580878i | ||||
\(454\) | − | 236.816i | − | 0.521621i | ||||||
\(455\) | 132.004 | − | 211.239i | 0.290118 | − | 0.464262i | ||||
\(456\) | 9.83910 | 0.0215770 | ||||||||
\(457\) | 18.0348 | + | 18.0348i | 0.0394635 | + | 0.0394635i | 0.726563 | − | 0.687100i | \(-0.241116\pi\) |
−0.687100 | + | 0.726563i | \(0.741116\pi\) | |||||||
\(458\) | −39.8738 | + | 39.8738i | −0.0870608 | + | 0.0870608i | ||||
\(459\) | 60.8559i | 0.132584i | ||||||||
\(460\) | −46.7294 | + | 10.7872i | −0.101586 | + | 0.0234504i | ||||
\(461\) | 746.316 | 1.61891 | 0.809453 | − | 0.587185i | \(-0.199764\pi\) | ||||
0.809453 | + | 0.587185i | \(0.199764\pi\) | |||||||
\(462\) | 237.041 | + | 237.041i | 0.513076 | + | 0.513076i | ||||
\(463\) | −178.472 | + | 178.472i | −0.385469 | + | 0.385469i | −0.873068 | − | 0.487599i | \(-0.837873\pi\) |
0.487599 | + | 0.873068i | \(0.337873\pi\) | |||||||
\(464\) | − | 61.2213i | − | 0.131943i | ||||||
\(465\) | 35.1052 | + | 152.073i | 0.0754950 | + | 0.327039i | ||||
\(466\) | 206.109 | 0.442294 | ||||||||
\(467\) | −246.803 | − | 246.803i | −0.528486 | − | 0.528486i | 0.391635 | − | 0.920121i | \(-0.371910\pi\) |
−0.920121 | + | 0.391635i | \(0.871910\pi\) | |||||||
\(468\) | −29.1102 | + | 29.1102i | −0.0622012 | + | 0.0622012i | ||||
\(469\) | 723.560i | 1.54277i | ||||||||
\(470\) | 180.329 | + | 112.688i | 0.383678 | + | 0.239761i | ||||
\(471\) | 292.671 | 0.621382 | ||||||||
\(472\) | 74.1160 | + | 74.1160i | 0.157026 | + | 0.157026i | ||||
\(473\) | 357.362 | − | 357.362i | 0.755522 | − | 0.755522i | ||||
\(474\) | − | 254.442i | − | 0.536797i | ||||||
\(475\) | −45.1294 | + | 22.0085i | −0.0950093 | + | 0.0463337i | ||||
\(476\) | −170.072 | −0.357294 | ||||||||
\(477\) | −92.0992 | − | 92.0992i | −0.193080 | − | 0.193080i | ||||
\(478\) | −395.064 | + | 395.064i | −0.826493 | + | 0.826493i | ||||
\(479\) | − | 171.427i | − | 0.357886i | −0.983859 | − | 0.178943i | \(-0.942732\pi\) | ||
0.983859 | − | 0.178943i | \(-0.0572678\pi\) | |||||||
\(480\) | −25.9616 | + | 41.5451i | −0.0540867 | + | 0.0865523i | ||||
\(481\) | −77.5314 | −0.161188 | ||||||||
\(482\) | 267.186 | + | 267.186i | 0.554327 | + | 0.554327i | ||||
\(483\) | 42.6473 | − | 42.6473i | 0.0882967 | − | 0.0882967i | ||||
\(484\) | 468.544i | 0.968066i | ||||||||
\(485\) | 726.235 | − | 167.647i | 1.49739 | − | 0.345664i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 68.8983 | + | 68.8983i | 0.141475 | + | 0.141475i | 0.774297 | − | 0.632822i | \(-0.218104\pi\) |
−0.632822 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(488\) | −131.803 | + | 131.803i | −0.270087 | + | 0.270087i | ||||
\(489\) | − | 55.4430i | − | 0.113380i | ||||||
\(490\) | 5.91449 | + | 25.6212i | 0.0120704 | + | 0.0522882i | ||||
\(491\) | −716.560 | −1.45939 | −0.729695 | − | 0.683773i | \(-0.760338\pi\) | ||||
−0.729695 | + | 0.683773i | \(0.760338\pi\) | |||||||
\(492\) | −21.0792 | − | 21.0792i | −0.0428440 | − | 0.0428440i | ||||
\(493\) | 126.750 | − | 126.750i | 0.257100 | − | 0.257100i | ||||
\(494\) | 19.4883i | 0.0394499i | ||||||||
\(495\) | 239.765 | + | 149.830i | 0.484374 | + | 0.302686i | ||||
\(496\) | 72.0868 | 0.145336 | ||||||||
\(497\) | 43.0467 | + | 43.0467i | 0.0866131 | + | 0.0866131i | ||||
\(498\) | 92.5822 | − | 92.5822i | 0.185908 | − | 0.185908i | ||||
\(499\) | 103.164i | 0.206742i | 0.994643 | + | 0.103371i | \(0.0329629\pi\) | ||||
−0.994643 | + | 0.103371i | \(0.967037\pi\) | |||||||
\(500\) | 26.1495 | − | 248.629i | 0.0522989 | − | 0.497257i | ||||
\(501\) | −127.304 | −0.254100 | ||||||||
\(502\) | −335.484 | − | 335.484i | −0.668294 | − | 0.668294i | ||||
\(503\) | −213.360 | + | 213.360i | −0.424176 | + | 0.424176i | −0.886639 | − | 0.462463i | \(-0.846966\pi\) |
0.462463 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(504\) | − | 61.6096i | − | 0.122241i | ||||||
\(505\) | −440.566 | + | 705.017i | −0.872409 | + | 1.39607i | ||||
\(506\) | 127.838 | 0.252644 | ||||||||
\(507\) | 149.324 | + | 149.324i | 0.294524 | + | 0.294524i | ||||
\(508\) | 142.239 | − | 142.239i | 0.279999 | − | 0.279999i | ||||
\(509\) | − | 65.8915i | − | 0.129453i | −0.997903 | − | 0.0647264i | \(-0.979383\pi\) | ||
0.997903 | − | 0.0647264i | \(-0.0206175\pi\) | |||||||
\(510\) | −139.763 | + | 32.2635i | −0.274045 | + | 0.0632617i | ||||
\(511\) | −811.127 | −1.58733 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −7.37933 | + | 7.37933i | −0.0143846 | + | 0.0143846i | ||||
\(514\) | 126.022i | 0.245180i | ||||||||
\(515\) | 17.2762 | + | 74.8393i | 0.0335460 | + | 0.145319i | ||||
\(516\) | −92.8824 | −0.180005 | ||||||||
\(517\) | −400.803 | − | 400.803i | −0.775248 | − | 0.775248i | ||||
\(518\) | 82.0448 | − | 82.0448i | 0.158388 | − | 0.158388i | ||||
\(519\) | 447.042i | 0.861352i | ||||||||
\(520\) | −82.2882 | − | 51.4220i | −0.158247 | − | 0.0988885i | ||||
\(521\) | 898.750 | 1.72505 | 0.862524 | − | 0.506016i | \(-0.168882\pi\) | ||||
0.862524 | + | 0.506016i | \(0.168882\pi\) | |||||||
\(522\) | 45.9160 | + | 45.9160i | 0.0879617 | + | 0.0879617i | ||||
\(523\) | 380.156 | − | 380.156i | 0.726876 | − | 0.726876i | −0.243120 | − | 0.969996i | \(-0.578171\pi\) |
0.969996 | + | 0.243120i | \(0.0781709\pi\) | |||||||
\(524\) | − | 271.486i | − | 0.518103i | ||||||
\(525\) | 137.811 | + | 282.587i | 0.262497 | + | 0.538262i | ||||
\(526\) | −284.827 | −0.541497 | ||||||||
\(527\) | 149.246 | + | 149.246i | 0.283199 | + | 0.283199i | ||||
\(528\) | 92.3392 | − | 92.3392i | 0.174885 | − | 0.174885i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 162.690 | − | 260.345i | 0.306962 | − | 0.491217i | ||||
\(531\) | −111.174 | −0.209367 | ||||||||
\(532\) | −20.6228 | − | 20.6228i | −0.0387646 | − | 0.0387646i | ||||
\(533\) | 41.7516 | − | 41.7516i | 0.0783331 | − | 0.0783331i | ||||
\(534\) | − | 343.446i | − | 0.643157i | ||||||
\(535\) | 128.653 | − | 29.6988i | 0.240474 | − | 0.0555118i | ||||
\(536\) | 281.862 | 0.525863 | ||||||||
\(537\) | −29.1741 | − | 29.1741i | −0.0543278 | − | 0.0543278i | ||||
\(538\) | 207.123 | − | 207.123i | 0.384987 | − | 0.384987i | ||||
\(539\) | − | 70.0921i | − | 0.130041i | ||||||
\(540\) | −11.6876 | − | 50.6300i | −0.0216437 | − | 0.0937593i | ||||
\(541\) | −181.504 | −0.335498 | −0.167749 | − | 0.985830i | \(-0.553650\pi\) | ||||
−0.167749 | + | 0.985830i | \(0.553650\pi\) | |||||||
\(542\) | −380.296 | − | 380.296i | −0.701654 | − | 0.701654i | ||||
\(543\) | 258.398 | − | 258.398i | 0.475871 | − | 0.475871i | ||||
\(544\) | 66.2515i | 0.121786i | ||||||||
\(545\) | −435.937 | − | 272.418i | −0.799884 | − | 0.499849i | ||||
\(546\) | 122.030 | 0.223498 | ||||||||
\(547\) | −369.884 | − | 369.884i | −0.676206 | − | 0.676206i | 0.282934 | − | 0.959139i | \(-0.408692\pi\) |
−0.959139 | + | 0.282934i | \(0.908692\pi\) | |||||||
\(548\) | 121.176 | − | 121.176i | 0.221124 | − | 0.221124i | ||||
\(549\) | − | 197.704i | − | 0.360117i | ||||||
\(550\) | −216.988 | + | 630.084i | −0.394524 | + | 1.14561i | ||||
\(551\) | 30.7392 | 0.0557880 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −533.310 | + | 533.310i | −0.964394 | + | 0.964394i | ||||
\(554\) | 405.882i | 0.732639i | ||||||||
\(555\) | 51.8592 | − | 82.9877i | 0.0934399 | − | 0.149527i | ||||
\(556\) | −454.394 | −0.817255 | ||||||||
\(557\) | 443.307 | + | 443.307i | 0.795884 | + | 0.795884i | 0.982444 | − | 0.186560i | \(-0.0597338\pi\) |
−0.186560 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(558\) | −54.0651 | + | 54.0651i | −0.0968909 | + | 0.0968909i | ||||
\(559\) | − | 183.972i | − | 0.329109i | ||||||
\(560\) | 141.494 | − | 32.6630i | 0.252668 | − | 0.0583268i | ||||
\(561\) | 382.351 | 0.681552 | ||||||||
\(562\) | −215.868 | − | 215.868i | −0.384108 | − | 0.384108i | ||||
\(563\) | 204.223 | − | 204.223i | 0.362742 | − | 0.362742i | −0.502080 | − | 0.864821i | \(-0.667432\pi\) |
0.864821 | + | 0.502080i | \(0.167432\pi\) | |||||||
\(564\) | 104.173i | 0.184704i | ||||||||
\(565\) | −29.1344 | − | 126.208i | −0.0515653 | − | 0.223378i | ||||
\(566\) | −563.953 | −0.996383 | ||||||||
\(567\) | 46.2072 | + | 46.2072i | 0.0814942 | + | 0.0814942i | ||||
\(568\) | 16.7688 | − | 16.7688i | 0.0295226 | − | 0.0295226i | ||||
\(569\) | 54.1051i | 0.0950881i | 0.998869 | + | 0.0475440i | \(0.0151394\pi\) | ||||
−0.998869 | + | 0.0475440i | \(0.984861\pi\) | |||||||
\(570\) | −20.8598 | − | 13.0353i | −0.0365961 | − | 0.0228690i | ||||
\(571\) | −1055.98 | −1.84935 | −0.924674 | − | 0.380759i | \(-0.875663\pi\) | ||||
−0.924674 | + | 0.380759i | \(0.875663\pi\) | |||||||
\(572\) | 182.896 | + | 182.896i | 0.319748 | + | 0.319748i | ||||
\(573\) | 131.275 | − | 131.275i | 0.229101 | − | 0.229101i | ||||
\(574\) | 88.3642i | 0.153945i | ||||||||
\(575\) | 113.362 | + | 39.0395i | 0.197151 | + | 0.0678948i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 128.192 | + | 128.192i | 0.222171 | + | 0.222171i | 0.809412 | − | 0.587241i | \(-0.199786\pi\) |
−0.587241 | + | 0.809412i | \(0.699786\pi\) | |||||||
\(578\) | 151.835 | − | 151.835i | 0.262691 | − | 0.262691i | ||||
\(579\) | 501.962i | 0.866946i | ||||||||
\(580\) | −81.1089 | + | 129.795i | −0.139843 | + | 0.223784i | ||||
\(581\) | −388.105 | −0.667995 | ||||||||
\(582\) | 258.191 | + | 258.191i | 0.443628 | + | 0.443628i | ||||
\(583\) | −578.649 | + | 578.649i | −0.992537 | + | 0.992537i | ||||
\(584\) | 315.974i | 0.541051i | ||||||||
\(585\) | 100.283 | − | 23.1496i | 0.171423 | − | 0.0395720i | ||||
\(586\) | −537.217 | −0.916752 | ||||||||
\(587\) | −18.1091 | − | 18.1091i | −0.0308503 | − | 0.0308503i | 0.691513 | − | 0.722364i | \(-0.256944\pi\) |
−0.722364 | + | 0.691513i | \(0.756944\pi\) | |||||||
\(588\) | −9.10886 | + | 9.10886i | −0.0154913 | + | 0.0154913i | ||||
\(589\) | 36.1948i | 0.0614512i | ||||||||
\(590\) | −58.9402 | − | 255.325i | −0.0998986 | − | 0.432754i | ||||
\(591\) | −451.101 | −0.763284 | ||||||||
\(592\) | −31.9605 | − | 31.9605i | −0.0539874 | − | 0.0539874i | ||||
\(593\) | −696.941 | + | 696.941i | −1.17528 | + | 1.17528i | −0.194348 | + | 0.980933i | \(0.562259\pi\) |
−0.980933 | + | 0.194348i | \(0.937741\pi\) | |||||||
\(594\) | 138.509i | 0.233180i | ||||||||
\(595\) | 360.568 | + | 225.320i | 0.605997 | + | 0.378688i | ||||
\(596\) | 280.463 | 0.470576 | ||||||||
\(597\) | −127.868 | − | 127.868i | −0.214185 | − | 0.214185i | ||||
\(598\) | 32.9058 | − | 32.9058i | 0.0550264 | − | 0.0550264i | ||||
\(599\) | − | 757.584i | − | 1.26475i | −0.774663 | − | 0.632374i | \(-0.782081\pi\) | ||
0.774663 | − | 0.632374i | \(-0.217919\pi\) | |||||||
\(600\) | 110.082 | − | 53.6842i | 0.183470 | − | 0.0894736i | ||||
\(601\) | 642.457 | 1.06898 | 0.534490 | − | 0.845175i | \(-0.320504\pi\) | ||||
0.534490 | + | 0.845175i | \(0.320504\pi\) | |||||||
\(602\) | 194.682 | + | 194.682i | 0.323391 | + | 0.323391i | ||||
\(603\) | −211.397 | + | 211.397i | −0.350575 | + | 0.350575i | ||||
\(604\) | 429.702i | 0.711427i | ||||||||
\(605\) | 620.749 | − | 993.355i | 1.02603 | − | 1.64191i | ||||
\(606\) | −407.278 | −0.672076 | ||||||||
\(607\) | −590.328 | − | 590.328i | −0.972534 | − | 0.972534i | 0.0270991 | − | 0.999633i | \(-0.491373\pi\) |
−0.999633 | + | 0.0270991i | \(0.991373\pi\) | |||||||
\(608\) | −8.03359 | + | 8.03359i | −0.0132131 | + | 0.0132131i | ||||
\(609\) | − | 192.480i | − | 0.316059i | ||||||
\(610\) | 454.052 | − | 104.815i | 0.744347 | − | 0.171828i | ||||
\(611\) | −206.335 | −0.337701 | ||||||||
\(612\) | −49.6886 | − | 49.6886i | −0.0811906 | − | 0.0811906i | ||||
\(613\) | 411.975 | − | 411.975i | 0.672064 | − | 0.672064i | −0.286128 | − | 0.958191i | \(-0.592368\pi\) |
0.958191 | + | 0.286128i | \(0.0923682\pi\) | |||||||
\(614\) | 485.810i | 0.791222i | ||||||||
\(615\) | 16.7631 | + | 72.6167i | 0.0272571 | + | 0.118076i | ||||
\(616\) | −387.086 | −0.628387 | ||||||||
\(617\) | −401.638 | − | 401.638i | −0.650953 | − | 0.650953i | 0.302270 | − | 0.953222i | \(-0.402256\pi\) |
−0.953222 | + | 0.302270i | \(0.902256\pi\) | |||||||
\(618\) | −26.6069 | + | 26.6069i | −0.0430532 | + | 0.0430532i | ||||
\(619\) | 753.916i | 1.21796i | 0.793186 | + | 0.608979i | \(0.208421\pi\) | ||||
−0.793186 | + | 0.608979i | \(0.791579\pi\) | |||||||
\(620\) | −152.831 | − | 95.5041i | −0.246501 | − | 0.154039i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | −207.359 | − | 207.359i | −0.333374 | − | 0.333374i | ||||
\(623\) | −719.863 | + | 719.863i | −1.15548 | + | 1.15548i | ||||
\(624\) | − | 47.5367i | − | 0.0761806i | ||||||
\(625\) | −384.834 | + | 492.471i | −0.615735 | + | 0.787953i | ||||
\(626\) | −562.953 | −0.899286 | ||||||||
\(627\) | 46.3635 | + | 46.3635i | 0.0739449 | + | 0.0739449i | ||||
\(628\) | −238.965 | + | 238.965i | −0.380517 | + | 0.380517i | ||||
\(629\) | − | 132.340i | − | 0.210397i | ||||||
\(630\) | −81.6233 | + | 130.618i | −0.129561 | + | 0.207330i | ||||
\(631\) | 737.230 | 1.16835 | 0.584176 | − | 0.811627i | \(-0.301418\pi\) | ||||
0.584176 | + | 0.811627i | \(0.301418\pi\) | |||||||
\(632\) | 207.751 | + | 207.751i | 0.328719 | + | 0.328719i | ||||
\(633\) | 158.356 | − | 158.356i | 0.250167 | − | 0.250167i | ||||
\(634\) | 489.370i | 0.771877i | ||||||||
\(635\) | −490.006 | + | 113.115i | −0.771662 | + | 0.178133i | ||||
\(636\) | 150.397 | 0.236474 | ||||||||
\(637\) | −18.0419 | − | 18.0419i | −0.0283232 | − | 0.0283232i | ||||
\(638\) | 288.485 | − | 288.485i | 0.452171 | − | 0.452171i | ||||
\(639\) | 25.1532i | 0.0393634i | ||||||||
\(640\) | −12.7239 | − | 55.1190i | −0.0198810 | − | 0.0861234i | ||||
\(641\) | −310.531 | −0.484448 | −0.242224 | − | 0.970220i | \(-0.577877\pi\) | ||||
−0.242224 | + | 0.970220i | \(0.577877\pi\) | |||||||
\(642\) | 45.7389 | + | 45.7389i | 0.0712444 | + | 0.0712444i | ||||
\(643\) | 433.442 | − | 433.442i | 0.674093 | − | 0.674093i | −0.284564 | − | 0.958657i | \(-0.591849\pi\) |
0.958657 | + | 0.284564i | \(0.0918487\pi\) | |||||||
\(644\) | 69.6428i | 0.108141i | ||||||||
\(645\) | 196.919 | + | 123.055i | 0.305301 | + | 0.190783i | ||||
\(646\) | −33.2649 | −0.0514936 | ||||||||
\(647\) | −123.580 | − | 123.580i | −0.191005 | − | 0.191005i | 0.605125 | − | 0.796130i | \(-0.293123\pi\) |
−0.796130 | + | 0.605125i | \(0.793123\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | 698.494i | 1.07626i | ||||||||
\(650\) | 106.332 | + | 218.039i | 0.163588 | + | 0.335444i | ||||
\(651\) | 226.641 | 0.348143 | ||||||||
\(652\) | 45.2690 | + | 45.2690i | 0.0694310 | + | 0.0694310i | ||||
\(653\) | −14.9705 | + | 14.9705i | −0.0229257 | + | 0.0229257i | −0.718477 | − | 0.695551i | \(-0.755160\pi\) |
0.695551 | + | 0.718477i | \(0.255160\pi\) | |||||||
\(654\) | − | 251.834i | − | 0.385068i | ||||||
\(655\) | −359.678 | + | 575.575i | −0.549126 | + | 0.878740i | ||||
\(656\) | 34.4223 | 0.0524729 | ||||||||
\(657\) | −236.981 | − | 236.981i | −0.360701 | − | 0.360701i | ||||
\(658\) | 218.347 | − | 218.347i | 0.331835 | − | 0.331835i | ||||
\(659\) | − | 340.257i | − | 0.516324i | −0.966102 | − | 0.258162i | \(-0.916883\pi\) | ||
0.966102 | − | 0.258162i | \(-0.0831168\pi\) | |||||||
\(660\) | −318.103 | + | 73.4320i | −0.481974 | + | 0.111261i | ||||
\(661\) | 694.682 | 1.05096 | 0.525478 | − | 0.850807i | \(-0.323886\pi\) | ||||
0.525478 | + | 0.850807i | \(0.323886\pi\) | |||||||
\(662\) | 638.751 | + | 638.751i | 0.964881 | + | 0.964881i | ||||
\(663\) | 98.4181 | − | 98.4181i | 0.148444 | − | 0.148444i | ||||
\(664\) | 151.186i | 0.227690i | ||||||||
\(665\) | 16.4001 | + | 71.0441i | 0.0246618 | + | 0.106833i | ||||
\(666\) | 47.9408 | 0.0719832 | ||||||||
\(667\) | −51.9029 | − | 51.9029i | −0.0778155 | − | 0.0778155i | ||||
\(668\) | 103.943 | − | 103.943i | 0.155604 | − | 0.155604i | ||||
\(669\) | 45.1604i | 0.0675043i | ||||||||
\(670\) | −597.573 | − | 373.425i | −0.891901 | − | 0.557350i | ||||
\(671\) | −1242.15 | −1.85119 | ||||||||
\(672\) | 50.3040 | + | 50.3040i | 0.0748572 | + | 0.0748572i | ||||
\(673\) | −625.021 | + | 625.021i | −0.928709 | + | 0.928709i | −0.997623 | − | 0.0689133i | \(-0.978047\pi\) |
0.0689133 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(674\) | 491.498i | 0.729225i | ||||||||
\(675\) | −42.2983 | + | 122.824i | −0.0626641 | + | 0.181962i | ||||
\(676\) | −243.844 | −0.360716 | ||||||||
\(677\) | −144.970 | − | 144.970i | −0.214135 | − | 0.214135i | 0.591886 | − | 0.806021i | \(-0.298383\pi\) |
−0.806021 | + | 0.591886i | \(0.798383\pi\) | |||||||
\(678\) | 44.8696 | − | 44.8696i | 0.0661794 | − | 0.0661794i | ||||
\(679\) | − | 1082.34i | − | 1.59402i | ||||||
\(680\) | 87.7732 | − | 140.459i | 0.129078 | − | 0.206558i | ||||
\(681\) | −290.039 | −0.425902 | ||||||||
\(682\) | 339.685 | + | 339.685i | 0.498072 | + | 0.498072i | ||||
\(683\) | −31.1325 | + | 31.1325i | −0.0455820 | + | 0.0455820i | −0.729530 | − | 0.683948i | \(-0.760261\pi\) |
0.683948 | + | 0.729530i | \(0.260261\pi\) | |||||||
\(684\) | − | 12.0504i | − | 0.0176175i | ||||||
\(685\) | −417.444 | + | 96.3644i | −0.609408 | + | 0.140678i | ||||
\(686\) | −464.961 | −0.677785 | ||||||||
\(687\) | 48.8353 | + | 48.8353i | 0.0710848 | + | 0.0710848i | ||||
\(688\) | 75.8382 | − | 75.8382i | 0.110230 | − | 0.110230i | ||||
\(689\) | 297.891i | 0.432353i | ||||||||
\(690\) | 13.2116 | + | 57.2316i | 0.0191472 | + | 0.0829443i | ||||
\(691\) | 287.872 | 0.416603 | 0.208301 | − | 0.978065i | \(-0.433207\pi\) | ||||
0.208301 | + | 0.978065i | \(0.433207\pi\) | |||||||
\(692\) | −365.008 | − | 365.008i | −0.527468 | − | 0.527468i | ||||
\(693\) | 290.315 | − | 290.315i | 0.418924 | − | 0.418924i | ||||
\(694\) | 302.994i | 0.436591i | ||||||||
\(695\) | 963.356 | + | 602.003i | 1.38612 | + | 0.866191i | ||||
\(696\) | −74.9805 | −0.107731 | ||||||||
\(697\) | 71.2665 | + | 71.2665i | 0.102247 | + | 0.102247i | ||||
\(698\) | 247.408 | − | 247.408i | 0.354452 | − | 0.354452i | ||||
\(699\) | − | 252.431i | − | 0.361131i | ||||||
\(700\) | −343.254 | − | 118.210i | −0.490363 | − | 0.168871i | ||||
\(701\) | 366.250 | 0.522468 | 0.261234 | − | 0.965276i | \(-0.415871\pi\) | ||||
0.261234 | + | 0.965276i | \(0.415871\pi\) | |||||||
\(702\) | 35.6525 | + | 35.6525i | 0.0507871 | + | 0.0507871i | ||||
\(703\) | 16.0474 | − | 16.0474i | 0.0228270 | − | 0.0228270i | ||||
\(704\) | 150.789i | 0.214189i | ||||||||
\(705\) | 138.014 | − | 220.857i | 0.195764 | − | 0.313272i | ||||
\(706\) | −608.159 | −0.861415 | ||||||||
\(707\) | 853.656 | + | 853.656i | 1.20743 | + | 1.20743i | ||||
\(708\) | 90.7732 | − | 90.7732i | 0.128211 | − | 0.128211i | ||||
\(709\) | − | 113.568i | − | 0.160180i | −0.996788 | − | 0.0800902i | \(-0.974479\pi\) | ||
0.996788 | − | 0.0800902i | \(-0.0255208\pi\) | |||||||
\(710\) | −57.7675 | + | 13.3353i | −0.0813627 | + | 0.0187821i | ||||
\(711\) | −311.626 | −0.438293 | ||||||||
\(712\) | 280.422 | + | 280.422i | 0.393852 | + | 0.393852i | ||||
\(713\) | 61.1146 | − | 61.1146i | 0.0857147 | − | 0.0857147i | ||||
\(714\) | 208.295i | 0.291730i | ||||||||
\(715\) | −145.446 | − | 630.065i | −0.203422 | − | 0.881209i | ||||
\(716\) | 47.6410 | 0.0665378 | ||||||||
\(717\) | 483.852 | + | 483.852i | 0.674829 | + | 0.674829i | ||||
\(718\) | 257.894 | − | 257.894i | 0.359184 | − | 0.359184i | ||||
\(719\) | − | 597.111i | − | 0.830475i | −0.909713 | − | 0.415237i | \(-0.863699\pi\) | ||
0.909713 | − | 0.415237i | \(-0.136301\pi\) | |||||||
\(720\) | 50.8821 | + | 31.7963i | 0.0706696 | + | 0.0441616i | ||||
\(721\) | 111.536 | 0.154696 | ||||||||
\(722\) | 356.966 | + | 356.966i | 0.494413 | + | 0.494413i | ||||
\(723\) | 327.234 | − | 327.234i | 0.452606 | − | 0.452606i | ||||
\(724\) | 421.962i | 0.582820i | ||||||||
\(725\) | 343.916 | − | 167.719i | 0.474367 | − | 0.231337i | ||||
\(726\) | 573.847 | 0.790422 | ||||||||
\(727\) | −648.585 | − | 648.585i | −0.892138 | − | 0.892138i | 0.102586 | − | 0.994724i | \(-0.467288\pi\) |
−0.994724 | + | 0.102586i | \(0.967288\pi\) | |||||||
\(728\) | −99.6370 | + | 99.6370i | −0.136864 | + | 0.136864i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 418.617 | − | 669.893i | 0.573448 | − | 0.917662i | ||||
\(731\) | 314.025 | 0.429582 | ||||||||
\(732\) | 161.425 | + | 161.425i | 0.220525 | + | 0.220525i | ||||
\(733\) | 998.046 | − | 998.046i | 1.36159 | − | 1.36159i | 0.489699 | − | 0.871892i | \(-0.337107\pi\) |
0.871892 | − | 0.489699i | \(-0.162893\pi\) | |||||||
\(734\) | − | 587.695i | − | 0.800675i | ||||||
\(735\) | 31.3794 | − | 7.24375i | 0.0426931 | − | 0.00985544i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | 1328.18 | + | 1328.18i | 1.80215 | + | 1.80215i | ||||
\(738\) | −25.8167 | + | 25.8167i | −0.0349820 | + | 0.0349820i | ||||
\(739\) | 1236.71i | 1.67349i | 0.547592 | + | 0.836745i | \(0.315544\pi\) | ||||
−0.547592 | + | 0.836745i | \(0.684456\pi\) | |||||||
\(740\) | 25.4164 | + | 110.102i | 0.0343464 | + | 0.148787i | ||||
\(741\) | 23.8681 | 0.0322107 | ||||||||
\(742\) | −315.233 | − | 315.233i | −0.424843 | − | 0.424843i | ||||
\(743\) | 666.268 | − | 666.268i | 0.896727 | − | 0.896727i | −0.0984183 | − | 0.995145i | \(-0.531378\pi\) |
0.995145 | + | 0.0984183i | \(0.0313783\pi\) | |||||||
\(744\) | − | 88.2880i | − | 0.118667i | ||||||
\(745\) | −594.607 | − | 371.571i | −0.798131 | − | 0.498753i | ||||
\(746\) | 828.725 | 1.11089 | ||||||||
\(747\) | −113.390 | − | 113.390i | −0.151793 | − | 0.151793i | ||||
\(748\) | −312.188 | + | 312.188i | −0.417364 | + | 0.417364i | ||||
\(749\) | − | 191.738i | − | 0.255992i | ||||||
\(750\) | −304.507 | − | 32.0264i | −0.406009 | − | 0.0427019i | ||||
\(751\) | 546.487 | 0.727679 | 0.363840 | − | 0.931462i | \(-0.381466\pi\) | ||||
0.363840 | + | 0.931462i | \(0.381466\pi\) | |||||||
\(752\) | −85.0571 | − | 85.0571i | −0.113108 | − | 0.113108i | ||||
\(753\) | −410.882 | + | 410.882i | −0.545660 | + | 0.545660i | ||||
\(754\) | − | 148.514i | − | 0.196968i | ||||||
\(755\) | 569.290 | − | 911.007i | 0.754026 | − | 1.20663i | ||||
\(756\) | −75.4561 | −0.0998096 | ||||||||
\(757\) | 395.410 | + | 395.410i | 0.522338 | + | 0.522338i | 0.918277 | − | 0.395939i | \(-0.129581\pi\) |
−0.395939 | + | 0.918277i | \(0.629581\pi\) | |||||||
\(758\) | 308.141 | − | 308.141i | 0.406518 | − | 0.406518i | ||||
\(759\) | − | 156.569i | − | 0.206283i | ||||||
\(760\) | 27.6752 | − | 6.38865i | 0.0364148 | − | 0.00840612i | ||||
\(761\) | 61.4799 | 0.0807883 | 0.0403941 | − | 0.999184i | \(-0.487139\pi\) | ||||
0.0403941 | + | 0.999184i | \(0.487139\pi\) | |||||||
\(762\) | −174.207 | − | 174.207i | −0.228618 | − | 0.228618i | ||||
\(763\) | −527.845 | + | 527.845i | −0.691802 | + | 0.691802i | ||||
\(764\) | 214.371i | 0.280590i | ||||||||
\(765\) | 39.5145 | + | 171.174i | 0.0516529 | + | 0.223757i | ||||
\(766\) | 412.390 | 0.538368 | ||||||||
\(767\) | 179.794 | + | 179.794i | 0.234412 | + | 0.234412i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 430.433i | 0.559731i | 0.960039 | + | 0.279865i | \(0.0902899\pi\) | ||||
−0.960039 | + | 0.279865i | \(0.909710\pi\) | |||||||
\(770\) | 820.657 | + | 512.830i | 1.06579 | + | 0.666013i | ||||
\(771\) | 154.345 | 0.200188 | ||||||||
\(772\) | −409.850 | − | 409.850i | −0.530894 | − | 0.530894i | ||||
\(773\) | 171.075 | − | 171.075i | 0.221313 | − | 0.221313i | −0.587738 | − | 0.809051i | \(-0.699981\pi\) |
0.809051 | + | 0.587738i | \(0.199981\pi\) | |||||||
\(774\) | 113.757i | 0.146973i | ||||||||
\(775\) | 197.486 | + | 404.954i | 0.254821 | + | 0.522522i | ||||
\(776\) | −421.625 | −0.543331 | ||||||||
\(777\) | −100.484 | − | 100.484i | −0.129323 | − | 0.129323i | ||||
\(778\) | 474.840 | − | 474.840i | 0.610334 | − | 0.610334i | ||||
\(779\) | 17.2834i | 0.0221866i | ||||||||
\(780\) | −62.9789 | + | 100.782i | −0.0807421 | + | 0.129208i | ||||
\(781\) | 158.035 | 0.202349 | ||||||||
\(782\) | 56.1675 | + | 56.1675i | 0.0718254 | + | 0.0718254i | ||||
\(783\) | 56.2354 | − | 56.2354i | 0.0718204 | − | 0.0718204i | ||||
\(784\) | − | 14.8747i | − | 0.0189728i | ||||||
\(785\) | 823.218 | − | 190.035i | 1.04869 | − | 0.242082i | ||||
\(786\) | −332.501 | −0.423029 | ||||||||
\(787\) | 76.7505 | + | 76.7505i | 0.0975229 | + | 0.0975229i | 0.754185 | − | 0.656662i | \(-0.228032\pi\) |
−0.656662 | + | 0.754185i | \(0.728032\pi\) | |||||||
\(788\) | 368.322 | − | 368.322i | 0.467414 | − | 0.467414i | ||||
\(789\) | 348.841i | 0.442130i | ||||||||
\(790\) | −165.212 | − | 715.688i | −0.209129 | − | 0.905934i | ||||
\(791\) | −188.094 | −0.237792 | ||||||||
\(792\) | −113.092 | − | 113.092i | −0.142793 | − | 0.142793i | ||||
\(793\) | −319.733 | + | 319.733i | −0.403194 | + | 0.403194i | ||||
\(794\) | − | 480.593i | − | 0.605281i | ||||||
\(795\) | −318.856 | − | 199.254i | −0.401077 | − | 0.250633i | ||||
\(796\) | 208.808 | 0.262322 | ||||||||
\(797\) | 661.678 | + | 661.678i | 0.830211 | + | 0.830211i | 0.987545 | − | 0.157334i | \(-0.0502900\pi\) |
−0.157334 | + | 0.987545i | \(0.550290\pi\) | |||||||
\(798\) | −25.2576 | + | 25.2576i | −0.0316512 | + | 0.0316512i | ||||
\(799\) | − | 352.198i | − | 0.440798i | ||||||
\(800\) | −46.0485 | + | 133.714i | −0.0575606 | + | 0.167143i | ||||
\(801\) | −420.634 | −0.525136 | ||||||||
\(802\) | 201.562 | + | 201.562i | 0.251324 | + | 0.251324i | ||||
\(803\) | −1488.92 | + | 1488.92i | −1.85420 | + | 1.85420i | ||||
\(804\) | − | 345.210i | − | 0.429365i | ||||||
\(805\) | 92.2661 | − | 147.649i | 0.114616 | − | 0.183415i | ||||
\(806\) | 174.872 | 0.216962 | ||||||||
\(807\) | −253.673 | − | 253.673i | −0.314340 | − | 0.314340i | ||||
\(808\) | 332.541 | − | 332.541i | 0.411561 | − | 0.411561i | ||||
\(809\) | − | 891.779i | − | 1.10232i | −0.834399 | − | 0.551161i | \(-0.814185\pi\) | ||
0.834399 | − | 0.551161i | \(-0.185815\pi\) | |||||||
\(810\) | −62.0089 | + | 14.3144i | −0.0765542 | + | 0.0176720i | ||||
\(811\) | 1023.79 | 1.26238 | 0.631191 | − | 0.775627i | \(-0.282566\pi\) | ||||
0.631191 | + | 0.775627i | \(0.282566\pi\) | |||||||
\(812\) | 157.159 | + | 157.159i | 0.193546 | + | 0.193546i | ||||
\(813\) | −465.766 | + | 465.766i | −0.572898 | + | 0.572898i | ||||
\(814\) | − | 301.207i | − | 0.370033i | ||||||
\(815\) | −35.9998 | − | 155.949i | −0.0441715 | − | 0.191348i | ||||
\(816\) | 81.1412 | 0.0994378 | ||||||||
\(817\) | 38.0783 | + | 38.0783i | 0.0466075 | + | 0.0466075i | ||||
\(818\) | 675.609 | − | 675.609i | 0.825928 | − | 0.825928i | ||||
\(819\) | − | 149.455i | − | 0.182485i | ||||||
\(820\) | −72.9783 | − | 45.6042i | −0.0889979 | − | 0.0556149i | ||||
\(821\) | 649.979 | 0.791692 | 0.395846 | − | 0.918317i | \(-0.370451\pi\) | ||||
0.395846 | + | 0.918317i | \(0.370451\pi\) | |||||||
\(822\) | −148.410 | − | 148.410i | −0.180547 | − | 0.180547i | ||||
\(823\) | −512.246 | + | 512.246i | −0.622413 | + | 0.622413i | −0.946148 | − | 0.323735i | \(-0.895061\pi\) |
0.323735 | + | 0.946148i | \(0.395061\pi\) | |||||||
\(824\) | − | 43.4489i | − | 0.0527292i | ||||||
\(825\) | 771.692 | + | 265.755i | 0.935385 | + | 0.322127i | ||||
\(826\) | −380.522 | −0.460680 | ||||||||
\(827\) | 223.488 | + | 223.488i | 0.270240 | + | 0.270240i | 0.829197 | − | 0.558957i | \(-0.188798\pi\) |
−0.558957 | + | 0.829197i | \(0.688798\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | − | 947.232i | − | 1.14262i | −0.820734 | − | 0.571310i | \(-0.806435\pi\) | ||
0.820734 | − | 0.571310i | \(-0.193565\pi\) | |||||||
\(830\) | 200.298 | − | 320.528i | 0.241323 | − | 0.386178i | ||||
\(831\) | 497.102 | 0.598198 | ||||||||
\(832\) | 38.8135 | + | 38.8135i | 0.0466509 | + | 0.0466509i | ||||
\(833\) | 30.7960 | − | 30.7960i | 0.0369700 | − | 0.0369700i | ||||
\(834\) | 556.517i | 0.667286i | ||||||||
\(835\) | −358.078 | + | 82.6600i | −0.428836 | + | 0.0989941i | ||||
\(836\) | −75.7112 | −0.0905637 | ||||||||
\(837\) | 66.2160 | + | 66.2160i | 0.0791111 | + | 0.0791111i | ||||
\(838\) | 384.622 | − | 384.622i | 0.458976 | − | 0.458976i | ||||
\(839\) | 200.541i | 0.239024i | 0.992833 | + | 0.119512i | \(0.0381330\pi\) | ||||
−0.992833 | + | 0.119512i | \(0.961867\pi\) | |||||||
\(840\) | −40.0039 | − | 173.294i | −0.0476237 | − | 0.206303i | ||||
\(841\) | 606.747 | 0.721459 | ||||||||
\(842\) | −454.018 | − | 454.018i | −0.539214 | − | 0.539214i | ||||
\(843\) | −264.384 | + | 264.384i | −0.313623 | + | 0.313623i | ||||
\(844\) | 258.594i | 0.306391i | ||||||||
\(845\) | 516.972 | + | 323.056i | 0.611801 | + | 0.382315i | ||||
\(846\) | 127.586 | 0.150810 | ||||||||
\(847\) | −1202.78 | − | 1202.78i | −1.42005 | − | 1.42005i | ||||
\(848\) | −122.799 | + | 122.799i | −0.144810 | + | 0.144810i | ||||
\(849\) | 690.699i | 0.813544i | ||||||||
\(850\) | −372.174 | + | 181.500i | −0.437852 | + | 0.213529i | ||||
\(851\) | −54.1917 | −0.0636801 | ||||||||
\(852\) | −20.5375 | − | 20.5375i | −0.0241051 | − | 0.0241051i | ||||
\(853\) | −595.648 | + | 595.648i | −0.698298 | + | 0.698298i | −0.964043 | − | 0.265745i | \(-0.914382\pi\) |
0.265745 | + | 0.964043i | \(0.414382\pi\) | |||||||
\(854\) | − | 676.693i | − | 0.792380i | ||||||
\(855\) | −15.9649 | + | 25.5479i | −0.0186724 | + | 0.0298806i | ||||
\(856\) | −74.6913 | −0.0872562 | ||||||||
\(857\) | 252.861 | + | 252.861i | 0.295054 | + | 0.295054i | 0.839073 | − | 0.544019i | \(-0.183098\pi\) |
−0.544019 | + | 0.839073i | \(0.683098\pi\) | |||||||
\(858\) | 224.001 | − | 224.001i | 0.261073 | − | 0.261073i | ||||
\(859\) | − | 377.138i | − | 0.439043i | −0.975608 | − | 0.219522i | \(-0.929550\pi\) | ||
0.975608 | − | 0.219522i | \(-0.0704497\pi\) | |||||||
\(860\) | −261.258 | + | 60.3097i | −0.303788 | + | 0.0701275i | ||||
\(861\) | 108.224 | 0.125695 | ||||||||
\(862\) | −241.139 | − | 241.139i | −0.279743 | − | 0.279743i | ||||
\(863\) | −131.835 | + | 131.835i | −0.152764 | + | 0.152764i | −0.779351 | − | 0.626587i | \(-0.784451\pi\) |
0.626587 | + | 0.779351i | \(0.284451\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 290.270 | + | 1257.43i | 0.335572 | + | 1.45368i | ||||
\(866\) | −556.865 | −0.643031 | ||||||||
\(867\) | −185.960 | − | 185.960i | −0.214486 | − | 0.214486i | ||||
\(868\) | −185.052 | + | 185.052i | −0.213193 | + | 0.213193i | ||||
\(869\) | 1957.91i | 2.25306i | ||||||||
\(870\) | 158.965 | + | 99.3377i | 0.182719 | + | 0.114181i | ||||
\(871\) | 683.755 | 0.785023 | ||||||||
\(872\) | 205.622 | + | 205.622i | 0.235805 | + | 0.235805i | ||||
\(873\) | 316.219 | − | 316.219i | 0.362221 | − | 0.362221i | ||||
\(874\) | 13.6216i | 0.0155854i | ||||||||
\(875\) | 571.119 | + | 705.374i | 0.652707 | + | 0.806142i | ||||
\(876\) | 386.988 | 0.441767 | ||||||||
\(877\) | −21.3642 | − | 21.3642i | −0.0243606 | − | 0.0243606i | 0.694822 | − | 0.719182i | \(-0.255483\pi\) |
−0.719182 | + | 0.694822i | \(0.755483\pi\) | |||||||
\(878\) | 439.356 | − | 439.356i | 0.500406 | − | 0.500406i | ||||
\(879\) | 657.954i | 0.748525i | ||||||||
\(880\) | 199.773 | − | 319.687i | 0.227015 | − | 0.363280i | ||||
\(881\) | 1643.48 | 1.86547 | 0.932737 | − | 0.360556i | \(-0.117413\pi\) | ||||
0.932737 | + | 0.360556i | \(0.117413\pi\) | |||||||
\(882\) | 11.1560 | + | 11.1560i | 0.0126486 | + | 0.0126486i | ||||
\(883\) | −784.243 | + | 784.243i | −0.888158 | + | 0.888158i | −0.994346 | − | 0.106188i | \(-0.966135\pi\) |
0.106188 | + | 0.994346i | \(0.466135\pi\) | |||||||
\(884\) | 160.716i | 0.181805i | ||||||||
\(885\) | −312.708 | + | 72.1867i | −0.353342 | + | 0.0815669i | ||||
\(886\) | −523.212 | −0.590532 | ||||||||
\(887\) | 473.986 | + | 473.986i | 0.534369 | + | 0.534369i | 0.921870 | − | 0.387500i | \(-0.126661\pi\) |
−0.387500 | + | 0.921870i | \(0.626661\pi\) | |||||||
\(888\) | −39.1435 | + | 39.1435i | −0.0440805 | + | 0.0440805i | ||||
\(889\) | 730.276i | 0.821458i | ||||||||
\(890\) | −223.004 | − | 966.037i | −0.250566 | − | 1.08544i | ||||
\(891\) | 169.638 | 0.190390 | ||||||||
\(892\) | −36.8733 | − | 36.8733i | −0.0413378 | − | 0.0413378i | ||||
\(893\) | 42.7071 | − | 42.7071i | 0.0478243 | − | 0.0478243i | ||||
\(894\) | − | 343.496i | − | 0.384224i | ||||||
\(895\) | −101.003 | − | 63.1171i | −0.112853 | − | 0.0705219i | ||||
\(896\) | −82.1462 | −0.0916810 | ||||||||
\(897\) | −40.3012 | − | 40.3012i | −0.0449289 | − | 0.0449289i | ||||
\(898\) | 876.612 | − | 876.612i | 0.976183 | − | 0.976183i | ||||
\(899\) | − | 275.828i | − | 0.306817i | ||||||
\(900\) | −65.7494 | − | 134.822i | −0.0730549 | − | 0.149802i | ||||
\(901\) | −508.476 | −0.564346 | ||||||||
\(902\) | 162.203 | + | 162.203i | 0.179826 | + | 0.179826i | ||||
\(903\) | 238.435 | − | 238.435i | 0.264048 | − | 0.264048i | ||||
\(904\) | 73.2718i | 0.0810529i | ||||||||
\(905\) | 559.035 | − | 894.597i | 0.617718 | − | 0.988505i | ||||
\(906\) | 526.275 | 0.580878 | ||||||||
\(907\) | 676.741 | + | 676.741i | 0.746131 | + | 0.746131i | 0.973750 | − | 0.227619i | \(-0.0730941\pi\) |
−0.227619 | + | 0.973750i | \(0.573094\pi\) | |||||||
\(908\) | 236.816 | − | 236.816i | 0.260811 | − | 0.260811i | ||||
\(909\) | 498.812i | 0.548748i | ||||||||
\(910\) | 343.243 | − | 79.2355i | 0.377190 | − | 0.0870720i | ||||
\(911\) | −273.437 | −0.300151 | −0.150075 | − | 0.988675i | \(-0.547952\pi\) | ||||
−0.150075 | + | 0.988675i | \(0.547952\pi\) | |||||||
\(912\) | 9.83910 | + | 9.83910i | 0.0107885 | + | 0.0107885i | ||||
\(913\) | −712.414 | + | 712.414i | −0.780300 | + | 0.780300i | ||||
\(914\) | 36.0696i | 0.0394635i | ||||||||
\(915\) | −128.372 | − | 556.098i | −0.140297 | − | 0.607757i | ||||
\(916\) | −79.7477 | −0.0870608 | ||||||||
\(917\) | 696.923 | + | 696.923i | 0.760003 | + | 0.760003i | ||||
\(918\) | −60.8559 | + | 60.8559i | −0.0662918 | + | 0.0662918i | ||||
\(919\) | 404.328i | 0.439965i | 0.975504 | + | 0.219983i | \(0.0706001\pi\) | ||||
−0.975504 | + | 0.219983i | \(0.929400\pi\) | |||||||
\(920\) | −57.5166 | − | 35.9422i | −0.0625180 | − | 0.0390676i | ||||
\(921\) | 594.994 | 0.646030 | ||||||||
\(922\) | 746.316 | + | 746.316i | 0.809453 | + | 0.809453i | ||||
\(923\) | 40.6786 | − | 40.6786i | 0.0440722 | − | 0.0440722i | ||||
\(924\) | 474.082i | 0.513076i | ||||||||
\(925\) | 91.9834 | − | 267.099i | 0.0994416 | − | 0.288756i | ||||
\(926\) | −356.944 | −0.385469 | ||||||||
\(927\) | 32.5866 | + | 32.5866i | 0.0351528 | + | 0.0351528i | ||||
\(928\) | 61.2213 | − | 61.2213i | 0.0659713 | − | 0.0659713i | ||||
\(929\) | 274.030i | 0.294973i | 0.989064 | + | 0.147487i | \(0.0471183\pi\) | ||||
−0.989064 | + | 0.147487i | \(0.952882\pi\) | |||||||
\(930\) | −116.968 | + | 187.178i | −0.125772 | + | 0.201267i | ||||
\(931\) | 7.46858 | 0.00802211 | ||||||||
\(932\) | 206.109 | + | 206.109i | 0.221147 | + | 0.221147i | ||||
\(933\) | −253.962 | + | 253.962i | −0.272199 | + | 0.272199i | ||||
\(934\) | − | 493.606i | − | 0.528486i | ||||||
\(935\) | 1075.47 | − | 248.265i | 1.15023 | − | 0.265524i | ||||
\(936\) | −58.2203 | −0.0622012 | ||||||||
\(937\) | 39.3211 | + | 39.3211i | 0.0419649 | + | 0.0419649i | 0.727778 | − | 0.685813i | \(-0.240553\pi\) |
−0.685813 | + | 0.727778i | \(0.740553\pi\) | |||||||
\(938\) | −723.560 | + | 723.560i | −0.771386 | + | 0.771386i | ||||
\(939\) | 689.474i | 0.734264i | ||||||||
\(940\) | 67.6410 | + | 293.016i | 0.0719585 | + | 0.311720i | ||||
\(941\) | −1723.79 | −1.83187 | −0.915935 | − | 0.401327i | \(-0.868549\pi\) | ||||
−0.915935 | + | 0.401327i | \(0.868549\pi\) | |||||||
\(942\) | 292.671 | + | 292.671i | 0.310691 | + | 0.310691i | ||||
\(943\) | 29.1829 | − | 29.1829i | 0.0309469 | − | 0.0309469i | ||||
\(944\) | 148.232i | 0.157026i | ||||||||
\(945\) | 159.974 | + | 99.9678i | 0.169284 | + | 0.105786i | ||||
\(946\) | 714.724 | 0.755522 | ||||||||
\(947\) | 205.982 | + | 205.982i | 0.217510 | + | 0.217510i | 0.807448 | − | 0.589938i | \(-0.200848\pi\) |
−0.589938 | + | 0.807448i | \(0.700848\pi\) | |||||||
\(948\) | 254.442 | − | 254.442i | 0.268398 | − | 0.268398i | ||||
\(949\) | 766.504i | 0.807697i | ||||||||
\(950\) | −67.1379 | − | 23.1209i | −0.0706715 | − | 0.0243378i | ||||
\(951\) | 599.354 | 0.630235 | ||||||||
\(952\) | −170.072 | − | 170.072i | −0.178647 | − | 0.178647i | ||||
\(953\) | −820.248 | + | 820.248i | −0.860701 | + | 0.860701i | −0.991419 | − | 0.130719i | \(-0.958271\pi\) |
0.130719 | + | 0.991419i | \(0.458271\pi\) | |||||||
\(954\) | − | 184.198i | − | 0.193080i | ||||||
\(955\) | 284.009 | − | 454.486i | 0.297391 | − | 0.475901i | ||||
\(956\) | −790.127 | −0.826493 | ||||||||
\(957\) | −353.321 | − | 353.321i | −0.369196 | − | 0.369196i | ||||
\(958\) | 171.427 | − | 171.427i | 0.178943 | − | 0.178943i | ||||
\(959\) | 622.135i | 0.648733i | ||||||||
\(960\) | −67.5067 | + | 15.5835i | −0.0703195 | + | 0.0162328i | ||||
\(961\) | −636.218 | −0.662037 | ||||||||
\(962\) | −77.5314 | − | 77.5314i | −0.0805939 | − | 0.0805939i | ||||
\(963\) | 56.0185 | − | 56.0185i | 0.0581708 | − | 0.0581708i | ||||
\(964\) | 534.371i | 0.554327i | ||||||||
\(965\) | 325.930 | + | 1411.91i | 0.337751 | + | 1.46312i | ||||
\(966\) | 85.2946 | 0.0882967 | ||||||||
\(967\) | 524.926 | + | 524.926i | 0.542839 | + | 0.542839i | 0.924360 | − | 0.381521i | \(-0.124600\pi\) |
−0.381521 | + | 0.924360i | \(0.624600\pi\) | |||||||
\(968\) | −468.544 | + | 468.544i | −0.484033 | + | 0.484033i | ||||
\(969\) | 40.7410i | 0.0420443i | ||||||||
\(970\) | 893.882 | + | 558.589i | 0.921528 | + | 0.575865i | ||||
\(971\) | −1740.45 | −1.79243 | −0.896215 | − | 0.443621i | \(-0.853694\pi\) | ||||
−0.896215 | + | 0.443621i | \(0.853694\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 1166.46 | − | 1166.46i | 1.19883 | − | 1.19883i | ||||
\(974\) | 137.797i | 0.141475i | ||||||||
\(975\) | 267.042 | − | 130.230i | 0.273889 | − | 0.133569i | ||||
\(976\) | −263.605 | −0.270087 | ||||||||
\(977\) | −1092.92 | − | 1092.92i | −1.11865 | − | 1.11865i | −0.991940 | − | 0.126706i | \(-0.959559\pi\) |
−0.126706 | − | 0.991940i | \(-0.540441\pi\) | |||||||
\(978\) | 55.4430 | − | 55.4430i | 0.0566902 | − | 0.0566902i | ||||
\(979\) | 2642.79i | 2.69948i | ||||||||
\(980\) | −19.7067 | + | 31.5357i | −0.0201089 | + | 0.0321793i | ||||
\(981\) | −308.433 | −0.314407 | ||||||||
\(982\) | −716.560 | − | 716.560i | −0.729695 | − | 0.729695i | ||||
\(983\) | 677.549 | − | 677.549i | 0.689266 | − | 0.689266i | −0.272804 | − | 0.962070i | \(-0.587951\pi\) |
0.962070 | + | 0.272804i | \(0.0879509\pi\) | |||||||
\(984\) | − | 42.1585i | − | 0.0428440i | ||||||
\(985\) | −1268.85 | + | 292.905i | −1.28817 | + | 0.297366i | ||||
\(986\) | 253.500 | 0.257100 | ||||||||
\(987\) | −267.420 | − | 267.420i | −0.270942 | − | 0.270942i | ||||
\(988\) | −19.4883 | + | 19.4883i | −0.0197250 | + | 0.0197250i | ||||
\(989\) | − | 128.590i | − | 0.130020i | ||||||
\(990\) | 89.9355 | + | 389.595i | 0.0908439 | + | 0.393530i | ||||
\(991\) | −1816.56 | −1.83305 | −0.916527 | − | 0.399973i | \(-0.869019\pi\) | ||||
−0.916527 | + | 0.399973i | \(0.869019\pi\) | |||||||
\(992\) | 72.0868 | + | 72.0868i | 0.0726682 | + | 0.0726682i | ||||
\(993\) | 782.307 | − | 782.307i | 0.787822 | − | 0.787822i | ||||
\(994\) | 86.0934i | 0.0866131i | ||||||||
\(995\) | −442.692 | − | 276.639i | −0.444917 | − | 0.278029i | ||||
\(996\) | 185.164 | 0.185908 | ||||||||
\(997\) | −369.067 | − | 369.067i | −0.370178 | − | 0.370178i | 0.497364 | − | 0.867542i | \(-0.334301\pi\) |
−0.867542 | + | 0.497364i | \(0.834301\pi\) | |||||||
\(998\) | −103.164 | + | 103.164i | −0.103371 | + | 0.103371i | ||||
\(999\) | − | 58.7153i | − | 0.0587740i |
(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 | 690.3.k.a.277.15 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.15 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.15 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.15 | yes | 40 | 5.3 | odd | 4 | inner |