Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [87,3,Mod(59,87)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(87, base_ring=CyclotomicField(2))
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("87.59");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 87 = 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 87.b (of order \(2\), degree \(1\), 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: | \(2.37057829993\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 54 x^{16} + 1187 x^{14} + 13673 x^{12} + 88449 x^{10} + 318861 x^{8} + 593533 x^{6} + \cdots + 15341 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 59.7 | ||
Root | \(-0.949055i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 87.59 |
Dual form | 87.3.b.a.59.12 |
$q$-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 \(\left(\mathbb{Z}/87\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(59\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.949055i | − | 0.474528i | −0.971445 | − | 0.237264i | \(-0.923749\pi\) | ||
0.971445 | − | 0.237264i | \(-0.0762506\pi\) | |||||||
\(3\) | −2.83105 | + | 0.992548i | −0.943684 | + | 0.330849i | ||||
\(4\) | 3.09929 | 0.774824 | ||||||||
\(5\) | − | 4.66941i | − | 0.933881i | −0.884289 | − | 0.466941i | \(-0.845356\pi\) | ||
0.884289 | − | 0.466941i | \(-0.154644\pi\) | |||||||
\(6\) | 0.941983 | + | 2.68682i | 0.156997 | + | 0.447804i | ||||
\(7\) | 2.70818 | 0.386883 | 0.193442 | − | 0.981112i | \(-0.438035\pi\) | ||||
0.193442 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(8\) | − | 6.73762i | − | 0.842203i | ||||||
\(9\) | 7.02970 | − | 5.61991i | 0.781077 | − | 0.624434i | ||||
\(10\) | −4.43152 | −0.443152 | ||||||||
\(11\) | − | 13.8330i | − | 1.25754i | −0.777589 | − | 0.628772i | \(-0.783558\pi\) | ||
0.777589 | − | 0.628772i | \(-0.216442\pi\) | |||||||
\(12\) | −8.77426 | + | 3.07620i | −0.731188 | + | 0.256350i | ||||
\(13\) | 6.42457 | 0.494198 | 0.247099 | − | 0.968990i | \(-0.420523\pi\) | ||||
0.247099 | + | 0.968990i | \(0.420523\pi\) | |||||||
\(14\) | − | 2.57021i | − | 0.183587i | ||||||
\(15\) | 4.63461 | + | 13.2193i | 0.308974 | + | 0.881288i | ||||
\(16\) | 6.00280 | 0.375175 | ||||||||
\(17\) | 8.06761i | 0.474565i | 0.971441 | + | 0.237283i | \(0.0762568\pi\) | ||||
−0.971441 | + | 0.237283i | \(0.923743\pi\) | |||||||
\(18\) | −5.33360 | − | 6.67157i | −0.296311 | − | 0.370643i | ||||
\(19\) | −18.9043 | −0.994964 | −0.497482 | − | 0.867474i | \(-0.665742\pi\) | ||||
−0.497482 | + | 0.867474i | \(0.665742\pi\) | |||||||
\(20\) | − | 14.4719i | − | 0.723593i | ||||||
\(21\) | −7.66700 | + | 2.68800i | −0.365095 | + | 0.128000i | ||||
\(22\) | −13.1283 | −0.596740 | ||||||||
\(23\) | 45.5759i | 1.98156i | 0.135481 | + | 0.990780i | \(0.456742\pi\) | ||||
−0.135481 | + | 0.990780i | \(0.543258\pi\) | |||||||
\(24\) | 6.68741 | + | 19.0745i | 0.278642 | + | 0.794773i | ||||
\(25\) | 3.19665 | 0.127866 | ||||||||
\(26\) | − | 6.09727i | − | 0.234511i | ||||||
\(27\) | −14.3234 | + | 22.8876i | −0.530496 | + | 0.847687i | ||||
\(28\) | 8.39346 | 0.299766 | ||||||||
\(29\) | 5.38516i | 0.185695i | ||||||||
\(30\) | 12.5459 | − | 4.39850i | 0.418196 | − | 0.146617i | ||||
\(31\) | 0.734353 | 0.0236888 | 0.0118444 | − | 0.999930i | \(-0.496230\pi\) | ||||
0.0118444 | + | 0.999930i | \(0.496230\pi\) | |||||||
\(32\) | − | 32.6475i | − | 1.02023i | ||||||
\(33\) | 13.7299 | + | 39.1619i | 0.416058 | + | 1.18672i | ||||
\(34\) | 7.65661 | 0.225194 | ||||||||
\(35\) | − | 12.6456i | − | 0.361303i | ||||||
\(36\) | 21.7871 | − | 17.4178i | 0.605197 | − | 0.483826i | ||||
\(37\) | 45.0418 | 1.21735 | 0.608673 | − | 0.793421i | \(-0.291702\pi\) | ||||
0.608673 | + | 0.793421i | \(0.291702\pi\) | |||||||
\(38\) | 17.9412i | 0.472138i | ||||||||
\(39\) | −18.1883 | + | 6.37670i | −0.466366 | + | 0.163505i | ||||
\(40\) | −31.4607 | −0.786517 | ||||||||
\(41\) | − | 22.1078i | − | 0.539216i | −0.962970 | − | 0.269608i | \(-0.913106\pi\) | ||
0.962970 | − | 0.269608i | \(-0.0868940\pi\) | |||||||
\(42\) | 2.55106 | + | 7.27641i | 0.0607396 | + | 0.173248i | ||||
\(43\) | −54.1714 | −1.25980 | −0.629900 | − | 0.776677i | \(-0.716904\pi\) | ||||
−0.629900 | + | 0.776677i | \(0.716904\pi\) | |||||||
\(44\) | − | 42.8725i | − | 0.974375i | ||||||
\(45\) | −26.2416 | − | 32.8245i | −0.583147 | − | 0.729433i | ||||
\(46\) | 43.2540 | 0.940305 | ||||||||
\(47\) | 52.7654i | 1.12267i | 0.827590 | + | 0.561334i | \(0.189712\pi\) | ||||
−0.827590 | + | 0.561334i | \(0.810288\pi\) | |||||||
\(48\) | −16.9942 | + | 5.95807i | −0.354047 | + | 0.124127i | ||||
\(49\) | −41.6657 | −0.850321 | ||||||||
\(50\) | − | 3.03380i | − | 0.0606760i | ||||||
\(51\) | −8.00749 | − | 22.8398i | −0.157010 | − | 0.447839i | ||||
\(52\) | 19.9116 | 0.382916 | ||||||||
\(53\) | − | 10.8047i | − | 0.203863i | −0.994791 | − | 0.101931i | \(-0.967498\pi\) | ||
0.994791 | − | 0.101931i | \(-0.0325022\pi\) | |||||||
\(54\) | 21.7216 | + | 13.5937i | 0.402251 | + | 0.251735i | ||||
\(55\) | −64.5918 | −1.17440 | ||||||||
\(56\) | − | 18.2467i | − | 0.325834i | ||||||
\(57\) | 53.5191 | − | 18.7635i | 0.938932 | − | 0.329183i | ||||
\(58\) | 5.11082 | 0.0881175 | ||||||||
\(59\) | 0.612120i | 0.0103749i | 0.999987 | + | 0.00518746i | \(0.00165123\pi\) | ||||
−0.999987 | + | 0.00518746i | \(0.998349\pi\) | |||||||
\(60\) | 14.3640 | + | 40.9706i | 0.239400 | + | 0.682843i | ||||
\(61\) | 24.1156 | 0.395337 | 0.197669 | − | 0.980269i | \(-0.436663\pi\) | ||||
0.197669 | + | 0.980269i | \(0.436663\pi\) | |||||||
\(62\) | − | 0.696942i | − | 0.0112410i | ||||||
\(63\) | 19.0377 | − | 15.2197i | 0.302186 | − | 0.241583i | ||||
\(64\) | −6.97304 | −0.108954 | ||||||||
\(65\) | − | 29.9989i | − | 0.461522i | ||||||
\(66\) | 37.1668 | − | 13.0304i | 0.563133 | − | 0.197431i | ||||
\(67\) | 106.201 | 1.58508 | 0.792541 | − | 0.609818i | \(-0.208758\pi\) | ||||
0.792541 | + | 0.609818i | \(0.208758\pi\) | |||||||
\(68\) | 25.0039i | 0.367704i | ||||||||
\(69\) | −45.2363 | − | 129.028i | −0.655598 | − | 1.86997i | ||||
\(70\) | −12.0014 | −0.171448 | ||||||||
\(71\) | 25.3182i | 0.356594i | 0.983977 | + | 0.178297i | \(0.0570588\pi\) | ||||
−0.983977 | + | 0.178297i | \(0.942941\pi\) | |||||||
\(72\) | −37.8648 | − | 47.3634i | −0.525900 | − | 0.657825i | ||||
\(73\) | −18.3423 | −0.251264 | −0.125632 | − | 0.992077i | \(-0.540096\pi\) | ||||
−0.125632 | + | 0.992077i | \(0.540096\pi\) | |||||||
\(74\) | − | 42.7471i | − | 0.577664i | ||||||
\(75\) | −9.04988 | + | 3.17283i | −0.120665 | + | 0.0423044i | ||||
\(76\) | −58.5901 | −0.770922 | ||||||||
\(77\) | − | 37.4623i | − | 0.486523i | ||||||
\(78\) | 6.05184 | + | 17.2617i | 0.0775877 | + | 0.221304i | ||||
\(79\) | 141.252 | 1.78801 | 0.894003 | − | 0.448061i | \(-0.147885\pi\) | ||||
0.894003 | + | 0.448061i | \(0.147885\pi\) | |||||||
\(80\) | − | 28.0295i | − | 0.350369i | ||||||
\(81\) | 17.8333 | − | 79.0125i | 0.220164 | − | 0.975463i | ||||
\(82\) | −20.9816 | −0.255873 | ||||||||
\(83\) | 155.906i | 1.87839i | 0.343390 | + | 0.939193i | \(0.388425\pi\) | ||||
−0.343390 | + | 0.939193i | \(0.611575\pi\) | |||||||
\(84\) | −23.7623 | + | 8.33091i | −0.282885 | + | 0.0991775i | ||||
\(85\) | 37.6709 | 0.443188 | ||||||||
\(86\) | 51.4116i | 0.597809i | ||||||||
\(87\) | −5.34504 | − | 15.2457i | −0.0614372 | − | 0.175238i | ||||
\(88\) | −93.2015 | −1.05911 | ||||||||
\(89\) | 63.6274i | 0.714914i | 0.933930 | + | 0.357457i | \(0.116356\pi\) | ||||
−0.933930 | + | 0.357457i | \(0.883644\pi\) | |||||||
\(90\) | −31.1523 | + | 24.9048i | −0.346136 | + | 0.276719i | ||||
\(91\) | 17.3989 | 0.191197 | ||||||||
\(92\) | 141.253i | 1.53536i | ||||||||
\(93\) | −2.07899 | + | 0.728881i | −0.0223547 | + | 0.00783743i | ||||
\(94\) | 50.0772 | 0.532737 | ||||||||
\(95\) | 88.2720i | 0.929178i | ||||||||
\(96\) | 32.4042 | + | 92.4267i | 0.337544 | + | 0.962778i | ||||
\(97\) | 12.1334 | 0.125086 | 0.0625431 | − | 0.998042i | \(-0.480079\pi\) | ||||
0.0625431 | + | 0.998042i | \(0.480079\pi\) | |||||||
\(98\) | 39.5431i | 0.403501i | ||||||||
\(99\) | −77.7401 | − | 97.2417i | −0.785254 | − | 0.982240i | ||||
\(100\) | 9.90737 | 0.0990737 | ||||||||
\(101\) | 43.8464i | 0.434123i | 0.976158 | + | 0.217061i | \(0.0696472\pi\) | ||||
−0.976158 | + | 0.217061i | \(0.930353\pi\) | |||||||
\(102\) | −21.6762 | + | 7.59955i | −0.212512 | + | 0.0745054i | ||||
\(103\) | −145.324 | −1.41091 | −0.705454 | − | 0.708756i | \(-0.749257\pi\) | ||||
−0.705454 | + | 0.708756i | \(0.749257\pi\) | |||||||
\(104\) | − | 43.2863i | − | 0.416215i | ||||||
\(105\) | 12.5514 | + | 35.8003i | 0.119537 | + | 0.340956i | ||||
\(106\) | −10.2543 | −0.0967385 | ||||||||
\(107\) | − | 66.5513i | − | 0.621975i | −0.950414 | − | 0.310988i | \(-0.899340\pi\) | ||
0.950414 | − | 0.310988i | \(-0.100660\pi\) | |||||||
\(108\) | −44.3924 | + | 70.9353i | −0.411041 | + | 0.656808i | ||||
\(109\) | −80.5353 | −0.738856 | −0.369428 | − | 0.929259i | \(-0.620446\pi\) | ||||
−0.369428 | + | 0.929259i | \(0.620446\pi\) | |||||||
\(110\) | 61.3012i | 0.557284i | ||||||||
\(111\) | −127.516 | + | 44.7061i | −1.14879 | + | 0.402758i | ||||
\(112\) | 16.2567 | 0.145149 | ||||||||
\(113\) | − | 90.4762i | − | 0.800675i | −0.916368 | − | 0.400337i | \(-0.868893\pi\) | ||
0.916368 | − | 0.400337i | \(-0.131107\pi\) | |||||||
\(114\) | −17.8076 | − | 50.7926i | −0.156207 | − | 0.445549i | ||||
\(115\) | 212.812 | 1.85054 | ||||||||
\(116\) | 16.6902i | 0.143881i | ||||||||
\(117\) | 45.1628 | − | 36.1055i | 0.386007 | − | 0.308594i | ||||
\(118\) | 0.580936 | 0.00492318 | ||||||||
\(119\) | 21.8486i | 0.183601i | ||||||||
\(120\) | 89.0668 | − | 31.2262i | 0.742223 | − | 0.260219i | ||||
\(121\) | −70.3516 | −0.581418 | ||||||||
\(122\) | − | 22.8870i | − | 0.187598i | ||||||
\(123\) | 21.9431 | + | 62.5884i | 0.178399 | + | 0.508849i | ||||
\(124\) | 2.27598 | 0.0183547 | ||||||||
\(125\) | − | 131.662i | − | 1.05329i | ||||||
\(126\) | −14.4444 | − | 18.0678i | −0.114638 | − | 0.143395i | ||||
\(127\) | −173.633 | −1.36719 | −0.683596 | − | 0.729861i | \(-0.739585\pi\) | ||||
−0.683596 | + | 0.729861i | \(0.739585\pi\) | |||||||
\(128\) | − | 123.972i | − | 0.968532i | ||||||
\(129\) | 153.362 | − | 53.7677i | 1.18885 | − | 0.416804i | ||||
\(130\) | −28.4706 | −0.219005 | ||||||||
\(131\) | − | 8.21316i | − | 0.0626959i | −0.999509 | − | 0.0313480i | \(-0.990020\pi\) | ||
0.999509 | − | 0.0313480i | \(-0.00998000\pi\) | |||||||
\(132\) | 42.5530 | + | 121.374i | 0.322371 | + | 0.919502i | ||||
\(133\) | −51.1964 | −0.384935 | ||||||||
\(134\) | − | 100.790i | − | 0.752165i | ||||||
\(135\) | 106.871 | + | 66.8817i | 0.791639 | + | 0.495420i | ||||
\(136\) | 54.3565 | 0.399680 | ||||||||
\(137\) | 168.338i | 1.22874i | 0.789017 | + | 0.614371i | \(0.210590\pi\) | ||||
−0.789017 | + | 0.614371i | \(0.789410\pi\) | |||||||
\(138\) | −122.454 | + | 42.9317i | −0.887350 | + | 0.311099i | ||||
\(139\) | 165.153 | 1.18815 | 0.594075 | − | 0.804410i | \(-0.297518\pi\) | ||||
0.594075 | + | 0.804410i | \(0.297518\pi\) | |||||||
\(140\) | − | 39.1925i | − | 0.279946i | ||||||
\(141\) | −52.3722 | − | 149.381i | −0.371434 | − | 1.05944i | ||||
\(142\) | 24.0283 | 0.169214 | ||||||||
\(143\) | − | 88.8711i | − | 0.621476i | ||||||
\(144\) | 42.1979 | − | 33.7352i | 0.293041 | − | 0.234272i | ||||
\(145\) | 25.1455 | 0.173417 | ||||||||
\(146\) | 17.4078i | 0.119232i | ||||||||
\(147\) | 117.958 | − | 41.3553i | 0.802434 | − | 0.281328i | ||||
\(148\) | 139.598 | 0.943228 | ||||||||
\(149\) | − | 38.0573i | − | 0.255418i | −0.991812 | − | 0.127709i | \(-0.959238\pi\) | ||
0.991812 | − | 0.127709i | \(-0.0407623\pi\) | |||||||
\(150\) | 3.01119 | + | 8.58884i | 0.0200746 | + | 0.0572589i | ||||
\(151\) | 9.99308 | 0.0661793 | 0.0330897 | − | 0.999452i | \(-0.489465\pi\) | ||||
0.0330897 | + | 0.999452i | \(0.489465\pi\) | |||||||
\(152\) | 127.370i | 0.837962i | ||||||||
\(153\) | 45.3392 | + | 56.7128i | 0.296335 | + | 0.370672i | ||||
\(154\) | −35.5538 | −0.230869 | ||||||||
\(155\) | − | 3.42899i | − | 0.0221225i | ||||||
\(156\) | −56.3709 | + | 19.7633i | −0.361352 | + | 0.126688i | ||||
\(157\) | −86.1231 | −0.548555 | −0.274277 | − | 0.961651i | \(-0.588439\pi\) | ||||
−0.274277 | + | 0.961651i | \(0.588439\pi\) | |||||||
\(158\) | − | 134.056i | − | 0.848458i | ||||||
\(159\) | 10.7242 | + | 30.5887i | 0.0674479 | + | 0.192382i | ||||
\(160\) | −152.444 | −0.952777 | ||||||||
\(161\) | 123.428i | 0.766632i | ||||||||
\(162\) | −74.9872 | − | 16.9247i | −0.462884 | − | 0.104474i | ||||
\(163\) | −186.345 | −1.14322 | −0.571611 | − | 0.820525i | \(-0.693681\pi\) | ||||
−0.571611 | + | 0.820525i | \(0.693681\pi\) | |||||||
\(164\) | − | 68.5187i | − | 0.417797i | ||||||
\(165\) | 182.863 | − | 64.1105i | 1.10826 | − | 0.388549i | ||||
\(166\) | 147.963 | 0.891346 | ||||||||
\(167\) | − | 285.991i | − | 1.71252i | −0.516546 | − | 0.856260i | \(-0.672782\pi\) | ||
0.516546 | − | 0.856260i | \(-0.327218\pi\) | |||||||
\(168\) | 18.1107 | + | 51.6574i | 0.107802 | + | 0.307484i | ||||
\(169\) | −127.725 | −0.755768 | ||||||||
\(170\) | − | 35.7518i | − | 0.210305i | ||||||
\(171\) | −132.892 | + | 106.241i | −0.777144 | + | 0.621290i | ||||
\(172\) | −167.893 | −0.976122 | ||||||||
\(173\) | 191.064i | 1.10441i | 0.833707 | + | 0.552207i | \(0.186214\pi\) | ||||
−0.833707 | + | 0.552207i | \(0.813786\pi\) | |||||||
\(174\) | −14.4690 | + | 5.07273i | −0.0831551 | + | 0.0291536i | ||||
\(175\) | 8.65712 | 0.0494692 | ||||||||
\(176\) | − | 83.0367i | − | 0.471800i | ||||||
\(177\) | −0.607559 | − | 1.73294i | −0.00343254 | − | 0.00979064i | ||||
\(178\) | 60.3859 | 0.339247 | ||||||||
\(179\) | − | 335.224i | − | 1.87276i | −0.350985 | − | 0.936381i | \(-0.614153\pi\) | ||
0.350985 | − | 0.936381i | \(-0.385847\pi\) | |||||||
\(180\) | −81.3305 | − | 101.733i | −0.451836 | − | 0.565182i | ||||
\(181\) | 209.048 | 1.15496 | 0.577480 | − | 0.816405i | \(-0.304036\pi\) | ||||
0.577480 | + | 0.816405i | \(0.304036\pi\) | |||||||
\(182\) | − | 16.5125i | − | 0.0907282i | ||||||
\(183\) | −68.2724 | + | 23.9359i | −0.373073 | + | 0.130797i | ||||
\(184\) | 307.073 | 1.66888 | ||||||||
\(185\) | − | 210.318i | − | 1.13686i | ||||||
\(186\) | 0.691748 | + | 1.97308i | 0.00371908 | + | 0.0106079i | ||||
\(187\) | 111.599 | 0.596787 | ||||||||
\(188\) | 163.535i | 0.869869i | ||||||||
\(189\) | −38.7904 | + | 61.9837i | −0.205240 | + | 0.327956i | ||||
\(190\) | 83.7749 | 0.440921 | ||||||||
\(191\) | 202.381i | 1.05959i | 0.848127 | + | 0.529794i | \(0.177731\pi\) | ||||
−0.848127 | + | 0.529794i | \(0.822269\pi\) | |||||||
\(192\) | 19.7410 | − | 6.92107i | 0.102818 | − | 0.0360473i | ||||
\(193\) | 324.176 | 1.67967 | 0.839834 | − | 0.542844i | \(-0.182652\pi\) | ||||
0.839834 | + | 0.542844i | \(0.182652\pi\) | |||||||
\(194\) | − | 11.5152i | − | 0.0593568i | ||||||
\(195\) | 29.7754 | + | 84.9285i | 0.152694 | + | 0.435531i | ||||
\(196\) | −129.134 | −0.658849 | ||||||||
\(197\) | − | 272.338i | − | 1.38243i | −0.722650 | − | 0.691214i | \(-0.757076\pi\) | ||
0.722650 | − | 0.691214i | \(-0.242924\pi\) | |||||||
\(198\) | −92.2877 | + | 73.7797i | −0.466100 | + | 0.372625i | ||||
\(199\) | −336.191 | −1.68940 | −0.844701 | − | 0.535238i | \(-0.820222\pi\) | ||||
−0.844701 | + | 0.535238i | \(0.820222\pi\) | |||||||
\(200\) | − | 21.5378i | − | 0.107689i | ||||||
\(201\) | −300.659 | + | 105.409i | −1.49582 | + | 0.524424i | ||||
\(202\) | 41.6126 | 0.206003 | ||||||||
\(203\) | 14.5840i | 0.0718424i | ||||||||
\(204\) | −24.8176 | − | 70.7873i | −0.121655 | − | 0.346997i | ||||
\(205\) | −103.230 | −0.503563 | ||||||||
\(206\) | 137.920i | 0.669515i | ||||||||
\(207\) | 256.132 | + | 320.385i | 1.23735 | + | 1.54775i | ||||
\(208\) | 38.5655 | 0.185411 | ||||||||
\(209\) | 261.503i | 1.25121i | ||||||||
\(210\) | 33.9765 | − | 11.9119i | 0.161793 | − | 0.0567235i | ||||
\(211\) | −262.151 | −1.24242 | −0.621212 | − | 0.783643i | \(-0.713359\pi\) | ||||
−0.621212 | + | 0.783643i | \(0.713359\pi\) | |||||||
\(212\) | − | 33.4870i | − | 0.157958i | ||||||
\(213\) | −25.1295 | − | 71.6770i | −0.117979 | − | 0.336512i | ||||
\(214\) | −63.1609 | −0.295144 | ||||||||
\(215\) | 252.948i | 1.17650i | ||||||||
\(216\) | 154.208 | + | 96.5056i | 0.713925 | + | 0.446785i | ||||
\(217\) | 1.98876 | 0.00916480 | ||||||||
\(218\) | 76.4324i | 0.350607i | ||||||||
\(219\) | 51.9279 | − | 18.2056i | 0.237114 | − | 0.0831305i | ||||
\(220\) | −200.189 | −0.909951 | ||||||||
\(221\) | 51.8310i | 0.234529i | ||||||||
\(222\) | 42.4286 | + | 121.019i | 0.191120 | + | 0.545132i | ||||
\(223\) | −37.9013 | −0.169961 | −0.0849805 | − | 0.996383i | \(-0.527083\pi\) | ||||
−0.0849805 | + | 0.996383i | \(0.527083\pi\) | |||||||
\(224\) | − | 88.4153i | − | 0.394711i | ||||||
\(225\) | 22.4715 | − | 17.9649i | 0.0998733 | − | 0.0798440i | ||||
\(226\) | −85.8669 | −0.379942 | ||||||||
\(227\) | − | 325.184i | − | 1.43253i | −0.697829 | − | 0.716265i | \(-0.745850\pi\) | ||
0.697829 | − | 0.716265i | \(-0.254150\pi\) | |||||||
\(228\) | 165.871 | − | 58.1535i | 0.727506 | − | 0.255059i | ||||
\(229\) | −184.820 | −0.807076 | −0.403538 | − | 0.914963i | \(-0.632220\pi\) | ||||
−0.403538 | + | 0.914963i | \(0.632220\pi\) | |||||||
\(230\) | − | 201.971i | − | 0.878133i | ||||||
\(231\) | 37.1831 | + | 106.058i | 0.160966 | + | 0.459124i | ||||
\(232\) | 36.2832 | 0.156393 | ||||||||
\(233\) | 243.534i | 1.04521i | 0.852574 | + | 0.522606i | \(0.175040\pi\) | ||||
−0.852574 | + | 0.522606i | \(0.824960\pi\) | |||||||
\(234\) | −34.2661 | − | 42.8620i | −0.146436 | − | 0.183171i | ||||
\(235\) | 246.383 | 1.04844 | ||||||||
\(236\) | 1.89714i | 0.00803873i | ||||||||
\(237\) | −399.893 | + | 140.200i | −1.68731 | + | 0.591561i | ||||
\(238\) | 20.7355 | 0.0871239 | ||||||||
\(239\) | − | 82.0366i | − | 0.343250i | −0.985162 | − | 0.171625i | \(-0.945098\pi\) | ||
0.985162 | − | 0.171625i | \(-0.0549017\pi\) | |||||||
\(240\) | 27.8207 | + | 79.3530i | 0.115919 | + | 0.330638i | ||||
\(241\) | 42.4682 | 0.176217 | 0.0881084 | − | 0.996111i | \(-0.471918\pi\) | ||||
0.0881084 | + | 0.996111i | \(0.471918\pi\) | |||||||
\(242\) | 66.7676i | 0.275899i | ||||||||
\(243\) | 27.9369 | + | 241.389i | 0.114967 | + | 0.993369i | ||||
\(244\) | 74.7413 | 0.306317 | ||||||||
\(245\) | 194.554i | 0.794099i | ||||||||
\(246\) | 59.3998 | − | 20.8252i | 0.241463 | − | 0.0846553i | ||||
\(247\) | −121.452 | −0.491709 | ||||||||
\(248\) | − | 4.94779i | − | 0.0199508i | ||||||
\(249\) | −154.744 | − | 441.378i | −0.621463 | − | 1.77260i | ||||
\(250\) | −124.954 | −0.499816 | ||||||||
\(251\) | 431.753i | 1.72013i | 0.510185 | + | 0.860065i | \(0.329577\pi\) | ||||
−0.510185 | + | 0.860065i | \(0.670423\pi\) | |||||||
\(252\) | 59.0034 | − | 47.1705i | 0.234141 | − | 0.187184i | ||||
\(253\) | 630.451 | 2.49190 | ||||||||
\(254\) | 164.788i | 0.648770i | ||||||||
\(255\) | −106.648 | + | 37.3902i | −0.418229 | + | 0.146628i | ||||
\(256\) | −145.549 | −0.568549 | ||||||||
\(257\) | − | 111.923i | − | 0.435499i | −0.976005 | − | 0.217749i | \(-0.930128\pi\) | ||
0.976005 | − | 0.217749i | \(-0.0698715\pi\) | |||||||
\(258\) | −51.0285 | − | 145.549i | −0.197785 | − | 0.564143i | ||||
\(259\) | 121.981 | 0.470971 | ||||||||
\(260\) | − | 92.9755i | − | 0.357598i | ||||||
\(261\) | 30.2641 | + | 37.8561i | 0.115955 | + | 0.145042i | ||||
\(262\) | −7.79474 | −0.0297509 | ||||||||
\(263\) | 109.884i | 0.417810i | 0.977936 | + | 0.208905i | \(0.0669899\pi\) | ||||
−0.977936 | + | 0.208905i | \(0.933010\pi\) | |||||||
\(264\) | 263.858 | − | 92.5069i | 0.999462 | − | 0.350405i | ||||
\(265\) | −50.4516 | −0.190384 | ||||||||
\(266\) | 48.5882i | 0.182662i | ||||||||
\(267\) | −63.1532 | − | 180.132i | −0.236529 | − | 0.674653i | ||||
\(268\) | 329.147 | 1.22816 | ||||||||
\(269\) | − | 452.187i | − | 1.68099i | −0.541817 | − | 0.840496i | \(-0.682263\pi\) | ||
0.541817 | − | 0.840496i | \(-0.317737\pi\) | |||||||
\(270\) | 63.4745 | − | 101.427i | 0.235091 | − | 0.375655i | ||||
\(271\) | 167.060 | 0.616457 | 0.308229 | − | 0.951312i | \(-0.400264\pi\) | ||||
0.308229 | + | 0.951312i | \(0.400264\pi\) | |||||||
\(272\) | 48.4283i | 0.178045i | ||||||||
\(273\) | −49.2572 | + | 17.2693i | −0.180429 | + | 0.0632574i | ||||
\(274\) | 159.762 | 0.583072 | ||||||||
\(275\) | − | 44.2193i | − | 0.160797i | ||||||
\(276\) | −140.200 | − | 399.895i | −0.507973 | − | 1.44889i | ||||
\(277\) | −57.7609 | −0.208523 | −0.104262 | − | 0.994550i | \(-0.533248\pi\) | ||||
−0.104262 | + | 0.994550i | \(0.533248\pi\) | |||||||
\(278\) | − | 156.739i | − | 0.563810i | ||||||
\(279\) | 5.16228 | − | 4.12700i | 0.0185028 | − | 0.0147921i | ||||
\(280\) | −85.2013 | −0.304290 | ||||||||
\(281\) | 205.841i | 0.732530i | 0.930511 | + | 0.366265i | \(0.119364\pi\) | ||||
−0.930511 | + | 0.366265i | \(0.880636\pi\) | |||||||
\(282\) | −141.771 | + | 49.7041i | −0.502735 | + | 0.176256i | ||||
\(283\) | −348.975 | −1.23313 | −0.616564 | − | 0.787305i | \(-0.711476\pi\) | ||||
−0.616564 | + | 0.787305i | \(0.711476\pi\) | |||||||
\(284\) | 78.4685i | 0.276297i | ||||||||
\(285\) | −87.6142 | − | 249.902i | −0.307418 | − | 0.876850i | ||||
\(286\) | −84.3435 | −0.294907 | ||||||||
\(287\) | − | 59.8721i | − | 0.208613i | ||||||
\(288\) | −183.476 | − | 229.502i | −0.637069 | − | 0.796881i | ||||
\(289\) | 223.914 | 0.774788 | ||||||||
\(290\) | − | 23.8645i | − | 0.0822913i | ||||||
\(291\) | −34.3501 | + | 12.0429i | −0.118042 | + | 0.0413847i | ||||
\(292\) | −56.8481 | −0.194685 | ||||||||
\(293\) | 77.4168i | 0.264221i | 0.991235 | + | 0.132111i | \(0.0421754\pi\) | ||||
−0.991235 | + | 0.132111i | \(0.957825\pi\) | |||||||
\(294\) | −39.2484 | − | 111.948i | −0.133498 | − | 0.380777i | ||||
\(295\) | 2.85824 | 0.00968894 | ||||||||
\(296\) | − | 303.474i | − | 1.02525i | ||||||
\(297\) | 316.603 | + | 198.135i | 1.06600 | + | 0.667123i | ||||
\(298\) | −36.1184 | −0.121203 | ||||||||
\(299\) | 292.806i | 0.979283i | ||||||||
\(300\) | −28.0483 | + | 9.83354i | −0.0934942 | + | 0.0327785i | ||||
\(301\) | −146.706 | −0.487395 | ||||||||
\(302\) | − | 9.48398i | − | 0.0314039i | ||||||
\(303\) | −43.5197 | − | 124.131i | −0.143629 | − | 0.409674i | ||||
\(304\) | −113.479 | −0.373286 | ||||||||
\(305\) | − | 112.605i | − | 0.369198i | ||||||
\(306\) | 53.8236 | − | 43.0294i | 0.175894 | − | 0.140619i | ||||
\(307\) | −107.603 | −0.350498 | −0.175249 | − | 0.984524i | \(-0.556073\pi\) | ||||
−0.175249 | + | 0.984524i | \(0.556073\pi\) | |||||||
\(308\) | − | 116.107i | − | 0.376970i | ||||||
\(309\) | 411.418 | − | 144.241i | 1.33145 | − | 0.466798i | ||||
\(310\) | −3.25430 | −0.0104978 | ||||||||
\(311\) | − | 219.086i | − | 0.704458i | −0.935914 | − | 0.352229i | \(-0.885424\pi\) | ||
0.935914 | − | 0.352229i | \(-0.114576\pi\) | |||||||
\(312\) | 42.9638 | + | 122.546i | 0.137704 | + | 0.392775i | ||||
\(313\) | −372.719 | −1.19080 | −0.595398 | − | 0.803431i | \(-0.703005\pi\) | ||||
−0.595398 | + | 0.803431i | \(0.703005\pi\) | |||||||
\(314\) | 81.7356i | 0.260304i | ||||||||
\(315\) | −71.0671 | − | 88.8948i | −0.225610 | − | 0.282206i | ||||
\(316\) | 437.783 | 1.38539 | ||||||||
\(317\) | 379.417i | 1.19690i | 0.801160 | + | 0.598450i | \(0.204216\pi\) | ||||
−0.801160 | + | 0.598450i | \(0.795784\pi\) | |||||||
\(318\) | 29.0304 | − | 10.1779i | 0.0912905 | − | 0.0320059i | ||||
\(319\) | 74.4929 | 0.233520 | ||||||||
\(320\) | 32.5599i | 0.101750i | ||||||||
\(321\) | 66.0554 | + | 188.410i | 0.205780 | + | 0.586948i | ||||
\(322\) | 117.140 | 0.363788 | ||||||||
\(323\) | − | 152.513i | − | 0.472176i | ||||||
\(324\) | 55.2705 | − | 244.883i | 0.170588 | − | 0.755812i | ||||
\(325\) | 20.5371 | 0.0631912 | ||||||||
\(326\) | 176.852i | 0.542490i | ||||||||
\(327\) | 228.000 | − | 79.9352i | 0.697246 | − | 0.244450i | ||||
\(328\) | −148.954 | −0.454129 | ||||||||
\(329\) | 142.898i | 0.434341i | ||||||||
\(330\) | −60.8444 | − | 173.547i | −0.184377 | − | 0.525900i | ||||
\(331\) | −32.9150 | −0.0994412 | −0.0497206 | − | 0.998763i | \(-0.515833\pi\) | ||||
−0.0497206 | + | 0.998763i | \(0.515833\pi\) | |||||||
\(332\) | 483.199i | 1.45542i | ||||||||
\(333\) | 316.630 | − | 253.131i | 0.950841 | − | 0.760152i | ||||
\(334\) | −271.421 | −0.812638 | ||||||||
\(335\) | − | 495.893i | − | 1.48028i | ||||||
\(336\) | −46.0235 | + | 16.1356i | −0.136975 | + | 0.0480225i | ||||
\(337\) | −69.7498 | −0.206973 | −0.103486 | − | 0.994631i | \(-0.533000\pi\) | ||||
−0.103486 | + | 0.994631i | \(0.533000\pi\) | |||||||
\(338\) | 121.218i | 0.358633i | ||||||||
\(339\) | 89.8020 | + | 256.143i | 0.264903 | + | 0.755583i | ||||
\(340\) | 116.753 | 0.343392 | ||||||||
\(341\) | − | 10.1583i | − | 0.0297897i | ||||||
\(342\) | 100.828 | + | 126.121i | 0.294819 | + | 0.368776i | ||||
\(343\) | −245.539 | −0.715858 | ||||||||
\(344\) | 364.986i | 1.06101i | ||||||||
\(345\) | −602.482 | + | 211.226i | −1.74633 | + | 0.612251i | ||||
\(346\) | 181.330 | 0.524075 | ||||||||
\(347\) | − | 218.421i | − | 0.629454i | −0.949182 | − | 0.314727i | \(-0.898087\pi\) | ||
0.949182 | − | 0.314727i | \(-0.101913\pi\) | |||||||
\(348\) | −16.5658 | − | 47.2508i | −0.0476030 | − | 0.135778i | ||||
\(349\) | 398.726 | 1.14248 | 0.571241 | − | 0.820782i | \(-0.306462\pi\) | ||||
0.571241 | + | 0.820782i | \(0.306462\pi\) | |||||||
\(350\) | − | 8.21608i | − | 0.0234745i | ||||||
\(351\) | −92.0217 | + | 147.043i | −0.262170 | + | 0.418925i | ||||
\(352\) | −451.612 | −1.28299 | ||||||||
\(353\) | 133.004i | 0.376782i | 0.982094 | + | 0.188391i | \(0.0603273\pi\) | ||||
−0.982094 | + | 0.188391i | \(0.939673\pi\) | |||||||
\(354\) | −1.64466 | + | 0.576607i | −0.00464593 | + | 0.00162883i | ||||
\(355\) | 118.221 | 0.333016 | ||||||||
\(356\) | 197.200i | 0.553933i | ||||||||
\(357\) | −21.6858 | − | 61.8544i | −0.0607444 | − | 0.173262i | ||||
\(358\) | −318.146 | −0.888677 | ||||||||
\(359\) | − | 99.0249i | − | 0.275835i | −0.990444 | − | 0.137918i | \(-0.955959\pi\) | ||
0.990444 | − | 0.137918i | \(-0.0440409\pi\) | |||||||
\(360\) | −221.159 | + | 176.806i | −0.614331 | + | 0.491128i | ||||
\(361\) | −3.62652 | −0.0100458 | ||||||||
\(362\) | − | 198.398i | − | 0.548061i | ||||||
\(363\) | 199.169 | − | 69.8274i | 0.548675 | − | 0.192362i | ||||
\(364\) | 53.9244 | 0.148144 | ||||||||
\(365\) | 85.6474i | 0.234651i | ||||||||
\(366\) | 22.7165 | + | 64.7943i | 0.0620668 | + | 0.177034i | ||||
\(367\) | 380.440 | 1.03662 | 0.518310 | − | 0.855193i | \(-0.326561\pi\) | ||||
0.518310 | + | 0.855193i | \(0.326561\pi\) | |||||||
\(368\) | 273.583i | 0.743432i | ||||||||
\(369\) | −124.244 | − | 155.411i | −0.336705 | − | 0.421169i | ||||
\(370\) | −199.604 | −0.539469 | ||||||||
\(371\) | − | 29.2612i | − | 0.0788711i | ||||||
\(372\) | −6.44341 | + | 2.25902i | −0.0173210 | + | 0.00607263i | ||||
\(373\) | −141.610 | −0.379651 | −0.189826 | − | 0.981818i | \(-0.560792\pi\) | ||||
−0.189826 | + | 0.981818i | \(0.560792\pi\) | |||||||
\(374\) | − | 105.914i | − | 0.283192i | ||||||
\(375\) | 130.680 | + | 372.741i | 0.348481 | + | 0.993975i | ||||
\(376\) | 355.513 | 0.945514 | ||||||||
\(377\) | 34.5974i | 0.0917703i | ||||||||
\(378\) | 58.8259 | + | 36.8142i | 0.155624 | + | 0.0973921i | ||||
\(379\) | 428.220 | 1.12987 | 0.564934 | − | 0.825136i | \(-0.308901\pi\) | ||||
0.564934 | + | 0.825136i | \(0.308901\pi\) | |||||||
\(380\) | 273.581i | 0.719949i | ||||||||
\(381\) | 491.565 | − | 172.339i | 1.29020 | − | 0.452335i | ||||
\(382\) | 192.071 | 0.502803 | ||||||||
\(383\) | 236.854i | 0.618419i | 0.950994 | + | 0.309209i | \(0.100064\pi\) | ||||
−0.950994 | + | 0.309209i | \(0.899936\pi\) | |||||||
\(384\) | 123.048 | + | 350.971i | 0.320438 | + | 0.913988i | ||||
\(385\) | −174.927 | −0.454355 | ||||||||
\(386\) | − | 307.661i | − | 0.797048i | ||||||
\(387\) | −380.808 | + | 304.438i | −0.984001 | + | 0.786662i | ||||
\(388\) | 37.6048 | 0.0969197 | ||||||||
\(389\) | − | 150.510i | − | 0.386916i | −0.981109 | − | 0.193458i | \(-0.938030\pi\) | ||
0.981109 | − | 0.193458i | \(-0.0619703\pi\) | |||||||
\(390\) | 80.6018 | − | 28.2585i | 0.206671 | − | 0.0724577i | ||||
\(391\) | −367.688 | −0.940380 | ||||||||
\(392\) | 280.728i | 0.716143i | ||||||||
\(393\) | 8.15196 | + | 23.2519i | 0.0207429 | + | 0.0591651i | ||||
\(394\) | −258.464 | −0.656000 | ||||||||
\(395\) | − | 659.565i | − | 1.66979i | ||||||
\(396\) | −240.940 | − | 301.381i | −0.608433 | − | 0.761062i | ||||
\(397\) | −421.169 | −1.06088 | −0.530439 | − | 0.847723i | \(-0.677973\pi\) | ||||
−0.530439 | + | 0.847723i | \(0.677973\pi\) | |||||||
\(398\) | 319.064i | 0.801668i | ||||||||
\(399\) | 144.940 | − | 50.8149i | 0.363257 | − | 0.127356i | ||||
\(400\) | 19.1889 | 0.0479722 | ||||||||
\(401\) | 399.836i | 0.997096i | 0.866862 | + | 0.498548i | \(0.166133\pi\) | ||||
−0.866862 | + | 0.498548i | \(0.833867\pi\) | |||||||
\(402\) | 100.039 | + | 285.342i | 0.248853 | + | 0.709806i | ||||
\(403\) | 4.71791 | 0.0117070 | ||||||||
\(404\) | 135.893i | 0.336369i | ||||||||
\(405\) | −368.941 | − | 83.2707i | −0.910966 | − | 0.205607i | ||||
\(406\) | 13.8410 | 0.0340912 | ||||||||
\(407\) | − | 623.063i | − | 1.53087i | ||||||
\(408\) | −153.886 | + | 53.9515i | −0.377172 | + | 0.132234i | ||||
\(409\) | −486.637 | −1.18982 | −0.594911 | − | 0.803791i | \(-0.702813\pi\) | ||||
−0.594911 | + | 0.803791i | \(0.702813\pi\) | |||||||
\(410\) | 97.9714i | 0.238955i | ||||||||
\(411\) | −167.083 | − | 476.572i | −0.406529 | − | 1.15954i | ||||
\(412\) | −450.400 | −1.09320 | ||||||||
\(413\) | 1.65773i | 0.00401388i | ||||||||
\(414\) | 304.063 | − | 243.084i | 0.734451 | − | 0.587159i | ||||
\(415\) | 727.988 | 1.75419 | ||||||||
\(416\) | − | 209.746i | − | 0.504197i | ||||||
\(417\) | −467.556 | + | 163.922i | −1.12124 | + | 0.393099i | ||||
\(418\) | 248.181 | 0.593735 | ||||||||
\(419\) | 508.231i | 1.21296i | 0.795098 | + | 0.606480i | \(0.207419\pi\) | ||||
−0.795098 | + | 0.606480i | \(0.792581\pi\) | |||||||
\(420\) | 38.9004 | + | 110.956i | 0.0926200 | + | 0.264181i | ||||
\(421\) | 502.174 | 1.19281 | 0.596406 | − | 0.802683i | \(-0.296595\pi\) | ||||
0.596406 | + | 0.802683i | \(0.296595\pi\) | |||||||
\(422\) | 248.796i | 0.589564i | ||||||||
\(423\) | 296.537 | + | 370.925i | 0.701032 | + | 0.876890i | ||||
\(424\) | −72.7981 | −0.171694 | ||||||||
\(425\) | 25.7893i | 0.0606808i | ||||||||
\(426\) | −68.0254 | + | 23.8493i | −0.159684 | + | 0.0559842i | ||||
\(427\) | 65.3094 | 0.152949 | ||||||||
\(428\) | − | 206.262i | − | 0.481921i | ||||||
\(429\) | 88.2088 | + | 251.598i | 0.205615 | + | 0.586477i | ||||
\(430\) | 240.062 | 0.558283 | ||||||||
\(431\) | − | 675.282i | − | 1.56678i | −0.621531 | − | 0.783390i | \(-0.713489\pi\) | ||
0.621531 | − | 0.783390i | \(-0.286511\pi\) | |||||||
\(432\) | −85.9805 | + | 137.390i | −0.199029 | + | 0.318031i | ||||
\(433\) | −103.034 | −0.237953 | −0.118977 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118977 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(434\) | − | 1.88745i | − | 0.00434895i | ||||||
\(435\) | −71.1882 | + | 24.9581i | −0.163651 | + | 0.0573750i | ||||
\(436\) | −249.603 | −0.572483 | ||||||||
\(437\) | − | 861.581i | − | 1.97158i | ||||||
\(438\) | −17.2781 | − | 49.2824i | −0.0394477 | − | 0.112517i | ||||
\(439\) | 15.7852 | 0.0359572 | 0.0179786 | − | 0.999838i | \(-0.494277\pi\) | ||||
0.0179786 | + | 0.999838i | \(0.494277\pi\) | |||||||
\(440\) | 435.195i | 0.989080i | ||||||||
\(441\) | −292.898 | + | 234.158i | −0.664167 | + | 0.530970i | ||||
\(442\) | 49.1904 | 0.111291 | ||||||||
\(443\) | 130.391i | 0.294336i | 0.989112 | + | 0.147168i | \(0.0470157\pi\) | ||||
−0.989112 | + | 0.147168i | \(0.952984\pi\) | |||||||
\(444\) | −395.208 | + | 138.558i | −0.890109 | + | 0.312066i | ||||
\(445\) | 297.102 | 0.667645 | ||||||||
\(446\) | 35.9704i | 0.0806511i | ||||||||
\(447\) | 37.7737 | + | 107.742i | 0.0845049 | + | 0.241034i | ||||
\(448\) | −18.8843 | −0.0421524 | ||||||||
\(449\) | 218.937i | 0.487609i | 0.969824 | + | 0.243805i | \(0.0783956\pi\) | ||||
−0.969824 | + | 0.243805i | \(0.921604\pi\) | |||||||
\(450\) | −17.0497 | − | 21.3267i | −0.0378882 | − | 0.0473926i | ||||
\(451\) | −305.817 | −0.678088 | ||||||||
\(452\) | − | 280.412i | − | 0.620382i | ||||||
\(453\) | −28.2909 | + | 9.91861i | −0.0624523 | + | 0.0218954i | ||||
\(454\) | −308.618 | −0.679774 | ||||||||
\(455\) | − | 81.2426i | − | 0.178555i | ||||||
\(456\) | −126.421 | − | 360.591i | −0.277239 | − | 0.790771i | ||||
\(457\) | −273.649 | −0.598795 | −0.299398 | − | 0.954128i | \(-0.596786\pi\) | ||||
−0.299398 | + | 0.954128i | \(0.596786\pi\) | |||||||
\(458\) | 175.405i | 0.382980i | ||||||||
\(459\) | −184.648 | − | 115.556i | −0.402283 | − | 0.251755i | ||||
\(460\) | 659.568 | 1.43384 | ||||||||
\(461\) | − | 472.126i | − | 1.02414i | −0.858945 | − | 0.512068i | \(-0.828880\pi\) | ||
0.858945 | − | 0.512068i | \(-0.171120\pi\) | |||||||
\(462\) | 100.654 | − | 35.2888i | 0.217867 | − | 0.0763827i | ||||
\(463\) | 225.800 | 0.487688 | 0.243844 | − | 0.969814i | \(-0.421592\pi\) | ||||
0.243844 | + | 0.969814i | \(0.421592\pi\) | |||||||
\(464\) | 32.3261i | 0.0696683i | ||||||||
\(465\) | 3.40344 | + | 9.70765i | 0.00731923 | + | 0.0208767i | ||||
\(466\) | 231.128 | 0.495982 | ||||||||
\(467\) | − | 727.136i | − | 1.55704i | −0.627622 | − | 0.778519i | \(-0.715971\pi\) | ||
0.627622 | − | 0.778519i | \(-0.284029\pi\) | |||||||
\(468\) | 139.973 | − | 111.902i | 0.299087 | − | 0.239106i | ||||
\(469\) | 287.610 | 0.613242 | ||||||||
\(470\) | − | 233.831i | − | 0.497513i | ||||||
\(471\) | 243.819 | − | 85.4813i | 0.517662 | − | 0.181489i | ||||
\(472\) | 4.12423 | 0.00873778 | ||||||||
\(473\) | 749.352i | 1.58425i | ||||||||
\(474\) | 133.057 | + | 379.520i | 0.280712 | + | 0.800676i | ||||
\(475\) | −60.4305 | −0.127222 | ||||||||
\(476\) | 67.7151i | 0.142259i | ||||||||
\(477\) | −60.7216 | − | 75.9539i | −0.127299 | − | 0.159233i | ||||
\(478\) | −77.8573 | −0.162881 | ||||||||
\(479\) | − | 436.959i | − | 0.912231i | −0.889921 | − | 0.456115i | \(-0.849240\pi\) | ||
0.889921 | − | 0.456115i | \(-0.150760\pi\) | |||||||
\(480\) | 431.578 | − | 151.308i | 0.899120 | − | 0.315226i | ||||
\(481\) | 289.374 | 0.601610 | ||||||||
\(482\) | − | 40.3047i | − | 0.0836197i | ||||||
\(483\) | −122.508 | − | 349.430i | −0.253640 | − | 0.723458i | ||||
\(484\) | −218.040 | −0.450497 | ||||||||
\(485\) | − | 56.6555i | − | 0.116816i | ||||||
\(486\) | 229.091 | − | 26.5136i | 0.471381 | − | 0.0545548i | ||||
\(487\) | −43.1395 | −0.0885821 | −0.0442910 | − | 0.999019i | \(-0.514103\pi\) | ||||
−0.0442910 | + | 0.999019i | \(0.514103\pi\) | |||||||
\(488\) | − | 162.482i | − | 0.332954i | ||||||
\(489\) | 527.553 | − | 184.957i | 1.07884 | − | 0.378234i | ||||
\(490\) | 184.643 | 0.376822 | ||||||||
\(491\) | − | 585.317i | − | 1.19209i | −0.802950 | − | 0.596046i | \(-0.796737\pi\) | ||
0.802950 | − | 0.596046i | \(-0.203263\pi\) | |||||||
\(492\) | 68.0081 | + | 193.980i | 0.138228 | + | 0.394268i | ||||
\(493\) | −43.4454 | −0.0881246 | ||||||||
\(494\) | 115.265i | 0.233330i | ||||||||
\(495\) | −454.061 | + | 363.000i | −0.917295 | + | 0.733334i | ||||
\(496\) | 4.40818 | 0.00888746 | ||||||||
\(497\) | 68.5662i | 0.137960i | ||||||||
\(498\) | −418.892 | + | 146.861i | −0.841148 | + | 0.294901i | ||||
\(499\) | 304.266 | 0.609752 | 0.304876 | − | 0.952392i | \(-0.401385\pi\) | ||||
0.304876 | + | 0.952392i | \(0.401385\pi\) | |||||||
\(500\) | − | 408.058i | − | 0.816116i | ||||||
\(501\) | 283.860 | + | 809.654i | 0.566586 | + | 1.61608i | ||||
\(502\) | 409.757 | 0.816249 | ||||||||
\(503\) | − | 929.099i | − | 1.84711i | −0.383460 | − | 0.923557i | \(-0.625268\pi\) | ||
0.383460 | − | 0.923557i | \(-0.374732\pi\) | |||||||
\(504\) | −102.545 | − | 128.269i | −0.203462 | − | 0.254502i | ||||
\(505\) | 204.737 | 0.405419 | ||||||||
\(506\) | − | 598.332i | − | 1.18248i | ||||||
\(507\) | 361.596 | − | 126.773i | 0.713206 | − | 0.250046i | ||||
\(508\) | −538.141 | −1.05933 | ||||||||
\(509\) | 309.936i | 0.608911i | 0.952527 | + | 0.304455i | \(0.0984745\pi\) | ||||
−0.952527 | + | 0.304455i | \(0.901526\pi\) | |||||||
\(510\) | 35.4854 | + | 101.215i | 0.0695792 | + | 0.198461i | ||||
\(511\) | −49.6742 | −0.0972098 | ||||||||
\(512\) | − | 357.755i | − | 0.698740i | ||||||
\(513\) | 270.774 | − | 432.674i | 0.527825 | − | 0.843419i | ||||
\(514\) | −106.221 | −0.206656 | ||||||||
\(515\) | 678.575i | 1.31762i | ||||||||
\(516\) | 475.314 | − | 166.642i | 0.921150 | − | 0.322949i | ||||
\(517\) | 729.903 | 1.41180 | ||||||||
\(518\) | − | 115.767i | − | 0.223489i | ||||||
\(519\) | −189.640 | − | 540.911i | −0.365395 | − | 1.04222i | ||||
\(520\) | −202.121 | −0.388695 | ||||||||
\(521\) | 523.170i | 1.00416i | 0.864820 | + | 0.502082i | \(0.167433\pi\) | ||||
−0.864820 | + | 0.502082i | \(0.832567\pi\) | |||||||
\(522\) | 35.9275 | − | 28.7223i | 0.0688266 | − | 0.0550236i | ||||
\(523\) | 458.129 | 0.875964 | 0.437982 | − | 0.898984i | \(-0.355693\pi\) | ||||
0.437982 | + | 0.898984i | \(0.355693\pi\) | |||||||
\(524\) | − | 25.4550i | − | 0.0485783i | ||||||
\(525\) | −24.5087 | + | 8.59261i | −0.0466833 | + | 0.0163669i | ||||
\(526\) | 104.286 | 0.198262 | ||||||||
\(527\) | 5.92447i | 0.0112419i | ||||||||
\(528\) | 82.4180 | + | 235.081i | 0.156095 | + | 0.445230i | ||||
\(529\) | −1548.16 | −2.92658 | ||||||||
\(530\) | 47.8814i | 0.0903422i | ||||||||
\(531\) | 3.44006 | + | 4.30302i | 0.00647846 | + | 0.00810361i | ||||
\(532\) | −158.673 | −0.298257 | ||||||||
\(533\) | − | 142.033i | − | 0.266479i | ||||||
\(534\) | −170.956 | + | 59.9359i | −0.320141 | + | 0.112240i | ||||
\(535\) | −310.755 | −0.580851 | ||||||||
\(536\) | − | 715.539i | − | 1.33496i | ||||||
\(537\) | 332.726 | + | 949.037i | 0.619602 | + | 1.76730i | ||||
\(538\) | −429.150 | −0.797677 | ||||||||
\(539\) | 576.362i | 1.06932i | ||||||||
\(540\) | 331.226 | + | 207.286i | 0.613381 | + | 0.383863i | ||||
\(541\) | −589.955 | −1.09049 | −0.545245 | − | 0.838277i | \(-0.683563\pi\) | ||||
−0.545245 | + | 0.838277i | \(0.683563\pi\) | |||||||
\(542\) | − | 158.549i | − | 0.292526i | ||||||
\(543\) | −591.825 | + | 207.490i | −1.08992 | + | 0.382118i | ||||
\(544\) | 263.387 | 0.484168 | ||||||||
\(545\) | 376.052i | 0.690004i | ||||||||
\(546\) | 16.3895 | + | 46.7478i | 0.0300174 | + | 0.0856187i | ||||
\(547\) | −673.623 | −1.23149 | −0.615743 | − | 0.787947i | \(-0.711144\pi\) | ||||
−0.615743 | + | 0.787947i | \(0.711144\pi\) | |||||||
\(548\) | 521.728i | 0.952058i | ||||||||
\(549\) | 169.525 | − | 135.527i | 0.308789 | − | 0.246862i | ||||
\(550\) | −41.9665 | −0.0763027 | ||||||||
\(551\) | − | 101.803i | − | 0.184760i | ||||||
\(552\) | −869.339 | + | 304.785i | −1.57489 | + | 0.552146i | ||||
\(553\) | 382.538 | 0.691750 | ||||||||
\(554\) | 54.8183i | 0.0989500i | ||||||||
\(555\) | 208.751 | + | 595.422i | 0.376128 | + | 1.07283i | ||||
\(556\) | 511.857 | 0.920606 | ||||||||
\(557\) | 242.707i | 0.435740i | 0.975978 | + | 0.217870i | \(0.0699109\pi\) | ||||
−0.975978 | + | 0.217870i | \(0.930089\pi\) | |||||||
\(558\) | −3.91675 | − | 4.89929i | −0.00701926 | − | 0.00878008i | ||||
\(559\) | −348.028 | −0.622590 | ||||||||
\(560\) | − | 75.9091i | − | 0.135552i | ||||||
\(561\) | −315.943 | + | 110.768i | −0.563178 | + | 0.197447i | ||||
\(562\) | 195.354 | 0.347606 | ||||||||
\(563\) | 264.932i | 0.470571i | 0.971926 | + | 0.235286i | \(0.0756025\pi\) | ||||
−0.971926 | + | 0.235286i | \(0.924397\pi\) | |||||||
\(564\) | −162.317 | − | 462.977i | −0.287796 | − | 0.820881i | ||||
\(565\) | −422.470 | −0.747735 | ||||||||
\(566\) | 331.197i | 0.585153i | ||||||||
\(567\) | 48.2957 | − | 213.980i | 0.0851776 | − | 0.377390i | ||||
\(568\) | 170.584 | 0.300324 | ||||||||
\(569\) | 1091.42i | 1.91813i | 0.283187 | + | 0.959065i | \(0.408608\pi\) | ||||
−0.283187 | + | 0.959065i | \(0.591392\pi\) | |||||||
\(570\) | −237.171 | + | 83.1507i | −0.416090 | + | 0.145878i | ||||
\(571\) | −401.706 | −0.703513 | −0.351757 | − | 0.936091i | \(-0.614416\pi\) | ||||
−0.351757 | + | 0.936091i | \(0.614416\pi\) | |||||||
\(572\) | − | 275.438i | − | 0.481534i | ||||||
\(573\) | −200.873 | − | 572.951i | −0.350564 | − | 0.999915i | ||||
\(574\) | −56.8219 | −0.0989928 | ||||||||
\(575\) | 145.690i | 0.253374i | ||||||||
\(576\) | −49.0183 | + | 39.1878i | −0.0851012 | + | 0.0680344i | ||||
\(577\) | 445.201 | 0.771579 | 0.385790 | − | 0.922587i | \(-0.373929\pi\) | ||||
0.385790 | + | 0.922587i | \(0.373929\pi\) | |||||||
\(578\) | − | 212.506i | − | 0.367658i | ||||||
\(579\) | −917.758 | + | 321.760i | −1.58507 | + | 0.555717i | ||||
\(580\) | 77.9334 | 0.134368 | ||||||||
\(581\) | 422.222i | 0.726716i | ||||||||
\(582\) | 11.4294 | + | 32.6002i | 0.0196382 | + | 0.0560140i | ||||
\(583\) | −149.462 | −0.256366 | ||||||||
\(584\) | 123.583i | 0.211615i | ||||||||
\(585\) | −168.591 | − | 210.883i | −0.288190 | − | 0.360484i | ||||
\(586\) | 73.4728 | 0.125380 | ||||||||
\(587\) | − | 396.043i | − | 0.674689i | −0.941381 | − | 0.337345i | \(-0.890471\pi\) | ||
0.941381 | − | 0.337345i | \(-0.109529\pi\) | |||||||
\(588\) | 365.586 | − | 128.172i | 0.621745 | − | 0.217980i | ||||
\(589\) | −13.8824 | −0.0235695 | ||||||||
\(590\) | − | 2.71262i | − | 0.00459767i | ||||||
\(591\) | 270.309 | + | 771.004i | 0.457376 | + | 1.30458i | ||||
\(592\) | 270.377 | 0.456718 | ||||||||
\(593\) | − | 212.616i | − | 0.358544i | −0.983800 | − | 0.179272i | \(-0.942626\pi\) | ||
0.983800 | − | 0.179272i | \(-0.0573741\pi\) | |||||||
\(594\) | 188.041 | − | 300.474i | 0.316568 | − | 0.505849i | ||||
\(595\) | 102.020 | 0.171462 | ||||||||
\(596\) | − | 117.951i | − | 0.197904i | ||||||
\(597\) | 951.774 | − | 333.686i | 1.59426 | − | 0.558938i | ||||
\(598\) | 277.889 | 0.464697 | ||||||||
\(599\) | − | 55.1819i | − | 0.0921234i | −0.998939 | − | 0.0460617i | \(-0.985333\pi\) | ||
0.998939 | − | 0.0460617i | \(-0.0146671\pi\) | |||||||
\(600\) | 21.3773 | + | 60.9747i | 0.0356289 | + | 0.101624i | ||||
\(601\) | 300.501 | 0.500002 | 0.250001 | − | 0.968246i | \(-0.419569\pi\) | ||||
0.250001 | + | 0.968246i | \(0.419569\pi\) | |||||||
\(602\) | 139.232i | 0.231282i | ||||||||
\(603\) | 746.557 | − | 596.837i | 1.23807 | − | 0.989780i | ||||
\(604\) | 30.9715 | 0.0512773 | ||||||||
\(605\) | 328.500i | 0.542976i | ||||||||
\(606\) | −117.808 | + | 41.3026i | −0.194402 | + | 0.0681560i | ||||
\(607\) | 560.525 | 0.923435 | 0.461717 | − | 0.887027i | \(-0.347233\pi\) | ||||
0.461717 | + | 0.887027i | \(0.347233\pi\) | |||||||
\(608\) | 617.178i | 1.01510i | ||||||||
\(609\) | −14.4753 | − | 41.2881i | −0.0237690 | − | 0.0677965i | ||||
\(610\) | −106.869 | −0.175195 | ||||||||
\(611\) | 338.995i | 0.554820i | ||||||||
\(612\) | 140.520 | + | 175.770i | 0.229607 | + | 0.287206i | ||||
\(613\) | −979.730 | −1.59825 | −0.799127 | − | 0.601162i | \(-0.794705\pi\) | ||||
−0.799127 | + | 0.601162i | \(0.794705\pi\) | |||||||
\(614\) | 102.121i | 0.166321i | ||||||||
\(615\) | 292.251 | − | 102.461i | 0.475204 | − | 0.166604i | ||||
\(616\) | −252.407 | −0.409751 | ||||||||
\(617\) | 155.269i | 0.251652i | 0.992052 | + | 0.125826i | \(0.0401581\pi\) | ||||
−0.992052 | + | 0.125826i | \(0.959842\pi\) | |||||||
\(618\) | −136.892 | − | 390.459i | −0.221509 | − | 0.631810i | ||||
\(619\) | 1038.72 | 1.67805 | 0.839027 | − | 0.544089i | \(-0.183125\pi\) | ||||
0.839027 | + | 0.544089i | \(0.183125\pi\) | |||||||
\(620\) | − | 10.6275i | − | 0.0171411i | ||||||
\(621\) | −1043.12 | − | 652.801i | −1.67974 | − | 1.05121i | ||||
\(622\) | −207.925 | −0.334285 | ||||||||
\(623\) | 172.315i | 0.276588i | ||||||||
\(624\) | −109.181 | + | 38.2781i | −0.174969 | + | 0.0613431i | ||||
\(625\) | −534.865 | −0.855784 | ||||||||
\(626\) | 353.731i | 0.565065i | ||||||||
\(627\) | −259.555 | − | 740.329i | −0.413963 | − | 1.18075i | ||||
\(628\) | −266.921 | −0.425033 | ||||||||
\(629\) | 363.380i | 0.577710i | ||||||||
\(630\) | −84.3660 | + | 67.4466i | −0.133914 | + | 0.107058i | ||||
\(631\) | 400.409 | 0.634562 | 0.317281 | − | 0.948332i | \(-0.397230\pi\) | ||||
0.317281 | + | 0.948332i | \(0.397230\pi\) | |||||||
\(632\) | − | 951.706i | − | 1.50586i | ||||||
\(633\) | 742.164 | − | 260.198i | 1.17245 | − | 0.411055i | ||||
\(634\) | 360.088 | 0.567962 | ||||||||
\(635\) | 810.765i | 1.27679i | ||||||||
\(636\) | 33.2375 | + | 94.8035i | 0.0522602 | + | 0.149062i | ||||
\(637\) | −267.685 | −0.420227 | ||||||||
\(638\) | − | 70.6979i | − | 0.110812i | ||||||
\(639\) | 142.286 | + | 177.979i | 0.222670 | + | 0.278527i | ||||
\(640\) | −578.876 | −0.904494 | ||||||||
\(641\) | 305.576i | 0.476717i | 0.971177 | + | 0.238358i | \(0.0766093\pi\) | ||||
−0.971177 | + | 0.238358i | \(0.923391\pi\) | |||||||
\(642\) | 178.812 | − | 62.6902i | 0.278523 | − | 0.0976483i | ||||
\(643\) | 1185.24 | 1.84330 | 0.921648 | − | 0.388026i | \(-0.126843\pi\) | ||||
0.921648 | + | 0.388026i | \(0.126843\pi\) | |||||||
\(644\) | 382.539i | 0.594005i | ||||||||
\(645\) | −251.063 | − | 716.109i | −0.389245 | − | 1.11025i | ||||
\(646\) | −144.743 | −0.224060 | ||||||||
\(647\) | − | 19.5144i | − | 0.0301614i | −0.999886 | − | 0.0150807i | \(-0.995199\pi\) | ||
0.999886 | − | 0.0150807i | \(-0.00480052\pi\) | |||||||
\(648\) | −532.356 | − | 120.154i | −0.821538 | − | 0.185422i | ||||
\(649\) | 8.46745 | 0.0130469 | ||||||||
\(650\) | − | 19.4909i | − | 0.0299859i | ||||||
\(651\) | −5.63029 | + | 1.97394i | −0.00864868 | + | 0.00303217i | ||||
\(652\) | −577.539 | −0.885795 | ||||||||
\(653\) | 287.643i | 0.440494i | 0.975444 | + | 0.220247i | \(0.0706864\pi\) | ||||
−0.975444 | + | 0.220247i | \(0.929314\pi\) | |||||||
\(654\) | −75.8629 | − | 216.384i | −0.115998 | − | 0.330863i | ||||
\(655\) | −38.3506 | −0.0585505 | ||||||||
\(656\) | − | 132.709i | − | 0.202300i | ||||||
\(657\) | −128.940 | + | 103.082i | −0.196256 | + | 0.156898i | ||||
\(658\) | 135.618 | 0.206107 | ||||||||
\(659\) | 195.498i | 0.296659i | 0.988938 | + | 0.148330i | \(0.0473896\pi\) | ||||
−0.988938 | + | 0.148330i | \(0.952610\pi\) | |||||||
\(660\) | 566.746 | − | 198.697i | 0.858705 | − | 0.301057i | ||||
\(661\) | −724.026 | −1.09535 | −0.547674 | − | 0.836692i | \(-0.684487\pi\) | ||||
−0.547674 | + | 0.836692i | \(0.684487\pi\) | |||||||
\(662\) | 31.2382i | 0.0471876i | ||||||||
\(663\) | −51.4447 | − | 146.736i | −0.0775938 | − | 0.221321i | ||||
\(664\) | 1050.44 | 1.58198 | ||||||||
\(665\) | 239.057i | 0.359484i | ||||||||
\(666\) | −240.235 | − | 300.499i | −0.360713 | − | 0.451200i | ||||
\(667\) | −245.434 | −0.367966 | ||||||||
\(668\) | − | 886.370i | − | 1.32690i | ||||||
\(669\) | 107.300 | − | 37.6189i | 0.160389 | − | 0.0562315i | ||||
\(670\) | −470.630 | −0.702433 | ||||||||
\(671\) | − | 333.591i | − | 0.497154i | ||||||
\(672\) | 87.7565 | + | 250.308i | 0.130590 | + | 0.372483i | ||||
\(673\) | 819.856 | 1.21821 | 0.609105 | − | 0.793089i | \(-0.291529\pi\) | ||||
0.609105 | + | 0.793089i | \(0.291529\pi\) | |||||||
\(674\) | 66.1964i | 0.0982142i | ||||||||
\(675\) | −45.7869 | + | 73.1636i | −0.0678325 | + | 0.108390i | ||||
\(676\) | −395.857 | −0.585587 | ||||||||
\(677\) | − | 478.457i | − | 0.706731i | −0.935485 | − | 0.353365i | \(-0.885037\pi\) | ||
0.935485 | − | 0.353365i | \(-0.114963\pi\) | |||||||
\(678\) | 243.094 | − | 85.2271i | 0.358545 | − | 0.125704i | ||||
\(679\) | 32.8593 | 0.0483937 | ||||||||
\(680\) | − | 253.813i | − | 0.373254i | ||||||
\(681\) | 322.761 | + | 920.613i | 0.473951 | + | 1.35185i | ||||
\(682\) | −9.64079 | −0.0141361 | ||||||||
\(683\) | 391.554i | 0.573286i | 0.958037 | + | 0.286643i | \(0.0925394\pi\) | ||||
−0.958037 | + | 0.286643i | \(0.907461\pi\) | |||||||
\(684\) | −411.870 | + | 329.271i | −0.602150 | + | 0.481390i | ||||
\(685\) | 786.037 | 1.14750 | ||||||||
\(686\) | 233.030i | 0.339695i | ||||||||
\(687\) | 523.236 | − | 183.443i | 0.761625 | − | 0.267021i | ||||
\(688\) | −325.180 | −0.472645 | ||||||||
\(689\) | − | 69.4157i | − | 0.100749i | ||||||
\(690\) | 200.466 | + | 571.789i | 0.290530 | + | 0.828679i | ||||
\(691\) | 2.76994 | 0.00400859 | 0.00200430 | − | 0.999998i | \(-0.499362\pi\) | ||||
0.00200430 | + | 0.999998i | \(0.499362\pi\) | |||||||
\(692\) | 592.163i | 0.855726i | ||||||||
\(693\) | −210.535 | − | 263.348i | −0.303802 | − | 0.380012i | ||||
\(694\) | −207.293 | −0.298693 | ||||||||
\(695\) | − | 771.165i | − | 1.10959i | ||||||
\(696\) | −102.720 | + | 36.0128i | −0.147586 | + | 0.0517426i | ||||
\(697\) | 178.357 | 0.255893 | ||||||||
\(698\) | − | 378.413i | − | 0.542139i | ||||||
\(699\) | −241.720 | − | 689.458i | −0.345808 | − | 0.986349i | ||||
\(700\) | 26.8310 | 0.0383299 | ||||||||
\(701\) | 549.171i | 0.783411i | 0.920091 | + | 0.391705i | \(0.128115\pi\) | ||||
−0.920091 | + | 0.391705i | \(0.871885\pi\) | |||||||
\(702\) | 139.552 | + | 87.3337i | 0.198792 | + | 0.124407i | ||||
\(703\) | −851.485 | −1.21122 | ||||||||
\(704\) | 96.4579i | 0.137014i | ||||||||
\(705\) | −697.523 | + | 244.547i | −0.989394 | + | 0.346875i | ||||
\(706\) | 126.228 | 0.178794 | ||||||||
\(707\) | 118.744i | 0.167955i | ||||||||
\(708\) | −1.88300 | − | 5.37090i | −0.00265961 | − | 0.00758602i | ||||
\(709\) | −113.955 | −0.160727 | −0.0803634 | − | 0.996766i | \(-0.525608\pi\) | ||||
−0.0803634 | + | 0.996766i | \(0.525608\pi\) | |||||||
\(710\) | − | 112.198i | − | 0.158025i | ||||||
\(711\) | 992.962 | − | 793.826i | 1.39657 | − | 1.11649i | ||||
\(712\) | 428.697 | 0.602103 | ||||||||
\(713\) | 33.4688i | 0.0469408i | ||||||||
\(714\) | −58.7032 | + | 20.5810i | −0.0822174 | + | 0.0288249i | ||||
\(715\) | −414.975 | −0.580385 | ||||||||
\(716\) | − | 1038.96i | − | 1.45106i | ||||||
\(717\) | 81.4253 | + | 232.250i | 0.113564 | + | 0.323919i | ||||
\(718\) | −93.9801 | −0.130891 | ||||||||
\(719\) | 750.475i | 1.04378i | 0.853014 | + | 0.521888i | \(0.174772\pi\) | ||||
−0.853014 | + | 0.521888i | \(0.825228\pi\) | |||||||
\(720\) | −157.523 | − | 197.039i | −0.218782 | − | 0.273665i | ||||
\(721\) | −393.563 | −0.545857 | ||||||||
\(722\) | 3.44177i | 0.00476700i | ||||||||
\(723\) | −120.230 | + | 42.1518i | −0.166293 | + | 0.0583012i | ||||
\(724\) | 647.901 | 0.894891 | ||||||||
\(725\) | 17.2145i | 0.0237441i | ||||||||
\(726\) | −66.2700 | − | 189.022i | −0.0912810 | − | 0.260361i | ||||
\(727\) | 222.043 | 0.305424 | 0.152712 | − | 0.988271i | \(-0.451199\pi\) | ||||
0.152712 | + | 0.988271i | \(0.451199\pi\) | |||||||
\(728\) | − | 117.227i | − | 0.161027i | ||||||
\(729\) | −318.681 | − | 655.655i | −0.437148 | − | 0.899390i | ||||
\(730\) | 81.2841 | 0.111348 | ||||||||
\(731\) | − | 437.033i | − | 0.597857i | ||||||
\(732\) | −211.596 | + | 74.1843i | −0.289066 | + | 0.101345i | ||||
\(733\) | −865.403 | −1.18063 | −0.590316 | − | 0.807173i | \(-0.700997\pi\) | ||||
−0.590316 | + | 0.807173i | \(0.700997\pi\) | |||||||
\(734\) | − | 361.058i | − | 0.491905i | ||||||
\(735\) | −193.104 | − | 550.793i | −0.262727 | − | 0.749378i | ||||
\(736\) | 1487.94 | 2.02165 | ||||||||
\(737\) | − | 1469.07i | − | 1.99331i | ||||||
\(738\) | −147.494 | + | 117.914i | −0.199856 | + | 0.159776i | ||||
\(739\) | −394.545 | −0.533891 | −0.266946 | − | 0.963712i | \(-0.586014\pi\) | ||||
−0.266946 | + | 0.963712i | \(0.586014\pi\) | |||||||
\(740\) | − | 651.839i | − | 0.880863i | ||||||
\(741\) | 343.837 | − | 120.547i | 0.464018 | − | 0.162682i | ||||
\(742\) | −27.7705 | −0.0374265 | ||||||||
\(743\) | 357.323i | 0.480919i | 0.970659 | + | 0.240459i | \(0.0772981\pi\) | ||||
−0.970659 | + | 0.240459i | \(0.922702\pi\) | |||||||
\(744\) | 4.91092 | + | 14.0075i | 0.00660070 | + | 0.0188272i | ||||
\(745\) | −177.705 | −0.238530 | ||||||||
\(746\) | 134.396i | 0.180155i | ||||||||
\(747\) | 876.178 | + | 1095.97i | 1.17293 | + | 1.46716i | ||||
\(748\) | 345.879 | 0.462405 | ||||||||
\(749\) | − | 180.233i | − | 0.240632i | ||||||
\(750\) | 353.751 | − | 124.023i | 0.471669 | − | 0.165364i | ||||
\(751\) | 475.360 | 0.632970 | 0.316485 | − | 0.948598i | \(-0.397497\pi\) | ||||
0.316485 | + | 0.948598i | \(0.397497\pi\) | |||||||
\(752\) | 316.740i | 0.421197i | ||||||||
\(753\) | −428.535 | − | 1222.31i | −0.569104 | − | 1.62326i | ||||
\(754\) | 32.8348 | 0.0435475 | ||||||||
\(755\) | − | 46.6617i | − | 0.0618036i | ||||||
\(756\) | −120.223 | + | 192.106i | −0.159025 | + | 0.254108i | ||||
\(757\) | −143.413 | −0.189449 | −0.0947243 | − | 0.995504i | \(-0.530197\pi\) | ||||
−0.0947243 | + | 0.995504i | \(0.530197\pi\) | |||||||
\(758\) | − | 406.405i | − | 0.536154i | ||||||
\(759\) | −1784.84 | + | 625.753i | −2.35157 | + | 0.824444i | ||||
\(760\) | 594.743 | 0.782557 | ||||||||
\(761\) | 67.5801i | 0.0888044i | 0.999014 | + | 0.0444022i | \(0.0141383\pi\) | ||||
−0.999014 | + | 0.0444022i | \(0.985862\pi\) | |||||||
\(762\) | −163.560 | − | 466.522i | −0.214645 | − | 0.612234i | ||||
\(763\) | −218.104 | −0.285851 | ||||||||
\(764\) | 627.239i | 0.820993i | ||||||||
\(765\) | 264.815 | − | 211.707i | 0.346164 | − | 0.276742i | ||||
\(766\) | 224.788 | 0.293457 | ||||||||
\(767\) | 3.93261i | 0.00512726i | ||||||||
\(768\) | 412.055 | − | 144.464i | 0.536530 | − | 0.188104i | ||||
\(769\) | 436.330 | 0.567399 | 0.283700 | − | 0.958913i | \(-0.408438\pi\) | ||||
0.283700 | + | 0.958913i | \(0.408438\pi\) | |||||||
\(770\) | 166.015i | 0.215604i | ||||||||
\(771\) | 111.089 | + | 316.860i | 0.144084 | + | 0.410973i | ||||
\(772\) | 1004.72 | 1.30145 | ||||||||
\(773\) | − | 1009.69i | − | 1.30620i | −0.757274 | − | 0.653098i | \(-0.773469\pi\) | ||
0.757274 | − | 0.653098i | \(-0.226531\pi\) | |||||||
\(774\) | 288.929 | + | 361.408i | 0.373293 | + | 0.466935i | ||||
\(775\) | 2.34747 | 0.00302900 | ||||||||
\(776\) | − | 81.7499i | − | 0.105348i | ||||||
\(777\) | −345.336 | + | 121.072i | −0.444447 | + | 0.155820i | ||||
\(778\) | −142.842 | −0.183602 | ||||||||
\(779\) | 417.934i | 0.536500i | ||||||||
\(780\) | 92.2827 | + | 263.218i | 0.118311 | + | 0.337460i | ||||
\(781\) | 350.226 | 0.448433 | ||||||||
\(782\) | 348.957i | 0.446236i | ||||||||
\(783\) | −123.253 | − | 77.1338i | −0.157412 | − | 0.0985107i | ||||
\(784\) | −250.111 | −0.319020 | ||||||||
\(785\) | 402.144i | 0.512285i | ||||||||
\(786\) | 22.0673 | − | 7.73666i | 0.0280755 | − | 0.00984308i | ||||
\(787\) | −601.017 | −0.763681 | −0.381841 | − | 0.924228i | \(-0.624710\pi\) | ||||
−0.381841 | + | 0.924228i | \(0.624710\pi\) | |||||||
\(788\) | − | 844.057i | − | 1.07114i | ||||||
\(789\) | −109.065 | − | 311.087i | −0.138232 | − | 0.394280i | ||||
\(790\) | −625.964 | −0.792359 | ||||||||
\(791\) | − | 245.026i | − | 0.309768i | ||||||
\(792\) | −655.178 | + | 523.784i | −0.827245 | + | 0.661343i | ||||
\(793\) | 154.932 | 0.195375 | ||||||||
\(794\) | 399.713i | 0.503416i | ||||||||
\(795\) | 142.831 | − | 50.0757i | 0.179662 | − | 0.0629883i | ||||
\(796\) | −1041.96 | −1.30899 | ||||||||
\(797\) | 1058.83i | 1.32852i | 0.747503 | + | 0.664258i | \(0.231252\pi\) | ||||
−0.747503 | + | 0.664258i | \(0.768748\pi\) | |||||||
\(798\) | −48.2261 | − | 137.556i | −0.0604337 | − | 0.172375i | ||||
\(799\) | −425.690 | −0.532779 | ||||||||
\(800\) | − | 104.363i | − | 0.130453i | ||||||
\(801\) | 357.580 | + | 447.281i | 0.446417 | + | 0.558403i | ||||
\(802\) | 379.466 | 0.473150 | ||||||||
\(803\) | 253.728i | 0.315975i | ||||||||
\(804\) | −931.831 | + | 326.694i | −1.15899 | + | 0.406336i | ||||
\(805\) | 576.335 | 0.715943 | ||||||||
\(806\) | − | 4.47755i | − | 0.00555528i | ||||||
\(807\) | 448.817 | + | 1280.16i | 0.556155 | + | 1.58633i | ||||
\(808\) | 295.420 | 0.365619 | ||||||||
\(809\) | 587.804i | 0.726581i | 0.931676 | + | 0.363290i | \(0.118347\pi\) | ||||
−0.931676 | + | 0.363290i | \(0.881653\pi\) | |||||||
\(810\) | −79.0285 | + | 350.146i | −0.0975660 | + | 0.432279i | ||||
\(811\) | −1241.37 | −1.53067 | −0.765336 | − | 0.643631i | \(-0.777427\pi\) | ||||
−0.765336 | + | 0.643631i | \(0.777427\pi\) | |||||||
\(812\) | 45.2001i | 0.0556652i | ||||||||
\(813\) | −472.955 | + | 165.815i | −0.581740 | + | 0.203954i | ||||
\(814\) | −591.321 | −0.726438 | ||||||||
\(815\) | 870.121i | 1.06763i | ||||||||
\(816\) | −48.0674 | − | 137.103i | −0.0589061 | − | 0.168018i | ||||
\(817\) | 1024.07 | 1.25346 | ||||||||
\(818\) | 461.846i | 0.564604i | ||||||||
\(819\) | 122.309 | − | 97.7803i | 0.149340 | − | 0.119390i | ||||
\(820\) | −319.942 | −0.390173 | ||||||||
\(821\) | − | 1271.68i | − | 1.54894i | −0.632613 | − | 0.774468i | \(-0.718018\pi\) | ||
0.632613 | − | 0.774468i | \(-0.281982\pi\) | |||||||
\(822\) | −452.293 | + | 158.571i | −0.550235 | + | 0.192909i | ||||
\(823\) | 1278.94 | 1.55400 | 0.777000 | − | 0.629501i | \(-0.216741\pi\) | ||||
0.777000 | + | 0.629501i | \(0.216741\pi\) | |||||||
\(824\) | 979.135i | 1.18827i | ||||||||
\(825\) | 43.8897 | + | 125.187i | 0.0531997 | + | 0.151742i | ||||
\(826\) | 1.57328 | 0.00190470 | ||||||||
\(827\) | 564.985i | 0.683175i | 0.939850 | + | 0.341587i | \(0.110964\pi\) | ||||
−0.939850 | + | 0.341587i | \(0.889036\pi\) | |||||||
\(828\) | 793.829 | + | 992.966i | 0.958731 | + | 1.19923i | ||||
\(829\) | 477.364 | 0.575831 | 0.287916 | − | 0.957656i | \(-0.407038\pi\) | ||||
0.287916 | + | 0.957656i | \(0.407038\pi\) | |||||||
\(830\) | − | 690.901i | − | 0.832411i | ||||||
\(831\) | 163.524 | − | 57.3305i | 0.196780 | − | 0.0689898i | ||||
\(832\) | −44.7988 | −0.0538447 | ||||||||
\(833\) | − | 336.143i | − | 0.403533i | ||||||
\(834\) | 155.571 | + | 443.736i | 0.186536 | + | 0.532058i | ||||
\(835\) | −1335.41 | −1.59929 | ||||||||
\(836\) | 810.476i | 0.969469i | ||||||||
\(837\) | −10.5184 | + | 16.8076i | −0.0125668 | + | 0.0200807i | ||||
\(838\) | 482.339 | 0.575583 | ||||||||
\(839\) | 650.601i | 0.775448i | 0.921776 | + | 0.387724i | \(0.126739\pi\) | ||||
−0.921776 | + | 0.387724i | \(0.873261\pi\) | |||||||
\(840\) | 241.209 | − | 84.5664i | 0.287154 | − | 0.100674i | ||||
\(841\) | −29.0000 | −0.0344828 | ||||||||
\(842\) | − | 476.590i | − | 0.566022i | ||||||
\(843\) | −204.307 | − | 582.746i | −0.242357 | − | 0.691277i | ||||
\(844\) | −812.484 | −0.962659 | ||||||||
\(845\) | 596.399i | 0.705798i | ||||||||
\(846\) | 352.028 | − | 281.430i | 0.416109 | − | 0.332659i | ||||
\(847\) | −190.525 | −0.224941 | ||||||||
\(848\) | − | 64.8586i | − | 0.0764843i | ||||||
\(849\) | 987.967 | − | 346.375i | 1.16368 | − | 0.407980i | ||||
\(850\) | 24.4755 | 0.0287947 | ||||||||
\(851\) | 2052.82i | 2.41224i | ||||||||
\(852\) | −77.8837 | − | 222.148i | −0.0914128 | − | 0.260737i | ||||
\(853\) | 1143.95 | 1.34109 | 0.670547 | − | 0.741867i | \(-0.266059\pi\) | ||||
0.670547 | + | 0.741867i | \(0.266059\pi\) | |||||||
\(854\) | − | 61.9822i | − | 0.0725787i | ||||||
\(855\) | 496.080 | + | 620.525i | 0.580211 | + | 0.725760i | ||||
\(856\) | −448.398 | −0.523829 | ||||||||
\(857\) | − | 882.999i | − | 1.03034i | −0.857089 | − | 0.515169i | \(-0.827729\pi\) | ||
0.857089 | − | 0.515169i | \(-0.172271\pi\) | |||||||
\(858\) | 238.781 | − | 83.7150i | 0.278299 | − | 0.0975700i | ||||
\(859\) | −1370.92 | −1.59595 | −0.797974 | − | 0.602692i | \(-0.794095\pi\) | ||||
−0.797974 | + | 0.602692i | \(0.794095\pi\) | |||||||
\(860\) | 783.961i | 0.911582i | ||||||||
\(861\) | 59.4259 | + | 169.501i | 0.0690196 | + | 0.196865i | ||||
\(862\) | −640.880 | −0.743480 | ||||||||
\(863\) | − | 720.415i | − | 0.834780i | −0.908727 | − | 0.417390i | \(-0.862945\pi\) | ||
0.908727 | − | 0.417390i | \(-0.137055\pi\) | |||||||
\(864\) | 747.221 | + | 467.623i | 0.864839 | + | 0.541230i | ||||
\(865\) | 892.154 | 1.03139 | ||||||||
\(866\) | 97.7847i | 0.112915i | ||||||||
\(867\) | −633.911 | + | 222.245i | −0.731154 | + | 0.256338i | ||||
\(868\) | 6.16376 | 0.00710111 | ||||||||
\(869\) | − | 1953.94i | − | 2.24850i | ||||||
\(870\) | 23.6866 | + | 67.5616i | 0.0272260 | + | 0.0776570i | ||||
\(871\) | 682.293 | 0.783345 | ||||||||
\(872\) | 542.616i | 0.622266i | ||||||||
\(873\) | 85.2938 | − | 68.1883i | 0.0977019 | − | 0.0781081i | ||||
\(874\) | −817.688 | −0.935570 | ||||||||
\(875\) | − | 356.564i | − | 0.407501i | ||||||
\(876\) | 160.940 | − | 56.4244i | 0.183721 | − | 0.0644115i | ||||
\(877\) | −978.182 | −1.11537 | −0.557686 | − | 0.830052i | \(-0.688311\pi\) | ||||
−0.557686 | + | 0.830052i | \(0.688311\pi\) | |||||||
\(878\) | − | 14.9810i | − | 0.0170627i | ||||||
\(879\) | −76.8399 | − | 219.171i | −0.0874174 | − | 0.249341i | ||||
\(880\) | −387.732 | −0.440605 | ||||||||
\(881\) | − | 685.916i | − | 0.778565i | −0.921118 | − | 0.389283i | \(-0.872723\pi\) | ||
0.921118 | − | 0.389283i | \(-0.127277\pi\) | |||||||
\(882\) | 222.229 | + | 277.976i | 0.251960 | + | 0.315165i | ||||
\(883\) | −644.054 | −0.729393 | −0.364696 | − | 0.931127i | \(-0.618827\pi\) | ||||
−0.364696 | + | 0.931127i | \(0.618827\pi\) | |||||||
\(884\) | 160.639i | 0.181719i | ||||||||
\(885\) | −8.09182 | + | 2.83694i | −0.00914329 | + | 0.00320558i | ||||
\(886\) | 123.748 | 0.139670 | ||||||||
\(887\) | − | 1680.35i | − | 1.89442i | −0.320608 | − | 0.947212i | \(-0.603887\pi\) | ||
0.320608 | − | 0.947212i | \(-0.396113\pi\) | |||||||
\(888\) | 301.213 | + | 859.152i | 0.339204 | + | 0.967513i | ||||
\(889\) | −470.231 | −0.528944 | ||||||||
\(890\) | − | 281.966i | − | 0.316816i | ||||||
\(891\) | −1092.98 | − | 246.687i | −1.22669 | − | 0.276866i | ||||
\(892\) | −117.467 | −0.131690 | ||||||||
\(893\) | − | 997.494i | − | 1.11701i | ||||||
\(894\) | 102.253 | − | 35.8493i | 0.114377 | − | 0.0400999i | ||||
\(895\) | −1565.30 | −1.74894 | ||||||||
\(896\) | − | 335.739i | − | 0.374709i | ||||||
\(897\) | −290.624 | − | 828.947i | −0.323995 | − | 0.924133i | ||||
\(898\) | 207.783 | 0.231384 | ||||||||
\(899\) | 3.95461i | 0.00439890i | ||||||||
\(900\) | 69.6458 | − | 55.6785i | 0.0773842 | − | 0.0618650i | ||||
\(901\) | 87.1683 | 0.0967462 | ||||||||
\(902\) | 290.238i | 0.321771i | ||||||||
\(903\) | 415.332 | − | 145.613i | 0.459947 | − | 0.161254i | ||||
\(904\) | −609.595 | −0.674330 | ||||||||
\(905\) | − | 976.130i | − | 1.07860i | ||||||
\(906\) | 9.41331 | + | 26.8496i | 0.0103900 | + | 0.0296354i | ||||
\(907\) | 46.1140 | 0.0508424 | 0.0254212 | − | 0.999677i | \(-0.491907\pi\) | ||||
0.0254212 | + | 0.999677i | \(0.491907\pi\) | |||||||
\(908\) | − | 1007.84i | − | 1.10996i | ||||||
\(909\) | 246.413 | + | 308.227i | 0.271081 | + | 0.339083i | ||||
\(910\) | −77.1037 | −0.0847294 | ||||||||
\(911\) | 1367.36i | 1.50094i | 0.660903 | + | 0.750471i | \(0.270173\pi\) | ||||
−0.660903 | + | 0.750471i | \(0.729827\pi\) | |||||||
\(912\) | 321.265 | − | 112.633i | 0.352264 | − | 0.123501i | ||||
\(913\) | 2156.65 | 2.36215 | ||||||||
\(914\) | 259.708i | 0.284145i | ||||||||
\(915\) | 111.766 | + | 318.792i | 0.122149 | + | 0.348406i | ||||
\(916\) | −572.813 | −0.625342 | ||||||||
\(917\) | − | 22.2427i | − | 0.0242560i | ||||||
\(918\) | −109.669 | + | 175.241i | −0.119465 | + | 0.190894i | ||||
\(919\) | 1162.56 | 1.26503 | 0.632514 | − | 0.774549i | \(-0.282023\pi\) | ||||
0.632514 | + | 0.774549i | \(0.282023\pi\) | |||||||
\(920\) | − | 1433.85i | − | 1.55853i | ||||||
\(921\) | 304.629 | − | 106.801i | 0.330759 | − | 0.115962i | ||||
\(922\) | −448.074 | −0.485980 | ||||||||
\(923\) | 162.658i | 0.176228i | ||||||||
\(924\) | 115.241 | + | 328.704i | 0.124720 | + | 0.355740i | ||||
\(925\) | 143.983 | 0.155657 | ||||||||
\(926\) | − | 214.296i | − | 0.231421i | ||||||
\(927\) | −1021.58 | + | 816.705i | −1.10203 | + | 0.881019i | ||||
\(928\) | 175.812 | 0.189453 | ||||||||
\(929\) | 1146.89i | 1.23455i | 0.786749 | + | 0.617273i | \(0.211762\pi\) | ||||
−0.786749 | + | 0.617273i | \(0.788238\pi\) | |||||||
\(930\) | 9.21310 | − | 3.23005i | 0.00990655 | − | 0.00347317i | ||||
\(931\) | 787.663 | 0.846039 | ||||||||
\(932\) | 754.785i | 0.809855i | ||||||||
\(933\) | 217.454 | + | 620.245i | 0.233070 | + | 0.664785i | ||||
\(934\) | −690.092 | −0.738857 | ||||||||
\(935\) | − | 521.102i | − | 0.557328i | ||||||
\(936\) | −243.265 | − | 304.290i | −0.259899 | − | 0.325096i | ||||
\(937\) | 965.585 | 1.03051 | 0.515254 | − | 0.857038i | \(-0.327698\pi\) | ||||
0.515254 | + | 0.857038i | \(0.327698\pi\) | |||||||
\(938\) | − | 272.958i | − | 0.291000i | ||||||
\(939\) | 1055.19 | − | 369.942i | 1.12373 | − | 0.393974i | ||||
\(940\) | 763.613 | 0.812355 | ||||||||
\(941\) | − | 787.513i | − | 0.836890i | −0.908242 | − | 0.418445i | \(-0.862575\pi\) | ||
0.908242 | − | 0.418445i | \(-0.137425\pi\) | |||||||
\(942\) | −81.1265 | − | 231.398i | −0.0861215 | − | 0.245645i | ||||
\(943\) | 1007.58 | 1.06849 | ||||||||
\(944\) | 3.67444i | 0.00389241i | ||||||||
\(945\) | 289.427 | + | 181.128i | 0.306272 | + | 0.191670i | ||||
\(946\) | 711.176 | 0.751772 | ||||||||
\(947\) | 177.474i | 0.187407i | 0.995600 | + | 0.0937033i | \(0.0298705\pi\) | ||||
−0.995600 | + | 0.0937033i | \(0.970129\pi\) | |||||||
\(948\) | −1239.39 | + | 434.521i | −1.30737 | + | 0.458355i | ||||
\(949\) | −117.841 | −0.124174 | ||||||||
\(950\) | 57.3519i | 0.0603704i | ||||||||
\(951\) | −376.590 | − | 1074.15i | −0.395994 | − | 1.12949i | ||||
\(952\) | 147.207 | 0.154630 | ||||||||
\(953\) | 216.064i | 0.226719i | 0.993554 | + | 0.113360i | \(0.0361612\pi\) | ||||
−0.993554 | + | 0.113360i | \(0.963839\pi\) | |||||||
\(954\) | −72.0845 | + | 57.6281i | −0.0755602 | + | 0.0604068i | ||||
\(955\) | 945.000 | 0.989529 | ||||||||
\(956\) | − | 254.256i | − | 0.265958i | ||||||
\(957\) | −210.893 | + | 73.9378i | −0.220369 | + | 0.0772600i | ||||
\(958\) | −414.698 | −0.432879 | ||||||||
\(959\) | 455.889i | 0.475380i | ||||||||
\(960\) | −32.3173 | − | 92.1788i | −0.0336639 | − | 0.0960196i | ||||
\(961\) | −960.461 | −0.999439 | ||||||||
\(962\) | − | 274.632i | − | 0.285480i | ||||||
\(963\) | −374.012 | − | 467.836i | −0.388383 | − | 0.485811i | ||||
\(964\) | 131.622 | 0.136537 | ||||||||
\(965\) | − | 1513.71i | − | 1.56861i | ||||||
\(966\) | −331.629 | + | 116.267i | −0.343301 | + | 0.120359i | ||||
\(967\) | 95.6676 | 0.0989324 | 0.0494662 | − | 0.998776i | \(-0.484248\pi\) | ||||
0.0494662 | + | 0.998776i | \(0.484248\pi\) | |||||||
\(968\) | 474.003i | 0.489672i | ||||||||
\(969\) | 151.376 | + | 431.771i | 0.156219 | + | 0.445584i | ||||
\(970\) | −53.7692 | −0.0554322 | ||||||||
\(971\) | − | 1116.58i | − | 1.14992i | −0.818180 | − | 0.574962i | \(-0.805017\pi\) | ||
0.818180 | − | 0.574962i | \(-0.194983\pi\) | |||||||
\(972\) | 86.5846 | + | 748.135i | 0.0890788 | + | 0.769686i | ||||
\(973\) | 447.264 | 0.459675 | ||||||||
\(974\) | 40.9417i | 0.0420346i | ||||||||
\(975\) | −58.1416 | + | 20.3841i | −0.0596325 | + | 0.0209068i | ||||
\(976\) | 144.761 | 0.148321 | ||||||||
\(977\) | 501.812i | 0.513625i | 0.966461 | + | 0.256812i | \(0.0826723\pi\) | ||||
−0.966461 | + | 0.256812i | \(0.917328\pi\) | |||||||
\(978\) | −175.534 | − | 500.676i | −0.179483 | − | 0.511939i | ||||
\(979\) | 880.157 | 0.899037 | ||||||||
\(980\) | 602.981i | 0.615287i | ||||||||
\(981\) | −566.139 | + | 452.601i | −0.577104 | + | 0.461367i | ||||
\(982\) | −555.498 | −0.565681 | ||||||||
\(983\) | − | 1252.51i | − | 1.27418i | −0.770791 | − | 0.637088i | \(-0.780139\pi\) | ||
0.770791 | − | 0.637088i | \(-0.219861\pi\) | |||||||
\(984\) | 421.697 | − | 147.844i | 0.428554 | − | 0.150248i | ||||
\(985\) | −1271.66 | −1.29102 | ||||||||
\(986\) | 41.2321i | 0.0418175i | ||||||||
\(987\) | −141.833 | − | 404.552i | −0.143702 | − | 0.409881i | ||||
\(988\) | −376.416 | −0.380988 | ||||||||
\(989\) | − | 2468.91i | − | 2.49637i | ||||||
\(990\) | 344.507 | + | 430.929i | 0.347987 | + | 0.435282i | ||||
\(991\) | −438.469 | −0.442451 | −0.221226 | − | 0.975223i | \(-0.571006\pi\) | ||||
−0.221226 | + | 0.975223i | \(0.571006\pi\) | |||||||
\(992\) | − | 23.9748i | − | 0.0241681i | ||||||
\(993\) | 93.1841 | − | 32.6698i | 0.0938410 | − | 0.0329001i | ||||
\(994\) | 65.0731 | 0.0654659 | ||||||||
\(995\) | 1569.81i | 1.57770i | ||||||||
\(996\) | −479.598 | − | 1367.96i | −0.481524 | − | 1.37345i | ||||
\(997\) | −107.167 | −0.107489 | −0.0537447 | − | 0.998555i | \(-0.517116\pi\) | ||||
−0.0537447 | + | 0.998555i | \(0.517116\pi\) | |||||||
\(998\) | − | 288.766i | − | 0.289344i | ||||||
\(999\) | −645.151 | + | 1030.90i | −0.645797 | + | 1.03193i |
(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 | 87.3.b.a.59.7 | ✓ | 18 | |
3.2 | odd | 2 | inner | 87.3.b.a.59.12 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.3.b.a.59.7 | ✓ | 18 | 1.1 | even | 1 | trivial | |
87.3.b.a.59.12 | yes | 18 | 3.2 | odd | 2 | inner |