Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,4,Mod(37,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.f (of order \(5\), degree \(4\), 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: | \(5.84118909057\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.682515625.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(0.581882 - 1.79085i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.91 |
Dual form | 99.4.f.b.37.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.02339 | − | 1.47008i | 0.715376 | − | 0.519751i | −0.169528 | − | 0.985525i | \(-0.554224\pi\) |
0.884903 | + | 0.465775i | \(0.154224\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.539165 | + | 1.65938i | −0.0673956 | + | 0.207422i | ||||
\(5\) | 8.44146 | + | 6.13308i | 0.755027 | + | 0.548559i | 0.897381 | − | 0.441257i | \(-0.145467\pi\) |
−0.142354 | + | 0.989816i | \(0.545467\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.1220 | + | 31.1524i | −0.546539 | + | 1.68207i | 0.170763 | + | 0.985312i | \(0.445377\pi\) |
−0.717302 | + | 0.696762i | \(0.754623\pi\) | |||||||
\(8\) | 7.53140 | + | 23.1793i | 0.332844 | + | 1.02439i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.0964 | 0.825242 | ||||||||
\(11\) | −12.6666 | − | 34.2134i | −0.347194 | − | 0.937793i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 59.2672 | − | 43.0601i | 1.26444 | − | 0.918672i | 0.265477 | − | 0.964117i | \(-0.414471\pi\) |
0.998967 | + | 0.0454454i | \(0.0144707\pi\) | |||||||
\(14\) | 25.3157 | + | 77.9137i | 0.483279 | + | 1.48738i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 38.0218 | + | 27.6245i | 0.594091 | + | 0.431633i | ||||
\(17\) | −44.7200 | − | 32.4909i | −0.638011 | − | 0.463542i | 0.221155 | − | 0.975239i | \(-0.429017\pi\) |
−0.859166 | + | 0.511697i | \(0.829017\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.9834 | + | 86.1240i | 0.337886 | + | 1.03990i | 0.965283 | + | 0.261206i | \(0.0841201\pi\) |
−0.627398 | + | 0.778699i | \(0.715880\pi\) | |||||||
\(20\) | −14.7284 | + | 10.7008i | −0.164669 | + | 0.119639i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −75.9259 | − | 50.6060i | −0.735793 | − | 0.490420i | ||||
\(23\) | 91.1987 | 0.826793 | 0.413397 | − | 0.910551i | \(-0.364342\pi\) | ||||
0.413397 | + | 0.910551i | \(0.364342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98357 | − | 15.3379i | −0.0398686 | − | 0.122703i | ||||
\(26\) | 56.6188 | − | 174.255i | 0.427072 | − | 1.31439i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −46.2362 | − | 33.5926i | −0.312065 | − | 0.226729i | ||||
\(29\) | 23.7073 | − | 72.9635i | 0.151805 | − | 0.467206i | −0.846019 | − | 0.533153i | \(-0.821007\pi\) |
0.997823 | + | 0.0659470i | \(0.0210068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.6296 | + | 13.5352i | −0.107935 | + | 0.0784193i | −0.640443 | − | 0.768005i | \(-0.721249\pi\) |
0.532509 | + | 0.846425i | \(0.321249\pi\) | |||||||
\(32\) | −77.4339 | −0.427766 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −138.250 | −0.697344 | ||||||||
\(35\) | −276.505 | + | 200.893i | −1.33537 | + | 0.970202i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.8841 | − | 119.673i | 0.172770 | − | 0.531732i | −0.826754 | − | 0.562563i | \(-0.809815\pi\) |
0.999525 | + | 0.0308308i | \(0.00981532\pi\) | |||||||
\(38\) | 183.230 | + | 133.124i | 0.782207 | + | 0.568306i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −78.5842 | + | 241.857i | −0.310631 | + | 0.956025i | ||||
\(41\) | −43.2807 | − | 133.204i | −0.164861 | − | 0.507391i | 0.834165 | − | 0.551515i | \(-0.185950\pi\) |
−0.999026 | + | 0.0441244i | \(0.985950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 146.015 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(44\) | 63.6024 | − | 2.57208i | 0.217919 | − | 0.00881262i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 184.530 | − | 134.069i | 0.591468 | − | 0.429727i | ||||
\(47\) | 68.4490 | + | 210.664i | 0.212432 | + | 0.653799i | 0.999326 | + | 0.0367105i | \(0.0116879\pi\) |
−0.786894 | + | 0.617088i | \(0.788312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −590.526 | − | 429.042i | −1.72165 | − | 1.25085i | ||||
\(50\) | −32.6315 | − | 23.7082i | −0.0922959 | − | 0.0670569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 39.4983 | + | 121.563i | 0.105335 | + | 0.324188i | ||||
\(53\) | −35.5597 | + | 25.8356i | −0.0921604 | + | 0.0669585i | −0.632911 | − | 0.774224i | \(-0.718140\pi\) |
0.540751 | + | 0.841183i | \(0.318140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 102.909 | − | 366.496i | 0.252294 | − | 0.898516i | ||||
\(56\) | −798.324 | −1.90501 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −59.2930 | − | 182.485i | −0.134234 | − | 0.413129i | ||||
\(59\) | 124.159 | − | 382.121i | 0.273967 | − | 0.843184i | −0.715524 | − | 0.698589i | \(-0.753812\pi\) |
0.989491 | − | 0.144596i | \(-0.0461882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 328.861 | + | 238.932i | 0.690269 | + | 0.501509i | 0.876748 | − | 0.480949i | \(-0.159708\pi\) |
−0.186480 | + | 0.982459i | \(0.559708\pi\) | |||||||
\(62\) | −17.7972 | + | 54.7740i | −0.0364555 | + | 0.112199i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −460.853 | + | 334.830i | −0.900104 | + | 0.653964i | ||||
\(65\) | 764.393 | 1.45863 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 221.234 | 0.403404 | 0.201702 | − | 0.979447i | \(-0.435353\pi\) | ||||
0.201702 | + | 0.979447i | \(0.435353\pi\) | |||||||
\(68\) | 78.0262 | − | 56.6893i | 0.139148 | − | 0.101097i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −264.149 | + | 812.968i | −0.451027 | + | 1.38812i | ||||
\(71\) | −606.376 | − | 440.558i | −1.01357 | − | 0.736403i | −0.0486165 | − | 0.998818i | \(-0.515481\pi\) |
−0.964955 | + | 0.262415i | \(0.915481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68.6023 | + | 211.136i | −0.109990 | + | 0.338516i | −0.990869 | − | 0.134826i | \(-0.956952\pi\) |
0.880879 | + | 0.473342i | \(0.156952\pi\) | |||||||
\(74\) | −97.2508 | − | 299.307i | −0.152773 | − | 0.470186i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −158.000 | −0.238471 | ||||||||
\(77\) | 1194.04 | − | 48.2871i | 1.76719 | − | 0.0714652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 954.850 | − | 693.739i | 1.35986 | − | 0.987997i | 0.361407 | − | 0.932408i | \(-0.382296\pi\) |
0.998454 | − | 0.0555887i | \(-0.0177036\pi\) | |||||||
\(80\) | 151.537 | + | 466.382i | 0.211779 | + | 0.651788i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −283.394 | − | 205.898i | −0.381655 | − | 0.277288i | ||||
\(83\) | 547.425 | + | 397.728i | 0.723948 | + | 0.525979i | 0.887643 | − | 0.460532i | \(-0.152341\pi\) |
−0.163695 | + | 0.986511i | \(0.552341\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −178.232 | − | 548.542i | −0.227435 | − | 0.699973i | ||||
\(86\) | 295.444 | − | 214.653i | 0.370449 | − | 0.269147i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 697.644 | − | 551.278i | 0.845103 | − | 0.667800i | ||||
\(89\) | −1054.06 | −1.25539 | −0.627695 | − | 0.778460i | \(-0.716001\pi\) | ||||
−0.627695 | + | 0.778460i | \(0.716001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 741.524 | + | 2282.17i | 0.854207 | + | 2.62898i | ||||
\(92\) | −49.1711 | + | 151.333i | −0.0557222 | + | 0.171495i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 448.192 | + | 325.630i | 0.491781 | + | 0.357300i | ||||
\(95\) | −291.985 | + | 898.636i | −0.315337 | + | 0.970506i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 198.573 | − | 144.272i | 0.207857 | − | 0.151017i | −0.478987 | − | 0.877822i | \(-0.658996\pi\) |
0.686843 | + | 0.726805i | \(0.258996\pi\) | |||||||
\(98\) | −1825.59 | −1.88176 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.1383 | 0.0281383 | ||||||||
\(101\) | 18.3580 | − | 13.3379i | 0.0180860 | − | 0.0131403i | −0.578706 | − | 0.815537i | \(-0.696442\pi\) |
0.596792 | + | 0.802396i | \(0.296442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 303.269 | − | 933.366i | 0.290116 | − | 0.892886i | −0.694702 | − | 0.719298i | \(-0.744464\pi\) |
0.984818 | − | 0.173588i | \(-0.0555363\pi\) | |||||||
\(104\) | 1444.47 | + | 1049.47i | 1.36194 | + | 0.989507i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −33.9707 | + | 104.551i | −0.0311276 | + | 0.0958009i | ||||
\(107\) | 205.796 | + | 633.375i | 0.185935 | + | 0.572249i | 0.999963 | − | 0.00857617i | \(-0.00272991\pi\) |
−0.814028 | + | 0.580825i | \(0.802730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 85.6516 | 0.0752654 | 0.0376327 | − | 0.999292i | \(-0.488018\pi\) | ||||
0.0376327 | + | 0.999292i | \(0.488018\pi\) | |||||||
\(110\) | −330.554 | − | 892.848i | −0.286519 | − | 0.773906i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1245.43 | + | 904.857i | −1.05073 | + | 0.763401i | ||||
\(113\) | 136.056 | + | 418.736i | 0.113266 | + | 0.348597i | 0.991581 | − | 0.129485i | \(-0.0413324\pi\) |
−0.878315 | + | 0.478081i | \(0.841332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 769.850 | + | 559.329i | 0.624251 | + | 0.453545i | ||||
\(116\) | 108.292 | + | 78.6787i | 0.0866780 | + | 0.0629753i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −310.526 | − | 955.701i | −0.242256 | − | 0.745588i | ||||
\(119\) | 1464.83 | − | 1064.26i | 1.12841 | − | 0.819838i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1010.11 | + | 866.737i | −0.758913 | + | 0.651192i | ||||
\(122\) | 1016.66 | 0.754461 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.4156 | − | 38.2113i | −0.00899157 | − | 0.0276732i | ||||
\(125\) | 455.043 | − | 1400.48i | 0.325603 | − | 1.00210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1314.97 | − | 955.382i | −0.918778 | − | 0.667531i | 0.0244418 | − | 0.999701i | \(-0.492219\pi\) |
−0.943219 | + | 0.332170i | \(0.892219\pi\) | |||||||
\(128\) | −248.833 | + | 765.829i | −0.171828 | + | 0.528831i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1546.66 | − | 1123.72i | 1.04347 | − | 0.758127i | ||||
\(131\) | −1049.60 | −0.700030 | −0.350015 | − | 0.936744i | \(-0.613823\pi\) | ||||
−0.350015 | + | 0.936744i | \(0.613823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2966.22 | −1.93386 | ||||||||
\(134\) | 447.642 | − | 325.231i | 0.288585 | − | 0.209669i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 416.312 | − | 1281.28i | 0.262489 | − | 0.807858i | ||||
\(137\) | −2486.37 | − | 1806.45i | −1.55055 | − | 1.12654i | −0.943260 | − | 0.332055i | \(-0.892258\pi\) |
−0.607287 | − | 0.794483i | \(-0.707742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −329.681 | + | 1014.65i | −0.201174 | + | 0.619149i | 0.798675 | + | 0.601762i | \(0.205535\pi\) |
−0.999849 | + | 0.0173866i | \(0.994465\pi\) | |||||||
\(140\) | −184.275 | − | 567.141i | −0.111244 | − | 0.342372i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1874.59 | −1.10783 | ||||||||
\(143\) | −2223.95 | − | 1482.31i | −1.30053 | − | 0.866829i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 647.615 | − | 470.520i | 0.370907 | − | 0.269480i | ||||
\(146\) | 171.578 | + | 528.061i | 0.0972593 | + | 0.299333i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 177.618 | + | 129.047i | 0.0986492 | + | 0.0716728i | ||||
\(149\) | 1706.92 | + | 1240.15i | 0.938501 | + | 0.681861i | 0.948059 | − | 0.318094i | \(-0.103043\pi\) |
−0.00955863 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 366.835 | + | 1129.00i | 0.197699 | + | 0.608456i | 0.999934 | + | 0.0114476i | \(0.00364398\pi\) |
−0.802235 | + | 0.597008i | \(0.796356\pi\) | |||||||
\(152\) | −1785.54 | + | 1297.27i | −0.952803 | + | 0.692252i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2345.03 | − | 1853.04i | 1.22706 | − | 0.969624i | ||||
\(155\) | −240.274 | −0.124511 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −571.355 | − | 1758.45i | −0.290440 | − | 0.893882i | −0.984715 | − | 0.174173i | \(-0.944275\pi\) |
0.694275 | − | 0.719710i | \(-0.255725\pi\) | |||||||
\(158\) | 912.182 | − | 2807.41i | 0.459299 | − | 1.41358i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −653.655 | − | 474.908i | −0.322975 | − | 0.234655i | ||||
\(161\) | −923.117 | + | 2841.06i | −0.451875 | + | 1.39073i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1466.71 | + | 1065.63i | −0.704796 | + | 0.512064i | −0.881491 | − | 0.472202i | \(-0.843459\pi\) |
0.176695 | + | 0.984266i | \(0.443459\pi\) | |||||||
\(164\) | 244.372 | 0.116355 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1692.34 | 0.791273 | ||||||||
\(167\) | 213.891 | − | 155.401i | 0.0991100 | − | 0.0720076i | −0.537127 | − | 0.843502i | \(-0.680490\pi\) |
0.636237 | + | 0.771494i | \(0.280490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 979.515 | − | 3014.64i | 0.445842 | − | 1.37216i | ||||
\(170\) | −1167.03 | − | 847.898i | −0.526513 | − | 0.382534i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −78.7260 | + | 242.294i | −0.0349000 | + | 0.107411i | ||||
\(173\) | 205.545 | + | 632.602i | 0.0903311 | + | 0.278011i | 0.986009 | − | 0.166693i | \(-0.0533089\pi\) |
−0.895678 | + | 0.444704i | \(0.853309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 528.256 | 0.228185 | ||||||||
\(176\) | 463.519 | − | 1650.77i | 0.198517 | − | 0.706995i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2132.76 | + | 1549.54i | −0.898075 | + | 0.652490i | ||||
\(179\) | 20.1093 | + | 61.8901i | 0.00839688 | + | 0.0258429i | 0.955167 | − | 0.296067i | \(-0.0956752\pi\) |
−0.946770 | + | 0.321910i | \(0.895675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 33.1354 | + | 24.0743i | 0.0136074 | + | 0.00988634i | 0.594568 | − | 0.804045i | \(-0.297323\pi\) |
−0.580961 | + | 0.813932i | \(0.697323\pi\) | |||||||
\(182\) | 4855.36 | + | 3527.63i | 1.97749 | + | 1.43673i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 686.854 | + | 2113.92i | 0.275193 | + | 0.846958i | ||||
\(185\) | 1062.20 | − | 771.734i | 0.422133 | − | 0.306697i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −545.175 | + | 1941.57i | −0.213193 | + | 0.759261i | ||||
\(188\) | −386.477 | −0.149929 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 730.266 | + | 2247.53i | 0.278837 | + | 0.858173i | ||||
\(191\) | −1415.27 | + | 4355.76i | −0.536155 | + | 1.65012i | 0.204985 | + | 0.978765i | \(0.434285\pi\) |
−0.741140 | + | 0.671351i | \(0.765715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4081.18 | + | 2965.15i | 1.52212 | + | 1.10589i | 0.960422 | + | 0.278550i | \(0.0898536\pi\) |
0.561703 | + | 0.827339i | \(0.310146\pi\) | |||||||
\(194\) | 189.700 | − | 583.837i | 0.0702045 | − | 0.216067i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1030.33 | − | 748.582i | 0.375486 | − | 0.272807i | ||||
\(197\) | −1703.26 | −0.616001 | −0.308000 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308000 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3326.11 | −1.18483 | −0.592416 | − | 0.805632i | \(-0.701826\pi\) | ||||
−0.592416 | + | 0.805632i | \(0.701826\pi\) | |||||||
\(200\) | 317.987 | − | 231.031i | 0.112425 | − | 0.0816818i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.5376 | − | 53.9753i | 0.00610863 | − | 0.0188004i | ||||
\(203\) | 2033.03 | + | 1477.08i | 0.702909 | + | 0.510693i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 451.600 | − | 1389.88i | 0.153859 | − | 0.473530i | ||||
\(206\) | −758.489 | − | 2334.39i | −0.256536 | − | 0.789537i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3442.96 | 1.14772 | ||||||||
\(209\) | 2592.14 | − | 2048.31i | 0.857904 | − | 0.677915i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4013.48 | + | 2915.96i | −1.30947 | + | 0.951389i | −0.309475 | + | 0.950908i | \(0.600153\pi\) |
−1.00000 | 0.000481181i | \(0.999847\pi\) | ||||||||
\(212\) | −23.6986 | − | 72.9367i | −0.00767747 | − | 0.0236288i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1347.52 | + | 979.027i | 0.430440 | + | 0.312733i | ||||
\(215\) | 1232.58 | + | 895.520i | 0.390982 | + | 0.284065i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233.085 | − | 717.363i | −0.0729164 | − | 0.224414i | ||||
\(218\) | 173.306 | − | 125.914i | 0.0538431 | − | 0.0391193i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 552.671 | + | 368.366i | 0.169369 | + | 0.112887i | ||||
\(221\) | −4049.49 | −1.23257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1136.92 | − | 3499.07i | −0.341406 | − | 1.05074i | −0.963480 | − | 0.267781i | \(-0.913710\pi\) |
0.622074 | − | 0.782959i | \(-0.286290\pi\) | |||||||
\(224\) | 783.789 | − | 2412.25i | 0.233791 | − | 0.719534i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 890.869 | + | 647.254i | 0.262211 | + | 0.190507i | ||||
\(227\) | −124.139 | + | 382.062i | −0.0362970 | + | 0.111711i | −0.967563 | − | 0.252628i | \(-0.918705\pi\) |
0.931266 | + | 0.364339i | \(0.118705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2388.11 | − | 1735.06i | 0.689129 | − | 0.500681i | −0.187245 | − | 0.982313i | \(-0.559956\pi\) |
0.876374 | + | 0.481632i | \(0.159956\pi\) | |||||||
\(230\) | 2379.96 | 0.682305 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1869.79 | 0.529128 | ||||||||
\(233\) | −1994.88 | + | 1449.36i | −0.560896 | + | 0.407515i | −0.831787 | − | 0.555095i | \(-0.812682\pi\) |
0.270891 | + | 0.962610i | \(0.412682\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −714.211 | + | 2198.12i | −0.198255 | + | 0.610167i | ||||
\(236\) | 567.141 | + | 412.052i | 0.156431 | + | 0.113654i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1399.37 | − | 4306.83i | 0.381125 | − | 1.17298i | ||||
\(239\) | 1311.91 | + | 4037.64i | 0.355064 | + | 1.09278i | 0.955972 | + | 0.293457i | \(0.0948059\pi\) |
−0.600908 | + | 0.799318i | \(0.705194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2686.25 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(242\) | −769.680 | + | 3238.69i | −0.204450 | + | 0.860293i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −573.789 | + | 416.882i | −0.150545 | + | 0.109378i | ||||
\(245\) | −2353.55 | − | 7243.49i | −0.613726 | − | 1.88885i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5367.01 | + | 3899.36i | 1.38257 | + | 1.00449i | ||||
\(248\) | −454.044 | − | 329.882i | −0.116257 | − | 0.0844659i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1138.08 | − | 3502.66i | −0.287915 | − | 0.886111i | ||||
\(251\) | 5951.11 | − | 4323.74i | 1.49654 | − | 1.08730i | 0.524802 | − | 0.851224i | \(-0.324139\pi\) |
0.971735 | − | 0.236074i | \(-0.0758607\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1155.18 | − | 3120.22i | −0.287058 | − | 0.775361i | ||||
\(254\) | −4065.18 | −1.00422 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −785.901 | − | 2418.75i | −0.191870 | − | 0.590516i | ||||
\(257\) | 147.792 | − | 454.856i | 0.0358716 | − | 0.110401i | −0.931517 | − | 0.363697i | \(-0.881514\pi\) |
0.967389 | + | 0.253295i | \(0.0815144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3334.52 | + | 2422.67i | 0.799987 | + | 0.581225i | ||||
\(260\) | −412.133 | + | 1268.42i | −0.0983055 | + | 0.302553i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2123.75 | + | 1542.99i | −0.500784 | + | 0.363841i | ||||
\(263\) | −3955.38 | −0.927373 | −0.463686 | − | 0.885999i | \(-0.653474\pi\) | ||||
−0.463686 | + | 0.885999i | \(0.653474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −458.628 | −0.106314 | ||||||||
\(266\) | −6001.82 | + | 4360.57i | −1.38344 | + | 1.00513i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −119.282 | + | 367.111i | −0.0271876 | + | 0.0836749i | ||||
\(269\) | −1059.90 | − | 770.065i | −0.240236 | − | 0.174542i | 0.461153 | − | 0.887321i | \(-0.347436\pi\) |
−0.701388 | + | 0.712779i | \(0.747436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1685.61 | + | 5187.78i | −0.377836 | + | 1.16286i | 0.563709 | + | 0.825974i | \(0.309374\pi\) |
−0.941545 | + | 0.336887i | \(0.890626\pi\) | |||||||
\(272\) | −802.789 | − | 2470.73i | −0.178957 | − | 0.550772i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7686.52 | −1.69474 | ||||||||
\(275\) | −461.635 | + | 364.784i | −0.101228 | + | 0.0799901i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3852.71 | − | 2799.16i | 0.835693 | − | 0.607167i | −0.0854711 | − | 0.996341i | \(-0.527240\pi\) |
0.921164 | + | 0.389174i | \(0.127240\pi\) | |||||||
\(278\) | 824.546 | + | 2537.69i | 0.177888 | + | 0.547484i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6739.02 | − | 4896.18i | −1.43833 | − | 1.04501i | ||||
\(281\) | −451.960 | − | 328.368i | −0.0959490 | − | 0.0697110i | 0.538776 | − | 0.842449i | \(-0.318887\pi\) |
−0.634725 | + | 0.772738i | \(0.718887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −638.145 | − | 1964.01i | −0.134042 | − | 0.412538i | 0.861398 | − | 0.507930i | \(-0.169589\pi\) |
−0.995440 | + | 0.0953928i | \(0.969589\pi\) | |||||||
\(284\) | 1057.99 | − | 768.674i | 0.221057 | − | 0.160607i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6679.02 | + | 270.099i | −1.38090 | + | 0.0558437i | ||||
\(287\) | 4587.73 | 0.943572 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −573.988 | − | 1766.55i | −0.116830 | − | 0.359567i | ||||
\(290\) | 618.676 | − | 1904.09i | 0.125275 | − | 0.385558i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −313.367 | − | 227.674i | −0.0628028 | − | 0.0456289i | ||||
\(293\) | 2316.44 | − | 7129.26i | 0.461869 | − | 1.42149i | −0.401008 | − | 0.916074i | \(-0.631340\pi\) |
0.862877 | − | 0.505413i | \(-0.168660\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3391.65 | − | 2464.18i | 0.669389 | − | 0.486340i | ||||
\(296\) | 3066.78 | 0.602206 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5276.89 | 1.02578 | ||||||||
\(299\) | 5405.09 | − | 3927.03i | 1.04543 | − | 0.759552i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1477.97 | + | 4548.72i | −0.283019 | + | 0.871042i | ||||
\(302\) | 2401.97 | + | 1745.13i | 0.457675 | + | 0.332520i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1315.15 | + | 4047.62i | −0.248122 | + | 0.763641i | ||||
\(305\) | 1310.68 | + | 4033.86i | 0.246064 | + | 0.757306i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1036.23 | 0.192640 | 0.0963201 | − | 0.995350i | \(-0.469293\pi\) | ||||
0.0963201 | + | 0.995350i | \(0.469293\pi\) | |||||||
\(308\) | −563.659 | + | 2007.40i | −0.104277 | + | 0.371372i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −486.167 | + | 353.221i | −0.0890724 | + | 0.0647149i | ||||
\(311\) | 3193.59 | + | 9828.85i | 0.582288 | + | 1.79210i | 0.609897 | + | 0.792481i | \(0.291211\pi\) |
−0.0276089 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5769.05 | − | 4191.46i | −1.04181 | − | 0.756918i | −0.0711707 | − | 0.997464i | \(-0.522674\pi\) |
−0.970638 | + | 0.240546i | \(0.922674\pi\) | |||||||
\(314\) | −3741.13 | − | 2718.09i | −0.672370 | − | 0.488505i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 636.354 | + | 1958.50i | 0.113284 | + | 0.348652i | ||||
\(317\) | −5215.16 | + | 3789.04i | −0.924014 | + | 0.671336i | −0.944520 | − | 0.328454i | \(-0.893472\pi\) |
0.0205056 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2796.62 | + | 113.095i | −0.490849 | + | 0.0198499i | ||||
\(320\) | −5943.81 | −1.03834 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2308.76 | + | 7105.63i | 0.399572 | + | 1.22976i | ||||
\(323\) | 1546.83 | − | 4760.67i | 0.266465 | − | 0.820095i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −955.812 | − | 694.438i | −0.163135 | − | 0.118525i | ||||
\(326\) | −1401.17 | + | 4312.36i | −0.238048 | + | 0.732636i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2761.61 | − | 2006.43i | 0.464892 | − | 0.337764i | ||||
\(329\) | −7255.55 | −1.21584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5634.51 | 0.935652 | 0.467826 | − | 0.883821i | \(-0.345037\pi\) | ||||
0.467826 | + | 0.883821i | \(0.345037\pi\) | |||||||
\(332\) | −955.133 | + | 693.945i | −0.157891 | + | 0.114714i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 204.333 | − | 628.872i | 0.0334749 | − | 0.103025i | ||||
\(335\) | 1867.54 | + | 1356.85i | 0.304580 | + | 0.221291i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 945.112 | − | 2908.76i | 0.152770 | − | 0.470178i | −0.845158 | − | 0.534517i | \(-0.820494\pi\) |
0.997928 | + | 0.0643383i | \(0.0204937\pi\) | |||||||
\(338\) | −2449.81 | − | 7539.74i | −0.394237 | − | 1.21334i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1006.33 | 0.160518 | ||||||||
\(341\) | 699.061 | + | 465.937i | 0.111015 | + | 0.0739939i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10253.6 | − | 7449.68i | 1.61412 | − | 1.17273i | ||||
\(344\) | 1099.70 | + | 3384.51i | 0.172359 | + | 0.530467i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1345.87 | + | 977.832i | 0.209117 | + | 0.151932i | ||||
\(347\) | −8507.85 | − | 6181.32i | −1.31621 | − | 0.956284i | −0.999971 | − | 0.00760501i | \(-0.997579\pi\) |
−0.316241 | − | 0.948679i | \(-0.602421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 465.051 | + | 1431.28i | 0.0713283 | + | 0.219526i | 0.980365 | − | 0.197189i | \(-0.0631813\pi\) |
−0.909037 | + | 0.416715i | \(0.863181\pi\) | |||||||
\(350\) | 1068.87 | − | 776.577i | 0.163238 | − | 0.118599i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 980.826 | + | 2649.28i | 0.148518 | + | 0.401156i | ||||
\(353\) | 11810.2 | 1.78071 | 0.890356 | − | 0.455264i | \(-0.150455\pi\) | ||||
0.890356 | + | 0.455264i | \(0.150455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2416.72 | − | 7437.90i | −0.361313 | − | 1.11201i | ||||
\(356\) | 568.309 | − | 1749.08i | 0.0846077 | − | 0.260396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 131.672 | + | 95.6655i | 0.0194388 | + | 0.0141231i | ||||
\(359\) | −1021.81 | + | 3144.82i | −0.150221 | + | 0.462332i | −0.997645 | − | 0.0685836i | \(-0.978152\pi\) |
0.847424 | + | 0.530916i | \(0.178152\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1085.22 | + | 788.459i | −0.158218 | + | 0.114952i | ||||
\(362\) | 102.437 | 0.0148728 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4186.79 | −0.602878 | ||||||||
\(365\) | −1874.02 | + | 1361.55i | −0.268741 | + | 0.195252i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1108.64 | + | 3412.03i | −0.157685 | + | 0.485304i | −0.998423 | − | 0.0561380i | \(-0.982121\pi\) |
0.840738 | + | 0.541442i | \(0.182121\pi\) | |||||||
\(368\) | 3467.54 | + | 2519.32i | 0.491191 | + | 0.356871i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1014.74 | − | 3123.04i | 0.142577 | − | 0.438808i | ||||
\(371\) | −444.906 | − | 1369.28i | −0.0622598 | − | 0.191616i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2022.36 | −0.280734 | −0.140367 | − | 0.990100i | \(-0.544828\pi\) | ||||
−0.140367 | + | 0.990100i | \(0.544828\pi\) | |||||||
\(374\) | 1751.16 | + | 4730.00i | 0.242113 | + | 0.653964i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4367.53 | + | 3173.19i | −0.599037 | + | 0.435226i | ||||
\(377\) | −1736.76 | − | 5345.18i | −0.237261 | − | 0.730215i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4696.18 | + | 3411.97i | 0.636482 | + | 0.462431i | 0.858640 | − | 0.512580i | \(-0.171310\pi\) |
−0.222158 | + | 0.975011i | \(0.571310\pi\) | |||||||
\(380\) | −1333.75 | − | 969.025i | −0.180052 | − | 0.130816i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3539.66 | + | 10894.0i | 0.474097 | + | 1.45912i | ||||
\(383\) | −4237.83 | + | 3078.96i | −0.565387 | + | 0.410777i | −0.833426 | − | 0.552630i | \(-0.813624\pi\) |
0.268040 | + | 0.963408i | \(0.413624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10375.6 | + | 6915.55i | 1.37348 | + | 0.915452i | ||||
\(386\) | 12616.8 | 1.66368 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 132.338 | + | 407.295i | 0.0173156 | + | 0.0532919i | ||||
\(389\) | 26.2617 | − | 80.8251i | 0.00342293 | − | 0.0105347i | −0.949330 | − | 0.314280i | \(-0.898237\pi\) |
0.952753 | + | 0.303745i | \(0.0982371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4078.40 | − | 2963.13i | −0.527503 | − | 0.383253i | ||||
\(392\) | 5497.40 | − | 16919.3i | 0.708318 | − | 2.17998i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3446.35 | + | 2503.92i | −0.440672 | + | 0.320167i | ||||
\(395\) | 12315.1 | 1.56871 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7187.71 | −0.908667 | −0.454334 | − | 0.890832i | \(-0.650123\pi\) | ||||
−0.454334 | + | 0.890832i | \(0.650123\pi\) | |||||||
\(398\) | −6730.01 | + | 4889.64i | −0.847600 | + | 0.615818i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 234.216 | − | 720.842i | 0.0292770 | − | 0.0901052i | ||||
\(401\) | 1839.76 | + | 1336.66i | 0.229110 | + | 0.166458i | 0.696418 | − | 0.717636i | \(-0.254776\pi\) |
−0.467308 | + | 0.884095i | \(0.654776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −521.298 | + | 1604.39i | −0.0644360 | + | 0.198314i | ||||
\(404\) | 12.2346 | + | 37.6541i | 0.00150666 | + | 0.00463704i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6285.02 | 0.768277 | ||||||||
\(407\) | −4586.94 | + | 185.496i | −0.558640 | + | 0.0225914i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7772.40 | − | 5646.98i | 0.939659 | − | 0.682702i | −0.00867953 | − | 0.999962i | \(-0.502763\pi\) |
0.948339 | + | 0.317260i | \(0.102763\pi\) | |||||||
\(410\) | −1129.47 | − | 3476.16i | −0.136050 | − | 0.418720i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1385.30 | + | 1006.48i | 0.165652 | + | 0.120353i | ||||
\(413\) | 10647.3 | + | 7735.68i | 1.26856 | + | 0.921666i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2181.77 | + | 6714.80i | 0.258070 | + | 0.794257i | ||||
\(416\) | −4589.29 | + | 3334.31i | −0.540886 | + | 0.392976i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2233.73 | − | 7955.16i | 0.261377 | − | 0.930861i | ||||
\(419\) | −10777.3 | −1.25658 | −0.628291 | − | 0.777979i | \(-0.716245\pi\) | ||||
−0.628291 | + | 0.777979i | \(0.716245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 380.512 | + | 1171.10i | 0.0440500 | + | 0.135572i | 0.970663 | − | 0.240445i | \(-0.0772934\pi\) |
−0.926613 | + | 0.376017i | \(0.877293\pi\) | |||||||
\(422\) | −3834.13 | + | 11800.2i | −0.442281 | + | 1.36120i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −866.665 | − | 629.669i | −0.0992665 | − | 0.0721213i | ||||
\(425\) | −275.476 | + | 847.829i | −0.0314413 | + | 0.0967665i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10772.1 | + | 7826.36i | −1.22083 | + | 0.886988i | ||||
\(428\) | −1161.97 | −0.131228 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3810.46 | 0.427342 | ||||||||
\(431\) | 7047.38 | − | 5120.22i | 0.787611 | − | 0.572233i | −0.119643 | − | 0.992817i | \(-0.538175\pi\) |
0.907253 | + | 0.420584i | \(0.138175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2313.66 | − | 7120.71i | 0.256784 | − | 0.790299i | −0.736689 | − | 0.676231i | \(-0.763612\pi\) |
0.993473 | − | 0.114068i | \(-0.0363880\pi\) | |||||||
\(434\) | −1526.20 | − | 1108.85i | −0.168802 | − | 0.122642i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.1803 | + | 142.128i | −0.00507256 | + | 0.0156117i | ||||
\(437\) | 2552.05 | + | 7854.40i | 0.279362 | + | 0.859787i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9595.95 | 1.04326 | 0.521628 | − | 0.853173i | \(-0.325325\pi\) | ||||
0.521628 | + | 0.853173i | \(0.325325\pi\) | |||||||
\(440\) | 9270.16 | − | 374.885i | 1.00440 | − | 0.0406180i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8193.69 | + | 5953.07i | −0.881752 | + | 0.640630i | ||||
\(443\) | −2871.05 | − | 8836.18i | −0.307918 | − | 0.947674i | −0.978572 | − | 0.205904i | \(-0.933987\pi\) |
0.670654 | − | 0.741770i | \(-0.266013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8897.76 | − | 6464.60i | −0.947853 | − | 0.688655i | ||||
\(446\) | −7444.32 | − | 5408.62i | −0.790356 | − | 0.574227i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5765.98 | − | 17745.9i | −0.608074 | − | 1.87146i | ||||
\(449\) | −5550.31 | + | 4032.54i | −0.583375 | + | 0.423847i | −0.839939 | − | 0.542680i | \(-0.817409\pi\) |
0.256564 | + | 0.966527i | \(0.417409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4009.15 | + | 3168.03i | −0.418589 | + | 0.330769i | ||||
\(452\) | −768.199 | −0.0799403 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 310.478 | + | 955.553i | 0.0320957 | + | 0.0987805i | ||||
\(455\) | −7737.22 | + | 23812.7i | −0.797201 | + | 2.45353i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −935.459 | − | 679.650i | −0.0957525 | − | 0.0695683i | 0.538879 | − | 0.842383i | \(-0.318848\pi\) |
−0.634631 | + | 0.772815i | \(0.718848\pi\) | |||||||
\(458\) | 2281.39 | − | 7021.40i | 0.232756 | − | 0.716351i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1343.21 | + | 975.902i | −0.136147 | + | 0.0989167i | ||||
\(461\) | 8394.87 | 0.848131 | 0.424065 | − | 0.905632i | \(-0.360603\pi\) | ||||
0.424065 | + | 0.905632i | \(0.360603\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1801.45 | 0.180822 | 0.0904108 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904108 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(464\) | 2916.97 | − | 2119.31i | 0.291847 | − | 0.212039i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1905.73 | + | 5865.25i | −0.189445 | + | 0.583052i | ||||
\(467\) | −15389.4 | − | 11181.0i | −1.52492 | − | 1.10792i | −0.958982 | − | 0.283466i | \(-0.908516\pi\) |
−0.565934 | − | 0.824451i | \(-0.691484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2239.34 | + | 6891.98i | −0.220476 | + | 0.678555i | ||||
\(470\) | 1786.27 | + | 5497.59i | 0.175308 | + | 0.539542i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9792.36 | 0.954936 | ||||||||
\(473\) | −1849.51 | − | 4995.66i | −0.179790 | − | 0.485625i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1181.50 | − | 858.410i | 0.114128 | − | 0.0829190i | ||||
\(476\) | 976.227 | + | 3004.52i | 0.0940027 | + | 0.289311i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8590.15 | + | 6241.11i | 0.821976 | + | 0.597200i | ||||
\(479\) | −13686.9 | − | 9944.13i | −1.30558 | − | 0.948557i | −0.305583 | − | 0.952165i | \(-0.598851\pi\) |
−0.999993 | + | 0.00360855i | \(0.998851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2848.58 | − | 8767.03i | −0.270029 | − | 0.831065i | ||||
\(482\) | −5435.33 | + | 3949.00i | −0.513636 | + | 0.373178i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −893.627 | − | 2143.47i | −0.0839244 | − | 0.201303i | ||||
\(485\) | 2561.08 | 0.239779 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2844.77 | − | 8755.32i | −0.264700 | − | 0.814664i | −0.991762 | − | 0.128092i | \(-0.959115\pi\) |
0.727062 | − | 0.686572i | \(-0.240885\pi\) | |||||||
\(488\) | −3061.48 | + | 9422.25i | −0.283989 | + | 0.874027i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15410.6 | − | 11196.5i | −1.42078 | − | 1.03226i | ||||
\(491\) | −5069.27 | + | 15601.6i | −0.465933 | + | 1.43399i | 0.391872 | + | 0.920020i | \(0.371827\pi\) |
−0.857805 | + | 0.513975i | \(0.828173\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3430.84 | + | 2492.65i | −0.313423 | + | 0.227715i | ||||
\(494\) | 16591.9 | 1.51114 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1082.24 | −0.0979715 | ||||||||
\(497\) | 19862.2 | − | 14430.7i | 1.79264 | − | 1.30243i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1431.17 | + | 4404.69i | −0.128393 | + | 0.395152i | −0.994504 | − | 0.104699i | \(-0.966612\pi\) |
0.866111 | + | 0.499851i | \(0.166612\pi\) | |||||||
\(500\) | 2078.58 | + | 1510.18i | 0.185914 | + | 0.135074i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5685.18 | − | 17497.2i | 0.505462 | − | 1.55565i | ||||
\(503\) | −6057.33 | − | 18642.5i | −0.536944 | − | 1.65255i | −0.739410 | − | 0.673256i | \(-0.764895\pi\) |
0.202465 | − | 0.979289i | \(-0.435105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 236.770 | 0.0208636 | ||||||||
\(506\) | −6924.34 | − | 4615.21i | −0.608349 | − | 0.405476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2294.33 | − | 1666.93i | 0.200382 | − | 0.145586i | ||||
\(509\) | −5031.84 | − | 15486.4i | −0.438178 | − | 1.34857i | −0.889795 | − | 0.456360i | \(-0.849153\pi\) |
0.451617 | − | 0.892212i | \(-0.350847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5883.02 | − | 4274.26i | −0.509294 | − | 0.370024i | ||||
\(512\) | −10357.6 | − | 7525.21i | −0.894031 | − | 0.649551i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −369.634 | − | 1137.62i | −0.0317196 | − | 0.0976227i | ||||
\(515\) | 8284.44 | − | 6019.00i | 0.708846 | − | 0.515007i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6340.52 | − | 5010.28i | 0.539373 | − | 0.426212i | ||||
\(518\) | 10308.5 | 0.874384 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5756.95 | + | 17718.1i | 0.485498 | + | 1.49421i | ||||
\(521\) | 3170.21 | − | 9756.91i | 0.266583 | − | 0.820457i | −0.724742 | − | 0.689020i | \(-0.758041\pi\) |
0.991325 | − | 0.131436i | \(-0.0419589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17290.3 | − | 12562.2i | −1.44561 | − | 1.05030i | −0.986833 | − | 0.161744i | \(-0.948288\pi\) |
−0.458776 | − | 0.888552i | \(-0.651712\pi\) | |||||||
\(524\) | 565.907 | − | 1741.68i | 0.0471789 | − | 0.145202i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8003.27 | + | 5814.71i | −0.663420 | + | 0.482003i | ||||
\(527\) | 1272.89 | 0.105214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3849.79 | −0.316413 | ||||||||
\(530\) | −927.982 | + | 674.218i | −0.0760546 | + | 0.0552569i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1599.28 | − | 4922.08i | 0.130334 | − | 0.401127i | ||||
\(533\) | −8300.93 | − | 6030.98i | −0.674584 | − | 0.490114i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2147.32 | + | 6608.77i | −0.173527 | + | 0.534060i | ||||
\(536\) | 1666.20 | + | 5128.04i | 0.134270 | + | 0.413242i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3276.65 | −0.262577 | ||||||||
\(539\) | −7199.02 | + | 25638.4i | −0.575295 | + | 2.04884i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17097.0 | + | 12421.7i | −1.35870 | + | 0.987157i | −0.360179 | + | 0.932883i | \(0.617284\pi\) |
−0.998526 | + | 0.0542736i | \(0.982716\pi\) | |||||||
\(542\) | 4215.79 | + | 12974.9i | 0.334103 | + | 1.02826i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3462.84 | + | 2515.90i | 0.272919 | + | 0.198287i | ||||
\(545\) | 723.024 | + | 525.308i | 0.0568274 | + | 0.0412875i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 214.684 | + | 660.729i | 0.0167810 | + | 0.0516467i | 0.959096 | − | 0.283080i | \(-0.0913561\pi\) |
−0.942315 | + | 0.334726i | \(0.891356\pi\) | |||||||
\(548\) | 4338.15 | − | 3151.85i | 0.338169 | − | 0.245694i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −397.806 | + | 1416.74i | −0.0308409 | + | 0.109836i | ||||
\(551\) | 6947.32 | 0.537143 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11946.6 | + | 36768.0i | 0.918667 | + | 2.82737i | ||||
\(554\) | 3680.55 | − | 11327.6i | 0.282259 | − | 0.868704i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1505.94 | − | 1094.13i | −0.114867 | − | 0.0834558i | ||||
\(557\) | −5531.72 | + | 17024.9i | −0.420801 | + | 1.29509i | 0.486156 | + | 0.873872i | \(0.338399\pi\) |
−0.906958 | + | 0.421222i | \(0.861601\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8653.88 | − | 6287.42i | 0.654777 | − | 0.475723i | ||||
\(560\) | −16062.8 | −1.21210 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1397.22 | −0.104872 | ||||||||
\(563\) | 12328.2 | − | 8956.97i | 0.922864 | − | 0.670500i | −0.0213713 | − | 0.999772i | \(-0.506803\pi\) |
0.944235 | + | 0.329272i | \(0.106803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1419.63 | + | 4369.19i | −0.105707 | + | 0.325333i | ||||
\(566\) | −4178.46 | − | 3035.83i | −0.310307 | − | 0.225451i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5644.95 | − | 17373.4i | 0.417001 | − | 1.28340i | ||||
\(569\) | 7618.38 | + | 23447.0i | 0.561299 | + | 1.72750i | 0.678700 | + | 0.734416i | \(0.262544\pi\) |
−0.117401 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20893.8 | 1.53131 | 0.765656 | − | 0.643250i | \(-0.222415\pi\) | ||||
0.765656 | + | 0.643250i | \(0.222415\pi\) | |||||||
\(572\) | 3658.78 | − | 2891.17i | 0.267450 | − | 0.211339i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9282.76 | − | 6744.32i | 0.675009 | − | 0.490422i | ||||
\(575\) | −454.495 | − | 1398.79i | −0.0329631 | − | 0.101450i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11720.4 | + | 8515.35i | 0.845624 | + | 0.614382i | 0.923936 | − | 0.382547i | \(-0.124953\pi\) |
−0.0783117 | + | 0.996929i | \(0.524953\pi\) | |||||||
\(578\) | −3758.37 | − | 2730.62i | −0.270463 | − | 0.196503i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 431.599 | + | 1328.33i | 0.0308986 | + | 0.0950961i | ||||
\(581\) | −17931.2 | + | 13027.8i | −1.28040 | + | 0.930266i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1334.35 | + | 889.368i | 0.0947907 | + | 0.0631798i | ||||
\(584\) | −5410.65 | −0.383381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5793.51 | − | 17830.6i | −0.408409 | − | 1.25695i | ||||
\(587\) | −2950.00 | + | 9079.16i | −0.207427 | + | 0.638394i | 0.792178 | + | 0.610290i | \(0.208947\pi\) |
−0.999605 | + | 0.0281041i | \(0.991053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1687.03 | − | 1225.70i | −0.118018 | − | 0.0857453i | ||||
\(590\) | 3240.10 | − | 9971.99i | 0.226089 | − | 0.695831i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4784.34 | − | 3476.03i | 0.332154 | − | 0.241324i | ||||
\(593\) | 15771.0 | 1.09213 | 0.546067 | − | 0.837741i | \(-0.316124\pi\) | ||||
0.546067 | + | 0.837741i | \(0.316124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18892.5 | 1.30171 | ||||||||
\(596\) | −2978.19 | + | 2163.78i | −0.204684 | + | 0.148712i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5163.56 | − | 15891.8i | 0.353100 | − | 1.08673i | ||||
\(599\) | 15970.3 | + | 11603.1i | 1.08936 | + | 0.791469i | 0.979292 | − | 0.202455i | \(-0.0648918\pi\) |
0.110072 | + | 0.993924i | \(0.464892\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 667.170 | − | 2053.34i | 0.0452819 | − | 0.139363i | −0.925859 | − | 0.377868i | \(-0.876657\pi\) |
0.971141 | + | 0.238505i | \(0.0766573\pi\) | |||||||
\(602\) | 3696.46 | + | 11376.5i | 0.250260 | + | 0.770221i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2071.22 | −0.139531 | ||||||||
\(605\) | −13842.6 | + | 1121.42i | −0.930217 | + | 0.0753591i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4096.74 | + | 2976.46i | −0.273940 | + | 0.199029i | −0.716270 | − | 0.697823i | \(-0.754152\pi\) |
0.442330 | + | 0.896852i | \(0.354152\pi\) | |||||||
\(608\) | −2166.86 | − | 6668.91i | −0.144536 | − | 0.444836i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8582.11 | + | 6235.27i | 0.569639 | + | 0.413867i | ||||
\(611\) | 13128.0 | + | 9538.06i | 0.869235 | + | 0.631536i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7547.95 | + | 23230.2i | 0.497323 | + | 1.53060i | 0.813305 | + | 0.581837i | \(0.197666\pi\) |
−0.315982 | + | 0.948765i | \(0.602334\pi\) | |||||||
\(614\) | 2096.69 | − | 1523.33i | 0.137810 | − | 0.100125i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10112.1 | + | 27313.4i | 0.661408 | + | 1.78650i | ||||
\(617\) | 13814.4 | 0.901369 | 0.450685 | − | 0.892683i | \(-0.351180\pi\) | ||||
0.450685 | + | 0.892683i | \(0.351180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1351.02 | − | 4158.01i | −0.0877255 | − | 0.269991i | 0.897564 | − | 0.440884i | \(-0.145335\pi\) |
−0.985290 | + | 0.170892i | \(0.945335\pi\) | |||||||
\(620\) | 129.547 | − | 398.705i | 0.00839151 | − | 0.0258264i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20911.0 | + | 15192.8i | 1.34800 | + | 0.979379i | ||||
\(623\) | 10669.2 | − | 32836.4i | 0.686119 | − | 2.11166i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10799.6 | − | 7846.36i | 0.691173 | − | 0.502167i | ||||
\(626\) | −17834.8 | −1.13869 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3225.99 | 0.204985 | ||||||||
\(629\) | −5627.18 | + | 4088.38i | −0.356710 | + | 0.259165i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −714.402 | + | 2198.70i | −0.0450711 | + | 0.138715i | −0.971060 | − | 0.238837i | \(-0.923234\pi\) |
0.925989 | + | 0.377552i | \(0.123234\pi\) | |||||||
\(632\) | 23271.7 | + | 16907.9i | 1.46471 | + | 1.06418i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4982.12 | + | 15333.4i | −0.312090 | + | 0.960514i | ||||
\(635\) | −5240.84 | − | 16129.6i | −0.327522 | − | 1.00801i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −53473.5 | −3.32605 | ||||||||
\(638\) | −5492.39 | + | 4340.09i | −0.340824 | + | 0.269319i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6797.40 | + | 4938.60i | −0.419829 | + | 0.305024i | ||||
\(641\) | 5704.03 | + | 17555.2i | 0.351475 | + | 1.08173i | 0.958025 | + | 0.286684i | \(0.0925529\pi\) |
−0.606550 | + | 0.795045i | \(0.707447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23792.8 | − | 17286.4i | −1.45925 | − | 1.06020i | −0.983559 | − | 0.180589i | \(-0.942200\pi\) |
−0.475686 | − | 0.879615i | \(-0.657800\pi\) | |||||||
\(644\) | −4216.69 | − | 3063.60i | −0.258014 | − | 0.187458i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3868.70 | − | 11906.6i | −0.235622 | − | 0.725171i | ||||
\(647\) | −1793.76 | + | 1303.24i | −0.108995 | + | 0.0791897i | −0.640948 | − | 0.767585i | \(-0.721458\pi\) |
0.531953 | + | 0.846774i | \(0.321458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14646.3 | + | 592.297i | −0.885852 | + | 0.0358238i | ||||
\(650\) | −2954.86 | −0.178306 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −977.481 | − | 3008.38i | −0.0587134 | − | 0.180701i | ||||
\(653\) | −6953.29 | + | 21400.0i | −0.416697 | + | 1.28246i | 0.494027 | + | 0.869447i | \(0.335524\pi\) |
−0.910724 | + | 0.413015i | \(0.864476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8860.14 | − | 6437.27i | −0.528541 | − | 0.384008i | ||||
\(656\) | 2034.09 | − | 6260.28i | 0.121064 | − | 0.372596i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14680.8 | + | 10666.2i | −0.869783 | + | 0.631934i | ||||
\(659\) | −5908.12 | −0.349238 | −0.174619 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174619 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22387.2 | 1.31734 | 0.658670 | − | 0.752432i | \(-0.271120\pi\) | ||||
0.658670 | + | 0.752432i | \(0.271120\pi\) | |||||||
\(662\) | 11400.8 | − | 8283.17i | 0.669343 | − | 0.486306i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5096.16 | + | 15684.4i | −0.297845 | + | 0.916673i | ||||
\(665\) | −25039.2 | − | 18192.1i | −1.46012 | − | 1.06084i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2162.07 | − | 6654.18i | 0.125511 | − | 0.386283i | ||||
\(668\) | 142.546 | + | 438.712i | 0.00825641 | + | 0.0254106i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5773.42 | 0.332906 | ||||||||
\(671\) | 4009.10 | − | 14277.9i | 0.230655 | − | 0.821450i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25692.3 | − | 18666.6i | 1.47157 | − | 1.06916i | 0.491416 | − | 0.870925i | \(-0.336480\pi\) |
0.980155 | − | 0.198233i | \(-0.0635204\pi\) | |||||||
\(674\) | −2363.77 | − | 7274.93i | −0.135087 | − | 0.415757i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4474.30 | + | 3250.77i | 0.254569 | + | 0.184955i | ||||
\(677\) | −2970.62 | − | 2158.28i | −0.168641 | − | 0.122525i | 0.500263 | − | 0.865873i | \(-0.333237\pi\) |
−0.668905 | + | 0.743348i | \(0.733237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2484.46 | + | 7646.38i | 0.140419 | + | 0.432166i | ||||
\(680\) | 11372.5 | − | 8262.58i | 0.641344 | − | 0.465964i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2099.44 | − | 84.9011i | 0.117876 | − | 0.00476691i | ||||
\(683\) | 11719.2 | 0.656549 | 0.328274 | − | 0.944582i | \(-0.393533\pi\) | ||||
0.328274 | + | 0.944582i | \(0.393533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9909.46 | − | 30498.2i | −0.552732 | − | 1.70113i | ||||
\(686\) | 9795.42 | − | 30147.2i | 0.545176 | − | 1.67788i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5551.75 | + | 4033.58i | 0.307643 | + | 0.223516i | ||||
\(689\) | −995.038 | + | 3062.41i | −0.0550188 | + | 0.169330i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −495.853 | + | 360.259i | −0.0272983 | + | 0.0198334i | −0.601351 | − | 0.798985i | \(-0.705371\pi\) |
0.574052 | + | 0.818819i | \(0.305371\pi\) | |||||||
\(692\) | −1160.55 | −0.0637535 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26301.7 | −1.43862 | ||||||||
\(695\) | −9005.93 | + | 6543.19i | −0.491531 | + | 0.357119i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2392.42 | + | 7363.13i | −0.130014 | + | 0.400141i | ||||
\(698\) | 3045.07 | + | 2212.37i | 0.165125 | + | 0.119971i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −284.817 | + | 876.576i | −0.0153787 | + | 0.0473306i | ||||
\(701\) | −8657.42 | − | 26644.8i | −0.466457 | − | 1.43561i | −0.857141 | − | 0.515082i | \(-0.827762\pi\) |
0.390684 | − | 0.920525i | \(-0.372238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11394.8 | 0.611328 | ||||||||
\(704\) | 17293.1 | + | 11526.2i | 0.925794 | + | 0.617060i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23896.5 | − | 17361.9i | 1.27388 | − | 0.925527i | ||||
\(707\) | 229.686 | + | 706.902i | 0.0122182 | + | 0.0376037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9146.28 | − | 6645.16i | −0.484479 | − | 0.351995i | 0.318578 | − | 0.947897i | \(-0.396795\pi\) |
−0.803057 | + | 0.595902i | \(0.796795\pi\) | |||||||
\(710\) | −15824.3 | − | 11497.0i | −0.836442 | − | 0.607711i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7938.51 | − | 24432.2i | −0.417849 | − | 1.28601i | ||||
\(713\) | −1699.00 | + | 1234.40i | −0.0892399 | + | 0.0648366i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9682.28 | − | 26152.5i | −0.506429 | − | 1.36790i | ||||
\(716\) | −113.541 | −0.00592631 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2555.60 | + | 7865.34i | 0.132833 | + | 0.408819i | ||||
\(719\) | −3455.04 | + | 10633.5i | −0.179209 | + | 0.551549i | −0.999801 | − | 0.0199662i | \(-0.993644\pi\) |
0.820592 | + | 0.571515i | \(0.193644\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26006.9 | + | 18895.1i | 1.34334 | + | 0.975994i | ||||
\(722\) | −1036.73 | + | 3190.72i | −0.0534390 | + | 0.164468i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −57.8138 | + | 42.0042i | −0.00296772 | + | 0.00215618i | ||||
\(725\) | −1237.25 | −0.0633798 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31428.7 | −1.60334 | −0.801669 | − | 0.597769i | \(-0.796054\pi\) | ||||
−0.801669 | + | 0.597769i | \(0.796054\pi\) | |||||||
\(728\) | −47314.4 | + | 34375.9i | −2.40878 | + | 1.75008i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1790.28 | + | 5509.91i | −0.0907687 | + | 0.279357i | ||||
\(731\) | −6529.77 | − | 4744.16i | −0.330386 | − | 0.240040i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 392.631 | − | 1208.39i | 0.0197847 | − | 0.0608910i | −0.940677 | − | 0.339304i | \(-0.889808\pi\) |
0.960461 | + | 0.278413i | \(0.0898084\pi\) | |||||||
\(734\) | 2772.75 | + | 8533.64i | 0.139433 | + | 0.429131i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7061.87 | −0.353674 | ||||||||
\(737\) | −2802.29 | − | 7569.17i | −0.140059 | − | 0.378309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10929.8 | + | 7940.95i | −0.544057 | + | 0.395281i | −0.825590 | − | 0.564271i | \(-0.809157\pi\) |
0.281532 | + | 0.959552i | \(0.409157\pi\) | |||||||
\(740\) | 707.898 | + | 2178.68i | 0.0351660 | + | 0.108230i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2913.17 | − | 2116.54i | −0.144132 | − | 0.104718i | ||||
\(743\) | 25972.0 | + | 18869.8i | 1.28240 | + | 0.931716i | 0.999623 | − | 0.0274700i | \(-0.00874508\pi\) |
0.282775 | + | 0.959186i | \(0.408745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6802.97 | + | 20937.4i | 0.334552 | + | 1.02965i | ||||
\(746\) | −4092.02 | + | 2973.03i | −0.200830 | + | 0.145912i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2927.86 | − | 1951.48i | −0.143119 | − | 0.0953918i | ||||
\(749\) | −21814.3 | −1.06419 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7329.02 | − | 22556.4i | −0.356111 | − | 1.09600i | −0.955362 | − | 0.295437i | \(-0.904535\pi\) |
0.599251 | − | 0.800561i | \(-0.295465\pi\) | |||||||
\(752\) | −3216.94 | + | 9900.71i | −0.155997 | + | 0.480109i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11372.0 | − | 8262.21i | −0.549260 | − | 0.399061i | ||||
\(755\) | −3827.63 | + | 11780.2i | −0.184506 | + | 0.567850i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18715.6 | − | 13597.7i | 0.898589 | − | 0.652863i | −0.0395142 | − | 0.999219i | \(-0.512581\pi\) |
0.938103 | + | 0.346356i | \(0.112581\pi\) | |||||||
\(758\) | 14518.1 | 0.695672 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23028.8 | −1.09913 | ||||||||
\(761\) | 667.872 | − | 485.238i | 0.0318139 | − | 0.0231141i | −0.571765 | − | 0.820418i | \(-0.693741\pi\) |
0.603579 | + | 0.797304i | \(0.293741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −866.969 | + | 2668.26i | −0.0411355 | + | 0.126602i | ||||
\(764\) | −6464.80 | − | 4696.95i | −0.306136 | − | 0.222421i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4048.46 | + | 12459.9i | −0.190962 | + | 0.587720i | ||||
\(767\) | −9095.64 | − | 27993.5i | −0.428194 | − | 1.31784i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9591.21 | 0.449763 | 0.224882 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224882 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(770\) | 31160.3 | − | 1260.12i | 1.45836 | − | 0.0589761i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7120.74 | + | 5173.52i | −0.331970 | + | 0.241191i | ||||
\(773\) | −724.297 | − | 2229.16i | −0.0337014 | − | 0.103722i | 0.932791 | − | 0.360418i | \(-0.117366\pi\) |
−0.966492 | + | 0.256696i | \(0.917366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 300.443 | + | 218.285i | 0.0139255 | + | 0.0101175i | ||||
\(776\) | 4839.66 | + | 3516.22i | 0.223883 | + | 0.162661i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −65.6816 | − | 202.147i | −0.00302674 | − | 0.00931533i | ||||
\(779\) | 10260.9 | − | 7455.02i | 0.471934 | − | 0.342880i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7392.24 | + | 26326.6i | −0.338688 | + | 1.20620i | ||||
\(782\) | −12608.2 | −0.576559 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10600.8 | − | 32626.0i | −0.482909 | − | 1.48624i | ||||
\(785\) | 5961.64 | − | 18348.0i | 0.271057 | − | 0.834229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21078.8 | + | 15314.6i | 0.954736 | + | 0.693656i | 0.951922 | − | 0.306340i | \(-0.0991044\pi\) |
0.00281375 | + | 0.999996i | \(0.499104\pi\) | |||||||
\(788\) | 918.337 | − | 2826.35i | 0.0415157 | − | 0.127772i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24918.2 | − | 18104.1i | 1.12221 | − | 0.815336i | ||||
\(791\) | −14421.8 | −0.648269 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29779.1 | 1.33353 | ||||||||
\(794\) | −14543.5 | + | 10566.5i | −0.650039 | + | 0.472281i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1793.32 | − | 5519.27i | 0.0798525 | − | 0.245761i | ||||
\(797\) | 35109.5 | + | 25508.5i | 1.56040 | + | 1.13370i | 0.935677 | + | 0.352856i | \(0.114790\pi\) |
0.624727 | + | 0.780844i | \(0.285210\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3783.65 | − | 11644.9i | 0.167529 | − | 0.515602i | ||||
\(800\) | 385.897 | + | 1187.67i | 0.0170544 | + | 0.0524881i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5687.54 | 0.250417 | ||||||||
\(803\) | 8092.65 | − | 327.267i | 0.355646 | − | 0.0143823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25216.9 | + | 18321.2i | −1.10407 | + | 0.802157i | ||||
\(806\) | 1303.79 | + | 4012.65i | 0.0569777 | + | 0.175359i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 447.423 | + | 325.072i | 0.0194805 | + | 0.0141534i | ||||
\(809\) | −6863.36 | − | 4986.53i | −0.298273 | − | 0.216708i | 0.428575 | − | 0.903506i | \(-0.359016\pi\) |
−0.726848 | + | 0.686798i | \(0.759016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1715.59 | + | 5280.06i | 0.0742820 | + | 0.228616i | 0.981303 | − | 0.192469i | \(-0.0616494\pi\) |
−0.907021 | + | 0.421085i | \(0.861649\pi\) | |||||||
\(812\) | −3547.17 | + | 2577.17i | −0.153302 | + | 0.111380i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9008.48 | + | 7118.49i | −0.387895 | + | 0.306515i | ||||
\(815\) | −18916.8 | −0.813037 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4085.98 | + | 12575.4i | 0.174970 | + | 0.538502i | ||||
\(818\) | 7425.09 | − | 22852.1i | 0.317374 | − | 0.976777i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2062.85 | + | 1498.75i | 0.0878512 | + | 0.0638276i | ||||
\(821\) | 32.7348 | − | 100.748i | 0.00139154 | − | 0.00428272i | −0.950358 | − | 0.311158i | \(-0.899283\pi\) |
0.951750 | + | 0.306875i | \(0.0992833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30200.5 | + | 21941.9i | −1.27913 | + | 0.929341i | −0.999526 | − | 0.0307751i | \(-0.990202\pi\) |
−0.279602 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(824\) | 23918.8 | 1.01123 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32915.6 | 1.38654 | ||||||||
\(827\) | −1408.83 | + | 1023.58i | −0.0592380 | + | 0.0430389i | −0.617010 | − | 0.786955i | \(-0.711656\pi\) |
0.557772 | + | 0.829994i | \(0.311656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1629.09 | + | 5013.82i | −0.0682516 | + | 0.210057i | −0.979365 | − | 0.202098i | \(-0.935224\pi\) |
0.911114 | + | 0.412155i | \(0.135224\pi\) | |||||||
\(830\) | 14285.8 | + | 10379.3i | 0.597432 | + | 0.434060i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12895.7 | + | 39688.8i | −0.537353 | + | 1.65380i | ||||
\(833\) | 12468.3 | + | 38373.5i | 0.518609 | + | 1.59611i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2758.64 | 0.114331 | ||||||||
\(836\) | 2001.33 | + | 5405.71i | 0.0827958 | + | 0.223637i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21806.7 | + | 15843.5i | −0.898928 | + | 0.653109i | ||||
\(839\) | −7446.81 | − | 22918.9i | −0.306427 | − | 0.943086i | −0.979141 | − | 0.203183i | \(-0.934871\pi\) |
0.672714 | − | 0.739903i | \(-0.265129\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14969.5 | + | 10876.0i | 0.613780 | + | 0.445937i | ||||
\(842\) | 2491.53 | + | 1810.20i | 0.101976 | + | 0.0740898i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2674.76 | − | 8232.06i | −0.109086 | − | 0.335734i | ||||
\(845\) | 26757.5 | − | 19440.5i | 1.08933 | − | 0.791447i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16776.6 | − | 40240.6i | −0.680578 | − | 1.63245i | ||||
\(848\) | −2065.74 | −0.0836531 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 688.979 | + | 2120.46i | 0.0278021 | + | 0.0855660i | ||||
\(851\) | 3546.18 | − | 10914.0i | 0.142845 | − | 0.439633i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22983.5 | + | 16698.5i | 0.922555 | + | 0.670275i | 0.944159 | − | 0.329491i | \(-0.106877\pi\) |
−0.0216040 | + | 0.999767i | \(0.506877\pi\) | |||||||
\(854\) | −10290.7 | + | 31671.5i | −0.412343 | + | 1.26906i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13131.2 | + | 9540.40i | −0.524318 | + | 0.380939i | ||||
\(857\) | 6941.16 | 0.276669 | 0.138335 | − | 0.990386i | \(-0.455825\pi\) | ||||
0.138335 | + | 0.990386i | \(0.455825\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21637.2 | 0.859430 | 0.429715 | − | 0.902965i | \(-0.358614\pi\) | ||||
0.429715 | + | 0.902965i | \(0.358614\pi\) | |||||||
\(860\) | −2150.57 | + | 1562.48i | −0.0852718 | + | 0.0619536i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6732.46 | − | 20720.4i | 0.266019 | − | 0.818723i | ||||
\(863\) | 6019.83 | + | 4373.67i | 0.237448 | + | 0.172516i | 0.700146 | − | 0.714000i | \(-0.253118\pi\) |
−0.462698 | + | 0.886516i | \(0.653118\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2144.70 | + | 6600.70i | −0.0843028 | + | 0.259457i | ||||
\(866\) | −5786.56 | − | 17809.2i | −0.227062 | − | 0.698824i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1316.05 | 0.0514626 | ||||||||
\(869\) | −35829.9 | − | 23881.3i | −1.39867 | − | 0.932242i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13111.9 | − | 9526.37i | 0.510081 | − | 0.370595i | ||||
\(872\) | 645.076 | + | 1985.34i | 0.0250516 | + | 0.0771010i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16710.4 | + | 12140.8i | 0.646723 | + | 0.469872i | ||||
\(875\) | 39022.4 | + | 28351.4i | 1.50765 | + | 1.09537i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9984.83 | − | 30730.2i | −0.384451 | − | 1.18322i | −0.936877 | − | 0.349658i | \(-0.886298\pi\) |
0.552426 | − | 0.833562i | \(-0.313702\pi\) | |||||||
\(878\) | 19416.3 | − | 14106.8i | 0.746320 | − | 0.542233i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14037.0 | − | 11092.1i | 0.537714 | − | 0.424902i | ||||
\(881\) | −21907.4 | −0.837774 | −0.418887 | − | 0.908038i | \(-0.637580\pi\) | ||||
−0.418887 | + | 0.908038i | \(0.637580\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −370.914 | − | 1141.56i | −0.0141362 | − | 0.0435067i | 0.943740 | − | 0.330689i | \(-0.107281\pi\) |
−0.957876 | + | 0.287183i | \(0.907281\pi\) | |||||||
\(884\) | 2183.34 | − | 6719.64i | 0.0830699 | − | 0.255663i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18799.1 | − | 13658.3i | −0.712831 | − | 0.517902i | ||||
\(887\) | 7342.41 | − | 22597.6i | 0.277941 | − | 0.855415i | −0.710485 | − | 0.703712i | \(-0.751524\pi\) |
0.988426 | − | 0.151703i | \(-0.0484757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43072.7 | − | 31294.1i | 1.62498 | − | 1.18062i | ||||
\(890\) | −27507.1 | −1.03600 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6419.26 | 0.240956 | ||||||||
\(893\) | −16227.8 | + | 11790.2i | −0.608111 | + | 0.441818i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −209.825 | + | 645.775i | −0.00783651 | + | 0.0241183i | ||||
\(896\) | −21338.7 | − | 15503.5i | −0.795622 | − | 0.578053i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5302.29 | + | 16318.8i | −0.197038 | + | 0.606419i | ||||
\(899\) | 545.919 | + | 1680.17i | 0.0202530 | + | 0.0623323i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2429.65 | 0.0898374 | ||||||||
\(902\) | −3454.82 | + | 12303.9i | −0.127531 | + | 0.454186i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8681.31 | + | 6307.34i | −0.319398 | + | 0.232057i | ||||
\(905\) | 132.062 | + | 406.444i | 0.00485069 | + | 0.0149289i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10232.4 | + | 7434.24i | 0.374597 | + | 0.272161i | 0.759115 | − | 0.650957i | \(-0.225632\pi\) |
−0.384517 | + | 0.923118i | \(0.625632\pi\) | |||||||
\(908\) | −567.053 | − | 411.988i | −0.0207250 | − | 0.0150576i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19351.1 | + | 59556.6i | 0.704927 | + | 2.16954i | ||||
\(911\) | −10814.5 | + | 7857.18i | −0.393304 | + | 0.285752i | −0.766808 | − | 0.641877i | \(-0.778156\pi\) |
0.373504 | + | 0.927628i | \(0.378156\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6673.58 | − | 23767.1i | 0.241909 | − | 0.861531i | ||||
\(914\) | −2891.93 | −0.104657 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1591.54 | + | 4898.26i | 0.0574082 | + | 0.176684i | ||||
\(917\) | 10624.1 | − | 32697.6i | 0.382593 | − | 1.17750i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14994.8 | + | 10894.4i | 0.538230 | + | 0.391047i | 0.823427 | − | 0.567422i | \(-0.192059\pi\) |
−0.285197 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(920\) | −7166.78 | + | 22057.1i | −0.256828 | + | 0.790435i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16986.1 | − | 12341.1i | 0.606732 | − | 0.440817i | ||||
\(923\) | −54908.7 | −1.95812 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2029.31 | −0.0721332 | ||||||||
\(926\) | 3645.03 | − | 2648.27i | 0.129355 | − | 0.0939822i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1835.75 | + | 5649.85i | −0.0649368 | + | 0.199855i | ||||
\(929\) | 21222.9 | + | 15419.3i | 0.749517 | + | 0.544556i | 0.895677 | − | 0.444705i | \(-0.146691\pi\) |
−0.146160 | + | 0.989261i | \(0.546691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20425.9 | − | 62864.5i | 0.719047 | − | 2.21300i | ||||
\(932\) | −1329.47 | − | 4091.70i | −0.0467257 | − | 0.143807i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −47575.7 | −1.66673 | ||||||||
\(935\) | −16509.9 | + | 13046.1i | −0.577466 | + | 0.456314i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11249.4 | − | 8173.17i | 0.392212 | − | 0.284958i | −0.374150 | − | 0.927368i | \(-0.622065\pi\) |
0.766361 | + | 0.642410i | \(0.222065\pi\) | |||||||
\(938\) | 5600.69 | + | 17237.2i | 0.194956 | + | 0.600014i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3262.43 | − | 2370.29i | −0.113201 | − | 0.0822452i | ||||
\(941\) | 29656.0 | + | 21546.4i | 1.02737 | + | 0.746431i | 0.967781 | − | 0.251792i | \(-0.0810199\pi\) |
0.0595926 | + | 0.998223i | \(0.481020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3947.15 | − | 12148.1i | −0.136306 | − | 0.419508i | ||||
\(944\) | 15276.6 | − | 11099.1i | 0.526707 | − | 0.382675i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11086.3 | − | 7389.23i | −0.381022 | − | 0.253958i | ||||
\(947\) | 9454.30 | 0.324417 | 0.162209 | − | 0.986756i | \(-0.448138\pi\) | ||||
0.162209 | + | 0.986756i | \(0.448138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5025.69 | + | 15467.5i | 0.171908 | + | 0.529079i | ||||
\(950\) | 1128.70 | − | 3473.79i | 0.0385473 | − | 0.118637i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35701.0 | + | 25938.3i | 1.21542 | + | 0.883052i | ||||
\(953\) | −9444.38 | + | 29066.8i | −0.321022 | + | 0.988003i | 0.652183 | + | 0.758062i | \(0.273853\pi\) |
−0.973204 | + | 0.229941i | \(0.926147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38661.2 | + | 28089.0i | −1.31000 | + | 0.951769i | ||||
\(956\) | −7407.31 | −0.250596 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −42312.6 | −1.42699 | ||||||||
\(959\) | 81442.6 | − | 59171.5i | 2.74235 | − | 1.99244i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9042.06 | + | 27828.6i | −0.303517 | + | 0.934128i | ||||
\(962\) | −18652.0 | − | 13551.5i | −0.625119 | − | 0.454175i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1448.33 | − | 4457.51i | 0.0483897 | − | 0.148928i | ||||
\(965\) | 16265.6 | + | 50060.4i | 0.542600 | + | 1.66995i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30119.6 | −1.00164 | −0.500818 | − | 0.865553i | \(-0.666967\pi\) | ||||
−0.500818 | + | 0.865553i | \(0.666967\pi\) | |||||||
\(968\) | −27697.9 | − | 16885.9i | −0.919673 | − | 0.560676i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5182.06 | − | 3764.99i | 0.171532 | − | 0.124625i | ||||
\(971\) | 9953.51 | + | 30633.7i | 0.328963 | + | 1.01244i | 0.969620 | + | 0.244617i | \(0.0786622\pi\) |
−0.640657 | + | 0.767828i | \(0.721338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28271.9 | − | 20540.7i | −0.931505 | − | 0.676778i | ||||
\(974\) | −18627.1 | − | 13533.4i | −0.612782 | − | 0.445212i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5903.55 | + | 18169.3i | 0.193615 | + | 0.595885i | ||||
\(977\) | −6868.82 | + | 4990.49i | −0.224926 | + | 0.163419i | −0.694541 | − | 0.719453i | \(-0.744393\pi\) |
0.469615 | + | 0.882871i | \(0.344393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13351.3 | + | 36062.8i | 0.435864 | + | 1.17730i | ||||
\(980\) | 13288.6 | 0.433153 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12678.5 | + | 39020.3i | 0.412003 | + | 1.26801i | ||||
\(983\) | 1043.50 | − | 3211.55i | 0.0338580 | − | 0.104204i | −0.932699 | − | 0.360655i | \(-0.882553\pi\) |
0.966557 | + | 0.256451i | \(0.0825532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14378.0 | − | 10446.2i | −0.465097 | − | 0.337913i | ||||
\(986\) | −3277.53 | + | 10087.2i | −0.105860 | + | 0.325803i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9364.21 | + | 6803.50i | −0.301534 | + | 0.219077i | ||||
\(989\) | 13316.4 | 0.428145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20081.5 | −0.643703 | −0.321851 | − | 0.946790i | \(-0.604305\pi\) | ||||
−0.321851 | + | 0.946790i | \(0.604305\pi\) | |||||||
\(992\) | 1442.57 | − | 1048.08i | 0.0461709 | − | 0.0335451i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18974.7 | − | 58398.0i | 0.605473 | − | 1.86345i | ||||
\(995\) | −28077.2 | − | 20399.3i | −0.894580 | − | 0.649951i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10625.0 | + | 32700.4i | −0.337510 | + | 1.03875i | 0.627962 | + | 0.778244i | \(0.283889\pi\) |
−0.965472 | + | 0.260506i | \(0.916111\pi\) | |||||||
\(998\) | 3579.42 | + | 11016.3i | 0.113532 | + | 0.349414i | ||||
\(999\) | 0 | 0 |
(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 | 99.4.f.b.91.2 | 8 | ||
3.2 | odd | 2 | 33.4.e.b.25.1 | yes | 8 | ||
11.2 | odd | 10 | 1089.4.a.z.1.4 | 4 | |||
11.4 | even | 5 | inner | 99.4.f.b.37.2 | 8 | ||
11.9 | even | 5 | 1089.4.a.bg.1.1 | 4 | |||
33.2 | even | 10 | 363.4.a.t.1.1 | 4 | |||
33.20 | odd | 10 | 363.4.a.p.1.4 | 4 | |||
33.26 | odd | 10 | 33.4.e.b.4.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.e.b.4.1 | ✓ | 8 | 33.26 | odd | 10 | ||
33.4.e.b.25.1 | yes | 8 | 3.2 | odd | 2 | ||
99.4.f.b.37.2 | 8 | 11.4 | even | 5 | inner | ||
99.4.f.b.91.2 | 8 | 1.1 | even | 1 | trivial | ||
363.4.a.p.1.4 | 4 | 33.20 | odd | 10 | |||
363.4.a.t.1.1 | 4 | 33.2 | even | 10 | |||
1089.4.a.z.1.4 | 4 | 11.2 | odd | 10 | |||
1089.4.a.bg.1.1 | 4 | 11.9 | even | 5 |