Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(168,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.168");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.b (of order \(2\), degree \(1\), not 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 168.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.168 |
Dual form | 169.4.b.f.168.4 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.56155i | − 0.905646i | −0.891601 | − | 0.452823i | \(-0.850417\pi\) | ||||
0.891601 | − | 0.452823i | \(-0.149583\pi\) | |||||||
\(3\) | −3.68466 | −0.709113 | −0.354556 | − | 0.935035i | \(-0.615368\pi\) | ||||
−0.354556 | + | 0.935035i | \(0.615368\pi\) | |||||||
\(4\) | 1.43845 | 0.179806 | ||||||||
\(5\) | − 0.561553i | − 0.0502268i | −0.999685 | − | 0.0251134i | \(-0.992005\pi\) | ||||
0.999685 | − | 0.0251134i | \(-0.00799469\pi\) | |||||||
\(6\) | 9.43845i | 0.642205i | ||||||||
\(7\) | 18.1771i | 0.981470i | 0.871309 | + | 0.490735i | \(0.163272\pi\) | ||||
−0.871309 | + | 0.490735i | \(0.836728\pi\) | |||||||
\(8\) | − 24.1771i | − 1.06849i | ||||||||
\(9\) | −13.4233 | −0.497159 | ||||||||
\(10\) | −1.43845 | −0.0454877 | ||||||||
\(11\) | 64.7386i | 1.77449i | 0.461295 | + | 0.887247i | \(0.347385\pi\) | ||||
−0.461295 | + | 0.887247i | \(0.652615\pi\) | |||||||
\(12\) | −5.30019 | −0.127503 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 46.5616 | 0.888864 | ||||||||
\(15\) | 2.06913i | 0.0356165i | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | 25.5464 | 0.364465 | 0.182233 | − | 0.983255i | \(-0.441668\pi\) | ||||
0.182233 | + | 0.983255i | \(0.441668\pi\) | |||||||
\(18\) | 34.3845i | 0.450250i | ||||||||
\(19\) | 107.970i | 1.30368i | 0.758356 | + | 0.651841i | \(0.226003\pi\) | ||||
−0.758356 | + | 0.651841i | \(0.773997\pi\) | |||||||
\(20\) | − 0.807764i | − 0.00903108i | ||||||||
\(21\) | − 66.9763i | − 0.695973i | ||||||||
\(22\) | 165.831 | 1.60706 | ||||||||
\(23\) | −73.2614 | −0.664176 | −0.332088 | − | 0.943248i | \(-0.607753\pi\) | ||||
−0.332088 | + | 0.943248i | \(0.607753\pi\) | |||||||
\(24\) | 89.0843i | 0.757677i | ||||||||
\(25\) | 124.685 | 0.997477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 148.946 | 1.06165 | ||||||||
\(28\) | 26.1468i | 0.176474i | ||||||||
\(29\) | 175.909 | 1.12640 | 0.563198 | − | 0.826322i | \(-0.309571\pi\) | ||||
0.563198 | + | 0.826322i | \(0.309571\pi\) | |||||||
\(30\) | 5.30019 | 0.0322559 | ||||||||
\(31\) | 113.093i | 0.655228i | 0.944812 | + | 0.327614i | \(0.106245\pi\) | ||||
−0.944812 | + | 0.327614i | \(0.893755\pi\) | |||||||
\(32\) | − 64.2547i | − 0.354961i | ||||||||
\(33\) | − 238.540i | − 1.25832i | ||||||||
\(34\) | − 65.4384i | − 0.330077i | ||||||||
\(35\) | 10.2074 | 0.0492961 | ||||||||
\(36\) | −19.3087 | −0.0893921 | ||||||||
\(37\) | 114.808i | 0.510116i | 0.966926 | + | 0.255058i | \(0.0820945\pi\) | ||||
−0.966926 | + | 0.255058i | \(0.917905\pi\) | |||||||
\(38\) | 276.570 | 1.18067 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.5767 | −0.0536666 | ||||||||
\(41\) | 69.6458i | 0.265289i | 0.991164 | + | 0.132645i | \(0.0423469\pi\) | ||||
−0.991164 | + | 0.132645i | \(0.957653\pi\) | |||||||
\(42\) | −171.563 | −0.630305 | ||||||||
\(43\) | −438.302 | −1.55443 | −0.777214 | − | 0.629236i | \(-0.783368\pi\) | ||||
−0.777214 | + | 0.629236i | \(0.783368\pi\) | |||||||
\(44\) | 93.1231i | 0.319064i | ||||||||
\(45\) | 7.53789i | 0.0249707i | ||||||||
\(46\) | 187.663i | 0.601508i | ||||||||
\(47\) | − 31.9479i | − 0.0991506i | −0.998770 | − | 0.0495753i | \(-0.984213\pi\) | ||||
0.998770 | − | 0.0495753i | \(-0.0157868\pi\) | |||||||
\(48\) | 185.793 | 0.558684 | ||||||||
\(49\) | 12.5937 | 0.0367164 | ||||||||
\(50\) | − 319.386i | − 0.903361i | ||||||||
\(51\) | −94.1298 | −0.258447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.84658 | 0.00737752 | 0.00368876 | − | 0.999993i | \(-0.498826\pi\) | ||||
0.00368876 | + | 0.999993i | \(0.498826\pi\) | |||||||
\(54\) | − 381.533i | − 0.961483i | ||||||||
\(55\) | 36.3542 | 0.0891272 | ||||||||
\(56\) | 439.469 | 1.04869 | ||||||||
\(57\) | − 397.831i | − 0.924457i | ||||||||
\(58\) | − 450.600i | − 1.02012i | ||||||||
\(59\) | 71.6325i | 0.158064i | 0.996872 | + | 0.0790319i | \(0.0251829\pi\) | ||||
−0.996872 | + | 0.0790319i | \(0.974817\pi\) | |||||||
\(60\) | 2.97633i | 0.00640405i | ||||||||
\(61\) | −920.695 | −1.93251 | −0.966253 | − | 0.257593i | \(-0.917071\pi\) | ||||
−0.966253 | + | 0.257593i | \(0.917071\pi\) | |||||||
\(62\) | 289.693 | 0.593404 | ||||||||
\(63\) | − 243.996i | − 0.487947i | ||||||||
\(64\) | −567.978 | −1.10933 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −611.032 | −1.13959 | ||||||||
\(67\) | 444.280i | 0.810112i | 0.914292 | + | 0.405056i | \(0.132748\pi\) | ||||
−0.914292 | + | 0.405056i | \(0.867252\pi\) | |||||||
\(68\) | 36.7471 | 0.0655330 | ||||||||
\(69\) | 269.943 | 0.470976 | ||||||||
\(70\) | − 26.1468i | − 0.0446448i | ||||||||
\(71\) | 541.719i | 0.905496i | 0.891639 | + | 0.452748i | \(0.149556\pi\) | ||||
−0.891639 | + | 0.452748i | \(0.850444\pi\) | |||||||
\(72\) | 324.536i | 0.531207i | ||||||||
\(73\) | 764.004i | 1.22493i | 0.790498 | + | 0.612465i | \(0.209822\pi\) | ||||
−0.790498 | + | 0.612465i | \(0.790178\pi\) | |||||||
\(74\) | 294.086 | 0.461984 | ||||||||
\(75\) | −459.420 | −0.707324 | ||||||||
\(76\) | 155.309i | 0.234410i | ||||||||
\(77\) | −1176.76 | −1.74161 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −421.538 | −0.600338 | −0.300169 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300169 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(80\) | 28.3153i | 0.0395719i | ||||||||
\(81\) | −186.386 | −0.255674 | ||||||||
\(82\) | 178.401 | 0.240258 | ||||||||
\(83\) | − 603.797i | − 0.798498i | −0.916842 | − | 0.399249i | \(-0.869271\pi\) | ||||
0.916842 | − | 0.399249i | \(-0.130729\pi\) | |||||||
\(84\) | − 96.3419i | − 0.125140i | ||||||||
\(85\) | − 14.3457i | − 0.0183059i | ||||||||
\(86\) | 1122.73i | 1.40776i | ||||||||
\(87\) | −648.165 | −0.798742 | ||||||||
\(88\) | 1565.19 | 1.89602 | ||||||||
\(89\) | − 1159.88i | − 1.38143i | −0.723127 | − | 0.690715i | \(-0.757296\pi\) | ||||
0.723127 | − | 0.690715i | \(-0.242704\pi\) | |||||||
\(90\) | 19.3087 | 0.0226146 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −105.383 | −0.119423 | ||||||||
\(93\) | − 416.708i | − 0.464631i | ||||||||
\(94\) | −81.8362 | −0.0897953 | ||||||||
\(95\) | 60.6307 | 0.0654798 | ||||||||
\(96\) | 236.757i | 0.251707i | ||||||||
\(97\) | − 583.269i | − 0.610536i | −0.952267 | − | 0.305268i | \(-0.901254\pi\) | ||||
0.952267 | − | 0.305268i | \(-0.0987460\pi\) | |||||||
\(98\) | − 32.2595i | − 0.0332521i | ||||||||
\(99\) | − 869.006i | − 0.882206i | ||||||||
\(100\) | 179.352 | 0.179352 | ||||||||
\(101\) | −921.740 | −0.908085 | −0.454043 | − | 0.890980i | \(-0.650019\pi\) | ||||
−0.454043 | + | 0.890980i | \(0.650019\pi\) | |||||||
\(102\) | 241.118i | 0.234061i | ||||||||
\(103\) | 930.712 | 0.890347 | 0.445174 | − | 0.895444i | \(-0.353142\pi\) | ||||
0.445174 | + | 0.895444i | \(0.353142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −37.6107 | −0.0349565 | ||||||||
\(106\) | − 7.29168i | − 0.00668142i | ||||||||
\(107\) | 857.383 | 0.774638 | 0.387319 | − | 0.921946i | \(-0.373401\pi\) | ||||
0.387319 | + | 0.921946i | \(0.373401\pi\) | |||||||
\(108\) | 214.251 | 0.190892 | ||||||||
\(109\) | − 671.853i | − 0.590384i | −0.955438 | − | 0.295192i | \(-0.904616\pi\) | ||||
0.955438 | − | 0.295192i | \(-0.0953836\pi\) | |||||||
\(110\) | − 93.1231i | − 0.0807176i | ||||||||
\(111\) | − 423.027i | − 0.361730i | ||||||||
\(112\) | − 916.548i | − 0.773265i | ||||||||
\(113\) | 641.474 | 0.534024 | 0.267012 | − | 0.963693i | \(-0.413964\pi\) | ||||
0.267012 | + | 0.963693i | \(0.413964\pi\) | |||||||
\(114\) | −1019.07 | −0.837231 | ||||||||
\(115\) | 41.1401i | 0.0333594i | ||||||||
\(116\) | 253.036 | 0.202533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 183.491 | 0.143150 | ||||||||
\(119\) | 464.359i | 0.357712i | ||||||||
\(120\) | 50.0255 | 0.0380557 | ||||||||
\(121\) | −2860.09 | −2.14883 | ||||||||
\(122\) | 2358.41i | 1.75017i | ||||||||
\(123\) | − 256.621i | − 0.188120i | ||||||||
\(124\) | 162.678i | 0.117814i | ||||||||
\(125\) | − 140.211i | − 0.100327i | ||||||||
\(126\) | −625.009 | −0.441907 | ||||||||
\(127\) | 553.174 | 0.386506 | 0.193253 | − | 0.981149i | \(-0.438096\pi\) | ||||
0.193253 | + | 0.981149i | \(0.438096\pi\) | |||||||
\(128\) | 940.868i | 0.649702i | ||||||||
\(129\) | 1614.99 | 1.10227 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2056.40 | 1.37152 | 0.685758 | − | 0.727830i | \(-0.259471\pi\) | ||||
0.685758 | + | 0.727830i | \(0.259471\pi\) | |||||||
\(132\) | − 343.127i | − 0.226253i | ||||||||
\(133\) | −1962.57 | −1.27952 | ||||||||
\(134\) | 1138.05 | 0.733674 | ||||||||
\(135\) | − 83.6411i | − 0.0533235i | ||||||||
\(136\) | − 617.637i | − 0.389426i | ||||||||
\(137\) | − 1808.57i | − 1.12786i | −0.825824 | − | 0.563928i | \(-0.809290\pi\) | ||||
0.825824 | − | 0.563928i | \(-0.190710\pi\) | |||||||
\(138\) | − 691.474i | − 0.426537i | ||||||||
\(139\) | 1493.64 | 0.911428 | 0.455714 | − | 0.890126i | \(-0.349384\pi\) | ||||
0.455714 | + | 0.890126i | \(0.349384\pi\) | |||||||
\(140\) | 14.6828 | 0.00886373 | ||||||||
\(141\) | 117.717i | 0.0703090i | ||||||||
\(142\) | 1387.64 | 0.820058 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 676.847 | 0.391694 | ||||||||
\(145\) | − 98.7822i | − 0.0565753i | ||||||||
\(146\) | 1957.04 | 1.10935 | ||||||||
\(147\) | −46.4036 | −0.0260361 | ||||||||
\(148\) | 165.145i | 0.0917218i | ||||||||
\(149\) | 2759.02i | 1.51696i | 0.651694 | + | 0.758482i | \(0.274059\pi\) | ||||
−0.651694 | + | 0.758482i | \(0.725941\pi\) | |||||||
\(150\) | 1176.83i | 0.640585i | ||||||||
\(151\) | − 976.355i | − 0.526190i | −0.964770 | − | 0.263095i | \(-0.915257\pi\) | ||||
0.964770 | − | 0.263095i | \(-0.0847432\pi\) | |||||||
\(152\) | 2610.39 | 1.39297 | ||||||||
\(153\) | −342.917 | −0.181197 | ||||||||
\(154\) | 3014.33i | 1.57728i | ||||||||
\(155\) | 63.5076 | 0.0329100 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −564.875 | −0.287146 | −0.143573 | − | 0.989640i | \(-0.545859\pi\) | ||||
−0.143573 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(158\) | 1079.79i | 0.543694i | ||||||||
\(159\) | −10.4887 | −0.00523149 | ||||||||
\(160\) | −36.0824 | −0.0178285 | ||||||||
\(161\) | − 1331.68i | − 0.651869i | ||||||||
\(162\) | 477.438i | 0.231550i | ||||||||
\(163\) | 1508.53i | 0.724892i | 0.932005 | + | 0.362446i | \(0.118058\pi\) | ||||
−0.932005 | + | 0.362446i | \(0.881942\pi\) | |||||||
\(164\) | 100.182i | 0.0477005i | ||||||||
\(165\) | −133.953 | −0.0632012 | ||||||||
\(166\) | −1546.66 | −0.723157 | ||||||||
\(167\) | 592.521i | 0.274555i | 0.990533 | + | 0.137277i | \(0.0438351\pi\) | ||||
−0.990533 | + | 0.137277i | \(0.956165\pi\) | |||||||
\(168\) | −1619.29 | −0.743638 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −36.7471 | −0.0165787 | ||||||||
\(171\) | − 1449.31i | − 0.648137i | ||||||||
\(172\) | −630.474 | −0.279495 | ||||||||
\(173\) | 4495.57 | 1.97568 | 0.987838 | − | 0.155488i | \(-0.0496952\pi\) | ||||
0.987838 | + | 0.155488i | \(0.0496952\pi\) | |||||||
\(174\) | 1660.31i | 0.723377i | ||||||||
\(175\) | 2266.40i | 0.978994i | ||||||||
\(176\) | − 3264.34i | − 1.39806i | ||||||||
\(177\) | − 263.941i | − 0.112085i | ||||||||
\(178\) | −2971.10 | −1.25109 | ||||||||
\(179\) | 154.285 | 0.0644235 | 0.0322117 | − | 0.999481i | \(-0.489745\pi\) | ||||
0.0322117 | + | 0.999481i | \(0.489745\pi\) | |||||||
\(180\) | 10.8429i | 0.00448988i | ||||||||
\(181\) | −1071.35 | −0.439959 | −0.219979 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219979 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3392.45 | 1.37037 | ||||||||
\(184\) | 1771.25i | 0.709663i | ||||||||
\(185\) | 64.4706 | 0.0256215 | ||||||||
\(186\) | −1067.42 | −0.420791 | ||||||||
\(187\) | 1653.84i | 0.646742i | ||||||||
\(188\) | − 45.9554i | − 0.0178279i | ||||||||
\(189\) | 2707.40i | 1.04198i | ||||||||
\(190\) | − 155.309i | − 0.0593015i | ||||||||
\(191\) | 677.203 | 0.256548 | 0.128274 | − | 0.991739i | \(-0.459056\pi\) | ||||
0.128274 | + | 0.991739i | \(0.459056\pi\) | |||||||
\(192\) | 2092.81 | 0.786642 | ||||||||
\(193\) | 1321.68i | 0.492936i | 0.969151 | + | 0.246468i | \(0.0792700\pi\) | ||||
−0.969151 | + | 0.246468i | \(0.920730\pi\) | |||||||
\(194\) | −1494.07 | −0.552929 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.1154 | 0.00660183 | ||||||||
\(197\) | − 1267.37i | − 0.458356i | −0.973385 | − | 0.229178i | \(-0.926396\pi\) | ||||
0.973385 | − | 0.229178i | \(-0.0736038\pi\) | |||||||
\(198\) | −2226.00 | −0.798966 | ||||||||
\(199\) | −2396.24 | −0.853593 | −0.426796 | − | 0.904348i | \(-0.640358\pi\) | ||||
−0.426796 | + | 0.904348i | \(0.640358\pi\) | |||||||
\(200\) | − 3014.51i | − 1.06579i | ||||||||
\(201\) | − 1637.02i | − 0.574460i | ||||||||
\(202\) | 2361.09i | 0.822403i | ||||||||
\(203\) | 3197.51i | 1.10552i | ||||||||
\(204\) | −135.401 | −0.0464703 | ||||||||
\(205\) | 39.1098 | 0.0133246 | ||||||||
\(206\) | − 2384.07i | − 0.806339i | ||||||||
\(207\) | 983.409 | 0.330201 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6989.81 | −2.31337 | ||||||||
\(210\) | 96.3419i | 0.0316582i | ||||||||
\(211\) | −91.5539 | −0.0298712 | −0.0149356 | − | 0.999888i | \(-0.504754\pi\) | ||||
−0.0149356 | + | 0.999888i | \(0.504754\pi\) | |||||||
\(212\) | 4.09466 | 0.00132652 | ||||||||
\(213\) | − 1996.05i | − 0.642099i | ||||||||
\(214\) | − 2196.23i | − 0.701548i | ||||||||
\(215\) | 246.130i | 0.0780740i | ||||||||
\(216\) | − 3601.08i | − 1.13436i | ||||||||
\(217\) | −2055.70 | −0.643087 | ||||||||
\(218\) | −1720.99 | −0.534679 | ||||||||
\(219\) | − 2815.09i | − 0.868613i | ||||||||
\(220\) | 52.2935 | 0.0160256 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1083.61 | −0.327599 | ||||||||
\(223\) | − 1235.42i | − 0.370985i | −0.982646 | − | 0.185493i | \(-0.940612\pi\) | ||||
0.982646 | − | 0.185493i | \(-0.0593880\pi\) | |||||||
\(224\) | 1167.96 | 0.348383 | ||||||||
\(225\) | −1673.68 | −0.495905 | ||||||||
\(226\) | − 1643.17i | − 0.483637i | ||||||||
\(227\) | − 3301.66i | − 0.965370i | −0.875794 | − | 0.482685i | \(-0.839662\pi\) | ||||
0.875794 | − | 0.482685i | \(-0.160338\pi\) | |||||||
\(228\) | − 572.260i | − 0.166223i | ||||||||
\(229\) | 211.283i | 0.0609694i | 0.999535 | + | 0.0304847i | \(0.00970508\pi\) | ||||
−0.999535 | + | 0.0304847i | \(0.990295\pi\) | |||||||
\(230\) | 105.383 | 0.0302118 | ||||||||
\(231\) | 4335.96 | 1.23500 | ||||||||
\(232\) | − 4252.97i | − 1.20354i | ||||||||
\(233\) | 256.724 | 0.0721827 | 0.0360913 | − | 0.999348i | \(-0.488509\pi\) | ||||
0.0360913 | + | 0.999348i | \(0.488509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.9404 | −0.00498002 | ||||||||
\(236\) | 103.040i | 0.0284208i | ||||||||
\(237\) | 1553.22 | 0.425708 | ||||||||
\(238\) | 1189.48 | 0.323960 | ||||||||
\(239\) | 3549.62i | 0.960694i | 0.877078 | + | 0.480347i | \(0.159489\pi\) | ||||
−0.877078 | + | 0.480347i | \(0.840511\pi\) | |||||||
\(240\) | − 104.332i | − 0.0280609i | ||||||||
\(241\) | − 5030.10i | − 1.34447i | −0.740338 | − | 0.672235i | \(-0.765335\pi\) | ||||
0.740338 | − | 0.672235i | \(-0.234665\pi\) | |||||||
\(242\) | 7326.27i | 1.94608i | ||||||||
\(243\) | −3334.77 | −0.880353 | ||||||||
\(244\) | −1324.37 | −0.347476 | ||||||||
\(245\) | − 7.07204i | − 0.00184415i | ||||||||
\(246\) | −657.349 | −0.170370 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2734.25 | 0.700102 | ||||||||
\(249\) | 2224.79i | 0.566226i | ||||||||
\(250\) | −359.158 | −0.0908606 | ||||||||
\(251\) | 718.784 | 0.180754 | 0.0903770 | − | 0.995908i | \(-0.471193\pi\) | ||||
0.0903770 | + | 0.995908i | \(0.471193\pi\) | |||||||
\(252\) | − 350.976i | − 0.0877357i | ||||||||
\(253\) | − 4742.84i | − 1.17858i | ||||||||
\(254\) | − 1416.98i | − 0.350038i | ||||||||
\(255\) | 52.8588i | 0.0129810i | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | −1280.79 | −0.310871 | −0.155435 | − | 0.987846i | \(-0.549678\pi\) | ||||
−0.155435 | + | 0.987846i | \(0.549678\pi\) | |||||||
\(258\) | − 4136.89i | − 0.998262i | ||||||||
\(259\) | −2086.87 | −0.500663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2361.28 | −0.559998 | ||||||||
\(262\) | − 5267.58i | − 1.24211i | ||||||||
\(263\) | 5225.55 | 1.22517 | 0.612587 | − | 0.790403i | \(-0.290129\pi\) | ||||
0.612587 | + | 0.790403i | \(0.290129\pi\) | |||||||
\(264\) | −5767.19 | −1.34449 | ||||||||
\(265\) | − 1.59851i | 0 0.000370549i | ||||||||
\(266\) | 5027.24i | 1.15880i | ||||||||
\(267\) | 4273.77i | 0.979590i | ||||||||
\(268\) | 639.074i | 0.145663i | ||||||||
\(269\) | 6443.80 | 1.46054 | 0.730270 | − | 0.683158i | \(-0.239394\pi\) | ||||
0.730270 | + | 0.683158i | \(0.239394\pi\) | |||||||
\(270\) | −214.251 | −0.0482922 | ||||||||
\(271\) | − 3929.93i | − 0.880909i | −0.897775 | − | 0.440455i | \(-0.854817\pi\) | ||||
0.897775 | − | 0.440455i | \(-0.145183\pi\) | |||||||
\(272\) | −1288.13 | −0.287149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4632.74 | −1.02144 | ||||||||
\(275\) | 8071.91i | 1.77002i | ||||||||
\(276\) | 388.299 | 0.0846842 | ||||||||
\(277\) | 5884.40 | 1.27639 | 0.638194 | − | 0.769876i | \(-0.279682\pi\) | ||||
0.638194 | + | 0.769876i | \(0.279682\pi\) | |||||||
\(278\) | − 3826.03i | − 0.825431i | ||||||||
\(279\) | − 1518.08i | − 0.325752i | ||||||||
\(280\) | − 246.785i | − 0.0526722i | ||||||||
\(281\) | 3529.79i | 0.749358i | 0.927155 | + | 0.374679i | \(0.122247\pi\) | ||||
−0.927155 | + | 0.374679i | \(0.877753\pi\) | |||||||
\(282\) | 301.538 | 0.0636750 | ||||||||
\(283\) | 2611.00 | 0.548438 | 0.274219 | − | 0.961667i | \(-0.411581\pi\) | ||||
0.274219 | + | 0.961667i | \(0.411581\pi\) | |||||||
\(284\) | 779.234i | 0.162813i | ||||||||
\(285\) | −223.403 | −0.0464325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1265.96 | −0.260373 | ||||||||
\(288\) | 862.510i | 0.176472i | ||||||||
\(289\) | −4260.38 | −0.867165 | ||||||||
\(290\) | −253.036 | −0.0512372 | ||||||||
\(291\) | 2149.15i | 0.432939i | ||||||||
\(292\) | 1098.98i | 0.220250i | ||||||||
\(293\) | − 5491.03i | − 1.09484i | −0.836857 | − | 0.547422i | \(-0.815609\pi\) | ||||
0.836857 | − | 0.547422i | \(-0.184391\pi\) | |||||||
\(294\) | 118.865i | 0.0235795i | ||||||||
\(295\) | 40.2255 | 0.00793904 | ||||||||
\(296\) | 2775.72 | 0.545052 | ||||||||
\(297\) | 9642.56i | 1.88390i | ||||||||
\(298\) | 7067.37 | 1.37383 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −660.852 | −0.127181 | ||||||||
\(301\) | − 7967.05i | − 1.52563i | ||||||||
\(302\) | −2500.99 | −0.476542 | ||||||||
\(303\) | 3396.30 | 0.643935 | ||||||||
\(304\) | − 5444.19i | − 1.02712i | ||||||||
\(305\) | 517.019i | 0.0970637i | ||||||||
\(306\) | 878.399i | 0.164100i | ||||||||
\(307\) | − 7307.59i | − 1.35852i | −0.733897 | − | 0.679261i | \(-0.762300\pi\) | ||||
0.733897 | − | 0.679261i | \(-0.237700\pi\) | |||||||
\(308\) | −1692.71 | −0.313152 | ||||||||
\(309\) | −3429.36 | −0.631357 | ||||||||
\(310\) | − 162.678i | − 0.0298048i | ||||||||
\(311\) | −7904.92 | −1.44131 | −0.720654 | − | 0.693295i | \(-0.756158\pi\) | ||||
−0.720654 | + | 0.693295i | \(0.756158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10002.4 | 1.80629 | 0.903145 | − | 0.429336i | \(-0.141252\pi\) | ||||
0.903145 | + | 0.429336i | \(0.141252\pi\) | |||||||
\(314\) | 1446.96i | 0.260053i | ||||||||
\(315\) | −137.017 | −0.0245080 | ||||||||
\(316\) | −606.360 | −0.107944 | ||||||||
\(317\) | 6230.81i | 1.10397i | 0.833856 | + | 0.551983i | \(0.186129\pi\) | ||||
−0.833856 | + | 0.551983i | \(0.813871\pi\) | |||||||
\(318\) | 26.8673i | 0.00473788i | ||||||||
\(319\) | 11388.1i | 1.99878i | ||||||||
\(320\) | 318.950i | 0.0557182i | ||||||||
\(321\) | −3159.16 | −0.549306 | ||||||||
\(322\) | −3411.16 | −0.590362 | ||||||||
\(323\) | 2758.24i | 0.475147i | ||||||||
\(324\) | −268.107 | −0.0459717 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3864.19 | 0.656495 | ||||||||
\(327\) | 2475.55i | 0.418649i | ||||||||
\(328\) | 1683.83 | 0.283458 | ||||||||
\(329\) | 580.719 | 0.0973134 | ||||||||
\(330\) | 343.127i | 0.0572379i | ||||||||
\(331\) | 4634.51i | 0.769594i | 0.923001 | + | 0.384797i | \(0.125729\pi\) | ||||
−0.923001 | + | 0.384797i | \(0.874271\pi\) | |||||||
\(332\) | − 868.531i | − 0.143575i | ||||||||
\(333\) | − 1541.10i | − 0.253609i | ||||||||
\(334\) | 1517.77 | 0.248649 | ||||||||
\(335\) | 249.487 | 0.0406893 | ||||||||
\(336\) | 3377.17i | 0.548332i | ||||||||
\(337\) | −3029.82 | −0.489747 | −0.244874 | − | 0.969555i | \(-0.578746\pi\) | ||||
−0.244874 | + | 0.969555i | \(0.578746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2363.61 | −0.378684 | ||||||||
\(340\) | − 20.6355i | − 0.00329151i | ||||||||
\(341\) | −7321.47 | −1.16270 | ||||||||
\(342\) | −3712.48 | −0.586982 | ||||||||
\(343\) | 6463.66i | 1.01751i | ||||||||
\(344\) | 10596.9i | 1.66089i | ||||||||
\(345\) | − 151.587i | − 0.0236556i | ||||||||
\(346\) | − 11515.6i | − 1.78926i | ||||||||
\(347\) | 2841.60 | 0.439611 | 0.219805 | − | 0.975544i | \(-0.429458\pi\) | ||||
0.219805 | + | 0.975544i | \(0.429458\pi\) | |||||||
\(348\) | −932.351 | −0.143619 | ||||||||
\(349\) | 7565.68i | 1.16040i | 0.814472 | + | 0.580202i | \(0.197027\pi\) | ||||
−0.814472 | + | 0.580202i | \(0.802973\pi\) | |||||||
\(350\) | 5805.51 | 0.886622 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4159.76 | 0.629875 | ||||||||
\(353\) | 2339.44i | 0.352736i | 0.984324 | + | 0.176368i | \(0.0564348\pi\) | ||||
−0.984324 | + | 0.176368i | \(0.943565\pi\) | |||||||
\(354\) | −676.100 | −0.101509 | ||||||||
\(355\) | 304.204 | 0.0454802 | ||||||||
\(356\) | − 1668.43i | − 0.248389i | ||||||||
\(357\) | − 1711.00i | − 0.253658i | ||||||||
\(358\) | − 395.209i | − 0.0583449i | ||||||||
\(359\) | − 2531.68i | − 0.372192i | −0.982532 | − | 0.186096i | \(-0.940417\pi\) | ||||
0.982532 | − | 0.186096i | \(-0.0595835\pi\) | |||||||
\(360\) | 182.244 | 0.0266809 | ||||||||
\(361\) | −4798.45 | −0.699585 | ||||||||
\(362\) | 2744.31i | 0.398447i | ||||||||
\(363\) | 10538.5 | 1.52376 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 429.028 | 0.0615243 | ||||||||
\(366\) | − 8689.93i | − 1.24107i | ||||||||
\(367\) | 6577.81 | 0.935583 | 0.467792 | − | 0.883839i | \(-0.345050\pi\) | ||||
0.467792 | + | 0.883839i | \(0.345050\pi\) | |||||||
\(368\) | 3694.08 | 0.523280 | ||||||||
\(369\) | − 934.876i | − 0.131891i | ||||||||
\(370\) | − 165.145i | − 0.0232040i | ||||||||
\(371\) | 51.7426i | 0.00724081i | ||||||||
\(372\) | − 599.413i | − 0.0835433i | ||||||||
\(373\) | 2902.72 | 0.402942 | 0.201471 | − | 0.979495i | \(-0.435428\pi\) | ||||
0.201471 | + | 0.979495i | \(0.435428\pi\) | |||||||
\(374\) | 4236.40 | 0.585719 | ||||||||
\(375\) | 516.630i | 0.0711431i | ||||||||
\(376\) | −772.407 | −0.105941 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6935.16 | 0.943667 | ||||||||
\(379\) | 1865.73i | 0.252866i | 0.991975 | + | 0.126433i | \(0.0403529\pi\) | ||||
−0.991975 | + | 0.126433i | \(0.959647\pi\) | |||||||
\(380\) | 87.2140 | 0.0117736 | ||||||||
\(381\) | −2038.26 | −0.274076 | ||||||||
\(382\) | − 1734.69i | − 0.232342i | ||||||||
\(383\) | − 10836.0i | − 1.44567i | −0.691019 | − | 0.722837i | \(-0.742838\pi\) | ||||
0.691019 | − | 0.722837i | \(-0.257162\pi\) | |||||||
\(384\) | − 3466.78i | − 0.460712i | ||||||||
\(385\) | 660.813i | 0.0874757i | ||||||||
\(386\) | 3385.55 | 0.446425 | ||||||||
\(387\) | 5883.46 | 0.772798 | ||||||||
\(388\) | − 839.001i | − 0.109778i | ||||||||
\(389\) | 9520.34 | 1.24088 | 0.620438 | − | 0.784256i | \(-0.286955\pi\) | ||||
0.620438 | + | 0.784256i | \(0.286955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1871.56 | −0.242069 | ||||||||
\(392\) | − 304.480i | − 0.0392310i | ||||||||
\(393\) | −7577.13 | −0.972559 | ||||||||
\(394\) | −3246.43 | −0.415108 | ||||||||
\(395\) | 236.716i | 0.0301531i | ||||||||
\(396\) | − 1250.02i | − 0.158626i | ||||||||
\(397\) | − 10108.8i | − 1.27796i | −0.769225 | − | 0.638978i | \(-0.779358\pi\) | ||||
0.769225 | − | 0.638978i | \(-0.220642\pi\) | |||||||
\(398\) | 6138.10i | 0.773053i | ||||||||
\(399\) | 7231.41 | 0.907327 | ||||||||
\(400\) | −6287.01 | −0.785876 | ||||||||
\(401\) | 2084.38i | 0.259573i | 0.991542 | + | 0.129787i | \(0.0414292\pi\) | ||||
−0.991542 | + | 0.129787i | \(0.958571\pi\) | |||||||
\(402\) | −4193.32 | −0.520258 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1325.88 | −0.163279 | ||||||||
\(405\) | 104.666i | 0.0128417i | ||||||||
\(406\) | 8190.60 | 1.00121 | ||||||||
\(407\) | −7432.50 | −0.905197 | ||||||||
\(408\) | 2275.78i | 0.276147i | ||||||||
\(409\) | 9716.53i | 1.17470i | 0.809334 | + | 0.587349i | \(0.199828\pi\) | ||||
−0.809334 | + | 0.587349i | \(0.800172\pi\) | |||||||
\(410\) | − 100.182i | − 0.0120674i | ||||||||
\(411\) | 6663.95i | 0.799777i | ||||||||
\(412\) | 1338.78 | 0.160090 | ||||||||
\(413\) | −1302.07 | −0.155135 | ||||||||
\(414\) | − 2519.05i | − 0.299045i | ||||||||
\(415\) | −339.064 | −0.0401060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5503.54 | −0.646305 | ||||||||
\(418\) | 17904.8i | 2.09510i | ||||||||
\(419\) | 13381.9 | 1.56026 | 0.780129 | − | 0.625619i | \(-0.215153\pi\) | ||||
0.780129 | + | 0.625619i | \(0.215153\pi\) | |||||||
\(420\) | −54.1011 | −0.00628539 | ||||||||
\(421\) | 9463.37i | 1.09553i | 0.836633 | + | 0.547763i | \(0.184521\pi\) | ||||
−0.836633 | + | 0.547763i | \(0.815479\pi\) | |||||||
\(422\) | 234.520i | 0.0270527i | ||||||||
\(423\) | 428.846i | 0.0492936i | ||||||||
\(424\) | − 68.8221i | − 0.00788278i | ||||||||
\(425\) | 3185.24 | 0.363546 | ||||||||
\(426\) | −5112.98 | −0.581514 | ||||||||
\(427\) | − 16735.5i | − 1.89670i | ||||||||
\(428\) | 1233.30 | 0.139285 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 630.474 | 0.0707074 | ||||||||
\(431\) | − 4852.28i | − 0.542288i | −0.962539 | − | 0.271144i | \(-0.912598\pi\) | ||||
0.962539 | − | 0.271144i | \(-0.0874019\pi\) | |||||||
\(432\) | −7510.35 | −0.836439 | ||||||||
\(433\) | 8208.00 | 0.910973 | 0.455486 | − | 0.890243i | \(-0.349465\pi\) | ||||
0.455486 | + | 0.890243i | \(0.349465\pi\) | |||||||
\(434\) | 5265.78i | 0.582409i | ||||||||
\(435\) | 363.979i | 0.0401183i | ||||||||
\(436\) | − 966.425i | − 0.106155i | ||||||||
\(437\) | − 7910.01i | − 0.865874i | ||||||||
\(438\) | −7211.01 | −0.786656 | ||||||||
\(439\) | 2993.80 | 0.325481 | 0.162741 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162741 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(440\) | − 878.938i | − 0.0952311i | ||||||||
\(441\) | −169.049 | −0.0182539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9743.67 | 1.04500 | 0.522501 | − | 0.852639i | \(-0.324999\pi\) | ||||
0.522501 | + | 0.852639i | \(0.324999\pi\) | |||||||
\(444\) | − 608.503i | − 0.0650411i | ||||||||
\(445\) | −651.335 | −0.0693848 | ||||||||
\(446\) | −3164.59 | −0.335981 | ||||||||
\(447\) | − 10166.0i | − 1.07570i | ||||||||
\(448\) | − 10324.2i | − 1.08878i | ||||||||
\(449\) | − 561.459i | − 0.0590131i | −0.999565 | − | 0.0295065i | \(-0.990606\pi\) | ||||
0.999565 | − | 0.0295065i | \(-0.00939359\pi\) | |||||||
\(450\) | 4287.22i | 0.449114i | ||||||||
\(451\) | −4508.78 | −0.470754 | ||||||||
\(452\) | 922.726 | 0.0960207 | ||||||||
\(453\) | 3597.54i | 0.373128i | ||||||||
\(454\) | −8457.38 | −0.874283 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9618.40 | −0.987770 | ||||||||
\(457\) | − 13758.4i | − 1.40830i | −0.710054 | − | 0.704148i | \(-0.751329\pi\) | ||||
0.710054 | − | 0.704148i | \(-0.248671\pi\) | |||||||
\(458\) | 541.213 | 0.0552166 | ||||||||
\(459\) | 3805.03 | 0.386936 | ||||||||
\(460\) | 59.1779i | 0.00599823i | ||||||||
\(461\) | − 12009.2i | − 1.21329i | −0.794974 | − | 0.606644i | \(-0.792515\pi\) | ||||
0.794974 | − | 0.606644i | \(-0.207485\pi\) | |||||||
\(462\) | − 11106.8i | − 1.11847i | ||||||||
\(463\) | 13635.7i | 1.36870i | 0.729156 | + | 0.684348i | \(0.239913\pi\) | ||||
−0.729156 | + | 0.684348i | \(0.760087\pi\) | |||||||
\(464\) | −8869.91 | −0.887447 | ||||||||
\(465\) | −234.004 | −0.0233369 | ||||||||
\(466\) | − 657.613i | − 0.0653719i | ||||||||
\(467\) | −8821.95 | −0.874157 | −0.437079 | − | 0.899423i | \(-0.643987\pi\) | ||||
−0.437079 | + | 0.899423i | \(0.643987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8075.72 | −0.795100 | ||||||||
\(470\) | 45.9554i | 0.00451013i | ||||||||
\(471\) | 2081.37 | 0.203619 | ||||||||
\(472\) | 1731.87 | 0.168889 | ||||||||
\(473\) | − 28375.1i | − 2.75832i | ||||||||
\(474\) | − 3978.66i | − 0.385540i | ||||||||
\(475\) | 13462.2i | 1.30039i | ||||||||
\(476\) | 667.956i | 0.0643187i | ||||||||
\(477\) | −38.2105 | −0.00366780 | ||||||||
\(478\) | 9092.54 | 0.870049 | ||||||||
\(479\) | − 14620.0i | − 1.39459i | −0.716786 | − | 0.697293i | \(-0.754388\pi\) | ||||
0.716786 | − | 0.697293i | \(-0.245612\pi\) | |||||||
\(480\) | 132.951 | 0.0126424 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12884.9 | −1.21761 | ||||||||
\(483\) | 4906.78i | 0.462249i | ||||||||
\(484\) | −4114.09 | −0.386372 | ||||||||
\(485\) | −327.536 | −0.0306653 | ||||||||
\(486\) | 8542.20i | 0.797288i | ||||||||
\(487\) | 9798.86i | 0.911763i | 0.890040 | + | 0.455882i | \(0.150676\pi\) | ||||
−0.890040 | + | 0.455882i | \(0.849324\pi\) | |||||||
\(488\) | 22259.7i | 2.06486i | ||||||||
\(489\) | − 5558.43i | − 0.514030i | ||||||||
\(490\) | −18.1154 | −0.00167014 | ||||||||
\(491\) | 10836.1 | 0.995977 | 0.497989 | − | 0.867184i | \(-0.334072\pi\) | ||||
0.497989 | + | 0.867184i | \(0.334072\pi\) | |||||||
\(492\) | − 369.136i | − 0.0338251i | ||||||||
\(493\) | 4493.84 | 0.410532 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −487.993 | −0.0443104 | ||||||||
\(496\) | − 5702.51i | − 0.516230i | ||||||||
\(497\) | −9846.86 | −0.888717 | ||||||||
\(498\) | 5698.91 | 0.512800 | ||||||||
\(499\) | − 2589.96i | − 0.232349i | −0.993229 | − | 0.116175i | \(-0.962937\pi\) | ||||
0.993229 | − | 0.116175i | \(-0.0370633\pi\) | |||||||
\(500\) | − 201.686i | − 0.0180394i | ||||||||
\(501\) | − 2183.24i | − 0.194690i | ||||||||
\(502\) | − 1841.20i | − 0.163699i | ||||||||
\(503\) | −17067.5 | −1.51292 | −0.756462 | − | 0.654038i | \(-0.773074\pi\) | ||||
−0.756462 | + | 0.654038i | \(0.773074\pi\) | |||||||
\(504\) | −5899.12 | −0.521364 | ||||||||
\(505\) | 517.606i | 0.0456102i | ||||||||
\(506\) | −12149.0 | −1.06737 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 795.712 | 0.0694961 | ||||||||
\(509\) | 1012.89i | 0.0882038i | 0.999027 | + | 0.0441019i | \(0.0140426\pi\) | ||||
−0.999027 | + | 0.0441019i | \(0.985957\pi\) | |||||||
\(510\) | 135.401 | 0.0117562 | ||||||||
\(511\) | −13887.4 | −1.20223 | ||||||||
\(512\) | 12992.6i | 1.12148i | ||||||||
\(513\) | 16081.7i | 1.38406i | ||||||||
\(514\) | 3280.82i | 0.281539i | ||||||||
\(515\) | − 522.644i | − 0.0447193i | ||||||||
\(516\) | 2323.08 | 0.198194 | ||||||||
\(517\) | 2068.26 | 0.175942 | ||||||||
\(518\) | 5345.63i | 0.453424i | ||||||||
\(519\) | −16564.6 | −1.40098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14367.7 | −1.20818 | −0.604089 | − | 0.796917i | \(-0.706463\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(522\) | 6048.54i | 0.507160i | ||||||||
\(523\) | −16219.9 | −1.35611 | −0.678057 | − | 0.735010i | \(-0.737178\pi\) | ||||
−0.678057 | + | 0.735010i | \(0.737178\pi\) | |||||||
\(524\) | 2958.02 | 0.246607 | ||||||||
\(525\) | − 8350.92i | − 0.694217i | ||||||||
\(526\) | − 13385.5i | − 1.10957i | ||||||||
\(527\) | 2889.11i | 0.238808i | ||||||||
\(528\) | 12028.0i | 0.991382i | ||||||||
\(529\) | −6799.77 | −0.558870 | ||||||||
\(530\) | −4.09466 | −0.000335586 0 | ||||||||
\(531\) | − 961.545i | − 0.0785828i | ||||||||
\(532\) | −2823.06 | −0.230066 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10947.5 | 0.887161 | ||||||||
\(535\) | − 481.466i | − 0.0389076i | ||||||||
\(536\) | 10741.4 | 0.865593 | ||||||||
\(537\) | −568.488 | −0.0456835 | ||||||||
\(538\) | − 16506.1i | − 1.32273i | ||||||||
\(539\) | 815.301i | 0.0651530i | ||||||||
\(540\) | − 120.313i | − 0.00958788i | ||||||||
\(541\) | 17592.2i | 1.39806i | 0.715094 | + | 0.699029i | \(0.246384\pi\) | ||||
−0.715094 | + | 0.699029i | \(0.753616\pi\) | |||||||
\(542\) | −10066.7 | −0.797792 | ||||||||
\(543\) | 3947.55 | 0.311980 | ||||||||
\(544\) | − 1641.48i | − 0.129371i | ||||||||
\(545\) | −377.281 | −0.0296531 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10504.6 | 0.821103 | 0.410552 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410552 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(548\) | − 2601.53i | − 0.202795i | ||||||||
\(549\) | 12358.8 | 0.960763 | ||||||||
\(550\) | 20676.6 | 1.60301 | ||||||||
\(551\) | 18992.8i | 1.46846i | ||||||||
\(552\) | − 6526.44i | − 0.503231i | ||||||||
\(553\) | − 7662.33i | − 0.589214i | ||||||||
\(554\) | − 15073.2i | − 1.15596i | ||||||||
\(555\) | −237.552 | −0.0181685 | ||||||||
\(556\) | 2148.52 | 0.163880 | ||||||||
\(557\) | − 507.558i | − 0.0386102i | −0.999814 | − | 0.0193051i | \(-0.993855\pi\) | ||||
0.999814 | − | 0.0193051i | \(-0.00614539\pi\) | |||||||
\(558\) | −3888.64 | −0.295016 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −514.690 | −0.0388386 | ||||||||
\(561\) | − 6093.83i | − 0.458613i | ||||||||
\(562\) | 9041.75 | 0.678653 | ||||||||
\(563\) | 3443.14 | 0.257746 | 0.128873 | − | 0.991661i | \(-0.458864\pi\) | ||||
0.128873 | + | 0.991661i | \(0.458864\pi\) | |||||||
\(564\) | 169.330i | 0.0126420i | ||||||||
\(565\) | − 360.221i | − 0.0268223i | ||||||||
\(566\) | − 6688.21i | − 0.496690i | ||||||||
\(567\) | − 3387.96i | − 0.250936i | ||||||||
\(568\) | 13097.2 | 0.967509 | ||||||||
\(569\) | −23972.2 | −1.76620 | −0.883098 | − | 0.469189i | \(-0.844546\pi\) | ||||
−0.883098 | + | 0.469189i | \(0.844546\pi\) | |||||||
\(570\) | 572.260i | 0.0420514i | ||||||||
\(571\) | 7458.32 | 0.546622 | 0.273311 | − | 0.961926i | \(-0.411881\pi\) | ||||
0.273311 | + | 0.961926i | \(0.411881\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2495.26 | −0.181922 | ||||||||
\(574\) | 3242.82i | 0.235806i | ||||||||
\(575\) | −9134.57 | −0.662501 | ||||||||
\(576\) | 7624.14 | 0.551515 | ||||||||
\(577\) | − 5669.57i | − 0.409059i | −0.978860 | − | 0.204530i | \(-0.934434\pi\) | ||||
0.978860 | − | 0.204530i | \(-0.0655665\pi\) | |||||||
\(578\) | 10913.2i | 0.785344i | ||||||||
\(579\) | − 4869.94i | − 0.349547i | ||||||||
\(580\) | − 142.093i | − 0.0101726i | ||||||||
\(581\) | 10975.3 | 0.783702 | ||||||||
\(582\) | 5505.15 | 0.392089 | ||||||||
\(583\) | 184.284i | 0.0130914i | ||||||||
\(584\) | 18471.4 | 1.30882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14065.6 | −0.991541 | ||||||||
\(587\) | − 1017.39i | − 0.0715371i | −0.999360 | − | 0.0357685i | \(-0.988612\pi\) | ||||
0.999360 | − | 0.0357685i | \(-0.0113879\pi\) | |||||||
\(588\) | −66.7491 | −0.00468144 | ||||||||
\(589\) | −12210.6 | −0.854208 | ||||||||
\(590\) | − 103.040i | − 0.00718996i | ||||||||
\(591\) | 4669.81i | 0.325026i | ||||||||
\(592\) | − 5788.99i | − 0.401902i | ||||||||
\(593\) | − 10198.2i | − 0.706221i | −0.935582 | − | 0.353111i | \(-0.885124\pi\) | ||||
0.935582 | − | 0.353111i | \(-0.114876\pi\) | |||||||
\(594\) | 24699.9 | 1.70615 | ||||||||
\(595\) | 260.762 | 0.0179667 | ||||||||
\(596\) | 3968.70i | 0.272759i | ||||||||
\(597\) | 8829.33 | 0.605294 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12516.3 | 0.853763 | 0.426881 | − | 0.904308i | \(-0.359612\pi\) | ||||
0.426881 | + | 0.904308i | \(0.359612\pi\) | |||||||
\(600\) | 11107.4i | 0.755766i | ||||||||
\(601\) | 9627.46 | 0.653431 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(602\) | −20408.0 | −1.38168 | ||||||||
\(603\) | − 5963.70i | − 0.402754i | ||||||||
\(604\) | − 1404.44i | − 0.0946120i | ||||||||
\(605\) | 1606.09i | 0.107929i | ||||||||
\(606\) | − 8699.80i | − 0.583177i | ||||||||
\(607\) | 6667.20 | 0.445821 | 0.222910 | − | 0.974839i | \(-0.428444\pi\) | ||||
0.222910 | + | 0.974839i | \(0.428444\pi\) | |||||||
\(608\) | 6937.56 | 0.462755 | ||||||||
\(609\) | − 11781.7i | − 0.783942i | ||||||||
\(610\) | 1324.37 | 0.0879053 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −493.268 | −0.0325803 | ||||||||
\(613\) | 23085.4i | 1.52106i | 0.649302 | + | 0.760530i | \(0.275061\pi\) | ||||
−0.649302 | + | 0.760530i | \(0.724939\pi\) | |||||||
\(614\) | −18718.8 | −1.23034 | ||||||||
\(615\) | −144.106 | −0.00944866 | ||||||||
\(616\) | 28450.6i | 1.86089i | ||||||||
\(617\) | − 3049.24i | − 0.198959i | −0.995040 | − | 0.0994796i | \(-0.968282\pi\) | ||||
0.995040 | − | 0.0994796i | \(-0.0317178\pi\) | |||||||
\(618\) | 8784.48i | 0.571786i | ||||||||
\(619\) | 7296.58i | 0.473787i | 0.971536 | + | 0.236894i | \(0.0761293\pi\) | ||||
−0.971536 | + | 0.236894i | \(0.923871\pi\) | |||||||
\(620\) | 91.3523 | 0.00591741 | ||||||||
\(621\) | −10912.0 | −0.705126 | ||||||||
\(622\) | 20248.9i | 1.30531i | ||||||||
\(623\) | 21083.3 | 1.35583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15506.8 | 0.992438 | ||||||||
\(626\) | − 25621.7i | − 1.63586i | ||||||||
\(627\) | 25755.1 | 1.64044 | ||||||||
\(628\) | −812.543 | −0.0516305 | ||||||||
\(629\) | 2932.92i | 0.185920i | ||||||||
\(630\) | 350.976i | 0.0221956i | ||||||||
\(631\) | − 23829.5i | − 1.50339i | −0.659512 | − | 0.751694i | \(-0.729237\pi\) | ||||
0.659512 | − | 0.751694i | \(-0.270763\pi\) | |||||||
\(632\) | 10191.6i | 0.641453i | ||||||||
\(633\) | 337.345 | 0.0211821 | ||||||||
\(634\) | 15960.5 | 0.999801 | ||||||||
\(635\) | − 310.637i | − 0.0194130i | ||||||||
\(636\) | −15.0874 | −0.000940653 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29171.3 | 1.81019 | ||||||||
\(639\) | − 7271.65i | − 0.450175i | ||||||||
\(640\) | 528.347 | 0.0326324 | ||||||||
\(641\) | −13405.3 | −0.826016 | −0.413008 | − | 0.910727i | \(-0.635522\pi\) | ||||
−0.413008 | + | 0.910727i | \(0.635522\pi\) | |||||||
\(642\) | 8092.36i | 0.497477i | ||||||||
\(643\) | − 5251.51i | − 0.322083i | −0.986948 | − | 0.161042i | \(-0.948515\pi\) | ||||
0.986948 | − | 0.161042i | \(-0.0514853\pi\) | |||||||
\(644\) | − 1915.55i | − 0.117210i | ||||||||
\(645\) | − 906.904i | − 0.0553633i | ||||||||
\(646\) | 7065.37 | 0.430315 | ||||||||
\(647\) | −21611.4 | −1.31319 | −0.656595 | − | 0.754244i | \(-0.728004\pi\) | ||||
−0.656595 | + | 0.754244i | \(0.728004\pi\) | |||||||
\(648\) | 4506.28i | 0.273184i | ||||||||
\(649\) | −4637.39 | −0.280483 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7574.54 | 0.456021 | ||||||||
\(652\) | 2169.94i | 0.130340i | ||||||||
\(653\) | −21595.8 | −1.29420 | −0.647099 | − | 0.762406i | \(-0.724018\pi\) | ||||
−0.647099 | + | 0.762406i | \(0.724018\pi\) | |||||||
\(654\) | 6341.25 | 0.379148 | ||||||||
\(655\) | − 1154.78i | − 0.0688869i | ||||||||
\(656\) | − 3511.77i | − 0.209012i | ||||||||
\(657\) | − 10255.4i | − 0.608985i | ||||||||
\(658\) | − 1487.54i | − 0.0881314i | ||||||||
\(659\) | −16642.6 | −0.983768 | −0.491884 | − | 0.870661i | \(-0.663692\pi\) | ||||
−0.491884 | + | 0.870661i | \(0.663692\pi\) | |||||||
\(660\) | −192.684 | −0.0113640 | ||||||||
\(661\) | 26981.1i | 1.58766i | 0.608139 | + | 0.793831i | \(0.291916\pi\) | ||||
−0.608139 | + | 0.793831i | \(0.708084\pi\) | |||||||
\(662\) | 11871.5 | 0.696980 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14598.1 | −0.853185 | ||||||||
\(665\) | 1102.09i | 0.0642664i | ||||||||
\(666\) | −3947.60 | −0.229680 | ||||||||
\(667\) | −12887.3 | −0.748126 | ||||||||
\(668\) | 852.310i | 0.0493665i | ||||||||
\(669\) | 4552.09i | 0.263070i | ||||||||
\(670\) | − 639.074i | − 0.0368501i | ||||||||
\(671\) | − 59604.5i | − 3.42922i | ||||||||
\(672\) | −4303.55 | −0.247043 | ||||||||
\(673\) | −11149.2 | −0.638591 | −0.319296 | − | 0.947655i | \(-0.603446\pi\) | ||||
−0.319296 | + | 0.947655i | \(0.603446\pi\) | |||||||
\(674\) | 7761.04i | 0.443537i | ||||||||
\(675\) | 18571.3 | 1.05898 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3314.33 | 0.188154 | 0.0940769 | − | 0.995565i | \(-0.470010\pi\) | ||||
0.0940769 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(678\) | 6054.51i | 0.342953i | ||||||||
\(679\) | 10602.1 | 0.599223 | ||||||||
\(680\) | −346.836 | −0.0195596 | ||||||||
\(681\) | 12165.5i | 0.684556i | ||||||||
\(682\) | 18754.3i | 1.05299i | ||||||||
\(683\) | 24505.2i | 1.37287i | 0.727193 | + | 0.686433i | \(0.240824\pi\) | ||||
−0.727193 | + | 0.686433i | \(0.759176\pi\) | |||||||
\(684\) | − 2084.75i | − 0.116539i | ||||||||
\(685\) | −1015.61 | −0.0566486 | ||||||||
\(686\) | 16557.0 | 0.921500 | ||||||||
\(687\) | − 778.506i | − 0.0432342i | ||||||||
\(688\) | 22100.6 | 1.22468 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −388.299 | −0.0214236 | ||||||||
\(691\) | 21752.8i | 1.19756i | 0.800912 | + | 0.598782i | \(0.204348\pi\) | ||||
−0.800912 | + | 0.598782i | \(0.795652\pi\) | |||||||
\(692\) | 6466.64 | 0.355238 | ||||||||
\(693\) | 15796.0 | 0.865858 | ||||||||
\(694\) | − 7278.90i | − 0.398132i | ||||||||
\(695\) | − 838.755i | − 0.0457781i | ||||||||
\(696\) | 15670.7i | 0.853445i | ||||||||
\(697\) | 1779.20i | 0.0966887i | ||||||||
\(698\) | 19379.9 | 1.05092 | ||||||||
\(699\) | −945.941 | −0.0511857 | ||||||||
\(700\) | 3260.10i | 0.176029i | ||||||||
\(701\) | −34250.9 | −1.84542 | −0.922709 | − | 0.385496i | \(-0.874030\pi\) | ||||
−0.922709 | + | 0.385496i | \(0.874030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12395.8 | −0.665028 | ||||||||
\(704\) | − 36770.1i | − 1.96850i | ||||||||
\(705\) | 66.1043 | 0.00353140 | ||||||||
\(706\) | 5992.59 | 0.319454 | ||||||||
\(707\) | − 16754.6i | − 0.891259i | ||||||||
\(708\) | − 379.666i | − 0.0201536i | ||||||||
\(709\) | − 5527.11i | − 0.292771i | −0.989228 | − | 0.146386i | \(-0.953236\pi\) | ||||
0.989228 | − | 0.146386i | \(-0.0467641\pi\) | |||||||
\(710\) | − 779.234i | − 0.0411889i | ||||||||
\(711\) | 5658.43 | 0.298464 | ||||||||
\(712\) | −28042.6 | −1.47604 | ||||||||
\(713\) | − 8285.33i | − 0.435187i | ||||||||
\(714\) | −4382.83 | −0.229724 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 221.931 | 0.0115837 | ||||||||
\(717\) | − 13079.1i | − 0.681241i | ||||||||
\(718\) | −6485.02 | −0.337074 | ||||||||
\(719\) | 3777.78 | 0.195949 | 0.0979745 | − | 0.995189i | \(-0.468764\pi\) | ||||
0.0979745 | + | 0.995189i | \(0.468764\pi\) | |||||||
\(720\) | − 380.085i | − 0.0196735i | ||||||||
\(721\) | 16917.6i | 0.873849i | ||||||||
\(722\) | 12291.5i | 0.633576i | ||||||||
\(723\) | 18534.2i | 0.953380i | ||||||||
\(724\) | −1541.08 | −0.0791072 | ||||||||
\(725\) | 21933.2 | 1.12355 | ||||||||
\(726\) | − 26994.8i | − 1.37999i | ||||||||
\(727\) | −19076.8 | −0.973204 | −0.486602 | − | 0.873624i | \(-0.661764\pi\) | ||||
−0.486602 | + | 0.873624i | \(0.661764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17319.9 | 0.879944 | ||||||||
\(730\) | − 1098.98i | − 0.0557192i | ||||||||
\(731\) | −11197.0 | −0.566535 | ||||||||
\(732\) | 4879.86 | 0.246400 | ||||||||
\(733\) | − 7997.30i | − 0.402984i | −0.979490 | − | 0.201492i | \(-0.935421\pi\) | ||||
0.979490 | − | 0.201492i | \(-0.0645790\pi\) | |||||||
\(734\) | − 16849.4i | − 0.847307i | ||||||||
\(735\) | 26.0581i | 0.00130771i | ||||||||
\(736\) | 4707.39i | 0.235756i | ||||||||
\(737\) | −28762.1 | −1.43754 | ||||||||
\(738\) | −2394.74 | −0.119446 | ||||||||
\(739\) | 28983.6i | 1.44273i | 0.692553 | + | 0.721367i | \(0.256486\pi\) | ||||
−0.692553 | + | 0.721367i | \(0.743514\pi\) | |||||||
\(740\) | 92.7376 | 0.00460689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 132.541 | 0.00655761 | ||||||||
\(743\) | 19145.4i | 0.945324i | 0.881244 | + | 0.472662i | \(0.156707\pi\) | ||||
−0.881244 | + | 0.472662i | \(0.843293\pi\) | |||||||
\(744\) | −10074.8 | −0.496451 | ||||||||
\(745\) | 1549.33 | 0.0761923 | ||||||||
\(746\) | − 7435.47i | − 0.364922i | ||||||||
\(747\) | 8104.95i | 0.396981i | ||||||||
\(748\) | 2378.96i | 0.116288i | ||||||||
\(749\) | 15584.7i | 0.760284i | ||||||||
\(750\) | 1323.38 | 0.0644304 | ||||||||
\(751\) | 25516.9 | 1.23985 | 0.619923 | − | 0.784663i | \(-0.287164\pi\) | ||||
0.619923 | + | 0.784663i | \(0.287164\pi\) | |||||||
\(752\) | 1610.92i | 0.0781172i | ||||||||
\(753\) | −2648.47 | −0.128175 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −548.275 | −0.0264288 | ||||||||
\(756\) | 3894.46i | 0.187355i | ||||||||
\(757\) | −17230.6 | −0.827289 | −0.413645 | − | 0.910438i | \(-0.635744\pi\) | ||||
−0.413645 | + | 0.910438i | \(0.635744\pi\) | |||||||
\(758\) | 4779.17 | 0.229007 | ||||||||
\(759\) | 17475.7i | 0.835744i | ||||||||
\(760\) | − 1465.87i | − 0.0699642i | ||||||||
\(761\) | − 2343.06i | − 0.111611i | −0.998442 | − | 0.0558053i | \(-0.982227\pi\) | ||||
0.998442 | − | 0.0558053i | \(-0.0177726\pi\) | |||||||
\(762\) | 5221.11i | 0.248216i | ||||||||
\(763\) | 12212.3 | 0.579444 | ||||||||
\(764\) | 974.121 | 0.0461289 | ||||||||
\(765\) | 192.566i | 0.00910096i | ||||||||
\(766\) | −27756.9 | −1.30927 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 7862.11 | 0.369400 | ||||||||
\(769\) | 7100.18i | 0.332950i | 0.986046 | + | 0.166475i | \(0.0532386\pi\) | ||||
−0.986046 | + | 0.166475i | \(0.946761\pi\) | |||||||
\(770\) | 1692.71 | 0.0792219 | ||||||||
\(771\) | 4719.29 | 0.220442 | ||||||||
\(772\) | 1901.17i | 0.0886328i | ||||||||
\(773\) | − 12270.4i | − 0.570940i | −0.958388 | − | 0.285470i | \(-0.907850\pi\) | ||||
0.958388 | − | 0.285470i | \(-0.0921498\pi\) | |||||||
\(774\) | − 15070.8i | − 0.699881i | ||||||||
\(775\) | 14100.9i | 0.653575i | ||||||||
\(776\) | −14101.7 | −0.652349 | ||||||||
\(777\) | 7689.40 | 0.355027 | ||||||||
\(778\) | − 24386.9i | − 1.12379i | ||||||||
\(779\) | −7519.64 | −0.345852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35070.1 | −1.60680 | ||||||||
\(782\) | 4794.11i | 0.219229i | ||||||||
\(783\) | 26201.0 | 1.19584 | ||||||||
\(784\) | −635.017 | −0.0289275 | ||||||||
\(785\) | 317.207i | 0.0144224i | ||||||||
\(786\) | 19409.2i | 0.880794i | ||||||||
\(787\) | 3425.04i | 0.155133i | 0.996987 | + | 0.0775663i | \(0.0247150\pi\) | ||||
−0.996987 | + | 0.0775663i | \(0.975285\pi\) | |||||||
\(788\) | − 1823.04i | − 0.0824151i | ||||||||
\(789\) | −19254.3 | −0.868787 | ||||||||
\(790\) | 606.360 | 0.0273080 | ||||||||
\(791\) | 11660.1i | 0.524129i | ||||||||
\(792\) | −21010.0 | −0.942624 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25894.3 | −1.15737 | ||||||||
\(795\) | 5.88995i | 0 0.000262761i | ||||||||
\(796\) | −3446.87 | −0.153481 | ||||||||
\(797\) | 11781.1 | 0.523600 | 0.261800 | − | 0.965122i | \(-0.415684\pi\) | ||||
0.261800 | + | 0.965122i | \(0.415684\pi\) | |||||||
\(798\) | − 18523.6i | − 0.821717i | ||||||||
\(799\) | − 816.154i | − 0.0361370i | ||||||||
\(800\) | − 8011.58i | − 0.354065i | ||||||||
\(801\) | 15569.4i | 0.686790i | ||||||||
\(802\) | 5339.24 | 0.235081 | ||||||||
\(803\) | −49460.6 | −2.17363 | ||||||||
\(804\) | − 2354.77i | − 0.103291i | ||||||||
\(805\) | −747.807 | −0.0327413 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23743.2 | −1.03569 | ||||||||
\(808\) | 22285.0i | 0.970276i | ||||||||
\(809\) | 18910.1 | 0.821810 | 0.410905 | − | 0.911678i | \(-0.365213\pi\) | ||||
0.410905 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(810\) | 268.107 | 0.0116300 | ||||||||
\(811\) | − 12803.3i | − 0.554359i | −0.960818 | − | 0.277180i | \(-0.910600\pi\) | ||||
0.960818 | − | 0.277180i | \(-0.0893997\pi\) | |||||||
\(812\) | 4599.45i | 0.198780i | ||||||||
\(813\) | 14480.5i | 0.624664i | ||||||||
\(814\) | 19038.7i | 0.819788i | ||||||||
\(815\) | 847.121 | 0.0364090 | ||||||||
\(816\) | 4746.33 | 0.203621 | ||||||||
\(817\) | − 47323.3i | − 2.02648i | ||||||||
\(818\) | 24889.4 | 1.06386 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56.2574 | 0.00239585 | ||||||||
\(821\) | − 19335.1i | − 0.821923i | −0.911653 | − | 0.410962i | \(-0.865193\pi\) | ||||
0.911653 | − | 0.410962i | \(-0.134807\pi\) | |||||||
\(822\) | 17070.1 | 0.724315 | ||||||||
\(823\) | 2125.90 | 0.0900417 | 0.0450209 | − | 0.998986i | \(-0.485665\pi\) | ||||
0.0450209 | + | 0.998986i | \(0.485665\pi\) | |||||||
\(824\) | − 22501.9i | − 0.951324i | ||||||||
\(825\) | − 29742.2i | − 1.25514i | ||||||||
\(826\) | 3335.32i | 0.140497i | ||||||||
\(827\) | − 6989.24i | − 0.293881i | −0.989145 | − | 0.146941i | \(-0.953057\pi\) | ||||
0.989145 | − | 0.146941i | \(-0.0469426\pi\) | |||||||
\(828\) | 1414.58 | 0.0593721 | ||||||||
\(829\) | 32649.7 | 1.36788 | 0.683938 | − | 0.729540i | \(-0.260266\pi\) | ||||
0.683938 | + | 0.729540i | \(0.260266\pi\) | |||||||
\(830\) | 868.531i | 0.0363219i | ||||||||
\(831\) | −21682.0 | −0.905103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 321.724 | 0.0133819 | ||||||||
\(834\) | 14097.6i | 0.585324i | ||||||||
\(835\) | 332.732 | 0.0137900 | ||||||||
\(836\) | −10054.5 | −0.415958 | ||||||||
\(837\) | 16844.7i | 0.695626i | ||||||||
\(838\) | − 34278.4i | − 1.41304i | ||||||||
\(839\) | − 4038.23i | − 0.166168i | −0.996543 | − | 0.0830841i | \(-0.973523\pi\) | ||||
0.996543 | − | 0.0830841i | \(-0.0264770\pi\) | |||||||
\(840\) | 909.318i | 0.0373505i | ||||||||
\(841\) | 6555.00 | 0.268769 | ||||||||
\(842\) | 24240.9 | 0.992159 | ||||||||
\(843\) | − 13006.1i | − 0.531380i | ||||||||
\(844\) | −131.695 | −0.00537102 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1098.51 | 0.0446426 | ||||||||
\(847\) | − 51988.1i | − 2.10901i | ||||||||
\(848\) | −143.534 | −0.00581248 | ||||||||
\(849\) | −9620.64 | −0.388904 | ||||||||
\(850\) | − 8159.17i | − 0.329244i | ||||||||
\(851\) | − 8410.97i | − 0.338807i | ||||||||
\(852\) | − 2871.21i | − 0.115453i | ||||||||
\(853\) | 8114.12i | 0.325700i | 0.986651 | + | 0.162850i | \(0.0520687\pi\) | ||||
−0.986651 | + | 0.162850i | \(0.947931\pi\) | |||||||
\(854\) | −42869.0 | −1.71774 | ||||||||
\(855\) | −813.863 | −0.0325538 | ||||||||
\(856\) | − 20729.0i | − 0.827690i | ||||||||
\(857\) | 22298.1 | 0.888786 | 0.444393 | − | 0.895832i | \(-0.353419\pi\) | ||||
0.444393 | + | 0.895832i | \(0.353419\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33550.5 | 1.33263 | 0.666315 | − | 0.745670i | \(-0.267870\pi\) | ||||
0.666315 | + | 0.745670i | \(0.267870\pi\) | |||||||
\(860\) | 354.045i | 0.0140382i | ||||||||
\(861\) | 4664.62 | 0.184634 | ||||||||
\(862\) | −12429.4 | −0.491121 | ||||||||
\(863\) | 14120.5i | 0.556972i | 0.960440 | + | 0.278486i | \(0.0898326\pi\) | ||||
−0.960440 | + | 0.278486i | \(0.910167\pi\) | |||||||
\(864\) | − 9570.49i | − 0.376846i | ||||||||
\(865\) | − 2524.50i | − 0.0992319i | ||||||||
\(866\) | − 21025.2i | − 0.825018i | ||||||||
\(867\) | 15698.1 | 0.614918 | ||||||||
\(868\) | −2957.01 | −0.115631 | ||||||||
\(869\) | − 27289.8i | − 1.06530i | ||||||||
\(870\) | 932.351 | 0.0363329 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16243.4 | −0.630817 | ||||||||
\(873\) | 7829.39i | 0.303533i | ||||||||
\(874\) | −20261.9 | −0.784175 | ||||||||
\(875\) | 2548.63 | 0.0984679 | ||||||||
\(876\) | − 4049.36i | − 0.156182i | ||||||||
\(877\) | 1941.69i | 0.0747619i | 0.999301 | + | 0.0373809i | \(0.0119015\pi\) | ||||
−0.999301 | + | 0.0373809i | \(0.988099\pi\) | |||||||
\(878\) | − 7668.78i | − 0.294771i | ||||||||
\(879\) | 20232.6i | 0.776368i | ||||||||
\(880\) | −1833.10 | −0.0702201 | ||||||||
\(881\) | 790.231 | 0.0302197 | 0.0151099 | − | 0.999886i | \(-0.495190\pi\) | ||||
0.0151099 | + | 0.999886i | \(0.495190\pi\) | |||||||
\(882\) | 433.029i | 0.0165316i | ||||||||
\(883\) | 36638.6 | 1.39636 | 0.698180 | − | 0.715922i | \(-0.253993\pi\) | ||||
0.698180 | + | 0.715922i | \(0.253993\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −148.217 | −0.00562968 | ||||||||
\(886\) | − 24958.9i | − 0.946401i | ||||||||
\(887\) | −40686.3 | −1.54015 | −0.770075 | − | 0.637954i | \(-0.779781\pi\) | ||||
−0.770075 | + | 0.637954i | \(0.779781\pi\) | |||||||
\(888\) | −10227.6 | −0.386503 | ||||||||
\(889\) | 10055.1i | 0.379344i | ||||||||
\(890\) | 1668.43i | 0.0628381i | ||||||||
\(891\) | − 12066.4i | − 0.453692i | ||||||||
\(892\) | − 1777.08i | − 0.0667053i | ||||||||
\(893\) | 3449.40 | 0.129261 | ||||||||
\(894\) | −26040.9 | −0.974202 | ||||||||
\(895\) | − 86.6392i | − 0.00323579i | ||||||||
\(896\) | −17102.2 | −0.637663 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1438.21 | −0.0534449 | ||||||||
\(899\) | 19894.0i | 0.738046i | ||||||||
\(900\) | −2407.50 | −0.0891666 | ||||||||
\(901\) | 72.7200 | 0.00268885 | ||||||||
\(902\) | 11549.5i | 0.426336i | ||||||||
\(903\) | 29355.9i | 1.08184i | ||||||||
\(904\) | − 15509.0i | − 0.570598i | ||||||||
\(905\) | 601.618i | 0.0220977i | ||||||||
\(906\) | 9215.28 | 0.337922 | ||||||||
\(907\) | 10464.4 | 0.383093 | 0.191547 | − | 0.981484i | \(-0.438650\pi\) | ||||
0.191547 | + | 0.981484i | \(0.438650\pi\) | |||||||
\(908\) | − 4749.26i | − 0.173579i | ||||||||
\(909\) | 12372.8 | 0.451463 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35611.5 | −1.29513 | −0.647563 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647563 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(912\) | 20060.0i | 0.728346i | ||||||||
\(913\) | 39089.0 | 1.41693 | ||||||||
\(914\) | −35242.9 | −1.27542 | ||||||||
\(915\) | − 1905.04i | − 0.0688291i | ||||||||
\(916\) | 303.920i | 0.0109627i | ||||||||
\(917\) | 37379.4i | 1.34610i | ||||||||
\(918\) | − 9746.80i | − 0.350427i | ||||||||
\(919\) | 1077.25 | 0.0386674 | 0.0193337 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193337 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(920\) | 994.648 | 0.0356441 | ||||||||
\(921\) | 26926.0i | 0.963346i | ||||||||
\(922\) | −30762.3 | −1.09881 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 6237.04 | 0.222060 | ||||||||
\(925\) | 14314.8i | 0.508829i | ||||||||
\(926\) | 34928.6 | 1.23955 | ||||||||
\(927\) | −12493.2 | −0.442644 | ||||||||
\(928\) | − 11303.0i | − 0.399826i | ||||||||
\(929\) | − 55733.8i | − 1.96832i | −0.177290 | − | 0.984159i | \(-0.556733\pi\) | ||||
0.177290 | − | 0.984159i | \(-0.443267\pi\) | |||||||
\(930\) | 599.413i | 0.0211350i | ||||||||
\(931\) | 1359.74i | 0.0478665i | ||||||||
\(932\) | 369.284 | 0.0129789 | ||||||||
\(933\) | 29126.9 | 1.02205 | ||||||||
\(934\) | 22597.9i | 0.791677i | ||||||||
\(935\) | 928.718 | 0.0324838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3198.60 | −0.111519 | −0.0557596 | − | 0.998444i | \(-0.517758\pi\) | ||||
−0.0557596 | + | 0.998444i | \(0.517758\pi\) | |||||||
\(938\) | 20686.4i | 0.720079i | ||||||||
\(939\) | −36855.4 | −1.28086 | ||||||||
\(940\) | −25.8064 | −0.000895437 0 | ||||||||
\(941\) | − 8823.35i | − 0.305667i | −0.988252 | − | 0.152834i | \(-0.951160\pi\) | ||||
0.988252 | − | 0.152834i | \(-0.0488399\pi\) | |||||||
\(942\) | − 5331.54i | − 0.184407i | ||||||||
\(943\) | − 5102.35i | − 0.176199i | ||||||||
\(944\) | − 3611.95i | − 0.124533i | ||||||||
\(945\) | 1520.35 | 0.0523354 | ||||||||
\(946\) | −72684.3 | −2.49806 | ||||||||
\(947\) | 28290.4i | 0.970766i | 0.874301 | + | 0.485383i | \(0.161320\pi\) | ||||
−0.874301 | + | 0.485383i | \(0.838680\pi\) | |||||||
\(948\) | 2234.23 | 0.0765447 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 34484.0 | 1.17769 | ||||||||
\(951\) | − 22958.4i | − 0.782836i | ||||||||
\(952\) | 11226.8 | 0.382210 | ||||||||
\(953\) | 12399.0 | 0.421452 | 0.210726 | − | 0.977545i | \(-0.432417\pi\) | ||||
0.210726 | + | 0.977545i | \(0.432417\pi\) | |||||||
\(954\) | 97.8783i | 0.00332173i | ||||||||
\(955\) | − 380.285i | − 0.0128856i | ||||||||
\(956\) | 5105.94i | 0.172739i | ||||||||
\(957\) | − 41961.3i | − 1.41736i | ||||||||
\(958\) | −37450.0 | −1.26300 | ||||||||
\(959\) | 32874.5 | 1.10696 | ||||||||
\(960\) | − 1175.22i | − 0.0395105i | ||||||||
\(961\) | 17001.0 | 0.570676 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11508.9 | −0.385118 | ||||||||
\(964\) | − 7235.53i | − 0.241744i | ||||||||
\(965\) | 742.193 | 0.0247586 | ||||||||
\(966\) | 12569.0 | 0.418634 | ||||||||
\(967\) | 26667.1i | 0.886820i | 0.896319 | + | 0.443410i | \(0.146231\pi\) | ||||
−0.896319 | + | 0.443410i | \(0.853769\pi\) | |||||||
\(968\) | 69148.6i | 2.29599i | ||||||||
\(969\) | − 10163.2i | − 0.336933i | ||||||||
\(970\) | 839.001i | 0.0277719i | ||||||||
\(971\) | 49420.7 | 1.63335 | 0.816676 | − | 0.577096i | \(-0.195814\pi\) | ||||
0.816676 | + | 0.577096i | \(0.195814\pi\) | |||||||
\(972\) | −4796.89 | −0.158293 | ||||||||
\(973\) | 27149.9i | 0.894539i | ||||||||
\(974\) | 25100.3 | 0.825735 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46424.5 | 1.52255 | ||||||||
\(977\) | − 778.759i | − 0.0255012i | −0.999919 | − | 0.0127506i | \(-0.995941\pi\) | ||||
0.999919 | − | 0.0127506i | \(-0.00405876\pi\) | |||||||
\(978\) | −14238.2 | −0.465529 | ||||||||
\(979\) | 75089.2 | 2.45134 | ||||||||
\(980\) | − 10.1728i | 0 0.000331589i | ||||||||
\(981\) | 9018.48i | 0.293515i | ||||||||
\(982\) | − 27757.2i | − 0.902003i | ||||||||
\(983\) | 5997.90i | 0.194612i | 0.995255 | + | 0.0973059i | \(0.0310225\pi\) | ||||
−0.995255 | + | 0.0973059i | \(0.968977\pi\) | |||||||
\(984\) | −6204.35 | −0.201004 | ||||||||
\(985\) | −711.693 | −0.0230218 | ||||||||
\(986\) | − 11511.2i | − 0.371797i | ||||||||
\(987\) | −2139.75 | −0.0690062 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32110.6 | 1.03241 | ||||||||
\(990\) | 1250.02i | 0.0401295i | ||||||||
\(991\) | 8974.94 | 0.287688 | 0.143844 | − | 0.989600i | \(-0.454054\pi\) | ||||
0.143844 | + | 0.989600i | \(0.454054\pi\) | |||||||
\(992\) | 7266.75 | 0.232580 | ||||||||
\(993\) | − 17076.6i | − 0.545729i | ||||||||
\(994\) | 25223.3i | 0.804863i | ||||||||
\(995\) | 1345.62i | 0.0428732i | ||||||||
\(996\) | 3200.24i | 0.101811i | ||||||||
\(997\) | 28530.2 | 0.906280 | 0.453140 | − | 0.891439i | \(-0.350304\pi\) | ||||
0.453140 | + | 0.891439i | \(0.350304\pi\) | |||||||
\(998\) | −6634.31 | −0.210426 | ||||||||
\(999\) | 17100.2i | 0.541567i |
(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 | 169.4.b.f.168.1 | 4 | ||
13.2 | odd | 12 | 169.4.c.j.22.2 | 4 | |||
13.3 | even | 3 | 169.4.e.f.147.4 | 8 | |||
13.4 | even | 6 | 169.4.e.f.23.4 | 8 | |||
13.5 | odd | 4 | 169.4.a.g.1.1 | 2 | |||
13.6 | odd | 12 | 169.4.c.j.146.2 | 4 | |||
13.7 | odd | 12 | 169.4.c.g.146.1 | 4 | |||
13.8 | odd | 4 | 13.4.a.b.1.2 | ✓ | 2 | ||
13.9 | even | 3 | 169.4.e.f.23.1 | 8 | |||
13.10 | even | 6 | 169.4.e.f.147.1 | 8 | |||
13.11 | odd | 12 | 169.4.c.g.22.1 | 4 | |||
13.12 | even | 2 | inner | 169.4.b.f.168.4 | 4 | ||
39.5 | even | 4 | 1521.4.a.r.1.2 | 2 | |||
39.8 | even | 4 | 117.4.a.d.1.1 | 2 | |||
52.47 | even | 4 | 208.4.a.h.1.2 | 2 | |||
65.8 | even | 4 | 325.4.b.e.274.1 | 4 | |||
65.34 | odd | 4 | 325.4.a.f.1.1 | 2 | |||
65.47 | even | 4 | 325.4.b.e.274.4 | 4 | |||
91.34 | even | 4 | 637.4.a.b.1.2 | 2 | |||
104.21 | odd | 4 | 832.4.a.s.1.2 | 2 | |||
104.99 | even | 4 | 832.4.a.z.1.1 | 2 | |||
143.21 | even | 4 | 1573.4.a.b.1.1 | 2 | |||
156.47 | odd | 4 | 1872.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.2 | ✓ | 2 | 13.8 | odd | 4 | ||
117.4.a.d.1.1 | 2 | 39.8 | even | 4 | |||
169.4.a.g.1.1 | 2 | 13.5 | odd | 4 | |||
169.4.b.f.168.1 | 4 | 1.1 | even | 1 | trivial | ||
169.4.b.f.168.4 | 4 | 13.12 | even | 2 | inner | ||
169.4.c.g.22.1 | 4 | 13.11 | odd | 12 | |||
169.4.c.g.146.1 | 4 | 13.7 | odd | 12 | |||
169.4.c.j.22.2 | 4 | 13.2 | odd | 12 | |||
169.4.c.j.146.2 | 4 | 13.6 | odd | 12 | |||
169.4.e.f.23.1 | 8 | 13.9 | even | 3 | |||
169.4.e.f.23.4 | 8 | 13.4 | even | 6 | |||
169.4.e.f.147.1 | 8 | 13.10 | even | 6 | |||
169.4.e.f.147.4 | 8 | 13.3 | even | 3 | |||
208.4.a.h.1.2 | 2 | 52.47 | even | 4 | |||
325.4.a.f.1.1 | 2 | 65.34 | odd | 4 | |||
325.4.b.e.274.1 | 4 | 65.8 | even | 4 | |||
325.4.b.e.274.4 | 4 | 65.47 | even | 4 | |||
637.4.a.b.1.2 | 2 | 91.34 | even | 4 | |||
832.4.a.s.1.2 | 2 | 104.21 | odd | 4 | |||
832.4.a.z.1.1 | 2 | 104.99 | even | 4 | |||
1521.4.a.r.1.2 | 2 | 39.5 | even | 4 | |||
1573.4.a.b.1.1 | 2 | 143.21 | even | 4 | |||
1872.4.a.bb.1.1 | 2 | 156.47 | odd | 4 |