Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,4,Mod(199,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.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: | \(16.2255252516\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.199 |
Dual form | 275.4.b.c.199.1 |
$q$-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 \(\left(\mathbb{Z}/275\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.73205i | 0.965926i | 0.875641 | + | 0.482963i | \(0.160439\pi\) | ||||
−0.875641 | + | 0.482963i | \(0.839561\pi\) | |||||||
\(3\) | 7.92820i | 1.52578i | 0.646526 | + | 0.762892i | \(0.276221\pi\) | ||||
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(4\) | 0.535898 | 0.0669873 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −21.6603 | −1.47379 | ||||||||
\(7\) | 3.07180i | 0.165861i | 0.996555 | + | 0.0829307i | \(0.0264280\pi\) | ||||
−0.996555 | + | 0.0829307i | \(0.973572\pi\) | |||||||
\(8\) | 23.3205i | 1.03063i | ||||||||
\(9\) | −35.8564 | −1.32802 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 4.24871i | 0.102208i | ||||||||
\(13\) | − 5.35898i | − 0.114332i | −0.998365 | − | 0.0571659i | \(-0.981794\pi\) | ||||
0.998365 | − | 0.0571659i | \(-0.0182064\pi\) | |||||||
\(14\) | −8.39230 | −0.160210 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −59.4256 | −0.928525 | ||||||||
\(17\) | − 41.2154i | − 0.588012i | −0.955804 | − | 0.294006i | \(-0.905011\pi\) | ||||
0.955804 | − | 0.294006i | \(-0.0949885\pi\) | |||||||
\(18\) | − 97.9615i | − 1.28276i | ||||||||
\(19\) | −139.923 | −1.68950 | −0.844751 | − | 0.535159i | \(-0.820252\pi\) | ||||
−0.844751 | + | 0.535159i | \(0.820252\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.3538 | −0.253069 | ||||||||
\(22\) | − 30.0526i | − 0.291238i | ||||||||
\(23\) | 111.354i | 1.00952i | 0.863261 | + | 0.504758i | \(0.168418\pi\) | ||||
−0.863261 | + | 0.504758i | \(0.831582\pi\) | |||||||
\(24\) | −184.890 | −1.57252 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.6410 | 0.110436 | ||||||||
\(27\) | − 70.2154i | − 0.500480i | ||||||||
\(28\) | 1.64617i | 0.0111106i | ||||||||
\(29\) | 24.9948 | 0.160049 | 0.0800246 | − | 0.996793i | \(-0.474500\pi\) | ||||
0.0800246 | + | 0.996793i | \(0.474500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.4974 | 0.182487 | 0.0912436 | − | 0.995829i | \(-0.470916\pi\) | ||||
0.0912436 | + | 0.995829i | \(0.470916\pi\) | |||||||
\(32\) | 24.2102i | 0.133744i | ||||||||
\(33\) | − 87.2102i | − 0.460041i | ||||||||
\(34\) | 112.603 | 0.567976 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19.2154 | −0.0889601 | ||||||||
\(37\) | 13.1436i | 0.0583998i | 0.999574 | + | 0.0291999i | \(0.00929594\pi\) | ||||
−0.999574 | + | 0.0291999i | \(0.990704\pi\) | |||||||
\(38\) | − 382.277i | − 1.63193i | ||||||||
\(39\) | 42.4871 | 0.174446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 261.072 | 0.994453 | 0.497226 | − | 0.867621i | \(-0.334352\pi\) | ||||
0.497226 | + | 0.867621i | \(0.334352\pi\) | |||||||
\(42\) | − 66.5359i | − 0.244446i | ||||||||
\(43\) | 57.7128i | 0.204677i | 0.994750 | + | 0.102339i | \(0.0326325\pi\) | ||||
−0.994750 | + | 0.102339i | \(0.967367\pi\) | |||||||
\(44\) | −5.89488 | −0.0201974 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −304.224 | −0.975118 | ||||||||
\(47\) | − 343.846i | − 1.06713i | −0.845759 | − | 0.533565i | \(-0.820852\pi\) | ||||
0.845759 | − | 0.533565i | \(-0.179148\pi\) | |||||||
\(48\) | − 471.138i | − 1.41673i | ||||||||
\(49\) | 333.564 | 0.972490 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 326.764 | 0.897179 | ||||||||
\(52\) | − 2.87187i | − 0.00765879i | ||||||||
\(53\) | 342.995i | 0.888943i | 0.895793 | + | 0.444471i | \(0.146608\pi\) | ||||
−0.895793 | + | 0.444471i | \(0.853392\pi\) | |||||||
\(54\) | 191.832 | 0.483426 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −71.6359 | −0.170942 | ||||||||
\(57\) | − 1109.34i | − 2.57782i | ||||||||
\(58\) | 68.2872i | 0.154596i | ||||||||
\(59\) | −88.3693 | −0.194995 | −0.0974975 | − | 0.995236i | \(-0.531084\pi\) | ||||
−0.0974975 | + | 0.995236i | \(0.531084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 738.697 | 1.55050 | 0.775250 | − | 0.631654i | \(-0.217624\pi\) | ||||
0.775250 | + | 0.631654i | \(0.217624\pi\) | |||||||
\(62\) | 86.0526i | 0.176269i | ||||||||
\(63\) | − 110.144i | − 0.220266i | ||||||||
\(64\) | −541.549 | −1.05771 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 238.263 | 0.444365 | ||||||||
\(67\) | 342.359i | 0.624266i | 0.950038 | + | 0.312133i | \(0.101043\pi\) | ||||
−0.950038 | + | 0.312133i | \(0.898957\pi\) | |||||||
\(68\) | − 22.0873i | − 0.0393893i | ||||||||
\(69\) | −882.836 | −1.54030 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −207.364 | −0.346614 | −0.173307 | − | 0.984868i | \(-0.555445\pi\) | ||||
−0.173307 | + | 0.984868i | \(0.555445\pi\) | |||||||
\(72\) | − 836.190i | − 1.36869i | ||||||||
\(73\) | 1010.60i | 1.62030i | 0.586224 | + | 0.810149i | \(0.300614\pi\) | ||||
−0.586224 | + | 0.810149i | \(0.699386\pi\) | |||||||
\(74\) | −35.9090 | −0.0564099 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −74.9845 | −0.113175 | ||||||||
\(77\) | − 33.7898i | − 0.0500091i | ||||||||
\(78\) | 116.077i | 0.168502i | ||||||||
\(79\) | −1294.23 | −1.84319 | −0.921593 | − | 0.388157i | \(-0.873112\pi\) | ||||
−0.921593 | + | 0.388157i | \(0.873112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −411.441 | −0.564391 | ||||||||
\(82\) | 713.261i | 0.960568i | ||||||||
\(83\) | − 441.846i | − 0.584324i | −0.956369 | − | 0.292162i | \(-0.905625\pi\) | ||||
0.956369 | − | 0.292162i | \(-0.0943747\pi\) | |||||||
\(84\) | −13.0512 | −0.0169524 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −157.674 | −0.197703 | ||||||||
\(87\) | 198.164i | 0.244200i | ||||||||
\(88\) | − 256.526i | − 0.310747i | ||||||||
\(89\) | 1489.11 | 1.77355 | 0.886773 | − | 0.462205i | \(-0.152942\pi\) | ||||
0.886773 | + | 0.462205i | \(0.152942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.4617 | 0.0189633 | ||||||||
\(92\) | 59.6743i | 0.0676248i | ||||||||
\(93\) | 249.718i | 0.278436i | ||||||||
\(94\) | 939.405 | 1.03077 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −191.944 | −0.204064 | ||||||||
\(97\) | 1346.42i | 1.40936i | 0.709526 | + | 0.704679i | \(0.248909\pi\) | ||||
−0.709526 | + | 0.704679i | \(0.751091\pi\) | |||||||
\(98\) | 911.314i | 0.939353i | ||||||||
\(99\) | 394.420 | 0.400412 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −161.461 | −0.159069 | −0.0795347 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795347 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(102\) | 892.736i | 0.866608i | ||||||||
\(103\) | 34.7592i | 0.0332517i | 0.999862 | + | 0.0166259i | \(0.00529242\pi\) | ||||
−0.999862 | + | 0.0166259i | \(0.994708\pi\) | |||||||
\(104\) | 124.974 | 0.117834 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −937.079 | −0.858653 | ||||||||
\(107\) | 832.179i | 0.751867i | 0.926647 | + | 0.375934i | \(0.122678\pi\) | ||||
−0.926647 | + | 0.375934i | \(0.877322\pi\) | |||||||
\(108\) | − 37.6283i | − 0.0335258i | ||||||||
\(109\) | −1044.26 | −0.917629 | −0.458815 | − | 0.888532i | \(-0.651726\pi\) | ||||
−0.458815 | + | 0.888532i | \(0.651726\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −104.205 | −0.0891055 | ||||||||
\(112\) | − 182.543i | − 0.154007i | ||||||||
\(113\) | − 295.082i | − 0.245654i | −0.992428 | − | 0.122827i | \(-0.960804\pi\) | ||||
0.992428 | − | 0.122827i | \(-0.0391961\pi\) | |||||||
\(114\) | 3030.77 | 2.48998 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 13.3947 | 0.0107213 | ||||||||
\(117\) | 192.154i | 0.151834i | ||||||||
\(118\) | − 241.429i | − 0.188351i | ||||||||
\(119\) | 126.605 | 0.0975285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 2018.16i | 1.49767i | ||||||||
\(123\) | 2069.83i | 1.51732i | ||||||||
\(124\) | 16.8794 | 0.0122243 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 300.918 | 0.212761 | ||||||||
\(127\) | − 1317.60i | − 0.920618i | −0.887759 | − | 0.460309i | \(-0.847739\pi\) | ||||
0.887759 | − | 0.460309i | \(-0.152261\pi\) | |||||||
\(128\) | − 1285.86i | − 0.887928i | ||||||||
\(129\) | −457.559 | −0.312293 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1600.71 | −1.06759 | −0.533797 | − | 0.845612i | \(-0.679235\pi\) | ||||
−0.533797 | + | 0.845612i | \(0.679235\pi\) | |||||||
\(132\) | − 46.7358i | − 0.0308169i | ||||||||
\(133\) | − 429.815i | − 0.280223i | ||||||||
\(134\) | −935.342 | −0.602994 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 961.164 | 0.606023 | ||||||||
\(137\) | 1611.68i | 1.00507i | 0.864556 | + | 0.502536i | \(0.167600\pi\) | ||||
−0.864556 | + | 0.502536i | \(0.832400\pi\) | |||||||
\(138\) | − 2411.95i | − 1.48782i | ||||||||
\(139\) | 31.8619 | 0.0194424 | 0.00972120 | − | 0.999953i | \(-0.496906\pi\) | ||||
0.00972120 | + | 0.999953i | \(0.496906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2726.08 | 1.62821 | ||||||||
\(142\) | − 566.529i | − 0.334803i | ||||||||
\(143\) | 58.9488i | 0.0344724i | ||||||||
\(144\) | 2130.79 | 1.23310 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2761.01 | −1.56509 | ||||||||
\(147\) | 2644.56i | 1.48381i | ||||||||
\(148\) | 7.04363i | 0.00391205i | ||||||||
\(149\) | 2428.34 | 1.33515 | 0.667576 | − | 0.744542i | \(-0.267332\pi\) | ||||
0.667576 | + | 0.744542i | \(0.267332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2576.68 | −1.38866 | −0.694328 | − | 0.719659i | \(-0.744298\pi\) | ||||
−0.694328 | + | 0.719659i | \(0.744298\pi\) | |||||||
\(152\) | − 3263.08i | − 1.74125i | ||||||||
\(153\) | 1477.84i | 0.780889i | ||||||||
\(154\) | 92.3154 | 0.0483051 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 22.7688 | 0.0116856 | ||||||||
\(157\) | 2475.94i | 1.25861i | 0.777158 | + | 0.629305i | \(0.216660\pi\) | ||||
−0.777158 | + | 0.629305i | \(0.783340\pi\) | |||||||
\(158\) | − 3535.89i | − 1.78038i | ||||||||
\(159\) | −2719.33 | −1.35633 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −342.056 | −0.167440 | ||||||||
\(162\) | − 1124.08i | − 0.545160i | ||||||||
\(163\) | 2725.11i | 1.30949i | 0.755850 | + | 0.654745i | \(0.227224\pi\) | ||||
−0.755850 | + | 0.654745i | \(0.772776\pi\) | |||||||
\(164\) | 139.908 | 0.0666157 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1207.15 | 0.564414 | ||||||||
\(167\) | 2737.30i | 1.26837i | 0.773180 | + | 0.634187i | \(0.218665\pi\) | ||||
−0.773180 | + | 0.634187i | \(0.781335\pi\) | |||||||
\(168\) | − 567.944i | − 0.260820i | ||||||||
\(169\) | 2168.28 | 0.986928 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5017.14 | 2.24368 | ||||||||
\(172\) | 30.9282i | 0.0137108i | ||||||||
\(173\) | − 2307.42i | − 1.01404i | −0.861933 | − | 0.507022i | \(-0.830746\pi\) | ||||
0.861933 | − | 0.507022i | \(-0.169254\pi\) | |||||||
\(174\) | −541.395 | −0.235879 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 653.682 | 0.279961 | ||||||||
\(177\) | − 700.610i | − 0.297520i | ||||||||
\(178\) | 4068.33i | 1.71311i | ||||||||
\(179\) | 1312.15 | 0.547905 | 0.273953 | − | 0.961743i | \(-0.411669\pi\) | ||||
0.273953 | + | 0.961743i | \(0.411669\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −803.174 | −0.329831 | −0.164916 | − | 0.986308i | \(-0.552735\pi\) | ||||
−0.164916 | + | 0.986308i | \(0.552735\pi\) | |||||||
\(182\) | 44.9742i | 0.0183171i | ||||||||
\(183\) | 5856.54i | 2.36573i | ||||||||
\(184\) | −2596.83 | −1.04044 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −682.242 | −0.268949 | ||||||||
\(187\) | 453.369i | 0.177292i | ||||||||
\(188\) | − 184.267i | − 0.0714842i | ||||||||
\(189\) | 215.687 | 0.0830103 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1718.25 | 0.650932 | 0.325466 | − | 0.945554i | \(-0.394479\pi\) | ||||
0.325466 | + | 0.945554i | \(0.394479\pi\) | |||||||
\(192\) | − 4293.51i | − 1.61384i | ||||||||
\(193\) | − 1340.18i | − 0.499837i | −0.968267 | − | 0.249919i | \(-0.919596\pi\) | ||||
0.968267 | − | 0.249919i | \(-0.0804038\pi\) | |||||||
\(194\) | −3678.48 | −1.36134 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 178.756 | 0.0651445 | ||||||||
\(197\) | − 3518.33i | − 1.27244i | −0.771508 | − | 0.636220i | \(-0.780497\pi\) | ||||
0.771508 | − | 0.636220i | \(-0.219503\pi\) | |||||||
\(198\) | 1077.58i | 0.386768i | ||||||||
\(199\) | −823.692 | −0.293417 | −0.146709 | − | 0.989180i | \(-0.546868\pi\) | ||||
−0.146709 | + | 0.989180i | \(0.546868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2714.29 | −0.952494 | ||||||||
\(202\) | − 441.121i | − 0.153649i | ||||||||
\(203\) | 76.7791i | 0.0265460i | ||||||||
\(204\) | 175.112 | 0.0600996 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −94.9639 | −0.0321187 | ||||||||
\(207\) | − 3992.75i | − 1.34065i | ||||||||
\(208\) | 318.461i | 0.106160i | ||||||||
\(209\) | 1539.15 | 0.509404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −107.343 | −0.0350228 | −0.0175114 | − | 0.999847i | \(-0.505574\pi\) | ||||
−0.0175114 | + | 0.999847i | \(0.505574\pi\) | |||||||
\(212\) | 183.810i | 0.0595479i | ||||||||
\(213\) | − 1644.03i | − 0.528858i | ||||||||
\(214\) | −2273.56 | −0.726248 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1637.46 | 0.515810 | ||||||||
\(217\) | 96.7537i | 0.0302676i | ||||||||
\(218\) | − 2852.96i | − 0.886362i | ||||||||
\(219\) | −8012.24 | −2.47222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −220.873 | −0.0672285 | ||||||||
\(222\) | − 284.694i | − 0.0860693i | ||||||||
\(223\) | 3933.68i | 1.18125i | 0.806946 | + | 0.590625i | \(0.201119\pi\) | ||||
−0.806946 | + | 0.590625i | \(0.798881\pi\) | |||||||
\(224\) | −74.3689 | −0.0221830 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 806.178 | 0.237284 | ||||||||
\(227\) | − 1771.90i | − 0.518085i | −0.965866 | − | 0.259042i | \(-0.916593\pi\) | ||||
0.965866 | − | 0.259042i | \(-0.0834069\pi\) | |||||||
\(228\) | − 594.493i | − 0.172681i | ||||||||
\(229\) | −1915.37 | −0.552713 | −0.276356 | − | 0.961055i | \(-0.589127\pi\) | ||||
−0.276356 | + | 0.961055i | \(0.589127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 267.892 | 0.0763031 | ||||||||
\(232\) | 582.892i | 0.164952i | ||||||||
\(233\) | − 4396.32i | − 1.23610i | −0.786137 | − | 0.618052i | \(-0.787922\pi\) | ||||
0.786137 | − | 0.618052i | \(-0.212078\pi\) | |||||||
\(234\) | −524.974 | −0.146661 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −47.3570 | −0.0130622 | ||||||||
\(237\) | − 10260.9i | − 2.81230i | ||||||||
\(238\) | 345.892i | 0.0942053i | ||||||||
\(239\) | 4084.49 | 1.10546 | 0.552728 | − | 0.833362i | \(-0.313587\pi\) | ||||
0.552728 | + | 0.833362i | \(0.313587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3908.58 | 1.04471 | 0.522353 | − | 0.852730i | \(-0.325054\pi\) | ||||
0.522353 | + | 0.852730i | \(0.325054\pi\) | |||||||
\(242\) | 330.578i | 0.0878114i | ||||||||
\(243\) | − 5157.80i | − 1.36162i | ||||||||
\(244\) | 395.867 | 0.103864 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5654.88 | −1.46562 | ||||||||
\(247\) | 749.845i | 0.193164i | ||||||||
\(248\) | 734.536i | 0.188077i | ||||||||
\(249\) | 3503.05 | 0.891552 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1094.89 | 0.275335 | 0.137667 | − | 0.990479i | \(-0.456040\pi\) | ||||
0.137667 | + | 0.990479i | \(0.456040\pi\) | |||||||
\(252\) | − 59.0258i | − 0.0147551i | ||||||||
\(253\) | − 1224.89i | − 0.304381i | ||||||||
\(254\) | 3599.76 | 0.889249 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −819.364 | −0.200040 | ||||||||
\(257\) | 783.179i | 0.190091i | 0.995473 | + | 0.0950454i | \(0.0302996\pi\) | ||||
−0.995473 | + | 0.0950454i | \(0.969700\pi\) | |||||||
\(258\) | − 1250.07i | − 0.301652i | ||||||||
\(259\) | −40.3744 | −0.00968628 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −896.225 | −0.212548 | ||||||||
\(262\) | − 4373.23i | − 1.03122i | ||||||||
\(263\) | − 6180.06i | − 1.44897i | −0.689292 | − | 0.724484i | \(-0.742078\pi\) | ||||
0.689292 | − | 0.724484i | \(-0.257922\pi\) | |||||||
\(264\) | 2033.79 | 0.474132 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1174.28 | 0.270675 | ||||||||
\(267\) | 11806.0i | 2.70605i | ||||||||
\(268\) | 183.470i | 0.0418179i | ||||||||
\(269\) | −986.965 | −0.223704 | −0.111852 | − | 0.993725i | \(-0.535678\pi\) | ||||
−0.111852 | + | 0.993725i | \(0.535678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4576.99 | 1.02595 | 0.512975 | − | 0.858404i | \(-0.328543\pi\) | ||||
0.512975 | + | 0.858404i | \(0.328543\pi\) | |||||||
\(272\) | 2449.25i | 0.545984i | ||||||||
\(273\) | 130.512i | 0.0289338i | ||||||||
\(274\) | −4403.18 | −0.970825 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −473.110 | −0.103181 | ||||||||
\(277\) | 567.836i | 0.123169i | 0.998102 | + | 0.0615847i | \(0.0196154\pi\) | ||||
−0.998102 | + | 0.0615847i | \(0.980385\pi\) | |||||||
\(278\) | 87.0484i | 0.0187799i | ||||||||
\(279\) | −1129.38 | −0.242346 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5311.01 | 1.12750 | 0.563752 | − | 0.825944i | \(-0.309357\pi\) | ||||
0.563752 | + | 0.825944i | \(0.309357\pi\) | |||||||
\(282\) | 7447.79i | 1.57273i | ||||||||
\(283\) | 4728.44i | 0.993204i | 0.867978 | + | 0.496602i | \(0.165419\pi\) | ||||
−0.867978 | + | 0.496602i | \(0.834581\pi\) | |||||||
\(284\) | −111.126 | −0.0232187 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −161.051 | −0.0332977 | ||||||||
\(287\) | 801.960i | 0.164941i | ||||||||
\(288\) | − 868.092i | − 0.177614i | ||||||||
\(289\) | 3214.29 | 0.654242 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10674.7 | −2.15038 | ||||||||
\(292\) | 541.579i | 0.108539i | ||||||||
\(293\) | − 2328.92i | − 0.464358i | −0.972673 | − | 0.232179i | \(-0.925415\pi\) | ||||
0.972673 | − | 0.232179i | \(-0.0745854\pi\) | |||||||
\(294\) | −7225.08 | −1.43325 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −306.515 | −0.0601886 | ||||||||
\(297\) | 772.369i | 0.150900i | ||||||||
\(298\) | 6634.36i | 1.28966i | ||||||||
\(299\) | 596.743 | 0.115420 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −177.282 | −0.0339481 | ||||||||
\(302\) | − 7039.61i | − 1.34134i | ||||||||
\(303\) | − 1280.10i | − 0.242705i | ||||||||
\(304\) | 8315.01 | 1.56875 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4037.52 | −0.754280 | ||||||||
\(307\) | − 1678.07i | − 0.311962i | −0.987760 | − | 0.155981i | \(-0.950146\pi\) | ||||
0.987760 | − | 0.155981i | \(-0.0498539\pi\) | |||||||
\(308\) | − 18.1079i | − 0.00334997i | ||||||||
\(309\) | −275.578 | −0.0507349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3572.71 | 0.651413 | 0.325707 | − | 0.945471i | \(-0.394398\pi\) | ||||
0.325707 | + | 0.945471i | \(0.394398\pi\) | |||||||
\(312\) | 990.821i | 0.179789i | ||||||||
\(313\) | − 7184.36i | − 1.29739i | −0.761047 | − | 0.648697i | \(-0.775314\pi\) | ||||
0.761047 | − | 0.648697i | \(-0.224686\pi\) | |||||||
\(314\) | −6764.40 | −1.21572 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −693.573 | −0.123470 | ||||||||
\(317\) | − 15.7077i | − 0.00278306i | −0.999999 | − | 0.00139153i | \(-0.999557\pi\) | ||||
0.999999 | − | 0.00139153i | \(-0.000442938\pi\) | |||||||
\(318\) | − 7429.36i | − 1.31012i | ||||||||
\(319\) | −274.943 | −0.0482566 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6597.69 | −1.14719 | ||||||||
\(322\) | − 934.515i | − 0.161734i | ||||||||
\(323\) | 5766.98i | 0.993447i | ||||||||
\(324\) | −220.491 | −0.0378070 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7445.13 | −1.26487 | ||||||||
\(327\) | − 8279.08i | − 1.40010i | ||||||||
\(328\) | 6088.33i | 1.02491i | ||||||||
\(329\) | 1056.23 | 0.176996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1318.95 | −0.219022 | −0.109511 | − | 0.993986i | \(-0.534928\pi\) | ||||
−0.109511 | + | 0.993986i | \(0.534928\pi\) | |||||||
\(332\) | − 236.785i | − 0.0391423i | ||||||||
\(333\) | − 471.282i | − 0.0775558i | ||||||||
\(334\) | −7478.43 | −1.22515 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1447.24 | 0.234981 | ||||||||
\(337\) | − 239.183i | − 0.0386621i | −0.999813 | − | 0.0193310i | \(-0.993846\pi\) | ||||
0.999813 | − | 0.0193310i | \(-0.00615365\pi\) | |||||||
\(338\) | 5923.85i | 0.953299i | ||||||||
\(339\) | 2339.47 | 0.374816 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −346.472 | −0.0550220 | ||||||||
\(342\) | 13707.1i | 2.16723i | ||||||||
\(343\) | 2078.27i | 0.327160i | ||||||||
\(344\) | −1345.89 | −0.210947 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6303.98 | 0.979491 | ||||||||
\(347\) | − 5862.79i | − 0.907006i | −0.891255 | − | 0.453503i | \(-0.850174\pi\) | ||||
0.891255 | − | 0.453503i | \(-0.149826\pi\) | |||||||
\(348\) | 106.196i | 0.0163583i | ||||||||
\(349\) | −3491.73 | −0.535553 | −0.267776 | − | 0.963481i | \(-0.586289\pi\) | ||||
−0.267776 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −376.283 | −0.0572208 | ||||||||
\(352\) | − 266.313i | − 0.0403253i | ||||||||
\(353\) | 10916.7i | 1.64600i | 0.568043 | + | 0.822999i | \(0.307701\pi\) | ||||
−0.568043 | + | 0.822999i | \(0.692299\pi\) | |||||||
\(354\) | 1914.10 | 0.287382 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 798.013 | 0.118805 | ||||||||
\(357\) | 1003.75i | 0.148807i | ||||||||
\(358\) | 3584.87i | 0.529236i | ||||||||
\(359\) | 11500.7 | 1.69077 | 0.845384 | − | 0.534160i | \(-0.179372\pi\) | ||||
0.845384 | + | 0.534160i | \(0.179372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12719.5 | 1.85442 | ||||||||
\(362\) | − 2194.31i | − 0.318592i | ||||||||
\(363\) | 959.313i | 0.138708i | ||||||||
\(364\) | 8.82180 | 0.00127030 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −16000.4 | −2.28512 | ||||||||
\(367\) | 6767.01i | 0.962493i | 0.876585 | + | 0.481246i | \(0.159816\pi\) | ||||
−0.876585 | + | 0.481246i | \(0.840184\pi\) | |||||||
\(368\) | − 6617.27i | − 0.937362i | ||||||||
\(369\) | −9361.10 | −1.32065 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1053.61 | −0.147441 | ||||||||
\(372\) | 133.823i | 0.0186517i | ||||||||
\(373\) | 5310.22i | 0.737139i | 0.929600 | + | 0.368569i | \(0.120152\pi\) | ||||
−0.929600 | + | 0.368569i | \(0.879848\pi\) | |||||||
\(374\) | −1238.63 | −0.171251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8018.67 | 1.09982 | ||||||||
\(377\) | − 133.947i | − 0.0182987i | ||||||||
\(378\) | 589.269i | 0.0801818i | ||||||||
\(379\) | 838.267 | 0.113612 | 0.0568059 | − | 0.998385i | \(-0.481908\pi\) | ||||
0.0568059 | + | 0.998385i | \(0.481908\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10446.2 | 1.40466 | ||||||||
\(382\) | 4694.34i | 0.628752i | ||||||||
\(383\) | 2832.16i | 0.377851i | 0.981991 | + | 0.188925i | \(0.0605004\pi\) | ||||
−0.981991 | + | 0.188925i | \(0.939500\pi\) | |||||||
\(384\) | 10194.5 | 1.35479 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3661.45 | 0.482806 | ||||||||
\(387\) | − 2069.37i | − 0.271814i | ||||||||
\(388\) | 721.542i | 0.0944091i | ||||||||
\(389\) | −3111.25 | −0.405519 | −0.202759 | − | 0.979229i | \(-0.564991\pi\) | ||||
−0.202759 | + | 0.979229i | \(0.564991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4589.49 | 0.593608 | ||||||||
\(392\) | 7778.88i | 1.00228i | ||||||||
\(393\) | − 12690.8i | − 1.62892i | ||||||||
\(394\) | 9612.25 | 1.22908 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 211.369 | 0.0268225 | ||||||||
\(397\) | 14208.7i | 1.79626i | 0.439728 | + | 0.898131i | \(0.355075\pi\) | ||||
−0.439728 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(398\) | − 2250.37i | − 0.283419i | ||||||||
\(399\) | 3407.66 | 0.427560 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6261.68 | −0.779784 | −0.389892 | − | 0.920861i | \(-0.627488\pi\) | ||||
−0.389892 | + | 0.920861i | \(0.627488\pi\) | |||||||
\(402\) | − 7415.58i | − 0.920039i | ||||||||
\(403\) | − 168.794i | − 0.0208641i | ||||||||
\(404\) | −86.5269 | −0.0106556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −209.764 | −0.0256415 | ||||||||
\(407\) | − 144.580i | − 0.0176082i | ||||||||
\(408\) | 7620.30i | 0.924660i | ||||||||
\(409\) | 4192.50 | 0.506860 | 0.253430 | − | 0.967354i | \(-0.418441\pi\) | ||||
0.253430 | + | 0.967354i | \(0.418441\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12777.7 | −1.53352 | ||||||||
\(412\) | 18.6274i | 0.00222744i | ||||||||
\(413\) | − 271.453i | − 0.0323421i | ||||||||
\(414\) | 10908.4 | 1.29497 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 129.742 | 0.0152912 | ||||||||
\(417\) | 252.608i | 0.0296649i | ||||||||
\(418\) | 4205.05i | 0.492047i | ||||||||
\(419\) | 9287.15 | 1.08283 | 0.541416 | − | 0.840755i | \(-0.317888\pi\) | ||||
0.541416 | + | 0.840755i | \(0.317888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13146.0 | 1.52185 | 0.760923 | − | 0.648842i | \(-0.224746\pi\) | ||||
0.760923 | + | 0.648842i | \(0.224746\pi\) | |||||||
\(422\) | − 293.267i | − 0.0338294i | ||||||||
\(423\) | 12329.1i | 1.41716i | ||||||||
\(424\) | −7998.81 | −0.916172 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4491.56 | 0.510838 | ||||||||
\(427\) | 2269.13i | 0.257168i | ||||||||
\(428\) | 445.964i | 0.0503656i | ||||||||
\(429\) | −467.358 | −0.0525974 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4909.67 | 0.548701 | 0.274351 | − | 0.961630i | \(-0.411537\pi\) | ||||
0.274351 | + | 0.961630i | \(0.411537\pi\) | |||||||
\(432\) | 4172.59i | 0.464708i | ||||||||
\(433\) | 11743.3i | 1.30334i | 0.758502 | + | 0.651671i | \(0.225932\pi\) | ||||
−0.758502 | + | 0.651671i | \(0.774068\pi\) | |||||||
\(434\) | −264.336 | −0.0292363 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −559.615 | −0.0614695 | ||||||||
\(437\) | − 15581.0i | − 1.70558i | ||||||||
\(438\) | − 21889.8i | − 2.38798i | ||||||||
\(439\) | 11824.2 | 1.28551 | 0.642754 | − | 0.766073i | \(-0.277792\pi\) | ||||
0.642754 | + | 0.766073i | \(0.277792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11960.4 | −1.29148 | ||||||||
\(442\) | − 603.435i | − 0.0649377i | ||||||||
\(443\) | − 10102.1i | − 1.08344i | −0.840558 | − | 0.541722i | \(-0.817772\pi\) | ||||
0.840558 | − | 0.541722i | \(-0.182228\pi\) | |||||||
\(444\) | −55.8433 | −0.00596894 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10747.0 | −1.14100 | ||||||||
\(447\) | 19252.4i | 2.03715i | ||||||||
\(448\) | − 1663.53i | − 0.175434i | ||||||||
\(449\) | 345.254 | 0.0362885 | 0.0181443 | − | 0.999835i | \(-0.494224\pi\) | ||||
0.0181443 | + | 0.999835i | \(0.494224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2871.79 | −0.299839 | ||||||||
\(452\) | − 158.134i | − 0.0164557i | ||||||||
\(453\) | − 20428.4i | − 2.11879i | ||||||||
\(454\) | 4840.93 | 0.500431 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 25870.3 | 2.65678 | ||||||||
\(457\) | − 10567.1i | − 1.08164i | −0.841138 | − | 0.540821i | \(-0.818114\pi\) | ||||
0.841138 | − | 0.540821i | \(-0.181886\pi\) | |||||||
\(458\) | − 5232.89i | − 0.533879i | ||||||||
\(459\) | −2893.95 | −0.294288 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4733.96 | 0.478270 | 0.239135 | − | 0.970986i | \(-0.423136\pi\) | ||||
0.239135 | + | 0.970986i | \(0.423136\pi\) | |||||||
\(462\) | 731.895i | 0.0737031i | ||||||||
\(463\) | − 3431.20i | − 0.344409i | −0.985061 | − | 0.172204i | \(-0.944911\pi\) | ||||
0.985061 | − | 0.172204i | \(-0.0550890\pi\) | |||||||
\(464\) | −1485.33 | −0.148610 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12011.0 | 1.19399 | ||||||||
\(467\) | 5116.96i | 0.507034i | 0.967331 | + | 0.253517i | \(0.0815873\pi\) | ||||
−0.967331 | + | 0.253517i | \(0.918413\pi\) | |||||||
\(468\) | 102.975i | 0.0101710i | ||||||||
\(469\) | −1051.66 | −0.103542 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19629.8 | −1.92037 | ||||||||
\(472\) | − 2060.82i | − 0.200968i | ||||||||
\(473\) | − 634.841i | − 0.0617125i | ||||||||
\(474\) | 28033.2 | 2.71648 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 67.8476 | 0.00653317 | ||||||||
\(477\) | − 12298.6i | − 1.18053i | ||||||||
\(478\) | 11159.0i | 1.06779i | ||||||||
\(479\) | −11566.9 | −1.10335 | −0.551675 | − | 0.834059i | \(-0.686011\pi\) | ||||
−0.551675 | + | 0.834059i | \(0.686011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 70.4363 | 0.00667696 | ||||||||
\(482\) | 10678.4i | 1.00911i | ||||||||
\(483\) | − 2711.89i | − 0.255477i | ||||||||
\(484\) | 64.8437 | 0.00608975 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14091.4 | 1.31522 | ||||||||
\(487\) | − 18326.5i | − 1.70525i | −0.522527 | − | 0.852623i | \(-0.675010\pi\) | ||||
0.522527 | − | 0.852623i | \(-0.324990\pi\) | |||||||
\(488\) | 17226.8i | 1.59799i | ||||||||
\(489\) | −21605.2 | −1.99800 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7617.58 | −0.700156 | −0.350078 | − | 0.936721i | \(-0.613845\pi\) | ||||
−0.350078 | + | 0.936721i | \(0.613845\pi\) | |||||||
\(492\) | 1109.22i | 0.101641i | ||||||||
\(493\) | − 1030.17i | − 0.0941108i | ||||||||
\(494\) | −2048.62 | −0.186582 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1871.75 | −0.169444 | ||||||||
\(497\) | − 636.980i | − 0.0574899i | ||||||||
\(498\) | 9570.50i | 0.861173i | ||||||||
\(499\) | −12909.1 | −1.15810 | −0.579050 | − | 0.815292i | \(-0.696576\pi\) | ||||
−0.579050 | + | 0.815292i | \(0.696576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21701.8 | −1.93526 | ||||||||
\(502\) | 2991.30i | 0.265953i | ||||||||
\(503\) | − 10165.7i | − 0.901121i | −0.892746 | − | 0.450561i | \(-0.851224\pi\) | ||||
0.892746 | − | 0.450561i | \(-0.148776\pi\) | |||||||
\(504\) | 2568.60 | 0.227013 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3346.47 | 0.294009 | ||||||||
\(507\) | 17190.6i | 1.50584i | ||||||||
\(508\) | − 706.102i | − 0.0616697i | ||||||||
\(509\) | −6449.93 | −0.561666 | −0.280833 | − | 0.959757i | \(-0.590611\pi\) | ||||
−0.280833 | + | 0.959757i | \(0.590611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3104.36 | −0.268745 | ||||||||
\(512\) | − 12525.4i | − 1.08115i | ||||||||
\(513\) | 9824.75i | 0.845562i | ||||||||
\(514\) | −2139.68 | −0.183614 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −245.205 | −0.0209197 | ||||||||
\(517\) | 3782.31i | 0.321752i | ||||||||
\(518\) | − 110.305i | − 0.00935623i | ||||||||
\(519\) | 18293.7 | 1.54721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19327.4 | −1.62524 | −0.812620 | − | 0.582794i | \(-0.801959\pi\) | ||||
−0.812620 | + | 0.582794i | \(0.801959\pi\) | |||||||
\(522\) | − 2448.53i | − 0.205305i | ||||||||
\(523\) | − 6259.09i | − 0.523310i | −0.965161 | − | 0.261655i | \(-0.915732\pi\) | ||||
0.965161 | − | 0.261655i | \(-0.0842682\pi\) | |||||||
\(524\) | −857.819 | −0.0715153 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16884.2 | 1.39960 | ||||||||
\(527\) | − 1298.18i | − 0.107305i | ||||||||
\(528\) | 5182.52i | 0.427160i | ||||||||
\(529\) | −232.675 | −0.0191235 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3168.61 | 0.258956 | ||||||||
\(532\) | − 230.337i | − 0.0187714i | ||||||||
\(533\) | − 1399.08i | − 0.113698i | ||||||||
\(534\) | −32254.6 | −2.61384 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7983.99 | −0.643387 | ||||||||
\(537\) | 10403.0i | 0.835985i | ||||||||
\(538\) | − 2696.44i | − 0.216081i | ||||||||
\(539\) | −3669.20 | −0.293217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14008.2 | −1.11323 | −0.556616 | − | 0.830770i | \(-0.687900\pi\) | ||||
−0.556616 | + | 0.830770i | \(0.687900\pi\) | |||||||
\(542\) | 12504.6i | 0.990991i | ||||||||
\(543\) | − 6367.72i | − 0.503251i | ||||||||
\(544\) | 997.834 | 0.0786430 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −356.565 | −0.0279479 | ||||||||
\(547\) | − 4949.45i | − 0.386879i | −0.981112 | − | 0.193440i | \(-0.938036\pi\) | ||||
0.981112 | − | 0.193440i | \(-0.0619644\pi\) | |||||||
\(548\) | 863.695i | 0.0673270i | ||||||||
\(549\) | −26487.0 | −2.05909 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3497.35 | −0.270404 | ||||||||
\(552\) | − 20588.2i | − 1.58748i | ||||||||
\(553\) | − 3975.60i | − 0.305714i | ||||||||
\(554\) | −1551.36 | −0.118973 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.0748 | 0.00130239 | ||||||||
\(557\) | − 3801.58i | − 0.289188i | −0.989491 | − | 0.144594i | \(-0.953812\pi\) | ||||
0.989491 | − | 0.144594i | \(-0.0461877\pi\) | |||||||
\(558\) | − 3085.54i | − 0.234088i | ||||||||
\(559\) | 309.282 | 0.0234011 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3594.40 | −0.270510 | ||||||||
\(562\) | 14510.0i | 1.08908i | ||||||||
\(563\) | 9900.11i | 0.741101i | 0.928812 | + | 0.370551i | \(0.120831\pi\) | ||||
−0.928812 | + | 0.370551i | \(0.879169\pi\) | |||||||
\(564\) | 1460.90 | 0.109069 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12918.3 | −0.959361 | ||||||||
\(567\) | − 1263.86i | − 0.0936107i | ||||||||
\(568\) | − 4835.84i | − 0.357231i | ||||||||
\(569\) | −5329.16 | −0.392636 | −0.196318 | − | 0.980540i | \(-0.562898\pi\) | ||||
−0.196318 | + | 0.980540i | \(0.562898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16962.6 | −1.24319 | −0.621597 | − | 0.783337i | \(-0.713516\pi\) | ||||
−0.621597 | + | 0.783337i | \(0.713516\pi\) | |||||||
\(572\) | 31.5906i | 0.00230921i | ||||||||
\(573\) | 13622.6i | 0.993181i | ||||||||
\(574\) | −2190.99 | −0.159321 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19418.0 | 1.40466 | ||||||||
\(577\) | − 15487.0i | − 1.11738i | −0.829375 | − | 0.558692i | \(-0.811303\pi\) | ||||
0.829375 | − | 0.558692i | \(-0.188697\pi\) | |||||||
\(578\) | 8781.61i | 0.631949i | ||||||||
\(579\) | 10625.3 | 0.762643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1357.26 | 0.0969169 | ||||||||
\(582\) | − 29163.7i | − 2.07710i | ||||||||
\(583\) | − 3772.94i | − 0.268026i | ||||||||
\(584\) | −23567.7 | −1.66993 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6362.72 | 0.448535 | ||||||||
\(587\) | 11084.2i | 0.779373i | 0.920948 | + | 0.389686i | \(0.127417\pi\) | ||||
−0.920948 | + | 0.389686i | \(0.872583\pi\) | |||||||
\(588\) | 1417.22i | 0.0993964i | ||||||||
\(589\) | −4407.22 | −0.308313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27894.0 | 1.94147 | ||||||||
\(592\) | − 781.066i | − 0.0542257i | ||||||||
\(593\) | − 4349.68i | − 0.301214i | −0.988594 | − | 0.150607i | \(-0.951877\pi\) | ||||
0.988594 | − | 0.150607i | \(-0.0481228\pi\) | |||||||
\(594\) | −2110.15 | −0.145759 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1301.34 | 0.0894382 | ||||||||
\(597\) | − 6530.40i | − 0.447691i | ||||||||
\(598\) | 1630.33i | 0.111487i | ||||||||
\(599\) | −13183.9 | −0.899299 | −0.449650 | − | 0.893205i | \(-0.648451\pi\) | ||||
−0.449650 | + | 0.893205i | \(0.648451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18765.0 | −1.27361 | −0.636806 | − | 0.771024i | \(-0.719745\pi\) | ||||
−0.636806 | + | 0.771024i | \(0.719745\pi\) | |||||||
\(602\) | − 484.344i | − 0.0327913i | ||||||||
\(603\) | − 12275.8i | − 0.829034i | ||||||||
\(604\) | −1380.84 | −0.0930223 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3497.29 | 0.234435 | ||||||||
\(607\) | 21871.4i | 1.46249i | 0.682116 | + | 0.731244i | \(0.261060\pi\) | ||||
−0.682116 | + | 0.731244i | \(0.738940\pi\) | |||||||
\(608\) | − 3387.57i | − 0.225961i | ||||||||
\(609\) | −608.720 | −0.0405034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1842.67 | −0.122007 | ||||||||
\(612\) | 791.970i | 0.0523096i | ||||||||
\(613\) | 3527.85i | 0.232445i | 0.993223 | + | 0.116222i | \(0.0370785\pi\) | ||||
−0.993223 | + | 0.116222i | \(0.962921\pi\) | |||||||
\(614\) | 4584.56 | 0.301332 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 787.994 | 0.0515409 | ||||||||
\(617\) | − 22728.1i | − 1.48298i | −0.670963 | − | 0.741490i | \(-0.734119\pi\) | ||||
0.670963 | − | 0.741490i | \(-0.265881\pi\) | |||||||
\(618\) | − 752.893i | − 0.0490062i | ||||||||
\(619\) | 21443.3 | 1.39237 | 0.696187 | − | 0.717861i | \(-0.254879\pi\) | ||||
0.696187 | + | 0.717861i | \(0.254879\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7818.75 | 0.505243 | ||||||||
\(622\) | 9760.81i | 0.629217i | ||||||||
\(623\) | 4574.25i | 0.294163i | ||||||||
\(624\) | −2524.82 | −0.161977 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 19628.0 | 1.25319 | ||||||||
\(627\) | 12202.7i | 0.777240i | ||||||||
\(628\) | 1326.85i | 0.0843109i | ||||||||
\(629\) | 541.718 | 0.0343398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21532.0 | 1.35844 | 0.679219 | − | 0.733936i | \(-0.262319\pi\) | ||||
0.679219 | + | 0.733936i | \(0.262319\pi\) | |||||||
\(632\) | − 30182.0i | − 1.89964i | ||||||||
\(633\) | − 851.038i | − 0.0534372i | ||||||||
\(634\) | 42.9141 | 0.00268823 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1457.29 | −0.0908572 | ||||||||
\(637\) | − 1787.56i | − 0.111187i | ||||||||
\(638\) | − 751.159i | − 0.0466123i | ||||||||
\(639\) | 7435.33 | 0.460309 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20148.3 | 1.24151 | 0.620756 | − | 0.784004i | \(-0.286826\pi\) | ||||
0.620756 | + | 0.784004i | \(0.286826\pi\) | |||||||
\(642\) | − 18025.2i | − 1.10810i | ||||||||
\(643\) | − 28869.7i | − 1.77062i | −0.465000 | − | 0.885310i | \(-0.653946\pi\) | ||||
0.465000 | − | 0.885310i | \(-0.346054\pi\) | |||||||
\(644\) | −183.307 | −0.0112163 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15755.7 | −0.959597 | ||||||||
\(647\) | − 1590.02i | − 0.0966155i | −0.998833 | − | 0.0483077i | \(-0.984617\pi\) | ||||
0.998833 | − | 0.0483077i | \(-0.0153828\pi\) | |||||||
\(648\) | − 9595.02i | − 0.581679i | ||||||||
\(649\) | 972.062 | 0.0587932 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −767.083 | −0.0461818 | ||||||||
\(652\) | 1460.38i | 0.0877192i | ||||||||
\(653\) | − 20028.1i | − 1.20024i | −0.799909 | − | 0.600122i | \(-0.795119\pi\) | ||||
0.799909 | − | 0.600122i | \(-0.204881\pi\) | |||||||
\(654\) | 22618.9 | 1.35240 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15514.4 | −0.923375 | ||||||||
\(657\) | − 36236.5i | − 2.15178i | ||||||||
\(658\) | 2885.66i | 0.170965i | ||||||||
\(659\) | 10520.7 | 0.621897 | 0.310948 | − | 0.950427i | \(-0.399353\pi\) | ||||
0.310948 | + | 0.950427i | \(0.399353\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3295.83 | 0.193938 | 0.0969690 | − | 0.995287i | \(-0.469085\pi\) | ||||
0.0969690 | + | 0.995287i | \(0.469085\pi\) | |||||||
\(662\) | − 3603.45i | − 0.211559i | ||||||||
\(663\) | − 1751.12i | − 0.102576i | ||||||||
\(664\) | 10304.1 | 0.602222 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1287.57 | 0.0749132 | ||||||||
\(667\) | 2783.27i | 0.161572i | ||||||||
\(668\) | 1466.91i | 0.0849649i | ||||||||
\(669\) | −31187.0 | −1.80233 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8125.67 | −0.467493 | ||||||||
\(672\) | − 589.612i | − 0.0338464i | ||||||||
\(673\) | 1187.64i | 0.0680239i | 0.999421 | + | 0.0340119i | \(0.0108284\pi\) | ||||
−0.999421 | + | 0.0340119i | \(0.989172\pi\) | |||||||
\(674\) | 653.460 | 0.0373447 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1161.98 | 0.0661117 | ||||||||
\(677\) | 13221.4i | 0.750574i | 0.926909 | + | 0.375287i | \(0.122456\pi\) | ||||
−0.926909 | + | 0.375287i | \(0.877544\pi\) | |||||||
\(678\) | 6391.55i | 0.362044i | ||||||||
\(679\) | −4135.91 | −0.233758 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14048.0 | 0.790485 | ||||||||
\(682\) | − 946.578i | − 0.0531471i | ||||||||
\(683\) | 13831.4i | 0.774882i | 0.921894 | + | 0.387441i | \(0.126641\pi\) | ||||
−0.921894 | + | 0.387441i | \(0.873359\pi\) | |||||||
\(684\) | 2688.68 | 0.150298 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5677.93 | −0.316012 | ||||||||
\(687\) | − 15185.4i | − 0.843320i | ||||||||
\(688\) | − 3429.62i | − 0.190048i | ||||||||
\(689\) | 1838.10 | 0.101635 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9817.07 | −0.540462 | −0.270231 | − | 0.962796i | \(-0.587100\pi\) | ||||
−0.270231 | + | 0.962796i | \(0.587100\pi\) | |||||||
\(692\) | − 1236.54i | − 0.0679280i | ||||||||
\(693\) | 1211.58i | 0.0664128i | ||||||||
\(694\) | 16017.4 | 0.876101 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4621.29 | −0.251680 | ||||||||
\(697\) | − 10760.2i | − 0.584750i | ||||||||
\(698\) | − 9539.58i | − 0.517304i | ||||||||
\(699\) | 34854.9 | 1.88603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29949.8 | 1.61368 | 0.806838 | − | 0.590773i | \(-0.201177\pi\) | ||||
0.806838 | + | 0.590773i | \(0.201177\pi\) | |||||||
\(702\) | − 1028.02i | − 0.0552711i | ||||||||
\(703\) | − 1839.09i | − 0.0986667i | ||||||||
\(704\) | 5957.03 | 0.318912 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29825.0 | −1.58991 | ||||||||
\(707\) | − 495.976i | − 0.0263835i | ||||||||
\(708\) | − 375.456i | − 0.0199301i | ||||||||
\(709\) | −11307.5 | −0.598959 | −0.299479 | − | 0.954103i | \(-0.596813\pi\) | ||||
−0.299479 | + | 0.954103i | \(0.596813\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46406.3 | 2.44778 | ||||||||
\(712\) | 34726.9i | 1.82787i | ||||||||
\(713\) | 3507.36i | 0.184224i | ||||||||
\(714\) | −2742.30 | −0.143737 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 703.181 | 0.0367027 | ||||||||
\(717\) | 32382.7i | 1.68669i | ||||||||
\(718\) | 31420.6i | 1.63316i | ||||||||
\(719\) | 32623.4 | 1.69214 | 0.846070 | − | 0.533071i | \(-0.178962\pi\) | ||||
0.846070 | + | 0.533071i | \(0.178962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −106.773 | −0.00551518 | ||||||||
\(722\) | 34750.2i | 1.79123i | ||||||||
\(723\) | 30988.0i | 1.59399i | ||||||||
\(724\) | −430.420 | −0.0220945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2620.89 | −0.133981 | ||||||||
\(727\) | − 502.545i | − 0.0256373i | −0.999918 | − | 0.0128187i | \(-0.995920\pi\) | ||||
0.999918 | − | 0.0128187i | \(-0.00408042\pi\) | |||||||
\(728\) | 383.895i | 0.0195441i | ||||||||
\(729\) | 29783.2 | 1.51314 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2378.66 | 0.120353 | ||||||||
\(732\) | 3138.51i | 0.158474i | ||||||||
\(733\) | − 8631.37i | − 0.434935i | −0.976068 | − | 0.217467i | \(-0.930220\pi\) | ||||
0.976068 | − | 0.217467i | \(-0.0697796\pi\) | |||||||
\(734\) | −18487.8 | −0.929697 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2695.90 | −0.135017 | ||||||||
\(737\) | − 3765.95i | − 0.188223i | ||||||||
\(738\) | − 25575.0i | − 1.27565i | ||||||||
\(739\) | 18357.5 | 0.913792 | 0.456896 | − | 0.889520i | \(-0.348961\pi\) | ||||
0.456896 | + | 0.889520i | \(0.348961\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5944.93 | −0.294726 | ||||||||
\(742\) | − 2878.52i | − 0.142417i | ||||||||
\(743\) | − 11182.6i | − 0.552155i | −0.961135 | − | 0.276078i | \(-0.910965\pi\) | ||||
0.961135 | − | 0.276078i | \(-0.0890347\pi\) | |||||||
\(744\) | −5823.55 | −0.286965 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14507.8 | −0.712021 | ||||||||
\(747\) | 15843.0i | 0.775991i | ||||||||
\(748\) | 242.960i | 0.0118763i | ||||||||
\(749\) | −2556.29 | −0.124706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16733.4 | 0.813063 | 0.406531 | − | 0.913637i | \(-0.366738\pi\) | ||||
0.406531 | + | 0.913637i | \(0.366738\pi\) | |||||||
\(752\) | 20433.3i | 0.990857i | ||||||||
\(753\) | 8680.53i | 0.420101i | ||||||||
\(754\) | 365.950 | 0.0176752 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 115.587 | 0.00556064 | ||||||||
\(757\) | − 24402.4i | − 1.17163i | −0.810446 | − | 0.585813i | \(-0.800775\pi\) | ||||
0.810446 | − | 0.585813i | \(-0.199225\pi\) | |||||||
\(758\) | 2290.19i | 0.109741i | ||||||||
\(759\) | 9711.19 | 0.464419 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8469.33 | 0.403434 | 0.201717 | − | 0.979444i | \(-0.435348\pi\) | ||||
0.201717 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(762\) | 28539.7i | 1.35680i | ||||||||
\(763\) | − 3207.74i | − 0.152199i | ||||||||
\(764\) | 920.805 | 0.0436042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7737.62 | −0.364976 | ||||||||
\(767\) | 473.570i | 0.0222941i | ||||||||
\(768\) | − 6496.08i | − 0.305218i | ||||||||
\(769\) | −32834.7 | −1.53973 | −0.769864 | − | 0.638208i | \(-0.779676\pi\) | ||||
−0.769864 | + | 0.638208i | \(0.779676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6209.20 | −0.290038 | ||||||||
\(772\) | − 718.202i | − 0.0334827i | ||||||||
\(773\) | 35571.4i | 1.65513i | 0.561371 | + | 0.827564i | \(0.310274\pi\) | ||||
−0.561371 | + | 0.827564i | \(0.689726\pi\) | |||||||
\(774\) | 5653.64 | 0.262553 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31399.1 | −1.45253 | ||||||||
\(777\) | − 320.097i | − 0.0147792i | ||||||||
\(778\) | − 8500.11i | − 0.391701i | ||||||||
\(779\) | −36530.0 | −1.68013 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2281.01 | 0.104508 | ||||||||
\(782\) | 12538.7i | 0.573381i | ||||||||
\(783\) | − 1755.02i | − 0.0801014i | ||||||||
\(784\) | −19822.3 | −0.902982 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34671.8 | 1.57341 | ||||||||
\(787\) | 15729.6i | 0.712452i | 0.934400 | + | 0.356226i | \(0.115937\pi\) | ||||
−0.934400 | + | 0.356226i | \(0.884063\pi\) | |||||||
\(788\) | − 1885.47i | − 0.0852373i | ||||||||
\(789\) | 48996.7 | 2.21081 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 906.431 | 0.0407446 | ||||||||
\(792\) | 9198.09i | 0.412676i | ||||||||
\(793\) | − 3958.67i | − 0.177272i | ||||||||
\(794\) | −38819.0 | −1.73506 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −441.415 | −0.0196552 | ||||||||
\(797\) | 7888.07i | 0.350577i | 0.984517 | + | 0.175288i | \(0.0560858\pi\) | ||||
−0.984517 | + | 0.175288i | \(0.943914\pi\) | |||||||
\(798\) | 9309.91i | 0.412991i | ||||||||
\(799\) | −14171.8 | −0.627485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −53394.2 | −2.35530 | ||||||||
\(802\) | − 17107.2i | − 0.753214i | ||||||||
\(803\) | − 11116.6i | − 0.488538i | ||||||||
\(804\) | −1454.58 | −0.0638050 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 461.154 | 0.0201532 | ||||||||
\(807\) | − 7824.86i | − 0.341323i | ||||||||
\(808\) | − 3765.36i | − 0.163942i | ||||||||
\(809\) | −5896.97 | −0.256275 | −0.128138 | − | 0.991756i | \(-0.540900\pi\) | ||||
−0.128138 | + | 0.991756i | \(0.540900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14197.9 | 0.614744 | 0.307372 | − | 0.951589i | \(-0.400550\pi\) | ||||
0.307372 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(812\) | 41.1458i | 0.00177824i | ||||||||
\(813\) | 36287.3i | 1.56538i | ||||||||
\(814\) | 394.999 | 0.0170082 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −19418.2 | −0.833053 | ||||||||
\(817\) | − 8075.35i | − 0.345803i | ||||||||
\(818\) | 11454.1i | 0.489589i | ||||||||
\(819\) | −590.258 | −0.0251835 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19841.7 | −0.843459 | −0.421729 | − | 0.906722i | \(-0.638577\pi\) | ||||
−0.421729 | + | 0.906722i | \(0.638577\pi\) | |||||||
\(822\) | − 34909.3i | − 1.48127i | ||||||||
\(823\) | 28202.2i | 1.19449i | 0.802058 | + | 0.597246i | \(0.203738\pi\) | ||||
−0.802058 | + | 0.597246i | \(0.796262\pi\) | |||||||
\(824\) | −810.602 | −0.0342702 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 741.622 | 0.0312401 | ||||||||
\(827\) | 34031.0i | 1.43092i | 0.698651 | + | 0.715462i | \(0.253784\pi\) | ||||
−0.698651 | + | 0.715462i | \(0.746216\pi\) | |||||||
\(828\) | − 2139.71i | − 0.0898067i | ||||||||
\(829\) | −4931.55 | −0.206610 | −0.103305 | − | 0.994650i | \(-0.532942\pi\) | ||||
−0.103305 | + | 0.994650i | \(0.532942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4501.92 | −0.187930 | ||||||||
\(832\) | 2902.15i | 0.120930i | ||||||||
\(833\) | − 13748.0i | − 0.571836i | ||||||||
\(834\) | −690.138 | −0.0286541 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 824.830 | 0.0341236 | ||||||||
\(837\) | − 2211.60i | − 0.0913312i | ||||||||
\(838\) | 25373.0i | 1.04594i | ||||||||
\(839\) | 38189.8 | 1.57146 | 0.785731 | − | 0.618568i | \(-0.212287\pi\) | ||||
0.785731 | + | 0.618568i | \(0.212287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23764.3 | −0.974384 | ||||||||
\(842\) | 35915.6i | 1.46999i | ||||||||
\(843\) | 42106.8i | 1.72033i | ||||||||
\(844\) | −57.5250 | −0.00234608 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −33683.7 | −1.36888 | ||||||||
\(847\) | 371.687i | 0.0150783i | ||||||||
\(848\) | − 20382.7i | − 0.825406i | ||||||||
\(849\) | −37488.0 | −1.51541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1463.59 | −0.0589556 | ||||||||
\(852\) | − 881.030i | − 0.0354268i | ||||||||
\(853\) | − 42966.8i | − 1.72469i | −0.506325 | − | 0.862343i | \(-0.668997\pi\) | ||||
0.506325 | − | 0.862343i | \(-0.331003\pi\) | |||||||
\(854\) | −6199.37 | −0.248405 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19406.8 | −0.774898 | ||||||||
\(857\) | − 17281.5i | − 0.688828i | −0.938818 | − | 0.344414i | \(-0.888078\pi\) | ||||
0.938818 | − | 0.344414i | \(-0.111922\pi\) | |||||||
\(858\) | − 1276.85i | − 0.0508052i | ||||||||
\(859\) | −9316.75 | −0.370062 | −0.185031 | − | 0.982733i | \(-0.559239\pi\) | ||||
−0.185031 | + | 0.982733i | \(0.559239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6358.10 | −0.251665 | ||||||||
\(862\) | 13413.5i | 0.530005i | ||||||||
\(863\) | 9647.65i | 0.380544i | 0.981731 | + | 0.190272i | \(0.0609370\pi\) | ||||
−0.981731 | + | 0.190272i | \(0.939063\pi\) | |||||||
\(864\) | 1699.93 | 0.0669361 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −32083.3 | −1.25893 | ||||||||
\(867\) | 25483.6i | 0.998232i | ||||||||
\(868\) | 51.8501i | 0.00202754i | ||||||||
\(869\) | 14236.5 | 0.555742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1834.70 | 0.0713735 | ||||||||
\(872\) | − 24352.6i | − 0.945737i | ||||||||
\(873\) | − 48277.6i | − 1.87165i | ||||||||
\(874\) | 42568.0 | 1.64746 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4293.75 | −0.165608 | ||||||||
\(877\) | 19728.7i | 0.759624i | 0.925064 | + | 0.379812i | \(0.124011\pi\) | ||||
−0.925064 | + | 0.379812i | \(0.875989\pi\) | |||||||
\(878\) | 32304.3i | 1.24171i | ||||||||
\(879\) | 18464.1 | 0.708509 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19473.9 | 0.744712 | 0.372356 | − | 0.928090i | \(-0.378550\pi\) | ||||
0.372356 | + | 0.928090i | \(0.378550\pi\) | |||||||
\(882\) | − 32676.4i | − 1.24748i | ||||||||
\(883\) | − 49092.4i | − 1.87100i | −0.353329 | − | 0.935499i | \(-0.614950\pi\) | ||||
0.353329 | − | 0.935499i | \(-0.385050\pi\) | |||||||
\(884\) | −118.365 | −0.00450346 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27599.5 | 1.04653 | ||||||||
\(887\) | 9292.86i | 0.351774i | 0.984410 | + | 0.175887i | \(0.0562793\pi\) | ||||
−0.984410 | + | 0.175887i | \(0.943721\pi\) | |||||||
\(888\) | − 2430.12i | − 0.0918348i | ||||||||
\(889\) | 4047.41 | 0.152695 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4525.85 | 0.170170 | ||||||||
\(892\) | 2108.05i | 0.0791288i | ||||||||
\(893\) | 48112.0i | 1.80292i | ||||||||
\(894\) | −52598.5 | −1.96774 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3949.89 | 0.147273 | ||||||||
\(897\) | 4731.10i | 0.176106i | ||||||||
\(898\) | 943.252i | 0.0350520i | ||||||||
\(899\) | 787.273 | 0.0292069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14136.7 | 0.522709 | ||||||||
\(902\) | − 7845.88i | − 0.289622i | ||||||||
\(903\) | − 1405.53i | − 0.0517974i | ||||||||
\(904\) | 6881.46 | 0.253179 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 55811.5 | 2.04659 | ||||||||
\(907\) | 37688.7i | 1.37975i | 0.723928 | + | 0.689875i | \(0.242335\pi\) | ||||
−0.723928 | + | 0.689875i | \(0.757665\pi\) | |||||||
\(908\) | − 949.559i | − 0.0347051i | ||||||||
\(909\) | 5789.42 | 0.211246 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33049.6 | 1.20196 | 0.600979 | − | 0.799265i | \(-0.294778\pi\) | ||||
0.600979 | + | 0.799265i | \(0.294778\pi\) | |||||||
\(912\) | 65923.1i | 2.39357i | ||||||||
\(913\) | 4860.31i | 0.176180i | ||||||||
\(914\) | 28870.0 | 1.04479 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1026.44 | −0.0370247 | ||||||||
\(917\) | − 4917.06i | − 0.177073i | ||||||||
\(918\) | − 7906.43i | − 0.284260i | ||||||||
\(919\) | 23148.0 | 0.830883 | 0.415442 | − | 0.909620i | \(-0.363627\pi\) | ||||
0.415442 | + | 0.909620i | \(0.363627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13304.1 | 0.475986 | ||||||||
\(922\) | 12933.4i | 0.461973i | ||||||||
\(923\) | 1111.26i | 0.0396290i | ||||||||
\(924\) | 143.563 | 0.00511134 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9374.21 | 0.332673 | ||||||||
\(927\) | − 1246.34i | − 0.0441588i | ||||||||
\(928\) | 605.131i | 0.0214056i | ||||||||
\(929\) | 23177.9 | 0.818561 | 0.409280 | − | 0.912409i | \(-0.365780\pi\) | ||||
0.409280 | + | 0.912409i | \(0.365780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46673.3 | −1.64302 | ||||||||
\(932\) | − 2355.98i | − 0.0828033i | ||||||||
\(933\) | 28325.1i | 0.993916i | ||||||||
\(934\) | −13979.8 | −0.489757 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4481.13 | −0.156485 | ||||||||
\(937\) | − 34574.7i | − 1.20545i | −0.797950 | − | 0.602724i | \(-0.794082\pi\) | ||||
0.797950 | − | 0.602724i | \(-0.205918\pi\) | |||||||
\(938\) | − 2873.18i | − 0.100014i | ||||||||
\(939\) | 56959.1 | 1.97954 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41831.2 | 1.44916 | 0.724578 | − | 0.689192i | \(-0.242034\pi\) | ||||
0.724578 | + | 0.689192i | \(0.242034\pi\) | |||||||
\(942\) | − 53629.6i | − 1.85493i | ||||||||
\(943\) | 29071.3i | 1.00392i | ||||||||
\(944\) | 5251.40 | 0.181058 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1734.42 | 0.0596097 | ||||||||
\(947\) | 27231.2i | 0.934419i | 0.884147 | + | 0.467209i | \(0.154741\pi\) | ||||
−0.884147 | + | 0.467209i | \(0.845259\pi\) | |||||||
\(948\) | − 5498.79i | − 0.188389i | ||||||||
\(949\) | 5415.79 | 0.185252 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 124.534 | 0.00424635 | ||||||||
\(952\) | 2952.50i | 0.100516i | ||||||||
\(953\) | − 40939.4i | − 1.39156i | −0.718254 | − | 0.695781i | \(-0.755058\pi\) | ||||
0.718254 | − | 0.695781i | \(-0.244942\pi\) | |||||||
\(954\) | 33600.3 | 1.14030 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2188.87 | 0.0740515 | ||||||||
\(957\) | − 2179.81i | − 0.0736292i | ||||||||
\(958\) | − 31601.3i | − 1.06575i | ||||||||
\(959\) | −4950.74 | −0.166703 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28798.9 | −0.966698 | ||||||||
\(962\) | 192.436i | 0.00644945i | ||||||||
\(963\) | − 29839.0i | − 0.998491i | ||||||||
\(964\) | 2094.60 | 0.0699820 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7409.03 | 0.246772 | ||||||||
\(967\) | − 46173.1i | − 1.53550i | −0.640750 | − | 0.767750i | \(-0.721376\pi\) | ||||
0.640750 | − | 0.767750i | \(-0.278624\pi\) | |||||||
\(968\) | 2821.78i | 0.0936937i | ||||||||
\(969\) | −45721.8 | −1.51579 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5153.91 | −0.170337 | −0.0851683 | − | 0.996367i | \(-0.527143\pi\) | ||||
−0.0851683 | + | 0.996367i | \(0.527143\pi\) | |||||||
\(972\) | − 2764.06i | − 0.0912111i | ||||||||
\(973\) | 97.8734i | 0.00322474i | ||||||||
\(974\) | 50069.0 | 1.64714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43897.6 | −1.43968 | ||||||||
\(977\) | 9692.13i | 0.317378i | 0.987329 | + | 0.158689i | \(0.0507268\pi\) | ||||
−0.987329 | + | 0.158689i | \(0.949273\pi\) | |||||||
\(978\) | − 59026.5i | − 1.92992i | ||||||||
\(979\) | −16380.2 | −0.534744 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37443.3 | 1.21863 | ||||||||
\(982\) | − 20811.6i | − 0.676299i | ||||||||
\(983\) | − 32915.7i | − 1.06800i | −0.845483 | − | 0.534002i | \(-0.820687\pi\) | ||||
0.845483 | − | 0.534002i | \(-0.179313\pi\) | |||||||
\(984\) | −48269.5 | −1.56380 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2814.48 | 0.0909041 | ||||||||
\(987\) | 8373.97i | 0.270057i | ||||||||
\(988\) | 401.841i | 0.0129395i | ||||||||
\(989\) | −6426.54 | −0.206625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29477.9 | 0.944901 | 0.472451 | − | 0.881357i | \(-0.343370\pi\) | ||||
0.472451 | + | 0.881357i | \(0.343370\pi\) | |||||||
\(992\) | 762.560i | 0.0244066i | ||||||||
\(993\) | − 10456.9i | − 0.334180i | ||||||||
\(994\) | 1740.26 | 0.0555310 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1877.28 | 0.0597227 | ||||||||
\(997\) | − 31944.4i | − 1.01473i | −0.861731 | − | 0.507366i | \(-0.830619\pi\) | ||||
0.861731 | − | 0.507366i | \(-0.169381\pi\) | |||||||
\(998\) | − 35268.4i | − 1.11864i | ||||||||
\(999\) | 922.883 | 0.0292279 |
(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 | 275.4.b.c.199.4 | 4 | ||
5.2 | odd | 4 | 275.4.a.b.1.1 | 2 | |||
5.3 | odd | 4 | 11.4.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 275.4.b.c.199.1 | 4 | ||
15.2 | even | 4 | 2475.4.a.q.1.2 | 2 | |||
15.8 | even | 4 | 99.4.a.c.1.1 | 2 | |||
20.3 | even | 4 | 176.4.a.i.1.2 | 2 | |||
35.13 | even | 4 | 539.4.a.e.1.2 | 2 | |||
40.3 | even | 4 | 704.4.a.n.1.1 | 2 | |||
40.13 | odd | 4 | 704.4.a.p.1.2 | 2 | |||
55.3 | odd | 20 | 121.4.c.c.9.2 | 8 | |||
55.8 | even | 20 | 121.4.c.f.9.1 | 8 | |||
55.13 | even | 20 | 121.4.c.f.81.2 | 8 | |||
55.18 | even | 20 | 121.4.c.f.27.1 | 8 | |||
55.28 | even | 20 | 121.4.c.f.3.2 | 8 | |||
55.38 | odd | 20 | 121.4.c.c.3.1 | 8 | |||
55.43 | even | 4 | 121.4.a.c.1.1 | 2 | |||
55.48 | odd | 20 | 121.4.c.c.27.2 | 8 | |||
55.53 | odd | 20 | 121.4.c.c.81.1 | 8 | |||
60.23 | odd | 4 | 1584.4.a.bc.1.1 | 2 | |||
65.38 | odd | 4 | 1859.4.a.a.1.1 | 2 | |||
165.98 | odd | 4 | 1089.4.a.v.1.2 | 2 | |||
220.43 | odd | 4 | 1936.4.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.4.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
99.4.a.c.1.1 | 2 | 15.8 | even | 4 | |||
121.4.a.c.1.1 | 2 | 55.43 | even | 4 | |||
121.4.c.c.3.1 | 8 | 55.38 | odd | 20 | |||
121.4.c.c.9.2 | 8 | 55.3 | odd | 20 | |||
121.4.c.c.27.2 | 8 | 55.48 | odd | 20 | |||
121.4.c.c.81.1 | 8 | 55.53 | odd | 20 | |||
121.4.c.f.3.2 | 8 | 55.28 | even | 20 | |||
121.4.c.f.9.1 | 8 | 55.8 | even | 20 | |||
121.4.c.f.27.1 | 8 | 55.18 | even | 20 | |||
121.4.c.f.81.2 | 8 | 55.13 | even | 20 | |||
176.4.a.i.1.2 | 2 | 20.3 | even | 4 | |||
275.4.a.b.1.1 | 2 | 5.2 | odd | 4 | |||
275.4.b.c.199.1 | 4 | 5.4 | even | 2 | inner | ||
275.4.b.c.199.4 | 4 | 1.1 | even | 1 | trivial | ||
539.4.a.e.1.2 | 2 | 35.13 | even | 4 | |||
704.4.a.n.1.1 | 2 | 40.3 | even | 4 | |||
704.4.a.p.1.2 | 2 | 40.13 | odd | 4 | |||
1089.4.a.v.1.2 | 2 | 165.98 | odd | 4 | |||
1584.4.a.bc.1.1 | 2 | 60.23 | odd | 4 | |||
1859.4.a.a.1.1 | 2 | 65.38 | odd | 4 | |||
1936.4.a.w.1.2 | 2 | 220.43 | odd | 4 | |||
2475.4.a.q.1.2 | 2 | 15.2 | even | 4 |