Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.23 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.24 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.35197 | 1.89221 | 0.946103 | − | 0.323865i | \(-0.104982\pi\) | ||||
0.946103 | + | 0.323865i | \(0.104982\pi\) | |||||||
\(3\) | 1.66219i | 0.319889i | 0.987126 | + | 0.159944i | \(0.0511315\pi\) | ||||
−0.987126 | + | 0.159944i | \(0.948868\pi\) | |||||||
\(4\) | 20.6436 | 2.58045 | ||||||||
\(5\) | − 5.96899i | − 0.533882i | −0.963713 | − | 0.266941i | \(-0.913987\pi\) | ||||
0.963713 | − | 0.266941i | \(-0.0860129\pi\) | |||||||
\(6\) | 8.89600i | 0.605296i | ||||||||
\(7\) | 27.8210i | 1.50219i | 0.660193 | + | 0.751096i | \(0.270475\pi\) | ||||
−0.660193 | + | 0.751096i | \(0.729525\pi\) | |||||||
\(8\) | 67.6680 | 2.99053 | ||||||||
\(9\) | 24.2371 | 0.897671 | ||||||||
\(10\) | − 31.9458i | − 1.01022i | ||||||||
\(11\) | − 18.6361i | − 0.510816i | −0.966833 | − | 0.255408i | \(-0.917790\pi\) | ||||
0.966833 | − | 0.255408i | \(-0.0822099\pi\) | |||||||
\(12\) | 34.3136i | 0.825456i | ||||||||
\(13\) | −42.5466 | −0.907715 | −0.453857 | − | 0.891074i | \(-0.649952\pi\) | ||||
−0.453857 | + | 0.891074i | \(0.649952\pi\) | |||||||
\(14\) | 148.897i | 2.84246i | ||||||||
\(15\) | 9.92160 | 0.170783 | ||||||||
\(16\) | 197.008 | 3.07826 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 129.716 | 1.69858 | ||||||||
\(19\) | −31.3435 | −0.378457 | −0.189229 | − | 0.981933i | \(-0.560599\pi\) | ||||
−0.189229 | + | 0.981933i | \(0.560599\pi\) | |||||||
\(20\) | − 123.221i | − 1.37765i | ||||||||
\(21\) | −46.2438 | −0.480535 | ||||||||
\(22\) | − 99.7396i | − 0.966570i | ||||||||
\(23\) | − 60.3201i | − 0.546853i | −0.961893 | − | 0.273426i | \(-0.911843\pi\) | ||||
0.961893 | − | 0.273426i | \(-0.0881570\pi\) | |||||||
\(24\) | 112.477i | 0.956638i | ||||||||
\(25\) | 89.3712 | 0.714970 | ||||||||
\(26\) | −227.708 | −1.71758 | ||||||||
\(27\) | 85.1659i | 0.607044i | ||||||||
\(28\) | 574.325i | 3.87633i | ||||||||
\(29\) | 117.647i | 0.753327i | 0.926350 | + | 0.376664i | \(0.122929\pi\) | ||||
−0.926350 | + | 0.376664i | \(0.877071\pi\) | |||||||
\(30\) | 53.1001 | 0.323157 | ||||||||
\(31\) | − 228.520i | − 1.32398i | −0.749512 | − | 0.661991i | \(-0.769712\pi\) | ||||
0.749512 | − | 0.661991i | \(-0.230288\pi\) | |||||||
\(32\) | 513.039 | 2.83417 | ||||||||
\(33\) | 30.9767 | 0.163405 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 166.063 | 0.801994 | ||||||||
\(36\) | 500.341 | 2.31639 | ||||||||
\(37\) | 99.4898i | 0.442055i | 0.975268 | + | 0.221027i | \(0.0709410\pi\) | ||||
−0.975268 | + | 0.221027i | \(0.929059\pi\) | |||||||
\(38\) | −167.749 | −0.716119 | ||||||||
\(39\) | − 70.7206i | − 0.290368i | ||||||||
\(40\) | − 403.909i | − 1.59659i | ||||||||
\(41\) | − 270.844i | − 1.03168i | −0.856686 | − | 0.515838i | \(-0.827481\pi\) | ||||
0.856686 | − | 0.515838i | \(-0.172519\pi\) | |||||||
\(42\) | −247.496 | −0.909271 | ||||||||
\(43\) | −108.891 | −0.386181 | −0.193091 | − | 0.981181i | \(-0.561851\pi\) | ||||
−0.193091 | + | 0.981181i | \(0.561851\pi\) | |||||||
\(44\) | − 384.715i | − 1.31813i | ||||||||
\(45\) | − 144.671i | − 0.479251i | ||||||||
\(46\) | − 322.831i | − 1.03476i | ||||||||
\(47\) | −250.032 | −0.775975 | −0.387988 | − | 0.921665i | \(-0.626830\pi\) | ||||
−0.387988 | + | 0.921665i | \(0.626830\pi\) | |||||||
\(48\) | 327.466i | 0.984700i | ||||||||
\(49\) | −431.008 | −1.25658 | ||||||||
\(50\) | 478.312 | 1.35287 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −878.313 | −2.34231 | ||||||||
\(53\) | −294.775 | −0.763971 | −0.381985 | − | 0.924168i | \(-0.624760\pi\) | ||||
−0.381985 | + | 0.924168i | \(0.624760\pi\) | |||||||
\(54\) | 455.805i | 1.14865i | ||||||||
\(55\) | −111.238 | −0.272716 | ||||||||
\(56\) | 1882.59i | 4.49235i | ||||||||
\(57\) | − 52.0989i | − 0.121064i | ||||||||
\(58\) | 629.643i | 1.42545i | ||||||||
\(59\) | −62.0744 | −0.136973 | −0.0684864 | − | 0.997652i | \(-0.521817\pi\) | ||||
−0.0684864 | + | 0.997652i | \(0.521817\pi\) | |||||||
\(60\) | 204.817 | 0.440697 | ||||||||
\(61\) | − 799.234i | − 1.67757i | −0.544466 | − | 0.838783i | \(-0.683268\pi\) | ||||
0.544466 | − | 0.838783i | \(-0.316732\pi\) | |||||||
\(62\) | − 1223.03i | − 2.50525i | ||||||||
\(63\) | 674.301i | 1.34847i | ||||||||
\(64\) | 1169.70 | 2.28457 | ||||||||
\(65\) | 253.960i | 0.484613i | ||||||||
\(66\) | 165.786 | 0.309195 | ||||||||
\(67\) | −645.320 | −1.17669 | −0.588346 | − | 0.808609i | \(-0.700221\pi\) | ||||
−0.588346 | + | 0.808609i | \(0.700221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 100.264 | 0.174932 | ||||||||
\(70\) | 888.765 | 1.51754 | ||||||||
\(71\) | 1148.97i | 1.92053i | 0.279096 | + | 0.960263i | \(0.409965\pi\) | ||||
−0.279096 | + | 0.960263i | \(0.590035\pi\) | |||||||
\(72\) | 1640.08 | 2.68451 | ||||||||
\(73\) | − 550.710i | − 0.882955i | −0.897272 | − | 0.441477i | \(-0.854455\pi\) | ||||
0.897272 | − | 0.441477i | \(-0.145545\pi\) | |||||||
\(74\) | 532.466i | 0.836459i | ||||||||
\(75\) | 148.552i | 0.228711i | ||||||||
\(76\) | −647.041 | −0.976588 | ||||||||
\(77\) | 518.474 | 0.767345 | ||||||||
\(78\) | − 378.494i | − 0.549436i | ||||||||
\(79\) | 253.834i | 0.361501i | 0.983529 | + | 0.180750i | \(0.0578526\pi\) | ||||
−0.983529 | + | 0.180750i | \(0.942147\pi\) | |||||||
\(80\) | − 1175.94i | − 1.64343i | ||||||||
\(81\) | 512.840 | 0.703484 | ||||||||
\(82\) | − 1449.55i | − 1.95214i | ||||||||
\(83\) | −717.541 | −0.948920 | −0.474460 | − | 0.880277i | \(-0.657357\pi\) | ||||
−0.474460 | + | 0.880277i | \(0.657357\pi\) | |||||||
\(84\) | −954.638 | −1.23999 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −582.784 | −0.730735 | ||||||||
\(87\) | −195.552 | −0.240981 | ||||||||
\(88\) | − 1261.06i | − 1.52761i | ||||||||
\(89\) | −1590.45 | −1.89424 | −0.947121 | − | 0.320877i | \(-0.896022\pi\) | ||||
−0.947121 | + | 0.320877i | \(0.896022\pi\) | |||||||
\(90\) | − 774.275i | − 0.906841i | ||||||||
\(91\) | − 1183.69i | − 1.36356i | ||||||||
\(92\) | − 1245.22i | − 1.41112i | ||||||||
\(93\) | 379.844 | 0.423527 | ||||||||
\(94\) | −1338.16 | −1.46831 | ||||||||
\(95\) | 187.089i | 0.202052i | ||||||||
\(96\) | 852.769i | 0.906619i | ||||||||
\(97\) | 255.084i | 0.267008i | 0.991048 | + | 0.133504i | \(0.0426230\pi\) | ||||
−0.991048 | + | 0.133504i | \(0.957377\pi\) | |||||||
\(98\) | −2306.74 | −2.37771 | ||||||||
\(99\) | − 451.684i | − 0.458545i | ||||||||
\(100\) | 1844.94 | 1.84494 | ||||||||
\(101\) | 1006.58 | 0.991663 | 0.495832 | − | 0.868419i | \(-0.334863\pi\) | ||||
0.495832 | + | 0.868419i | \(0.334863\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1631.61 | 1.56084 | 0.780422 | − | 0.625253i | \(-0.215004\pi\) | ||||
0.780422 | + | 0.625253i | \(0.215004\pi\) | |||||||
\(104\) | −2879.04 | −2.71455 | ||||||||
\(105\) | 276.029i | 0.256549i | ||||||||
\(106\) | −1577.63 | −1.44559 | ||||||||
\(107\) | − 42.5550i | − 0.0384481i | −0.999815 | − | 0.0192241i | \(-0.993880\pi\) | ||||
0.999815 | − | 0.0192241i | \(-0.00611958\pi\) | |||||||
\(108\) | 1758.13i | 1.56644i | ||||||||
\(109\) | − 1862.24i | − 1.63643i | −0.574914 | − | 0.818214i | \(-0.694964\pi\) | ||||
0.574914 | − | 0.818214i | \(-0.305036\pi\) | |||||||
\(110\) | −595.344 | −0.516035 | ||||||||
\(111\) | −165.371 | −0.141408 | ||||||||
\(112\) | 5480.97i | 4.62414i | ||||||||
\(113\) | − 13.5364i | − 0.0112690i | −0.999984 | − | 0.00563452i | \(-0.998206\pi\) | ||||
0.999984 | − | 0.00563452i | \(-0.00179353\pi\) | |||||||
\(114\) | − 278.832i | − 0.229079i | ||||||||
\(115\) | −360.050 | −0.291955 | ||||||||
\(116\) | 2428.65i | 1.94392i | ||||||||
\(117\) | −1031.21 | −0.814829 | ||||||||
\(118\) | −332.220 | −0.259181 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 671.375 | 0.510732 | ||||||||
\(121\) | 983.698 | 0.739067 | ||||||||
\(122\) | − 4277.48i | − 3.17430i | ||||||||
\(123\) | 450.195 | 0.330022 | ||||||||
\(124\) | − 4717.47i | − 3.41646i | ||||||||
\(125\) | − 1279.58i | − 0.915592i | ||||||||
\(126\) | 3608.84i | 2.55159i | ||||||||
\(127\) | 1239.07 | 0.865744 | 0.432872 | − | 0.901455i | \(-0.357500\pi\) | ||||
0.432872 | + | 0.901455i | \(0.357500\pi\) | |||||||
\(128\) | 2155.89 | 1.48872 | ||||||||
\(129\) | − 180.998i | − 0.123535i | ||||||||
\(130\) | 1359.19i | 0.916988i | ||||||||
\(131\) | 1310.04i | 0.873733i | 0.899526 | + | 0.436866i | \(0.143912\pi\) | ||||
−0.899526 | + | 0.436866i | \(0.856088\pi\) | |||||||
\(132\) | 639.470 | 0.421657 | ||||||||
\(133\) | − 872.007i | − 0.568516i | ||||||||
\(134\) | −3453.73 | −2.22655 | ||||||||
\(135\) | 508.354 | 0.324090 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −592.057 | −0.369218 | −0.184609 | − | 0.982812i | \(-0.559102\pi\) | ||||
−0.184609 | + | 0.982812i | \(0.559102\pi\) | |||||||
\(138\) | 536.608 | 0.331008 | ||||||||
\(139\) | 1723.70i | 1.05182i | 0.850541 | + | 0.525908i | \(0.176275\pi\) | ||||
−0.850541 | + | 0.525908i | \(0.823725\pi\) | |||||||
\(140\) | 3428.14 | 2.06950 | ||||||||
\(141\) | − 415.600i | − 0.248226i | ||||||||
\(142\) | 6149.24i | 3.63403i | ||||||||
\(143\) | 792.900i | 0.463676i | ||||||||
\(144\) | 4774.92 | 2.76326 | ||||||||
\(145\) | 702.233 | 0.402188 | ||||||||
\(146\) | − 2947.38i | − 1.67073i | ||||||||
\(147\) | − 716.418i | − 0.401967i | ||||||||
\(148\) | 2053.82i | 1.14070i | ||||||||
\(149\) | −230.059 | −0.126491 | −0.0632456 | − | 0.997998i | \(-0.520145\pi\) | ||||
−0.0632456 | + | 0.997998i | \(0.520145\pi\) | |||||||
\(150\) | 795.046i | 0.432768i | ||||||||
\(151\) | 1876.54 | 1.01133 | 0.505663 | − | 0.862731i | \(-0.331248\pi\) | ||||
0.505663 | + | 0.862731i | \(0.331248\pi\) | |||||||
\(152\) | −2120.95 | −1.13179 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2774.85 | 1.45197 | ||||||||
\(155\) | −1364.03 | −0.706851 | ||||||||
\(156\) | − 1459.92i | − 0.749279i | ||||||||
\(157\) | 1076.29 | 0.547118 | 0.273559 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273559 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(158\) | 1358.51i | 0.684034i | ||||||||
\(159\) | − 489.973i | − 0.244386i | ||||||||
\(160\) | − 3062.32i | − 1.51311i | ||||||||
\(161\) | 1678.17 | 0.821478 | ||||||||
\(162\) | 2744.70 | 1.33114 | ||||||||
\(163\) | 1240.38i | 0.596037i | 0.954560 | + | 0.298018i | \(0.0963257\pi\) | ||||
−0.954560 | + | 0.298018i | \(0.903674\pi\) | |||||||
\(164\) | − 5591.18i | − 2.66218i | ||||||||
\(165\) | − 184.899i | − 0.0872388i | ||||||||
\(166\) | −3840.26 | −1.79555 | ||||||||
\(167\) | 2692.11i | 1.24743i | 0.781650 | + | 0.623717i | \(0.214378\pi\) | ||||
−0.781650 | + | 0.623717i | \(0.785622\pi\) | |||||||
\(168\) | −3129.23 | −1.43705 | ||||||||
\(169\) | −386.790 | −0.176054 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −759.675 | −0.339730 | ||||||||
\(172\) | −2247.91 | −0.996520 | ||||||||
\(173\) | 1819.34i | 0.799548i | 0.916614 | + | 0.399774i | \(0.130911\pi\) | ||||
−0.916614 | + | 0.399774i | \(0.869089\pi\) | |||||||
\(174\) | −1046.59 | −0.455986 | ||||||||
\(175\) | 2486.40i | 1.07402i | ||||||||
\(176\) | − 3671.46i | − 1.57242i | ||||||||
\(177\) | − 103.180i | − 0.0438161i | ||||||||
\(178\) | −8512.05 | −3.58430 | ||||||||
\(179\) | 2087.72 | 0.871752 | 0.435876 | − | 0.900007i | \(-0.356439\pi\) | ||||
0.435876 | + | 0.900007i | \(0.356439\pi\) | |||||||
\(180\) | − 2986.53i | − 1.23668i | ||||||||
\(181\) | 2882.67i | 1.18380i | 0.806013 | + | 0.591898i | \(0.201621\pi\) | ||||
−0.806013 | + | 0.591898i | \(0.798379\pi\) | |||||||
\(182\) | − 6335.06i | − 2.58014i | ||||||||
\(183\) | 1328.48 | 0.536635 | ||||||||
\(184\) | − 4081.74i | − 1.63538i | ||||||||
\(185\) | 593.853 | 0.236005 | ||||||||
\(186\) | 2032.92 | 0.801401 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5161.54 | −2.00236 | ||||||||
\(189\) | −2369.40 | −0.911897 | ||||||||
\(190\) | 1001.29i | 0.382323i | ||||||||
\(191\) | −242.916 | −0.0920249 | −0.0460124 | − | 0.998941i | \(-0.514651\pi\) | ||||
−0.0460124 | + | 0.998941i | \(0.514651\pi\) | |||||||
\(192\) | 1944.27i | 0.730810i | ||||||||
\(193\) | − 3202.66i | − 1.19447i | −0.802067 | − | 0.597234i | \(-0.796266\pi\) | ||||
0.802067 | − | 0.597234i | \(-0.203734\pi\) | |||||||
\(194\) | 1365.20i | 0.505235i | ||||||||
\(195\) | −422.130 | −0.155022 | ||||||||
\(196\) | −8897.54 | −3.24254 | ||||||||
\(197\) | 3624.82i | 1.31095i | 0.755215 | + | 0.655477i | \(0.227532\pi\) | ||||
−0.755215 | + | 0.655477i | \(0.772468\pi\) | |||||||
\(198\) | − 2417.40i | − 0.867662i | ||||||||
\(199\) | − 65.9115i | − 0.0234791i | −0.999931 | − | 0.0117395i | \(-0.996263\pi\) | ||||
0.999931 | − | 0.0117395i | \(-0.00373690\pi\) | |||||||
\(200\) | 6047.57 | 2.13814 | ||||||||
\(201\) | − 1072.65i | − 0.376411i | ||||||||
\(202\) | 5387.16 | 1.87643 | ||||||||
\(203\) | −3273.06 | −1.13164 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1616.66 | −0.550793 | ||||||||
\(206\) | 8732.31 | 2.95344 | ||||||||
\(207\) | − 1461.99i | − 0.490894i | ||||||||
\(208\) | −8382.03 | −2.79418 | ||||||||
\(209\) | 584.119i | 0.193322i | ||||||||
\(210\) | 1477.30i | 0.485444i | ||||||||
\(211\) | − 3523.72i | − 1.14968i | −0.818265 | − | 0.574841i | \(-0.805064\pi\) | ||||
0.818265 | − | 0.574841i | \(-0.194936\pi\) | |||||||
\(212\) | −6085.21 | −1.97139 | ||||||||
\(213\) | −1909.80 | −0.614355 | ||||||||
\(214\) | − 227.753i | − 0.0727518i | ||||||||
\(215\) | 649.972i | 0.206175i | ||||||||
\(216\) | 5763.01i | 1.81538i | ||||||||
\(217\) | 6357.66 | 1.98888 | ||||||||
\(218\) | − 9966.68i | − 3.09646i | ||||||||
\(219\) | 915.385 | 0.282447 | ||||||||
\(220\) | −2296.36 | −0.703729 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −885.061 | −0.267574 | ||||||||
\(223\) | 935.115 | 0.280807 | 0.140404 | − | 0.990094i | \(-0.455160\pi\) | ||||
0.140404 | + | 0.990094i | \(0.455160\pi\) | |||||||
\(224\) | 14273.3i | 4.25747i | ||||||||
\(225\) | 2166.10 | 0.641808 | ||||||||
\(226\) | − 72.4466i | − 0.0213233i | ||||||||
\(227\) | 4987.57i | 1.45831i | 0.684349 | + | 0.729155i | \(0.260087\pi\) | ||||
−0.684349 | + | 0.729155i | \(0.739913\pi\) | |||||||
\(228\) | − 1075.51i | − 0.312400i | ||||||||
\(229\) | 181.488 | 0.0523714 | 0.0261857 | − | 0.999657i | \(-0.491664\pi\) | ||||
0.0261857 | + | 0.999657i | \(0.491664\pi\) | |||||||
\(230\) | −1926.98 | −0.552439 | ||||||||
\(231\) | 861.803i | 0.245465i | ||||||||
\(232\) | 7960.94i | 2.25285i | ||||||||
\(233\) | − 2290.78i | − 0.644095i | −0.946723 | − | 0.322048i | \(-0.895629\pi\) | ||||
0.946723 | − | 0.322048i | \(-0.104371\pi\) | |||||||
\(234\) | −5518.98 | −1.54183 | ||||||||
\(235\) | 1492.43i | 0.414280i | ||||||||
\(236\) | −1281.44 | −0.353451 | ||||||||
\(237\) | −421.921 | −0.115640 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 809.874 | 0.219190 | 0.109595 | − | 0.993976i | \(-0.465045\pi\) | ||||
0.109595 | + | 0.993976i | \(0.465045\pi\) | |||||||
\(240\) | 1954.64 | 0.525714 | ||||||||
\(241\) | − 5634.28i | − 1.50596i | −0.658044 | − | 0.752979i | \(-0.728616\pi\) | ||||
0.658044 | − | 0.752979i | \(-0.271384\pi\) | |||||||
\(242\) | 5264.72 | 1.39847 | ||||||||
\(243\) | 3151.92i | 0.832081i | ||||||||
\(244\) | − 16499.1i | − 4.32887i | ||||||||
\(245\) | 2572.68i | 0.670867i | ||||||||
\(246\) | 2409.43 | 0.624469 | ||||||||
\(247\) | 1333.56 | 0.343531 | ||||||||
\(248\) | − 15463.5i | − 3.95941i | ||||||||
\(249\) | − 1192.69i | − 0.303549i | ||||||||
\(250\) | − 6848.27i | − 1.73249i | ||||||||
\(251\) | 3676.86 | 0.924627 | 0.462314 | − | 0.886717i | \(-0.347019\pi\) | ||||
0.462314 | + | 0.886717i | \(0.347019\pi\) | |||||||
\(252\) | 13920.0i | 3.47967i | ||||||||
\(253\) | −1124.13 | −0.279341 | ||||||||
\(254\) | 6631.45 | 1.63817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2180.66 | 0.532389 | ||||||||
\(257\) | 180.020 | 0.0436938 | 0.0218469 | − | 0.999761i | \(-0.493045\pi\) | ||||
0.0218469 | + | 0.999761i | \(0.493045\pi\) | |||||||
\(258\) | − 968.698i | − 0.233754i | ||||||||
\(259\) | −2767.91 | −0.664051 | ||||||||
\(260\) | 5242.64i | 1.25052i | ||||||||
\(261\) | 2851.42i | 0.676240i | ||||||||
\(262\) | 7011.31i | 1.65328i | ||||||||
\(263\) | 2035.20 | 0.477171 | 0.238586 | − | 0.971121i | \(-0.423316\pi\) | ||||
0.238586 | + | 0.971121i | \(0.423316\pi\) | |||||||
\(264\) | 2096.13 | 0.488666 | ||||||||
\(265\) | 1759.51i | 0.407871i | ||||||||
\(266\) | − 4666.95i | − 1.07575i | ||||||||
\(267\) | − 2643.64i | − 0.605947i | ||||||||
\(268\) | −13321.7 | −3.03639 | ||||||||
\(269\) | 2036.45i | 0.461578i | 0.973004 | + | 0.230789i | \(0.0741308\pi\) | ||||
−0.973004 | + | 0.230789i | \(0.925869\pi\) | |||||||
\(270\) | 2720.70 | 0.613245 | ||||||||
\(271\) | 5126.86 | 1.14920 | 0.574602 | − | 0.818433i | \(-0.305157\pi\) | ||||
0.574602 | + | 0.818433i | \(0.305157\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1967.52 | 0.436189 | ||||||||
\(274\) | −3168.67 | −0.698637 | ||||||||
\(275\) | − 1665.53i | − 0.365218i | ||||||||
\(276\) | 2069.80 | 0.451403 | ||||||||
\(277\) | 4012.79i | 0.870415i | 0.900330 | + | 0.435208i | \(0.143325\pi\) | ||||
−0.900330 | + | 0.435208i | \(0.856675\pi\) | |||||||
\(278\) | 9225.20i | 1.99025i | ||||||||
\(279\) | − 5538.67i | − 1.18850i | ||||||||
\(280\) | 11237.2 | 2.39839 | ||||||||
\(281\) | 6603.25 | 1.40184 | 0.700920 | − | 0.713240i | \(-0.252773\pi\) | ||||
0.700920 | + | 0.713240i | \(0.252773\pi\) | |||||||
\(282\) | − 2224.28i | − 0.469695i | ||||||||
\(283\) | − 108.788i | − 0.0228508i | −0.999935 | − | 0.0114254i | \(-0.996363\pi\) | ||||
0.999935 | − | 0.0114254i | \(-0.00363689\pi\) | |||||||
\(284\) | 23718.8i | 4.95582i | ||||||||
\(285\) | −310.977 | −0.0646341 | ||||||||
\(286\) | 4243.58i | 0.877370i | ||||||||
\(287\) | 7535.15 | 1.54978 | ||||||||
\(288\) | 12434.6 | 2.54415 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 3758.33 | 0.761023 | ||||||||
\(291\) | −423.998 | −0.0854131 | ||||||||
\(292\) | − 11368.6i | − 2.27842i | ||||||||
\(293\) | 9133.49 | 1.82111 | 0.910553 | − | 0.413393i | \(-0.135656\pi\) | ||||
0.910553 | + | 0.413393i | \(0.135656\pi\) | |||||||
\(294\) | − 3834.25i | − 0.760605i | ||||||||
\(295\) | 370.521i | 0.0731274i | ||||||||
\(296\) | 6732.27i | 1.32198i | ||||||||
\(297\) | 1587.16 | 0.310088 | ||||||||
\(298\) | −1231.27 | −0.239348 | ||||||||
\(299\) | 2566.41i | 0.496387i | ||||||||
\(300\) | 3066.65i | 0.590176i | ||||||||
\(301\) | − 3029.47i | − 0.580119i | ||||||||
\(302\) | 10043.2 | 1.91364 | ||||||||
\(303\) | 1673.12i | 0.317222i | ||||||||
\(304\) | −6174.93 | −1.16499 | ||||||||
\(305\) | −4770.62 | −0.895622 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4469.59 | −0.830921 | −0.415461 | − | 0.909611i | \(-0.636380\pi\) | ||||
−0.415461 | + | 0.909611i | \(0.636380\pi\) | |||||||
\(308\) | 10703.1 | 1.98009 | ||||||||
\(309\) | 2712.04i | 0.499297i | ||||||||
\(310\) | −7300.27 | −1.33751 | ||||||||
\(311\) | − 9396.83i | − 1.71333i | −0.515874 | − | 0.856664i | \(-0.672533\pi\) | ||||
0.515874 | − | 0.856664i | \(-0.327467\pi\) | |||||||
\(312\) | − 4785.52i | − 0.868355i | ||||||||
\(313\) | 10276.8i | 1.85583i | 0.372786 | + | 0.927917i | \(0.378403\pi\) | ||||
−0.372786 | + | 0.927917i | \(0.621597\pi\) | |||||||
\(314\) | 5760.29 | 1.03526 | ||||||||
\(315\) | 4024.89 | 0.719927 | ||||||||
\(316\) | 5240.04i | 0.932833i | ||||||||
\(317\) | 7547.44i | 1.33724i | 0.743602 | + | 0.668622i | \(0.233116\pi\) | ||||
−0.743602 | + | 0.668622i | \(0.766884\pi\) | |||||||
\(318\) | − 2622.32i | − 0.462429i | ||||||||
\(319\) | 2192.48 | 0.384812 | ||||||||
\(320\) | − 6981.93i | − 1.21969i | ||||||||
\(321\) | 70.7346 | 0.0122991 | ||||||||
\(322\) | 8981.49 | 1.55441 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 10586.9 | 1.81530 | ||||||||
\(325\) | −3802.44 | −0.648989 | ||||||||
\(326\) | 6638.47i | 1.12782i | ||||||||
\(327\) | 3095.41 | 0.523475 | ||||||||
\(328\) | − 18327.5i | − 3.08526i | ||||||||
\(329\) | − 6956.13i | − 1.16566i | ||||||||
\(330\) | − 989.576i | − 0.165074i | ||||||||
\(331\) | −6285.90 | −1.04382 | −0.521910 | − | 0.853000i | \(-0.674780\pi\) | ||||
−0.521910 | + | 0.853000i | \(0.674780\pi\) | |||||||
\(332\) | −14812.6 | −2.44864 | ||||||||
\(333\) | 2411.35i | 0.396820i | ||||||||
\(334\) | 14408.1i | 2.36040i | ||||||||
\(335\) | 3851.91i | 0.628215i | ||||||||
\(336\) | −9110.43 | −1.47921 | ||||||||
\(337\) | 464.322i | 0.0750541i | 0.999296 | + | 0.0375271i | \(0.0119480\pi\) | ||||
−0.999296 | + | 0.0375271i | \(0.988052\pi\) | |||||||
\(338\) | −2070.09 | −0.333130 | ||||||||
\(339\) | 22.5002 | 0.00360484 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4258.71 | −0.676312 | ||||||||
\(342\) | −4065.76 | −0.642839 | ||||||||
\(343\) | − 2448.47i | − 0.385437i | ||||||||
\(344\) | −7368.47 | −1.15489 | ||||||||
\(345\) | − 598.472i | − 0.0933932i | ||||||||
\(346\) | 9737.05i | 1.51291i | ||||||||
\(347\) | − 7445.29i | − 1.15183i | −0.817510 | − | 0.575914i | \(-0.804646\pi\) | ||||
0.817510 | − | 0.575914i | \(-0.195354\pi\) | |||||||
\(348\) | −4036.89 | −0.621839 | ||||||||
\(349\) | −6395.90 | −0.980987 | −0.490494 | − | 0.871445i | \(-0.663184\pi\) | ||||
−0.490494 | + | 0.871445i | \(0.663184\pi\) | |||||||
\(350\) | 13307.1i | 2.03227i | ||||||||
\(351\) | − 3623.52i | − 0.551023i | ||||||||
\(352\) | − 9561.02i | − 1.44774i | ||||||||
\(353\) | −8031.82 | −1.21102 | −0.605511 | − | 0.795837i | \(-0.707031\pi\) | ||||
−0.605511 | + | 0.795837i | \(0.707031\pi\) | |||||||
\(354\) | − 552.214i | − 0.0829091i | ||||||||
\(355\) | 6858.17 | 1.02534 | ||||||||
\(356\) | −32832.6 | −4.88799 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11173.4 | 1.64953 | ||||||||
\(359\) | 2730.88 | 0.401477 | 0.200738 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200738 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(360\) | − 9789.60i | − 1.43321i | ||||||||
\(361\) | −5876.59 | −0.856770 | ||||||||
\(362\) | 15428.0i | 2.23999i | ||||||||
\(363\) | 1635.09i | 0.236419i | ||||||||
\(364\) | − 24435.5i | − 3.51860i | ||||||||
\(365\) | −3287.18 | −0.471394 | ||||||||
\(366\) | 7109.99 | 1.01542 | ||||||||
\(367\) | − 2802.02i | − 0.398541i | −0.979945 | − | 0.199270i | \(-0.936143\pi\) | ||||
0.979945 | − | 0.199270i | \(-0.0638572\pi\) | |||||||
\(368\) | − 11883.6i | − 1.68335i | ||||||||
\(369\) | − 6564.48i | − 0.926106i | ||||||||
\(370\) | 3178.28 | 0.446570 | ||||||||
\(371\) | − 8200.93i | − 1.14763i | ||||||||
\(372\) | 7841.35 | 1.09289 | ||||||||
\(373\) | 8987.58 | 1.24761 | 0.623806 | − | 0.781579i | \(-0.285585\pi\) | ||||
0.623806 | + | 0.781579i | \(0.285585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2126.91 | 0.292888 | ||||||||
\(376\) | −16919.1 | −2.32058 | ||||||||
\(377\) | − 5005.47i | − 0.683807i | ||||||||
\(378\) | −12681.0 | −1.72550 | ||||||||
\(379\) | 7786.77i | 1.05536i | 0.849445 | + | 0.527678i | \(0.176937\pi\) | ||||
−0.849445 | + | 0.527678i | \(0.823063\pi\) | |||||||
\(380\) | 3862.18i | 0.521383i | ||||||||
\(381\) | 2059.57i | 0.276942i | ||||||||
\(382\) | −1300.08 | −0.174130 | ||||||||
\(383\) | −7557.45 | −1.00827 | −0.504135 | − | 0.863625i | \(-0.668189\pi\) | ||||
−0.504135 | + | 0.863625i | \(0.668189\pi\) | |||||||
\(384\) | 3583.51i | 0.476225i | ||||||||
\(385\) | − 3094.76i | − 0.409672i | ||||||||
\(386\) | − 17140.5i | − 2.26018i | ||||||||
\(387\) | −2639.22 | −0.346664 | ||||||||
\(388\) | 5265.84i | 0.689001i | ||||||||
\(389\) | −10883.8 | −1.41859 | −0.709296 | − | 0.704911i | \(-0.750987\pi\) | ||||
−0.709296 | + | 0.704911i | \(0.750987\pi\) | |||||||
\(390\) | −2259.23 | −0.293334 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −29165.4 | −3.75785 | ||||||||
\(393\) | −2177.54 | −0.279497 | ||||||||
\(394\) | 19399.9i | 2.48060i | ||||||||
\(395\) | 1515.13 | 0.192999 | ||||||||
\(396\) | − 9324.37i | − 1.18325i | ||||||||
\(397\) | − 2103.72i | − 0.265952i | −0.991119 | − | 0.132976i | \(-0.957547\pi\) | ||||
0.991119 | − | 0.132976i | \(-0.0424533\pi\) | |||||||
\(398\) | − 352.756i | − 0.0444273i | ||||||||
\(399\) | 1449.44 | 0.181862 | ||||||||
\(400\) | 17606.9 | 2.20086 | ||||||||
\(401\) | − 10029.6i | − 1.24901i | −0.781021 | − | 0.624505i | \(-0.785301\pi\) | ||||
0.781021 | − | 0.624505i | \(-0.214699\pi\) | |||||||
\(402\) | − 5740.77i | − 0.712247i | ||||||||
\(403\) | 9722.75i | 1.20180i | ||||||||
\(404\) | 20779.3 | 2.55893 | ||||||||
\(405\) | − 3061.13i | − 0.375578i | ||||||||
\(406\) | −17517.3 | −2.14130 | ||||||||
\(407\) | 1854.10 | 0.225809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −515.825 | −0.0623616 | −0.0311808 | − | 0.999514i | \(-0.509927\pi\) | ||||
−0.0311808 | + | 0.999514i | \(0.509927\pi\) | |||||||
\(410\) | −8652.33 | −1.04222 | ||||||||
\(411\) | − 984.113i | − 0.118109i | ||||||||
\(412\) | 33682.2 | 4.02767 | ||||||||
\(413\) | − 1726.97i | − 0.205760i | ||||||||
\(414\) | − 7824.50i | − 0.928873i | ||||||||
\(415\) | 4282.99i | 0.506611i | ||||||||
\(416\) | −21828.1 | −2.57262 | ||||||||
\(417\) | −2865.12 | −0.336465 | ||||||||
\(418\) | 3126.18i | 0.365805i | ||||||||
\(419\) | − 9370.98i | − 1.09261i | −0.837587 | − | 0.546304i | \(-0.816034\pi\) | ||||
0.837587 | − | 0.546304i | \(-0.183966\pi\) | |||||||
\(420\) | 5698.22i | 0.662011i | ||||||||
\(421\) | −283.696 | −0.0328421 | −0.0164210 | − | 0.999865i | \(-0.505227\pi\) | ||||
−0.0164210 | + | 0.999865i | \(0.505227\pi\) | |||||||
\(422\) | − 18858.8i | − 2.17544i | ||||||||
\(423\) | −6060.04 | −0.696571 | ||||||||
\(424\) | −19946.8 | −2.28468 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10221.2 | −1.16249 | ||||||||
\(427\) | 22235.5 | 2.52003 | ||||||||
\(428\) | − 878.487i | − 0.0992133i | ||||||||
\(429\) | −1317.95 | −0.148325 | ||||||||
\(430\) | 3478.63i | 0.390126i | ||||||||
\(431\) | 8243.79i | 0.921321i | 0.887576 | + | 0.460661i | \(0.152387\pi\) | ||||
−0.887576 | + | 0.460661i | \(0.847613\pi\) | |||||||
\(432\) | 16778.4i | 1.86864i | ||||||||
\(433\) | 1340.39 | 0.148765 | 0.0743824 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743824 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(434\) | 34026.0 | 3.76336 | ||||||||
\(435\) | 1167.25i | 0.128656i | ||||||||
\(436\) | − 38443.4i | − 4.22272i | ||||||||
\(437\) | 1890.64i | 0.206960i | ||||||||
\(438\) | 4899.11 | 0.534449 | ||||||||
\(439\) | 4717.90i | 0.512923i | 0.966554 | + | 0.256461i | \(0.0825566\pi\) | ||||
−0.966554 | + | 0.256461i | \(0.917443\pi\) | |||||||
\(440\) | −7527.27 | −0.815565 | ||||||||
\(441\) | −10446.4 | −1.12800 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14002.0 | 1.50171 | 0.750855 | − | 0.660467i | \(-0.229642\pi\) | ||||
0.750855 | + | 0.660467i | \(0.229642\pi\) | |||||||
\(444\) | −3413.85 | −0.364897 | ||||||||
\(445\) | 9493.38i | 1.01130i | ||||||||
\(446\) | 5004.71 | 0.531345 | ||||||||
\(447\) | − 382.403i | − 0.0404632i | ||||||||
\(448\) | 32542.3i | 3.43187i | ||||||||
\(449\) | 4574.27i | 0.480787i | 0.970676 | + | 0.240393i | \(0.0772764\pi\) | ||||
−0.970676 | + | 0.240393i | \(0.922724\pi\) | |||||||
\(450\) | 11592.9 | 1.21443 | ||||||||
\(451\) | −5047.46 | −0.526997 | ||||||||
\(452\) | − 279.440i | − 0.0290791i | ||||||||
\(453\) | 3119.16i | 0.323512i | ||||||||
\(454\) | 26693.3i | 2.75942i | ||||||||
\(455\) | −7065.42 | −0.727982 | ||||||||
\(456\) | − 3525.43i | − 0.362046i | ||||||||
\(457\) | 1535.79 | 0.157202 | 0.0786009 | − | 0.996906i | \(-0.474955\pi\) | ||||
0.0786009 | + | 0.996906i | \(0.474955\pi\) | |||||||
\(458\) | 971.318 | 0.0990976 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7432.72 | −0.753374 | ||||||||
\(461\) | −14514.7 | −1.46642 | −0.733209 | − | 0.680003i | \(-0.761978\pi\) | ||||
−0.733209 | + | 0.680003i | \(0.761978\pi\) | |||||||
\(462\) | 4612.34i | 0.464471i | ||||||||
\(463\) | 145.386 | 0.0145932 | 0.00729659 | − | 0.999973i | \(-0.497677\pi\) | ||||
0.00729659 | + | 0.999973i | \(0.497677\pi\) | |||||||
\(464\) | 23177.4i | 2.31894i | ||||||||
\(465\) | − 2267.29i | − 0.226114i | ||||||||
\(466\) | − 12260.2i | − 1.21876i | ||||||||
\(467\) | −6038.32 | −0.598330 | −0.299165 | − | 0.954201i | \(-0.596708\pi\) | ||||
−0.299165 | + | 0.954201i | \(0.596708\pi\) | |||||||
\(468\) | −21287.8 | −2.10262 | ||||||||
\(469\) | − 17953.4i | − 1.76762i | ||||||||
\(470\) | 7987.46i | 0.783903i | ||||||||
\(471\) | 1789.01i | 0.175017i | ||||||||
\(472\) | −4200.45 | −0.409622 | ||||||||
\(473\) | 2029.31i | 0.197268i | ||||||||
\(474\) | −2258.11 | −0.218815 | ||||||||
\(475\) | −2801.20 | −0.270585 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7144.50 | −0.685795 | ||||||||
\(478\) | 4334.42 | 0.414753 | ||||||||
\(479\) | 9142.21i | 0.872063i | 0.899931 | + | 0.436031i | \(0.143616\pi\) | ||||
−0.899931 | + | 0.436031i | \(0.856384\pi\) | |||||||
\(480\) | 5090.17 | 0.484028 | ||||||||
\(481\) | − 4232.95i | − 0.401260i | ||||||||
\(482\) | − 30154.5i | − 2.84958i | ||||||||
\(483\) | 2789.43i | 0.262782i | ||||||||
\(484\) | 20307.0 | 1.90712 | ||||||||
\(485\) | 1522.59 | 0.142551 | ||||||||
\(486\) | 16869.0i | 1.57447i | ||||||||
\(487\) | − 4376.57i | − 0.407231i | −0.979051 | − | 0.203615i | \(-0.934731\pi\) | ||||
0.979051 | − | 0.203615i | \(-0.0652692\pi\) | |||||||
\(488\) | − 54082.6i | − 5.01681i | ||||||||
\(489\) | −2061.75 | −0.190666 | ||||||||
\(490\) | 13768.9i | 1.26942i | ||||||||
\(491\) | −9490.30 | −0.872284 | −0.436142 | − | 0.899878i | \(-0.643655\pi\) | ||||
−0.436142 | + | 0.899878i | \(0.643655\pi\) | |||||||
\(492\) | 9293.62 | 0.851603 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7137.16 | 0.650032 | ||||||||
\(495\) | −2696.10 | −0.244809 | ||||||||
\(496\) | − 45020.4i | − 4.07556i | ||||||||
\(497\) | −31965.4 | −2.88500 | ||||||||
\(498\) | − 6383.24i | − 0.574377i | ||||||||
\(499\) | 2331.32i | 0.209147i | 0.994517 | + | 0.104573i | \(0.0333477\pi\) | ||||
−0.994517 | + | 0.104573i | \(0.966652\pi\) | |||||||
\(500\) | − 26415.1i | − 2.36264i | ||||||||
\(501\) | −4474.80 | −0.399041 | ||||||||
\(502\) | 19678.4 | 1.74959 | ||||||||
\(503\) | − 4372.95i | − 0.387635i | −0.981038 | − | 0.193817i | \(-0.937913\pi\) | ||||
0.981038 | − | 0.193817i | \(-0.0620869\pi\) | |||||||
\(504\) | 45628.6i | 4.03266i | ||||||||
\(505\) | − 6008.23i | − 0.529431i | ||||||||
\(506\) | −6016.30 | −0.528572 | ||||||||
\(507\) | − 642.919i | − 0.0563176i | ||||||||
\(508\) | 25578.8 | 2.23401 | ||||||||
\(509\) | 4983.33 | 0.433954 | 0.216977 | − | 0.976177i | \(-0.430380\pi\) | ||||
0.216977 | + | 0.976177i | \(0.430380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15321.3 | 1.32637 | ||||||||
\(512\) | −5576.30 | −0.481328 | ||||||||
\(513\) | − 2669.40i | − 0.229740i | ||||||||
\(514\) | 963.460 | 0.0826778 | ||||||||
\(515\) | − 9739.03i | − 0.833307i | ||||||||
\(516\) | − 3736.46i | − 0.318776i | ||||||||
\(517\) | 4659.60i | 0.396381i | ||||||||
\(518\) | −14813.7 | −1.25652 | ||||||||
\(519\) | −3024.09 | −0.255767 | ||||||||
\(520\) | 17185.0i | 1.44925i | ||||||||
\(521\) | 6480.02i | 0.544903i | 0.962169 | + | 0.272452i | \(0.0878345\pi\) | ||||
−0.962169 | + | 0.272452i | \(0.912166\pi\) | |||||||
\(522\) | 15260.7i | 1.27959i | ||||||||
\(523\) | −15597.0 | −1.30403 | −0.652017 | − | 0.758204i | \(-0.726077\pi\) | ||||
−0.652017 | + | 0.758204i | \(0.726077\pi\) | |||||||
\(524\) | 27044.0i | 2.25462i | ||||||||
\(525\) | −4132.87 | −0.343568 | ||||||||
\(526\) | 10892.4 | 0.902907 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 6102.67 | 0.503001 | ||||||||
\(529\) | 8528.48 | 0.700952 | ||||||||
\(530\) | 9416.83i | 0.771775i | ||||||||
\(531\) | −1504.50 | −0.122957 | ||||||||
\(532\) | − 18001.3i | − 1.46702i | ||||||||
\(533\) | 11523.5i | 0.936468i | ||||||||
\(534\) | − 14148.7i | − 1.14658i | ||||||||
\(535\) | −254.010 | −0.0205268 | ||||||||
\(536\) | −43667.5 | −3.51894 | ||||||||
\(537\) | 3470.19i | 0.278864i | ||||||||
\(538\) | 10899.0i | 0.873402i | ||||||||
\(539\) | 8032.29i | 0.641883i | ||||||||
\(540\) | 10494.2 | 0.836297 | ||||||||
\(541\) | − 10629.6i | − 0.844739i | −0.906424 | − | 0.422370i | \(-0.861198\pi\) | ||||
0.906424 | − | 0.422370i | \(-0.138802\pi\) | |||||||
\(542\) | 27438.8 | 2.17453 | ||||||||
\(543\) | −4791.55 | −0.378683 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11115.7 | −0.873660 | ||||||||
\(546\) | 10530.1 | 0.825359 | ||||||||
\(547\) | 12199.5i | 0.953588i | 0.879015 | + | 0.476794i | \(0.158201\pi\) | ||||
−0.879015 | + | 0.476794i | \(0.841799\pi\) | |||||||
\(548\) | −12222.2 | −0.952747 | ||||||||
\(549\) | − 19371.1i | − 1.50590i | ||||||||
\(550\) | − 8913.85i | − 0.691068i | ||||||||
\(551\) | − 3687.46i | − 0.285102i | ||||||||
\(552\) | 6784.64 | 0.523140 | ||||||||
\(553\) | −7061.91 | −0.543044 | ||||||||
\(554\) | 21476.3i | 1.64701i | ||||||||
\(555\) | 987.098i | 0.0754954i | ||||||||
\(556\) | 35583.4i | 2.71416i | ||||||||
\(557\) | −17588.3 | −1.33796 | −0.668978 | − | 0.743282i | \(-0.733268\pi\) | ||||
−0.668978 | + | 0.743282i | \(0.733268\pi\) | |||||||
\(558\) | − 29642.8i | − 2.24889i | ||||||||
\(559\) | 4632.96 | 0.350542 | ||||||||
\(560\) | 32715.8 | 2.46874 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 35340.4 | 2.65257 | ||||||||
\(563\) | 4001.08 | 0.299513 | 0.149756 | − | 0.988723i | \(-0.452151\pi\) | ||||
0.149756 | + | 0.988723i | \(0.452151\pi\) | |||||||
\(564\) | − 8579.48i | − 0.640534i | ||||||||
\(565\) | −80.7988 | −0.00601634 | ||||||||
\(566\) | − 582.229i | − 0.0432384i | ||||||||
\(567\) | 14267.7i | 1.05677i | ||||||||
\(568\) | 77748.3i | 5.74339i | ||||||||
\(569\) | 8055.37 | 0.593495 | 0.296747 | − | 0.954956i | \(-0.404098\pi\) | ||||
0.296747 | + | 0.954956i | \(0.404098\pi\) | |||||||
\(570\) | −1664.34 | −0.122301 | ||||||||
\(571\) | − 12525.5i | − 0.917998i | −0.888437 | − | 0.458999i | \(-0.848208\pi\) | ||||
0.888437 | − | 0.458999i | \(-0.151792\pi\) | |||||||
\(572\) | 16368.3i | 1.19649i | ||||||||
\(573\) | − 403.772i | − 0.0294378i | ||||||||
\(574\) | 40327.9 | 2.93250 | ||||||||
\(575\) | − 5390.88i | − 0.390983i | ||||||||
\(576\) | 28350.2 | 2.05080 | ||||||||
\(577\) | 7783.77 | 0.561599 | 0.280799 | − | 0.959766i | \(-0.409400\pi\) | ||||
0.280799 | + | 0.959766i | \(0.409400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5323.43 | 0.382097 | ||||||||
\(580\) | 14496.6 | 1.03782 | ||||||||
\(581\) | − 19962.7i | − 1.42546i | ||||||||
\(582\) | −2269.22 | −0.161619 | ||||||||
\(583\) | 5493.44i | 0.390249i | ||||||||
\(584\) | − 37265.4i | − 2.64050i | ||||||||
\(585\) | 6155.25i | 0.435023i | ||||||||
\(586\) | 48882.1 | 3.44591 | ||||||||
\(587\) | −17282.7 | −1.21522 | −0.607608 | − | 0.794237i | \(-0.707871\pi\) | ||||
−0.607608 | + | 0.794237i | \(0.707871\pi\) | |||||||
\(588\) | − 14789.4i | − 1.03725i | ||||||||
\(589\) | 7162.62i | 0.501070i | ||||||||
\(590\) | 1983.02i | 0.138372i | ||||||||
\(591\) | −6025.15 | −0.419360 | ||||||||
\(592\) | 19600.3i | 1.36076i | ||||||||
\(593\) | −22285.6 | −1.54327 | −0.771636 | − | 0.636065i | \(-0.780561\pi\) | ||||
−0.771636 | + | 0.636065i | \(0.780561\pi\) | |||||||
\(594\) | 8494.41 | 0.586751 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4749.25 | −0.326404 | ||||||||
\(597\) | 109.557 | 0.00751070 | ||||||||
\(598\) | 13735.4i | 0.939266i | ||||||||
\(599\) | 14494.3 | 0.988681 | 0.494340 | − | 0.869268i | \(-0.335410\pi\) | ||||
0.494340 | + | 0.869268i | \(0.335410\pi\) | |||||||
\(600\) | 10052.2i | 0.683967i | ||||||||
\(601\) | − 13389.8i | − 0.908790i | −0.890800 | − | 0.454395i | \(-0.849856\pi\) | ||||
0.890800 | − | 0.454395i | \(-0.150144\pi\) | |||||||
\(602\) | − 16213.6i | − 1.09770i | ||||||||
\(603\) | −15640.7 | −1.05628 | ||||||||
\(604\) | 38738.4 | 2.60967 | ||||||||
\(605\) | − 5871.68i | − 0.394575i | ||||||||
\(606\) | 8954.49i | 0.600250i | ||||||||
\(607\) | 5081.09i | 0.339761i | 0.985465 | + | 0.169881i | \(0.0543382\pi\) | ||||
−0.985465 | + | 0.169881i | \(0.945662\pi\) | |||||||
\(608\) | −16080.4 | −1.07261 | ||||||||
\(609\) | − 5440.45i | − 0.362000i | ||||||||
\(610\) | −25532.2 | −1.69470 | ||||||||
\(611\) | 10638.0 | 0.704365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29310.1 | −1.93120 | −0.965598 | − | 0.260040i | \(-0.916264\pi\) | ||||
−0.965598 | + | 0.260040i | \(0.916264\pi\) | |||||||
\(614\) | −23921.1 | −1.57227 | ||||||||
\(615\) | − 2687.20i | − 0.176193i | ||||||||
\(616\) | 35084.1 | 2.29477 | ||||||||
\(617\) | − 9815.75i | − 0.640466i | −0.947339 | − | 0.320233i | \(-0.896239\pi\) | ||||
0.947339 | − | 0.320233i | \(-0.103761\pi\) | |||||||
\(618\) | 14514.8i | 0.944773i | ||||||||
\(619\) | − 10696.9i | − 0.694579i | −0.937758 | − | 0.347290i | \(-0.887102\pi\) | ||||
0.937758 | − | 0.347290i | \(-0.112898\pi\) | |||||||
\(620\) | −28158.5 | −1.82399 | ||||||||
\(621\) | 5137.22 | 0.331964 | ||||||||
\(622\) | − 50291.5i | − 3.24197i | ||||||||
\(623\) | − 44247.9i | − 2.84552i | ||||||||
\(624\) | − 13932.5i | − 0.893827i | ||||||||
\(625\) | 3533.62 | 0.226151 | ||||||||
\(626\) | 55000.8i | 3.51162i | ||||||||
\(627\) | −970.917 | −0.0618416 | ||||||||
\(628\) | 22218.5 | 1.41181 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 21541.1 | 1.36225 | ||||||||
\(631\) | 6104.87 | 0.385152 | 0.192576 | − | 0.981282i | \(-0.438316\pi\) | ||||
0.192576 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(632\) | 17176.4i | 1.08108i | ||||||||
\(633\) | 5857.10 | 0.367771 | ||||||||
\(634\) | 40393.7i | 2.53034i | ||||||||
\(635\) | − 7395.98i | − 0.462205i | ||||||||
\(636\) | − 10114.8i | − 0.630625i | ||||||||
\(637\) | 18337.9 | 1.14062 | ||||||||
\(638\) | 11734.1 | 0.728144 | ||||||||
\(639\) | 27847.7i | 1.72400i | ||||||||
\(640\) | − 12868.5i | − 0.794800i | ||||||||
\(641\) | − 3753.93i | − 0.231312i | −0.993289 | − | 0.115656i | \(-0.963103\pi\) | ||||
0.993289 | − | 0.115656i | \(-0.0368971\pi\) | |||||||
\(642\) | 378.569 | 0.0232725 | ||||||||
\(643\) | 22480.9i | 1.37879i | 0.724386 | + | 0.689394i | \(0.242123\pi\) | ||||
−0.724386 | + | 0.689394i | \(0.757877\pi\) | |||||||
\(644\) | 34643.3 | 2.11978 | ||||||||
\(645\) | −1080.38 | −0.0659532 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20385.1 | 1.23867 | 0.619337 | − | 0.785126i | \(-0.287402\pi\) | ||||
0.619337 | + | 0.785126i | \(0.287402\pi\) | |||||||
\(648\) | 34702.9 | 2.10379 | ||||||||
\(649\) | 1156.82i | 0.0699680i | ||||||||
\(650\) | −20350.5 | −1.22802 | ||||||||
\(651\) | 10567.7i | 0.636220i | ||||||||
\(652\) | 25605.9i | 1.53804i | ||||||||
\(653\) | − 7944.24i | − 0.476083i | −0.971255 | − | 0.238041i | \(-0.923495\pi\) | ||||
0.971255 | − | 0.238041i | \(-0.0765054\pi\) | |||||||
\(654\) | 16566.5 | 0.990524 | ||||||||
\(655\) | 7819.63 | 0.466470 | ||||||||
\(656\) | − 53358.5i | − 3.17576i | ||||||||
\(657\) | − 13347.6i | − 0.792603i | ||||||||
\(658\) | − 37229.0i | − 2.20568i | ||||||||
\(659\) | −672.385 | −0.0397457 | −0.0198728 | − | 0.999803i | \(-0.506326\pi\) | ||||
−0.0198728 | + | 0.999803i | \(0.506326\pi\) | |||||||
\(660\) | − 3816.98i | − 0.225115i | ||||||||
\(661\) | 7967.64 | 0.468843 | 0.234421 | − | 0.972135i | \(-0.424680\pi\) | ||||
0.234421 | + | 0.972135i | \(0.424680\pi\) | |||||||
\(662\) | −33642.0 | −1.97512 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −48554.5 | −2.83777 | ||||||||
\(665\) | −5205.00 | −0.303520 | ||||||||
\(666\) | 12905.4i | 0.750865i | ||||||||
\(667\) | 7096.48 | 0.411959 | ||||||||
\(668\) | 55574.7i | 3.21894i | ||||||||
\(669\) | 1554.34i | 0.0898271i | ||||||||
\(670\) | 20615.3i | 1.18871i | ||||||||
\(671\) | −14894.6 | −0.856928 | ||||||||
\(672\) | −23724.9 | −1.36192 | ||||||||
\(673\) | − 20798.2i | − 1.19125i | −0.803262 | − | 0.595626i | \(-0.796904\pi\) | ||||
0.803262 | − | 0.595626i | \(-0.203096\pi\) | |||||||
\(674\) | 2485.04i | 0.142018i | ||||||||
\(675\) | 7611.38i | 0.434018i | ||||||||
\(676\) | −7984.72 | −0.454297 | ||||||||
\(677\) | − 19180.9i | − 1.08890i | −0.838794 | − | 0.544449i | \(-0.816739\pi\) | ||||
0.838794 | − | 0.544449i | \(-0.183261\pi\) | |||||||
\(678\) | 120.420 | 0.00682110 | ||||||||
\(679\) | −7096.68 | −0.401098 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8290.29 | −0.466497 | ||||||||
\(682\) | −22792.5 | −1.27972 | ||||||||
\(683\) | − 7081.83i | − 0.396748i | −0.980126 | − | 0.198374i | \(-0.936434\pi\) | ||||
0.980126 | − | 0.198374i | \(-0.0635661\pi\) | |||||||
\(684\) | −15682.4 | −0.876655 | ||||||||
\(685\) | 3533.98i | 0.197119i | ||||||||
\(686\) | − 13104.1i | − 0.729326i | ||||||||
\(687\) | 301.668i | 0.0167530i | ||||||||
\(688\) | −21452.5 | −1.18876 | ||||||||
\(689\) | 12541.7 | 0.693468 | ||||||||
\(690\) | − 3203.00i | − 0.176719i | ||||||||
\(691\) | 27665.8i | 1.52309i | 0.648110 | + | 0.761547i | \(0.275560\pi\) | ||||
−0.648110 | + | 0.761547i | \(0.724440\pi\) | |||||||
\(692\) | 37557.7i | 2.06319i | ||||||||
\(693\) | 12566.3 | 0.688823 | ||||||||
\(694\) | − 39847.0i | − 2.17950i | ||||||||
\(695\) | 10288.8 | 0.561546 | ||||||||
\(696\) | −13232.6 | −0.720662 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −34230.7 | −1.85623 | ||||||||
\(699\) | 3807.72 | 0.206039 | ||||||||
\(700\) | 51328.1i | 2.77146i | ||||||||
\(701\) | −7813.26 | −0.420974 | −0.210487 | − | 0.977597i | \(-0.567505\pi\) | ||||
−0.210487 | + | 0.977597i | \(0.567505\pi\) | |||||||
\(702\) | − 19393.0i | − 1.04265i | ||||||||
\(703\) | − 3118.36i | − 0.167299i | ||||||||
\(704\) | − 21798.6i | − 1.16700i | ||||||||
\(705\) | −2480.71 | −0.132523 | ||||||||
\(706\) | −42986.0 | −2.29150 | ||||||||
\(707\) | 28003.9i | 1.48967i | ||||||||
\(708\) | − 2129.99i | − 0.113065i | ||||||||
\(709\) | − 21810.2i | − 1.15529i | −0.816288 | − | 0.577645i | \(-0.803972\pi\) | ||||
0.816288 | − | 0.577645i | \(-0.196028\pi\) | |||||||
\(710\) | 36704.7 | 1.94015 | ||||||||
\(711\) | 6152.20i | 0.324509i | ||||||||
\(712\) | −107623. | −5.66479 | ||||||||
\(713\) | −13784.4 | −0.724023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4732.81 | 0.247548 | ||||||||
\(716\) | 43098.0 | 2.24951 | ||||||||
\(717\) | 1346.17i | 0.0701164i | ||||||||
\(718\) | 14615.6 | 0.759677 | ||||||||
\(719\) | − 2333.31i | − 0.121026i | −0.998167 | − | 0.0605131i | \(-0.980726\pi\) | ||||
0.998167 | − | 0.0605131i | \(-0.0192737\pi\) | |||||||
\(720\) | − 28501.4i | − 1.47526i | ||||||||
\(721\) | 45392.9i | 2.34469i | ||||||||
\(722\) | −31451.3 | −1.62119 | ||||||||
\(723\) | 9365.26 | 0.481740 | ||||||||
\(724\) | 59508.6i | 3.05472i | ||||||||
\(725\) | 10514.3i | 0.538606i | ||||||||
\(726\) | 8750.97i | 0.447354i | ||||||||
\(727\) | 545.182 | 0.0278125 | 0.0139063 | − | 0.999903i | \(-0.495573\pi\) | ||||
0.0139063 | + | 0.999903i | \(0.495573\pi\) | |||||||
\(728\) | − 80097.8i | − 4.07778i | ||||||||
\(729\) | 8607.59 | 0.437311 | ||||||||
\(730\) | −17592.9 | −0.891975 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 27424.6 | 1.38476 | ||||||||
\(733\) | 2753.41 | 0.138744 | 0.0693721 | − | 0.997591i | \(-0.477900\pi\) | ||||
0.0693721 | + | 0.997591i | \(0.477900\pi\) | |||||||
\(734\) | − 14996.4i | − 0.754122i | ||||||||
\(735\) | −4276.29 | −0.214603 | ||||||||
\(736\) | − 30946.6i | − 1.54987i | ||||||||
\(737\) | 12026.2i | 0.601074i | ||||||||
\(738\) | − 35132.9i | − 1.75238i | ||||||||
\(739\) | −25776.3 | −1.28308 | −0.641540 | − | 0.767089i | \(-0.721704\pi\) | ||||
−0.641540 | + | 0.767089i | \(0.721704\pi\) | |||||||
\(740\) | 12259.2 | 0.608999 | ||||||||
\(741\) | 2216.63i | 0.109892i | ||||||||
\(742\) | − 43891.1i | − 2.17156i | ||||||||
\(743\) | − 17597.0i | − 0.868872i | −0.900703 | − | 0.434436i | \(-0.856948\pi\) | ||||
0.900703 | − | 0.434436i | \(-0.143052\pi\) | |||||||
\(744\) | 25703.3 | 1.26657 | ||||||||
\(745\) | 1373.22i | 0.0675314i | ||||||||
\(746\) | 48101.3 | 2.36074 | ||||||||
\(747\) | −17391.1 | −0.851818 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1183.92 | 0.0577565 | ||||||||
\(750\) | 11383.1 | 0.554204 | ||||||||
\(751\) | 1515.51i | 0.0736373i | 0.999322 | + | 0.0368186i | \(0.0117224\pi\) | ||||
−0.999322 | + | 0.0368186i | \(0.988278\pi\) | |||||||
\(752\) | −49258.3 | −2.38865 | ||||||||
\(753\) | 6111.65i | 0.295778i | ||||||||
\(754\) | − 26789.1i | − 1.29390i | ||||||||
\(755\) | − 11201.0i | − 0.539929i | ||||||||
\(756\) | −48912.9 | −2.35310 | ||||||||
\(757\) | −19464.1 | −0.934523 | −0.467261 | − | 0.884119i | \(-0.654759\pi\) | ||||
−0.467261 | + | 0.884119i | \(0.654759\pi\) | |||||||
\(758\) | 41674.6i | 1.99695i | ||||||||
\(759\) | − 1868.52i | − 0.0893583i | ||||||||
\(760\) | 12659.9i | 0.604242i | ||||||||
\(761\) | 11937.8 | 0.568652 | 0.284326 | − | 0.958728i | \(-0.408230\pi\) | ||||
0.284326 | + | 0.958728i | \(0.408230\pi\) | |||||||
\(762\) | 11022.7i | 0.524031i | ||||||||
\(763\) | 51809.5 | 2.45823 | ||||||||
\(764\) | −5014.65 | −0.237465 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40447.2 | −1.90786 | ||||||||
\(767\) | 2641.05 | 0.124332 | ||||||||
\(768\) | 3624.68i | 0.170305i | ||||||||
\(769\) | 26884.3 | 1.26069 | 0.630345 | − | 0.776315i | \(-0.282913\pi\) | ||||
0.630345 | + | 0.776315i | \(0.282913\pi\) | |||||||
\(770\) | − 16563.1i | − 0.775184i | ||||||||
\(771\) | 299.227i | 0.0139772i | ||||||||
\(772\) | − 66114.3i | − 3.08226i | ||||||||
\(773\) | 12551.4 | 0.584013 | 0.292006 | − | 0.956416i | \(-0.405677\pi\) | ||||
0.292006 | + | 0.956416i | \(0.405677\pi\) | |||||||
\(774\) | −14125.0 | −0.655959 | ||||||||
\(775\) | − 20423.1i | − 0.946607i | ||||||||
\(776\) | 17261.0i | 0.798497i | ||||||||
\(777\) | − 4600.79i | − 0.212423i | ||||||||
\(778\) | −58249.9 | −2.68427 | ||||||||
\(779\) | 8489.19i | 0.390445i | ||||||||
\(780\) | −8714.27 | −0.400027 | ||||||||
\(781\) | 21412.2 | 0.981036 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10019.5 | −0.457303 | ||||||||
\(784\) | −84912.2 | −3.86808 | ||||||||
\(785\) | − 6424.38i | − 0.292097i | ||||||||
\(786\) | −11654.1 | −0.528867 | ||||||||
\(787\) | 17781.7i | 0.805400i | 0.915332 | + | 0.402700i | \(0.131928\pi\) | ||||
−0.915332 | + | 0.402700i | \(0.868072\pi\) | |||||||
\(788\) | 74829.3i | 3.38285i | ||||||||
\(789\) | 3382.90i | 0.152642i | ||||||||
\(790\) | 8108.94 | 0.365194 | ||||||||
\(791\) | 376.597 | 0.0169283 | ||||||||
\(792\) | − 30564.6i | − 1.37129i | ||||||||
\(793\) | 34004.7i | 1.52275i | ||||||||
\(794\) | − 11259.1i | − 0.503235i | ||||||||
\(795\) | −2924.64 | −0.130473 | ||||||||
\(796\) | − 1360.65i | − 0.0605865i | ||||||||
\(797\) | −36529.5 | −1.62352 | −0.811758 | − | 0.583995i | \(-0.801489\pi\) | ||||
−0.811758 | + | 0.583995i | \(0.801489\pi\) | |||||||
\(798\) | 7757.37 | 0.344120 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 45850.9 | 2.02634 | ||||||||
\(801\) | −38548.0 | −1.70041 | ||||||||
\(802\) | − 53677.9i | − 2.36338i | ||||||||
\(803\) | −10263.1 | −0.451028 | ||||||||
\(804\) | − 22143.2i | − 0.971308i | ||||||||
\(805\) | − 10017.0i | − 0.438573i | ||||||||
\(806\) | 52035.9i | 2.27405i | ||||||||
\(807\) | −3384.97 | −0.147654 | ||||||||
\(808\) | 68112.9 | 2.96560 | ||||||||
\(809\) | 19732.6i | 0.857555i | 0.903410 | + | 0.428777i | \(0.141055\pi\) | ||||
−0.903410 | + | 0.428777i | \(0.858945\pi\) | |||||||
\(810\) | − 16383.1i | − 0.710671i | ||||||||
\(811\) | − 14943.7i | − 0.647035i | −0.946222 | − | 0.323517i | \(-0.895135\pi\) | ||||
0.946222 | − | 0.323517i | \(-0.104865\pi\) | |||||||
\(812\) | −67567.6 | −2.92014 | ||||||||
\(813\) | 8521.82i | 0.367618i | ||||||||
\(814\) | 9923.07 | 0.427277 | ||||||||
\(815\) | 7403.80 | 0.318213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3413.04 | 0.146153 | ||||||||
\(818\) | −2760.68 | −0.118001 | ||||||||
\(819\) | − 28689.2i | − 1.22403i | ||||||||
\(820\) | −33373.7 | −1.42129 | ||||||||
\(821\) | 31002.2i | 1.31789i | 0.752193 | + | 0.658943i | \(0.228996\pi\) | ||||
−0.752193 | + | 0.658943i | \(0.771004\pi\) | |||||||
\(822\) | − 5266.94i | − 0.223486i | ||||||||
\(823\) | − 27393.7i | − 1.16025i | −0.814528 | − | 0.580124i | \(-0.803004\pi\) | ||||
0.814528 | − | 0.580124i | \(-0.196996\pi\) | |||||||
\(824\) | 110408. | 4.66775 | ||||||||
\(825\) | 2768.42 | 0.116829 | ||||||||
\(826\) | − 9242.70i | − 0.389340i | ||||||||
\(827\) | − 674.496i | − 0.0283610i | −0.999899 | − | 0.0141805i | \(-0.995486\pi\) | ||||
0.999899 | − | 0.0141805i | \(-0.00451394\pi\) | |||||||
\(828\) | − 30180.6i | − 1.26673i | ||||||||
\(829\) | 42790.2 | 1.79272 | 0.896359 | − | 0.443328i | \(-0.146202\pi\) | ||||
0.896359 | + | 0.443328i | \(0.146202\pi\) | |||||||
\(830\) | 22922.4i | 0.958613i | ||||||||
\(831\) | −6670.02 | −0.278436 | ||||||||
\(832\) | −49766.8 | −2.07374 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15334.1 | −0.636661 | ||||||||
\(835\) | 16069.2 | 0.665983 | ||||||||
\(836\) | 12058.3i | 0.498857i | ||||||||
\(837\) | 19462.1 | 0.803715 | ||||||||
\(838\) | − 50153.2i | − 2.06744i | ||||||||
\(839\) | 25582.3i | 1.05268i | 0.850274 | + | 0.526340i | \(0.176436\pi\) | ||||
−0.850274 | + | 0.526340i | \(0.823564\pi\) | |||||||
\(840\) | 18678.3i | 0.767218i | ||||||||
\(841\) | 10548.2 | 0.432498 | ||||||||
\(842\) | −1518.33 | −0.0621440 | ||||||||
\(843\) | 10975.9i | 0.448433i | ||||||||
\(844\) | − 72742.2i | − 2.96669i | ||||||||
\(845\) | 2308.74i | 0.0939919i | ||||||||
\(846\) | −32433.2 | −1.31806 | ||||||||
\(847\) | 27367.4i | 1.11022i | ||||||||
\(848\) | −58073.2 | −2.35170 | ||||||||
\(849\) | 180.826 | 0.00730971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6001.24 | 0.241739 | ||||||||
\(852\) | −39425.2 | −1.58531 | ||||||||
\(853\) | − 26776.3i | − 1.07480i | −0.843328 | − | 0.537400i | \(-0.819407\pi\) | ||||
0.843328 | − | 0.537400i | \(-0.180593\pi\) | |||||||
\(854\) | 119004. | 4.76841 | ||||||||
\(855\) | 4534.49i | 0.181376i | ||||||||
\(856\) | − 2879.61i | − 0.114980i | ||||||||
\(857\) | − 2239.80i | − 0.0892767i | −0.999003 | − | 0.0446383i | \(-0.985786\pi\) | ||||
0.999003 | − | 0.0446383i | \(-0.0142135\pi\) | |||||||
\(858\) | −7053.64 | −0.280661 | ||||||||
\(859\) | 13841.5 | 0.549784 | 0.274892 | − | 0.961475i | \(-0.411358\pi\) | ||||
0.274892 | + | 0.961475i | \(0.411358\pi\) | |||||||
\(860\) | 13417.7i | 0.532024i | ||||||||
\(861\) | 12524.9i | 0.495756i | ||||||||
\(862\) | 44120.5i | 1.74333i | ||||||||
\(863\) | 41377.2 | 1.63209 | 0.816046 | − | 0.577987i | \(-0.196161\pi\) | ||||
0.816046 | + | 0.577987i | \(0.196161\pi\) | |||||||
\(864\) | 43693.4i | 1.72046i | ||||||||
\(865\) | 10859.6 | 0.426864 | ||||||||
\(866\) | 7173.74 | 0.281494 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 131245. | 5.13219 | ||||||||
\(869\) | 4730.46 | 0.184660 | ||||||||
\(870\) | 6247.07i | 0.243443i | ||||||||
\(871\) | 27456.2 | 1.06810 | ||||||||
\(872\) | − 126014.i | − 4.89379i | ||||||||
\(873\) | 6182.49i | 0.239686i | ||||||||
\(874\) | 10118.7i | 0.391612i | ||||||||
\(875\) | 35599.2 | 1.37540 | ||||||||
\(876\) | 18896.8 | 0.728840 | ||||||||
\(877\) | 12605.0i | 0.485337i | 0.970109 | + | 0.242668i | \(0.0780227\pi\) | ||||
−0.970109 | + | 0.242668i | \(0.921977\pi\) | |||||||
\(878\) | 25250.1i | 0.970556i | ||||||||
\(879\) | 15181.6i | 0.582552i | ||||||||
\(880\) | −21914.9 | −0.839489 | ||||||||
\(881\) | − 20007.8i | − 0.765132i | −0.923928 | − | 0.382566i | \(-0.875040\pi\) | ||||
0.923928 | − | 0.382566i | \(-0.124960\pi\) | |||||||
\(882\) | −55908.8 | −2.13441 | ||||||||
\(883\) | 43309.8 | 1.65061 | 0.825307 | − | 0.564685i | \(-0.191002\pi\) | ||||
0.825307 | + | 0.564685i | \(0.191002\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −615.877 | −0.0233926 | ||||||||
\(886\) | 74938.5 | 2.84154 | ||||||||
\(887\) | 39472.3i | 1.49420i | 0.664714 | + | 0.747098i | \(0.268553\pi\) | ||||
−0.664714 | + | 0.747098i | \(0.731447\pi\) | |||||||
\(888\) | −11190.3 | −0.422886 | ||||||||
\(889\) | 34472.1i | 1.30051i | ||||||||
\(890\) | 50808.3i | 1.91359i | ||||||||
\(891\) | − 9557.31i | − 0.359351i | ||||||||
\(892\) | 19304.1 | 0.724607 | ||||||||
\(893\) | 7836.86 | 0.293673 | ||||||||
\(894\) | − 2046.61i | − 0.0765647i | ||||||||
\(895\) | − 12461.6i | − 0.465413i | ||||||||
\(896\) | 59979.1i | 2.23634i | ||||||||
\(897\) | −4265.87 | −0.158789 | ||||||||
\(898\) | 24481.4i | 0.909748i | ||||||||
\(899\) | 26884.7 | 0.997392 | ||||||||
\(900\) | 44716.1 | 1.65615 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −27013.9 | −0.997187 | ||||||||
\(903\) | 5035.56 | 0.185574 | ||||||||
\(904\) | − 915.984i | − 0.0337004i | ||||||||
\(905\) | 17206.6 | 0.632008 | ||||||||
\(906\) | 16693.7i | 0.612152i | ||||||||
\(907\) | 8879.42i | 0.325068i | 0.986703 | + | 0.162534i | \(0.0519667\pi\) | ||||
−0.986703 | + | 0.162534i | \(0.948033\pi\) | |||||||
\(908\) | 102961.i | 3.76309i | ||||||||
\(909\) | 24396.5 | 0.890187 | ||||||||
\(910\) | −37813.9 | −1.37749 | ||||||||
\(911\) | − 9321.10i | − 0.338992i | −0.985531 | − | 0.169496i | \(-0.945786\pi\) | ||||
0.985531 | − | 0.169496i | \(-0.0542140\pi\) | |||||||
\(912\) | − 10263.9i | − 0.372667i | ||||||||
\(913\) | 13372.1i | 0.484724i | ||||||||
\(914\) | 8219.50 | 0.297458 | ||||||||
\(915\) | − 7929.68i | − 0.286500i | ||||||||
\(916\) | 3746.56 | 0.135142 | ||||||||
\(917\) | −36446.7 | −1.31251 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8783.98 | −0.315296 | −0.157648 | − | 0.987495i | \(-0.550391\pi\) | ||||
−0.157648 | + | 0.987495i | \(0.550391\pi\) | |||||||
\(920\) | −24363.9 | −0.873101 | ||||||||
\(921\) | − 7429.31i | − 0.265803i | ||||||||
\(922\) | −77682.5 | −2.77477 | ||||||||
\(923\) | − 48884.6i | − 1.74329i | ||||||||
\(924\) | 17790.7i | 0.633410i | ||||||||
\(925\) | 8891.52i | 0.316056i | ||||||||
\(926\) | 778.100 | 0.0276133 | ||||||||
\(927\) | 39545.4 | 1.40112 | ||||||||
\(928\) | 60357.5i | 2.13506i | ||||||||
\(929\) | 24381.1i | 0.861054i | 0.902578 | + | 0.430527i | \(0.141672\pi\) | ||||
−0.902578 | + | 0.430527i | \(0.858328\pi\) | |||||||
\(930\) | − 12134.4i | − 0.427854i | ||||||||
\(931\) | 13509.3 | 0.475563 | ||||||||
\(932\) | − 47289.9i | − 1.66205i | ||||||||
\(933\) | 15619.3 | 0.548075 | ||||||||
\(934\) | −32316.9 | −1.13216 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −69779.7 | −2.43677 | ||||||||
\(937\) | −23120.9 | −0.806113 | −0.403056 | − | 0.915175i | \(-0.632052\pi\) | ||||
−0.403056 | + | 0.915175i | \(0.632052\pi\) | |||||||
\(938\) | − 96086.3i | − 3.34470i | ||||||||
\(939\) | −17081.9 | −0.593661 | ||||||||
\(940\) | 30809.2i | 1.06903i | ||||||||
\(941\) | − 46768.5i | − 1.62020i | −0.586291 | − | 0.810101i | \(-0.699412\pi\) | ||||
0.586291 | − | 0.810101i | \(-0.300588\pi\) | |||||||
\(942\) | 9574.70i | 0.331168i | ||||||||
\(943\) | −16337.3 | −0.564175 | ||||||||
\(944\) | −12229.2 | −0.421638 | ||||||||
\(945\) | 14142.9i | 0.486846i | ||||||||
\(946\) | 10860.8i | 0.373271i | ||||||||
\(947\) | 38093.5i | 1.30715i | 0.756861 | + | 0.653576i | \(0.226732\pi\) | ||||
−0.756861 | + | 0.653576i | \(0.773268\pi\) | |||||||
\(948\) | −8709.95 | −0.298403 | ||||||||
\(949\) | 23430.8i | 0.801471i | ||||||||
\(950\) | −14992.0 | −0.512003 | ||||||||
\(951\) | −12545.3 | −0.427770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31247.7 | −1.06213 | −0.531066 | − | 0.847330i | \(-0.678208\pi\) | ||||
−0.531066 | + | 0.847330i | \(0.678208\pi\) | |||||||
\(954\) | −38237.1 | −1.29767 | ||||||||
\(955\) | 1449.96i | 0.0491305i | ||||||||
\(956\) | 16718.7 | 0.565608 | ||||||||
\(957\) | 3644.31i | 0.123097i | ||||||||
\(958\) | 48928.8i | 1.65012i | ||||||||
\(959\) | − 16471.6i | − 0.554637i | ||||||||
\(960\) | 11605.3 | 0.390166 | ||||||||
\(961\) | −22430.5 | −0.752928 | ||||||||
\(962\) | − 22654.6i | − 0.759266i | ||||||||
\(963\) | − 1031.41i | − 0.0345138i | ||||||||
\(964\) | − 116312.i | − 3.88604i | ||||||||
\(965\) | −19116.6 | −0.637705 | ||||||||
\(966\) | 14929.0i | 0.497238i | ||||||||
\(967\) | 48567.3 | 1.61512 | 0.807558 | − | 0.589788i | \(-0.200789\pi\) | ||||
0.807558 | + | 0.589788i | \(0.200789\pi\) | |||||||
\(968\) | 66564.8 | 2.21020 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8148.86 | 0.269736 | ||||||||
\(971\) | −16286.5 | −0.538267 | −0.269133 | − | 0.963103i | \(-0.586737\pi\) | ||||
−0.269133 | + | 0.963103i | \(0.586737\pi\) | |||||||
\(972\) | 65066.9i | 2.14714i | ||||||||
\(973\) | −47955.1 | −1.58003 | ||||||||
\(974\) | − 23423.3i | − 0.770565i | ||||||||
\(975\) | − 6320.38i | − 0.207604i | ||||||||
\(976\) | − 157456.i | − 5.16398i | ||||||||
\(977\) | −12003.7 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(978\) | −11034.4 | −0.360779 | ||||||||
\(979\) | 29639.7i | 0.967610i | ||||||||
\(980\) | 53109.3i | 1.73114i | ||||||||
\(981\) | − 45135.4i | − 1.46897i | ||||||||
\(982\) | −50791.8 | −1.65054 | ||||||||
\(983\) | 10008.2i | 0.324731i | 0.986731 | + | 0.162365i | \(0.0519124\pi\) | ||||
−0.986731 | + | 0.162365i | \(0.948088\pi\) | |||||||
\(984\) | 30463.8 | 0.986940 | ||||||||
\(985\) | 21636.5 | 0.699895 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11562.4 | 0.372883 | ||||||||
\(988\) | 27529.4 | 0.886464 | ||||||||
\(989\) | 6568.35i | 0.211184i | ||||||||
\(990\) | −14429.4 | −0.463229 | ||||||||
\(991\) | 13384.7i | 0.429040i | 0.976720 | + | 0.214520i | \(0.0688187\pi\) | ||||
−0.976720 | + | 0.214520i | \(0.931181\pi\) | |||||||
\(992\) | − 117240.i | − 3.75239i | ||||||||
\(993\) | − 10448.4i | − 0.333907i | ||||||||
\(994\) | −171078. | −5.45902 | ||||||||
\(995\) | −393.425 | −0.0125351 | ||||||||
\(996\) | − 24621.4i | − 0.783292i | ||||||||
\(997\) | − 21615.7i | − 0.686635i | −0.939219 | − | 0.343317i | \(-0.888449\pi\) | ||||
0.939219 | − | 0.343317i | \(-0.111551\pi\) | |||||||
\(998\) | 12477.1i | 0.395748i | ||||||||
\(999\) | −8473.14 | −0.268347 |
(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 | 289.4.b.f.288.23 | 24 | ||
17.4 | even | 4 | 289.4.a.i.1.1 | yes | 12 | ||
17.13 | even | 4 | 289.4.a.h.1.1 | ✓ | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.24 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.1 | ✓ | 12 | 17.13 | even | 4 | ||
289.4.a.i.1.1 | yes | 12 | 17.4 | even | 4 | ||
289.4.b.f.288.23 | 24 | 1.1 | even | 1 | trivial | ||
289.4.b.f.288.24 | 24 | 17.16 | even | 2 | inner |