Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.4 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.31 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 50.9791i | − | 1.59310i | −0.604575 | − | 0.796548i | \(-0.706657\pi\) | ||
0.604575 | − | 0.796548i | \(-0.293343\pi\) | |||||||
\(3\) | 197.849i | 0.814193i | 0.913385 | + | 0.407097i | \(0.133459\pi\) | ||||
−0.913385 | + | 0.407097i | \(0.866541\pi\) | |||||||
\(4\) | −1574.87 | −1.53796 | ||||||||
\(5\) | − | 5530.45i | − | 1.76975i | −0.465833 | − | 0.884873i | \(-0.654245\pi\) | ||
0.465833 | − | 0.884873i | \(-0.345755\pi\) | |||||||
\(6\) | 10086.2 | 1.29709 | ||||||||
\(7\) | 21393.6i | 1.27290i | 0.771319 | + | 0.636449i | \(0.219597\pi\) | ||||
−0.771319 | + | 0.636449i | \(0.780403\pi\) | |||||||
\(8\) | 28082.7i | 0.857017i | ||||||||
\(9\) | 19904.8 | 0.337089 | ||||||||
\(10\) | −281938. | −2.81938 | ||||||||
\(11\) | −131052. | −0.813730 | −0.406865 | − | 0.913488i | \(-0.633378\pi\) | ||||
−0.406865 | + | 0.913488i | \(0.633378\pi\) | |||||||
\(12\) | − | 311586.i | − | 1.25219i | ||||||
\(13\) | −588595. | −1.58526 | −0.792628 | − | 0.609705i | \(-0.791288\pi\) | ||||
−0.792628 | + | 0.609705i | \(0.791288\pi\) | |||||||
\(14\) | 1.09063e6 | 2.02785 | ||||||||
\(15\) | 1.09419e6 | 1.44092 | ||||||||
\(16\) | −181032. | −0.172645 | ||||||||
\(17\) | −270179. | −0.190286 | −0.0951432 | − | 0.995464i | \(-0.530331\pi\) | ||||
−0.0951432 | + | 0.995464i | \(0.530331\pi\) | |||||||
\(18\) | − | 1.01473e6i | − | 0.537016i | ||||||
\(19\) | 2.93766e6i | 1.18641i | 0.805052 | + | 0.593204i | \(0.202137\pi\) | ||||
−0.805052 | + | 0.593204i | \(0.797863\pi\) | |||||||
\(20\) | 8.70974e6i | 2.72179i | ||||||||
\(21\) | −4.23270e6 | −1.03638 | ||||||||
\(22\) | 6.68092e6i | 1.29635i | ||||||||
\(23\) | 1.08666e7 | 1.68832 | 0.844161 | − | 0.536089i | \(-0.180099\pi\) | ||||
0.844161 | + | 0.536089i | \(0.180099\pi\) | |||||||
\(24\) | −5.55614e6 | −0.697778 | ||||||||
\(25\) | −2.08203e7 | −2.13200 | ||||||||
\(26\) | 3.00060e7i | 2.52547i | ||||||||
\(27\) | 1.56209e7i | 1.08865i | ||||||||
\(28\) | − | 3.36921e7i | − | 1.95766i | ||||||
\(29\) | − | 7.43530e6i | − | 0.362501i | −0.983437 | − | 0.181250i | \(-0.941986\pi\) | ||
0.983437 | − | 0.181250i | \(-0.0580144\pi\) | |||||||
\(30\) | − | 5.57811e7i | − | 2.29552i | ||||||
\(31\) | 4.62840e7 | 1.61667 | 0.808337 | − | 0.588720i | \(-0.200368\pi\) | ||||
0.808337 | + | 0.588720i | \(0.200368\pi\) | |||||||
\(32\) | 3.79856e7i | 1.13206i | ||||||||
\(33\) | − | 2.59285e7i | − | 0.662534i | ||||||
\(34\) | 1.37735e7i | 0.303145i | ||||||||
\(35\) | 1.18316e8 | 2.25270 | ||||||||
\(36\) | −3.13474e7 | −0.518429 | ||||||||
\(37\) | 6.79130e7i | 0.979364i | 0.871901 | + | 0.489682i | \(0.162887\pi\) | ||||
−0.871901 | + | 0.489682i | \(0.837113\pi\) | |||||||
\(38\) | 1.49759e8 | 1.89006 | ||||||||
\(39\) | − | 1.16453e8i | − | 1.29071i | ||||||
\(40\) | 1.55310e8 | 1.51670 | ||||||||
\(41\) | 7.10053e7 | 0.612874 | 0.306437 | − | 0.951891i | \(-0.400863\pi\) | ||||
0.306437 | + | 0.951891i | \(0.400863\pi\) | |||||||
\(42\) | 2.15779e8i | 1.65106i | ||||||||
\(43\) | −1.24384e8 | + | 7.83589e7i | −0.846101 | + | 0.533023i | ||||
\(44\) | 2.06390e8 | 1.25148 | ||||||||
\(45\) | − | 1.10082e8i | − | 0.596562i | ||||||
\(46\) | − | 5.53971e8i | − | 2.68966i | ||||||
\(47\) | −3.33454e8 | −1.45394 | −0.726971 | − | 0.686668i | \(-0.759072\pi\) | ||||
−0.726971 | + | 0.686668i | \(0.759072\pi\) | |||||||
\(48\) | − | 3.58170e7i | − | 0.140567i | ||||||
\(49\) | −1.75210e8 | −0.620268 | ||||||||
\(50\) | 1.06140e9i | 3.39648i | ||||||||
\(51\) | − | 5.34547e7i | − | 0.154930i | ||||||
\(52\) | 9.26959e8 | 2.43806 | ||||||||
\(53\) | −3.32431e8 | −0.794919 | −0.397459 | − | 0.917620i | \(-0.630108\pi\) | ||||
−0.397459 | + | 0.917620i | \(0.630108\pi\) | |||||||
\(54\) | 7.96341e8 | 1.73432 | ||||||||
\(55\) | 7.24778e8i | 1.44010i | ||||||||
\(56\) | −6.00791e8 | −1.09090 | ||||||||
\(57\) | −5.81213e8 | −0.965965 | ||||||||
\(58\) | −3.79045e8 | −0.577498 | ||||||||
\(59\) | −7.48163e7 | −0.104649 | −0.0523247 | − | 0.998630i | \(-0.516663\pi\) | ||||
−0.0523247 | + | 0.998630i | \(0.516663\pi\) | |||||||
\(60\) | −1.72321e9 | −2.21607 | ||||||||
\(61\) | 7.63592e8i | 0.904091i | 0.891995 | + | 0.452046i | \(0.149306\pi\) | ||||
−0.891995 | + | 0.452046i | \(0.850694\pi\) | |||||||
\(62\) | − | 2.35952e9i | − | 2.57552i | ||||||
\(63\) | 4.25835e8i | 0.429080i | ||||||||
\(64\) | 1.75109e9 | 1.63083 | ||||||||
\(65\) | 3.25520e9i | 2.80550i | ||||||||
\(66\) | −1.32181e9 | −1.05548 | ||||||||
\(67\) | 5.79974e8 | 0.429570 | 0.214785 | − | 0.976661i | \(-0.431095\pi\) | ||||
0.214785 | + | 0.976661i | \(0.431095\pi\) | |||||||
\(68\) | 4.25497e8 | 0.292652 | ||||||||
\(69\) | 2.14995e9i | 1.37462i | ||||||||
\(70\) | − | 6.03166e9i | − | 3.58878i | ||||||
\(71\) | 9.90329e8i | 0.548893i | 0.961602 | + | 0.274446i | \(0.0884946\pi\) | ||||
−0.961602 | + | 0.274446i | \(0.911505\pi\) | |||||||
\(72\) | 5.58981e8i | 0.288891i | ||||||||
\(73\) | − | 8.61773e8i | − | 0.415698i | −0.978161 | − | 0.207849i | \(-0.933354\pi\) | ||
0.978161 | − | 0.207849i | \(-0.0666463\pi\) | |||||||
\(74\) | 3.46214e9 | 1.56022 | ||||||||
\(75\) | − | 4.11928e9i | − | 1.73586i | ||||||
\(76\) | − | 4.62643e9i | − | 1.82464i | ||||||
\(77\) | − | 2.80367e9i | − | 1.03580i | ||||||
\(78\) | −5.93666e9 | −2.05622 | ||||||||
\(79\) | −4.77088e9 | −1.55047 | −0.775235 | − | 0.631673i | \(-0.782368\pi\) | ||||
−0.775235 | + | 0.631673i | \(0.782368\pi\) | |||||||
\(80\) | 1.00119e9i | 0.305539i | ||||||||
\(81\) | −1.91523e9 | −0.549282 | ||||||||
\(82\) | − | 3.61979e9i | − | 0.976368i | ||||||
\(83\) | −1.89897e9 | −0.482088 | −0.241044 | − | 0.970514i | \(-0.577490\pi\) | ||||
−0.241044 | + | 0.970514i | \(0.577490\pi\) | |||||||
\(84\) | 6.66594e9 | 1.59391 | ||||||||
\(85\) | 1.49422e9i | 0.336759i | ||||||||
\(86\) | 3.99466e9 | + | 6.34098e9i | 0.849157 | + | 1.34792i | ||||
\(87\) | 1.47107e9 | 0.295146 | ||||||||
\(88\) | − | 3.68030e9i | − | 0.697381i | ||||||
\(89\) | 1.53171e9i | 0.274300i | 0.990550 | + | 0.137150i | \(0.0437942\pi\) | ||||
−0.990550 | + | 0.137150i | \(0.956206\pi\) | |||||||
\(90\) | −5.61190e9 | −0.950381 | ||||||||
\(91\) | − | 1.25922e10i | − | 2.01787i | ||||||
\(92\) | −1.71135e10 | −2.59657 | ||||||||
\(93\) | 9.15724e9i | 1.31628i | ||||||||
\(94\) | 1.69992e10i | 2.31627i | ||||||||
\(95\) | 1.62466e10 | 2.09964 | ||||||||
\(96\) | −7.51541e9 | −0.921714 | ||||||||
\(97\) | −1.02062e10 | −1.18852 | −0.594259 | − | 0.804274i | \(-0.702555\pi\) | ||||
−0.594259 | + | 0.804274i | \(0.702555\pi\) | |||||||
\(98\) | 8.93206e9i | 0.988147i | ||||||||
\(99\) | −2.60856e9 | −0.274300 | ||||||||
\(100\) | 3.27892e10 | 3.27892 | ||||||||
\(101\) | 7.39786e9 | 0.703881 | 0.351941 | − | 0.936022i | \(-0.385522\pi\) | ||||
0.351941 | + | 0.936022i | \(0.385522\pi\) | |||||||
\(102\) | −2.72507e9 | −0.246818 | ||||||||
\(103\) | 1.89500e9 | 0.163464 | 0.0817320 | − | 0.996654i | \(-0.473955\pi\) | ||||
0.0817320 | + | 0.996654i | \(0.473955\pi\) | |||||||
\(104\) | − | 1.65294e10i | − | 1.35859i | ||||||
\(105\) | 2.34088e10i | 1.83414i | ||||||||
\(106\) | 1.69471e10i | 1.26638i | ||||||||
\(107\) | −3.52939e9 | −0.251640 | −0.125820 | − | 0.992053i | \(-0.540156\pi\) | ||||
−0.125820 | + | 0.992053i | \(0.540156\pi\) | |||||||
\(108\) | − | 2.46009e10i | − | 1.67430i | ||||||
\(109\) | −2.09373e10 | −1.36078 | −0.680391 | − | 0.732849i | \(-0.738190\pi\) | ||||
−0.680391 | + | 0.732849i | \(0.738190\pi\) | |||||||
\(110\) | 3.69485e10 | 2.29421 | ||||||||
\(111\) | −1.34365e10 | −0.797392 | ||||||||
\(112\) | − | 3.87292e9i | − | 0.219760i | ||||||
\(113\) | 1.44266e9i | 0.0783016i | 0.999233 | + | 0.0391508i | \(0.0124653\pi\) | ||||
−0.999233 | + | 0.0391508i | \(0.987535\pi\) | |||||||
\(114\) | 2.96297e10i | 1.53888i | ||||||||
\(115\) | − | 6.00974e10i | − | 2.98790i | ||||||
\(116\) | 1.17096e10i | 0.557510i | ||||||||
\(117\) | −1.17158e10 | −0.534373 | ||||||||
\(118\) | 3.81407e9i | 0.166716i | ||||||||
\(119\) | − | 5.78011e9i | − | 0.242215i | ||||||
\(120\) | 3.07280e10i | 1.23489i | ||||||||
\(121\) | −8.76277e9 | −0.337843 | ||||||||
\(122\) | 3.89272e10 | 1.44030 | ||||||||
\(123\) | 1.40483e10i | 0.498998i | ||||||||
\(124\) | −7.28912e10 | −2.48637 | ||||||||
\(125\) | 6.11374e10i | 2.00335i | ||||||||
\(126\) | 2.17087e10 | 0.683566 | ||||||||
\(127\) | 3.60104e10 | 1.08996 | 0.544979 | − | 0.838450i | \(-0.316538\pi\) | ||||
0.544979 | + | 0.838450i | \(0.316538\pi\) | |||||||
\(128\) | − | 5.03719e10i | − | 1.46602i | ||||||
\(129\) | −1.55032e10 | − | 2.46092e10i | −0.433984 | − | 0.688890i | ||||
\(130\) | 1.65947e11 | 4.46943 | ||||||||
\(131\) | 1.97020e10i | 0.510685i | 0.966851 | + | 0.255342i | \(0.0821882\pi\) | ||||
−0.966851 | + | 0.255342i | \(0.917812\pi\) | |||||||
\(132\) | 4.08340e10i | 1.01895i | ||||||||
\(133\) | −6.28471e10 | −1.51017 | ||||||||
\(134\) | − | 2.95665e10i | − | 0.684347i | ||||||
\(135\) | 8.63908e10 | 1.92663 | ||||||||
\(136\) | − | 7.58738e9i | − | 0.163079i | ||||||
\(137\) | − | 5.16409e10i | − | 1.07002i | −0.844847 | − | 0.535008i | \(-0.820308\pi\) | ||
0.844847 | − | 0.535008i | \(-0.179692\pi\) | |||||||
\(138\) | 1.09603e11 | 2.18990 | ||||||||
\(139\) | −5.56775e10 | −1.07302 | −0.536508 | − | 0.843895i | \(-0.680257\pi\) | ||||
−0.536508 | + | 0.843895i | \(0.680257\pi\) | |||||||
\(140\) | −1.86332e11 | −3.46456 | ||||||||
\(141\) | − | 6.59736e10i | − | 1.18379i | ||||||
\(142\) | 5.04861e10 | 0.874440 | ||||||||
\(143\) | 7.71366e10 | 1.28997 | ||||||||
\(144\) | −3.60340e9 | −0.0581969 | ||||||||
\(145\) | −4.11206e10 | −0.641534 | ||||||||
\(146\) | −4.39324e10 | −0.662248 | ||||||||
\(147\) | − | 3.46652e10i | − | 0.505018i | ||||||
\(148\) | − | 1.06954e11i | − | 1.50622i | ||||||
\(149\) | − | 5.02449e10i | − | 0.684164i | −0.939670 | − | 0.342082i | \(-0.888868\pi\) | ||
0.939670 | − | 0.342082i | \(-0.111132\pi\) | |||||||
\(150\) | −2.09997e11 | −2.76539 | ||||||||
\(151\) | 1.21272e11i | 1.54481i | 0.635131 | + | 0.772404i | \(0.280946\pi\) | ||||
−0.635131 | + | 0.772404i | \(0.719054\pi\) | |||||||
\(152\) | −8.24976e10 | −1.01677 | ||||||||
\(153\) | −5.37786e9 | −0.0641435 | ||||||||
\(154\) | −1.42929e11 | −1.65012 | ||||||||
\(155\) | − | 2.55972e11i | − | 2.86110i | ||||||
\(156\) | 1.83398e11i | 1.98505i | ||||||||
\(157\) | − | 1.55559e10i | − | 0.163079i | −0.996670 | − | 0.0815394i | \(-0.974016\pi\) | ||
0.996670 | − | 0.0815394i | \(-0.0259836\pi\) | |||||||
\(158\) | 2.43215e11i | 2.47005i | ||||||||
\(159\) | − | 6.57712e10i | − | 0.647218i | ||||||
\(160\) | 2.10077e11 | 2.00346 | ||||||||
\(161\) | 2.32476e11i | 2.14906i | ||||||||
\(162\) | 9.76365e10i | 0.875059i | ||||||||
\(163\) | 5.97193e9i | 0.0519011i | 0.999663 | + | 0.0259506i | \(0.00826125\pi\) | ||||
−0.999663 | + | 0.0259506i | \(0.991739\pi\) | |||||||
\(164\) | −1.11824e11 | −0.942574 | ||||||||
\(165\) | −1.43397e11 | −1.17252 | ||||||||
\(166\) | 9.68076e10i | 0.768014i | ||||||||
\(167\) | −2.25335e11 | −1.73479 | −0.867395 | − | 0.497621i | \(-0.834207\pi\) | ||||
−0.867395 | + | 0.497621i | \(0.834207\pi\) | |||||||
\(168\) | − | 1.18866e11i | − | 0.888200i | ||||||
\(169\) | 2.08585e11 | 1.51304 | ||||||||
\(170\) | 7.61737e10 | 0.536489 | ||||||||
\(171\) | 5.84735e10i | 0.399925i | ||||||||
\(172\) | 1.95888e11 | − | 1.23405e11i | 1.30127 | − | 0.819766i | ||||
\(173\) | −1.73165e11 | −1.11746 | −0.558728 | − | 0.829351i | \(-0.688710\pi\) | ||||
−0.558728 | + | 0.829351i | \(0.688710\pi\) | |||||||
\(174\) | − | 7.49937e10i | − | 0.470195i | ||||||
\(175\) | − | 4.45421e11i | − | 2.71382i | ||||||
\(176\) | 2.37246e10 | 0.140487 | ||||||||
\(177\) | − | 1.48023e10i | − | 0.0852048i | ||||||
\(178\) | 7.80850e10 | 0.436986 | ||||||||
\(179\) | − | 9.54014e10i | − | 0.519146i | −0.965724 | − | 0.259573i | \(-0.916418\pi\) | ||
0.965724 | − | 0.259573i | \(-0.0835818\pi\) | |||||||
\(180\) | 1.73365e11i | 0.917487i | ||||||||
\(181\) | 2.69717e11 | 1.38840 | 0.694202 | − | 0.719780i | \(-0.255757\pi\) | ||||
0.694202 | + | 0.719780i | \(0.255757\pi\) | |||||||
\(182\) | −6.41936e11 | −3.21466 | ||||||||
\(183\) | −1.51076e11 | −0.736105 | ||||||||
\(184\) | 3.05165e11i | 1.44692i | ||||||||
\(185\) | 3.75590e11 | 1.73322 | ||||||||
\(186\) | 4.66828e11 | 2.09697 | ||||||||
\(187\) | 3.54076e10 | 0.154842 | ||||||||
\(188\) | 5.25146e11 | 2.23610 | ||||||||
\(189\) | −3.34188e11 | −1.38574 | ||||||||
\(190\) | − | 8.28237e11i | − | 3.34493i | ||||||
\(191\) | 5.74703e10i | 0.226087i | 0.993590 | + | 0.113044i | \(0.0360600\pi\) | ||||
−0.993590 | + | 0.113044i | \(0.963940\pi\) | |||||||
\(192\) | 3.46452e11i | 1.32781i | ||||||||
\(193\) | 4.85240e9 | 0.0181205 | 0.00906025 | − | 0.999959i | \(-0.497116\pi\) | ||||
0.00906025 | + | 0.999959i | \(0.497116\pi\) | |||||||
\(194\) | 5.20303e11i | 1.89342i | ||||||||
\(195\) | −6.44037e11 | −2.28422 | ||||||||
\(196\) | 2.75933e11 | 0.953945 | ||||||||
\(197\) | −1.37673e11 | −0.463999 | −0.232000 | − | 0.972716i | \(-0.574527\pi\) | ||||
−0.232000 | + | 0.972716i | \(0.574527\pi\) | |||||||
\(198\) | 1.32982e11i | 0.436986i | ||||||||
\(199\) | 1.32479e11i | 0.424504i | 0.977215 | + | 0.212252i | \(0.0680798\pi\) | ||||
−0.977215 | + | 0.212252i | \(0.931920\pi\) | |||||||
\(200\) | − | 5.84691e11i | − | 1.82716i | ||||||
\(201\) | 1.14747e11i | 0.349753i | ||||||||
\(202\) | − | 3.77136e11i | − | 1.12135i | ||||||
\(203\) | 1.59068e11 | 0.461426 | ||||||||
\(204\) | 8.41841e10i | 0.238276i | ||||||||
\(205\) | − | 3.92692e11i | − | 1.08463i | ||||||
\(206\) | − | 9.66052e10i | − | 0.260414i | ||||||
\(207\) | 2.16298e11 | 0.569115 | ||||||||
\(208\) | 1.06554e11 | 0.273687 | ||||||||
\(209\) | − | 3.84987e11i | − | 0.965416i | ||||||
\(210\) | 1.19336e12 | 2.92196 | ||||||||
\(211\) | 1.43647e11i | 0.343466i | 0.985143 | + | 0.171733i | \(0.0549367\pi\) | ||||
−0.985143 | + | 0.171733i | \(0.945063\pi\) | |||||||
\(212\) | 5.23536e11 | 1.22255 | ||||||||
\(213\) | −1.95936e11 | −0.446905 | ||||||||
\(214\) | 1.79925e11i | 0.400887i | ||||||||
\(215\) | 4.33360e11 | + | 6.87900e11i | 0.943315 | + | 1.49738i | ||||
\(216\) | −4.38678e11 | −0.932991 | ||||||||
\(217\) | 9.90181e11i | 2.05786i | ||||||||
\(218\) | 1.06737e12i | 2.16786i | ||||||||
\(219\) | 1.70501e11 | 0.338459 | ||||||||
\(220\) | − | 1.14143e12i | − | 2.21481i | ||||||
\(221\) | 1.59026e11 | 0.301653 | ||||||||
\(222\) | 6.84981e11i | 1.27032i | ||||||||
\(223\) | 1.22924e11i | 0.222902i | 0.993770 | + | 0.111451i | \(0.0355498\pi\) | ||||
−0.993770 | + | 0.111451i | \(0.964450\pi\) | |||||||
\(224\) | −8.12648e11 | −1.44099 | ||||||||
\(225\) | −4.14424e11 | −0.718674 | ||||||||
\(226\) | 7.35453e10 | 0.124742 | ||||||||
\(227\) | − | 6.76953e11i | − | 1.12313i | −0.827433 | − | 0.561564i | \(-0.810200\pi\) | ||
0.827433 | − | 0.561564i | \(-0.189800\pi\) | |||||||
\(228\) | 9.15334e11 | 1.48561 | ||||||||
\(229\) | −2.91880e11 | −0.463476 | −0.231738 | − | 0.972778i | \(-0.574441\pi\) | ||||
−0.231738 | + | 0.972778i | \(0.574441\pi\) | |||||||
\(230\) | −3.06371e12 | −4.76002 | ||||||||
\(231\) | 5.54704e11 | 0.843338 | ||||||||
\(232\) | 2.08804e11 | 0.310669 | ||||||||
\(233\) | 6.90403e11i | 1.00536i | 0.864472 | + | 0.502681i | \(0.167653\pi\) | ||||
−0.864472 | + | 0.502681i | \(0.832347\pi\) | |||||||
\(234\) | 5.97263e11i | 0.851308i | ||||||||
\(235\) | 1.84415e12i | 2.57311i | ||||||||
\(236\) | 1.17826e11 | 0.160946 | ||||||||
\(237\) | − | 9.43914e11i | − | 1.26238i | ||||||
\(238\) | −2.94665e11 | −0.385872 | ||||||||
\(239\) | −3.17121e11 | −0.406664 | −0.203332 | − | 0.979110i | \(-0.565177\pi\) | ||||
−0.203332 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(240\) | −1.98084e11 | −0.248767 | ||||||||
\(241\) | − | 7.71400e11i | − | 0.948843i | −0.880298 | − | 0.474422i | \(-0.842657\pi\) | ||
0.880298 | − | 0.474422i | \(-0.157343\pi\) | |||||||
\(242\) | 4.46718e11i | 0.538216i | ||||||||
\(243\) | 5.43474e11i | 0.641428i | ||||||||
\(244\) | − | 1.20256e12i | − | 1.39045i | ||||||
\(245\) | 9.68993e11i | 1.09772i | ||||||||
\(246\) | 7.16171e11 | 0.794952 | ||||||||
\(247\) | − | 1.72909e12i | − | 1.88076i | ||||||
\(248\) | 1.29978e12i | 1.38552i | ||||||||
\(249\) | − | 3.75709e11i | − | 0.392513i | ||||||
\(250\) | 3.11673e12 | 3.19153 | ||||||||
\(251\) | −1.41940e12 | −1.42474 | −0.712371 | − | 0.701803i | \(-0.752379\pi\) | ||||
−0.712371 | + | 0.701803i | \(0.752379\pi\) | |||||||
\(252\) | − | 6.70633e11i | − | 0.659906i | ||||||
\(253\) | −1.42409e12 | −1.37384 | ||||||||
\(254\) | − | 1.83578e12i | − | 1.73641i | ||||||
\(255\) | −2.95629e11 | −0.274187 | ||||||||
\(256\) | −7.74795e11 | −0.704672 | ||||||||
\(257\) | − | 1.85716e12i | − | 1.65647i | −0.560381 | − | 0.828235i | \(-0.689345\pi\) | ||
0.560381 | − | 0.828235i | \(-0.310655\pi\) | |||||||
\(258\) | −1.25456e12 | + | 7.90340e11i | −1.09747 | + | 0.691378i | ||||
\(259\) | −1.45290e12 | −1.24663 | ||||||||
\(260\) | − | 5.12650e12i | − | 4.31474i | ||||||
\(261\) | − | 1.47998e11i | − | 0.122195i | ||||||
\(262\) | 1.00439e12 | 0.813570 | ||||||||
\(263\) | − | 1.35241e12i | − | 1.07481i | −0.843325 | − | 0.537403i | \(-0.819405\pi\) | ||
0.843325 | − | 0.537403i | \(-0.180595\pi\) | |||||||
\(264\) | 7.28144e11 | 0.567803 | ||||||||
\(265\) | 1.83850e12i | 1.40680i | ||||||||
\(266\) | 3.20389e12i | 2.40585i | ||||||||
\(267\) | −3.03047e11 | −0.223333 | ||||||||
\(268\) | −9.13382e11 | −0.660660 | ||||||||
\(269\) | 1.33910e12 | 0.950721 | 0.475360 | − | 0.879791i | \(-0.342318\pi\) | ||||
0.475360 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(270\) | − | 4.40413e12i | − | 3.06931i | ||||||
\(271\) | 2.01872e12 | 1.38111 | 0.690557 | − | 0.723278i | \(-0.257366\pi\) | ||||
0.690557 | + | 0.723278i | \(0.257366\pi\) | |||||||
\(272\) | 4.89111e10 | 0.0328521 | ||||||||
\(273\) | 2.49134e12 | 1.64294 | ||||||||
\(274\) | −2.63260e12 | −1.70464 | ||||||||
\(275\) | 2.72854e12 | 1.73487 | ||||||||
\(276\) | − | 3.38589e12i | − | 2.11411i | ||||||
\(277\) | 3.00986e12i | 1.84564i | 0.385228 | + | 0.922822i | \(0.374123\pi\) | ||||
−0.385228 | + | 0.922822i | \(0.625877\pi\) | |||||||
\(278\) | 2.83839e12i | 1.70942i | ||||||||
\(279\) | 9.21272e11 | 0.544963 | ||||||||
\(280\) | 3.32265e12i | 1.93061i | ||||||||
\(281\) | −3.85491e11 | −0.220030 | −0.110015 | − | 0.993930i | \(-0.535090\pi\) | ||||
−0.110015 | + | 0.993930i | \(0.535090\pi\) | |||||||
\(282\) | −3.36327e12 | −1.88589 | ||||||||
\(283\) | 1.81571e12 | 1.00026 | 0.500130 | − | 0.865950i | \(-0.333285\pi\) | ||||
0.500130 | + | 0.865950i | \(0.333285\pi\) | |||||||
\(284\) | − | 1.55964e12i | − | 0.844174i | ||||||
\(285\) | 3.21437e12i | 1.70951i | ||||||||
\(286\) | − | 3.93235e12i | − | 2.05505i | ||||||
\(287\) | 1.51906e12i | 0.780126i | ||||||||
\(288\) | 7.56094e11i | 0.381605i | ||||||||
\(289\) | −1.94300e12 | −0.963791 | ||||||||
\(290\) | 2.09629e12i | 1.02203i | ||||||||
\(291\) | − | 2.01929e12i | − | 0.967684i | ||||||
\(292\) | 1.35718e12i | 0.639326i | ||||||||
\(293\) | 1.66503e12 | 0.771052 | 0.385526 | − | 0.922697i | \(-0.374020\pi\) | ||||
0.385526 | + | 0.922697i | \(0.374020\pi\) | |||||||
\(294\) | −1.76720e12 | −0.804543 | ||||||||
\(295\) | 4.13768e11i | 0.185203i | ||||||||
\(296\) | −1.90718e12 | −0.839332 | ||||||||
\(297\) | − | 2.04716e12i | − | 0.885867i | ||||||
\(298\) | −2.56144e12 | −1.08994 | ||||||||
\(299\) | −6.39604e12 | −2.67642 | ||||||||
\(300\) | 6.48732e12i | 2.66968i | ||||||||
\(301\) | −1.67638e12 | − | 2.66102e12i | −0.678484 | − | 1.07700i | ||||
\(302\) | 6.18232e12 | 2.46103 | ||||||||
\(303\) | 1.46366e12i | 0.573095i | ||||||||
\(304\) | − | 5.31810e11i | − | 0.204828i | ||||||
\(305\) | 4.22301e12 | 1.60001 | ||||||||
\(306\) | 2.74159e11i | 0.102187i | ||||||||
\(307\) | 2.43294e11 | 0.0892154 | 0.0446077 | − | 0.999005i | \(-0.485796\pi\) | ||||
0.0446077 | + | 0.999005i | \(0.485796\pi\) | |||||||
\(308\) | 4.41542e12i | 1.59301i | ||||||||
\(309\) | 3.74923e11i | 0.133091i | ||||||||
\(310\) | −1.30492e13 | −4.55801 | ||||||||
\(311\) | 8.12366e11 | 0.279222 | 0.139611 | − | 0.990206i | \(-0.455415\pi\) | ||||
0.139611 | + | 0.990206i | \(0.455415\pi\) | |||||||
\(312\) | 3.27032e12 | 1.10616 | ||||||||
\(313\) | 3.63754e12i | 1.21084i | 0.795907 | + | 0.605419i | \(0.206994\pi\) | ||||
−0.795907 | + | 0.605419i | \(0.793006\pi\) | |||||||
\(314\) | −7.93027e11 | −0.259800 | ||||||||
\(315\) | 2.35506e12 | 0.759362 | ||||||||
\(316\) | 7.51351e12 | 2.38455 | ||||||||
\(317\) | −2.91949e12 | −0.912033 | −0.456017 | − | 0.889971i | \(-0.650724\pi\) | ||||
−0.456017 | + | 0.889971i | \(0.650724\pi\) | |||||||
\(318\) | −3.35296e12 | −1.03108 | ||||||||
\(319\) | 9.74412e11i | 0.294978i | ||||||||
\(320\) | − | 9.68434e12i | − | 2.88616i | ||||||
\(321\) | − | 6.98285e11i | − | 0.204884i | ||||||
\(322\) | 1.18514e13 | 3.42366 | ||||||||
\(323\) | − | 7.93696e11i | − | 0.225757i | ||||||
\(324\) | 3.01623e12 | 0.844772 | ||||||||
\(325\) | 1.22547e13 | 3.37977 | ||||||||
\(326\) | 3.04444e11 | 0.0826835 | ||||||||
\(327\) | − | 4.14243e12i | − | 1.10794i | ||||||
\(328\) | 1.99402e12i | 0.525244i | ||||||||
\(329\) | − | 7.13378e12i | − | 1.85072i | ||||||
\(330\) | 7.31023e12i | 1.86793i | ||||||||
\(331\) | 4.66102e12i | 1.17312i | 0.809907 | + | 0.586558i | \(0.199518\pi\) | ||||
−0.809907 | + | 0.586558i | \(0.800482\pi\) | |||||||
\(332\) | 2.99062e12 | 0.741431 | ||||||||
\(333\) | 1.35179e12i | 0.330133i | ||||||||
\(334\) | 1.14874e13i | 2.76369i | ||||||||
\(335\) | − | 3.20752e12i | − | 0.760230i | ||||||
\(336\) | 7.66254e11 | 0.178927 | ||||||||
\(337\) | −6.14610e12 | −1.41400 | −0.707001 | − | 0.707213i | \(-0.749952\pi\) | ||||
−0.707001 | + | 0.707213i | \(0.749952\pi\) | |||||||
\(338\) | − | 1.06335e13i | − | 2.41042i | ||||||
\(339\) | −2.85428e11 | −0.0637527 | ||||||||
\(340\) | − | 2.35319e12i | − | 0.517920i | ||||||
\(341\) | −6.06561e12 | −1.31554 | ||||||||
\(342\) | 2.98093e12 | 0.637119 | ||||||||
\(343\) | 2.29478e12i | 0.483360i | ||||||||
\(344\) | −2.20053e12 | − | 3.49304e12i | −0.456810 | − | 0.725123i | ||||
\(345\) | 1.18902e13 | 2.43273 | ||||||||
\(346\) | 8.82781e12i | 1.78022i | ||||||||
\(347\) | 2.05674e12i | 0.408820i | 0.978885 | + | 0.204410i | \(0.0655276\pi\) | ||||
−0.978885 | + | 0.204410i | \(0.934472\pi\) | |||||||
\(348\) | −2.31674e12 | −0.453921 | ||||||||
\(349\) | 2.78036e12i | 0.537000i | 0.963280 | + | 0.268500i | \(0.0865279\pi\) | ||||
−0.963280 | + | 0.268500i | \(0.913472\pi\) | |||||||
\(350\) | −2.27072e13 | −4.32337 | ||||||||
\(351\) | − | 9.19439e12i | − | 1.72579i | ||||||
\(352\) | − | 4.97809e12i | − | 0.921190i | ||||||
\(353\) | 5.01751e12 | 0.915409 | 0.457704 | − | 0.889104i | \(-0.348672\pi\) | ||||
0.457704 | + | 0.889104i | \(0.348672\pi\) | |||||||
\(354\) | −7.54610e11 | −0.135739 | ||||||||
\(355\) | 5.47697e12 | 0.971401 | ||||||||
\(356\) | − | 2.41224e12i | − | 0.421862i | ||||||
\(357\) | 1.14359e12 | 0.197210 | ||||||||
\(358\) | −4.86347e12 | −0.827050 | ||||||||
\(359\) | 1.73968e12 | 0.291741 | 0.145870 | − | 0.989304i | \(-0.453402\pi\) | ||||
0.145870 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(360\) | 3.09142e12 | 0.511264 | ||||||||
\(361\) | −2.49879e12 | −0.407562 | ||||||||
\(362\) | − | 1.37499e13i | − | 2.21186i | ||||||
\(363\) | − | 1.73371e12i | − | 0.275069i | ||||||
\(364\) | 1.98310e13i | 3.10340i | ||||||||
\(365\) | −4.76599e12 | −0.735680 | ||||||||
\(366\) | 7.70171e12i | 1.17269i | ||||||||
\(367\) | 2.47571e12 | 0.371851 | 0.185925 | − | 0.982564i | \(-0.440472\pi\) | ||||
0.185925 | + | 0.982564i | \(0.440472\pi\) | |||||||
\(368\) | −1.96721e12 | −0.291481 | ||||||||
\(369\) | 1.41334e12 | 0.206593 | ||||||||
\(370\) | − | 1.91472e13i | − | 2.76119i | ||||||
\(371\) | − | 7.11190e12i | − | 1.01185i | ||||||
\(372\) | − | 1.44214e13i | − | 2.02439i | ||||||
\(373\) | − | 6.84223e12i | − | 0.947662i | −0.880616 | − | 0.473831i | \(-0.842871\pi\) | ||
0.880616 | − | 0.473831i | \(-0.157129\pi\) | |||||||
\(374\) | − | 1.80505e12i | − | 0.246678i | ||||||
\(375\) | −1.20960e13 | −1.63111 | ||||||||
\(376\) | − | 9.36431e12i | − | 1.24605i | ||||||
\(377\) | 4.37638e12i | 0.574656i | ||||||||
\(378\) | 1.70366e13i | 2.20762i | ||||||||
\(379\) | 1.09466e13 | 1.39986 | 0.699929 | − | 0.714213i | \(-0.253215\pi\) | ||||
0.699929 | + | 0.714213i | \(0.253215\pi\) | |||||||
\(380\) | −2.55863e13 | −3.22915 | ||||||||
\(381\) | 7.12462e12i | 0.887436i | ||||||||
\(382\) | 2.92978e12 | 0.360179 | ||||||||
\(383\) | 1.95855e12i | 0.237652i | 0.992915 | + | 0.118826i | \(0.0379131\pi\) | ||||
−0.992915 | + | 0.118826i | \(0.962087\pi\) | |||||||
\(384\) | 9.96603e12 | 1.19362 | ||||||||
\(385\) | −1.55056e13 | −1.83309 | ||||||||
\(386\) | − | 2.47371e11i | − | 0.0288677i | ||||||
\(387\) | −2.47583e12 | + | 1.55972e12i | −0.285211 | + | 0.179676i | ||||
\(388\) | 1.60734e13 | 1.82789 | ||||||||
\(389\) | 7.18199e11i | 0.0806301i | 0.999187 | + | 0.0403150i | \(0.0128362\pi\) | ||||
−0.999187 | + | 0.0403150i | \(0.987164\pi\) | |||||||
\(390\) | 3.28324e13i | 3.63898i | ||||||||
\(391\) | −2.93594e12 | −0.321265 | ||||||||
\(392\) | − | 4.92039e12i | − | 0.531580i | ||||||
\(393\) | −3.89801e12 | −0.415796 | ||||||||
\(394\) | 7.01844e12i | 0.739196i | ||||||||
\(395\) | 2.63851e13i | 2.74394i | ||||||||
\(396\) | 4.10814e12 | 0.421861 | ||||||||
\(397\) | −2.00526e12 | −0.203338 | −0.101669 | − | 0.994818i | \(-0.532418\pi\) | ||||
−0.101669 | + | 0.994818i | \(0.532418\pi\) | |||||||
\(398\) | 6.75366e12 | 0.676276 | ||||||||
\(399\) | − | 1.24342e13i | − | 1.22957i | ||||||
\(400\) | 3.76914e12 | 0.368080 | ||||||||
\(401\) | 1.26762e13 | 1.22256 | 0.611278 | − | 0.791416i | \(-0.290656\pi\) | ||||
0.611278 | + | 0.791416i | \(0.290656\pi\) | |||||||
\(402\) | 5.84971e12 | 0.557191 | ||||||||
\(403\) | −2.72425e13 | −2.56284 | ||||||||
\(404\) | −1.16507e13 | −1.08254 | ||||||||
\(405\) | 1.05921e13i | 0.972089i | ||||||||
\(406\) | − | 8.10913e12i | − | 0.735096i | ||||||
\(407\) | − | 8.90014e12i | − | 0.796938i | ||||||
\(408\) | 1.50116e12 | 0.132778 | ||||||||
\(409\) | − | 4.94819e12i | − | 0.432344i | −0.976355 | − | 0.216172i | \(-0.930643\pi\) | ||
0.976355 | − | 0.216172i | \(-0.0693573\pi\) | |||||||
\(410\) | −2.00191e13 | −1.72792 | ||||||||
\(411\) | 1.02171e13 | 0.871201 | ||||||||
\(412\) | −2.98437e12 | −0.251401 | ||||||||
\(413\) | − | 1.60059e12i | − | 0.133208i | ||||||
\(414\) | − | 1.10267e13i | − | 0.906656i | ||||||
\(415\) | 1.05021e13i | 0.853174i | ||||||||
\(416\) | − | 2.23581e13i | − | 1.79460i | ||||||
\(417\) | − | 1.10157e13i | − | 0.873642i | ||||||
\(418\) | −1.96263e13 | −1.53800 | ||||||||
\(419\) | 1.99645e13i | 1.54592i | 0.634453 | + | 0.772962i | \(0.281225\pi\) | ||||
−0.634453 | + | 0.772962i | \(0.718775\pi\) | |||||||
\(420\) | − | 3.68657e13i | − | 2.82082i | ||||||
\(421\) | − | 1.11863e13i | − | 0.845815i | −0.906173 | − | 0.422908i | \(-0.861009\pi\) | ||
0.906173 | − | 0.422908i | \(-0.138991\pi\) | |||||||
\(422\) | 7.32300e12 | 0.547175 | ||||||||
\(423\) | −6.63733e12 | −0.490108 | ||||||||
\(424\) | − | 9.33559e12i | − | 0.681259i | ||||||
\(425\) | 5.62522e12 | 0.405690 | ||||||||
\(426\) | 9.98862e12i | 0.711963i | ||||||||
\(427\) | −1.63360e13 | −1.15082 | ||||||||
\(428\) | 5.55832e12 | 0.387012 | ||||||||
\(429\) | 1.52614e13i | 1.05029i | ||||||||
\(430\) | 3.50685e13 | − | 2.20923e13i | 2.38548 | − | 1.50279i | ||||
\(431\) | −2.48302e12 | −0.166953 | −0.0834766 | − | 0.996510i | \(-0.526602\pi\) | ||||
−0.0834766 | + | 0.996510i | \(0.526602\pi\) | |||||||
\(432\) | − | 2.82789e12i | − | 0.187950i | ||||||
\(433\) | 2.28933e13i | 1.50407i | 0.659122 | + | 0.752036i | \(0.270928\pi\) | ||||
−0.659122 | + | 0.752036i | \(0.729072\pi\) | |||||||
\(434\) | 5.04785e13 | 3.27837 | ||||||||
\(435\) | − | 8.13567e12i | − | 0.522333i | ||||||
\(436\) | 3.29735e13 | 2.09282 | ||||||||
\(437\) | 3.19225e13i | 2.00304i | ||||||||
\(438\) | − | 8.69198e12i | − | 0.539198i | ||||||
\(439\) | 1.49219e13 | 0.915171 | 0.457586 | − | 0.889166i | \(-0.348714\pi\) | ||||
0.457586 | + | 0.889166i | \(0.348714\pi\) | |||||||
\(440\) | −2.03537e13 | −1.23419 | ||||||||
\(441\) | −3.48752e12 | −0.209086 | ||||||||
\(442\) | − | 8.10701e12i | − | 0.480562i | ||||||
\(443\) | 6.06514e12 | 0.355486 | 0.177743 | − | 0.984077i | \(-0.443120\pi\) | ||||
0.177743 | + | 0.984077i | \(0.443120\pi\) | |||||||
\(444\) | 2.11607e13 | 1.22635 | ||||||||
\(445\) | 8.47104e12 | 0.485441 | ||||||||
\(446\) | 6.26657e12 | 0.355104 | ||||||||
\(447\) | 9.94089e12 | 0.557042 | ||||||||
\(448\) | 3.74622e13i | 2.07588i | ||||||||
\(449\) | − | 2.97603e13i | − | 1.63082i | −0.578886 | − | 0.815408i | \(-0.696512\pi\) | ||
0.578886 | − | 0.815408i | \(-0.303488\pi\) | |||||||
\(450\) | 2.11269e13i | 1.14492i | ||||||||
\(451\) | −9.30539e12 | −0.498715 | ||||||||
\(452\) | − | 2.27199e12i | − | 0.120425i | ||||||
\(453\) | −2.39935e13 | −1.25777 | ||||||||
\(454\) | −3.45104e13 | −1.78925 | ||||||||
\(455\) | −6.96403e13 | −3.57112 | ||||||||
\(456\) | − | 1.63221e13i | − | 0.827849i | ||||||
\(457\) | − | 1.82891e13i | − | 0.917509i | −0.888563 | − | 0.458754i | \(-0.848296\pi\) | ||
0.888563 | − | 0.458754i | \(-0.151704\pi\) | |||||||
\(458\) | 1.48798e13i | 0.738363i | ||||||||
\(459\) | − | 4.22045e12i | − | 0.207155i | ||||||
\(460\) | 9.46454e13i | 4.59526i | ||||||||
\(461\) | −6.48572e12 | −0.311497 | −0.155748 | − | 0.987797i | \(-0.549779\pi\) | ||||
−0.155748 | + | 0.987797i | \(0.549779\pi\) | |||||||
\(462\) | − | 2.82783e13i | − | 1.34352i | ||||||
\(463\) | 4.91343e12i | 0.230930i | 0.993312 | + | 0.115465i | \(0.0368358\pi\) | ||||
−0.993312 | + | 0.115465i | \(0.963164\pi\) | |||||||
\(464\) | 1.34603e12i | 0.0625841i | ||||||||
\(465\) | 5.06437e13 | 2.32949 | ||||||||
\(466\) | 3.51961e13 | 1.60164 | ||||||||
\(467\) | − | 1.64010e13i | − | 0.738391i | −0.929352 | − | 0.369195i | \(-0.879633\pi\) | ||
0.929352 | − | 0.369195i | \(-0.120367\pi\) | |||||||
\(468\) | 1.84509e13 | 0.821842 | ||||||||
\(469\) | 1.24077e13i | 0.546799i | ||||||||
\(470\) | 9.40133e13 | 4.09921 | ||||||||
\(471\) | 3.07772e12 | 0.132778 | ||||||||
\(472\) | − | 2.10105e12i | − | 0.0896863i | ||||||
\(473\) | 1.63008e13 | − | 1.02691e13i | 0.688498 | − | 0.433737i | ||||
\(474\) | −4.81199e13 | −2.01110 | ||||||||
\(475\) | − | 6.11630e13i | − | 2.52942i | ||||||
\(476\) | 9.10291e12i | 0.372516i | ||||||||
\(477\) | −6.61697e12 | −0.267959 | ||||||||
\(478\) | 1.61666e13i | 0.647855i | ||||||||
\(479\) | 5.14118e12 | 0.203885 | 0.101943 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101943 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(480\) | 4.15636e13i | 1.63120i | ||||||||
\(481\) | − | 3.99732e13i | − | 1.55254i | ||||||
\(482\) | −3.93253e13 | −1.51160 | ||||||||
\(483\) | −4.59952e13 | −1.74975 | ||||||||
\(484\) | 1.38002e13 | 0.519588 | ||||||||
\(485\) | 5.64450e13i | 2.10338i | ||||||||
\(486\) | 2.77058e13 | 1.02186 | ||||||||
\(487\) | 1.42608e13 | 0.520594 | 0.260297 | − | 0.965529i | \(-0.416180\pi\) | ||||
0.260297 | + | 0.965529i | \(0.416180\pi\) | |||||||
\(488\) | −2.14438e13 | −0.774822 | ||||||||
\(489\) | −1.18154e12 | −0.0422576 | ||||||||
\(490\) | 4.93984e13 | 1.74877 | ||||||||
\(491\) | 2.22525e12i | 0.0779778i | 0.999240 | + | 0.0389889i | \(0.0124137\pi\) | ||||
−0.999240 | + | 0.0389889i | \(0.987586\pi\) | |||||||
\(492\) | − | 2.21243e13i | − | 0.767438i | ||||||
\(493\) | 2.00887e12i | 0.0689789i | ||||||||
\(494\) | −8.81475e13 | −2.99623 | ||||||||
\(495\) | 1.44265e13i | 0.485441i | ||||||||
\(496\) | −8.37888e12 | −0.279111 | ||||||||
\(497\) | −2.11867e13 | −0.698684 | ||||||||
\(498\) | −1.91533e13 | −0.625312 | ||||||||
\(499\) | 8.67993e12i | 0.280552i | 0.990112 | + | 0.140276i | \(0.0447990\pi\) | ||||
−0.990112 | + | 0.140276i | \(0.955201\pi\) | |||||||
\(500\) | − | 9.62833e13i | − | 3.08107i | ||||||
\(501\) | − | 4.45824e13i | − | 1.41245i | ||||||
\(502\) | 7.23598e13i | 2.26975i | ||||||||
\(503\) | − | 2.35785e13i | − | 0.732278i | −0.930560 | − | 0.366139i | \(-0.880680\pi\) | ||
0.930560 | − | 0.366139i | \(-0.119320\pi\) | |||||||
\(504\) | −1.19586e13 | −0.367729 | ||||||||
\(505\) | − | 4.09135e13i | − | 1.24569i | ||||||
\(506\) | 7.25990e13i | 2.18866i | ||||||||
\(507\) | 4.12684e13i | 1.23191i | ||||||||
\(508\) | −5.67116e13 | −1.67631 | ||||||||
\(509\) | 4.27361e13 | 1.25085 | 0.625426 | − | 0.780283i | \(-0.284925\pi\) | ||||
0.625426 | + | 0.780283i | \(0.284925\pi\) | |||||||
\(510\) | 1.50709e13i | 0.436806i | ||||||||
\(511\) | 1.84364e13 | 0.529141 | ||||||||
\(512\) | − | 1.20825e13i | − | 0.343405i | ||||||
\(513\) | −4.58890e13 | −1.29158 | ||||||||
\(514\) | −9.46763e13 | −2.63892 | ||||||||
\(515\) | − | 1.04802e13i | − | 0.289290i | ||||||
\(516\) | 2.44155e13 | + | 3.87563e13i | 0.667448 | + | 1.05948i | ||||
\(517\) | 4.36999e13 | 1.18312 | ||||||||
\(518\) | 7.40676e13i | 1.98600i | ||||||||
\(519\) | − | 3.42606e13i | − | 0.909825i | ||||||
\(520\) | −9.14148e13 | −2.40436 | ||||||||
\(521\) | − | 2.84719e13i | − | 0.741700i | −0.928693 | − | 0.370850i | \(-0.879066\pi\) | ||
0.928693 | − | 0.370850i | \(-0.120934\pi\) | |||||||
\(522\) | −7.54481e12 | −0.194668 | ||||||||
\(523\) | − | 5.37208e13i | − | 1.37288i | −0.727185 | − | 0.686442i | \(-0.759172\pi\) | ||
0.727185 | − | 0.686442i | \(-0.240828\pi\) | |||||||
\(524\) | − | 3.10280e13i | − | 0.785411i | ||||||
\(525\) | 8.81261e13 | 2.20957 | ||||||||
\(526\) | −6.89448e13 | −1.71227 | ||||||||
\(527\) | −1.25050e13 | −0.307631 | ||||||||
\(528\) | 4.69389e12i | 0.114383i | ||||||||
\(529\) | 7.66570e13 | 1.85043 | ||||||||
\(530\) | 9.37249e13 | 2.24117 | ||||||||
\(531\) | −1.48920e12 | −0.0352761 | ||||||||
\(532\) | 9.89759e13 | 2.32258 | ||||||||
\(533\) | −4.17933e13 | −0.971563 | ||||||||
\(534\) | 1.54490e13i | 0.355791i | ||||||||
\(535\) | 1.95191e13i | 0.445339i | ||||||||
\(536\) | 1.62872e13i | 0.368149i | ||||||||
\(537\) | 1.88751e13 | 0.422685 | ||||||||
\(538\) | − | 6.82663e13i | − | 1.51459i | ||||||
\(539\) | 2.29617e13 | 0.504731 | ||||||||
\(540\) | −1.36054e14 | −2.96308 | ||||||||
\(541\) | −7.63520e13 | −1.64753 | −0.823766 | − | 0.566930i | \(-0.808131\pi\) | ||||
−0.823766 | + | 0.566930i | \(0.808131\pi\) | |||||||
\(542\) | − | 1.02912e14i | − | 2.20025i | ||||||
\(543\) | 5.33633e13i | 1.13043i | ||||||||
\(544\) | − | 1.02629e13i | − | 0.215415i | ||||||
\(545\) | 1.15793e14i | 2.40824i | ||||||||
\(546\) | − | 1.27006e14i | − | 2.61736i | ||||||
\(547\) | −1.59858e13 | −0.326435 | −0.163218 | − | 0.986590i | \(-0.552187\pi\) | ||||
−0.163218 | + | 0.986590i | \(0.552187\pi\) | |||||||
\(548\) | 8.13275e13i | 1.64564i | ||||||||
\(549\) | 1.51991e13i | 0.304759i | ||||||||
\(550\) | − | 1.39099e14i | − | 2.76382i | ||||||
\(551\) | 2.18424e13 | 0.430073 | ||||||||
\(552\) | −6.03765e13 | −1.17807 | ||||||||
\(553\) | − | 1.02066e14i | − | 1.97359i | ||||||
\(554\) | 1.53440e14 | 2.94029 | ||||||||
\(555\) | 7.43100e13i | 1.41118i | ||||||||
\(556\) | 8.76847e13 | 1.65025 | ||||||||
\(557\) | −3.99128e13 | −0.744451 | −0.372226 | − | 0.928142i | \(-0.621405\pi\) | ||||
−0.372226 | + | 0.928142i | \(0.621405\pi\) | |||||||
\(558\) | − | 4.69656e13i | − | 0.868179i | ||||||
\(559\) | 7.32117e13 | − | 4.61216e13i | 1.34129 | − | 0.844978i | ||||
\(560\) | −2.14190e13 | −0.388919 | ||||||||
\(561\) | 7.00536e12i | 0.126071i | ||||||||
\(562\) | 1.96520e13i | 0.350530i | ||||||||
\(563\) | −9.10884e13 | −1.61035 | −0.805177 | − | 0.593035i | \(-0.797930\pi\) | ||||
−0.805177 | + | 0.593035i | \(0.797930\pi\) | |||||||
\(564\) | 1.03900e14i | 1.82062i | ||||||||
\(565\) | 7.97855e12 | 0.138574 | ||||||||
\(566\) | − | 9.25630e13i | − | 1.59351i | ||||||
\(567\) | − | 4.09736e13i | − | 0.699179i | ||||||
\(568\) | −2.78112e13 | −0.470411 | ||||||||
\(569\) | 1.13563e14 | 1.90403 | 0.952017 | − | 0.306044i | \(-0.0990055\pi\) | ||||
0.952017 | + | 0.306044i | \(0.0990055\pi\) | |||||||
\(570\) | 1.63866e14 | 2.72342 | ||||||||
\(571\) | − | 3.43432e13i | − | 0.565797i | −0.959150 | − | 0.282898i | \(-0.908704\pi\) | ||
0.959150 | − | 0.282898i | \(-0.0912960\pi\) | |||||||
\(572\) | −1.21480e14 | −1.98392 | ||||||||
\(573\) | −1.13704e13 | −0.184079 | ||||||||
\(574\) | 7.74402e13 | 1.24282 | ||||||||
\(575\) | −2.26246e14 | −3.59950 | ||||||||
\(576\) | 3.48551e13 | 0.549736 | ||||||||
\(577\) | − | 3.09732e13i | − | 0.484292i | −0.970240 | − | 0.242146i | \(-0.922149\pi\) | ||
0.970240 | − | 0.242146i | \(-0.0778512\pi\) | |||||||
\(578\) | 9.90522e13i | 1.53541i | ||||||||
\(579\) | 9.60043e11i | 0.0147536i | ||||||||
\(580\) | 6.47595e13 | 0.986651 | ||||||||
\(581\) | − | 4.06257e13i | − | 0.613649i | ||||||
\(582\) | −1.02942e14 | −1.54161 | ||||||||
\(583\) | 4.35658e13 | 0.646850 | ||||||||
\(584\) | 2.42009e13 | 0.356261 | ||||||||
\(585\) | 6.47940e13i | 0.945704i | ||||||||
\(586\) | − | 8.48816e13i | − | 1.22836i | ||||||
\(587\) | − | 2.52840e13i | − | 0.362790i | −0.983410 | − | 0.181395i | \(-0.941939\pi\) | ||
0.983410 | − | 0.181395i | \(-0.0580613\pi\) | |||||||
\(588\) | 5.45931e13i | 0.776696i | ||||||||
\(589\) | 1.35967e14i | 1.91803i | ||||||||
\(590\) | 2.10935e13 | 0.295046 | ||||||||
\(591\) | − | 2.72384e13i | − | 0.377785i | ||||||
\(592\) | − | 1.22944e13i | − | 0.169083i | ||||||
\(593\) | 8.57912e13i | 1.16996i | 0.811049 | + | 0.584978i | \(0.198897\pi\) | ||||
−0.811049 | + | 0.584978i | \(0.801103\pi\) | |||||||
\(594\) | −1.04362e14 | −1.41127 | ||||||||
\(595\) | −3.19666e13 | −0.428659 | ||||||||
\(596\) | 7.91290e13i | 1.05221i | ||||||||
\(597\) | −2.62108e13 | −0.345628 | ||||||||
\(598\) | 3.26064e14i | 4.26380i | ||||||||
\(599\) | −1.40363e14 | −1.82020 | −0.910101 | − | 0.414386i | \(-0.863996\pi\) | ||||
−0.910101 | + | 0.414386i | \(0.863996\pi\) | |||||||
\(600\) | 1.15681e14 | 1.48766 | ||||||||
\(601\) | − | 5.65527e13i | − | 0.721242i | −0.932712 | − | 0.360621i | \(-0.882565\pi\) | ||
0.932712 | − | 0.360621i | \(-0.117435\pi\) | |||||||
\(602\) | −1.35656e14 | + | 8.54602e13i | −1.71576 | + | 1.08089i | ||||
\(603\) | 1.15442e13 | 0.144803 | ||||||||
\(604\) | − | 1.90987e14i | − | 2.37585i | ||||||
\(605\) | 4.84621e13i | 0.597896i | ||||||||
\(606\) | 7.46160e13 | 0.912996 | ||||||||
\(607\) | 1.13844e14i | 1.38156i | 0.723067 | + | 0.690778i | \(0.242732\pi\) | ||||
−0.723067 | + | 0.690778i | \(0.757268\pi\) | |||||||
\(608\) | −1.11589e14 | −1.34308 | ||||||||
\(609\) | 3.14714e13i | 0.375690i | ||||||||
\(610\) | − | 2.15285e14i | − | 2.54897i | ||||||
\(611\) | 1.96269e14 | 2.30487 | ||||||||
\(612\) | 8.46942e12 | 0.0986499 | ||||||||
\(613\) | −1.16539e13 | −0.134639 | −0.0673194 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673194 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(614\) | − | 1.24029e13i | − | 0.142129i | ||||||
\(615\) | 7.76936e13 | 0.883100 | ||||||||
\(616\) | 7.87349e13 | 0.887695 | ||||||||
\(617\) | 1.26157e14 | 1.41087 | 0.705435 | − | 0.708775i | \(-0.250752\pi\) | ||||
0.705435 | + | 0.708775i | \(0.250752\pi\) | |||||||
\(618\) | 1.91132e13 | 0.212027 | ||||||||
\(619\) | −3.11922e13 | −0.343236 | −0.171618 | − | 0.985164i | \(-0.554899\pi\) | ||||
−0.171618 | + | 0.985164i | \(0.554899\pi\) | |||||||
\(620\) | 4.03121e14i | 4.40025i | ||||||||
\(621\) | 1.69747e14i | 1.83799i | ||||||||
\(622\) | − | 4.14137e13i | − | 0.444828i | ||||||
\(623\) | −3.27687e13 | −0.349156 | ||||||||
\(624\) | 2.10817e13i | 0.222834i | ||||||||
\(625\) | 1.34794e14 | 1.41342 | ||||||||
\(626\) | 1.85438e14 | 1.92898 | ||||||||
\(627\) | 7.61692e13 | 0.786035 | ||||||||
\(628\) | 2.44985e13i | 0.250808i | ||||||||
\(629\) | − | 1.83487e13i | − | 0.186360i | ||||||
\(630\) | − | 1.20059e14i | − | 1.20974i | ||||||
\(631\) | 1.30583e14i | 1.30539i | 0.757623 | + | 0.652693i | \(0.226361\pi\) | ||||
−0.757623 | + | 0.652693i | \(0.773639\pi\) | |||||||
\(632\) | − | 1.33979e14i | − | 1.32878i | ||||||
\(633\) | −2.84204e13 | −0.279648 | ||||||||
\(634\) | 1.48833e14i | 1.45296i | ||||||||
\(635\) | − | 1.99154e14i | − | 1.92895i | ||||||
\(636\) | 1.03581e14i | 0.995393i | ||||||||
\(637\) | 1.03128e14 | 0.983284 | ||||||||
\(638\) | 4.96746e13 | 0.469928 | ||||||||
\(639\) | 1.97123e13i | 0.185026i | ||||||||
\(640\) | −2.78580e14 | −2.59448 | ||||||||
\(641\) | − | 1.44466e14i | − | 1.33498i | −0.744617 | − | 0.667492i | \(-0.767368\pi\) | ||
0.744617 | − | 0.667492i | \(-0.232632\pi\) | |||||||
\(642\) | −3.55980e13 | −0.326400 | ||||||||
\(643\) | 1.10913e14 | 1.00909 | 0.504544 | − | 0.863386i | \(-0.331661\pi\) | ||||
0.504544 | + | 0.863386i | \(0.331661\pi\) | |||||||
\(644\) | − | 3.66119e14i | − | 3.30516i | ||||||
\(645\) | −1.36100e14 | + | 8.57399e13i | −1.21916 | + | 0.768041i | ||||
\(646\) | −4.04619e13 | −0.359653 | ||||||||
\(647\) | − | 8.03445e13i | − | 0.708654i | −0.935121 | − | 0.354327i | \(-0.884710\pi\) | ||
0.935121 | − | 0.354327i | \(-0.115290\pi\) | |||||||
\(648\) | − | 5.37848e13i | − | 0.470744i | ||||||
\(649\) | 9.80484e12 | 0.0851563 | ||||||||
\(650\) | − | 6.24735e14i | − | 5.38429i | ||||||
\(651\) | −1.95906e14 | −1.67550 | ||||||||
\(652\) | − | 9.40500e12i | − | 0.0798217i | ||||||
\(653\) | 1.33993e12i | 0.0112854i | 0.999984 | + | 0.00564269i | \(0.00179613\pi\) | ||||
−0.999984 | + | 0.00564269i | \(0.998204\pi\) | |||||||
\(654\) | −2.11177e14 | −1.76506 | ||||||||
\(655\) | 1.08961e14 | 0.903782 | ||||||||
\(656\) | −1.28542e13 | −0.105810 | ||||||||
\(657\) | − | 1.71534e13i | − | 0.140127i | ||||||
\(658\) | −3.63674e14 | −2.94837 | ||||||||
\(659\) | −1.00852e14 | −0.811439 | −0.405719 | − | 0.913998i | \(-0.632979\pi\) | ||||
−0.405719 | + | 0.913998i | \(0.632979\pi\) | |||||||
\(660\) | 2.25831e14 | 1.80328 | ||||||||
\(661\) | 3.71317e13 | 0.294264 | 0.147132 | − | 0.989117i | \(-0.452996\pi\) | ||||
0.147132 | + | 0.989117i | \(0.452996\pi\) | |||||||
\(662\) | 2.37615e14 | 1.86889 | ||||||||
\(663\) | 3.14632e13i | 0.245604i | ||||||||
\(664\) | − | 5.33282e13i | − | 0.413158i | ||||||
\(665\) | 3.47573e14i | 2.67263i | ||||||||
\(666\) | 6.89132e13 | 0.525934 | ||||||||
\(667\) | − | 8.07966e13i | − | 0.612018i | ||||||
\(668\) | 3.54873e14 | 2.66803 | ||||||||
\(669\) | −2.43205e13 | −0.181485 | ||||||||
\(670\) | −1.63516e14 | −1.21112 | ||||||||
\(671\) | − | 1.00070e14i | − | 0.735687i | ||||||
\(672\) | − | 1.60782e14i | − | 1.17325i | ||||||
\(673\) | 2.46169e14i | 1.78303i | 0.452990 | + | 0.891515i | \(0.350357\pi\) | ||||
−0.452990 | + | 0.891515i | \(0.649643\pi\) | |||||||
\(674\) | 3.13323e14i | 2.25264i | ||||||||
\(675\) | − | 3.25232e14i | − | 2.32100i | ||||||
\(676\) | −3.28494e14 | −2.32699 | ||||||||
\(677\) | 2.33878e14i | 1.64454i | 0.569095 | + | 0.822272i | \(0.307294\pi\) | ||||
−0.569095 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(678\) | 1.45509e13i | 0.101564i | ||||||||
\(679\) | − | 2.18348e14i | − | 1.51286i | ||||||
\(680\) | −4.19617e13 | −0.288608 | ||||||||
\(681\) | 1.33934e14 | 0.914443 | ||||||||
\(682\) | 3.09220e14i | 2.09578i | ||||||||
\(683\) | 6.44757e13 | 0.433803 | 0.216902 | − | 0.976193i | \(-0.430405\pi\) | ||||
0.216902 | + | 0.976193i | \(0.430405\pi\) | |||||||
\(684\) | − | 9.20880e13i | − | 0.615067i | ||||||
\(685\) | −2.85597e14 | −1.89366 | ||||||||
\(686\) | 1.16986e14 | 0.770039 | ||||||||
\(687\) | − | 5.77483e13i | − | 0.377359i | ||||||
\(688\) | 2.25175e13 | − | 1.41855e13i | 0.146075 | − | 0.0920240i | ||||
\(689\) | 1.95667e14 | 1.26015 | ||||||||
\(690\) | − | 6.06152e14i | − | 3.87557i | ||||||
\(691\) | − | 7.37386e12i | − | 0.0468063i | −0.999726 | − | 0.0234032i | \(-0.992550\pi\) | ||
0.999726 | − | 0.0234032i | \(-0.00745014\pi\) | |||||||
\(692\) | 2.72713e14 | 1.71860 | ||||||||
\(693\) | − | 5.58065e13i | − | 0.349155i | ||||||
\(694\) | 1.04851e14 | 0.651290 | ||||||||
\(695\) | 3.07922e14i | 1.89896i | ||||||||
\(696\) | 4.13116e13i | 0.252945i | ||||||||
\(697\) | −1.91842e13 | −0.116622 | ||||||||
\(698\) | 1.41740e14 | 0.855493 | ||||||||
\(699\) | −1.36595e14 | −0.818560 | ||||||||
\(700\) | 7.01479e14i | 4.17373i | ||||||||
\(701\) | 4.68867e13 | 0.276987 | 0.138494 | − | 0.990363i | \(-0.455774\pi\) | ||||
0.138494 | + | 0.990363i | \(0.455774\pi\) | |||||||
\(702\) | −4.68722e14 | −2.74935 | ||||||||
\(703\) | −1.99505e14 | −1.16192 | ||||||||
\(704\) | −2.29484e14 | −1.32706 | ||||||||
\(705\) | −3.64864e14 | −2.09501 | ||||||||
\(706\) | − | 2.55788e14i | − | 1.45833i | ||||||
\(707\) | 1.58267e14i | 0.895968i | ||||||||
\(708\) | 2.33117e13i | 0.131041i | ||||||||
\(709\) | 1.01880e14 | 0.568668 | 0.284334 | − | 0.958725i | \(-0.408228\pi\) | ||||
0.284334 | + | 0.958725i | \(0.408228\pi\) | |||||||
\(710\) | − | 2.79211e14i | − | 1.54754i | ||||||
\(711\) | −9.49633e13 | −0.522646 | ||||||||
\(712\) | −4.30145e13 | −0.235080 | ||||||||
\(713\) | 5.02951e14 | 2.72947 | ||||||||
\(714\) | − | 5.82991e13i | − | 0.314174i | ||||||
\(715\) | − | 4.26600e14i | − | 2.28292i | ||||||
\(716\) | 1.50245e14i | 0.798424i | ||||||||
\(717\) | − | 6.27421e13i | − | 0.331103i | ||||||
\(718\) | − | 8.86873e13i | − | 0.464771i | ||||||
\(719\) | −4.02819e12 | −0.0209636 | −0.0104818 | − | 0.999945i | \(-0.503337\pi\) | ||||
−0.0104818 | + | 0.999945i | \(0.503337\pi\) | |||||||
\(720\) | 1.99284e13i | 0.102994i | ||||||||
\(721\) | 4.05408e13i | 0.208073i | ||||||||
\(722\) | 1.27386e14i | 0.649286i | ||||||||
\(723\) | 1.52621e14 | 0.772542 | ||||||||
\(724\) | −4.24769e14 | −2.13531 | ||||||||
\(725\) | 1.54805e14i | 0.772851i | ||||||||
\(726\) | −8.83827e13 | −0.438212 | ||||||||
\(727\) | 2.88334e14i | 1.41979i | 0.704308 | + | 0.709894i | \(0.251257\pi\) | ||||
−0.704308 | + | 0.709894i | \(0.748743\pi\) | |||||||
\(728\) | 3.53622e14 | 1.72935 | ||||||||
\(729\) | −2.20618e14 | −1.07153 | ||||||||
\(730\) | 2.42966e14i | 1.17201i | ||||||||
\(731\) | 3.36060e13 | − | 2.11710e13i | 0.161001 | − | 0.101427i | ||||
\(732\) | 2.37925e14 | 1.13210 | ||||||||
\(733\) | 1.60551e14i | 0.758739i | 0.925245 | + | 0.379369i | \(0.123859\pi\) | ||||
−0.925245 | + | 0.379369i | \(0.876141\pi\) | |||||||
\(734\) | − | 1.26209e14i | − | 0.592394i | ||||||
\(735\) | −1.91714e14 | −0.893753 | ||||||||
\(736\) | 4.12775e14i | 1.91128i | ||||||||
\(737\) | −7.60068e13 | −0.349554 | ||||||||
\(738\) | − | 7.20510e13i | − | 0.329123i | ||||||
\(739\) | − | 3.52502e14i | − | 1.59933i | −0.600443 | − | 0.799667i | \(-0.705009\pi\) | ||
0.600443 | − | 0.799667i | \(-0.294991\pi\) | |||||||
\(740\) | −5.91504e14 | −2.66563 | ||||||||
\(741\) | 3.42099e14 | 1.53130 | ||||||||
\(742\) | −3.62558e14 | −1.61198 | ||||||||
\(743\) | 2.04821e14i | 0.904545i | 0.891880 | + | 0.452272i | \(0.149386\pi\) | ||||
−0.891880 | + | 0.452272i | \(0.850614\pi\) | |||||||
\(744\) | −2.57160e14 | −1.12808 | ||||||||
\(745\) | −2.77877e14 | −1.21080 | ||||||||
\(746\) | −3.48811e14 | −1.50972 | ||||||||
\(747\) | −3.77985e13 | −0.162507 | ||||||||
\(748\) | −5.57623e13 | −0.238140 | ||||||||
\(749\) | − | 7.55062e13i | − | 0.320312i | ||||||
\(750\) | 6.16642e14i | 2.59852i | ||||||||
\(751\) | 1.68853e14i | 0.706822i | 0.935468 | + | 0.353411i | \(0.114978\pi\) | ||||
−0.935468 | + | 0.353411i | \(0.885022\pi\) | |||||||
\(752\) | 6.03658e13 | 0.251016 | ||||||||
\(753\) | − | 2.80827e14i | − | 1.16002i | ||||||
\(754\) | 2.23104e14 | 0.915483 | ||||||||
\(755\) | 6.70687e14 | 2.73392 | ||||||||
\(756\) | 5.26301e14 | 2.13121 | ||||||||
\(757\) | − | 1.93219e14i | − | 0.777267i | −0.921392 | − | 0.388634i | \(-0.872947\pi\) | ||
0.921392 | − | 0.388634i | \(-0.127053\pi\) | |||||||
\(758\) | − | 5.58049e14i | − | 2.23011i | ||||||
\(759\) | − | 2.81756e14i | − | 1.11857i | ||||||
\(760\) | 4.56249e14i | 1.79943i | ||||||||
\(761\) | − | 2.44903e14i | − | 0.959558i | −0.877389 | − | 0.479779i | \(-0.840717\pi\) | ||
0.877389 | − | 0.479779i | \(-0.159283\pi\) | |||||||
\(762\) | 3.63207e14 | 1.41377 | ||||||||
\(763\) | − | 4.47924e14i | − | 1.73214i | ||||||
\(764\) | − | 9.05081e13i | − | 0.347713i | ||||||
\(765\) | 2.97420e13i | 0.113518i | ||||||||
\(766\) | 9.98453e13 | 0.378603 | ||||||||
\(767\) | 4.40365e13 | 0.165896 | ||||||||
\(768\) | − | 1.53292e14i | − | 0.573739i | ||||||
\(769\) | 3.72779e14 | 1.38618 | 0.693090 | − | 0.720851i | \(-0.256249\pi\) | ||||
0.693090 | + | 0.720851i | \(0.256249\pi\) | |||||||
\(770\) | 7.90461e14i | 2.92030i | ||||||||
\(771\) | 3.67437e14 | 1.34869 | ||||||||
\(772\) | −7.64189e12 | −0.0278685 | ||||||||
\(773\) | − | 5.95281e13i | − | 0.215687i | −0.994168 | − | 0.107844i | \(-0.965605\pi\) | ||
0.994168 | − | 0.107844i | \(-0.0343946\pi\) | |||||||
\(774\) | 7.95129e13 | + | 1.26216e14i | 0.286242 | + | 0.454369i | ||||
\(775\) | −9.63647e14 | −3.44675 | ||||||||
\(776\) | − | 2.86618e14i | − | 1.01858i | ||||||
\(777\) | − | 2.87455e14i | − | 1.01500i | ||||||
\(778\) | 3.66131e13 | 0.128451 | ||||||||
\(779\) | 2.08590e14i | 0.727119i | ||||||||
\(780\) | 1.01427e15 | 3.51303 | ||||||||
\(781\) | − | 1.29785e14i | − | 0.446651i | ||||||
\(782\) | 1.49671e14i | 0.511806i | ||||||||
\(783\) | 1.16146e14 | 0.394636 | ||||||||
\(784\) | 3.17187e13 | 0.107086 | ||||||||
\(785\) | −8.60313e13 | −0.288608 | ||||||||
\(786\) | 1.98717e14i | 0.662403i | ||||||||
\(787\) | 5.23929e13 | 0.173540 | 0.0867698 | − | 0.996228i | \(-0.472346\pi\) | ||||
0.0867698 | + | 0.996228i | \(0.472346\pi\) | |||||||
\(788\) | 2.16817e14 | 0.713611 | ||||||||
\(789\) | 2.67573e14 | 0.875101 | ||||||||
\(790\) | 1.34509e15 | 4.37135 | ||||||||
\(791\) | −3.08636e13 | −0.0996699 | ||||||||
\(792\) | − | 7.32556e13i | − | 0.235080i | ||||||
\(793\) | − | 4.49446e14i | − | 1.43322i | ||||||
\(794\) | 1.02226e14i | 0.323936i | ||||||||
\(795\) | −3.63745e14 | −1.14541 | ||||||||
\(796\) | − | 2.08637e14i | − | 0.652869i | ||||||
\(797\) | −4.11512e14 | −1.27965 | −0.639825 | − | 0.768521i | \(-0.720993\pi\) | ||||
−0.639825 | + | 0.768521i | \(0.720993\pi\) | |||||||
\(798\) | −6.33886e14 | −1.95883 | ||||||||
\(799\) | 9.00925e13 | 0.276665 | ||||||||
\(800\) | − | 7.90871e14i | − | 2.41355i | ||||||
\(801\) | 3.04883e13i | 0.0924635i | ||||||||
\(802\) | − | 6.46224e14i | − | 1.94765i | ||||||
\(803\) | 1.12937e14i | 0.338266i | ||||||||
\(804\) | − | 1.80712e14i | − | 0.537905i | ||||||
\(805\) | 1.28570e15 | 3.80329 | ||||||||
\(806\) | 1.38880e15i | 4.08286i | ||||||||
\(807\) | 2.64940e14i | 0.774070i | ||||||||
\(808\) | 2.07752e14i | 0.603238i | ||||||||
\(809\) | −6.39654e14 | −1.84588 | −0.922938 | − | 0.384949i | \(-0.874219\pi\) | ||||
−0.922938 | + | 0.384949i | \(0.874219\pi\) | |||||||
\(810\) | 5.39974e14 | 1.54863 | ||||||||
\(811\) | − | 7.09487e13i | − | 0.202228i | −0.994875 | − | 0.101114i | \(-0.967759\pi\) | ||
0.994875 | − | 0.101114i | \(-0.0322406\pi\) | |||||||
\(812\) | −2.50511e14 | −0.709653 | ||||||||
\(813\) | 3.99401e14i | 1.12449i | ||||||||
\(814\) | −4.53721e14 | −1.26960 | ||||||||
\(815\) | 3.30275e13 | 0.0918518 | ||||||||
\(816\) | 9.67701e12i | 0.0267479i | ||||||||
\(817\) | −2.30192e14 | − | 3.65398e14i | −0.632382 | − | 1.00382i | ||||
\(818\) | −2.52254e14 | −0.688767 | ||||||||
\(819\) | − | 2.50644e14i | − | 0.680202i | ||||||
\(820\) | 6.18437e14i | 1.66812i | ||||||||
\(821\) | 3.35194e14 | 0.898630 | 0.449315 | − | 0.893373i | \(-0.351668\pi\) | ||||
0.449315 | + | 0.893373i | \(0.351668\pi\) | |||||||
\(822\) | − | 5.20858e14i | − | 1.38791i | ||||||
\(823\) | −4.93906e14 | −1.30811 | −0.654056 | − | 0.756446i | \(-0.726934\pi\) | ||||
−0.654056 | + | 0.756446i | \(0.726934\pi\) | |||||||
\(824\) | 5.32167e13i | 0.140092i | ||||||||
\(825\) | 5.39840e14i | 1.41252i | ||||||||
\(826\) | −8.15966e13 | −0.212213 | ||||||||
\(827\) | −5.62974e14 | −1.45533 | −0.727664 | − | 0.685934i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685934i | \(0.759394\pi\) | |||||||
\(828\) | −3.40640e14 | −0.875275 | ||||||||
\(829\) | − | 3.77737e14i | − | 0.964755i | −0.875964 | − | 0.482377i | \(-0.839773\pi\) | ||
0.875964 | − | 0.482377i | \(-0.160227\pi\) | |||||||
\(830\) | 5.35390e14 | 1.35919 | ||||||||
\(831\) | −5.95498e14 | −1.50271 | ||||||||
\(832\) | −1.03068e15 | −2.58529 | ||||||||
\(833\) | 4.73382e13 | 0.118029 | ||||||||
\(834\) | −5.61572e14 | −1.39180 | ||||||||
\(835\) | 1.24621e15i | 3.07014i | ||||||||
\(836\) | 6.06303e14i | 1.48477i | ||||||||
\(837\) | 7.22999e14i | 1.75999i | ||||||||
\(838\) | 1.01777e15 | 2.46280 | ||||||||
\(839\) | − | 5.00215e14i | − | 1.20322i | −0.798788 | − | 0.601612i | \(-0.794525\pi\) | ||
0.798788 | − | 0.601612i | \(-0.205475\pi\) | |||||||
\(840\) | −6.57382e14 | −1.57189 | ||||||||
\(841\) | 3.65424e14 | 0.868593 | ||||||||
\(842\) | −5.70267e14 | −1.34747 | ||||||||
\(843\) | − | 7.62690e13i | − | 0.179147i | ||||||
\(844\) | − | 2.26225e14i | − | 0.528237i | ||||||
\(845\) | − | 1.15357e15i | − | 2.67769i | ||||||
\(846\) | 3.38365e14i | 0.780789i | ||||||||
\(847\) | − | 1.87467e14i | − | 0.430039i | ||||||
\(848\) | 6.01807e13 | 0.137239 | ||||||||
\(849\) | 3.59235e14i | 0.814406i | ||||||||
\(850\) | − | 2.86769e14i | − | 0.646304i | ||||||
\(851\) | 7.37985e14i | 1.65348i | ||||||||
\(852\) | 3.08573e14 | 0.687321 | ||||||||
\(853\) | 5.34608e14 | 1.18383 | 0.591917 | − | 0.805999i | \(-0.298371\pi\) | ||||
0.591917 | + | 0.805999i | \(0.298371\pi\) | |||||||
\(854\) | 8.32793e14i | 1.83336i | ||||||||
\(855\) | 3.23385e14 | 0.707765 | ||||||||
\(856\) | − | 9.91148e13i | − | 0.215660i | ||||||
\(857\) | −3.44240e14 | −0.744658 | −0.372329 | − | 0.928101i | \(-0.621441\pi\) | ||||
−0.372329 | + | 0.928101i | \(0.621441\pi\) | |||||||
\(858\) | 7.78012e14 | 1.67321 | ||||||||
\(859\) | − | 5.39638e14i | − | 1.15382i | −0.816809 | − | 0.576908i | \(-0.804259\pi\) | ||
0.816809 | − | 0.576908i | \(-0.195741\pi\) | |||||||
\(860\) | −6.82485e14 | − | 1.08335e15i | −1.45078 | − | 2.30291i | ||||
\(861\) | −3.00544e14 | −0.635174 | ||||||||
\(862\) | 1.26582e14i | 0.265973i | ||||||||
\(863\) | 5.40273e14i | 1.12865i | 0.825553 | + | 0.564325i | \(0.190863\pi\) | ||||
−0.825553 | + | 0.564325i | \(0.809137\pi\) | |||||||
\(864\) | −5.93370e14 | −1.23241 | ||||||||
\(865\) | 9.57683e14i | 1.97761i | ||||||||
\(866\) | 1.16708e15 | 2.39613 | ||||||||
\(867\) | − | 3.84420e14i | − | 0.784712i | ||||||
\(868\) | − | 1.55940e15i | − | 3.16490i | ||||||
\(869\) | 6.25234e14 | 1.26166 | ||||||||
\(870\) | −4.14749e14 | −0.832126 | ||||||||
\(871\) | −3.41369e14 | −0.680979 | ||||||||
\(872\) | − | 5.87977e14i | − | 1.16621i | ||||||
\(873\) | −2.03152e14 | −0.400637 | ||||||||
\(874\) | 1.62738e15 | 3.19103 | ||||||||
\(875\) | −1.30795e15 | −2.55006 | ||||||||
\(876\) | −2.68516e14 | −0.520535 | ||||||||
\(877\) | −4.60940e14 | −0.888478 | −0.444239 | − | 0.895908i | \(-0.646526\pi\) | ||||
−0.444239 | + | 0.895908i | \(0.646526\pi\) | |||||||
\(878\) | − | 7.60706e14i | − | 1.45796i | ||||||
\(879\) | 3.29424e14i | 0.627785i | ||||||||
\(880\) | − | 1.31208e14i | − | 0.248626i | ||||||
\(881\) | 1.80069e14 | 0.339282 | 0.169641 | − | 0.985506i | \(-0.445739\pi\) | ||||
0.169641 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(882\) | 1.77791e14i | 0.333094i | ||||||||
\(883\) | −1.06400e15 | −1.98215 | −0.991074 | − | 0.133313i | \(-0.957439\pi\) | ||||
−0.991074 | + | 0.133313i | \(0.957439\pi\) | |||||||
\(884\) | −2.50445e14 | −0.463929 | ||||||||
\(885\) | −8.18637e13 | −0.150791 | ||||||||
\(886\) | − | 3.09195e14i | − | 0.566323i | ||||||
\(887\) | 9.07453e14i | 1.65275i | 0.563124 | + | 0.826373i | \(0.309599\pi\) | ||||
−0.563124 | + | 0.826373i | \(0.690401\pi\) | |||||||
\(888\) | − | 3.77334e14i | − | 0.683378i | ||||||
\(889\) | 7.70392e14i | 1.38740i | ||||||||
\(890\) | − | 4.31846e14i | − | 0.773355i | ||||||
\(891\) | 2.50995e14 | 0.446967 | ||||||||
\(892\) | − | 1.93590e14i | − | 0.342813i | ||||||
\(893\) | − | 9.79576e14i | − | 1.72497i | ||||||
\(894\) | − | 5.06778e14i | − | 0.887422i | ||||||
\(895\) | −5.27613e14 | −0.918756 | ||||||||
\(896\) | 1.07764e15 | 1.86609 | ||||||||
\(897\) | − | 1.26545e15i | − | 2.17913i | ||||||
\(898\) | −1.51715e15 | −2.59805 | ||||||||
\(899\) | − | 3.44135e14i | − | 0.586045i | ||||||
\(900\) | 6.52662e14 | 1.10529 | ||||||||
\(901\) | 8.98162e13 | 0.151262 | ||||||||
\(902\) | 4.74381e14i | 0.794500i | ||||||||
\(903\) | 5.26480e14 | − | 3.31670e14i | 0.876886 | − | 0.552417i | ||||
\(904\) | −4.05138e13 | −0.0671058 | ||||||||
\(905\) | − | 1.49166e15i | − | 2.45712i | ||||||
\(906\) | 1.22317e15i | 2.00375i | ||||||||
\(907\) | 1.44142e14 | 0.234830 | 0.117415 | − | 0.993083i | \(-0.462539\pi\) | ||||
0.117415 | + | 0.993083i | \(0.462539\pi\) | |||||||
\(908\) | 1.06611e15i | 1.72732i | ||||||||
\(909\) | 1.47253e14 | 0.237271 | ||||||||
\(910\) | 3.55020e15i | 5.68913i | ||||||||
\(911\) | 7.70778e14i | 1.22839i | 0.789153 | + | 0.614197i | \(0.210520\pi\) | ||||
−0.789153 | + | 0.614197i | \(0.789480\pi\) | |||||||
\(912\) | 1.05218e14 | 0.166769 | ||||||||
\(913\) | 2.48864e14 | 0.392290 | ||||||||
\(914\) | −9.32360e14 | −1.46168 | ||||||||
\(915\) | 8.35519e14i | 1.30272i | ||||||||
\(916\) | 4.59673e14 | 0.712807 | ||||||||
\(917\) | −4.21495e14 | −0.650049 | ||||||||
\(918\) | −2.15155e14 | −0.330018 | ||||||||
\(919\) | 8.00837e14 | 1.22171 | 0.610853 | − | 0.791744i | \(-0.290827\pi\) | ||||
0.610853 | + | 0.791744i | \(0.290827\pi\) | |||||||
\(920\) | 1.68770e15 | 2.56068 | ||||||||
\(921\) | 4.81355e13i | 0.0726386i | ||||||||
\(922\) | 3.30636e14i | 0.496244i | ||||||||
\(923\) | − | 5.82902e14i | − | 0.870136i | ||||||
\(924\) | −8.73586e14 | −1.29702 | ||||||||
\(925\) | − | 1.41397e15i | − | 2.08800i | ||||||
\(926\) | 2.50482e14 | 0.367894 | ||||||||
\(927\) | 3.77195e13 | 0.0551020 | ||||||||
\(928\) | 2.82434e14 | 0.410372 | ||||||||
\(929\) | 1.22462e15i | 1.76979i | 0.465792 | + | 0.884894i | \(0.345769\pi\) | ||||
−0.465792 | + | 0.884894i | \(0.654231\pi\) | |||||||
\(930\) | − | 2.58177e15i | − | 3.71110i | ||||||
\(931\) | − | 5.14709e14i | − | 0.735890i | ||||||
\(932\) | − | 1.08729e15i | − | 1.54620i | ||||||
\(933\) | 1.60726e14i | 0.227341i | ||||||||
\(934\) | −8.36109e14 | −1.17633 | ||||||||
\(935\) | − | 1.95820e14i | − | 0.274031i | ||||||
\(936\) | − | 3.29013e14i | − | 0.457967i | ||||||
\(937\) | − | 9.82082e14i | − | 1.35972i | −0.733342 | − | 0.679860i | \(-0.762040\pi\) | ||
0.733342 | − | 0.679860i | \(-0.237960\pi\) | |||||||
\(938\) | 6.32534e14 | 0.871103 | ||||||||
\(939\) | −7.19683e14 | −0.985855 | ||||||||
\(940\) | − | 2.90430e15i | − | 3.95733i | ||||||
\(941\) | −5.70713e14 | −0.773516 | −0.386758 | − | 0.922181i | \(-0.626405\pi\) | ||||
−0.386758 | + | 0.922181i | \(0.626405\pi\) | |||||||
\(942\) | − | 1.56900e14i | − | 0.211528i | ||||||
\(943\) | 7.71588e14 | 1.03473 | ||||||||
\(944\) | 1.35441e13 | 0.0180672 | ||||||||
\(945\) | 1.84821e15i | 2.45240i | ||||||||
\(946\) | −5.23509e14 | − | 8.30999e14i | −0.690985 | − | 1.09684i | ||||
\(947\) | −5.95016e14 | −0.781230 | −0.390615 | − | 0.920554i | \(-0.627738\pi\) | ||||
−0.390615 | + | 0.920554i | \(0.627738\pi\) | |||||||
\(948\) | 1.48654e15i | 1.94149i | ||||||||
\(949\) | 5.07235e14i | 0.658989i | ||||||||
\(950\) | −3.11804e15 | −4.02961 | ||||||||
\(951\) | − | 5.77618e14i | − | 0.742571i | ||||||
\(952\) | 1.62321e14 | 0.207583 | ||||||||
\(953\) | 1.14344e15i | 1.45462i | 0.686308 | + | 0.727311i | \(0.259230\pi\) | ||||
−0.686308 | + | 0.727311i | \(0.740770\pi\) | |||||||
\(954\) | 3.37327e14i | 0.426884i | ||||||||
\(955\) | 3.17837e14 | 0.400117 | ||||||||
\(956\) | 4.99424e14 | 0.625432 | ||||||||
\(957\) | −1.92786e14 | −0.240169 | ||||||||
\(958\) | − | 2.62093e14i | − | 0.324809i | ||||||
\(959\) | 1.10478e15 | 1.36202 | ||||||||
\(960\) | 1.91604e15 | 2.34989 | ||||||||
\(961\) | 1.32258e15 | 1.61363 | ||||||||
\(962\) | −2.03780e15 | −2.47335 | ||||||||
\(963\) | −7.02516e13 | −0.0848252 | ||||||||
\(964\) | 1.21485e15i | 1.45928i | ||||||||
\(965\) | − | 2.68360e13i | − | 0.0320687i | ||||||
\(966\) | 2.34479e15i | 2.78752i | ||||||||
\(967\) | 8.71718e14 | 1.03096 | 0.515482 | − | 0.856900i | \(-0.327613\pi\) | ||||
0.515482 | + | 0.856900i | \(0.327613\pi\) | |||||||
\(968\) | − | 2.46083e14i | − | 0.289537i | ||||||
\(969\) | 1.57032e14 | 0.183810 | ||||||||
\(970\) | 2.87751e15 | 3.35088 | ||||||||
\(971\) | 5.35212e14 | 0.620054 | 0.310027 | − | 0.950728i | \(-0.399662\pi\) | ||||
0.310027 | + | 0.950728i | \(0.399662\pi\) | |||||||
\(972\) | − | 8.55900e14i | − | 0.986488i | ||||||
\(973\) | − | 1.19114e15i | − | 1.36584i | ||||||
\(974\) | − | 7.27002e14i | − | 0.829356i | ||||||
\(975\) | 2.42458e15i | 2.75178i | ||||||||
\(976\) | − | 1.38235e14i | − | 0.156087i | ||||||
\(977\) | 1.43367e15 | 1.61056 | 0.805279 | − | 0.592895i | \(-0.202015\pi\) | ||||
0.805279 | + | 0.592895i | \(0.202015\pi\) | |||||||
\(978\) | 6.02339e13i | 0.0673204i | ||||||||
\(979\) | − | 2.00733e14i | − | 0.223206i | ||||||
\(980\) | − | 1.52604e15i | − | 1.68824i | ||||||
\(981\) | −4.16753e14 | −0.458705 | ||||||||
\(982\) | 1.13441e14 | 0.124226 | ||||||||
\(983\) | − | 9.15106e14i | − | 0.997020i | −0.866884 | − | 0.498510i | \(-0.833881\pi\) | ||
0.866884 | − | 0.498510i | \(-0.166119\pi\) | |||||||
\(984\) | −3.94516e14 | −0.427650 | ||||||||
\(985\) | 7.61394e14i | 0.821161i | ||||||||
\(986\) | 1.02410e14 | 0.109890 | ||||||||
\(987\) | 1.41141e15 | 1.50684 | ||||||||
\(988\) | 2.72309e15i | 2.89253i | ||||||||
\(989\) | −1.35163e15 | + | 8.51496e14i | −1.42849 | + | 0.899915i | ||||
\(990\) | 7.35452e14 | 0.773354 | ||||||||
\(991\) | − | 2.75669e14i | − | 0.288417i | −0.989547 | − | 0.144208i | \(-0.953936\pi\) | ||
0.989547 | − | 0.144208i | \(-0.0460636\pi\) | |||||||
\(992\) | 1.75812e15i | 1.83017i | ||||||||
\(993\) | −9.22179e14 | −0.955144 | ||||||||
\(994\) | 1.08008e15i | 1.11307i | ||||||||
\(995\) | 7.32669e14 | 0.751264 | ||||||||
\(996\) | 5.91691e14i | 0.603668i | ||||||||
\(997\) | 2.18999e13i | 0.0222313i | 0.999938 | + | 0.0111157i | \(0.00353830\pi\) | ||||
−0.999938 | + | 0.0111157i | \(0.996462\pi\) | |||||||
\(998\) | 4.42495e14 | 0.446947 | ||||||||
\(999\) | −1.06086e15 | −1.06618 |
(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 | 43.11.b.b.42.4 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.31 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.4 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.31 | yes | 34 | 43.42 | odd | 2 | inner |