Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.19123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.19123 | −1.87438 | −0.937188 | − | 0.348824i | \(-0.886581\pi\) | ||||
−0.937188 | + | 0.348824i | \(0.886581\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.48485 | −0.939187 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.19123 | 1.32538 | ||||||||
\(11\) | −3.45337 | −1.04123 | −0.520615 | − | 0.853791i | \(-0.674297\pi\) | ||||
−0.520615 | + | 0.853791i | \(0.674297\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 2.48485 | 0.664105 | ||||||||
\(15\) | −4.19123 | −1.08217 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.15125 | 1.00683 | 0.503413 | − | 0.864046i | \(-0.332077\pi\) | ||||
0.503413 | + | 0.864046i | \(0.332077\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.49203 | −0.342295 | −0.171148 | − | 0.985245i | \(-0.554748\pi\) | ||||
−0.171148 | + | 0.985245i | \(0.554748\pi\) | |||||||
\(20\) | −4.19123 | −0.937188 | ||||||||
\(21\) | −2.48485 | −0.542240 | ||||||||
\(22\) | 3.45337 | 0.736261 | ||||||||
\(23\) | −1.16579 | −0.243084 | −0.121542 | − | 0.992586i | \(-0.538784\pi\) | ||||
−0.121542 | + | 0.992586i | \(0.538784\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 12.5664 | 2.51329 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.48485 | −0.469593 | ||||||||
\(29\) | 3.97697 | 0.738505 | 0.369253 | − | 0.929329i | \(-0.379614\pi\) | ||||
0.369253 | + | 0.929329i | \(0.379614\pi\) | |||||||
\(30\) | 4.19123 | 0.765211 | ||||||||
\(31\) | 6.19959 | 1.11348 | 0.556740 | − | 0.830687i | \(-0.312052\pi\) | ||||
0.556740 | + | 0.830687i | \(0.312052\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.45337 | −0.601155 | ||||||||
\(34\) | −4.15125 | −0.711933 | ||||||||
\(35\) | 10.4146 | 1.76039 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.938276 | 0.154252 | 0.0771258 | − | 0.997021i | \(-0.475426\pi\) | ||||
0.0771258 | + | 0.997021i | \(0.475426\pi\) | |||||||
\(38\) | 1.49203 | 0.242039 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 4.19123 | 0.662692 | ||||||||
\(41\) | −8.24288 | −1.28732 | −0.643661 | − | 0.765311i | \(-0.722585\pi\) | ||||
−0.643661 | + | 0.765311i | \(0.722585\pi\) | |||||||
\(42\) | 2.48485 | 0.383421 | ||||||||
\(43\) | −1.09636 | −0.167193 | −0.0835964 | − | 0.996500i | \(-0.526641\pi\) | ||||
−0.0835964 | + | 0.996500i | \(0.526641\pi\) | |||||||
\(44\) | −3.45337 | −0.520615 | ||||||||
\(45\) | −4.19123 | −0.624792 | ||||||||
\(46\) | 1.16579 | 0.171886 | ||||||||
\(47\) | 1.91281 | 0.279012 | 0.139506 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139506 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −0.825500 | −0.117929 | ||||||||
\(50\) | −12.5664 | −1.77716 | ||||||||
\(51\) | 4.15125 | 0.581291 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −3.82574 | −0.525505 | −0.262753 | − | 0.964863i | \(-0.584630\pi\) | ||||
−0.262753 | + | 0.964863i | \(0.584630\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 14.4739 | 1.95166 | ||||||||
\(56\) | 2.48485 | 0.332053 | ||||||||
\(57\) | −1.49203 | −0.197624 | ||||||||
\(58\) | −3.97697 | −0.522202 | ||||||||
\(59\) | 8.10947 | 1.05576 | 0.527882 | − | 0.849318i | \(-0.322986\pi\) | ||||
0.527882 | + | 0.849318i | \(0.322986\pi\) | |||||||
\(60\) | −4.19123 | −0.541086 | ||||||||
\(61\) | 5.11955 | 0.655491 | 0.327745 | − | 0.944766i | \(-0.393711\pi\) | ||||
0.327745 | + | 0.944766i | \(0.393711\pi\) | |||||||
\(62\) | −6.19959 | −0.787349 | ||||||||
\(63\) | −2.48485 | −0.313062 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.19123 | 0.519859 | ||||||||
\(66\) | 3.45337 | 0.425080 | ||||||||
\(67\) | 13.0998 | 1.60040 | 0.800198 | − | 0.599736i | \(-0.204728\pi\) | ||||
0.800198 | + | 0.599736i | \(0.204728\pi\) | |||||||
\(68\) | 4.15125 | 0.503413 | ||||||||
\(69\) | −1.16579 | −0.140345 | ||||||||
\(70\) | −10.4146 | −1.24478 | ||||||||
\(71\) | 0.896009 | 0.106337 | 0.0531683 | − | 0.998586i | \(-0.483068\pi\) | ||||
0.0531683 | + | 0.998586i | \(0.483068\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.857920 | −0.100412 | −0.0502059 | − | 0.998739i | \(-0.515988\pi\) | ||||
−0.0502059 | + | 0.998739i | \(0.515988\pi\) | |||||||
\(74\) | −0.938276 | −0.109072 | ||||||||
\(75\) | 12.5664 | 1.45105 | ||||||||
\(76\) | −1.49203 | −0.171148 | ||||||||
\(77\) | 8.58112 | 0.977909 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 4.36696 | 0.491322 | 0.245661 | − | 0.969356i | \(-0.420995\pi\) | ||||
0.245661 | + | 0.969356i | \(0.420995\pi\) | |||||||
\(80\) | −4.19123 | −0.468594 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.24288 | 0.910274 | ||||||||
\(83\) | −1.28939 | −0.141529 | −0.0707644 | − | 0.997493i | \(-0.522544\pi\) | ||||
−0.0707644 | + | 0.997493i | \(0.522544\pi\) | |||||||
\(84\) | −2.48485 | −0.271120 | ||||||||
\(85\) | −17.3989 | −1.88717 | ||||||||
\(86\) | 1.09636 | 0.118223 | ||||||||
\(87\) | 3.97697 | 0.426376 | ||||||||
\(88\) | 3.45337 | 0.368130 | ||||||||
\(89\) | 1.33376 | 0.141378 | 0.0706891 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706891 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(90\) | 4.19123 | 0.441795 | ||||||||
\(91\) | 2.48485 | 0.260483 | ||||||||
\(92\) | −1.16579 | −0.121542 | ||||||||
\(93\) | 6.19959 | 0.642868 | ||||||||
\(94\) | −1.91281 | −0.197292 | ||||||||
\(95\) | 6.25345 | 0.641590 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.09589 | −0.111271 | −0.0556355 | − | 0.998451i | \(-0.517718\pi\) | ||||
−0.0556355 | + | 0.998451i | \(0.517718\pi\) | |||||||
\(98\) | 0.825500 | 0.0833881 | ||||||||
\(99\) | −3.45337 | −0.347077 | ||||||||
\(100\) | 12.5664 | 1.25664 | ||||||||
\(101\) | −12.2271 | −1.21664 | −0.608320 | − | 0.793692i | \(-0.708156\pi\) | ||||
−0.608320 | + | 0.793692i | \(0.708156\pi\) | |||||||
\(102\) | −4.15125 | −0.411035 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 10.4146 | 1.01636 | ||||||||
\(106\) | 3.82574 | 0.371588 | ||||||||
\(107\) | −17.9304 | −1.73340 | −0.866700 | − | 0.498830i | \(-0.833763\pi\) | ||||
−0.866700 | + | 0.498830i | \(0.833763\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 18.1175 | 1.73534 | 0.867670 | − | 0.497140i | \(-0.165617\pi\) | ||||
0.867670 | + | 0.497140i | \(0.165617\pi\) | |||||||
\(110\) | −14.4739 | −1.38003 | ||||||||
\(111\) | 0.938276 | 0.0890572 | ||||||||
\(112\) | −2.48485 | −0.234797 | ||||||||
\(113\) | 16.6258 | 1.56402 | 0.782011 | − | 0.623264i | \(-0.214194\pi\) | ||||
0.782011 | + | 0.623264i | \(0.214194\pi\) | |||||||
\(114\) | 1.49203 | 0.139741 | ||||||||
\(115\) | 4.88610 | 0.455631 | ||||||||
\(116\) | 3.97697 | 0.369253 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −8.10947 | −0.746538 | ||||||||
\(119\) | −10.3152 | −0.945597 | ||||||||
\(120\) | 4.19123 | 0.382606 | ||||||||
\(121\) | 0.925764 | 0.0841604 | ||||||||
\(122\) | −5.11955 | −0.463502 | ||||||||
\(123\) | −8.24288 | −0.743236 | ||||||||
\(124\) | 6.19959 | 0.556740 | ||||||||
\(125\) | −31.7127 | −2.83647 | ||||||||
\(126\) | 2.48485 | 0.221368 | ||||||||
\(127\) | −6.45305 | −0.572615 | −0.286308 | − | 0.958138i | \(-0.592428\pi\) | ||||
−0.286308 | + | 0.958138i | \(0.592428\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.09636 | −0.0965288 | ||||||||
\(130\) | −4.19123 | −0.367596 | ||||||||
\(131\) | −5.48297 | −0.479049 | −0.239525 | − | 0.970890i | \(-0.576992\pi\) | ||||
−0.239525 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(132\) | −3.45337 | −0.300577 | ||||||||
\(133\) | 3.70748 | 0.321479 | ||||||||
\(134\) | −13.0998 | −1.13165 | ||||||||
\(135\) | −4.19123 | −0.360724 | ||||||||
\(136\) | −4.15125 | −0.355967 | ||||||||
\(137\) | 9.92674 | 0.848098 | 0.424049 | − | 0.905639i | \(-0.360608\pi\) | ||||
0.424049 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(138\) | 1.16579 | 0.0992386 | ||||||||
\(139\) | 3.44571 | 0.292261 | 0.146131 | − | 0.989265i | \(-0.453318\pi\) | ||||
0.146131 | + | 0.989265i | \(0.453318\pi\) | |||||||
\(140\) | 10.4146 | 0.880195 | ||||||||
\(141\) | 1.91281 | 0.161088 | ||||||||
\(142\) | −0.896009 | −0.0751914 | ||||||||
\(143\) | 3.45337 | 0.288785 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −16.6684 | −1.38424 | ||||||||
\(146\) | 0.857920 | 0.0710019 | ||||||||
\(147\) | −0.825500 | −0.0680861 | ||||||||
\(148\) | 0.938276 | 0.0771258 | ||||||||
\(149\) | −4.22838 | −0.346403 | −0.173201 | − | 0.984886i | \(-0.555411\pi\) | ||||
−0.173201 | + | 0.984886i | \(0.555411\pi\) | |||||||
\(150\) | −12.5664 | −1.02605 | ||||||||
\(151\) | −14.8402 | −1.20768 | −0.603840 | − | 0.797106i | \(-0.706363\pi\) | ||||
−0.603840 | + | 0.797106i | \(0.706363\pi\) | |||||||
\(152\) | 1.49203 | 0.121020 | ||||||||
\(153\) | 4.15125 | 0.335609 | ||||||||
\(154\) | −8.58112 | −0.691486 | ||||||||
\(155\) | −25.9839 | −2.08708 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 11.3687 | 0.907322 | 0.453661 | − | 0.891174i | \(-0.350118\pi\) | ||||
0.453661 | + | 0.891174i | \(0.350118\pi\) | |||||||
\(158\) | −4.36696 | −0.347417 | ||||||||
\(159\) | −3.82574 | −0.303401 | ||||||||
\(160\) | 4.19123 | 0.331346 | ||||||||
\(161\) | 2.89682 | 0.228301 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 17.4080 | 1.36350 | 0.681750 | − | 0.731585i | \(-0.261219\pi\) | ||||
0.681750 | + | 0.731585i | \(0.261219\pi\) | |||||||
\(164\) | −8.24288 | −0.643661 | ||||||||
\(165\) | 14.4739 | 1.12679 | ||||||||
\(166\) | 1.28939 | 0.100076 | ||||||||
\(167\) | −19.8534 | −1.53630 | −0.768151 | − | 0.640268i | \(-0.778823\pi\) | ||||
−0.768151 | + | 0.640268i | \(0.778823\pi\) | |||||||
\(168\) | 2.48485 | 0.191711 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 17.3989 | 1.33443 | ||||||||
\(171\) | −1.49203 | −0.114098 | ||||||||
\(172\) | −1.09636 | −0.0835964 | ||||||||
\(173\) | 8.38483 | 0.637487 | 0.318744 | − | 0.947841i | \(-0.396739\pi\) | ||||
0.318744 | + | 0.947841i | \(0.396739\pi\) | |||||||
\(174\) | −3.97697 | −0.301493 | ||||||||
\(175\) | −31.2258 | −2.36045 | ||||||||
\(176\) | −3.45337 | −0.260308 | ||||||||
\(177\) | 8.10947 | 0.609545 | ||||||||
\(178\) | −1.33376 | −0.0999695 | ||||||||
\(179\) | 24.2415 | 1.81189 | 0.905946 | − | 0.423394i | \(-0.139161\pi\) | ||||
0.905946 | + | 0.423394i | \(0.139161\pi\) | |||||||
\(180\) | −4.19123 | −0.312396 | ||||||||
\(181\) | 1.00614 | 0.0747858 | 0.0373929 | − | 0.999301i | \(-0.488095\pi\) | ||||
0.0373929 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(182\) | −2.48485 | −0.184190 | ||||||||
\(183\) | 5.11955 | 0.378448 | ||||||||
\(184\) | 1.16579 | 0.0859431 | ||||||||
\(185\) | −3.93253 | −0.289126 | ||||||||
\(186\) | −6.19959 | −0.454576 | ||||||||
\(187\) | −14.3358 | −1.04834 | ||||||||
\(188\) | 1.91281 | 0.139506 | ||||||||
\(189\) | −2.48485 | −0.180747 | ||||||||
\(190\) | −6.25345 | −0.453673 | ||||||||
\(191\) | −17.7258 | −1.28259 | −0.641295 | − | 0.767294i | \(-0.721603\pi\) | ||||
−0.641295 | + | 0.767294i | \(0.721603\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −8.92394 | −0.642359 | −0.321180 | − | 0.947018i | \(-0.604079\pi\) | ||||
−0.321180 | + | 0.947018i | \(0.604079\pi\) | |||||||
\(194\) | 1.09589 | 0.0786805 | ||||||||
\(195\) | 4.19123 | 0.300140 | ||||||||
\(196\) | −0.825500 | −0.0589643 | ||||||||
\(197\) | −5.72916 | −0.408186 | −0.204093 | − | 0.978952i | \(-0.565425\pi\) | ||||
−0.204093 | + | 0.978952i | \(0.565425\pi\) | |||||||
\(198\) | 3.45337 | 0.245420 | ||||||||
\(199\) | 4.04033 | 0.286412 | 0.143206 | − | 0.989693i | \(-0.454259\pi\) | ||||
0.143206 | + | 0.989693i | \(0.454259\pi\) | |||||||
\(200\) | −12.5664 | −0.888582 | ||||||||
\(201\) | 13.0998 | 0.923989 | ||||||||
\(202\) | 12.2271 | 0.860295 | ||||||||
\(203\) | −9.88220 | −0.693594 | ||||||||
\(204\) | 4.15125 | 0.290646 | ||||||||
\(205\) | 34.5479 | 2.41293 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −1.16579 | −0.0810279 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 5.15253 | 0.356408 | ||||||||
\(210\) | −10.4146 | −0.718676 | ||||||||
\(211\) | −18.1802 | −1.25158 | −0.625789 | − | 0.779992i | \(-0.715223\pi\) | ||||
−0.625789 | + | 0.779992i | \(0.715223\pi\) | |||||||
\(212\) | −3.82574 | −0.262753 | ||||||||
\(213\) | 0.896009 | 0.0613935 | ||||||||
\(214\) | 17.9304 | 1.22570 | ||||||||
\(215\) | 4.59509 | 0.313382 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −15.4051 | −1.04577 | ||||||||
\(218\) | −18.1175 | −1.22707 | ||||||||
\(219\) | −0.857920 | −0.0579728 | ||||||||
\(220\) | 14.4739 | 0.975829 | ||||||||
\(221\) | −4.15125 | −0.279243 | ||||||||
\(222\) | −0.938276 | −0.0629730 | ||||||||
\(223\) | −15.7232 | −1.05290 | −0.526452 | − | 0.850205i | \(-0.676478\pi\) | ||||
−0.526452 | + | 0.850205i | \(0.676478\pi\) | |||||||
\(224\) | 2.48485 | 0.166026 | ||||||||
\(225\) | 12.5664 | 0.837763 | ||||||||
\(226\) | −16.6258 | −1.10593 | ||||||||
\(227\) | 5.43218 | 0.360546 | 0.180273 | − | 0.983617i | \(-0.442302\pi\) | ||||
0.180273 | + | 0.983617i | \(0.442302\pi\) | |||||||
\(228\) | −1.49203 | −0.0988121 | ||||||||
\(229\) | 14.2912 | 0.944386 | 0.472193 | − | 0.881495i | \(-0.343462\pi\) | ||||
0.472193 | + | 0.881495i | \(0.343462\pi\) | |||||||
\(230\) | −4.88610 | −0.322180 | ||||||||
\(231\) | 8.58112 | 0.564596 | ||||||||
\(232\) | −3.97697 | −0.261101 | ||||||||
\(233\) | −15.7787 | −1.03370 | −0.516848 | − | 0.856077i | \(-0.672895\pi\) | ||||
−0.516848 | + | 0.856077i | \(0.672895\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −8.01704 | −0.522974 | ||||||||
\(236\) | 8.10947 | 0.527882 | ||||||||
\(237\) | 4.36696 | 0.283665 | ||||||||
\(238\) | 10.3152 | 0.668638 | ||||||||
\(239\) | −24.0758 | −1.55733 | −0.778667 | − | 0.627438i | \(-0.784104\pi\) | ||||
−0.778667 | + | 0.627438i | \(0.784104\pi\) | |||||||
\(240\) | −4.19123 | −0.270543 | ||||||||
\(241\) | −24.3323 | −1.56738 | −0.783689 | − | 0.621153i | \(-0.786665\pi\) | ||||
−0.783689 | + | 0.621153i | \(0.786665\pi\) | |||||||
\(242\) | −0.925764 | −0.0595104 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.11955 | 0.327745 | ||||||||
\(245\) | 3.45987 | 0.221043 | ||||||||
\(246\) | 8.24288 | 0.525547 | ||||||||
\(247\) | 1.49203 | 0.0949356 | ||||||||
\(248\) | −6.19959 | −0.393675 | ||||||||
\(249\) | −1.28939 | −0.0817117 | ||||||||
\(250\) | 31.7127 | 2.00569 | ||||||||
\(251\) | 8.22652 | 0.519253 | 0.259627 | − | 0.965709i | \(-0.416400\pi\) | ||||
0.259627 | + | 0.965709i | \(0.416400\pi\) | |||||||
\(252\) | −2.48485 | −0.156531 | ||||||||
\(253\) | 4.02590 | 0.253106 | ||||||||
\(254\) | 6.45305 | 0.404900 | ||||||||
\(255\) | −17.3989 | −1.08956 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2253 | 1.19924 | 0.599620 | − | 0.800285i | \(-0.295319\pi\) | ||||
0.599620 | + | 0.800285i | \(0.295319\pi\) | |||||||
\(258\) | 1.09636 | 0.0682562 | ||||||||
\(259\) | −2.33148 | −0.144871 | ||||||||
\(260\) | 4.19123 | 0.259929 | ||||||||
\(261\) | 3.97697 | 0.246168 | ||||||||
\(262\) | 5.48297 | 0.338739 | ||||||||
\(263\) | −26.5673 | −1.63821 | −0.819104 | − | 0.573644i | \(-0.805529\pi\) | ||||
−0.819104 | + | 0.573644i | \(0.805529\pi\) | |||||||
\(264\) | 3.45337 | 0.212540 | ||||||||
\(265\) | 16.0346 | 0.984995 | ||||||||
\(266\) | −3.70748 | −0.227320 | ||||||||
\(267\) | 1.33376 | 0.0816248 | ||||||||
\(268\) | 13.0998 | 0.800198 | ||||||||
\(269\) | 3.93881 | 0.240154 | 0.120077 | − | 0.992765i | \(-0.461686\pi\) | ||||
0.120077 | + | 0.992765i | \(0.461686\pi\) | |||||||
\(270\) | 4.19123 | 0.255070 | ||||||||
\(271\) | −6.13049 | −0.372401 | −0.186200 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186200 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(272\) | 4.15125 | 0.251706 | ||||||||
\(273\) | 2.48485 | 0.150390 | ||||||||
\(274\) | −9.92674 | −0.599696 | ||||||||
\(275\) | −43.3966 | −2.61691 | ||||||||
\(276\) | −1.16579 | −0.0701723 | ||||||||
\(277\) | −3.38074 | −0.203129 | −0.101564 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101564 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(278\) | −3.44571 | −0.206660 | ||||||||
\(279\) | 6.19959 | 0.371160 | ||||||||
\(280\) | −10.4146 | −0.622392 | ||||||||
\(281\) | −5.93074 | −0.353798 | −0.176899 | − | 0.984229i | \(-0.556607\pi\) | ||||
−0.176899 | + | 0.984229i | \(0.556607\pi\) | |||||||
\(282\) | −1.91281 | −0.113906 | ||||||||
\(283\) | 23.4537 | 1.39418 | 0.697088 | − | 0.716985i | \(-0.254479\pi\) | ||||
0.697088 | + | 0.716985i | \(0.254479\pi\) | |||||||
\(284\) | 0.896009 | 0.0531683 | ||||||||
\(285\) | 6.25345 | 0.370422 | ||||||||
\(286\) | −3.45337 | −0.204202 | ||||||||
\(287\) | 20.4824 | 1.20904 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0.232872 | 0.0136984 | ||||||||
\(290\) | 16.6684 | 0.978803 | ||||||||
\(291\) | −1.09589 | −0.0642424 | ||||||||
\(292\) | −0.857920 | −0.0502059 | ||||||||
\(293\) | −29.0023 | −1.69433 | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||||
−0.847167 | + | 0.531327i | \(0.821693\pi\) | |||||||
\(294\) | 0.825500 | 0.0481442 | ||||||||
\(295\) | −33.9887 | −1.97890 | ||||||||
\(296\) | −0.938276 | −0.0545362 | ||||||||
\(297\) | −3.45337 | −0.200385 | ||||||||
\(298\) | 4.22838 | 0.244944 | ||||||||
\(299\) | 1.16579 | 0.0674193 | ||||||||
\(300\) | 12.5664 | 0.725524 | ||||||||
\(301\) | 2.72429 | 0.157025 | ||||||||
\(302\) | 14.8402 | 0.853959 | ||||||||
\(303\) | −12.2271 | −0.702428 | ||||||||
\(304\) | −1.49203 | −0.0855738 | ||||||||
\(305\) | −21.4572 | −1.22864 | ||||||||
\(306\) | −4.15125 | −0.237311 | ||||||||
\(307\) | 25.5987 | 1.46100 | 0.730499 | − | 0.682914i | \(-0.239288\pi\) | ||||
0.730499 | + | 0.682914i | \(0.239288\pi\) | |||||||
\(308\) | 8.58112 | 0.488955 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 25.9839 | 1.47579 | ||||||||
\(311\) | −14.8637 | −0.842842 | −0.421421 | − | 0.906865i | \(-0.638468\pi\) | ||||
−0.421421 | + | 0.906865i | \(0.638468\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 11.2838 | 0.637798 | 0.318899 | − | 0.947789i | \(-0.396687\pi\) | ||||
0.318899 | + | 0.947789i | \(0.396687\pi\) | |||||||
\(314\) | −11.3687 | −0.641574 | ||||||||
\(315\) | 10.4146 | 0.586796 | ||||||||
\(316\) | 4.36696 | 0.245661 | ||||||||
\(317\) | 3.43988 | 0.193203 | 0.0966013 | − | 0.995323i | \(-0.469203\pi\) | ||||
0.0966013 | + | 0.995323i | \(0.469203\pi\) | |||||||
\(318\) | 3.82574 | 0.214537 | ||||||||
\(319\) | −13.7340 | −0.768954 | ||||||||
\(320\) | −4.19123 | −0.234297 | ||||||||
\(321\) | −17.9304 | −1.00078 | ||||||||
\(322\) | −2.89682 | −0.161433 | ||||||||
\(323\) | −6.19379 | −0.344632 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −12.5664 | −0.697061 | ||||||||
\(326\) | −17.4080 | −0.964140 | ||||||||
\(327\) | 18.1175 | 1.00190 | ||||||||
\(328\) | 8.24288 | 0.455137 | ||||||||
\(329\) | −4.75306 | −0.262045 | ||||||||
\(330\) | −14.4739 | −0.796761 | ||||||||
\(331\) | −6.84967 | −0.376492 | −0.188246 | − | 0.982122i | \(-0.560280\pi\) | ||||
−0.188246 | + | 0.982122i | \(0.560280\pi\) | |||||||
\(332\) | −1.28939 | −0.0707644 | ||||||||
\(333\) | 0.938276 | 0.0514172 | ||||||||
\(334\) | 19.8534 | 1.08633 | ||||||||
\(335\) | −54.9043 | −2.99974 | ||||||||
\(336\) | −2.48485 | −0.135560 | ||||||||
\(337\) | 8.11014 | 0.441788 | 0.220894 | − | 0.975298i | \(-0.429103\pi\) | ||||
0.220894 | + | 0.975298i | \(0.429103\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 16.6258 | 0.902989 | ||||||||
\(340\) | −17.3989 | −0.943586 | ||||||||
\(341\) | −21.4095 | −1.15939 | ||||||||
\(342\) | 1.49203 | 0.0806798 | ||||||||
\(343\) | 19.4452 | 1.04994 | ||||||||
\(344\) | 1.09636 | 0.0591116 | ||||||||
\(345\) | 4.88610 | 0.263059 | ||||||||
\(346\) | −8.38483 | −0.450772 | ||||||||
\(347\) | −15.6913 | −0.842351 | −0.421176 | − | 0.906979i | \(-0.638382\pi\) | ||||
−0.421176 | + | 0.906979i | \(0.638382\pi\) | |||||||
\(348\) | 3.97697 | 0.213188 | ||||||||
\(349\) | −16.5396 | −0.885347 | −0.442673 | − | 0.896683i | \(-0.645970\pi\) | ||||
−0.442673 | + | 0.896683i | \(0.645970\pi\) | |||||||
\(350\) | 31.2258 | 1.66909 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.45337 | 0.184065 | ||||||||
\(353\) | −28.2812 | −1.50525 | −0.752627 | − | 0.658447i | \(-0.771214\pi\) | ||||
−0.752627 | + | 0.658447i | \(0.771214\pi\) | |||||||
\(354\) | −8.10947 | −0.431014 | ||||||||
\(355\) | −3.75538 | −0.199315 | ||||||||
\(356\) | 1.33376 | 0.0706891 | ||||||||
\(357\) | −10.3152 | −0.545941 | ||||||||
\(358\) | −24.2415 | −1.28120 | ||||||||
\(359\) | −21.2405 | −1.12103 | −0.560516 | − | 0.828143i | \(-0.689397\pi\) | ||||
−0.560516 | + | 0.828143i | \(0.689397\pi\) | |||||||
\(360\) | 4.19123 | 0.220897 | ||||||||
\(361\) | −16.7738 | −0.882834 | ||||||||
\(362\) | −1.00614 | −0.0528815 | ||||||||
\(363\) | 0.925764 | 0.0485900 | ||||||||
\(364\) | 2.48485 | 0.130242 | ||||||||
\(365\) | 3.59574 | 0.188210 | ||||||||
\(366\) | −5.11955 | −0.267603 | ||||||||
\(367\) | −4.96807 | −0.259331 | −0.129666 | − | 0.991558i | \(-0.541390\pi\) | ||||
−0.129666 | + | 0.991558i | \(0.541390\pi\) | |||||||
\(368\) | −1.16579 | −0.0607710 | ||||||||
\(369\) | −8.24288 | −0.429107 | ||||||||
\(370\) | 3.93253 | 0.204443 | ||||||||
\(371\) | 9.50640 | 0.493547 | ||||||||
\(372\) | 6.19959 | 0.321434 | ||||||||
\(373\) | −1.35351 | −0.0700822 | −0.0350411 | − | 0.999386i | \(-0.511156\pi\) | ||||
−0.0350411 | + | 0.999386i | \(0.511156\pi\) | |||||||
\(374\) | 14.3358 | 0.741287 | ||||||||
\(375\) | −31.7127 | −1.63764 | ||||||||
\(376\) | −1.91281 | −0.0986458 | ||||||||
\(377\) | −3.97697 | −0.204824 | ||||||||
\(378\) | 2.48485 | 0.127807 | ||||||||
\(379\) | 1.33194 | 0.0684173 | 0.0342086 | − | 0.999415i | \(-0.489109\pi\) | ||||
0.0342086 | + | 0.999415i | \(0.489109\pi\) | |||||||
\(380\) | 6.25345 | 0.320795 | ||||||||
\(381\) | −6.45305 | −0.330600 | ||||||||
\(382\) | 17.7258 | 0.906929 | ||||||||
\(383\) | −5.46332 | −0.279162 | −0.139581 | − | 0.990211i | \(-0.544576\pi\) | ||||
−0.139581 | + | 0.990211i | \(0.544576\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −35.9655 | −1.83297 | ||||||||
\(386\) | 8.92394 | 0.454217 | ||||||||
\(387\) | −1.09636 | −0.0557309 | ||||||||
\(388\) | −1.09589 | −0.0556355 | ||||||||
\(389\) | 5.47837 | 0.277764 | 0.138882 | − | 0.990309i | \(-0.455649\pi\) | ||||
0.138882 | + | 0.990309i | \(0.455649\pi\) | |||||||
\(390\) | −4.19123 | −0.212231 | ||||||||
\(391\) | −4.83948 | −0.244743 | ||||||||
\(392\) | 0.825500 | 0.0416941 | ||||||||
\(393\) | −5.48297 | −0.276579 | ||||||||
\(394\) | 5.72916 | 0.288631 | ||||||||
\(395\) | −18.3030 | −0.920922 | ||||||||
\(396\) | −3.45337 | −0.173538 | ||||||||
\(397\) | −32.9394 | −1.65318 | −0.826589 | − | 0.562806i | \(-0.809722\pi\) | ||||
−0.826589 | + | 0.562806i | \(0.809722\pi\) | |||||||
\(398\) | −4.04033 | −0.202524 | ||||||||
\(399\) | 3.70748 | 0.185606 | ||||||||
\(400\) | 12.5664 | 0.628322 | ||||||||
\(401\) | 7.80301 | 0.389664 | 0.194832 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194832 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(402\) | −13.0998 | −0.653359 | ||||||||
\(403\) | −6.19959 | −0.308824 | ||||||||
\(404\) | −12.2271 | −0.608320 | ||||||||
\(405\) | −4.19123 | −0.208264 | ||||||||
\(406\) | 9.88220 | 0.490445 | ||||||||
\(407\) | −3.24021 | −0.160611 | ||||||||
\(408\) | −4.15125 | −0.205517 | ||||||||
\(409\) | 25.9347 | 1.28239 | 0.641194 | − | 0.767378i | \(-0.278439\pi\) | ||||
0.641194 | + | 0.767378i | \(0.278439\pi\) | |||||||
\(410\) | −34.5479 | −1.70620 | ||||||||
\(411\) | 9.92674 | 0.489650 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −20.1509 | −0.991559 | ||||||||
\(414\) | 1.16579 | 0.0572954 | ||||||||
\(415\) | 5.40413 | 0.265278 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 3.44571 | 0.168737 | ||||||||
\(418\) | −5.15253 | −0.252019 | ||||||||
\(419\) | −11.8178 | −0.577339 | −0.288670 | − | 0.957429i | \(-0.593213\pi\) | ||||
−0.288670 | + | 0.957429i | \(0.593213\pi\) | |||||||
\(420\) | 10.4146 | 0.508181 | ||||||||
\(421\) | −28.3038 | −1.37944 | −0.689720 | − | 0.724076i | \(-0.742267\pi\) | ||||
−0.689720 | + | 0.724076i | \(0.742267\pi\) | |||||||
\(422\) | 18.1802 | 0.884999 | ||||||||
\(423\) | 1.91281 | 0.0930041 | ||||||||
\(424\) | 3.82574 | 0.185794 | ||||||||
\(425\) | 52.1664 | 2.53044 | ||||||||
\(426\) | −0.896009 | −0.0434118 | ||||||||
\(427\) | −12.7213 | −0.615628 | ||||||||
\(428\) | −17.9304 | −0.866700 | ||||||||
\(429\) | 3.45337 | 0.166730 | ||||||||
\(430\) | −4.59509 | −0.221595 | ||||||||
\(431\) | −11.3047 | −0.544528 | −0.272264 | − | 0.962223i | \(-0.587772\pi\) | ||||
−0.272264 | + | 0.962223i | \(0.587772\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −13.6585 | −0.656385 | −0.328193 | − | 0.944611i | \(-0.606439\pi\) | ||||
−0.328193 | + | 0.944611i | \(0.606439\pi\) | |||||||
\(434\) | 15.4051 | 0.739468 | ||||||||
\(435\) | −16.6684 | −0.799190 | ||||||||
\(436\) | 18.1175 | 0.867670 | ||||||||
\(437\) | 1.73939 | 0.0832064 | ||||||||
\(438\) | 0.857920 | 0.0409930 | ||||||||
\(439\) | −10.1305 | −0.483503 | −0.241751 | − | 0.970338i | \(-0.577722\pi\) | ||||
−0.241751 | + | 0.970338i | \(0.577722\pi\) | |||||||
\(440\) | −14.4739 | −0.690015 | ||||||||
\(441\) | −0.825500 | −0.0393095 | ||||||||
\(442\) | 4.15125 | 0.197455 | ||||||||
\(443\) | −24.1352 | −1.14670 | −0.573348 | − | 0.819312i | \(-0.694356\pi\) | ||||
−0.573348 | + | 0.819312i | \(0.694356\pi\) | |||||||
\(444\) | 0.938276 | 0.0445286 | ||||||||
\(445\) | −5.59010 | −0.264996 | ||||||||
\(446\) | 15.7232 | 0.744515 | ||||||||
\(447\) | −4.22838 | −0.199996 | ||||||||
\(448\) | −2.48485 | −0.117398 | ||||||||
\(449\) | 34.6217 | 1.63390 | 0.816951 | − | 0.576708i | \(-0.195663\pi\) | ||||
0.816951 | + | 0.576708i | \(0.195663\pi\) | |||||||
\(450\) | −12.5664 | −0.592388 | ||||||||
\(451\) | 28.4657 | 1.34040 | ||||||||
\(452\) | 16.6258 | 0.782011 | ||||||||
\(453\) | −14.8402 | −0.697254 | ||||||||
\(454\) | −5.43218 | −0.254945 | ||||||||
\(455\) | −10.4146 | −0.488244 | ||||||||
\(456\) | 1.49203 | 0.0698707 | ||||||||
\(457\) | −31.4318 | −1.47032 | −0.735158 | − | 0.677896i | \(-0.762892\pi\) | ||||
−0.735158 | + | 0.677896i | \(0.762892\pi\) | |||||||
\(458\) | −14.2912 | −0.667782 | ||||||||
\(459\) | 4.15125 | 0.193764 | ||||||||
\(460\) | 4.88610 | 0.227815 | ||||||||
\(461\) | 17.5107 | 0.815554 | 0.407777 | − | 0.913082i | \(-0.366304\pi\) | ||||
0.407777 | + | 0.913082i | \(0.366304\pi\) | |||||||
\(462\) | −8.58112 | −0.399230 | ||||||||
\(463\) | 10.4776 | 0.486933 | 0.243467 | − | 0.969909i | \(-0.421715\pi\) | ||||
0.243467 | + | 0.969909i | \(0.421715\pi\) | |||||||
\(464\) | 3.97697 | 0.184626 | ||||||||
\(465\) | −25.9839 | −1.20498 | ||||||||
\(466\) | 15.7787 | 0.730934 | ||||||||
\(467\) | 0.734108 | 0.0339705 | 0.0169852 | − | 0.999856i | \(-0.494593\pi\) | ||||
0.0169852 | + | 0.999856i | \(0.494593\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −32.5511 | −1.50307 | ||||||||
\(470\) | 8.01704 | 0.369799 | ||||||||
\(471\) | 11.3687 | 0.523843 | ||||||||
\(472\) | −8.10947 | −0.373269 | ||||||||
\(473\) | 3.78613 | 0.174086 | ||||||||
\(474\) | −4.36696 | −0.200581 | ||||||||
\(475\) | −18.7495 | −0.860287 | ||||||||
\(476\) | −10.3152 | −0.472799 | ||||||||
\(477\) | −3.82574 | −0.175168 | ||||||||
\(478\) | 24.0758 | 1.10120 | ||||||||
\(479\) | 40.2600 | 1.83952 | 0.919762 | − | 0.392475i | \(-0.128381\pi\) | ||||
0.919762 | + | 0.392475i | \(0.128381\pi\) | |||||||
\(480\) | 4.19123 | 0.191303 | ||||||||
\(481\) | −0.938276 | −0.0427817 | ||||||||
\(482\) | 24.3323 | 1.10830 | ||||||||
\(483\) | 2.89682 | 0.131810 | ||||||||
\(484\) | 0.925764 | 0.0420802 | ||||||||
\(485\) | 4.59314 | 0.208564 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 10.8019 | 0.489482 | 0.244741 | − | 0.969589i | \(-0.421297\pi\) | ||||
0.244741 | + | 0.969589i | \(0.421297\pi\) | |||||||
\(488\) | −5.11955 | −0.231751 | ||||||||
\(489\) | 17.4080 | 0.787217 | ||||||||
\(490\) | −3.45987 | −0.156301 | ||||||||
\(491\) | 21.2973 | 0.961134 | 0.480567 | − | 0.876958i | \(-0.340431\pi\) | ||||
0.480567 | + | 0.876958i | \(0.340431\pi\) | |||||||
\(492\) | −8.24288 | −0.371618 | ||||||||
\(493\) | 16.5094 | 0.743546 | ||||||||
\(494\) | −1.49203 | −0.0671296 | ||||||||
\(495\) | 14.4739 | 0.650553 | ||||||||
\(496\) | 6.19959 | 0.278370 | ||||||||
\(497\) | −2.22645 | −0.0998700 | ||||||||
\(498\) | 1.28939 | 0.0577789 | ||||||||
\(499\) | −26.0360 | −1.16553 | −0.582765 | − | 0.812640i | \(-0.698029\pi\) | ||||
−0.582765 | + | 0.812640i | \(0.698029\pi\) | |||||||
\(500\) | −31.7127 | −1.41824 | ||||||||
\(501\) | −19.8534 | −0.886985 | ||||||||
\(502\) | −8.22652 | −0.367168 | ||||||||
\(503\) | −16.2381 | −0.724020 | −0.362010 | − | 0.932174i | \(-0.617909\pi\) | ||||
−0.362010 | + | 0.932174i | \(0.617909\pi\) | |||||||
\(504\) | 2.48485 | 0.110684 | ||||||||
\(505\) | 51.2466 | 2.28044 | ||||||||
\(506\) | −4.02590 | −0.178973 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −6.45305 | −0.286308 | ||||||||
\(509\) | 2.48262 | 0.110040 | 0.0550202 | − | 0.998485i | \(-0.482478\pi\) | ||||
0.0550202 | + | 0.998485i | \(0.482478\pi\) | |||||||
\(510\) | 17.3989 | 0.770434 | ||||||||
\(511\) | 2.13180 | 0.0943055 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.49203 | −0.0658747 | ||||||||
\(514\) | −19.2253 | −0.847990 | ||||||||
\(515\) | −4.19123 | −0.184688 | ||||||||
\(516\) | −1.09636 | −0.0482644 | ||||||||
\(517\) | −6.60565 | −0.290516 | ||||||||
\(518\) | 2.33148 | 0.102439 | ||||||||
\(519\) | 8.38483 | 0.368053 | ||||||||
\(520\) | −4.19123 | −0.183798 | ||||||||
\(521\) | −1.51427 | −0.0663415 | −0.0331707 | − | 0.999450i | \(-0.510561\pi\) | ||||
−0.0331707 | + | 0.999450i | \(0.510561\pi\) | |||||||
\(522\) | −3.97697 | −0.174067 | ||||||||
\(523\) | 11.1517 | 0.487628 | 0.243814 | − | 0.969822i | \(-0.421601\pi\) | ||||
0.243814 | + | 0.969822i | \(0.421601\pi\) | |||||||
\(524\) | −5.48297 | −0.239525 | ||||||||
\(525\) | −31.2258 | −1.36280 | ||||||||
\(526\) | 26.5673 | 1.15839 | ||||||||
\(527\) | 25.7361 | 1.12108 | ||||||||
\(528\) | −3.45337 | −0.150289 | ||||||||
\(529\) | −21.6409 | −0.940910 | ||||||||
\(530\) | −16.0346 | −0.696497 | ||||||||
\(531\) | 8.10947 | 0.351921 | ||||||||
\(532\) | 3.70748 | 0.160740 | ||||||||
\(533\) | 8.24288 | 0.357039 | ||||||||
\(534\) | −1.33376 | −0.0577174 | ||||||||
\(535\) | 75.1506 | 3.24904 | ||||||||
\(536\) | −13.0998 | −0.565825 | ||||||||
\(537\) | 24.2415 | 1.04610 | ||||||||
\(538\) | −3.93881 | −0.169814 | ||||||||
\(539\) | 2.85076 | 0.122791 | ||||||||
\(540\) | −4.19123 | −0.180362 | ||||||||
\(541\) | 23.9397 | 1.02925 | 0.514623 | − | 0.857416i | \(-0.327932\pi\) | ||||
0.514623 | + | 0.857416i | \(0.327932\pi\) | |||||||
\(542\) | 6.13049 | 0.263327 | ||||||||
\(543\) | 1.00614 | 0.0431776 | ||||||||
\(544\) | −4.15125 | −0.177983 | ||||||||
\(545\) | −75.9346 | −3.25268 | ||||||||
\(546\) | −2.48485 | −0.106342 | ||||||||
\(547\) | 26.2096 | 1.12064 | 0.560321 | − | 0.828275i | \(-0.310678\pi\) | ||||
0.560321 | + | 0.828275i | \(0.310678\pi\) | |||||||
\(548\) | 9.92674 | 0.424049 | ||||||||
\(549\) | 5.11955 | 0.218497 | ||||||||
\(550\) | 43.3966 | 1.85044 | ||||||||
\(551\) | −5.93376 | −0.252787 | ||||||||
\(552\) | 1.16579 | 0.0496193 | ||||||||
\(553\) | −10.8513 | −0.461443 | ||||||||
\(554\) | 3.38074 | 0.143634 | ||||||||
\(555\) | −3.93253 | −0.166927 | ||||||||
\(556\) | 3.44571 | 0.146131 | ||||||||
\(557\) | −8.02154 | −0.339884 | −0.169942 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169942 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(558\) | −6.19959 | −0.262450 | ||||||||
\(559\) | 1.09636 | 0.0463709 | ||||||||
\(560\) | 10.4146 | 0.440097 | ||||||||
\(561\) | −14.3358 | −0.605258 | ||||||||
\(562\) | 5.93074 | 0.250173 | ||||||||
\(563\) | 13.6134 | 0.573736 | 0.286868 | − | 0.957970i | \(-0.407386\pi\) | ||||
0.286868 | + | 0.957970i | \(0.407386\pi\) | |||||||
\(564\) | 1.91281 | 0.0805439 | ||||||||
\(565\) | −69.6826 | −2.93157 | ||||||||
\(566\) | −23.4537 | −0.985831 | ||||||||
\(567\) | −2.48485 | −0.104354 | ||||||||
\(568\) | −0.896009 | −0.0375957 | ||||||||
\(569\) | 41.8088 | 1.75272 | 0.876358 | − | 0.481659i | \(-0.159966\pi\) | ||||
0.876358 | + | 0.481659i | \(0.159966\pi\) | |||||||
\(570\) | −6.25345 | −0.261928 | ||||||||
\(571\) | 3.05692 | 0.127928 | 0.0639640 | − | 0.997952i | \(-0.479626\pi\) | ||||
0.0639640 | + | 0.997952i | \(0.479626\pi\) | |||||||
\(572\) | 3.45337 | 0.144393 | ||||||||
\(573\) | −17.7258 | −0.740504 | ||||||||
\(574\) | −20.4824 | −0.854917 | ||||||||
\(575\) | −14.6498 | −0.610940 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.43693 | 0.226342 | 0.113171 | − | 0.993576i | \(-0.463899\pi\) | ||||
0.113171 | + | 0.993576i | \(0.463899\pi\) | |||||||
\(578\) | −0.232872 | −0.00968622 | ||||||||
\(579\) | −8.92394 | −0.370866 | ||||||||
\(580\) | −16.6684 | −0.692118 | ||||||||
\(581\) | 3.20394 | 0.132922 | ||||||||
\(582\) | 1.09589 | 0.0454262 | ||||||||
\(583\) | 13.2117 | 0.547172 | ||||||||
\(584\) | 0.857920 | 0.0355010 | ||||||||
\(585\) | 4.19123 | 0.173286 | ||||||||
\(586\) | 29.0023 | 1.19807 | ||||||||
\(587\) | 20.2161 | 0.834406 | 0.417203 | − | 0.908813i | \(-0.363010\pi\) | ||||
0.417203 | + | 0.908813i | \(0.363010\pi\) | |||||||
\(588\) | −0.825500 | −0.0340431 | ||||||||
\(589\) | −9.24998 | −0.381139 | ||||||||
\(590\) | 33.9887 | 1.39929 | ||||||||
\(591\) | −5.72916 | −0.235666 | ||||||||
\(592\) | 0.938276 | 0.0385629 | ||||||||
\(593\) | 36.5479 | 1.50084 | 0.750422 | − | 0.660959i | \(-0.229850\pi\) | ||||
0.750422 | + | 0.660959i | \(0.229850\pi\) | |||||||
\(594\) | 3.45337 | 0.141693 | ||||||||
\(595\) | 43.2336 | 1.77241 | ||||||||
\(596\) | −4.22838 | −0.173201 | ||||||||
\(597\) | 4.04033 | 0.165360 | ||||||||
\(598\) | −1.16579 | −0.0476727 | ||||||||
\(599\) | 5.09064 | 0.207998 | 0.103999 | − | 0.994577i | \(-0.466836\pi\) | ||||
0.103999 | + | 0.994577i | \(0.466836\pi\) | |||||||
\(600\) | −12.5664 | −0.513023 | ||||||||
\(601\) | 4.56186 | 0.186082 | 0.0930410 | − | 0.995662i | \(-0.470341\pi\) | ||||
0.0930410 | + | 0.995662i | \(0.470341\pi\) | |||||||
\(602\) | −2.72429 | −0.111034 | ||||||||
\(603\) | 13.0998 | 0.533465 | ||||||||
\(604\) | −14.8402 | −0.603840 | ||||||||
\(605\) | −3.88010 | −0.157748 | ||||||||
\(606\) | 12.2271 | 0.496691 | ||||||||
\(607\) | −20.6660 | −0.838806 | −0.419403 | − | 0.907800i | \(-0.637761\pi\) | ||||
−0.419403 | + | 0.907800i | \(0.637761\pi\) | |||||||
\(608\) | 1.49203 | 0.0605098 | ||||||||
\(609\) | −9.88220 | −0.400447 | ||||||||
\(610\) | 21.4572 | 0.868777 | ||||||||
\(611\) | −1.91281 | −0.0773841 | ||||||||
\(612\) | 4.15125 | 0.167804 | ||||||||
\(613\) | 27.3650 | 1.10526 | 0.552630 | − | 0.833426i | \(-0.313624\pi\) | ||||
0.552630 | + | 0.833426i | \(0.313624\pi\) | |||||||
\(614\) | −25.5987 | −1.03308 | ||||||||
\(615\) | 34.5479 | 1.39310 | ||||||||
\(616\) | −8.58112 | −0.345743 | ||||||||
\(617\) | −42.5586 | −1.71334 | −0.856672 | − | 0.515861i | \(-0.827472\pi\) | ||||
−0.856672 | + | 0.515861i | \(0.827472\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −15.1000 | −0.606920 | −0.303460 | − | 0.952844i | \(-0.598142\pi\) | ||||
−0.303460 | + | 0.952844i | \(0.598142\pi\) | |||||||
\(620\) | −25.9839 | −1.04354 | ||||||||
\(621\) | −1.16579 | −0.0467815 | ||||||||
\(622\) | 14.8637 | 0.595979 | ||||||||
\(623\) | −3.31420 | −0.132781 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 70.0832 | 2.80333 | ||||||||
\(626\) | −11.2838 | −0.450992 | ||||||||
\(627\) | 5.15253 | 0.205772 | ||||||||
\(628\) | 11.3687 | 0.453661 | ||||||||
\(629\) | 3.89502 | 0.155305 | ||||||||
\(630\) | −10.4146 | −0.414928 | ||||||||
\(631\) | −11.6996 | −0.465755 | −0.232878 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232878 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(632\) | −4.36696 | −0.173708 | ||||||||
\(633\) | −18.1802 | −0.722599 | ||||||||
\(634\) | −3.43988 | −0.136615 | ||||||||
\(635\) | 27.0462 | 1.07330 | ||||||||
\(636\) | −3.82574 | −0.151700 | ||||||||
\(637\) | 0.825500 | 0.0327075 | ||||||||
\(638\) | 13.7340 | 0.543733 | ||||||||
\(639\) | 0.896009 | 0.0354456 | ||||||||
\(640\) | 4.19123 | 0.165673 | ||||||||
\(641\) | 6.02988 | 0.238166 | 0.119083 | − | 0.992884i | \(-0.462005\pi\) | ||||
0.119083 | + | 0.992884i | \(0.462005\pi\) | |||||||
\(642\) | 17.9304 | 0.707657 | ||||||||
\(643\) | 40.2778 | 1.58840 | 0.794201 | − | 0.607655i | \(-0.207890\pi\) | ||||
0.794201 | + | 0.607655i | \(0.207890\pi\) | |||||||
\(644\) | 2.89682 | 0.114151 | ||||||||
\(645\) | 4.59509 | 0.180931 | ||||||||
\(646\) | 6.19379 | 0.243691 | ||||||||
\(647\) | 34.4114 | 1.35285 | 0.676426 | − | 0.736511i | \(-0.263528\pi\) | ||||
0.676426 | + | 0.736511i | \(0.263528\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −28.0050 | −1.09929 | ||||||||
\(650\) | 12.5664 | 0.492896 | ||||||||
\(651\) | −15.4051 | −0.603773 | ||||||||
\(652\) | 17.4080 | 0.681750 | ||||||||
\(653\) | −18.8545 | −0.737835 | −0.368917 | − | 0.929462i | \(-0.620272\pi\) | ||||
−0.368917 | + | 0.929462i | \(0.620272\pi\) | |||||||
\(654\) | −18.1175 | −0.708450 | ||||||||
\(655\) | 22.9804 | 0.897918 | ||||||||
\(656\) | −8.24288 | −0.321831 | ||||||||
\(657\) | −0.857920 | −0.0334706 | ||||||||
\(658\) | 4.75306 | 0.185294 | ||||||||
\(659\) | −33.2202 | −1.29408 | −0.647038 | − | 0.762458i | \(-0.723992\pi\) | ||||
−0.647038 | + | 0.762458i | \(0.723992\pi\) | |||||||
\(660\) | 14.4739 | 0.563395 | ||||||||
\(661\) | 16.0955 | 0.626041 | 0.313021 | − | 0.949746i | \(-0.398659\pi\) | ||||
0.313021 | + | 0.949746i | \(0.398659\pi\) | |||||||
\(662\) | 6.84967 | 0.266220 | ||||||||
\(663\) | −4.15125 | −0.161221 | ||||||||
\(664\) | 1.28939 | 0.0500380 | ||||||||
\(665\) | −15.5389 | −0.602573 | ||||||||
\(666\) | −0.938276 | −0.0363575 | ||||||||
\(667\) | −4.63631 | −0.179519 | ||||||||
\(668\) | −19.8534 | −0.768151 | ||||||||
\(669\) | −15.7232 | −0.607894 | ||||||||
\(670\) | 54.9043 | 2.12114 | ||||||||
\(671\) | −17.6797 | −0.682517 | ||||||||
\(672\) | 2.48485 | 0.0958553 | ||||||||
\(673\) | 16.4323 | 0.633419 | 0.316709 | − | 0.948523i | \(-0.397422\pi\) | ||||
0.316709 | + | 0.948523i | \(0.397422\pi\) | |||||||
\(674\) | −8.11014 | −0.312391 | ||||||||
\(675\) | 12.5664 | 0.483683 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −14.8423 | −0.570436 | −0.285218 | − | 0.958463i | \(-0.592066\pi\) | ||||
−0.285218 | + | 0.958463i | \(0.592066\pi\) | |||||||
\(678\) | −16.6258 | −0.638509 | ||||||||
\(679\) | 2.72313 | 0.104504 | ||||||||
\(680\) | 17.3989 | 0.667216 | ||||||||
\(681\) | 5.43218 | 0.208162 | ||||||||
\(682\) | 21.4095 | 0.819812 | ||||||||
\(683\) | 30.6457 | 1.17262 | 0.586312 | − | 0.810086i | \(-0.300579\pi\) | ||||
0.586312 | + | 0.810086i | \(0.300579\pi\) | |||||||
\(684\) | −1.49203 | −0.0570492 | ||||||||
\(685\) | −41.6053 | −1.58966 | ||||||||
\(686\) | −19.4452 | −0.742422 | ||||||||
\(687\) | 14.2912 | 0.545242 | ||||||||
\(688\) | −1.09636 | −0.0417982 | ||||||||
\(689\) | 3.82574 | 0.145749 | ||||||||
\(690\) | −4.88610 | −0.186010 | ||||||||
\(691\) | 9.94855 | 0.378461 | 0.189230 | − | 0.981933i | \(-0.439401\pi\) | ||||
0.189230 | + | 0.981933i | \(0.439401\pi\) | |||||||
\(692\) | 8.38483 | 0.318744 | ||||||||
\(693\) | 8.58112 | 0.325970 | ||||||||
\(694\) | 15.6913 | 0.595632 | ||||||||
\(695\) | −14.4418 | −0.547808 | ||||||||
\(696\) | −3.97697 | −0.150747 | ||||||||
\(697\) | −34.2183 | −1.29611 | ||||||||
\(698\) | 16.5396 | 0.626035 | ||||||||
\(699\) | −15.7787 | −0.596805 | ||||||||
\(700\) | −31.2258 | −1.18022 | ||||||||
\(701\) | 0.606614 | 0.0229115 | 0.0114557 | − | 0.999934i | \(-0.496353\pi\) | ||||
0.0114557 | + | 0.999934i | \(0.496353\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −1.39994 | −0.0527996 | ||||||||
\(704\) | −3.45337 | −0.130154 | ||||||||
\(705\) | −8.01704 | −0.301939 | ||||||||
\(706\) | 28.2812 | 1.06438 | ||||||||
\(707\) | 30.3825 | 1.14265 | ||||||||
\(708\) | 8.10947 | 0.304773 | ||||||||
\(709\) | −12.3399 | −0.463436 | −0.231718 | − | 0.972783i | \(-0.574435\pi\) | ||||
−0.231718 | + | 0.972783i | \(0.574435\pi\) | |||||||
\(710\) | 3.75538 | 0.140937 | ||||||||
\(711\) | 4.36696 | 0.163774 | ||||||||
\(712\) | −1.33376 | −0.0499848 | ||||||||
\(713\) | −7.22742 | −0.270669 | ||||||||
\(714\) | 10.3152 | 0.386038 | ||||||||
\(715\) | −14.4739 | −0.541292 | ||||||||
\(716\) | 24.2415 | 0.905946 | ||||||||
\(717\) | −24.0758 | −0.899127 | ||||||||
\(718\) | 21.2405 | 0.792690 | ||||||||
\(719\) | −25.0439 | −0.933980 | −0.466990 | − | 0.884263i | \(-0.654662\pi\) | ||||
−0.466990 | + | 0.884263i | \(0.654662\pi\) | |||||||
\(720\) | −4.19123 | −0.156198 | ||||||||
\(721\) | −2.48485 | −0.0925408 | ||||||||
\(722\) | 16.7738 | 0.624258 | ||||||||
\(723\) | −24.3323 | −0.904926 | ||||||||
\(724\) | 1.00614 | 0.0373929 | ||||||||
\(725\) | 49.9764 | 1.85608 | ||||||||
\(726\) | −0.925764 | −0.0343583 | ||||||||
\(727\) | −36.0438 | −1.33679 | −0.668396 | − | 0.743806i | \(-0.733019\pi\) | ||||
−0.668396 | + | 0.743806i | \(0.733019\pi\) | |||||||
\(728\) | −2.48485 | −0.0920948 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.59574 | −0.133084 | ||||||||
\(731\) | −4.55125 | −0.168334 | ||||||||
\(732\) | 5.11955 | 0.189224 | ||||||||
\(733\) | 34.1416 | 1.26105 | 0.630525 | − | 0.776169i | \(-0.282840\pi\) | ||||
0.630525 | + | 0.776169i | \(0.282840\pi\) | |||||||
\(734\) | 4.96807 | 0.183375 | ||||||||
\(735\) | 3.45987 | 0.127619 | ||||||||
\(736\) | 1.16579 | 0.0429716 | ||||||||
\(737\) | −45.2385 | −1.66638 | ||||||||
\(738\) | 8.24288 | 0.303425 | ||||||||
\(739\) | −34.8852 | −1.28327 | −0.641636 | − | 0.767010i | \(-0.721744\pi\) | ||||
−0.641636 | + | 0.767010i | \(0.721744\pi\) | |||||||
\(740\) | −3.93253 | −0.144563 | ||||||||
\(741\) | 1.49203 | 0.0548111 | ||||||||
\(742\) | −9.50640 | −0.348991 | ||||||||
\(743\) | −28.9668 | −1.06269 | −0.531345 | − | 0.847156i | \(-0.678313\pi\) | ||||
−0.531345 | + | 0.847156i | \(0.678313\pi\) | |||||||
\(744\) | −6.19959 | −0.227288 | ||||||||
\(745\) | 17.7221 | 0.649289 | ||||||||
\(746\) | 1.35351 | 0.0495556 | ||||||||
\(747\) | −1.28939 | −0.0471763 | ||||||||
\(748\) | −14.3358 | −0.524169 | ||||||||
\(749\) | 44.5545 | 1.62799 | ||||||||
\(750\) | 31.7127 | 1.15798 | ||||||||
\(751\) | −19.0257 | −0.694258 | −0.347129 | − | 0.937817i | \(-0.612843\pi\) | ||||
−0.347129 | + | 0.937817i | \(0.612843\pi\) | |||||||
\(752\) | 1.91281 | 0.0697531 | ||||||||
\(753\) | 8.22652 | 0.299791 | ||||||||
\(754\) | 3.97697 | 0.144833 | ||||||||
\(755\) | 62.1988 | 2.26365 | ||||||||
\(756\) | −2.48485 | −0.0903733 | ||||||||
\(757\) | 53.9813 | 1.96198 | 0.980991 | − | 0.194052i | \(-0.0621631\pi\) | ||||
0.980991 | + | 0.194052i | \(0.0621631\pi\) | |||||||
\(758\) | −1.33194 | −0.0483783 | ||||||||
\(759\) | 4.02590 | 0.146131 | ||||||||
\(760\) | −6.25345 | −0.226836 | ||||||||
\(761\) | −2.12579 | −0.0770600 | −0.0385300 | − | 0.999257i | \(-0.512268\pi\) | ||||
−0.0385300 | + | 0.999257i | \(0.512268\pi\) | |||||||
\(762\) | 6.45305 | 0.233769 | ||||||||
\(763\) | −45.0193 | −1.62981 | ||||||||
\(764\) | −17.7258 | −0.641295 | ||||||||
\(765\) | −17.3989 | −0.629057 | ||||||||
\(766\) | 5.46332 | 0.197398 | ||||||||
\(767\) | −8.10947 | −0.292816 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −25.5752 | −0.922264 | −0.461132 | − | 0.887332i | \(-0.652557\pi\) | ||||
−0.461132 | + | 0.887332i | \(0.652557\pi\) | |||||||
\(770\) | 35.9655 | 1.29611 | ||||||||
\(771\) | 19.2253 | 0.692381 | ||||||||
\(772\) | −8.92394 | −0.321180 | ||||||||
\(773\) | 10.8883 | 0.391626 | 0.195813 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195813 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(774\) | 1.09636 | 0.0394077 | ||||||||
\(775\) | 77.9068 | 2.79850 | ||||||||
\(776\) | 1.09589 | 0.0393403 | ||||||||
\(777\) | −2.33148 | −0.0836414 | ||||||||
\(778\) | −5.47837 | −0.196409 | ||||||||
\(779\) | 12.2986 | 0.440644 | ||||||||
\(780\) | 4.19123 | 0.150070 | ||||||||
\(781\) | −3.09425 | −0.110721 | ||||||||
\(782\) | 4.83948 | 0.173060 | ||||||||
\(783\) | 3.97697 | 0.142125 | ||||||||
\(784\) | −0.825500 | −0.0294822 | ||||||||
\(785\) | −47.6489 | −1.70066 | ||||||||
\(786\) | 5.48297 | 0.195571 | ||||||||
\(787\) | 8.06590 | 0.287518 | 0.143759 | − | 0.989613i | \(-0.454081\pi\) | ||||
0.143759 | + | 0.989613i | \(0.454081\pi\) | |||||||
\(788\) | −5.72916 | −0.204093 | ||||||||
\(789\) | −26.5673 | −0.945820 | ||||||||
\(790\) | 18.3030 | 0.651190 | ||||||||
\(791\) | −41.3126 | −1.46891 | ||||||||
\(792\) | 3.45337 | 0.122710 | ||||||||
\(793\) | −5.11955 | −0.181800 | ||||||||
\(794\) | 32.9394 | 1.16897 | ||||||||
\(795\) | 16.0346 | 0.568687 | ||||||||
\(796\) | 4.04033 | 0.143206 | ||||||||
\(797\) | −9.83867 | −0.348503 | −0.174252 | − | 0.984701i | \(-0.555751\pi\) | ||||
−0.174252 | + | 0.984701i | \(0.555751\pi\) | |||||||
\(798\) | −3.70748 | −0.131243 | ||||||||
\(799\) | 7.94056 | 0.280917 | ||||||||
\(800\) | −12.5664 | −0.444291 | ||||||||
\(801\) | 1.33376 | 0.0471261 | ||||||||
\(802\) | −7.80301 | −0.275534 | ||||||||
\(803\) | 2.96271 | 0.104552 | ||||||||
\(804\) | 13.0998 | 0.461994 | ||||||||
\(805\) | −12.1412 | −0.427922 | ||||||||
\(806\) | 6.19959 | 0.218371 | ||||||||
\(807\) | 3.93881 | 0.138653 | ||||||||
\(808\) | 12.2271 | 0.430147 | ||||||||
\(809\) | −23.3970 | −0.822595 | −0.411298 | − | 0.911501i | \(-0.634924\pi\) | ||||
−0.411298 | + | 0.911501i | \(0.634924\pi\) | |||||||
\(810\) | 4.19123 | 0.147265 | ||||||||
\(811\) | 24.8923 | 0.874087 | 0.437044 | − | 0.899440i | \(-0.356026\pi\) | ||||
0.437044 | + | 0.899440i | \(0.356026\pi\) | |||||||
\(812\) | −9.88220 | −0.346797 | ||||||||
\(813\) | −6.13049 | −0.215006 | ||||||||
\(814\) | 3.24021 | 0.113569 | ||||||||
\(815\) | −72.9610 | −2.55571 | ||||||||
\(816\) | 4.15125 | 0.145323 | ||||||||
\(817\) | 1.63580 | 0.0572293 | ||||||||
\(818\) | −25.9347 | −0.906786 | ||||||||
\(819\) | 2.48485 | 0.0868278 | ||||||||
\(820\) | 34.5479 | 1.20646 | ||||||||
\(821\) | 7.39290 | 0.258014 | 0.129007 | − | 0.991644i | \(-0.458821\pi\) | ||||
0.129007 | + | 0.991644i | \(0.458821\pi\) | |||||||
\(822\) | −9.92674 | −0.346235 | ||||||||
\(823\) | −37.2278 | −1.29768 | −0.648839 | − | 0.760925i | \(-0.724745\pi\) | ||||
−0.648839 | + | 0.760925i | \(0.724745\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −43.3966 | −1.51087 | ||||||||
\(826\) | 20.1509 | 0.701138 | ||||||||
\(827\) | 37.7529 | 1.31280 | 0.656399 | − | 0.754414i | \(-0.272079\pi\) | ||||
0.656399 | + | 0.754414i | \(0.272079\pi\) | |||||||
\(828\) | −1.16579 | −0.0405140 | ||||||||
\(829\) | −17.6399 | −0.612660 | −0.306330 | − | 0.951925i | \(-0.599101\pi\) | ||||
−0.306330 | + | 0.951925i | \(0.599101\pi\) | |||||||
\(830\) | −5.40413 | −0.187580 | ||||||||
\(831\) | −3.38074 | −0.117277 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −3.42686 | −0.118734 | ||||||||
\(834\) | −3.44571 | −0.119315 | ||||||||
\(835\) | 83.2103 | 2.87961 | ||||||||
\(836\) | 5.15253 | 0.178204 | ||||||||
\(837\) | 6.19959 | 0.214289 | ||||||||
\(838\) | 11.8178 | 0.408241 | ||||||||
\(839\) | −36.9424 | −1.27539 | −0.637696 | − | 0.770288i | \(-0.720112\pi\) | ||||
−0.637696 | + | 0.770288i | \(0.720112\pi\) | |||||||
\(840\) | −10.4146 | −0.359338 | ||||||||
\(841\) | −13.1837 | −0.454610 | ||||||||
\(842\) | 28.3038 | 0.975412 | ||||||||
\(843\) | −5.93074 | −0.204265 | ||||||||
\(844\) | −18.1802 | −0.625789 | ||||||||
\(845\) | −4.19123 | −0.144183 | ||||||||
\(846\) | −1.91281 | −0.0657638 | ||||||||
\(847\) | −2.30039 | −0.0790423 | ||||||||
\(848\) | −3.82574 | −0.131376 | ||||||||
\(849\) | 23.4537 | 0.804928 | ||||||||
\(850\) | −52.1664 | −1.78929 | ||||||||
\(851\) | −1.09383 | −0.0374961 | ||||||||
\(852\) | 0.896009 | 0.0306967 | ||||||||
\(853\) | −37.4443 | −1.28207 | −0.641034 | − | 0.767512i | \(-0.721494\pi\) | ||||
−0.641034 | + | 0.767512i | \(0.721494\pi\) | |||||||
\(854\) | 12.7213 | 0.435315 | ||||||||
\(855\) | 6.25345 | 0.213863 | ||||||||
\(856\) | 17.9304 | 0.612849 | ||||||||
\(857\) | −9.08161 | −0.310222 | −0.155111 | − | 0.987897i | \(-0.549574\pi\) | ||||
−0.155111 | + | 0.987897i | \(0.549574\pi\) | |||||||
\(858\) | −3.45337 | −0.117896 | ||||||||
\(859\) | −17.8016 | −0.607384 | −0.303692 | − | 0.952770i | \(-0.598219\pi\) | ||||
−0.303692 | + | 0.952770i | \(0.598219\pi\) | |||||||
\(860\) | 4.59509 | 0.156691 | ||||||||
\(861\) | 20.4824 | 0.698037 | ||||||||
\(862\) | 11.3047 | 0.385040 | ||||||||
\(863\) | 57.5943 | 1.96053 | 0.980266 | − | 0.197681i | \(-0.0633410\pi\) | ||||
0.980266 | + | 0.197681i | \(0.0633410\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −35.1428 | −1.19489 | ||||||||
\(866\) | 13.6585 | 0.464134 | ||||||||
\(867\) | 0.232872 | 0.00790876 | ||||||||
\(868\) | −15.4051 | −0.522883 | ||||||||
\(869\) | −15.0807 | −0.511579 | ||||||||
\(870\) | 16.6684 | 0.565112 | ||||||||
\(871\) | −13.0998 | −0.443870 | ||||||||
\(872\) | −18.1175 | −0.613535 | ||||||||
\(873\) | −1.09589 | −0.0370904 | ||||||||
\(874\) | −1.73939 | −0.0588358 | ||||||||
\(875\) | 78.8015 | 2.66398 | ||||||||
\(876\) | −0.857920 | −0.0289864 | ||||||||
\(877\) | −29.6978 | −1.00282 | −0.501412 | − | 0.865208i | \(-0.667186\pi\) | ||||
−0.501412 | + | 0.865208i | \(0.667186\pi\) | |||||||
\(878\) | 10.1305 | 0.341888 | ||||||||
\(879\) | −29.0023 | −0.978224 | ||||||||
\(880\) | 14.4739 | 0.487914 | ||||||||
\(881\) | 48.3041 | 1.62741 | 0.813703 | − | 0.581281i | \(-0.197448\pi\) | ||||
0.813703 | + | 0.581281i | \(0.197448\pi\) | |||||||
\(882\) | 0.825500 | 0.0277960 | ||||||||
\(883\) | −22.8351 | −0.768463 | −0.384231 | − | 0.923237i | \(-0.625534\pi\) | ||||
−0.384231 | + | 0.923237i | \(0.625534\pi\) | |||||||
\(884\) | −4.15125 | −0.139622 | ||||||||
\(885\) | −33.9887 | −1.14252 | ||||||||
\(886\) | 24.1352 | 0.810837 | ||||||||
\(887\) | −32.2578 | −1.08311 | −0.541556 | − | 0.840664i | \(-0.682165\pi\) | ||||
−0.541556 | + | 0.840664i | \(0.682165\pi\) | |||||||
\(888\) | −0.938276 | −0.0314865 | ||||||||
\(889\) | 16.0349 | 0.537793 | ||||||||
\(890\) | 5.59010 | 0.187381 | ||||||||
\(891\) | −3.45337 | −0.115692 | ||||||||
\(892\) | −15.7232 | −0.526452 | ||||||||
\(893\) | −2.85397 | −0.0955046 | ||||||||
\(894\) | 4.22838 | 0.141418 | ||||||||
\(895\) | −101.602 | −3.39617 | ||||||||
\(896\) | 2.48485 | 0.0830131 | ||||||||
\(897\) | 1.16579 | 0.0389246 | ||||||||
\(898\) | −34.6217 | −1.15534 | ||||||||
\(899\) | 24.6556 | 0.822311 | ||||||||
\(900\) | 12.5664 | 0.418881 | ||||||||
\(901\) | −15.8816 | −0.529092 | ||||||||
\(902\) | −28.4657 | −0.947805 | ||||||||
\(903\) | 2.72429 | 0.0906586 | ||||||||
\(904\) | −16.6258 | −0.552965 | ||||||||
\(905\) | −4.21697 | −0.140177 | ||||||||
\(906\) | 14.8402 | 0.493033 | ||||||||
\(907\) | −1.51747 | −0.0503868 | −0.0251934 | − | 0.999683i | \(-0.508020\pi\) | ||||
−0.0251934 | + | 0.999683i | \(0.508020\pi\) | |||||||
\(908\) | 5.43218 | 0.180273 | ||||||||
\(909\) | −12.2271 | −0.405547 | ||||||||
\(910\) | 10.4146 | 0.345241 | ||||||||
\(911\) | 37.8108 | 1.25273 | 0.626364 | − | 0.779531i | \(-0.284543\pi\) | ||||
0.626364 | + | 0.779531i | \(0.284543\pi\) | |||||||
\(912\) | −1.49203 | −0.0494061 | ||||||||
\(913\) | 4.45274 | 0.147364 | ||||||||
\(914\) | 31.4318 | 1.03967 | ||||||||
\(915\) | −21.4572 | −0.709354 | ||||||||
\(916\) | 14.2912 | 0.472193 | ||||||||
\(917\) | 13.6244 | 0.449916 | ||||||||
\(918\) | −4.15125 | −0.137012 | ||||||||
\(919\) | 58.1081 | 1.91681 | 0.958405 | − | 0.285412i | \(-0.0921304\pi\) | ||||
0.958405 | + | 0.285412i | \(0.0921304\pi\) | |||||||
\(920\) | −4.88610 | −0.161090 | ||||||||
\(921\) | 25.5987 | 0.843507 | ||||||||
\(922\) | −17.5107 | −0.576684 | ||||||||
\(923\) | −0.896009 | −0.0294925 | ||||||||
\(924\) | 8.58112 | 0.282298 | ||||||||
\(925\) | 11.7908 | 0.387679 | ||||||||
\(926\) | −10.4776 | −0.344314 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −3.97697 | −0.130551 | ||||||||
\(929\) | 8.37459 | 0.274761 | 0.137381 | − | 0.990518i | \(-0.456132\pi\) | ||||
0.137381 | + | 0.990518i | \(0.456132\pi\) | |||||||
\(930\) | 25.9839 | 0.852047 | ||||||||
\(931\) | 1.23167 | 0.0403664 | ||||||||
\(932\) | −15.7787 | −0.516848 | ||||||||
\(933\) | −14.8637 | −0.486615 | ||||||||
\(934\) | −0.734108 | −0.0240207 | ||||||||
\(935\) | 60.0847 | 1.96498 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 12.3552 | 0.403625 | 0.201813 | − | 0.979424i | \(-0.435317\pi\) | ||||
0.201813 | + | 0.979424i | \(0.435317\pi\) | |||||||
\(938\) | 32.5511 | 1.06283 | ||||||||
\(939\) | 11.2838 | 0.368233 | ||||||||
\(940\) | −8.01704 | −0.261487 | ||||||||
\(941\) | 20.5177 | 0.668859 | 0.334429 | − | 0.942421i | \(-0.391456\pi\) | ||||
0.334429 | + | 0.942421i | \(0.391456\pi\) | |||||||
\(942\) | −11.3687 | −0.370413 | ||||||||
\(943\) | 9.60946 | 0.312927 | ||||||||
\(944\) | 8.10947 | 0.263941 | ||||||||
\(945\) | 10.4146 | 0.338787 | ||||||||
\(946\) | −3.78613 | −0.123098 | ||||||||
\(947\) | −7.31607 | −0.237740 | −0.118870 | − | 0.992910i | \(-0.537927\pi\) | ||||
−0.118870 | + | 0.992910i | \(0.537927\pi\) | |||||||
\(948\) | 4.36696 | 0.141832 | ||||||||
\(949\) | 0.857920 | 0.0278492 | ||||||||
\(950\) | 18.7495 | 0.608314 | ||||||||
\(951\) | 3.43988 | 0.111546 | ||||||||
\(952\) | 10.3152 | 0.334319 | ||||||||
\(953\) | 25.3981 | 0.822726 | 0.411363 | − | 0.911471i | \(-0.365053\pi\) | ||||
0.411363 | + | 0.911471i | \(0.365053\pi\) | |||||||
\(954\) | 3.82574 | 0.123863 | ||||||||
\(955\) | 74.2928 | 2.40406 | ||||||||
\(956\) | −24.0758 | −0.778667 | ||||||||
\(957\) | −13.7340 | −0.443956 | ||||||||
\(958\) | −40.2600 | −1.30074 | ||||||||
\(959\) | −24.6665 | −0.796523 | ||||||||
\(960\) | −4.19123 | −0.135271 | ||||||||
\(961\) | 7.43497 | 0.239838 | ||||||||
\(962\) | 0.938276 | 0.0302512 | ||||||||
\(963\) | −17.9304 | −0.577800 | ||||||||
\(964\) | −24.3323 | −0.783689 | ||||||||
\(965\) | 37.4023 | 1.20402 | ||||||||
\(966\) | −2.89682 | −0.0932035 | ||||||||
\(967\) | −46.8399 | −1.50627 | −0.753134 | − | 0.657867i | \(-0.771459\pi\) | ||||
−0.753134 | + | 0.657867i | \(0.771459\pi\) | |||||||
\(968\) | −0.925764 | −0.0297552 | ||||||||
\(969\) | −6.19379 | −0.198973 | ||||||||
\(970\) | −4.59314 | −0.147477 | ||||||||
\(971\) | −40.4508 | −1.29813 | −0.649063 | − | 0.760734i | \(-0.724839\pi\) | ||||
−0.649063 | + | 0.760734i | \(0.724839\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −8.56209 | −0.274488 | ||||||||
\(974\) | −10.8019 | −0.346116 | ||||||||
\(975\) | −12.5664 | −0.402448 | ||||||||
\(976\) | 5.11955 | 0.163873 | ||||||||
\(977\) | 7.12306 | 0.227887 | 0.113943 | − | 0.993487i | \(-0.463652\pi\) | ||||
0.113943 | + | 0.993487i | \(0.463652\pi\) | |||||||
\(978\) | −17.4080 | −0.556647 | ||||||||
\(979\) | −4.60597 | −0.147207 | ||||||||
\(980\) | 3.45987 | 0.110521 | ||||||||
\(981\) | 18.1175 | 0.578447 | ||||||||
\(982\) | −21.2973 | −0.679624 | ||||||||
\(983\) | −35.6158 | −1.13597 | −0.567984 | − | 0.823040i | \(-0.692276\pi\) | ||||
−0.567984 | + | 0.823040i | \(0.692276\pi\) | |||||||
\(984\) | 8.24288 | 0.262774 | ||||||||
\(985\) | 24.0123 | 0.765094 | ||||||||
\(986\) | −16.5094 | −0.525767 | ||||||||
\(987\) | −4.75306 | −0.151292 | ||||||||
\(988\) | 1.49203 | 0.0474678 | ||||||||
\(989\) | 1.27812 | 0.0406419 | ||||||||
\(990\) | −14.4739 | −0.460010 | ||||||||
\(991\) | 5.41675 | 0.172069 | 0.0860344 | − | 0.996292i | \(-0.472581\pi\) | ||||
0.0860344 | + | 0.996292i | \(0.472581\pi\) | |||||||
\(992\) | −6.19959 | −0.196837 | ||||||||
\(993\) | −6.84967 | −0.217368 | ||||||||
\(994\) | 2.22645 | 0.0706187 | ||||||||
\(995\) | −16.9340 | −0.536843 | ||||||||
\(996\) | −1.28939 | −0.0408558 | ||||||||
\(997\) | −49.4466 | −1.56599 | −0.782995 | − | 0.622028i | \(-0.786309\pi\) | ||||
−0.782995 | + | 0.622028i | \(0.786309\pi\) | |||||||
\(998\) | 26.0360 | 0.824155 | ||||||||
\(999\) | 0.938276 | 0.0296857 |
(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 | 8034.2.a.bb.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.1 | ✓ | 14 | 1.1 | even | 1 | trivial |