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: | \(0\) |
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: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.59859\) 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 | ||||||||
\(5\) | 1.59859 | 0.714909 | 0.357455 | − | 0.933931i | \(-0.383645\pi\) | ||||
0.357455 | + | 0.933931i | \(0.383645\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.24832 | 1.60571 | 0.802856 | − | 0.596172i | \(-0.203313\pi\) | ||||
0.802856 | + | 0.596172i | \(0.203313\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.59859 | −0.505517 | ||||||||
\(11\) | 4.07067 | 1.22735 | 0.613676 | − | 0.789558i | \(-0.289690\pi\) | ||||
0.613676 | + | 0.789558i | \(0.289690\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −4.24832 | −1.13541 | ||||||||
\(15\) | −1.59859 | −0.412753 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.06157 | −0.985076 | −0.492538 | − | 0.870291i | \(-0.663931\pi\) | ||||
−0.492538 | + | 0.870291i | \(0.663931\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.43588 | 0.788246 | 0.394123 | − | 0.919058i | \(-0.371048\pi\) | ||||
0.394123 | + | 0.919058i | \(0.371048\pi\) | |||||||
\(20\) | 1.59859 | 0.357455 | ||||||||
\(21\) | −4.24832 | −0.927059 | ||||||||
\(22\) | −4.07067 | −0.867869 | ||||||||
\(23\) | 9.26262 | 1.93139 | 0.965695 | − | 0.259679i | \(-0.0836166\pi\) | ||||
0.965695 | + | 0.259679i | \(0.0836166\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.44452 | −0.488905 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.24832 | 0.802856 | ||||||||
\(29\) | 7.09160 | 1.31688 | 0.658439 | − | 0.752634i | \(-0.271217\pi\) | ||||
0.658439 | + | 0.752634i | \(0.271217\pi\) | |||||||
\(30\) | 1.59859 | 0.291860 | ||||||||
\(31\) | −10.7030 | −1.92232 | −0.961159 | − | 0.275995i | \(-0.910993\pi\) | ||||
−0.961159 | + | 0.275995i | \(0.910993\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.07067 | −0.708612 | ||||||||
\(34\) | 4.06157 | 0.696554 | ||||||||
\(35\) | 6.79130 | 1.14794 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.89679 | 0.969427 | 0.484713 | − | 0.874673i | \(-0.338924\pi\) | ||||
0.484713 | + | 0.874673i | \(0.338924\pi\) | |||||||
\(38\) | −3.43588 | −0.557374 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.59859 | −0.252759 | ||||||||
\(41\) | −5.28889 | −0.825986 | −0.412993 | − | 0.910734i | \(-0.635517\pi\) | ||||
−0.412993 | + | 0.910734i | \(0.635517\pi\) | |||||||
\(42\) | 4.24832 | 0.655530 | ||||||||
\(43\) | −1.53277 | −0.233745 | −0.116873 | − | 0.993147i | \(-0.537287\pi\) | ||||
−0.116873 | + | 0.993147i | \(0.537287\pi\) | |||||||
\(44\) | 4.07067 | 0.613676 | ||||||||
\(45\) | 1.59859 | 0.238303 | ||||||||
\(46\) | −9.26262 | −1.36570 | ||||||||
\(47\) | −9.61413 | −1.40236 | −0.701182 | − | 0.712982i | \(-0.747344\pi\) | ||||
−0.701182 | + | 0.712982i | \(0.747344\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.0482 | 1.57831 | ||||||||
\(50\) | 2.44452 | 0.345708 | ||||||||
\(51\) | 4.06157 | 0.568734 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 10.0672 | 1.38283 | 0.691416 | − | 0.722457i | \(-0.256987\pi\) | ||||
0.691416 | + | 0.722457i | \(0.256987\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 6.50731 | 0.877446 | ||||||||
\(56\) | −4.24832 | −0.567705 | ||||||||
\(57\) | −3.43588 | −0.455094 | ||||||||
\(58\) | −7.09160 | −0.931173 | ||||||||
\(59\) | 5.95635 | 0.775451 | 0.387726 | − | 0.921775i | \(-0.373261\pi\) | ||||
0.387726 | + | 0.921775i | \(0.373261\pi\) | |||||||
\(60\) | −1.59859 | −0.206377 | ||||||||
\(61\) | 6.49344 | 0.831399 | 0.415700 | − | 0.909502i | \(-0.363537\pi\) | ||||
0.415700 | + | 0.909502i | \(0.363537\pi\) | |||||||
\(62\) | 10.7030 | 1.35928 | ||||||||
\(63\) | 4.24832 | 0.535238 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.59859 | 0.198280 | ||||||||
\(66\) | 4.07067 | 0.501065 | ||||||||
\(67\) | 4.52053 | 0.552271 | 0.276135 | − | 0.961119i | \(-0.410946\pi\) | ||||
0.276135 | + | 0.961119i | \(0.410946\pi\) | |||||||
\(68\) | −4.06157 | −0.492538 | ||||||||
\(69\) | −9.26262 | −1.11509 | ||||||||
\(70\) | −6.79130 | −0.811715 | ||||||||
\(71\) | −13.3814 | −1.58808 | −0.794042 | − | 0.607863i | \(-0.792027\pi\) | ||||
−0.794042 | + | 0.607863i | \(0.792027\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.94293 | 0.461485 | 0.230742 | − | 0.973015i | \(-0.425885\pi\) | ||||
0.230742 | + | 0.973015i | \(0.425885\pi\) | |||||||
\(74\) | −5.89679 | −0.685488 | ||||||||
\(75\) | 2.44452 | 0.282269 | ||||||||
\(76\) | 3.43588 | 0.394123 | ||||||||
\(77\) | 17.2935 | 1.97078 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 1.53043 | 0.172187 | 0.0860936 | − | 0.996287i | \(-0.472562\pi\) | ||||
0.0860936 | + | 0.996287i | \(0.472562\pi\) | |||||||
\(80\) | 1.59859 | 0.178727 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.28889 | 0.584060 | ||||||||
\(83\) | 9.36721 | 1.02818 | 0.514092 | − | 0.857735i | \(-0.328129\pi\) | ||||
0.514092 | + | 0.857735i | \(0.328129\pi\) | |||||||
\(84\) | −4.24832 | −0.463529 | ||||||||
\(85\) | −6.49277 | −0.704240 | ||||||||
\(86\) | 1.53277 | 0.165283 | ||||||||
\(87\) | −7.09160 | −0.760300 | ||||||||
\(88\) | −4.07067 | −0.433935 | ||||||||
\(89\) | −8.97228 | −0.951060 | −0.475530 | − | 0.879700i | \(-0.657744\pi\) | ||||
−0.475530 | + | 0.879700i | \(0.657744\pi\) | |||||||
\(90\) | −1.59859 | −0.168506 | ||||||||
\(91\) | 4.24832 | 0.445345 | ||||||||
\(92\) | 9.26262 | 0.965695 | ||||||||
\(93\) | 10.7030 | 1.10985 | ||||||||
\(94\) | 9.61413 | 0.991621 | ||||||||
\(95\) | 5.49256 | 0.563524 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.0823 | 1.42984 | 0.714922 | − | 0.699204i | \(-0.246462\pi\) | ||||
0.714922 | + | 0.699204i | \(0.246462\pi\) | |||||||
\(98\) | −11.0482 | −1.11604 | ||||||||
\(99\) | 4.07067 | 0.409118 | ||||||||
\(100\) | −2.44452 | −0.244452 | ||||||||
\(101\) | −0.882768 | −0.0878387 | −0.0439193 | − | 0.999035i | \(-0.513984\pi\) | ||||
−0.0439193 | + | 0.999035i | \(0.513984\pi\) | |||||||
\(102\) | −4.06157 | −0.402155 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −6.79130 | −0.662763 | ||||||||
\(106\) | −10.0672 | −0.977809 | ||||||||
\(107\) | −6.27951 | −0.607063 | −0.303531 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303531 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 17.7587 | 1.70097 | 0.850485 | − | 0.525999i | \(-0.176308\pi\) | ||||
0.850485 | + | 0.525999i | \(0.176308\pi\) | |||||||
\(110\) | −6.50731 | −0.620448 | ||||||||
\(111\) | −5.89679 | −0.559699 | ||||||||
\(112\) | 4.24832 | 0.401428 | ||||||||
\(113\) | −3.56157 | −0.335044 | −0.167522 | − | 0.985868i | \(-0.553577\pi\) | ||||
−0.167522 | + | 0.985868i | \(0.553577\pi\) | |||||||
\(114\) | 3.43588 | 0.321800 | ||||||||
\(115\) | 14.8071 | 1.38077 | ||||||||
\(116\) | 7.09160 | 0.658439 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −5.95635 | −0.548327 | ||||||||
\(119\) | −17.2548 | −1.58175 | ||||||||
\(120\) | 1.59859 | 0.145930 | ||||||||
\(121\) | 5.57034 | 0.506394 | ||||||||
\(122\) | −6.49344 | −0.587888 | ||||||||
\(123\) | 5.28889 | 0.476883 | ||||||||
\(124\) | −10.7030 | −0.961159 | ||||||||
\(125\) | −11.9007 | −1.06443 | ||||||||
\(126\) | −4.24832 | −0.378470 | ||||||||
\(127\) | 19.4121 | 1.72255 | 0.861274 | − | 0.508141i | \(-0.169667\pi\) | ||||
0.861274 | + | 0.508141i | \(0.169667\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.53277 | 0.134953 | ||||||||
\(130\) | −1.59859 | −0.140205 | ||||||||
\(131\) | −11.1778 | −0.976605 | −0.488302 | − | 0.872674i | \(-0.662384\pi\) | ||||
−0.488302 | + | 0.872674i | \(0.662384\pi\) | |||||||
\(132\) | −4.07067 | −0.354306 | ||||||||
\(133\) | 14.5967 | 1.26570 | ||||||||
\(134\) | −4.52053 | −0.390515 | ||||||||
\(135\) | −1.59859 | −0.137584 | ||||||||
\(136\) | 4.06157 | 0.348277 | ||||||||
\(137\) | −18.9130 | −1.61585 | −0.807924 | − | 0.589286i | \(-0.799409\pi\) | ||||
−0.807924 | + | 0.589286i | \(0.799409\pi\) | |||||||
\(138\) | 9.26262 | 0.788487 | ||||||||
\(139\) | −2.52047 | −0.213783 | −0.106892 | − | 0.994271i | \(-0.534090\pi\) | ||||
−0.106892 | + | 0.994271i | \(0.534090\pi\) | |||||||
\(140\) | 6.79130 | 0.573969 | ||||||||
\(141\) | 9.61413 | 0.809655 | ||||||||
\(142\) | 13.3814 | 1.12294 | ||||||||
\(143\) | 4.07067 | 0.340406 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.3365 | 0.941448 | ||||||||
\(146\) | −3.94293 | −0.326319 | ||||||||
\(147\) | −11.0482 | −0.911240 | ||||||||
\(148\) | 5.89679 | 0.484713 | ||||||||
\(149\) | 21.9555 | 1.79866 | 0.899332 | − | 0.437267i | \(-0.144053\pi\) | ||||
0.899332 | + | 0.437267i | \(0.144053\pi\) | |||||||
\(150\) | −2.44452 | −0.199595 | ||||||||
\(151\) | 9.14572 | 0.744268 | 0.372134 | − | 0.928179i | \(-0.378626\pi\) | ||||
0.372134 | + | 0.928179i | \(0.378626\pi\) | |||||||
\(152\) | −3.43588 | −0.278687 | ||||||||
\(153\) | −4.06157 | −0.328359 | ||||||||
\(154\) | −17.2935 | −1.39355 | ||||||||
\(155\) | −17.1097 | −1.37428 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −14.6803 | −1.17161 | −0.585807 | − | 0.810450i | \(-0.699223\pi\) | ||||
−0.585807 | + | 0.810450i | \(0.699223\pi\) | |||||||
\(158\) | −1.53043 | −0.121755 | ||||||||
\(159\) | −10.0672 | −0.798378 | ||||||||
\(160\) | −1.59859 | −0.126379 | ||||||||
\(161\) | 39.3506 | 3.10126 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 12.9771 | 1.01644 | 0.508222 | − | 0.861226i | \(-0.330303\pi\) | ||||
0.508222 | + | 0.861226i | \(0.330303\pi\) | |||||||
\(164\) | −5.28889 | −0.412993 | ||||||||
\(165\) | −6.50731 | −0.506593 | ||||||||
\(166\) | −9.36721 | −0.727036 | ||||||||
\(167\) | −3.95923 | −0.306374 | −0.153187 | − | 0.988197i | \(-0.548954\pi\) | ||||
−0.153187 | + | 0.988197i | \(0.548954\pi\) | |||||||
\(168\) | 4.24832 | 0.327765 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.49277 | 0.497973 | ||||||||
\(171\) | 3.43588 | 0.262749 | ||||||||
\(172\) | −1.53277 | −0.116873 | ||||||||
\(173\) | −2.24677 | −0.170819 | −0.0854094 | − | 0.996346i | \(-0.527220\pi\) | ||||
−0.0854094 | + | 0.996346i | \(0.527220\pi\) | |||||||
\(174\) | 7.09160 | 0.537613 | ||||||||
\(175\) | −10.3851 | −0.785041 | ||||||||
\(176\) | 4.07067 | 0.306838 | ||||||||
\(177\) | −5.95635 | −0.447707 | ||||||||
\(178\) | 8.97228 | 0.672501 | ||||||||
\(179\) | 6.03133 | 0.450803 | 0.225401 | − | 0.974266i | \(-0.427631\pi\) | ||||
0.225401 | + | 0.974266i | \(0.427631\pi\) | |||||||
\(180\) | 1.59859 | 0.119152 | ||||||||
\(181\) | 10.1195 | 0.752177 | 0.376088 | − | 0.926584i | \(-0.377269\pi\) | ||||
0.376088 | + | 0.926584i | \(0.377269\pi\) | |||||||
\(182\) | −4.24832 | −0.314906 | ||||||||
\(183\) | −6.49344 | −0.480009 | ||||||||
\(184\) | −9.26262 | −0.682850 | ||||||||
\(185\) | 9.42653 | 0.693052 | ||||||||
\(186\) | −10.7030 | −0.784783 | ||||||||
\(187\) | −16.5333 | −1.20904 | ||||||||
\(188\) | −9.61413 | −0.701182 | ||||||||
\(189\) | −4.24832 | −0.309020 | ||||||||
\(190\) | −5.49256 | −0.398472 | ||||||||
\(191\) | 4.42049 | 0.319856 | 0.159928 | − | 0.987129i | \(-0.448874\pi\) | ||||
0.159928 | + | 0.987129i | \(0.448874\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −9.36665 | −0.674226 | −0.337113 | − | 0.941464i | \(-0.609450\pi\) | ||||
−0.337113 | + | 0.941464i | \(0.609450\pi\) | |||||||
\(194\) | −14.0823 | −1.01105 | ||||||||
\(195\) | −1.59859 | −0.114477 | ||||||||
\(196\) | 11.0482 | 0.789157 | ||||||||
\(197\) | −19.1911 | −1.36731 | −0.683656 | − | 0.729805i | \(-0.739611\pi\) | ||||
−0.683656 | + | 0.729805i | \(0.739611\pi\) | |||||||
\(198\) | −4.07067 | −0.289290 | ||||||||
\(199\) | −7.97460 | −0.565305 | −0.282652 | − | 0.959222i | \(-0.591214\pi\) | ||||
−0.282652 | + | 0.959222i | \(0.591214\pi\) | |||||||
\(200\) | 2.44452 | 0.172854 | ||||||||
\(201\) | −4.52053 | −0.318854 | ||||||||
\(202\) | 0.882768 | 0.0621113 | ||||||||
\(203\) | 30.1274 | 2.11453 | ||||||||
\(204\) | 4.06157 | 0.284367 | ||||||||
\(205\) | −8.45474 | −0.590505 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 9.26262 | 0.643797 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 13.9863 | 0.967456 | ||||||||
\(210\) | 6.79130 | 0.468644 | ||||||||
\(211\) | 12.3843 | 0.852570 | 0.426285 | − | 0.904589i | \(-0.359822\pi\) | ||||
0.426285 | + | 0.904589i | \(0.359822\pi\) | |||||||
\(212\) | 10.0672 | 0.691416 | ||||||||
\(213\) | 13.3814 | 0.916880 | ||||||||
\(214\) | 6.27951 | 0.429258 | ||||||||
\(215\) | −2.45026 | −0.167107 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −45.4698 | −3.08669 | ||||||||
\(218\) | −17.7587 | −1.20277 | ||||||||
\(219\) | −3.94293 | −0.266438 | ||||||||
\(220\) | 6.50731 | 0.438723 | ||||||||
\(221\) | −4.06157 | −0.273211 | ||||||||
\(222\) | 5.89679 | 0.395767 | ||||||||
\(223\) | 25.3964 | 1.70067 | 0.850336 | − | 0.526241i | \(-0.176399\pi\) | ||||
0.850336 | + | 0.526241i | \(0.176399\pi\) | |||||||
\(224\) | −4.24832 | −0.283853 | ||||||||
\(225\) | −2.44452 | −0.162968 | ||||||||
\(226\) | 3.56157 | 0.236912 | ||||||||
\(227\) | −21.9470 | −1.45667 | −0.728336 | − | 0.685220i | \(-0.759706\pi\) | ||||
−0.728336 | + | 0.685220i | \(0.759706\pi\) | |||||||
\(228\) | −3.43588 | −0.227547 | ||||||||
\(229\) | −2.07670 | −0.137232 | −0.0686162 | − | 0.997643i | \(-0.521858\pi\) | ||||
−0.0686162 | + | 0.997643i | \(0.521858\pi\) | |||||||
\(230\) | −14.8071 | −0.976351 | ||||||||
\(231\) | −17.2935 | −1.13783 | ||||||||
\(232\) | −7.09160 | −0.465587 | ||||||||
\(233\) | −5.85936 | −0.383859 | −0.191930 | − | 0.981409i | \(-0.561475\pi\) | ||||
−0.191930 | + | 0.981409i | \(0.561475\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −15.3690 | −1.00256 | ||||||||
\(236\) | 5.95635 | 0.387726 | ||||||||
\(237\) | −1.53043 | −0.0994124 | ||||||||
\(238\) | 17.2548 | 1.11847 | ||||||||
\(239\) | −26.0203 | −1.68311 | −0.841557 | − | 0.540168i | \(-0.818361\pi\) | ||||
−0.841557 | + | 0.540168i | \(0.818361\pi\) | |||||||
\(240\) | −1.59859 | −0.103188 | ||||||||
\(241\) | −19.3616 | −1.24719 | −0.623595 | − | 0.781748i | \(-0.714329\pi\) | ||||
−0.623595 | + | 0.781748i | \(0.714329\pi\) | |||||||
\(242\) | −5.57034 | −0.358075 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.49344 | 0.415700 | ||||||||
\(245\) | 17.6615 | 1.12835 | ||||||||
\(246\) | −5.28889 | −0.337207 | ||||||||
\(247\) | 3.43588 | 0.218620 | ||||||||
\(248\) | 10.7030 | 0.679642 | ||||||||
\(249\) | −9.36721 | −0.593623 | ||||||||
\(250\) | 11.9007 | 0.752667 | ||||||||
\(251\) | −17.1426 | −1.08203 | −0.541015 | − | 0.841013i | \(-0.681960\pi\) | ||||
−0.541015 | + | 0.841013i | \(0.681960\pi\) | |||||||
\(252\) | 4.24832 | 0.267619 | ||||||||
\(253\) | 37.7051 | 2.37050 | ||||||||
\(254\) | −19.4121 | −1.21803 | ||||||||
\(255\) | 6.49277 | 0.406593 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.7734 | 1.23343 | 0.616716 | − | 0.787186i | \(-0.288463\pi\) | ||||
0.616716 | + | 0.787186i | \(0.288463\pi\) | |||||||
\(258\) | −1.53277 | −0.0954261 | ||||||||
\(259\) | 25.0514 | 1.55662 | ||||||||
\(260\) | 1.59859 | 0.0991401 | ||||||||
\(261\) | 7.09160 | 0.438959 | ||||||||
\(262\) | 11.1778 | 0.690564 | ||||||||
\(263\) | −30.8363 | −1.90145 | −0.950725 | − | 0.310036i | \(-0.899659\pi\) | ||||
−0.950725 | + | 0.310036i | \(0.899659\pi\) | |||||||
\(264\) | 4.07067 | 0.250532 | ||||||||
\(265\) | 16.0932 | 0.988599 | ||||||||
\(266\) | −14.5967 | −0.894983 | ||||||||
\(267\) | 8.97228 | 0.549095 | ||||||||
\(268\) | 4.52053 | 0.276135 | ||||||||
\(269\) | 14.5206 | 0.885336 | 0.442668 | − | 0.896686i | \(-0.354032\pi\) | ||||
0.442668 | + | 0.896686i | \(0.354032\pi\) | |||||||
\(270\) | 1.59859 | 0.0972868 | ||||||||
\(271\) | −26.3261 | −1.59920 | −0.799598 | − | 0.600536i | \(-0.794954\pi\) | ||||
−0.799598 | + | 0.600536i | \(0.794954\pi\) | |||||||
\(272\) | −4.06157 | −0.246269 | ||||||||
\(273\) | −4.24832 | −0.257120 | ||||||||
\(274\) | 18.9130 | 1.14258 | ||||||||
\(275\) | −9.95085 | −0.600059 | ||||||||
\(276\) | −9.26262 | −0.557544 | ||||||||
\(277\) | −25.8739 | −1.55461 | −0.777305 | − | 0.629124i | \(-0.783414\pi\) | ||||
−0.777305 | + | 0.629124i | \(0.783414\pi\) | |||||||
\(278\) | 2.52047 | 0.151168 | ||||||||
\(279\) | −10.7030 | −0.640773 | ||||||||
\(280\) | −6.79130 | −0.405858 | ||||||||
\(281\) | 3.93838 | 0.234944 | 0.117472 | − | 0.993076i | \(-0.462521\pi\) | ||||
0.117472 | + | 0.993076i | \(0.462521\pi\) | |||||||
\(282\) | −9.61413 | −0.572513 | ||||||||
\(283\) | 14.0958 | 0.837907 | 0.418953 | − | 0.908008i | \(-0.362397\pi\) | ||||
0.418953 | + | 0.908008i | \(0.362397\pi\) | |||||||
\(284\) | −13.3814 | −0.794042 | ||||||||
\(285\) | −5.49256 | −0.325351 | ||||||||
\(286\) | −4.07067 | −0.240704 | ||||||||
\(287\) | −22.4689 | −1.32630 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −0.503638 | −0.0296258 | ||||||||
\(290\) | −11.3365 | −0.665704 | ||||||||
\(291\) | −14.0823 | −0.825521 | ||||||||
\(292\) | 3.94293 | 0.230742 | ||||||||
\(293\) | −5.42241 | −0.316781 | −0.158390 | − | 0.987377i | \(-0.550630\pi\) | ||||
−0.158390 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(294\) | 11.0482 | 0.644344 | ||||||||
\(295\) | 9.52174 | 0.554377 | ||||||||
\(296\) | −5.89679 | −0.342744 | ||||||||
\(297\) | −4.07067 | −0.236204 | ||||||||
\(298\) | −21.9555 | −1.27185 | ||||||||
\(299\) | 9.26262 | 0.535671 | ||||||||
\(300\) | 2.44452 | 0.141135 | ||||||||
\(301\) | −6.51169 | −0.375328 | ||||||||
\(302\) | −9.14572 | −0.526277 | ||||||||
\(303\) | 0.882768 | 0.0507137 | ||||||||
\(304\) | 3.43588 | 0.197061 | ||||||||
\(305\) | 10.3803 | 0.594375 | ||||||||
\(306\) | 4.06157 | 0.232185 | ||||||||
\(307\) | −18.0104 | −1.02791 | −0.513953 | − | 0.857818i | \(-0.671820\pi\) | ||||
−0.513953 | + | 0.857818i | \(0.671820\pi\) | |||||||
\(308\) | 17.2935 | 0.985388 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 17.1097 | 0.971765 | ||||||||
\(311\) | −5.11921 | −0.290284 | −0.145142 | − | 0.989411i | \(-0.546364\pi\) | ||||
−0.145142 | + | 0.989411i | \(0.546364\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −17.4175 | −0.984495 | −0.492248 | − | 0.870455i | \(-0.663825\pi\) | ||||
−0.492248 | + | 0.870455i | \(0.663825\pi\) | |||||||
\(314\) | 14.6803 | 0.828457 | ||||||||
\(315\) | 6.79130 | 0.382646 | ||||||||
\(316\) | 1.53043 | 0.0860936 | ||||||||
\(317\) | 5.40980 | 0.303845 | 0.151922 | − | 0.988392i | \(-0.451454\pi\) | ||||
0.151922 | + | 0.988392i | \(0.451454\pi\) | |||||||
\(318\) | 10.0672 | 0.564538 | ||||||||
\(319\) | 28.8676 | 1.61627 | ||||||||
\(320\) | 1.59859 | 0.0893637 | ||||||||
\(321\) | 6.27951 | 0.350488 | ||||||||
\(322\) | −39.3506 | −2.19292 | ||||||||
\(323\) | −13.9551 | −0.776482 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.44452 | −0.135598 | ||||||||
\(326\) | −12.9771 | −0.718735 | ||||||||
\(327\) | −17.7587 | −0.982056 | ||||||||
\(328\) | 5.28889 | 0.292030 | ||||||||
\(329\) | −40.8438 | −2.25179 | ||||||||
\(330\) | 6.50731 | 0.358216 | ||||||||
\(331\) | 20.5502 | 1.12954 | 0.564770 | − | 0.825248i | \(-0.308965\pi\) | ||||
0.564770 | + | 0.825248i | \(0.308965\pi\) | |||||||
\(332\) | 9.36721 | 0.514092 | ||||||||
\(333\) | 5.89679 | 0.323142 | ||||||||
\(334\) | 3.95923 | 0.216639 | ||||||||
\(335\) | 7.22646 | 0.394824 | ||||||||
\(336\) | −4.24832 | −0.231765 | ||||||||
\(337\) | 25.2019 | 1.37283 | 0.686416 | − | 0.727209i | \(-0.259183\pi\) | ||||
0.686416 | + | 0.727209i | \(0.259183\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 3.56157 | 0.193438 | ||||||||
\(340\) | −6.49277 | −0.352120 | ||||||||
\(341\) | −43.5684 | −2.35936 | ||||||||
\(342\) | −3.43588 | −0.185791 | ||||||||
\(343\) | 17.1980 | 0.928606 | ||||||||
\(344\) | 1.53277 | 0.0826414 | ||||||||
\(345\) | −14.8071 | −0.797187 | ||||||||
\(346\) | 2.24677 | 0.120787 | ||||||||
\(347\) | −4.37034 | −0.234612 | −0.117306 | − | 0.993096i | \(-0.537426\pi\) | ||||
−0.117306 | + | 0.993096i | \(0.537426\pi\) | |||||||
\(348\) | −7.09160 | −0.380150 | ||||||||
\(349\) | 10.6522 | 0.570199 | 0.285099 | − | 0.958498i | \(-0.407973\pi\) | ||||
0.285099 | + | 0.958498i | \(0.407973\pi\) | |||||||
\(350\) | 10.3851 | 0.555108 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.07067 | −0.216967 | ||||||||
\(353\) | −28.9724 | −1.54205 | −0.771023 | − | 0.636808i | \(-0.780255\pi\) | ||||
−0.771023 | + | 0.636808i | \(0.780255\pi\) | |||||||
\(354\) | 5.95635 | 0.316577 | ||||||||
\(355\) | −21.3914 | −1.13534 | ||||||||
\(356\) | −8.97228 | −0.475530 | ||||||||
\(357\) | 17.2548 | 0.913223 | ||||||||
\(358\) | −6.03133 | −0.318766 | ||||||||
\(359\) | −0.959221 | −0.0506258 | −0.0253129 | − | 0.999680i | \(-0.508058\pi\) | ||||
−0.0253129 | + | 0.999680i | \(0.508058\pi\) | |||||||
\(360\) | −1.59859 | −0.0842529 | ||||||||
\(361\) | −7.19470 | −0.378668 | ||||||||
\(362\) | −10.1195 | −0.531869 | ||||||||
\(363\) | −5.57034 | −0.292367 | ||||||||
\(364\) | 4.24832 | 0.222672 | ||||||||
\(365\) | 6.30311 | 0.329920 | ||||||||
\(366\) | 6.49344 | 0.339417 | ||||||||
\(367\) | −38.0272 | −1.98501 | −0.992503 | − | 0.122220i | \(-0.960999\pi\) | ||||
−0.992503 | + | 0.122220i | \(0.960999\pi\) | |||||||
\(368\) | 9.26262 | 0.482848 | ||||||||
\(369\) | −5.28889 | −0.275329 | ||||||||
\(370\) | −9.42653 | −0.490062 | ||||||||
\(371\) | 42.7685 | 2.22043 | ||||||||
\(372\) | 10.7030 | 0.554925 | ||||||||
\(373\) | −21.3704 | −1.10652 | −0.553258 | − | 0.833010i | \(-0.686616\pi\) | ||||
−0.553258 | + | 0.833010i | \(0.686616\pi\) | |||||||
\(374\) | 16.5333 | 0.854917 | ||||||||
\(375\) | 11.9007 | 0.614550 | ||||||||
\(376\) | 9.61413 | 0.495811 | ||||||||
\(377\) | 7.09160 | 0.365236 | ||||||||
\(378\) | 4.24832 | 0.218510 | ||||||||
\(379\) | 12.3795 | 0.635892 | 0.317946 | − | 0.948109i | \(-0.397007\pi\) | ||||
0.317946 | + | 0.948109i | \(0.397007\pi\) | |||||||
\(380\) | 5.49256 | 0.281762 | ||||||||
\(381\) | −19.4121 | −0.994514 | ||||||||
\(382\) | −4.42049 | −0.226172 | ||||||||
\(383\) | 21.8227 | 1.11509 | 0.557543 | − | 0.830148i | \(-0.311744\pi\) | ||||
0.557543 | + | 0.830148i | \(0.311744\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 27.6451 | 1.40893 | ||||||||
\(386\) | 9.36665 | 0.476750 | ||||||||
\(387\) | −1.53277 | −0.0779151 | ||||||||
\(388\) | 14.0823 | 0.714922 | ||||||||
\(389\) | −3.84107 | −0.194750 | −0.0973751 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973751 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(390\) | 1.59859 | 0.0809475 | ||||||||
\(391\) | −37.6208 | −1.90257 | ||||||||
\(392\) | −11.0482 | −0.558018 | ||||||||
\(393\) | 11.1778 | 0.563843 | ||||||||
\(394\) | 19.1911 | 0.966835 | ||||||||
\(395\) | 2.44653 | 0.123098 | ||||||||
\(396\) | 4.07067 | 0.204559 | ||||||||
\(397\) | 34.7939 | 1.74626 | 0.873128 | − | 0.487491i | \(-0.162088\pi\) | ||||
0.873128 | + | 0.487491i | \(0.162088\pi\) | |||||||
\(398\) | 7.97460 | 0.399731 | ||||||||
\(399\) | −14.5967 | −0.730750 | ||||||||
\(400\) | −2.44452 | −0.122226 | ||||||||
\(401\) | 19.8607 | 0.991795 | 0.495898 | − | 0.868381i | \(-0.334839\pi\) | ||||
0.495898 | + | 0.868381i | \(0.334839\pi\) | |||||||
\(402\) | 4.52053 | 0.225464 | ||||||||
\(403\) | −10.7030 | −0.533155 | ||||||||
\(404\) | −0.882768 | −0.0439193 | ||||||||
\(405\) | 1.59859 | 0.0794344 | ||||||||
\(406\) | −30.1274 | −1.49520 | ||||||||
\(407\) | 24.0039 | 1.18983 | ||||||||
\(408\) | −4.06157 | −0.201078 | ||||||||
\(409\) | 12.2273 | 0.604600 | 0.302300 | − | 0.953213i | \(-0.402246\pi\) | ||||
0.302300 | + | 0.953213i | \(0.402246\pi\) | |||||||
\(410\) | 8.45474 | 0.417550 | ||||||||
\(411\) | 18.9130 | 0.932911 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 25.3045 | 1.24515 | ||||||||
\(414\) | −9.26262 | −0.455233 | ||||||||
\(415\) | 14.9743 | 0.735059 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 2.52047 | 0.123428 | ||||||||
\(418\) | −13.9863 | −0.684094 | ||||||||
\(419\) | 20.6126 | 1.00699 | 0.503495 | − | 0.863998i | \(-0.332047\pi\) | ||||
0.503495 | + | 0.863998i | \(0.332047\pi\) | |||||||
\(420\) | −6.79130 | −0.331381 | ||||||||
\(421\) | −0.0477608 | −0.00232772 | −0.00116386 | − | 0.999999i | \(-0.500370\pi\) | ||||
−0.00116386 | + | 0.999999i | \(0.500370\pi\) | |||||||
\(422\) | −12.3843 | −0.602858 | ||||||||
\(423\) | −9.61413 | −0.467455 | ||||||||
\(424\) | −10.0672 | −0.488905 | ||||||||
\(425\) | 9.92861 | 0.481608 | ||||||||
\(426\) | −13.3814 | −0.648332 | ||||||||
\(427\) | 27.5862 | 1.33499 | ||||||||
\(428\) | −6.27951 | −0.303531 | ||||||||
\(429\) | −4.07067 | −0.196534 | ||||||||
\(430\) | 2.45026 | 0.118162 | ||||||||
\(431\) | 22.7229 | 1.09453 | 0.547263 | − | 0.836961i | \(-0.315670\pi\) | ||||
0.547263 | + | 0.836961i | \(0.315670\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.8185 | −0.952418 | −0.476209 | − | 0.879332i | \(-0.657989\pi\) | ||||
−0.476209 | + | 0.879332i | \(0.657989\pi\) | |||||||
\(434\) | 45.4698 | 2.18262 | ||||||||
\(435\) | −11.3365 | −0.543545 | ||||||||
\(436\) | 17.7587 | 0.850485 | ||||||||
\(437\) | 31.8253 | 1.52241 | ||||||||
\(438\) | 3.94293 | 0.188400 | ||||||||
\(439\) | −4.57038 | −0.218132 | −0.109066 | − | 0.994034i | \(-0.534786\pi\) | ||||
−0.109066 | + | 0.994034i | \(0.534786\pi\) | |||||||
\(440\) | −6.50731 | −0.310224 | ||||||||
\(441\) | 11.0482 | 0.526105 | ||||||||
\(442\) | 4.06157 | 0.193189 | ||||||||
\(443\) | 14.7085 | 0.698821 | 0.349410 | − | 0.936970i | \(-0.386382\pi\) | ||||
0.349410 | + | 0.936970i | \(0.386382\pi\) | |||||||
\(444\) | −5.89679 | −0.279849 | ||||||||
\(445\) | −14.3430 | −0.679922 | ||||||||
\(446\) | −25.3964 | −1.20256 | ||||||||
\(447\) | −21.9555 | −1.03846 | ||||||||
\(448\) | 4.24832 | 0.200714 | ||||||||
\(449\) | −0.731479 | −0.0345206 | −0.0172603 | − | 0.999851i | \(-0.505494\pi\) | ||||
−0.0172603 | + | 0.999851i | \(0.505494\pi\) | |||||||
\(450\) | 2.44452 | 0.115236 | ||||||||
\(451\) | −21.5293 | −1.01378 | ||||||||
\(452\) | −3.56157 | −0.167522 | ||||||||
\(453\) | −9.14572 | −0.429703 | ||||||||
\(454\) | 21.9470 | 1.03002 | ||||||||
\(455\) | 6.79130 | 0.318381 | ||||||||
\(456\) | 3.43588 | 0.160900 | ||||||||
\(457\) | 14.3463 | 0.671092 | 0.335546 | − | 0.942024i | \(-0.391079\pi\) | ||||
0.335546 | + | 0.942024i | \(0.391079\pi\) | |||||||
\(458\) | 2.07670 | 0.0970379 | ||||||||
\(459\) | 4.06157 | 0.189578 | ||||||||
\(460\) | 14.8071 | 0.690384 | ||||||||
\(461\) | 19.4261 | 0.904764 | 0.452382 | − | 0.891824i | \(-0.350574\pi\) | ||||
0.452382 | + | 0.891824i | \(0.350574\pi\) | |||||||
\(462\) | 17.2935 | 0.804566 | ||||||||
\(463\) | 15.2359 | 0.708073 | 0.354036 | − | 0.935232i | \(-0.384809\pi\) | ||||
0.354036 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(464\) | 7.09160 | 0.329219 | ||||||||
\(465\) | 17.1097 | 0.793443 | ||||||||
\(466\) | 5.85936 | 0.271429 | ||||||||
\(467\) | 24.1527 | 1.11765 | 0.558826 | − | 0.829285i | \(-0.311252\pi\) | ||||
0.558826 | + | 0.829285i | \(0.311252\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 19.2047 | 0.886789 | ||||||||
\(470\) | 15.3690 | 0.708919 | ||||||||
\(471\) | 14.6803 | 0.676432 | ||||||||
\(472\) | −5.95635 | −0.274163 | ||||||||
\(473\) | −6.23940 | −0.286888 | ||||||||
\(474\) | 1.53043 | 0.0702952 | ||||||||
\(475\) | −8.39910 | −0.385377 | ||||||||
\(476\) | −17.2548 | −0.790874 | ||||||||
\(477\) | 10.0672 | 0.460944 | ||||||||
\(478\) | 26.0203 | 1.19014 | ||||||||
\(479\) | −9.59696 | −0.438496 | −0.219248 | − | 0.975669i | \(-0.570360\pi\) | ||||
−0.219248 | + | 0.975669i | \(0.570360\pi\) | |||||||
\(480\) | 1.59859 | 0.0729651 | ||||||||
\(481\) | 5.89679 | 0.268871 | ||||||||
\(482\) | 19.3616 | 0.881896 | ||||||||
\(483\) | −39.3506 | −1.79051 | ||||||||
\(484\) | 5.57034 | 0.253197 | ||||||||
\(485\) | 22.5118 | 1.02221 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −2.95817 | −0.134048 | −0.0670238 | − | 0.997751i | \(-0.521350\pi\) | ||||
−0.0670238 | + | 0.997751i | \(0.521350\pi\) | |||||||
\(488\) | −6.49344 | −0.293944 | ||||||||
\(489\) | −12.9771 | −0.586844 | ||||||||
\(490\) | −17.6615 | −0.797865 | ||||||||
\(491\) | −5.44956 | −0.245935 | −0.122968 | − | 0.992411i | \(-0.539241\pi\) | ||||
−0.122968 | + | 0.992411i | \(0.539241\pi\) | |||||||
\(492\) | 5.28889 | 0.238442 | ||||||||
\(493\) | −28.8031 | −1.29722 | ||||||||
\(494\) | −3.43588 | −0.154588 | ||||||||
\(495\) | 6.50731 | 0.292482 | ||||||||
\(496\) | −10.7030 | −0.480580 | ||||||||
\(497\) | −56.8486 | −2.55001 | ||||||||
\(498\) | 9.36721 | 0.419755 | ||||||||
\(499\) | 34.6498 | 1.55114 | 0.775568 | − | 0.631264i | \(-0.217464\pi\) | ||||
0.775568 | + | 0.631264i | \(0.217464\pi\) | |||||||
\(500\) | −11.9007 | −0.532216 | ||||||||
\(501\) | 3.95923 | 0.176885 | ||||||||
\(502\) | 17.1426 | 0.765111 | ||||||||
\(503\) | −10.2622 | −0.457568 | −0.228784 | − | 0.973477i | \(-0.573475\pi\) | ||||
−0.228784 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(504\) | −4.24832 | −0.189235 | ||||||||
\(505\) | −1.41118 | −0.0627967 | ||||||||
\(506\) | −37.7051 | −1.67619 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 19.4121 | 0.861274 | ||||||||
\(509\) | 7.73873 | 0.343013 | 0.171506 | − | 0.985183i | \(-0.445137\pi\) | ||||
0.171506 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(510\) | −6.49277 | −0.287505 | ||||||||
\(511\) | 16.7508 | 0.741012 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.43588 | −0.151698 | ||||||||
\(514\) | −19.7734 | −0.872168 | ||||||||
\(515\) | −1.59859 | −0.0704421 | ||||||||
\(516\) | 1.53277 | 0.0674765 | ||||||||
\(517\) | −39.1359 | −1.72120 | ||||||||
\(518\) | −25.0514 | −1.10070 | ||||||||
\(519\) | 2.24677 | 0.0986222 | ||||||||
\(520\) | −1.59859 | −0.0701026 | ||||||||
\(521\) | −31.0891 | −1.36204 | −0.681020 | − | 0.732265i | \(-0.738463\pi\) | ||||
−0.681020 | + | 0.732265i | \(0.738463\pi\) | |||||||
\(522\) | −7.09160 | −0.310391 | ||||||||
\(523\) | 0.0814933 | 0.00356345 | 0.00178173 | − | 0.999998i | \(-0.499433\pi\) | ||||
0.00178173 | + | 0.999998i | \(0.499433\pi\) | |||||||
\(524\) | −11.1778 | −0.488302 | ||||||||
\(525\) | 10.3851 | 0.453243 | ||||||||
\(526\) | 30.8363 | 1.34453 | ||||||||
\(527\) | 43.4711 | 1.89363 | ||||||||
\(528\) | −4.07067 | −0.177153 | ||||||||
\(529\) | 62.7962 | 2.73027 | ||||||||
\(530\) | −16.0932 | −0.699045 | ||||||||
\(531\) | 5.95635 | 0.258484 | ||||||||
\(532\) | 14.5967 | 0.632848 | ||||||||
\(533\) | −5.28889 | −0.229087 | ||||||||
\(534\) | −8.97228 | −0.388269 | ||||||||
\(535\) | −10.0383 | −0.433995 | ||||||||
\(536\) | −4.52053 | −0.195257 | ||||||||
\(537\) | −6.03133 | −0.260271 | ||||||||
\(538\) | −14.5206 | −0.626027 | ||||||||
\(539\) | 44.9735 | 1.93715 | ||||||||
\(540\) | −1.59859 | −0.0687922 | ||||||||
\(541\) | 13.8662 | 0.596155 | 0.298077 | − | 0.954542i | \(-0.403655\pi\) | ||||
0.298077 | + | 0.954542i | \(0.403655\pi\) | |||||||
\(542\) | 26.3261 | 1.13080 | ||||||||
\(543\) | −10.1195 | −0.434270 | ||||||||
\(544\) | 4.06157 | 0.174138 | ||||||||
\(545\) | 28.3887 | 1.21604 | ||||||||
\(546\) | 4.24832 | 0.181811 | ||||||||
\(547\) | −16.8456 | −0.720266 | −0.360133 | − | 0.932901i | \(-0.617269\pi\) | ||||
−0.360133 | + | 0.932901i | \(0.617269\pi\) | |||||||
\(548\) | −18.9130 | −0.807924 | ||||||||
\(549\) | 6.49344 | 0.277133 | ||||||||
\(550\) | 9.95085 | 0.424305 | ||||||||
\(551\) | 24.3659 | 1.03802 | ||||||||
\(552\) | 9.26262 | 0.394243 | ||||||||
\(553\) | 6.50177 | 0.276483 | ||||||||
\(554\) | 25.8739 | 1.09928 | ||||||||
\(555\) | −9.42653 | −0.400134 | ||||||||
\(556\) | −2.52047 | −0.106892 | ||||||||
\(557\) | −14.4179 | −0.610907 | −0.305453 | − | 0.952207i | \(-0.598808\pi\) | ||||
−0.305453 | + | 0.952207i | \(0.598808\pi\) | |||||||
\(558\) | 10.7030 | 0.453095 | ||||||||
\(559\) | −1.53277 | −0.0648293 | ||||||||
\(560\) | 6.79130 | 0.286985 | ||||||||
\(561\) | 16.5333 | 0.698037 | ||||||||
\(562\) | −3.93838 | −0.166130 | ||||||||
\(563\) | 1.38354 | 0.0583093 | 0.0291546 | − | 0.999575i | \(-0.490718\pi\) | ||||
0.0291546 | + | 0.999575i | \(0.490718\pi\) | |||||||
\(564\) | 9.61413 | 0.404828 | ||||||||
\(565\) | −5.69347 | −0.239526 | ||||||||
\(566\) | −14.0958 | −0.592490 | ||||||||
\(567\) | 4.24832 | 0.178413 | ||||||||
\(568\) | 13.3814 | 0.561472 | ||||||||
\(569\) | 20.7925 | 0.871667 | 0.435833 | − | 0.900027i | \(-0.356454\pi\) | ||||
0.435833 | + | 0.900027i | \(0.356454\pi\) | |||||||
\(570\) | 5.49256 | 0.230058 | ||||||||
\(571\) | 7.49899 | 0.313823 | 0.156912 | − | 0.987613i | \(-0.449846\pi\) | ||||
0.156912 | + | 0.987613i | \(0.449846\pi\) | |||||||
\(572\) | 4.07067 | 0.170203 | ||||||||
\(573\) | −4.42049 | −0.184669 | ||||||||
\(574\) | 22.4689 | 0.937833 | ||||||||
\(575\) | −22.6427 | −0.944266 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −27.2468 | −1.13430 | −0.567150 | − | 0.823615i | \(-0.691954\pi\) | ||||
−0.567150 | + | 0.823615i | \(0.691954\pi\) | |||||||
\(578\) | 0.503638 | 0.0209486 | ||||||||
\(579\) | 9.36665 | 0.389265 | ||||||||
\(580\) | 11.3365 | 0.470724 | ||||||||
\(581\) | 39.7949 | 1.65097 | ||||||||
\(582\) | 14.0823 | 0.583732 | ||||||||
\(583\) | 40.9801 | 1.69722 | ||||||||
\(584\) | −3.94293 | −0.163159 | ||||||||
\(585\) | 1.59859 | 0.0660934 | ||||||||
\(586\) | 5.42241 | 0.223998 | ||||||||
\(587\) | −10.2970 | −0.425004 | −0.212502 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212502 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(588\) | −11.0482 | −0.455620 | ||||||||
\(589\) | −36.7743 | −1.51526 | ||||||||
\(590\) | −9.52174 | −0.392004 | ||||||||
\(591\) | 19.1911 | 0.789417 | ||||||||
\(592\) | 5.89679 | 0.242357 | ||||||||
\(593\) | −45.7540 | −1.87889 | −0.939445 | − | 0.342698i | \(-0.888659\pi\) | ||||
−0.939445 | + | 0.342698i | \(0.888659\pi\) | |||||||
\(594\) | 4.07067 | 0.167022 | ||||||||
\(595\) | −27.5833 | −1.13081 | ||||||||
\(596\) | 21.9555 | 0.899332 | ||||||||
\(597\) | 7.97460 | 0.326379 | ||||||||
\(598\) | −9.26262 | −0.378777 | ||||||||
\(599\) | −47.0310 | −1.92163 | −0.960817 | − | 0.277184i | \(-0.910599\pi\) | ||||
−0.960817 | + | 0.277184i | \(0.910599\pi\) | |||||||
\(600\) | −2.44452 | −0.0997973 | ||||||||
\(601\) | 5.91612 | 0.241324 | 0.120662 | − | 0.992694i | \(-0.461498\pi\) | ||||
0.120662 | + | 0.992694i | \(0.461498\pi\) | |||||||
\(602\) | 6.51169 | 0.265397 | ||||||||
\(603\) | 4.52053 | 0.184090 | ||||||||
\(604\) | 9.14572 | 0.372134 | ||||||||
\(605\) | 8.90466 | 0.362026 | ||||||||
\(606\) | −0.882768 | −0.0358600 | ||||||||
\(607\) | 42.5328 | 1.72635 | 0.863177 | − | 0.504901i | \(-0.168471\pi\) | ||||
0.863177 | + | 0.504901i | \(0.168471\pi\) | |||||||
\(608\) | −3.43588 | −0.139344 | ||||||||
\(609\) | −30.1274 | −1.22082 | ||||||||
\(610\) | −10.3803 | −0.420287 | ||||||||
\(611\) | −9.61413 | −0.388946 | ||||||||
\(612\) | −4.06157 | −0.164179 | ||||||||
\(613\) | −24.0594 | −0.971750 | −0.485875 | − | 0.874028i | \(-0.661499\pi\) | ||||
−0.485875 | + | 0.874028i | \(0.661499\pi\) | |||||||
\(614\) | 18.0104 | 0.726840 | ||||||||
\(615\) | 8.45474 | 0.340928 | ||||||||
\(616\) | −17.2935 | −0.696774 | ||||||||
\(617\) | −9.78867 | −0.394077 | −0.197039 | − | 0.980396i | \(-0.563132\pi\) | ||||
−0.197039 | + | 0.980396i | \(0.563132\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 14.6203 | 0.587638 | 0.293819 | − | 0.955861i | \(-0.405074\pi\) | ||||
0.293819 | + | 0.955861i | \(0.405074\pi\) | |||||||
\(620\) | −17.1097 | −0.687141 | ||||||||
\(621\) | −9.26262 | −0.371696 | ||||||||
\(622\) | 5.11921 | 0.205262 | ||||||||
\(623\) | −38.1171 | −1.52713 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −6.80168 | −0.272067 | ||||||||
\(626\) | 17.4175 | 0.696143 | ||||||||
\(627\) | −13.9863 | −0.558561 | ||||||||
\(628\) | −14.6803 | −0.585807 | ||||||||
\(629\) | −23.9502 | −0.954959 | ||||||||
\(630\) | −6.79130 | −0.270572 | ||||||||
\(631\) | −19.6291 | −0.781421 | −0.390711 | − | 0.920514i | \(-0.627771\pi\) | ||||
−0.390711 | + | 0.920514i | \(0.627771\pi\) | |||||||
\(632\) | −1.53043 | −0.0608774 | ||||||||
\(633\) | −12.3843 | −0.492231 | ||||||||
\(634\) | −5.40980 | −0.214851 | ||||||||
\(635\) | 31.0320 | 1.23147 | ||||||||
\(636\) | −10.0672 | −0.399189 | ||||||||
\(637\) | 11.0482 | 0.437745 | ||||||||
\(638\) | −28.8676 | −1.14288 | ||||||||
\(639\) | −13.3814 | −0.529361 | ||||||||
\(640\) | −1.59859 | −0.0631896 | ||||||||
\(641\) | 46.0956 | 1.82067 | 0.910333 | − | 0.413876i | \(-0.135825\pi\) | ||||
0.910333 | + | 0.413876i | \(0.135825\pi\) | |||||||
\(642\) | −6.27951 | −0.247832 | ||||||||
\(643\) | −9.48958 | −0.374233 | −0.187116 | − | 0.982338i | \(-0.559914\pi\) | ||||
−0.187116 | + | 0.982338i | \(0.559914\pi\) | |||||||
\(644\) | 39.3506 | 1.55063 | ||||||||
\(645\) | 2.45026 | 0.0964791 | ||||||||
\(646\) | 13.9551 | 0.549056 | ||||||||
\(647\) | 45.7314 | 1.79789 | 0.898943 | − | 0.438066i | \(-0.144336\pi\) | ||||
0.898943 | + | 0.438066i | \(0.144336\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 24.2463 | 0.951752 | ||||||||
\(650\) | 2.44452 | 0.0958821 | ||||||||
\(651\) | 45.4698 | 1.78210 | ||||||||
\(652\) | 12.9771 | 0.508222 | ||||||||
\(653\) | 36.9714 | 1.44680 | 0.723401 | − | 0.690428i | \(-0.242578\pi\) | ||||
0.723401 | + | 0.690428i | \(0.242578\pi\) | |||||||
\(654\) | 17.7587 | 0.694418 | ||||||||
\(655\) | −17.8686 | −0.698184 | ||||||||
\(656\) | −5.28889 | −0.206496 | ||||||||
\(657\) | 3.94293 | 0.153828 | ||||||||
\(658\) | 40.8438 | 1.59226 | ||||||||
\(659\) | −17.9184 | −0.698002 | −0.349001 | − | 0.937122i | \(-0.613479\pi\) | ||||
−0.349001 | + | 0.937122i | \(0.613479\pi\) | |||||||
\(660\) | −6.50731 | −0.253297 | ||||||||
\(661\) | −16.9012 | −0.657381 | −0.328690 | − | 0.944438i | \(-0.606607\pi\) | ||||
−0.328690 | + | 0.944438i | \(0.606607\pi\) | |||||||
\(662\) | −20.5502 | −0.798705 | ||||||||
\(663\) | 4.06157 | 0.157738 | ||||||||
\(664\) | −9.36721 | −0.363518 | ||||||||
\(665\) | 23.3341 | 0.904858 | ||||||||
\(666\) | −5.89679 | −0.228496 | ||||||||
\(667\) | 65.6868 | 2.54340 | ||||||||
\(668\) | −3.95923 | −0.153187 | ||||||||
\(669\) | −25.3964 | −0.981883 | ||||||||
\(670\) | −7.22646 | −0.279182 | ||||||||
\(671\) | 26.4326 | 1.02042 | ||||||||
\(672\) | 4.24832 | 0.163882 | ||||||||
\(673\) | 2.00945 | 0.0774586 | 0.0387293 | − | 0.999250i | \(-0.487669\pi\) | ||||
0.0387293 | + | 0.999250i | \(0.487669\pi\) | |||||||
\(674\) | −25.2019 | −0.970739 | ||||||||
\(675\) | 2.44452 | 0.0940898 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −24.1860 | −0.929543 | −0.464771 | − | 0.885431i | \(-0.653863\pi\) | ||||
−0.464771 | + | 0.885431i | \(0.653863\pi\) | |||||||
\(678\) | −3.56157 | −0.136781 | ||||||||
\(679\) | 59.8262 | 2.29592 | ||||||||
\(680\) | 6.49277 | 0.248986 | ||||||||
\(681\) | 21.9470 | 0.841010 | ||||||||
\(682\) | 43.5684 | 1.66832 | ||||||||
\(683\) | 4.78586 | 0.183126 | 0.0915630 | − | 0.995799i | \(-0.470814\pi\) | ||||
0.0915630 | + | 0.995799i | \(0.470814\pi\) | |||||||
\(684\) | 3.43588 | 0.131374 | ||||||||
\(685\) | −30.2341 | −1.15519 | ||||||||
\(686\) | −17.1980 | −0.656623 | ||||||||
\(687\) | 2.07670 | 0.0792311 | ||||||||
\(688\) | −1.53277 | −0.0584363 | ||||||||
\(689\) | 10.0672 | 0.383528 | ||||||||
\(690\) | 14.8071 | 0.563696 | ||||||||
\(691\) | 48.4363 | 1.84261 | 0.921303 | − | 0.388847i | \(-0.127126\pi\) | ||||
0.921303 | + | 0.388847i | \(0.127126\pi\) | |||||||
\(692\) | −2.24677 | −0.0854094 | ||||||||
\(693\) | 17.2935 | 0.656925 | ||||||||
\(694\) | 4.37034 | 0.165896 | ||||||||
\(695\) | −4.02919 | −0.152836 | ||||||||
\(696\) | 7.09160 | 0.268807 | ||||||||
\(697\) | 21.4812 | 0.813658 | ||||||||
\(698\) | −10.6522 | −0.403192 | ||||||||
\(699\) | 5.85936 | 0.221621 | ||||||||
\(700\) | −10.3851 | −0.392520 | ||||||||
\(701\) | −26.6389 | −1.00614 | −0.503069 | − | 0.864246i | \(-0.667796\pi\) | ||||
−0.503069 | + | 0.864246i | \(0.667796\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 20.2607 | 0.764147 | ||||||||
\(704\) | 4.07067 | 0.153419 | ||||||||
\(705\) | 15.3690 | 0.578830 | ||||||||
\(706\) | 28.9724 | 1.09039 | ||||||||
\(707\) | −3.75028 | −0.141044 | ||||||||
\(708\) | −5.95635 | −0.223853 | ||||||||
\(709\) | −36.4512 | −1.36895 | −0.684476 | − | 0.729035i | \(-0.739969\pi\) | ||||
−0.684476 | + | 0.729035i | \(0.739969\pi\) | |||||||
\(710\) | 21.3914 | 0.802803 | ||||||||
\(711\) | 1.53043 | 0.0573958 | ||||||||
\(712\) | 8.97228 | 0.336250 | ||||||||
\(713\) | −99.1380 | −3.71275 | ||||||||
\(714\) | −17.2548 | −0.645746 | ||||||||
\(715\) | 6.50731 | 0.243360 | ||||||||
\(716\) | 6.03133 | 0.225401 | ||||||||
\(717\) | 26.0203 | 0.971747 | ||||||||
\(718\) | 0.959221 | 0.0357978 | ||||||||
\(719\) | 36.4041 | 1.35764 | 0.678821 | − | 0.734304i | \(-0.262491\pi\) | ||||
0.678821 | + | 0.734304i | \(0.262491\pi\) | |||||||
\(720\) | 1.59859 | 0.0595758 | ||||||||
\(721\) | −4.24832 | −0.158216 | ||||||||
\(722\) | 7.19470 | 0.267759 | ||||||||
\(723\) | 19.3616 | 0.720065 | ||||||||
\(724\) | 10.1195 | 0.376088 | ||||||||
\(725\) | −17.3356 | −0.643828 | ||||||||
\(726\) | 5.57034 | 0.206735 | ||||||||
\(727\) | 17.9375 | 0.665266 | 0.332633 | − | 0.943056i | \(-0.392063\pi\) | ||||
0.332633 | + | 0.943056i | \(0.392063\pi\) | |||||||
\(728\) | −4.24832 | −0.157453 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.30311 | −0.233288 | ||||||||
\(731\) | 6.22546 | 0.230257 | ||||||||
\(732\) | −6.49344 | −0.240004 | ||||||||
\(733\) | −49.0928 | −1.81329 | −0.906643 | − | 0.421900i | \(-0.861363\pi\) | ||||
−0.906643 | + | 0.421900i | \(0.861363\pi\) | |||||||
\(734\) | 38.0272 | 1.40361 | ||||||||
\(735\) | −17.6615 | −0.651454 | ||||||||
\(736\) | −9.26262 | −0.341425 | ||||||||
\(737\) | 18.4016 | 0.677831 | ||||||||
\(738\) | 5.28889 | 0.194687 | ||||||||
\(739\) | 8.22116 | 0.302420 | 0.151210 | − | 0.988502i | \(-0.451683\pi\) | ||||
0.151210 | + | 0.988502i | \(0.451683\pi\) | |||||||
\(740\) | 9.42653 | 0.346526 | ||||||||
\(741\) | −3.43588 | −0.126220 | ||||||||
\(742\) | −42.7685 | −1.57008 | ||||||||
\(743\) | −3.27036 | −0.119978 | −0.0599889 | − | 0.998199i | \(-0.519107\pi\) | ||||
−0.0599889 | + | 0.998199i | \(0.519107\pi\) | |||||||
\(744\) | −10.7030 | −0.392392 | ||||||||
\(745\) | 35.0977 | 1.28588 | ||||||||
\(746\) | 21.3704 | 0.782425 | ||||||||
\(747\) | 9.36721 | 0.342728 | ||||||||
\(748\) | −16.5333 | −0.604518 | ||||||||
\(749\) | −26.6773 | −0.974768 | ||||||||
\(750\) | −11.9007 | −0.434552 | ||||||||
\(751\) | −10.3651 | −0.378226 | −0.189113 | − | 0.981955i | \(-0.560561\pi\) | ||||
−0.189113 | + | 0.981955i | \(0.560561\pi\) | |||||||
\(752\) | −9.61413 | −0.350591 | ||||||||
\(753\) | 17.1426 | 0.624711 | ||||||||
\(754\) | −7.09160 | −0.258261 | ||||||||
\(755\) | 14.6202 | 0.532084 | ||||||||
\(756\) | −4.24832 | −0.154510 | ||||||||
\(757\) | −29.6110 | −1.07623 | −0.538115 | − | 0.842872i | \(-0.680863\pi\) | ||||
−0.538115 | + | 0.842872i | \(0.680863\pi\) | |||||||
\(758\) | −12.3795 | −0.449644 | ||||||||
\(759\) | −37.7051 | −1.36861 | ||||||||
\(760\) | −5.49256 | −0.199236 | ||||||||
\(761\) | −8.57839 | −0.310966 | −0.155483 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155483 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(762\) | 19.4121 | 0.703227 | ||||||||
\(763\) | 75.4444 | 2.73127 | ||||||||
\(764\) | 4.42049 | 0.159928 | ||||||||
\(765\) | −6.49277 | −0.234747 | ||||||||
\(766\) | −21.8227 | −0.788485 | ||||||||
\(767\) | 5.95635 | 0.215071 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 22.5442 | 0.812963 | 0.406481 | − | 0.913659i | \(-0.366756\pi\) | ||||
0.406481 | + | 0.913659i | \(0.366756\pi\) | |||||||
\(770\) | −27.6451 | −0.996261 | ||||||||
\(771\) | −19.7734 | −0.712123 | ||||||||
\(772\) | −9.36665 | −0.337113 | ||||||||
\(773\) | −9.40688 | −0.338342 | −0.169171 | − | 0.985587i | \(-0.554109\pi\) | ||||
−0.169171 | + | 0.985587i | \(0.554109\pi\) | |||||||
\(774\) | 1.53277 | 0.0550943 | ||||||||
\(775\) | 26.1638 | 0.939831 | ||||||||
\(776\) | −14.0823 | −0.505526 | ||||||||
\(777\) | −25.0514 | −0.898715 | ||||||||
\(778\) | 3.84107 | 0.137709 | ||||||||
\(779\) | −18.1720 | −0.651080 | ||||||||
\(780\) | −1.59859 | −0.0572385 | ||||||||
\(781\) | −54.4714 | −1.94914 | ||||||||
\(782\) | 37.6208 | 1.34532 | ||||||||
\(783\) | −7.09160 | −0.253433 | ||||||||
\(784\) | 11.0482 | 0.394578 | ||||||||
\(785\) | −23.4677 | −0.837598 | ||||||||
\(786\) | −11.1778 | −0.398697 | ||||||||
\(787\) | 3.23611 | 0.115355 | 0.0576774 | − | 0.998335i | \(-0.481631\pi\) | ||||
0.0576774 | + | 0.998335i | \(0.481631\pi\) | |||||||
\(788\) | −19.1911 | −0.683656 | ||||||||
\(789\) | 30.8363 | 1.09780 | ||||||||
\(790\) | −2.44653 | −0.0870436 | ||||||||
\(791\) | −15.1307 | −0.537985 | ||||||||
\(792\) | −4.07067 | −0.144645 | ||||||||
\(793\) | 6.49344 | 0.230589 | ||||||||
\(794\) | −34.7939 | −1.23479 | ||||||||
\(795\) | −16.0932 | −0.570768 | ||||||||
\(796\) | −7.97460 | −0.282652 | ||||||||
\(797\) | 6.70287 | 0.237428 | 0.118714 | − | 0.992929i | \(-0.462123\pi\) | ||||
0.118714 | + | 0.992929i | \(0.462123\pi\) | |||||||
\(798\) | 14.5967 | 0.516719 | ||||||||
\(799\) | 39.0485 | 1.38144 | ||||||||
\(800\) | 2.44452 | 0.0864270 | ||||||||
\(801\) | −8.97228 | −0.317020 | ||||||||
\(802\) | −19.8607 | −0.701305 | ||||||||
\(803\) | 16.0503 | 0.566404 | ||||||||
\(804\) | −4.52053 | −0.159427 | ||||||||
\(805\) | 62.9052 | 2.21712 | ||||||||
\(806\) | 10.7030 | 0.376998 | ||||||||
\(807\) | −14.5206 | −0.511149 | ||||||||
\(808\) | 0.882768 | 0.0310557 | ||||||||
\(809\) | −14.5042 | −0.509940 | −0.254970 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254970 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(810\) | −1.59859 | −0.0561686 | ||||||||
\(811\) | 15.3324 | 0.538392 | 0.269196 | − | 0.963085i | \(-0.413242\pi\) | ||||
0.269196 | + | 0.963085i | \(0.413242\pi\) | |||||||
\(812\) | 30.1274 | 1.05726 | ||||||||
\(813\) | 26.3261 | 0.923296 | ||||||||
\(814\) | −24.0039 | −0.841336 | ||||||||
\(815\) | 20.7450 | 0.726665 | ||||||||
\(816\) | 4.06157 | 0.142183 | ||||||||
\(817\) | −5.26642 | −0.184249 | ||||||||
\(818\) | −12.2273 | −0.427517 | ||||||||
\(819\) | 4.24832 | 0.148448 | ||||||||
\(820\) | −8.45474 | −0.295252 | ||||||||
\(821\) | 22.1171 | 0.771892 | 0.385946 | − | 0.922521i | \(-0.373875\pi\) | ||||
0.385946 | + | 0.922521i | \(0.373875\pi\) | |||||||
\(822\) | −18.9130 | −0.659668 | ||||||||
\(823\) | 47.2667 | 1.64761 | 0.823807 | − | 0.566871i | \(-0.191846\pi\) | ||||
0.823807 | + | 0.566871i | \(0.191846\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 9.95085 | 0.346444 | ||||||||
\(826\) | −25.3045 | −0.880455 | ||||||||
\(827\) | −30.7775 | −1.07024 | −0.535119 | − | 0.844777i | \(-0.679733\pi\) | ||||
−0.535119 | + | 0.844777i | \(0.679733\pi\) | |||||||
\(828\) | 9.26262 | 0.321898 | ||||||||
\(829\) | 8.14728 | 0.282967 | 0.141483 | − | 0.989941i | \(-0.454813\pi\) | ||||
0.141483 | + | 0.989941i | \(0.454813\pi\) | |||||||
\(830\) | −14.9743 | −0.519765 | ||||||||
\(831\) | 25.8739 | 0.897555 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −44.8730 | −1.55476 | ||||||||
\(834\) | −2.52047 | −0.0872767 | ||||||||
\(835\) | −6.32917 | −0.219030 | ||||||||
\(836\) | 13.9863 | 0.483728 | ||||||||
\(837\) | 10.7030 | 0.369950 | ||||||||
\(838\) | −20.6126 | −0.712050 | ||||||||
\(839\) | 43.8092 | 1.51246 | 0.756230 | − | 0.654306i | \(-0.227039\pi\) | ||||
0.756230 | + | 0.654306i | \(0.227039\pi\) | |||||||
\(840\) | 6.79130 | 0.234322 | ||||||||
\(841\) | 21.2908 | 0.734167 | ||||||||
\(842\) | 0.0477608 | 0.00164595 | ||||||||
\(843\) | −3.93838 | −0.135645 | ||||||||
\(844\) | 12.3843 | 0.426285 | ||||||||
\(845\) | 1.59859 | 0.0549930 | ||||||||
\(846\) | 9.61413 | 0.330540 | ||||||||
\(847\) | 23.6646 | 0.813124 | ||||||||
\(848\) | 10.0672 | 0.345708 | ||||||||
\(849\) | −14.0958 | −0.483766 | ||||||||
\(850\) | −9.92861 | −0.340548 | ||||||||
\(851\) | 54.6198 | 1.87234 | ||||||||
\(852\) | 13.3814 | 0.458440 | ||||||||
\(853\) | −9.63132 | −0.329770 | −0.164885 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164885 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(854\) | −27.5862 | −0.943980 | ||||||||
\(855\) | 5.49256 | 0.187841 | ||||||||
\(856\) | 6.27951 | 0.214629 | ||||||||
\(857\) | −17.7935 | −0.607813 | −0.303907 | − | 0.952702i | \(-0.598291\pi\) | ||||
−0.303907 | + | 0.952702i | \(0.598291\pi\) | |||||||
\(858\) | 4.07067 | 0.138970 | ||||||||
\(859\) | −29.9098 | −1.02051 | −0.510255 | − | 0.860023i | \(-0.670449\pi\) | ||||
−0.510255 | + | 0.860023i | \(0.670449\pi\) | |||||||
\(860\) | −2.45026 | −0.0835533 | ||||||||
\(861\) | 22.4689 | 0.765737 | ||||||||
\(862\) | −22.7229 | −0.773946 | ||||||||
\(863\) | −14.1444 | −0.481481 | −0.240740 | − | 0.970590i | \(-0.577390\pi\) | ||||
−0.240740 | + | 0.970590i | \(0.577390\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.59165 | −0.122120 | ||||||||
\(866\) | 19.8185 | 0.673461 | ||||||||
\(867\) | 0.503638 | 0.0171044 | ||||||||
\(868\) | −45.4698 | −1.54335 | ||||||||
\(869\) | 6.22989 | 0.211335 | ||||||||
\(870\) | 11.3365 | 0.384345 | ||||||||
\(871\) | 4.52053 | 0.153172 | ||||||||
\(872\) | −17.7587 | −0.601384 | ||||||||
\(873\) | 14.0823 | 0.476615 | ||||||||
\(874\) | −31.8253 | −1.07651 | ||||||||
\(875\) | −50.5580 | −1.70917 | ||||||||
\(876\) | −3.94293 | −0.133219 | ||||||||
\(877\) | 17.5745 | 0.593449 | 0.296725 | − | 0.954963i | \(-0.404106\pi\) | ||||
0.296725 | + | 0.954963i | \(0.404106\pi\) | |||||||
\(878\) | 4.57038 | 0.154243 | ||||||||
\(879\) | 5.42241 | 0.182893 | ||||||||
\(880\) | 6.50731 | 0.219361 | ||||||||
\(881\) | 8.38259 | 0.282417 | 0.141208 | − | 0.989980i | \(-0.454901\pi\) | ||||
0.141208 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(882\) | −11.0482 | −0.372012 | ||||||||
\(883\) | 11.6637 | 0.392514 | 0.196257 | − | 0.980552i | \(-0.437121\pi\) | ||||
0.196257 | + | 0.980552i | \(0.437121\pi\) | |||||||
\(884\) | −4.06157 | −0.136605 | ||||||||
\(885\) | −9.52174 | −0.320070 | ||||||||
\(886\) | −14.7085 | −0.494141 | ||||||||
\(887\) | 41.4609 | 1.39212 | 0.696060 | − | 0.717983i | \(-0.254935\pi\) | ||||
0.696060 | + | 0.717983i | \(0.254935\pi\) | |||||||
\(888\) | 5.89679 | 0.197883 | ||||||||
\(889\) | 82.4689 | 2.76592 | ||||||||
\(890\) | 14.3430 | 0.480777 | ||||||||
\(891\) | 4.07067 | 0.136373 | ||||||||
\(892\) | 25.3964 | 0.850336 | ||||||||
\(893\) | −33.0330 | −1.10541 | ||||||||
\(894\) | 21.9555 | 0.734301 | ||||||||
\(895\) | 9.64160 | 0.322283 | ||||||||
\(896\) | −4.24832 | −0.141926 | ||||||||
\(897\) | −9.26262 | −0.309270 | ||||||||
\(898\) | 0.731479 | 0.0244098 | ||||||||
\(899\) | −75.9015 | −2.53146 | ||||||||
\(900\) | −2.44452 | −0.0814841 | ||||||||
\(901\) | −40.8885 | −1.36219 | ||||||||
\(902\) | 21.5293 | 0.716848 | ||||||||
\(903\) | 6.51169 | 0.216696 | ||||||||
\(904\) | 3.56157 | 0.118456 | ||||||||
\(905\) | 16.1769 | 0.537738 | ||||||||
\(906\) | 9.14572 | 0.303846 | ||||||||
\(907\) | −22.5841 | −0.749894 | −0.374947 | − | 0.927046i | \(-0.622339\pi\) | ||||
−0.374947 | + | 0.927046i | \(0.622339\pi\) | |||||||
\(908\) | −21.9470 | −0.728336 | ||||||||
\(909\) | −0.882768 | −0.0292796 | ||||||||
\(910\) | −6.79130 | −0.225129 | ||||||||
\(911\) | −11.3659 | −0.376571 | −0.188285 | − | 0.982114i | \(-0.560293\pi\) | ||||
−0.188285 | + | 0.982114i | \(0.560293\pi\) | |||||||
\(912\) | −3.43588 | −0.113774 | ||||||||
\(913\) | 38.1308 | 1.26195 | ||||||||
\(914\) | −14.3463 | −0.474534 | ||||||||
\(915\) | −10.3803 | −0.343163 | ||||||||
\(916\) | −2.07670 | −0.0686162 | ||||||||
\(917\) | −47.4866 | −1.56815 | ||||||||
\(918\) | −4.06157 | −0.134052 | ||||||||
\(919\) | 0.383465 | 0.0126494 | 0.00632468 | − | 0.999980i | \(-0.497987\pi\) | ||||
0.00632468 | + | 0.999980i | \(0.497987\pi\) | |||||||
\(920\) | −14.8071 | −0.488175 | ||||||||
\(921\) | 18.0104 | 0.593462 | ||||||||
\(922\) | −19.4261 | −0.639765 | ||||||||
\(923\) | −13.3814 | −0.440455 | ||||||||
\(924\) | −17.2935 | −0.568914 | ||||||||
\(925\) | −14.4149 | −0.473957 | ||||||||
\(926\) | −15.2359 | −0.500683 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −7.09160 | −0.232793 | ||||||||
\(929\) | −7.21929 | −0.236857 | −0.118429 | − | 0.992963i | \(-0.537786\pi\) | ||||
−0.118429 | + | 0.992963i | \(0.537786\pi\) | |||||||
\(930\) | −17.1097 | −0.561049 | ||||||||
\(931\) | 37.9603 | 1.24410 | ||||||||
\(932\) | −5.85936 | −0.191930 | ||||||||
\(933\) | 5.11921 | 0.167595 | ||||||||
\(934\) | −24.1527 | −0.790300 | ||||||||
\(935\) | −26.4299 | −0.864350 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 14.5225 | 0.474428 | 0.237214 | − | 0.971457i | \(-0.423766\pi\) | ||||
0.237214 | + | 0.971457i | \(0.423766\pi\) | |||||||
\(938\) | −19.2047 | −0.627054 | ||||||||
\(939\) | 17.4175 | 0.568399 | ||||||||
\(940\) | −15.3690 | −0.501282 | ||||||||
\(941\) | 19.2395 | 0.627189 | 0.313595 | − | 0.949557i | \(-0.398467\pi\) | ||||
0.313595 | + | 0.949557i | \(0.398467\pi\) | |||||||
\(942\) | −14.6803 | −0.478310 | ||||||||
\(943\) | −48.9890 | −1.59530 | ||||||||
\(944\) | 5.95635 | 0.193863 | ||||||||
\(945\) | −6.79130 | −0.220921 | ||||||||
\(946\) | 6.23940 | 0.202860 | ||||||||
\(947\) | −13.0006 | −0.422462 | −0.211231 | − | 0.977436i | \(-0.567747\pi\) | ||||
−0.211231 | + | 0.977436i | \(0.567747\pi\) | |||||||
\(948\) | −1.53043 | −0.0497062 | ||||||||
\(949\) | 3.94293 | 0.127993 | ||||||||
\(950\) | 8.39910 | 0.272503 | ||||||||
\(951\) | −5.40980 | −0.175425 | ||||||||
\(952\) | 17.2548 | 0.559233 | ||||||||
\(953\) | 50.2787 | 1.62869 | 0.814344 | − | 0.580383i | \(-0.197097\pi\) | ||||
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(954\) | −10.0672 | −0.325936 | ||||||||
\(955\) | 7.06653 | 0.228668 | ||||||||
\(956\) | −26.0203 | −0.841557 | ||||||||
\(957\) | −28.8676 | −0.933156 | ||||||||
\(958\) | 9.59696 | 0.310064 | ||||||||
\(959\) | −80.3485 | −2.59459 | ||||||||
\(960\) | −1.59859 | −0.0515941 | ||||||||
\(961\) | 83.5545 | 2.69531 | ||||||||
\(962\) | −5.89679 | −0.190120 | ||||||||
\(963\) | −6.27951 | −0.202354 | ||||||||
\(964\) | −19.3616 | −0.623595 | ||||||||
\(965\) | −14.9734 | −0.482010 | ||||||||
\(966\) | 39.3506 | 1.26608 | ||||||||
\(967\) | 49.3254 | 1.58620 | 0.793099 | − | 0.609093i | \(-0.208466\pi\) | ||||
0.793099 | + | 0.609093i | \(0.208466\pi\) | |||||||
\(968\) | −5.57034 | −0.179037 | ||||||||
\(969\) | 13.9551 | 0.448302 | ||||||||
\(970\) | −22.5118 | −0.722811 | ||||||||
\(971\) | 40.9504 | 1.31416 | 0.657080 | − | 0.753821i | \(-0.271791\pi\) | ||||
0.657080 | + | 0.753821i | \(0.271791\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −10.7078 | −0.343275 | ||||||||
\(974\) | 2.95817 | 0.0947860 | ||||||||
\(975\) | 2.44452 | 0.0782874 | ||||||||
\(976\) | 6.49344 | 0.207850 | ||||||||
\(977\) | −31.8994 | −1.02055 | −0.510276 | − | 0.860010i | \(-0.670457\pi\) | ||||
−0.510276 | + | 0.860010i | \(0.670457\pi\) | |||||||
\(978\) | 12.9771 | 0.414962 | ||||||||
\(979\) | −36.5232 | −1.16729 | ||||||||
\(980\) | 17.6615 | 0.564176 | ||||||||
\(981\) | 17.7587 | 0.566990 | ||||||||
\(982\) | 5.44956 | 0.173903 | ||||||||
\(983\) | −25.2819 | −0.806366 | −0.403183 | − | 0.915119i | \(-0.632096\pi\) | ||||
−0.403183 | + | 0.915119i | \(0.632096\pi\) | |||||||
\(984\) | −5.28889 | −0.168604 | ||||||||
\(985\) | −30.6787 | −0.977503 | ||||||||
\(986\) | 28.8031 | 0.917276 | ||||||||
\(987\) | 40.8438 | 1.30007 | ||||||||
\(988\) | 3.43588 | 0.109310 | ||||||||
\(989\) | −14.1975 | −0.451453 | ||||||||
\(990\) | −6.50731 | −0.206816 | ||||||||
\(991\) | −25.8319 | −0.820577 | −0.410289 | − | 0.911956i | \(-0.634572\pi\) | ||||
−0.410289 | + | 0.911956i | \(0.634572\pi\) | |||||||
\(992\) | 10.7030 | 0.339821 | ||||||||
\(993\) | −20.5502 | −0.652140 | ||||||||
\(994\) | 56.8486 | 1.80313 | ||||||||
\(995\) | −12.7481 | −0.404142 | ||||||||
\(996\) | −9.36721 | −0.296811 | ||||||||
\(997\) | 51.0358 | 1.61632 | 0.808160 | − | 0.588962i | \(-0.200463\pi\) | ||||
0.808160 | + | 0.588962i | \(0.200463\pi\) | |||||||
\(998\) | −34.6498 | −1.09682 | ||||||||
\(999\) | −5.89679 | −0.186566 |
(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.z.1.11 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.11 | ✓ | 14 | 1.1 | even | 1 | trivial |