Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −3.09428 | −1.78648 | −0.893241 | − | 0.449578i | \(-0.851574\pi\) | ||||
−0.893241 | + | 0.449578i | \(0.851574\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.68879 | 1.20246 | 0.601232 | − | 0.799075i | \(-0.294677\pi\) | ||||
0.601232 | + | 0.799075i | \(0.294677\pi\) | |||||||
\(6\) | −3.09428 | −1.26323 | ||||||||
\(7\) | 2.69798 | 1.01974 | 0.509871 | − | 0.860251i | \(-0.329693\pi\) | ||||
0.509871 | + | 0.860251i | \(0.329693\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.57455 | 2.19152 | ||||||||
\(10\) | 2.68879 | 0.850270 | ||||||||
\(11\) | −5.80467 | −1.75017 | −0.875087 | − | 0.483965i | \(-0.839196\pi\) | ||||
−0.875087 | + | 0.483965i | \(0.839196\pi\) | |||||||
\(12\) | −3.09428 | −0.893241 | ||||||||
\(13\) | −1.02008 | −0.282918 | −0.141459 | − | 0.989944i | \(-0.545179\pi\) | ||||
−0.141459 | + | 0.989944i | \(0.545179\pi\) | |||||||
\(14\) | 2.69798 | 0.721067 | ||||||||
\(15\) | −8.31986 | −2.14818 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.21133 | −1.26393 | −0.631967 | − | 0.774996i | \(-0.717752\pi\) | ||||
−0.631967 | + | 0.774996i | \(0.717752\pi\) | |||||||
\(18\) | 6.57455 | 1.54964 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.68879 | 0.601232 | ||||||||
\(21\) | −8.34831 | −1.82175 | ||||||||
\(22\) | −5.80467 | −1.23756 | ||||||||
\(23\) | 4.91566 | 1.02499 | 0.512493 | − | 0.858691i | \(-0.328722\pi\) | ||||
0.512493 | + | 0.858691i | \(0.328722\pi\) | |||||||
\(24\) | −3.09428 | −0.631617 | ||||||||
\(25\) | 2.22960 | 0.445919 | ||||||||
\(26\) | −1.02008 | −0.200054 | ||||||||
\(27\) | −11.0607 | −2.12862 | ||||||||
\(28\) | 2.69798 | 0.509871 | ||||||||
\(29\) | 3.23208 | 0.600182 | 0.300091 | − | 0.953911i | \(-0.402983\pi\) | ||||
0.300091 | + | 0.953911i | \(0.402983\pi\) | |||||||
\(30\) | −8.31986 | −1.51899 | ||||||||
\(31\) | 6.99206 | 1.25581 | 0.627905 | − | 0.778290i | \(-0.283913\pi\) | ||||
0.627905 | + | 0.778290i | \(0.283913\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 17.9613 | 3.12666 | ||||||||
\(34\) | −5.21133 | −0.893736 | ||||||||
\(35\) | 7.25432 | 1.22620 | ||||||||
\(36\) | 6.57455 | 1.09576 | ||||||||
\(37\) | −9.62772 | −1.58279 | −0.791394 | − | 0.611307i | \(-0.790644\pi\) | ||||
−0.791394 | + | 0.611307i | \(0.790644\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 3.15640 | 0.505429 | ||||||||
\(40\) | 2.68879 | 0.425135 | ||||||||
\(41\) | −5.63748 | −0.880427 | −0.440214 | − | 0.897893i | \(-0.645097\pi\) | ||||
−0.440214 | + | 0.897893i | \(0.645097\pi\) | |||||||
\(42\) | −8.34831 | −1.28817 | ||||||||
\(43\) | −4.61898 | −0.704388 | −0.352194 | − | 0.935927i | \(-0.614564\pi\) | ||||
−0.352194 | + | 0.935927i | \(0.614564\pi\) | |||||||
\(44\) | −5.80467 | −0.875087 | ||||||||
\(45\) | 17.6776 | 2.63522 | ||||||||
\(46\) | 4.91566 | 0.724775 | ||||||||
\(47\) | −2.14466 | −0.312831 | −0.156416 | − | 0.987691i | \(-0.549994\pi\) | ||||
−0.156416 | + | 0.987691i | \(0.549994\pi\) | |||||||
\(48\) | −3.09428 | −0.446620 | ||||||||
\(49\) | 0.279119 | 0.0398741 | ||||||||
\(50\) | 2.22960 | 0.315312 | ||||||||
\(51\) | 16.1253 | 2.25799 | ||||||||
\(52\) | −1.02008 | −0.141459 | ||||||||
\(53\) | −10.0456 | −1.37986 | −0.689932 | − | 0.723874i | \(-0.742360\pi\) | ||||
−0.689932 | + | 0.723874i | \(0.742360\pi\) | |||||||
\(54\) | −11.0607 | −1.50516 | ||||||||
\(55\) | −15.6075 | −2.10452 | ||||||||
\(56\) | 2.69798 | 0.360533 | ||||||||
\(57\) | −3.09428 | −0.409847 | ||||||||
\(58\) | 3.23208 | 0.424393 | ||||||||
\(59\) | 5.68410 | 0.740007 | 0.370003 | − | 0.929030i | \(-0.379357\pi\) | ||||
0.370003 | + | 0.929030i | \(0.379357\pi\) | |||||||
\(60\) | −8.31986 | −1.07409 | ||||||||
\(61\) | −8.48789 | −1.08676 | −0.543381 | − | 0.839486i | \(-0.682856\pi\) | ||||
−0.543381 | + | 0.839486i | \(0.682856\pi\) | |||||||
\(62\) | 6.99206 | 0.887992 | ||||||||
\(63\) | 17.7380 | 2.23478 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.74277 | −0.340199 | ||||||||
\(66\) | 17.9613 | 2.21088 | ||||||||
\(67\) | −4.70299 | −0.574562 | −0.287281 | − | 0.957846i | \(-0.592751\pi\) | ||||
−0.287281 | + | 0.957846i | \(0.592751\pi\) | |||||||
\(68\) | −5.21133 | −0.631967 | ||||||||
\(69\) | −15.2104 | −1.83112 | ||||||||
\(70\) | 7.25432 | 0.867056 | ||||||||
\(71\) | 6.37379 | 0.756430 | 0.378215 | − | 0.925718i | \(-0.376538\pi\) | ||||
0.378215 | + | 0.925718i | \(0.376538\pi\) | |||||||
\(72\) | 6.57455 | 0.774818 | ||||||||
\(73\) | −12.3353 | −1.44374 | −0.721868 | − | 0.692031i | \(-0.756716\pi\) | ||||
−0.721868 | + | 0.692031i | \(0.756716\pi\) | |||||||
\(74\) | −9.62772 | −1.11920 | ||||||||
\(75\) | −6.89899 | −0.796627 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −15.6609 | −1.78473 | ||||||||
\(78\) | 3.15640 | 0.357392 | ||||||||
\(79\) | 2.49251 | 0.280429 | 0.140214 | − | 0.990121i | \(-0.455221\pi\) | ||||
0.140214 | + | 0.990121i | \(0.455221\pi\) | |||||||
\(80\) | 2.68879 | 0.300616 | ||||||||
\(81\) | 14.5011 | 1.61123 | ||||||||
\(82\) | −5.63748 | −0.622556 | ||||||||
\(83\) | −6.10451 | −0.670057 | −0.335028 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335028 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(84\) | −8.34831 | −0.910875 | ||||||||
\(85\) | −14.0122 | −1.51983 | ||||||||
\(86\) | −4.61898 | −0.498078 | ||||||||
\(87\) | −10.0009 | −1.07221 | ||||||||
\(88\) | −5.80467 | −0.618780 | ||||||||
\(89\) | −2.99680 | −0.317660 | −0.158830 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158830 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(90\) | 17.6776 | 1.86338 | ||||||||
\(91\) | −2.75215 | −0.288504 | ||||||||
\(92\) | 4.91566 | 0.512493 | ||||||||
\(93\) | −21.6354 | −2.24348 | ||||||||
\(94\) | −2.14466 | −0.221205 | ||||||||
\(95\) | 2.68879 | 0.275864 | ||||||||
\(96\) | −3.09428 | −0.315808 | ||||||||
\(97\) | 4.49014 | 0.455904 | 0.227952 | − | 0.973672i | \(-0.426797\pi\) | ||||
0.227952 | + | 0.973672i | \(0.426797\pi\) | |||||||
\(98\) | 0.279119 | 0.0281953 | ||||||||
\(99\) | −38.1631 | −3.83554 | ||||||||
\(100\) | 2.22960 | 0.222960 | ||||||||
\(101\) | 6.09662 | 0.606637 | 0.303318 | − | 0.952889i | \(-0.401905\pi\) | ||||
0.303318 | + | 0.952889i | \(0.401905\pi\) | |||||||
\(102\) | 16.1253 | 1.59664 | ||||||||
\(103\) | 2.01258 | 0.198306 | 0.0991529 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991529 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(104\) | −1.02008 | −0.100027 | ||||||||
\(105\) | −22.4469 | −2.19059 | ||||||||
\(106\) | −10.0456 | −0.975711 | ||||||||
\(107\) | 2.95811 | 0.285971 | 0.142985 | − | 0.989725i | \(-0.454330\pi\) | ||||
0.142985 | + | 0.989725i | \(0.454330\pi\) | |||||||
\(108\) | −11.0607 | −1.06431 | ||||||||
\(109\) | 12.9724 | 1.24253 | 0.621264 | − | 0.783601i | \(-0.286619\pi\) | ||||
0.621264 | + | 0.783601i | \(0.286619\pi\) | |||||||
\(110\) | −15.6075 | −1.48812 | ||||||||
\(111\) | 29.7908 | 2.82762 | ||||||||
\(112\) | 2.69798 | 0.254936 | ||||||||
\(113\) | −11.0538 | −1.03985 | −0.519927 | − | 0.854211i | \(-0.674041\pi\) | ||||
−0.519927 | + | 0.854211i | \(0.674041\pi\) | |||||||
\(114\) | −3.09428 | −0.289806 | ||||||||
\(115\) | 13.2172 | 1.23251 | ||||||||
\(116\) | 3.23208 | 0.300091 | ||||||||
\(117\) | −6.70655 | −0.620021 | ||||||||
\(118\) | 5.68410 | 0.523264 | ||||||||
\(119\) | −14.0601 | −1.28889 | ||||||||
\(120\) | −8.31986 | −0.759496 | ||||||||
\(121\) | 22.6942 | 2.06311 | ||||||||
\(122\) | −8.48789 | −0.768457 | ||||||||
\(123\) | 17.4439 | 1.57287 | ||||||||
\(124\) | 6.99206 | 0.627905 | ||||||||
\(125\) | −7.44904 | −0.666262 | ||||||||
\(126\) | 17.7380 | 1.58023 | ||||||||
\(127\) | −6.99251 | −0.620485 | −0.310243 | − | 0.950657i | \(-0.600410\pi\) | ||||
−0.310243 | + | 0.950657i | \(0.600410\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 14.2924 | 1.25838 | ||||||||
\(130\) | −2.74277 | −0.240557 | ||||||||
\(131\) | −21.2407 | −1.85581 | −0.927903 | − | 0.372821i | \(-0.878391\pi\) | ||||
−0.927903 | + | 0.372821i | \(0.878391\pi\) | |||||||
\(132\) | 17.9613 | 1.56333 | ||||||||
\(133\) | 2.69798 | 0.233945 | ||||||||
\(134\) | −4.70299 | −0.406277 | ||||||||
\(135\) | −29.7398 | −2.55959 | ||||||||
\(136\) | −5.21133 | −0.446868 | ||||||||
\(137\) | 16.9283 | 1.44629 | 0.723143 | − | 0.690699i | \(-0.242697\pi\) | ||||
0.723143 | + | 0.690699i | \(0.242697\pi\) | |||||||
\(138\) | −15.2104 | −1.29480 | ||||||||
\(139\) | 0.538672 | 0.0456896 | 0.0228448 | − | 0.999739i | \(-0.492728\pi\) | ||||
0.0228448 | + | 0.999739i | \(0.492728\pi\) | |||||||
\(140\) | 7.25432 | 0.613102 | ||||||||
\(141\) | 6.63618 | 0.558867 | ||||||||
\(142\) | 6.37379 | 0.534877 | ||||||||
\(143\) | 5.92121 | 0.495157 | ||||||||
\(144\) | 6.57455 | 0.547879 | ||||||||
\(145\) | 8.69038 | 0.721697 | ||||||||
\(146\) | −12.3353 | −1.02088 | ||||||||
\(147\) | −0.863671 | −0.0712344 | ||||||||
\(148\) | −9.62772 | −0.791394 | ||||||||
\(149\) | −22.0651 | −1.80764 | −0.903821 | − | 0.427910i | \(-0.859250\pi\) | ||||
−0.903821 | + | 0.427910i | \(0.859250\pi\) | |||||||
\(150\) | −6.89899 | −0.563300 | ||||||||
\(151\) | 11.2101 | 0.912263 | 0.456131 | − | 0.889912i | \(-0.349235\pi\) | ||||
0.456131 | + | 0.889912i | \(0.349235\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −34.2622 | −2.76993 | ||||||||
\(154\) | −15.6609 | −1.26199 | ||||||||
\(155\) | 18.8002 | 1.51007 | ||||||||
\(156\) | 3.15640 | 0.252714 | ||||||||
\(157\) | −3.27420 | −0.261309 | −0.130655 | − | 0.991428i | \(-0.541708\pi\) | ||||
−0.130655 | + | 0.991428i | \(0.541708\pi\) | |||||||
\(158\) | 2.49251 | 0.198293 | ||||||||
\(159\) | 31.0838 | 2.46510 | ||||||||
\(160\) | 2.68879 | 0.212568 | ||||||||
\(161\) | 13.2624 | 1.04522 | ||||||||
\(162\) | 14.5011 | 1.13931 | ||||||||
\(163\) | −21.6594 | −1.69649 | −0.848247 | − | 0.529601i | \(-0.822342\pi\) | ||||
−0.848247 | + | 0.529601i | \(0.822342\pi\) | |||||||
\(164\) | −5.63748 | −0.440214 | ||||||||
\(165\) | 48.2941 | 3.75969 | ||||||||
\(166\) | −6.10451 | −0.473802 | ||||||||
\(167\) | 18.4021 | 1.42400 | 0.711998 | − | 0.702181i | \(-0.247790\pi\) | ||||
0.711998 | + | 0.702181i | \(0.247790\pi\) | |||||||
\(168\) | −8.34831 | −0.644086 | ||||||||
\(169\) | −11.9594 | −0.919957 | ||||||||
\(170\) | −14.0122 | −1.07468 | ||||||||
\(171\) | 6.57455 | 0.502769 | ||||||||
\(172\) | −4.61898 | −0.352194 | ||||||||
\(173\) | 24.7440 | 1.88125 | 0.940625 | − | 0.339448i | \(-0.110240\pi\) | ||||
0.940625 | + | 0.339448i | \(0.110240\pi\) | |||||||
\(174\) | −10.0009 | −0.758170 | ||||||||
\(175\) | 6.01541 | 0.454723 | ||||||||
\(176\) | −5.80467 | −0.437544 | ||||||||
\(177\) | −17.5882 | −1.32201 | ||||||||
\(178\) | −2.99680 | −0.224620 | ||||||||
\(179\) | −23.0901 | −1.72584 | −0.862918 | − | 0.505343i | \(-0.831366\pi\) | ||||
−0.862918 | + | 0.505343i | \(0.831366\pi\) | |||||||
\(180\) | 17.6776 | 1.31761 | ||||||||
\(181\) | 5.37021 | 0.399165 | 0.199582 | − | 0.979881i | \(-0.436041\pi\) | ||||
0.199582 | + | 0.979881i | \(0.436041\pi\) | |||||||
\(182\) | −2.75215 | −0.204003 | ||||||||
\(183\) | 26.2639 | 1.94148 | ||||||||
\(184\) | 4.91566 | 0.362387 | ||||||||
\(185\) | −25.8869 | −1.90324 | ||||||||
\(186\) | −21.6354 | −1.58638 | ||||||||
\(187\) | 30.2501 | 2.21210 | ||||||||
\(188\) | −2.14466 | −0.156416 | ||||||||
\(189\) | −29.8415 | −2.17065 | ||||||||
\(190\) | 2.68879 | 0.195065 | ||||||||
\(191\) | 3.26272 | 0.236082 | 0.118041 | − | 0.993009i | \(-0.462339\pi\) | ||||
0.118041 | + | 0.993009i | \(0.462339\pi\) | |||||||
\(192\) | −3.09428 | −0.223310 | ||||||||
\(193\) | 5.16392 | 0.371707 | 0.185853 | − | 0.982577i | \(-0.440495\pi\) | ||||
0.185853 | + | 0.982577i | \(0.440495\pi\) | |||||||
\(194\) | 4.49014 | 0.322373 | ||||||||
\(195\) | 8.48690 | 0.607760 | ||||||||
\(196\) | 0.279119 | 0.0199371 | ||||||||
\(197\) | −1.77258 | −0.126291 | −0.0631455 | − | 0.998004i | \(-0.520113\pi\) | ||||
−0.0631455 | + | 0.998004i | \(0.520113\pi\) | |||||||
\(198\) | −38.1631 | −2.71213 | ||||||||
\(199\) | 3.95646 | 0.280466 | 0.140233 | − | 0.990119i | \(-0.455215\pi\) | ||||
0.140233 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(200\) | 2.22960 | 0.157656 | ||||||||
\(201\) | 14.5524 | 1.02644 | ||||||||
\(202\) | 6.09662 | 0.428957 | ||||||||
\(203\) | 8.72009 | 0.612031 | ||||||||
\(204\) | 16.1253 | 1.12900 | ||||||||
\(205\) | −15.1580 | −1.05868 | ||||||||
\(206\) | 2.01258 | 0.140223 | ||||||||
\(207\) | 32.3183 | 2.24627 | ||||||||
\(208\) | −1.02008 | −0.0707296 | ||||||||
\(209\) | −5.80467 | −0.401518 | ||||||||
\(210\) | −22.4469 | −1.54898 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −10.0456 | −0.689932 | ||||||||
\(213\) | −19.7223 | −1.35135 | ||||||||
\(214\) | 2.95811 | 0.202212 | ||||||||
\(215\) | −12.4195 | −0.847001 | ||||||||
\(216\) | −11.0607 | −0.752582 | ||||||||
\(217\) | 18.8645 | 1.28060 | ||||||||
\(218\) | 12.9724 | 0.878600 | ||||||||
\(219\) | 38.1688 | 2.57921 | ||||||||
\(220\) | −15.6075 | −1.05226 | ||||||||
\(221\) | 5.31596 | 0.357590 | ||||||||
\(222\) | 29.7908 | 1.99943 | ||||||||
\(223\) | −11.7745 | −0.788478 | −0.394239 | − | 0.919008i | \(-0.628992\pi\) | ||||
−0.394239 | + | 0.919008i | \(0.628992\pi\) | |||||||
\(224\) | 2.69798 | 0.180267 | ||||||||
\(225\) | 14.6586 | 0.977240 | ||||||||
\(226\) | −11.0538 | −0.735287 | ||||||||
\(227\) | 20.7359 | 1.37629 | 0.688145 | − | 0.725573i | \(-0.258425\pi\) | ||||
0.688145 | + | 0.725573i | \(0.258425\pi\) | |||||||
\(228\) | −3.09428 | −0.204924 | ||||||||
\(229\) | −7.70226 | −0.508979 | −0.254490 | − | 0.967075i | \(-0.581907\pi\) | ||||
−0.254490 | + | 0.967075i | \(0.581907\pi\) | |||||||
\(230\) | 13.2172 | 0.871515 | ||||||||
\(231\) | 48.4592 | 3.18838 | ||||||||
\(232\) | 3.23208 | 0.212196 | ||||||||
\(233\) | −13.0991 | −0.858148 | −0.429074 | − | 0.903269i | \(-0.641160\pi\) | ||||
−0.429074 | + | 0.903269i | \(0.641160\pi\) | |||||||
\(234\) | −6.70655 | −0.438421 | ||||||||
\(235\) | −5.76655 | −0.376168 | ||||||||
\(236\) | 5.68410 | 0.370003 | ||||||||
\(237\) | −7.71250 | −0.500981 | ||||||||
\(238\) | −14.0601 | −0.911380 | ||||||||
\(239\) | 3.58986 | 0.232209 | 0.116104 | − | 0.993237i | \(-0.462959\pi\) | ||||
0.116104 | + | 0.993237i | \(0.462959\pi\) | |||||||
\(240\) | −8.31986 | −0.537045 | ||||||||
\(241\) | −20.7327 | −1.33551 | −0.667756 | − | 0.744380i | \(-0.732745\pi\) | ||||
−0.667756 | + | 0.744380i | \(0.732745\pi\) | |||||||
\(242\) | 22.6942 | 1.45884 | ||||||||
\(243\) | −11.6884 | −0.749811 | ||||||||
\(244\) | −8.48789 | −0.543381 | ||||||||
\(245\) | 0.750492 | 0.0479472 | ||||||||
\(246\) | 17.4439 | 1.11219 | ||||||||
\(247\) | −1.02008 | −0.0649059 | ||||||||
\(248\) | 6.99206 | 0.443996 | ||||||||
\(249\) | 18.8890 | 1.19704 | ||||||||
\(250\) | −7.44904 | −0.471118 | ||||||||
\(251\) | 20.0261 | 1.26404 | 0.632018 | − | 0.774953i | \(-0.282227\pi\) | ||||
0.632018 | + | 0.774953i | \(0.282227\pi\) | |||||||
\(252\) | 17.7380 | 1.11739 | ||||||||
\(253\) | −28.5338 | −1.79390 | ||||||||
\(254\) | −6.99251 | −0.438749 | ||||||||
\(255\) | 43.3576 | 2.71516 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.5611 | −1.28257 | −0.641283 | − | 0.767304i | \(-0.721598\pi\) | ||||
−0.641283 | + | 0.767304i | \(0.721598\pi\) | |||||||
\(258\) | 14.2924 | 0.889807 | ||||||||
\(259\) | −25.9754 | −1.61403 | ||||||||
\(260\) | −2.74277 | −0.170100 | ||||||||
\(261\) | 21.2495 | 1.31531 | ||||||||
\(262\) | −21.2407 | −1.31225 | ||||||||
\(263\) | 18.8516 | 1.16244 | 0.581219 | − | 0.813747i | \(-0.302576\pi\) | ||||
0.581219 | + | 0.813747i | \(0.302576\pi\) | |||||||
\(264\) | 17.9613 | 1.10544 | ||||||||
\(265\) | −27.0104 | −1.65924 | ||||||||
\(266\) | 2.69798 | 0.165424 | ||||||||
\(267\) | 9.27294 | 0.567495 | ||||||||
\(268\) | −4.70299 | −0.287281 | ||||||||
\(269\) | 12.3597 | 0.753585 | 0.376792 | − | 0.926298i | \(-0.377027\pi\) | ||||
0.376792 | + | 0.926298i | \(0.377027\pi\) | |||||||
\(270\) | −29.7398 | −1.80991 | ||||||||
\(271\) | −9.97986 | −0.606233 | −0.303117 | − | 0.952953i | \(-0.598027\pi\) | ||||
−0.303117 | + | 0.952953i | \(0.598027\pi\) | |||||||
\(272\) | −5.21133 | −0.315983 | ||||||||
\(273\) | 8.51592 | 0.515407 | ||||||||
\(274\) | 16.9283 | 1.02268 | ||||||||
\(275\) | −12.9421 | −0.780436 | ||||||||
\(276\) | −15.2104 | −0.915560 | ||||||||
\(277\) | −16.2948 | −0.979059 | −0.489530 | − | 0.871987i | \(-0.662832\pi\) | ||||
−0.489530 | + | 0.871987i | \(0.662832\pi\) | |||||||
\(278\) | 0.538672 | 0.0323074 | ||||||||
\(279\) | 45.9696 | 2.75213 | ||||||||
\(280\) | 7.25432 | 0.433528 | ||||||||
\(281\) | 7.82076 | 0.466547 | 0.233274 | − | 0.972411i | \(-0.425056\pi\) | ||||
0.233274 | + | 0.972411i | \(0.425056\pi\) | |||||||
\(282\) | 6.63618 | 0.395179 | ||||||||
\(283\) | −16.2700 | −0.967153 | −0.483577 | − | 0.875302i | \(-0.660663\pi\) | ||||
−0.483577 | + | 0.875302i | \(0.660663\pi\) | |||||||
\(284\) | 6.37379 | 0.378215 | ||||||||
\(285\) | −8.31986 | −0.492826 | ||||||||
\(286\) | 5.92121 | 0.350129 | ||||||||
\(287\) | −15.2098 | −0.897809 | ||||||||
\(288\) | 6.57455 | 0.387409 | ||||||||
\(289\) | 10.1580 | 0.597527 | ||||||||
\(290\) | 8.69038 | 0.510317 | ||||||||
\(291\) | −13.8937 | −0.814465 | ||||||||
\(292\) | −12.3353 | −0.721868 | ||||||||
\(293\) | 4.48833 | 0.262211 | 0.131106 | − | 0.991368i | \(-0.458147\pi\) | ||||
0.131106 | + | 0.991368i | \(0.458147\pi\) | |||||||
\(294\) | −0.863671 | −0.0503703 | ||||||||
\(295\) | 15.2834 | 0.889831 | ||||||||
\(296\) | −9.62772 | −0.559600 | ||||||||
\(297\) | 64.2035 | 3.72546 | ||||||||
\(298\) | −22.0651 | −1.27820 | ||||||||
\(299\) | −5.01435 | −0.289987 | ||||||||
\(300\) | −6.89899 | −0.398313 | ||||||||
\(301\) | −12.4619 | −0.718294 | ||||||||
\(302\) | 11.2101 | 0.645067 | ||||||||
\(303\) | −18.8646 | −1.08375 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −22.8222 | −1.30679 | ||||||||
\(306\) | −34.2622 | −1.95864 | ||||||||
\(307\) | 11.5583 | 0.659666 | 0.329833 | − | 0.944039i | \(-0.393008\pi\) | ||||
0.329833 | + | 0.944039i | \(0.393008\pi\) | |||||||
\(308\) | −15.6609 | −0.892363 | ||||||||
\(309\) | −6.22749 | −0.354270 | ||||||||
\(310\) | 18.8002 | 1.06778 | ||||||||
\(311\) | 11.3152 | 0.641629 | 0.320814 | − | 0.947142i | \(-0.396043\pi\) | ||||
0.320814 | + | 0.947142i | \(0.396043\pi\) | |||||||
\(312\) | 3.15640 | 0.178696 | ||||||||
\(313\) | −22.1917 | −1.25435 | −0.627174 | − | 0.778879i | \(-0.715789\pi\) | ||||
−0.627174 | + | 0.778879i | \(0.715789\pi\) | |||||||
\(314\) | −3.27420 | −0.184774 | ||||||||
\(315\) | 47.6939 | 2.68725 | ||||||||
\(316\) | 2.49251 | 0.140214 | ||||||||
\(317\) | 10.0320 | 0.563453 | 0.281726 | − | 0.959495i | \(-0.409093\pi\) | ||||
0.281726 | + | 0.959495i | \(0.409093\pi\) | |||||||
\(318\) | 31.0838 | 1.74309 | ||||||||
\(319\) | −18.7612 | −1.05042 | ||||||||
\(320\) | 2.68879 | 0.150308 | ||||||||
\(321\) | −9.15320 | −0.510882 | ||||||||
\(322\) | 13.2624 | 0.739083 | ||||||||
\(323\) | −5.21133 | −0.289966 | ||||||||
\(324\) | 14.5011 | 0.805616 | ||||||||
\(325\) | −2.27436 | −0.126159 | ||||||||
\(326\) | −21.6594 | −1.19960 | ||||||||
\(327\) | −40.1401 | −2.21975 | ||||||||
\(328\) | −5.63748 | −0.311278 | ||||||||
\(329\) | −5.78627 | −0.319007 | ||||||||
\(330\) | 48.2941 | 2.65850 | ||||||||
\(331\) | 6.12083 | 0.336431 | 0.168216 | − | 0.985750i | \(-0.446200\pi\) | ||||
0.168216 | + | 0.985750i | \(0.446200\pi\) | |||||||
\(332\) | −6.10451 | −0.335028 | ||||||||
\(333\) | −63.2979 | −3.46871 | ||||||||
\(334\) | 18.4021 | 1.00692 | ||||||||
\(335\) | −12.6454 | −0.690890 | ||||||||
\(336\) | −8.34831 | −0.455438 | ||||||||
\(337\) | −30.1681 | −1.64336 | −0.821681 | − | 0.569948i | \(-0.806963\pi\) | ||||
−0.821681 | + | 0.569948i | \(0.806963\pi\) | |||||||
\(338\) | −11.9594 | −0.650508 | ||||||||
\(339\) | 34.2035 | 1.85768 | ||||||||
\(340\) | −14.0122 | −0.759917 | ||||||||
\(341\) | −40.5866 | −2.19789 | ||||||||
\(342\) | 6.57455 | 0.355511 | ||||||||
\(343\) | −18.1328 | −0.979081 | ||||||||
\(344\) | −4.61898 | −0.249039 | ||||||||
\(345\) | −40.8976 | −2.20185 | ||||||||
\(346\) | 24.7440 | 1.33024 | ||||||||
\(347\) | −6.59271 | −0.353915 | −0.176958 | − | 0.984218i | \(-0.556626\pi\) | ||||
−0.176958 | + | 0.984218i | \(0.556626\pi\) | |||||||
\(348\) | −10.0009 | −0.536107 | ||||||||
\(349\) | −8.52462 | −0.456312 | −0.228156 | − | 0.973625i | \(-0.573270\pi\) | ||||
−0.228156 | + | 0.973625i | \(0.573270\pi\) | |||||||
\(350\) | 6.01541 | 0.321537 | ||||||||
\(351\) | 11.2827 | 0.602227 | ||||||||
\(352\) | −5.80467 | −0.309390 | ||||||||
\(353\) | −10.3889 | −0.552947 | −0.276474 | − | 0.961021i | \(-0.589166\pi\) | ||||
−0.276474 | + | 0.961021i | \(0.589166\pi\) | |||||||
\(354\) | −17.5882 | −0.934801 | ||||||||
\(355\) | 17.1378 | 0.909579 | ||||||||
\(356\) | −2.99680 | −0.158830 | ||||||||
\(357\) | 43.5058 | 2.30257 | ||||||||
\(358\) | −23.0901 | −1.22035 | ||||||||
\(359\) | 25.3768 | 1.33933 | 0.669667 | − | 0.742661i | \(-0.266437\pi\) | ||||
0.669667 | + | 0.742661i | \(0.266437\pi\) | |||||||
\(360\) | 17.6776 | 0.931691 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.37021 | 0.282252 | ||||||||
\(363\) | −70.2222 | −3.68571 | ||||||||
\(364\) | −2.75215 | −0.144252 | ||||||||
\(365\) | −33.1670 | −1.73604 | ||||||||
\(366\) | 26.2639 | 1.37283 | ||||||||
\(367\) | 14.9400 | 0.779864 | 0.389932 | − | 0.920844i | \(-0.372499\pi\) | ||||
0.389932 | + | 0.920844i | \(0.372499\pi\) | |||||||
\(368\) | 4.91566 | 0.256247 | ||||||||
\(369\) | −37.0639 | −1.92947 | ||||||||
\(370\) | −25.8869 | −1.34580 | ||||||||
\(371\) | −27.1028 | −1.40711 | ||||||||
\(372\) | −21.6354 | −1.12174 | ||||||||
\(373\) | −18.2635 | −0.945650 | −0.472825 | − | 0.881156i | \(-0.656766\pi\) | ||||
−0.472825 | + | 0.881156i | \(0.656766\pi\) | |||||||
\(374\) | 30.2501 | 1.56419 | ||||||||
\(375\) | 23.0494 | 1.19027 | ||||||||
\(376\) | −2.14466 | −0.110603 | ||||||||
\(377\) | −3.29697 | −0.169802 | ||||||||
\(378\) | −29.8415 | −1.53488 | ||||||||
\(379\) | −15.4863 | −0.795477 | −0.397738 | − | 0.917499i | \(-0.630205\pi\) | ||||
−0.397738 | + | 0.917499i | \(0.630205\pi\) | |||||||
\(380\) | 2.68879 | 0.137932 | ||||||||
\(381\) | 21.6368 | 1.10849 | ||||||||
\(382\) | 3.26272 | 0.166935 | ||||||||
\(383\) | 8.99696 | 0.459723 | 0.229862 | − | 0.973223i | \(-0.426173\pi\) | ||||
0.229862 | + | 0.973223i | \(0.426173\pi\) | |||||||
\(384\) | −3.09428 | −0.157904 | ||||||||
\(385\) | −42.1089 | −2.14607 | ||||||||
\(386\) | 5.16392 | 0.262836 | ||||||||
\(387\) | −30.3677 | −1.54368 | ||||||||
\(388\) | 4.49014 | 0.227952 | ||||||||
\(389\) | 22.4887 | 1.14022 | 0.570112 | − | 0.821567i | \(-0.306900\pi\) | ||||
0.570112 | + | 0.821567i | \(0.306900\pi\) | |||||||
\(390\) | 8.48690 | 0.429751 | ||||||||
\(391\) | −25.6171 | −1.29551 | ||||||||
\(392\) | 0.279119 | 0.0140976 | ||||||||
\(393\) | 65.7246 | 3.31537 | ||||||||
\(394\) | −1.77258 | −0.0893013 | ||||||||
\(395\) | 6.70183 | 0.337205 | ||||||||
\(396\) | −38.1631 | −1.91777 | ||||||||
\(397\) | 13.8583 | 0.695526 | 0.347763 | − | 0.937582i | \(-0.386941\pi\) | ||||
0.347763 | + | 0.937582i | \(0.386941\pi\) | |||||||
\(398\) | 3.95646 | 0.198319 | ||||||||
\(399\) | −8.34831 | −0.417938 | ||||||||
\(400\) | 2.22960 | 0.111480 | ||||||||
\(401\) | −16.8575 | −0.841824 | −0.420912 | − | 0.907101i | \(-0.638290\pi\) | ||||
−0.420912 | + | 0.907101i | \(0.638290\pi\) | |||||||
\(402\) | 14.5524 | 0.725806 | ||||||||
\(403\) | −7.13243 | −0.355292 | ||||||||
\(404\) | 6.09662 | 0.303318 | ||||||||
\(405\) | 38.9904 | 1.93745 | ||||||||
\(406\) | 8.72009 | 0.432771 | ||||||||
\(407\) | 55.8858 | 2.77015 | ||||||||
\(408\) | 16.1253 | 0.798321 | ||||||||
\(409\) | 10.9497 | 0.541430 | 0.270715 | − | 0.962660i | \(-0.412740\pi\) | ||||
0.270715 | + | 0.962660i | \(0.412740\pi\) | |||||||
\(410\) | −15.1580 | −0.748601 | ||||||||
\(411\) | −52.3810 | −2.58376 | ||||||||
\(412\) | 2.01258 | 0.0991529 | ||||||||
\(413\) | 15.3356 | 0.754616 | ||||||||
\(414\) | 32.3183 | 1.58836 | ||||||||
\(415\) | −16.4137 | −0.805719 | ||||||||
\(416\) | −1.02008 | −0.0500134 | ||||||||
\(417\) | −1.66680 | −0.0816236 | ||||||||
\(418\) | −5.80467 | −0.283916 | ||||||||
\(419\) | 10.0233 | 0.489668 | 0.244834 | − | 0.969565i | \(-0.421266\pi\) | ||||
0.244834 | + | 0.969565i | \(0.421266\pi\) | |||||||
\(420\) | −22.4469 | −1.09529 | ||||||||
\(421\) | 10.6602 | 0.519548 | 0.259774 | − | 0.965669i | \(-0.416352\pi\) | ||||
0.259774 | + | 0.965669i | \(0.416352\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −14.1002 | −0.685575 | ||||||||
\(424\) | −10.0456 | −0.487856 | ||||||||
\(425\) | −11.6192 | −0.563612 | ||||||||
\(426\) | −19.7223 | −0.955547 | ||||||||
\(427\) | −22.9002 | −1.10822 | ||||||||
\(428\) | 2.95811 | 0.142985 | ||||||||
\(429\) | −18.3219 | −0.884588 | ||||||||
\(430\) | −12.4195 | −0.598920 | ||||||||
\(431\) | 29.9005 | 1.44025 | 0.720127 | − | 0.693842i | \(-0.244084\pi\) | ||||
0.720127 | + | 0.693842i | \(0.244084\pi\) | |||||||
\(432\) | −11.0607 | −0.532156 | ||||||||
\(433\) | −2.10175 | −0.101004 | −0.0505018 | − | 0.998724i | \(-0.516082\pi\) | ||||
−0.0505018 | + | 0.998724i | \(0.516082\pi\) | |||||||
\(434\) | 18.8645 | 0.905523 | ||||||||
\(435\) | −26.8904 | −1.28930 | ||||||||
\(436\) | 12.9724 | 0.621264 | ||||||||
\(437\) | 4.91566 | 0.235148 | ||||||||
\(438\) | 38.1688 | 1.82377 | ||||||||
\(439\) | −29.7140 | −1.41817 | −0.709086 | − | 0.705122i | \(-0.750892\pi\) | ||||
−0.709086 | + | 0.705122i | \(0.750892\pi\) | |||||||
\(440\) | −15.6075 | −0.744061 | ||||||||
\(441\) | 1.83508 | 0.0873848 | ||||||||
\(442\) | 5.31596 | 0.252854 | ||||||||
\(443\) | −29.1694 | −1.38588 | −0.692941 | − | 0.720994i | \(-0.743685\pi\) | ||||
−0.692941 | + | 0.720994i | \(0.743685\pi\) | |||||||
\(444\) | 29.7908 | 1.41381 | ||||||||
\(445\) | −8.05778 | −0.381975 | ||||||||
\(446\) | −11.7745 | −0.557538 | ||||||||
\(447\) | 68.2755 | 3.22932 | ||||||||
\(448\) | 2.69798 | 0.127468 | ||||||||
\(449\) | −21.3994 | −1.00990 | −0.504950 | − | 0.863148i | \(-0.668489\pi\) | ||||
−0.504950 | + | 0.863148i | \(0.668489\pi\) | |||||||
\(450\) | 14.6586 | 0.691013 | ||||||||
\(451\) | 32.7238 | 1.54090 | ||||||||
\(452\) | −11.0538 | −0.519927 | ||||||||
\(453\) | −34.6871 | −1.62974 | ||||||||
\(454\) | 20.7359 | 0.973184 | ||||||||
\(455\) | −7.39996 | −0.346915 | ||||||||
\(456\) | −3.09428 | −0.144903 | ||||||||
\(457\) | 25.2187 | 1.17968 | 0.589841 | − | 0.807519i | \(-0.299190\pi\) | ||||
0.589841 | + | 0.807519i | \(0.299190\pi\) | |||||||
\(458\) | −7.70226 | −0.359903 | ||||||||
\(459\) | 57.6407 | 2.69044 | ||||||||
\(460\) | 13.2172 | 0.616254 | ||||||||
\(461\) | −18.4586 | −0.859703 | −0.429852 | − | 0.902900i | \(-0.641434\pi\) | ||||
−0.429852 | + | 0.902900i | \(0.641434\pi\) | |||||||
\(462\) | 48.4592 | 2.25453 | ||||||||
\(463\) | −30.6189 | −1.42298 | −0.711491 | − | 0.702695i | \(-0.751980\pi\) | ||||
−0.711491 | + | 0.702695i | \(0.751980\pi\) | |||||||
\(464\) | 3.23208 | 0.150045 | ||||||||
\(465\) | −58.1730 | −2.69771 | ||||||||
\(466\) | −13.0991 | −0.606803 | ||||||||
\(467\) | −20.9490 | −0.969403 | −0.484701 | − | 0.874680i | \(-0.661072\pi\) | ||||
−0.484701 | + | 0.874680i | \(0.661072\pi\) | |||||||
\(468\) | −6.70655 | −0.310010 | ||||||||
\(469\) | −12.6886 | −0.585905 | ||||||||
\(470\) | −5.76655 | −0.265991 | ||||||||
\(471\) | 10.1313 | 0.466824 | ||||||||
\(472\) | 5.68410 | 0.261632 | ||||||||
\(473\) | 26.8117 | 1.23280 | ||||||||
\(474\) | −7.71250 | −0.354247 | ||||||||
\(475\) | 2.22960 | 0.102301 | ||||||||
\(476\) | −14.0601 | −0.644443 | ||||||||
\(477\) | −66.0451 | −3.02400 | ||||||||
\(478\) | 3.58986 | 0.164196 | ||||||||
\(479\) | −18.1492 | −0.829258 | −0.414629 | − | 0.909990i | \(-0.636089\pi\) | ||||
−0.414629 | + | 0.909990i | \(0.636089\pi\) | |||||||
\(480\) | −8.31986 | −0.379748 | ||||||||
\(481\) | 9.82101 | 0.447800 | ||||||||
\(482\) | −20.7327 | −0.944350 | ||||||||
\(483\) | −41.0375 | −1.86727 | ||||||||
\(484\) | 22.6942 | 1.03156 | ||||||||
\(485\) | 12.0730 | 0.548208 | ||||||||
\(486\) | −11.6884 | −0.530196 | ||||||||
\(487\) | −12.2598 | −0.555546 | −0.277773 | − | 0.960647i | \(-0.589596\pi\) | ||||
−0.277773 | + | 0.960647i | \(0.589596\pi\) | |||||||
\(488\) | −8.48789 | −0.384229 | ||||||||
\(489\) | 67.0201 | 3.03076 | ||||||||
\(490\) | 0.750492 | 0.0339038 | ||||||||
\(491\) | 0.409512 | 0.0184810 | 0.00924052 | − | 0.999957i | \(-0.497059\pi\) | ||||
0.00924052 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(492\) | 17.4439 | 0.786434 | ||||||||
\(493\) | −16.8434 | −0.758590 | ||||||||
\(494\) | −1.02008 | −0.0458954 | ||||||||
\(495\) | −102.613 | −4.61210 | ||||||||
\(496\) | 6.99206 | 0.313953 | ||||||||
\(497\) | 17.1964 | 0.771363 | ||||||||
\(498\) | 18.8890 | 0.846438 | ||||||||
\(499\) | 19.8019 | 0.886453 | 0.443227 | − | 0.896410i | \(-0.353834\pi\) | ||||
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(500\) | −7.44904 | −0.333131 | ||||||||
\(501\) | −56.9412 | −2.54394 | ||||||||
\(502\) | 20.0261 | 0.893809 | ||||||||
\(503\) | −8.25561 | −0.368100 | −0.184050 | − | 0.982917i | \(-0.558921\pi\) | ||||
−0.184050 | + | 0.982917i | \(0.558921\pi\) | |||||||
\(504\) | 17.7380 | 0.790115 | ||||||||
\(505\) | 16.3925 | 0.729459 | ||||||||
\(506\) | −28.5338 | −1.26848 | ||||||||
\(507\) | 37.0058 | 1.64349 | ||||||||
\(508\) | −6.99251 | −0.310243 | ||||||||
\(509\) | −15.8574 | −0.702867 | −0.351433 | − | 0.936213i | \(-0.614306\pi\) | ||||
−0.351433 | + | 0.936213i | \(0.614306\pi\) | |||||||
\(510\) | 43.3576 | 1.91990 | ||||||||
\(511\) | −33.2804 | −1.47224 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −11.0607 | −0.488340 | ||||||||
\(514\) | −20.5611 | −0.906911 | ||||||||
\(515\) | 5.41142 | 0.238456 | ||||||||
\(516\) | 14.2924 | 0.629188 | ||||||||
\(517\) | 12.4491 | 0.547509 | ||||||||
\(518\) | −25.9754 | −1.14129 | ||||||||
\(519\) | −76.5647 | −3.36082 | ||||||||
\(520\) | −2.74277 | −0.120279 | ||||||||
\(521\) | 15.9390 | 0.698302 | 0.349151 | − | 0.937067i | \(-0.386470\pi\) | ||||
0.349151 | + | 0.937067i | \(0.386470\pi\) | |||||||
\(522\) | 21.2495 | 0.930064 | ||||||||
\(523\) | 4.73045 | 0.206848 | 0.103424 | − | 0.994637i | \(-0.467020\pi\) | ||||
0.103424 | + | 0.994637i | \(0.467020\pi\) | |||||||
\(524\) | −21.2407 | −0.927903 | ||||||||
\(525\) | −18.6134 | −0.812354 | ||||||||
\(526\) | 18.8516 | 0.821968 | ||||||||
\(527\) | −36.4379 | −1.58726 | ||||||||
\(528\) | 17.9613 | 0.781664 | ||||||||
\(529\) | 1.16372 | 0.0505965 | ||||||||
\(530\) | −27.0104 | −1.17326 | ||||||||
\(531\) | 37.3704 | 1.62174 | ||||||||
\(532\) | 2.69798 | 0.116972 | ||||||||
\(533\) | 5.75067 | 0.249089 | ||||||||
\(534\) | 9.27294 | 0.401279 | ||||||||
\(535\) | 7.95373 | 0.343870 | ||||||||
\(536\) | −4.70299 | −0.203138 | ||||||||
\(537\) | 71.4472 | 3.08318 | ||||||||
\(538\) | 12.3597 | 0.532865 | ||||||||
\(539\) | −1.62019 | −0.0697867 | ||||||||
\(540\) | −29.7398 | −1.27980 | ||||||||
\(541\) | −28.9967 | −1.24666 | −0.623332 | − | 0.781957i | \(-0.714221\pi\) | ||||
−0.623332 | + | 0.781957i | \(0.714221\pi\) | |||||||
\(542\) | −9.97986 | −0.428672 | ||||||||
\(543\) | −16.6169 | −0.713100 | ||||||||
\(544\) | −5.21133 | −0.223434 | ||||||||
\(545\) | 34.8800 | 1.49410 | ||||||||
\(546\) | 8.51592 | 0.364448 | ||||||||
\(547\) | −28.4124 | −1.21483 | −0.607414 | − | 0.794385i | \(-0.707793\pi\) | ||||
−0.607414 | + | 0.794385i | \(0.707793\pi\) | |||||||
\(548\) | 16.9283 | 0.723143 | ||||||||
\(549\) | −55.8040 | −2.38166 | ||||||||
\(550\) | −12.9421 | −0.551852 | ||||||||
\(551\) | 3.23208 | 0.137691 | ||||||||
\(552\) | −15.2104 | −0.647398 | ||||||||
\(553\) | 6.72474 | 0.285965 | ||||||||
\(554\) | −16.2948 | −0.692300 | ||||||||
\(555\) | 80.1013 | 3.40011 | ||||||||
\(556\) | 0.538672 | 0.0228448 | ||||||||
\(557\) | 34.4257 | 1.45866 | 0.729331 | − | 0.684161i | \(-0.239831\pi\) | ||||
0.729331 | + | 0.684161i | \(0.239831\pi\) | |||||||
\(558\) | 45.9696 | 1.94605 | ||||||||
\(559\) | 4.71172 | 0.199284 | ||||||||
\(560\) | 7.25432 | 0.306551 | ||||||||
\(561\) | −93.6021 | −3.95188 | ||||||||
\(562\) | 7.82076 | 0.329899 | ||||||||
\(563\) | −6.20147 | −0.261361 | −0.130680 | − | 0.991425i | \(-0.541716\pi\) | ||||
−0.130680 | + | 0.991425i | \(0.541716\pi\) | |||||||
\(564\) | 6.63618 | 0.279434 | ||||||||
\(565\) | −29.7213 | −1.25039 | ||||||||
\(566\) | −16.2700 | −0.683881 | ||||||||
\(567\) | 39.1237 | 1.64304 | ||||||||
\(568\) | 6.37379 | 0.267438 | ||||||||
\(569\) | −42.3188 | −1.77410 | −0.887049 | − | 0.461675i | \(-0.847248\pi\) | ||||
−0.887049 | + | 0.461675i | \(0.847248\pi\) | |||||||
\(570\) | −8.31986 | −0.348481 | ||||||||
\(571\) | −6.92442 | −0.289778 | −0.144889 | − | 0.989448i | \(-0.546282\pi\) | ||||
−0.144889 | + | 0.989448i | \(0.546282\pi\) | |||||||
\(572\) | 5.92121 | 0.247578 | ||||||||
\(573\) | −10.0958 | −0.421756 | ||||||||
\(574\) | −15.2098 | −0.634847 | ||||||||
\(575\) | 10.9599 | 0.457061 | ||||||||
\(576\) | 6.57455 | 0.273940 | ||||||||
\(577\) | −11.0193 | −0.458741 | −0.229370 | − | 0.973339i | \(-0.573667\pi\) | ||||
−0.229370 | + | 0.973339i | \(0.573667\pi\) | |||||||
\(578\) | 10.1580 | 0.422515 | ||||||||
\(579\) | −15.9786 | −0.664048 | ||||||||
\(580\) | 8.69038 | 0.360848 | ||||||||
\(581\) | −16.4699 | −0.683285 | ||||||||
\(582\) | −13.8937 | −0.575913 | ||||||||
\(583\) | 58.3112 | 2.41500 | ||||||||
\(584\) | −12.3353 | −0.510438 | ||||||||
\(585\) | −18.0325 | −0.745552 | ||||||||
\(586\) | 4.48833 | 0.185411 | ||||||||
\(587\) | −28.6989 | −1.18453 | −0.592265 | − | 0.805743i | \(-0.701766\pi\) | ||||
−0.592265 | + | 0.805743i | \(0.701766\pi\) | |||||||
\(588\) | −0.863671 | −0.0356172 | ||||||||
\(589\) | 6.99206 | 0.288103 | ||||||||
\(590\) | 15.2834 | 0.629206 | ||||||||
\(591\) | 5.48485 | 0.225617 | ||||||||
\(592\) | −9.62772 | −0.395697 | ||||||||
\(593\) | −47.1414 | −1.93586 | −0.967932 | − | 0.251211i | \(-0.919171\pi\) | ||||
−0.967932 | + | 0.251211i | \(0.919171\pi\) | |||||||
\(594\) | 64.2035 | 2.63430 | ||||||||
\(595\) | −37.8046 | −1.54984 | ||||||||
\(596\) | −22.0651 | −0.903821 | ||||||||
\(597\) | −12.2424 | −0.501047 | ||||||||
\(598\) | −5.01435 | −0.205052 | ||||||||
\(599\) | −12.8321 | −0.524304 | −0.262152 | − | 0.965027i | \(-0.584432\pi\) | ||||
−0.262152 | + | 0.965027i | \(0.584432\pi\) | |||||||
\(600\) | −6.89899 | −0.281650 | ||||||||
\(601\) | 30.4272 | 1.24115 | 0.620577 | − | 0.784146i | \(-0.286899\pi\) | ||||
0.620577 | + | 0.784146i | \(0.286899\pi\) | |||||||
\(602\) | −12.4619 | −0.507911 | ||||||||
\(603\) | −30.9201 | −1.25916 | ||||||||
\(604\) | 11.2101 | 0.456131 | ||||||||
\(605\) | 61.0200 | 2.48082 | ||||||||
\(606\) | −18.8646 | −0.766324 | ||||||||
\(607\) | −3.64491 | −0.147942 | −0.0739712 | − | 0.997260i | \(-0.523567\pi\) | ||||
−0.0739712 | + | 0.997260i | \(0.523567\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −26.9824 | −1.09338 | ||||||||
\(610\) | −22.8222 | −0.924042 | ||||||||
\(611\) | 2.18772 | 0.0885057 | ||||||||
\(612\) | −34.2622 | −1.38497 | ||||||||
\(613\) | 18.6551 | 0.753473 | 0.376736 | − | 0.926321i | \(-0.377046\pi\) | ||||
0.376736 | + | 0.926321i | \(0.377046\pi\) | |||||||
\(614\) | 11.5583 | 0.466455 | ||||||||
\(615\) | 46.9031 | 1.89132 | ||||||||
\(616\) | −15.6609 | −0.630996 | ||||||||
\(617\) | 14.6266 | 0.588843 | 0.294422 | − | 0.955676i | \(-0.404873\pi\) | ||||
0.294422 | + | 0.955676i | \(0.404873\pi\) | |||||||
\(618\) | −6.22749 | −0.250507 | ||||||||
\(619\) | 1.44896 | 0.0582387 | 0.0291194 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291194 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(620\) | 18.8002 | 0.755033 | ||||||||
\(621\) | −54.3704 | −2.18181 | ||||||||
\(622\) | 11.3152 | 0.453700 | ||||||||
\(623\) | −8.08533 | −0.323932 | ||||||||
\(624\) | 3.15640 | 0.126357 | ||||||||
\(625\) | −31.1769 | −1.24708 | ||||||||
\(626\) | −22.1917 | −0.886958 | ||||||||
\(627\) | 17.9613 | 0.717304 | ||||||||
\(628\) | −3.27420 | −0.130655 | ||||||||
\(629\) | 50.1732 | 2.00054 | ||||||||
\(630\) | 47.6939 | 1.90017 | ||||||||
\(631\) | −17.2479 | −0.686629 | −0.343315 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343315 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(632\) | 2.49251 | 0.0991465 | ||||||||
\(633\) | 3.09428 | 0.122986 | ||||||||
\(634\) | 10.0320 | 0.398421 | ||||||||
\(635\) | −18.8014 | −0.746111 | ||||||||
\(636\) | 31.0838 | 1.23255 | ||||||||
\(637\) | −0.284723 | −0.0112811 | ||||||||
\(638\) | −18.7612 | −0.742761 | ||||||||
\(639\) | 41.9048 | 1.65773 | ||||||||
\(640\) | 2.68879 | 0.106284 | ||||||||
\(641\) | 23.3046 | 0.920477 | 0.460238 | − | 0.887795i | \(-0.347764\pi\) | ||||
0.460238 | + | 0.887795i | \(0.347764\pi\) | |||||||
\(642\) | −9.15320 | −0.361248 | ||||||||
\(643\) | −29.2777 | −1.15460 | −0.577300 | − | 0.816532i | \(-0.695894\pi\) | ||||
−0.577300 | + | 0.816532i | \(0.695894\pi\) | |||||||
\(644\) | 13.2624 | 0.522611 | ||||||||
\(645\) | 38.4293 | 1.51315 | ||||||||
\(646\) | −5.21133 | −0.205037 | ||||||||
\(647\) | 24.3443 | 0.957074 | 0.478537 | − | 0.878067i | \(-0.341167\pi\) | ||||
0.478537 | + | 0.878067i | \(0.341167\pi\) | |||||||
\(648\) | 14.5011 | 0.569656 | ||||||||
\(649\) | −32.9943 | −1.29514 | ||||||||
\(650\) | −2.27436 | −0.0892077 | ||||||||
\(651\) | −58.3719 | −2.28777 | ||||||||
\(652\) | −21.6594 | −0.848247 | ||||||||
\(653\) | −20.2614 | −0.792891 | −0.396445 | − | 0.918058i | \(-0.629756\pi\) | ||||
−0.396445 | + | 0.918058i | \(0.629756\pi\) | |||||||
\(654\) | −40.1401 | −1.56960 | ||||||||
\(655\) | −57.1117 | −2.23154 | ||||||||
\(656\) | −5.63748 | −0.220107 | ||||||||
\(657\) | −81.0989 | −3.16397 | ||||||||
\(658\) | −5.78627 | −0.225572 | ||||||||
\(659\) | −46.0440 | −1.79362 | −0.896809 | − | 0.442418i | \(-0.854121\pi\) | ||||
−0.896809 | + | 0.442418i | \(0.854121\pi\) | |||||||
\(660\) | 48.2941 | 1.87984 | ||||||||
\(661\) | 0.200679 | 0.00780551 | 0.00390276 | − | 0.999992i | \(-0.498758\pi\) | ||||
0.00390276 | + | 0.999992i | \(0.498758\pi\) | |||||||
\(662\) | 6.12083 | 0.237893 | ||||||||
\(663\) | −16.4490 | −0.638828 | ||||||||
\(664\) | −6.10451 | −0.236901 | ||||||||
\(665\) | 7.25432 | 0.281310 | ||||||||
\(666\) | −63.2979 | −2.45275 | ||||||||
\(667\) | 15.8878 | 0.615178 | ||||||||
\(668\) | 18.4021 | 0.711998 | ||||||||
\(669\) | 36.4335 | 1.40860 | ||||||||
\(670\) | −12.6454 | −0.488533 | ||||||||
\(671\) | 49.2694 | 1.90202 | ||||||||
\(672\) | −8.34831 | −0.322043 | ||||||||
\(673\) | −10.8814 | −0.419448 | −0.209724 | − | 0.977761i | \(-0.567257\pi\) | ||||
−0.209724 | + | 0.977761i | \(0.567257\pi\) | |||||||
\(674\) | −30.1681 | −1.16203 | ||||||||
\(675\) | −24.6608 | −0.949194 | ||||||||
\(676\) | −11.9594 | −0.459979 | ||||||||
\(677\) | −16.8531 | −0.647718 | −0.323859 | − | 0.946105i | \(-0.604980\pi\) | ||||
−0.323859 | + | 0.946105i | \(0.604980\pi\) | |||||||
\(678\) | 34.2035 | 1.31358 | ||||||||
\(679\) | 12.1143 | 0.464905 | ||||||||
\(680\) | −14.0122 | −0.537342 | ||||||||
\(681\) | −64.1626 | −2.45872 | ||||||||
\(682\) | −40.5866 | −1.55414 | ||||||||
\(683\) | 3.36580 | 0.128789 | 0.0643944 | − | 0.997925i | \(-0.479488\pi\) | ||||
0.0643944 | + | 0.997925i | \(0.479488\pi\) | |||||||
\(684\) | 6.57455 | 0.251384 | ||||||||
\(685\) | 45.5168 | 1.73911 | ||||||||
\(686\) | −18.1328 | −0.692315 | ||||||||
\(687\) | 23.8329 | 0.909282 | ||||||||
\(688\) | −4.61898 | −0.176097 | ||||||||
\(689\) | 10.2472 | 0.390389 | ||||||||
\(690\) | −40.8976 | −1.55695 | ||||||||
\(691\) | 13.1189 | 0.499068 | 0.249534 | − | 0.968366i | \(-0.419723\pi\) | ||||
0.249534 | + | 0.968366i | \(0.419723\pi\) | |||||||
\(692\) | 24.7440 | 0.940625 | ||||||||
\(693\) | −102.963 | −3.91126 | ||||||||
\(694\) | −6.59271 | −0.250256 | ||||||||
\(695\) | 1.44838 | 0.0549401 | ||||||||
\(696\) | −10.0009 | −0.379085 | ||||||||
\(697\) | 29.3788 | 1.11280 | ||||||||
\(698\) | −8.52462 | −0.322662 | ||||||||
\(699\) | 40.5322 | 1.53307 | ||||||||
\(700\) | 6.01541 | 0.227361 | ||||||||
\(701\) | −15.8741 | −0.599557 | −0.299779 | − | 0.954009i | \(-0.596913\pi\) | ||||
−0.299779 | + | 0.954009i | \(0.596913\pi\) | |||||||
\(702\) | 11.2827 | 0.425839 | ||||||||
\(703\) | −9.62772 | −0.363116 | ||||||||
\(704\) | −5.80467 | −0.218772 | ||||||||
\(705\) | 17.8433 | 0.672018 | ||||||||
\(706\) | −10.3889 | −0.390993 | ||||||||
\(707\) | 16.4486 | 0.618613 | ||||||||
\(708\) | −17.5882 | −0.661004 | ||||||||
\(709\) | −1.40514 | −0.0527710 | −0.0263855 | − | 0.999652i | \(-0.508400\pi\) | ||||
−0.0263855 | + | 0.999652i | \(0.508400\pi\) | |||||||
\(710\) | 17.1378 | 0.643170 | ||||||||
\(711\) | 16.3871 | 0.614565 | ||||||||
\(712\) | −2.99680 | −0.112310 | ||||||||
\(713\) | 34.3706 | 1.28719 | ||||||||
\(714\) | 43.5058 | 1.62816 | ||||||||
\(715\) | 15.9209 | 0.595408 | ||||||||
\(716\) | −23.0901 | −0.862918 | ||||||||
\(717\) | −11.1080 | −0.414836 | ||||||||
\(718\) | 25.3768 | 0.947052 | ||||||||
\(719\) | 50.1743 | 1.87119 | 0.935593 | − | 0.353081i | \(-0.114866\pi\) | ||||
0.935593 | + | 0.353081i | \(0.114866\pi\) | |||||||
\(720\) | 17.6776 | 0.658805 | ||||||||
\(721\) | 5.42992 | 0.202221 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 64.1528 | 2.38587 | ||||||||
\(724\) | 5.37021 | 0.199582 | ||||||||
\(725\) | 7.20623 | 0.267633 | ||||||||
\(726\) | −70.2222 | −2.60619 | ||||||||
\(727\) | −7.84044 | −0.290786 | −0.145393 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145393 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(728\) | −2.75215 | −0.102001 | ||||||||
\(729\) | −7.33610 | −0.271708 | ||||||||
\(730\) | −33.1670 | −1.22757 | ||||||||
\(731\) | 24.0710 | 0.890299 | ||||||||
\(732\) | 26.2639 | 0.970741 | ||||||||
\(733\) | −19.6031 | −0.724056 | −0.362028 | − | 0.932167i | \(-0.617916\pi\) | ||||
−0.362028 | + | 0.932167i | \(0.617916\pi\) | |||||||
\(734\) | 14.9400 | 0.551447 | ||||||||
\(735\) | −2.32223 | −0.0856568 | ||||||||
\(736\) | 4.91566 | 0.181194 | ||||||||
\(737\) | 27.2993 | 1.00558 | ||||||||
\(738\) | −37.0639 | −1.36434 | ||||||||
\(739\) | 38.6814 | 1.42292 | 0.711459 | − | 0.702728i | \(-0.248035\pi\) | ||||
0.711459 | + | 0.702728i | \(0.248035\pi\) | |||||||
\(740\) | −25.8869 | −0.951622 | ||||||||
\(741\) | 3.15640 | 0.115953 | ||||||||
\(742\) | −27.1028 | −0.994974 | ||||||||
\(743\) | 35.4939 | 1.30214 | 0.651072 | − | 0.759016i | \(-0.274320\pi\) | ||||
0.651072 | + | 0.759016i | \(0.274320\pi\) | |||||||
\(744\) | −21.6354 | −0.793191 | ||||||||
\(745\) | −59.3284 | −2.17362 | ||||||||
\(746\) | −18.2635 | −0.668676 | ||||||||
\(747\) | −40.1344 | −1.46844 | ||||||||
\(748\) | 30.2501 | 1.10605 | ||||||||
\(749\) | 7.98092 | 0.291617 | ||||||||
\(750\) | 23.0494 | 0.841645 | ||||||||
\(751\) | 3.42607 | 0.125019 | 0.0625095 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625095 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(752\) | −2.14466 | −0.0782078 | ||||||||
\(753\) | −61.9663 | −2.25818 | ||||||||
\(754\) | −3.29697 | −0.120068 | ||||||||
\(755\) | 30.1415 | 1.09696 | ||||||||
\(756\) | −29.8415 | −1.08532 | ||||||||
\(757\) | 47.2149 | 1.71605 | 0.858027 | − | 0.513604i | \(-0.171690\pi\) | ||||
0.858027 | + | 0.513604i | \(0.171690\pi\) | |||||||
\(758\) | −15.4863 | −0.562487 | ||||||||
\(759\) | 88.2915 | 3.20478 | ||||||||
\(760\) | 2.68879 | 0.0975327 | ||||||||
\(761\) | 18.0283 | 0.653524 | 0.326762 | − | 0.945107i | \(-0.394042\pi\) | ||||
0.326762 | + | 0.945107i | \(0.394042\pi\) | |||||||
\(762\) | 21.6368 | 0.783818 | ||||||||
\(763\) | 34.9993 | 1.26706 | ||||||||
\(764\) | 3.26272 | 0.118041 | ||||||||
\(765\) | −92.1238 | −3.33074 | ||||||||
\(766\) | 8.99696 | 0.325073 | ||||||||
\(767\) | −5.79822 | −0.209361 | ||||||||
\(768\) | −3.09428 | −0.111655 | ||||||||
\(769\) | 12.5508 | 0.452595 | 0.226298 | − | 0.974058i | \(-0.427338\pi\) | ||||
0.226298 | + | 0.974058i | \(0.427338\pi\) | |||||||
\(770\) | −42.1089 | −1.51750 | ||||||||
\(771\) | 63.6218 | 2.29128 | ||||||||
\(772\) | 5.16392 | 0.185853 | ||||||||
\(773\) | −17.9794 | −0.646676 | −0.323338 | − | 0.946284i | \(-0.604805\pi\) | ||||
−0.323338 | + | 0.946284i | \(0.604805\pi\) | |||||||
\(774\) | −30.3677 | −1.09155 | ||||||||
\(775\) | 15.5895 | 0.559990 | ||||||||
\(776\) | 4.49014 | 0.161186 | ||||||||
\(777\) | 80.3752 | 2.88344 | ||||||||
\(778\) | 22.4887 | 0.806261 | ||||||||
\(779\) | −5.63748 | −0.201984 | ||||||||
\(780\) | 8.48690 | 0.303880 | ||||||||
\(781\) | −36.9978 | −1.32388 | ||||||||
\(782\) | −25.6171 | −0.916067 | ||||||||
\(783\) | −35.7489 | −1.27756 | ||||||||
\(784\) | 0.279119 | 0.00996853 | ||||||||
\(785\) | −8.80363 | −0.314215 | ||||||||
\(786\) | 65.7246 | 2.34432 | ||||||||
\(787\) | −48.5559 | −1.73083 | −0.865416 | − | 0.501054i | \(-0.832946\pi\) | ||||
−0.865416 | + | 0.501054i | \(0.832946\pi\) | |||||||
\(788\) | −1.77258 | −0.0631455 | ||||||||
\(789\) | −58.3320 | −2.07668 | ||||||||
\(790\) | 6.70183 | 0.238440 | ||||||||
\(791\) | −29.8230 | −1.06038 | ||||||||
\(792\) | −38.1631 | −1.35607 | ||||||||
\(793\) | 8.65829 | 0.307465 | ||||||||
\(794\) | 13.8583 | 0.491811 | ||||||||
\(795\) | 83.5777 | 2.96420 | ||||||||
\(796\) | 3.95646 | 0.140233 | ||||||||
\(797\) | 48.3845 | 1.71387 | 0.856934 | − | 0.515426i | \(-0.172366\pi\) | ||||
0.856934 | + | 0.515426i | \(0.172366\pi\) | |||||||
\(798\) | −8.34831 | −0.295527 | ||||||||
\(799\) | 11.1765 | 0.395398 | ||||||||
\(800\) | 2.22960 | 0.0788281 | ||||||||
\(801\) | −19.7026 | −0.696158 | ||||||||
\(802\) | −16.8575 | −0.595260 | ||||||||
\(803\) | 71.6023 | 2.52679 | ||||||||
\(804\) | 14.5524 | 0.513222 | ||||||||
\(805\) | 35.6598 | 1.25684 | ||||||||
\(806\) | −7.13243 | −0.251229 | ||||||||
\(807\) | −38.2444 | −1.34627 | ||||||||
\(808\) | 6.09662 | 0.214479 | ||||||||
\(809\) | −2.93682 | −0.103253 | −0.0516266 | − | 0.998666i | \(-0.516441\pi\) | ||||
−0.0516266 | + | 0.998666i | \(0.516441\pi\) | |||||||
\(810\) | 38.9904 | 1.36998 | ||||||||
\(811\) | 30.0317 | 1.05456 | 0.527278 | − | 0.849693i | \(-0.323213\pi\) | ||||
0.527278 | + | 0.849693i | \(0.323213\pi\) | |||||||
\(812\) | 8.72009 | 0.306015 | ||||||||
\(813\) | 30.8804 | 1.08302 | ||||||||
\(814\) | 55.8858 | 1.95879 | ||||||||
\(815\) | −58.2376 | −2.03997 | ||||||||
\(816\) | 16.1253 | 0.564498 | ||||||||
\(817\) | −4.61898 | −0.161598 | ||||||||
\(818\) | 10.9497 | 0.382849 | ||||||||
\(819\) | −18.0942 | −0.632261 | ||||||||
\(820\) | −15.1580 | −0.529341 | ||||||||
\(821\) | −46.8286 | −1.63433 | −0.817164 | − | 0.576405i | \(-0.804455\pi\) | ||||
−0.817164 | + | 0.576405i | \(0.804455\pi\) | |||||||
\(822\) | −52.3810 | −1.82700 | ||||||||
\(823\) | −40.0217 | −1.39507 | −0.697535 | − | 0.716551i | \(-0.745720\pi\) | ||||
−0.697535 | + | 0.716551i | \(0.745720\pi\) | |||||||
\(824\) | 2.01258 | 0.0701117 | ||||||||
\(825\) | 40.0464 | 1.39424 | ||||||||
\(826\) | 15.3356 | 0.533594 | ||||||||
\(827\) | 31.9683 | 1.11165 | 0.555823 | − | 0.831301i | \(-0.312403\pi\) | ||||
0.555823 | + | 0.831301i | \(0.312403\pi\) | |||||||
\(828\) | 32.3183 | 1.12314 | ||||||||
\(829\) | 28.3019 | 0.982965 | 0.491482 | − | 0.870887i | \(-0.336455\pi\) | ||||
0.491482 | + | 0.870887i | \(0.336455\pi\) | |||||||
\(830\) | −16.4137 | −0.569729 | ||||||||
\(831\) | 50.4206 | 1.74907 | ||||||||
\(832\) | −1.02008 | −0.0353648 | ||||||||
\(833\) | −1.45458 | −0.0503982 | ||||||||
\(834\) | −1.66680 | −0.0577166 | ||||||||
\(835\) | 49.4794 | 1.71230 | ||||||||
\(836\) | −5.80467 | −0.200759 | ||||||||
\(837\) | −77.3367 | −2.67315 | ||||||||
\(838\) | 10.0233 | 0.346248 | ||||||||
\(839\) | −18.3322 | −0.632897 | −0.316448 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316448 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(840\) | −22.4469 | −0.774490 | ||||||||
\(841\) | −18.5537 | −0.639782 | ||||||||
\(842\) | 10.6602 | 0.367376 | ||||||||
\(843\) | −24.1996 | −0.833478 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −32.1564 | −1.10622 | ||||||||
\(846\) | −14.1002 | −0.484775 | ||||||||
\(847\) | 61.2287 | 2.10384 | ||||||||
\(848\) | −10.0456 | −0.344966 | ||||||||
\(849\) | 50.3440 | 1.72780 | ||||||||
\(850\) | −11.6192 | −0.398534 | ||||||||
\(851\) | −47.3266 | −1.62233 | ||||||||
\(852\) | −19.7223 | −0.675674 | ||||||||
\(853\) | 2.64013 | 0.0903964 | 0.0451982 | − | 0.998978i | \(-0.485608\pi\) | ||||
0.0451982 | + | 0.998978i | \(0.485608\pi\) | |||||||
\(854\) | −22.9002 | −0.783628 | ||||||||
\(855\) | 17.6776 | 0.604561 | ||||||||
\(856\) | 2.95811 | 0.101106 | ||||||||
\(857\) | 51.8234 | 1.77025 | 0.885127 | − | 0.465349i | \(-0.154071\pi\) | ||||
0.885127 | + | 0.465349i | \(0.154071\pi\) | |||||||
\(858\) | −18.3219 | −0.625498 | ||||||||
\(859\) | −10.1640 | −0.346790 | −0.173395 | − | 0.984852i | \(-0.555474\pi\) | ||||
−0.173395 | + | 0.984852i | \(0.555474\pi\) | |||||||
\(860\) | −12.4195 | −0.423501 | ||||||||
\(861\) | 47.0635 | 1.60392 | ||||||||
\(862\) | 29.9005 | 1.01841 | ||||||||
\(863\) | 5.69497 | 0.193859 | 0.0969296 | − | 0.995291i | \(-0.469098\pi\) | ||||
0.0969296 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(864\) | −11.0607 | −0.376291 | ||||||||
\(865\) | 66.5314 | 2.26213 | ||||||||
\(866\) | −2.10175 | −0.0714204 | ||||||||
\(867\) | −31.4315 | −1.06747 | ||||||||
\(868\) | 18.8645 | 0.640302 | ||||||||
\(869\) | −14.4682 | −0.490799 | ||||||||
\(870\) | −26.8904 | −0.911672 | ||||||||
\(871\) | 4.79741 | 0.162554 | ||||||||
\(872\) | 12.9724 | 0.439300 | ||||||||
\(873\) | 29.5206 | 0.999122 | ||||||||
\(874\) | 4.91566 | 0.166275 | ||||||||
\(875\) | −20.0974 | −0.679416 | ||||||||
\(876\) | 38.1688 | 1.28960 | ||||||||
\(877\) | 33.4559 | 1.12973 | 0.564863 | − | 0.825185i | \(-0.308929\pi\) | ||||
0.564863 | + | 0.825185i | \(0.308929\pi\) | |||||||
\(878\) | −29.7140 | −1.00280 | ||||||||
\(879\) | −13.8881 | −0.468436 | ||||||||
\(880\) | −15.6075 | −0.526130 | ||||||||
\(881\) | −10.5076 | −0.354009 | −0.177004 | − | 0.984210i | \(-0.556641\pi\) | ||||
−0.177004 | + | 0.984210i | \(0.556641\pi\) | |||||||
\(882\) | 1.83508 | 0.0617904 | ||||||||
\(883\) | 8.18920 | 0.275589 | 0.137794 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137794 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(884\) | 5.31596 | 0.178795 | ||||||||
\(885\) | −47.2909 | −1.58967 | ||||||||
\(886\) | −29.1694 | −0.979966 | ||||||||
\(887\) | 0.0122459 | 0.000411177 0 | 0.000205589 | − | 1.00000i | \(-0.499935\pi\) | ||||
0.000205589 | 1.00000i | \(0.499935\pi\) | ||||||||
\(888\) | 29.7908 | 0.999715 | ||||||||
\(889\) | −18.8657 | −0.632735 | ||||||||
\(890\) | −8.05778 | −0.270097 | ||||||||
\(891\) | −84.1740 | −2.81994 | ||||||||
\(892\) | −11.7745 | −0.394239 | ||||||||
\(893\) | −2.14466 | −0.0717684 | ||||||||
\(894\) | 68.2755 | 2.28347 | ||||||||
\(895\) | −62.0845 | −2.07526 | ||||||||
\(896\) | 2.69798 | 0.0901333 | ||||||||
\(897\) | 15.5158 | 0.518057 | ||||||||
\(898\) | −21.3994 | −0.714107 | ||||||||
\(899\) | 22.5989 | 0.753715 | ||||||||
\(900\) | 14.6586 | 0.488620 | ||||||||
\(901\) | 52.3507 | 1.74406 | ||||||||
\(902\) | 32.7238 | 1.08958 | ||||||||
\(903\) | 38.5607 | 1.28322 | ||||||||
\(904\) | −11.0538 | −0.367644 | ||||||||
\(905\) | 14.4394 | 0.479981 | ||||||||
\(906\) | −34.6871 | −1.15240 | ||||||||
\(907\) | −39.5002 | −1.31158 | −0.655791 | − | 0.754943i | \(-0.727665\pi\) | ||||
−0.655791 | + | 0.754943i | \(0.727665\pi\) | |||||||
\(908\) | 20.7359 | 0.688145 | ||||||||
\(909\) | 40.0826 | 1.32946 | ||||||||
\(910\) | −7.39996 | −0.245306 | ||||||||
\(911\) | −7.57559 | −0.250991 | −0.125495 | − | 0.992094i | \(-0.540052\pi\) | ||||
−0.125495 | + | 0.992094i | \(0.540052\pi\) | |||||||
\(912\) | −3.09428 | −0.102462 | ||||||||
\(913\) | 35.4347 | 1.17272 | ||||||||
\(914\) | 25.2187 | 0.834161 | ||||||||
\(915\) | 70.6181 | 2.33456 | ||||||||
\(916\) | −7.70226 | −0.254490 | ||||||||
\(917\) | −57.3070 | −1.89244 | ||||||||
\(918\) | 57.6407 | 1.90243 | ||||||||
\(919\) | 58.2143 | 1.92031 | 0.960157 | − | 0.279463i | \(-0.0901563\pi\) | ||||
0.960157 | + | 0.279463i | \(0.0901563\pi\) | |||||||
\(920\) | 13.2172 | 0.435758 | ||||||||
\(921\) | −35.7645 | −1.17848 | ||||||||
\(922\) | −18.4586 | −0.607902 | ||||||||
\(923\) | −6.50175 | −0.214008 | ||||||||
\(924\) | 48.4592 | 1.59419 | ||||||||
\(925\) | −21.4659 | −0.705795 | ||||||||
\(926\) | −30.6189 | −1.00620 | ||||||||
\(927\) | 13.2318 | 0.434591 | ||||||||
\(928\) | 3.23208 | 0.106098 | ||||||||
\(929\) | 51.2285 | 1.68075 | 0.840376 | − | 0.542004i | \(-0.182334\pi\) | ||||
0.840376 | + | 0.542004i | \(0.182334\pi\) | |||||||
\(930\) | −58.1730 | −1.90757 | ||||||||
\(931\) | 0.279119 | 0.00914775 | ||||||||
\(932\) | −13.0991 | −0.429074 | ||||||||
\(933\) | −35.0125 | −1.14626 | ||||||||
\(934\) | −20.9490 | −0.685471 | ||||||||
\(935\) | 81.3361 | 2.65997 | ||||||||
\(936\) | −6.70655 | −0.219210 | ||||||||
\(937\) | 10.3375 | 0.337712 | 0.168856 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168856 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(938\) | −12.6886 | −0.414298 | ||||||||
\(939\) | 68.6673 | 2.24087 | ||||||||
\(940\) | −5.76655 | −0.188084 | ||||||||
\(941\) | 35.7453 | 1.16526 | 0.582632 | − | 0.812736i | \(-0.302023\pi\) | ||||
0.582632 | + | 0.812736i | \(0.302023\pi\) | |||||||
\(942\) | 10.1313 | 0.330095 | ||||||||
\(943\) | −27.7120 | −0.902426 | ||||||||
\(944\) | 5.68410 | 0.185002 | ||||||||
\(945\) | −80.2375 | −2.61013 | ||||||||
\(946\) | 26.8117 | 0.871723 | ||||||||
\(947\) | −6.11275 | −0.198638 | −0.0993189 | − | 0.995056i | \(-0.531666\pi\) | ||||
−0.0993189 | + | 0.995056i | \(0.531666\pi\) | |||||||
\(948\) | −7.71250 | −0.250490 | ||||||||
\(949\) | 12.5829 | 0.408459 | ||||||||
\(950\) | 2.22960 | 0.0723376 | ||||||||
\(951\) | −31.0418 | −1.00660 | ||||||||
\(952\) | −14.0601 | −0.455690 | ||||||||
\(953\) | 6.85567 | 0.222077 | 0.111038 | − | 0.993816i | \(-0.464582\pi\) | ||||
0.111038 | + | 0.993816i | \(0.464582\pi\) | |||||||
\(954\) | −66.0451 | −2.13829 | ||||||||
\(955\) | 8.77277 | 0.283880 | ||||||||
\(956\) | 3.58986 | 0.116104 | ||||||||
\(957\) | 58.0522 | 1.87656 | ||||||||
\(958\) | −18.1492 | −0.586374 | ||||||||
\(959\) | 45.6724 | 1.47484 | ||||||||
\(960\) | −8.31986 | −0.268522 | ||||||||
\(961\) | 17.8889 | 0.577060 | ||||||||
\(962\) | 9.82101 | 0.316642 | ||||||||
\(963\) | 19.4482 | 0.626710 | ||||||||
\(964\) | −20.7327 | −0.667756 | ||||||||
\(965\) | 13.8847 | 0.446964 | ||||||||
\(966\) | −41.0375 | −1.32036 | ||||||||
\(967\) | 49.1958 | 1.58203 | 0.791015 | − | 0.611796i | \(-0.209553\pi\) | ||||
0.791015 | + | 0.611796i | \(0.209553\pi\) | |||||||
\(968\) | 22.6942 | 0.729420 | ||||||||
\(969\) | 16.1253 | 0.518019 | ||||||||
\(970\) | 12.0730 | 0.387642 | ||||||||
\(971\) | 22.2753 | 0.714850 | 0.357425 | − | 0.933942i | \(-0.383655\pi\) | ||||
0.357425 | + | 0.933942i | \(0.383655\pi\) | |||||||
\(972\) | −11.6884 | −0.374905 | ||||||||
\(973\) | 1.45333 | 0.0465916 | ||||||||
\(974\) | −12.2598 | −0.392830 | ||||||||
\(975\) | 7.03750 | 0.225380 | ||||||||
\(976\) | −8.48789 | −0.271691 | ||||||||
\(977\) | 54.6672 | 1.74896 | 0.874479 | − | 0.485063i | \(-0.161204\pi\) | ||||
0.874479 | + | 0.485063i | \(0.161204\pi\) | |||||||
\(978\) | 67.0201 | 2.14307 | ||||||||
\(979\) | 17.3955 | 0.555961 | ||||||||
\(980\) | 0.750492 | 0.0239736 | ||||||||
\(981\) | 85.2876 | 2.72302 | ||||||||
\(982\) | 0.409512 | 0.0130681 | ||||||||
\(983\) | −20.5308 | −0.654832 | −0.327416 | − | 0.944880i | \(-0.606178\pi\) | ||||
−0.327416 | + | 0.944880i | \(0.606178\pi\) | |||||||
\(984\) | 17.4439 | 0.556093 | ||||||||
\(985\) | −4.76610 | −0.151860 | ||||||||
\(986\) | −16.8434 | −0.536404 | ||||||||
\(987\) | 17.9043 | 0.569901 | ||||||||
\(988\) | −1.02008 | −0.0324530 | ||||||||
\(989\) | −22.7053 | −0.721988 | ||||||||
\(990\) | −102.613 | −3.26124 | ||||||||
\(991\) | −33.6003 | −1.06735 | −0.533675 | − | 0.845690i | \(-0.679189\pi\) | ||||
−0.533675 | + | 0.845690i | \(0.679189\pi\) | |||||||
\(992\) | 6.99206 | 0.221998 | ||||||||
\(993\) | −18.9395 | −0.601028 | ||||||||
\(994\) | 17.1964 | 0.545436 | ||||||||
\(995\) | 10.6381 | 0.337250 | ||||||||
\(996\) | 18.8890 | 0.598522 | ||||||||
\(997\) | 33.3144 | 1.05508 | 0.527538 | − | 0.849531i | \(-0.323115\pi\) | ||||
0.527538 | + | 0.849531i | \(0.323115\pi\) | |||||||
\(998\) | 19.8019 | 0.626817 | ||||||||
\(999\) | 106.489 | 3.36916 |
(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 | 8018.2.a.d.1.2 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.2 | ✓ | 30 | 1.1 | even | 1 | trivial |