Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.980818 | −0.693543 | −0.346772 | − | 0.937950i | \(-0.612722\pi\) | ||||
−0.346772 | + | 0.937950i | \(0.612722\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.03800 | −0.518998 | ||||||||
\(5\) | 1.00436 | 0.449163 | 0.224582 | − | 0.974455i | \(-0.427898\pi\) | ||||
0.224582 | + | 0.974455i | \(0.427898\pi\) | |||||||
\(6\) | 0.980818 | 0.400417 | ||||||||
\(7\) | −3.53145 | −1.33476 | −0.667382 | − | 0.744716i | \(-0.732585\pi\) | ||||
−0.667382 | + | 0.744716i | \(0.732585\pi\) | |||||||
\(8\) | 2.97972 | 1.05349 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.985094 | −0.311514 | ||||||||
\(11\) | 6.32698 | 1.90766 | 0.953828 | − | 0.300353i | \(-0.0971046\pi\) | ||||
0.953828 | + | 0.300353i | \(0.0971046\pi\) | |||||||
\(12\) | 1.03800 | 0.299644 | ||||||||
\(13\) | 3.86467 | 1.07187 | 0.535933 | − | 0.844260i | \(-0.319960\pi\) | ||||
0.535933 | + | 0.844260i | \(0.319960\pi\) | |||||||
\(14\) | 3.46371 | 0.925716 | ||||||||
\(15\) | −1.00436 | −0.259325 | ||||||||
\(16\) | −0.846572 | −0.211643 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.980818 | −0.231181 | ||||||||
\(19\) | −2.59733 | −0.595868 | −0.297934 | − | 0.954586i | \(-0.596298\pi\) | ||||
−0.297934 | + | 0.954586i | \(0.596298\pi\) | |||||||
\(20\) | −1.04252 | −0.233115 | ||||||||
\(21\) | 3.53145 | 0.770626 | ||||||||
\(22\) | −6.20562 | −1.32304 | ||||||||
\(23\) | 6.45448 | 1.34585 | 0.672926 | − | 0.739710i | \(-0.265037\pi\) | ||||
0.672926 | + | 0.739710i | \(0.265037\pi\) | |||||||
\(24\) | −2.97972 | −0.608233 | ||||||||
\(25\) | −3.99126 | −0.798252 | ||||||||
\(26\) | −3.79054 | −0.743385 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.66564 | 0.692740 | ||||||||
\(29\) | −7.53770 | −1.39972 | −0.699858 | − | 0.714282i | \(-0.746753\pi\) | ||||
−0.699858 | + | 0.714282i | \(0.746753\pi\) | |||||||
\(30\) | 0.985094 | 0.179853 | ||||||||
\(31\) | −4.09152 | −0.734858 | −0.367429 | − | 0.930051i | \(-0.619762\pi\) | ||||
−0.367429 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(32\) | −5.12911 | −0.906707 | ||||||||
\(33\) | −6.32698 | −1.10139 | ||||||||
\(34\) | 0.980818 | 0.168209 | ||||||||
\(35\) | −3.54685 | −0.599527 | ||||||||
\(36\) | −1.03800 | −0.172999 | ||||||||
\(37\) | 6.50621 | 1.06961 | 0.534807 | − | 0.844974i | \(-0.320384\pi\) | ||||
0.534807 | + | 0.844974i | \(0.320384\pi\) | |||||||
\(38\) | 2.54751 | 0.413260 | ||||||||
\(39\) | −3.86467 | −0.618842 | ||||||||
\(40\) | 2.99271 | 0.473189 | ||||||||
\(41\) | −9.61376 | −1.50142 | −0.750709 | − | 0.660633i | \(-0.770288\pi\) | ||||
−0.750709 | + | 0.660633i | \(0.770288\pi\) | |||||||
\(42\) | −3.46371 | −0.534463 | ||||||||
\(43\) | 7.33861 | 1.11913 | 0.559564 | − | 0.828787i | \(-0.310969\pi\) | ||||
0.559564 | + | 0.828787i | \(0.310969\pi\) | |||||||
\(44\) | −6.56738 | −0.990070 | ||||||||
\(45\) | 1.00436 | 0.149721 | ||||||||
\(46\) | −6.33067 | −0.933406 | ||||||||
\(47\) | −4.71120 | −0.687198 | −0.343599 | − | 0.939116i | \(-0.611646\pi\) | ||||
−0.343599 | + | 0.939116i | \(0.611646\pi\) | |||||||
\(48\) | 0.846572 | 0.122192 | ||||||||
\(49\) | 5.47117 | 0.781595 | ||||||||
\(50\) | 3.91470 | 0.553622 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −4.01151 | −0.556297 | ||||||||
\(53\) | 2.16439 | 0.297301 | 0.148651 | − | 0.988890i | \(-0.452507\pi\) | ||||
0.148651 | + | 0.988890i | \(0.452507\pi\) | |||||||
\(54\) | 0.980818 | 0.133472 | ||||||||
\(55\) | 6.35456 | 0.856849 | ||||||||
\(56\) | −10.5227 | −1.40616 | ||||||||
\(57\) | 2.59733 | 0.344025 | ||||||||
\(58\) | 7.39311 | 0.970764 | ||||||||
\(59\) | 3.64108 | 0.474028 | 0.237014 | − | 0.971506i | \(-0.423831\pi\) | ||||
0.237014 | + | 0.971506i | \(0.423831\pi\) | |||||||
\(60\) | 1.04252 | 0.134589 | ||||||||
\(61\) | 7.27575 | 0.931564 | 0.465782 | − | 0.884899i | \(-0.345773\pi\) | ||||
0.465782 | + | 0.884899i | \(0.345773\pi\) | |||||||
\(62\) | 4.01303 | 0.509656 | ||||||||
\(63\) | −3.53145 | −0.444921 | ||||||||
\(64\) | 6.72387 | 0.840483 | ||||||||
\(65\) | 3.88152 | 0.481443 | ||||||||
\(66\) | 6.20562 | 0.763858 | ||||||||
\(67\) | −6.61390 | −0.808016 | −0.404008 | − | 0.914755i | \(-0.632383\pi\) | ||||
−0.404008 | + | 0.914755i | \(0.632383\pi\) | |||||||
\(68\) | 1.03800 | 0.125876 | ||||||||
\(69\) | −6.45448 | −0.777028 | ||||||||
\(70\) | 3.47881 | 0.415798 | ||||||||
\(71\) | −11.6229 | −1.37939 | −0.689695 | − | 0.724100i | \(-0.742255\pi\) | ||||
−0.689695 | + | 0.724100i | \(0.742255\pi\) | |||||||
\(72\) | 2.97972 | 0.351164 | ||||||||
\(73\) | −10.8308 | −1.26765 | −0.633826 | − | 0.773476i | \(-0.718516\pi\) | ||||
−0.633826 | + | 0.773476i | \(0.718516\pi\) | |||||||
\(74\) | −6.38141 | −0.741824 | ||||||||
\(75\) | 3.99126 | 0.460871 | ||||||||
\(76\) | 2.69602 | 0.309254 | ||||||||
\(77\) | −22.3434 | −2.54627 | ||||||||
\(78\) | 3.79054 | 0.429194 | ||||||||
\(79\) | −16.2317 | −1.82621 | −0.913103 | − | 0.407728i | \(-0.866321\pi\) | ||||
−0.913103 | + | 0.407728i | \(0.866321\pi\) | |||||||
\(80\) | −0.850263 | −0.0950623 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.42935 | 1.04130 | ||||||||
\(83\) | −8.05337 | −0.883972 | −0.441986 | − | 0.897022i | \(-0.645726\pi\) | ||||
−0.441986 | + | 0.897022i | \(0.645726\pi\) | |||||||
\(84\) | −3.66564 | −0.399954 | ||||||||
\(85\) | −1.00436 | −0.108938 | ||||||||
\(86\) | −7.19784 | −0.776163 | ||||||||
\(87\) | 7.53770 | 0.808127 | ||||||||
\(88\) | 18.8526 | 2.00970 | ||||||||
\(89\) | 2.16759 | 0.229764 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(90\) | −0.985094 | −0.103838 | ||||||||
\(91\) | −13.6479 | −1.43069 | ||||||||
\(92\) | −6.69972 | −0.698494 | ||||||||
\(93\) | 4.09152 | 0.424271 | ||||||||
\(94\) | 4.62082 | 0.476602 | ||||||||
\(95\) | −2.60865 | −0.267642 | ||||||||
\(96\) | 5.12911 | 0.523488 | ||||||||
\(97\) | 3.94258 | 0.400308 | 0.200154 | − | 0.979764i | \(-0.435856\pi\) | ||||
0.200154 | + | 0.979764i | \(0.435856\pi\) | |||||||
\(98\) | −5.36622 | −0.542070 | ||||||||
\(99\) | 6.32698 | 0.635885 | ||||||||
\(100\) | 4.14291 | 0.414291 | ||||||||
\(101\) | −12.4762 | −1.24143 | −0.620715 | − | 0.784037i | \(-0.713157\pi\) | ||||
−0.620715 | + | 0.784037i | \(0.713157\pi\) | |||||||
\(102\) | −0.980818 | −0.0971155 | ||||||||
\(103\) | 5.58186 | 0.549997 | 0.274998 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274998 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(104\) | 11.5156 | 1.12920 | ||||||||
\(105\) | 3.54685 | 0.346137 | ||||||||
\(106\) | −2.12287 | −0.206191 | ||||||||
\(107\) | 8.77058 | 0.847884 | 0.423942 | − | 0.905689i | \(-0.360646\pi\) | ||||
0.423942 | + | 0.905689i | \(0.360646\pi\) | |||||||
\(108\) | 1.03800 | 0.0998812 | ||||||||
\(109\) | 8.70332 | 0.833626 | 0.416813 | − | 0.908992i | \(-0.363147\pi\) | ||||
0.416813 | + | 0.908992i | \(0.363147\pi\) | |||||||
\(110\) | −6.23267 | −0.594262 | ||||||||
\(111\) | −6.50621 | −0.617542 | ||||||||
\(112\) | 2.98963 | 0.282494 | ||||||||
\(113\) | −8.93732 | −0.840753 | −0.420376 | − | 0.907350i | \(-0.638102\pi\) | ||||
−0.420376 | + | 0.907350i | \(0.638102\pi\) | |||||||
\(114\) | −2.54751 | −0.238596 | ||||||||
\(115\) | 6.48262 | 0.604507 | ||||||||
\(116\) | 7.82411 | 0.726450 | ||||||||
\(117\) | 3.86467 | 0.357289 | ||||||||
\(118\) | −3.57124 | −0.328759 | ||||||||
\(119\) | 3.53145 | 0.323728 | ||||||||
\(120\) | −2.99271 | −0.273196 | ||||||||
\(121\) | 29.0307 | 2.63915 | ||||||||
\(122\) | −7.13619 | −0.646080 | ||||||||
\(123\) | 9.61376 | 0.866844 | ||||||||
\(124\) | 4.24698 | 0.381390 | ||||||||
\(125\) | −9.03046 | −0.807709 | ||||||||
\(126\) | 3.46371 | 0.308572 | ||||||||
\(127\) | 7.22565 | 0.641173 | 0.320587 | − | 0.947219i | \(-0.396120\pi\) | ||||
0.320587 | + | 0.947219i | \(0.396120\pi\) | |||||||
\(128\) | 3.66333 | 0.323796 | ||||||||
\(129\) | −7.33861 | −0.646129 | ||||||||
\(130\) | −3.80706 | −0.333901 | ||||||||
\(131\) | 15.2193 | 1.32971 | 0.664856 | − | 0.746971i | \(-0.268493\pi\) | ||||
0.664856 | + | 0.746971i | \(0.268493\pi\) | |||||||
\(132\) | 6.56738 | 0.571617 | ||||||||
\(133\) | 9.17235 | 0.795343 | ||||||||
\(134\) | 6.48703 | 0.560394 | ||||||||
\(135\) | −1.00436 | −0.0864415 | ||||||||
\(136\) | −2.97972 | −0.255509 | ||||||||
\(137\) | 17.4584 | 1.49157 | 0.745787 | − | 0.666185i | \(-0.232074\pi\) | ||||
0.745787 | + | 0.666185i | \(0.232074\pi\) | |||||||
\(138\) | 6.33067 | 0.538902 | ||||||||
\(139\) | 23.1304 | 1.96189 | 0.980946 | − | 0.194278i | \(-0.0622365\pi\) | ||||
0.980946 | + | 0.194278i | \(0.0622365\pi\) | |||||||
\(140\) | 3.68162 | 0.311153 | ||||||||
\(141\) | 4.71120 | 0.396754 | ||||||||
\(142\) | 11.4000 | 0.956666 | ||||||||
\(143\) | 24.4517 | 2.04475 | ||||||||
\(144\) | −0.846572 | −0.0705477 | ||||||||
\(145\) | −7.57056 | −0.628701 | ||||||||
\(146\) | 10.6231 | 0.879171 | ||||||||
\(147\) | −5.47117 | −0.451254 | ||||||||
\(148\) | −6.75342 | −0.555128 | ||||||||
\(149\) | 7.85577 | 0.643570 | 0.321785 | − | 0.946813i | \(-0.395717\pi\) | ||||
0.321785 | + | 0.946813i | \(0.395717\pi\) | |||||||
\(150\) | −3.91470 | −0.319634 | ||||||||
\(151\) | −1.61453 | −0.131388 | −0.0656941 | − | 0.997840i | \(-0.520926\pi\) | ||||
−0.0656941 | + | 0.997840i | \(0.520926\pi\) | |||||||
\(152\) | −7.73932 | −0.627741 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 21.9148 | 1.76595 | ||||||||
\(155\) | −4.10936 | −0.330071 | ||||||||
\(156\) | 4.01151 | 0.321178 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 15.9203 | 1.26655 | ||||||||
\(159\) | −2.16439 | −0.171647 | ||||||||
\(160\) | −5.15147 | −0.407259 | ||||||||
\(161\) | −22.7937 | −1.79639 | ||||||||
\(162\) | −0.980818 | −0.0770603 | ||||||||
\(163\) | −21.9925 | −1.72258 | −0.861291 | − | 0.508112i | \(-0.830344\pi\) | ||||
−0.861291 | + | 0.508112i | \(0.830344\pi\) | |||||||
\(164\) | 9.97905 | 0.779233 | ||||||||
\(165\) | −6.35456 | −0.494702 | ||||||||
\(166\) | 7.89889 | 0.613073 | ||||||||
\(167\) | 0.0214142 | 0.00165708 | 0.000828541 | − | 1.00000i | \(-0.499736\pi\) | ||||
0.000828541 | 1.00000i | \(0.499736\pi\) | ||||||||
\(168\) | 10.5227 | 0.811848 | ||||||||
\(169\) | 1.93567 | 0.148897 | ||||||||
\(170\) | 0.985094 | 0.0755533 | ||||||||
\(171\) | −2.59733 | −0.198623 | ||||||||
\(172\) | −7.61745 | −0.580825 | ||||||||
\(173\) | 5.93545 | 0.451264 | 0.225632 | − | 0.974213i | \(-0.427555\pi\) | ||||
0.225632 | + | 0.974213i | \(0.427555\pi\) | |||||||
\(174\) | −7.39311 | −0.560471 | ||||||||
\(175\) | 14.0950 | 1.06548 | ||||||||
\(176\) | −5.35624 | −0.403742 | ||||||||
\(177\) | −3.64108 | −0.273680 | ||||||||
\(178\) | −2.12601 | −0.159351 | ||||||||
\(179\) | −14.6954 | −1.09838 | −0.549191 | − | 0.835697i | \(-0.685064\pi\) | ||||
−0.549191 | + | 0.835697i | \(0.685064\pi\) | |||||||
\(180\) | −1.04252 | −0.0777050 | ||||||||
\(181\) | −4.11606 | −0.305944 | −0.152972 | − | 0.988230i | \(-0.548885\pi\) | ||||
−0.152972 | + | 0.988230i | \(0.548885\pi\) | |||||||
\(182\) | 13.3861 | 0.992244 | ||||||||
\(183\) | −7.27575 | −0.537839 | ||||||||
\(184\) | 19.2325 | 1.41784 | ||||||||
\(185\) | 6.53457 | 0.480431 | ||||||||
\(186\) | −4.01303 | −0.294250 | ||||||||
\(187\) | −6.32698 | −0.462675 | ||||||||
\(188\) | 4.89020 | 0.356655 | ||||||||
\(189\) | 3.53145 | 0.256875 | ||||||||
\(190\) | 2.55861 | 0.185621 | ||||||||
\(191\) | −7.47583 | −0.540932 | −0.270466 | − | 0.962730i | \(-0.587178\pi\) | ||||
−0.270466 | + | 0.962730i | \(0.587178\pi\) | |||||||
\(192\) | −6.72387 | −0.485253 | ||||||||
\(193\) | 2.58077 | 0.185768 | 0.0928839 | − | 0.995677i | \(-0.470391\pi\) | ||||
0.0928839 | + | 0.995677i | \(0.470391\pi\) | |||||||
\(194\) | −3.86695 | −0.277631 | ||||||||
\(195\) | −3.88152 | −0.277961 | ||||||||
\(196\) | −5.67905 | −0.405646 | ||||||||
\(197\) | −20.6346 | −1.47016 | −0.735079 | − | 0.677982i | \(-0.762855\pi\) | ||||
−0.735079 | + | 0.677982i | \(0.762855\pi\) | |||||||
\(198\) | −6.20562 | −0.441014 | ||||||||
\(199\) | −13.6167 | −0.965264 | −0.482632 | − | 0.875823i | \(-0.660319\pi\) | ||||
−0.482632 | + | 0.875823i | \(0.660319\pi\) | |||||||
\(200\) | −11.8928 | −0.840951 | ||||||||
\(201\) | 6.61390 | 0.466508 | ||||||||
\(202\) | 12.2369 | 0.860984 | ||||||||
\(203\) | 26.6191 | 1.86829 | ||||||||
\(204\) | −1.03800 | −0.0726743 | ||||||||
\(205\) | −9.65568 | −0.674382 | ||||||||
\(206\) | −5.47478 | −0.381446 | ||||||||
\(207\) | 6.45448 | 0.448617 | ||||||||
\(208\) | −3.27172 | −0.226853 | ||||||||
\(209\) | −16.4332 | −1.13671 | ||||||||
\(210\) | −3.47881 | −0.240061 | ||||||||
\(211\) | −22.0131 | −1.51544 | −0.757722 | − | 0.652578i | \(-0.773688\pi\) | ||||
−0.757722 | + | 0.652578i | \(0.773688\pi\) | |||||||
\(212\) | −2.24662 | −0.154299 | ||||||||
\(213\) | 11.6229 | 0.796391 | ||||||||
\(214\) | −8.60234 | −0.588044 | ||||||||
\(215\) | 7.37061 | 0.502671 | ||||||||
\(216\) | −2.97972 | −0.202744 | ||||||||
\(217\) | 14.4490 | 0.980863 | ||||||||
\(218\) | −8.53637 | −0.578156 | ||||||||
\(219\) | 10.8308 | 0.731879 | ||||||||
\(220\) | −6.59601 | −0.444703 | ||||||||
\(221\) | −3.86467 | −0.259966 | ||||||||
\(222\) | 6.38141 | 0.428292 | ||||||||
\(223\) | 17.6054 | 1.17895 | 0.589474 | − | 0.807787i | \(-0.299335\pi\) | ||||
0.589474 | + | 0.807787i | \(0.299335\pi\) | |||||||
\(224\) | 18.1132 | 1.21024 | ||||||||
\(225\) | −3.99126 | −0.266084 | ||||||||
\(226\) | 8.76589 | 0.583098 | ||||||||
\(227\) | −21.1832 | −1.40598 | −0.702991 | − | 0.711199i | \(-0.748152\pi\) | ||||
−0.702991 | + | 0.711199i | \(0.748152\pi\) | |||||||
\(228\) | −2.69602 | −0.178548 | ||||||||
\(229\) | −18.7107 | −1.23644 | −0.618220 | − | 0.786005i | \(-0.712146\pi\) | ||||
−0.618220 | + | 0.786005i | \(0.712146\pi\) | |||||||
\(230\) | −6.35827 | −0.419252 | ||||||||
\(231\) | 22.3434 | 1.47009 | ||||||||
\(232\) | −22.4603 | −1.47459 | ||||||||
\(233\) | −1.35758 | −0.0889379 | −0.0444689 | − | 0.999011i | \(-0.514160\pi\) | ||||
−0.0444689 | + | 0.999011i | \(0.514160\pi\) | |||||||
\(234\) | −3.79054 | −0.247795 | ||||||||
\(235\) | −4.73173 | −0.308664 | ||||||||
\(236\) | −3.77943 | −0.246020 | ||||||||
\(237\) | 16.2317 | 1.05436 | ||||||||
\(238\) | −3.46371 | −0.224519 | ||||||||
\(239\) | 15.1210 | 0.978094 | 0.489047 | − | 0.872257i | \(-0.337345\pi\) | ||||
0.489047 | + | 0.872257i | \(0.337345\pi\) | |||||||
\(240\) | 0.850263 | 0.0548842 | ||||||||
\(241\) | 16.4242 | 1.05797 | 0.528987 | − | 0.848630i | \(-0.322572\pi\) | ||||
0.528987 | + | 0.848630i | \(0.322572\pi\) | |||||||
\(242\) | −28.4738 | −1.83037 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.55220 | −0.483480 | ||||||||
\(245\) | 5.49502 | 0.351064 | ||||||||
\(246\) | −9.42935 | −0.601193 | ||||||||
\(247\) | −10.0378 | −0.638691 | ||||||||
\(248\) | −12.1916 | −0.774166 | ||||||||
\(249\) | 8.05337 | 0.510361 | ||||||||
\(250\) | 8.85724 | 0.560181 | ||||||||
\(251\) | 7.14002 | 0.450674 | 0.225337 | − | 0.974281i | \(-0.427652\pi\) | ||||
0.225337 | + | 0.974281i | \(0.427652\pi\) | |||||||
\(252\) | 3.66564 | 0.230913 | ||||||||
\(253\) | 40.8373 | 2.56742 | ||||||||
\(254\) | −7.08705 | −0.444681 | ||||||||
\(255\) | 1.00436 | 0.0628954 | ||||||||
\(256\) | −17.0408 | −1.06505 | ||||||||
\(257\) | −9.05691 | −0.564955 | −0.282477 | − | 0.959274i | \(-0.591156\pi\) | ||||
−0.282477 | + | 0.959274i | \(0.591156\pi\) | |||||||
\(258\) | 7.19784 | 0.448118 | ||||||||
\(259\) | −22.9764 | −1.42768 | ||||||||
\(260\) | −4.02900 | −0.249868 | ||||||||
\(261\) | −7.53770 | −0.466572 | ||||||||
\(262\) | −14.9273 | −0.922213 | ||||||||
\(263\) | 5.55816 | 0.342731 | 0.171365 | − | 0.985208i | \(-0.445182\pi\) | ||||
0.171365 | + | 0.985208i | \(0.445182\pi\) | |||||||
\(264\) | −18.8526 | −1.16030 | ||||||||
\(265\) | 2.17382 | 0.133537 | ||||||||
\(266\) | −8.99640 | −0.551605 | ||||||||
\(267\) | −2.16759 | −0.132654 | ||||||||
\(268\) | 6.86520 | 0.419359 | ||||||||
\(269\) | 12.5220 | 0.763478 | 0.381739 | − | 0.924270i | \(-0.375325\pi\) | ||||
0.381739 | + | 0.924270i | \(0.375325\pi\) | |||||||
\(270\) | 0.985094 | 0.0599509 | ||||||||
\(271\) | 2.37609 | 0.144337 | 0.0721686 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721686 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(272\) | 0.846572 | 0.0513310 | ||||||||
\(273\) | 13.6479 | 0.826009 | ||||||||
\(274\) | −17.1235 | −1.03447 | ||||||||
\(275\) | −25.2526 | −1.52279 | ||||||||
\(276\) | 6.69972 | 0.403276 | ||||||||
\(277\) | −21.2558 | −1.27714 | −0.638569 | − | 0.769564i | \(-0.720473\pi\) | ||||
−0.638569 | + | 0.769564i | \(0.720473\pi\) | |||||||
\(278\) | −22.6867 | −1.36066 | ||||||||
\(279\) | −4.09152 | −0.244953 | ||||||||
\(280\) | −10.5686 | −0.631596 | ||||||||
\(281\) | −8.43216 | −0.503020 | −0.251510 | − | 0.967855i | \(-0.580927\pi\) | ||||
−0.251510 | + | 0.967855i | \(0.580927\pi\) | |||||||
\(282\) | −4.62082 | −0.275166 | ||||||||
\(283\) | 5.80167 | 0.344873 | 0.172437 | − | 0.985021i | \(-0.444836\pi\) | ||||
0.172437 | + | 0.985021i | \(0.444836\pi\) | |||||||
\(284\) | 12.0646 | 0.715900 | ||||||||
\(285\) | 2.60865 | 0.154523 | ||||||||
\(286\) | −23.9826 | −1.41812 | ||||||||
\(287\) | 33.9506 | 2.00404 | ||||||||
\(288\) | −5.12911 | −0.302236 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.42535 | 0.436031 | ||||||||
\(291\) | −3.94258 | −0.231118 | ||||||||
\(292\) | 11.2424 | 0.657909 | ||||||||
\(293\) | −25.3292 | −1.47975 | −0.739874 | − | 0.672745i | \(-0.765115\pi\) | ||||
−0.739874 | + | 0.672745i | \(0.765115\pi\) | |||||||
\(294\) | 5.36622 | 0.312964 | ||||||||
\(295\) | 3.65695 | 0.212916 | ||||||||
\(296\) | 19.3867 | 1.12683 | ||||||||
\(297\) | −6.32698 | −0.367129 | ||||||||
\(298\) | −7.70508 | −0.446343 | ||||||||
\(299\) | 24.9444 | 1.44257 | ||||||||
\(300\) | −4.14291 | −0.239191 | ||||||||
\(301\) | −25.9160 | −1.49377 | ||||||||
\(302\) | 1.58356 | 0.0911234 | ||||||||
\(303\) | 12.4762 | 0.716739 | ||||||||
\(304\) | 2.19883 | 0.126111 | ||||||||
\(305\) | 7.30747 | 0.418424 | ||||||||
\(306\) | 0.980818 | 0.0560696 | ||||||||
\(307\) | −8.84271 | −0.504680 | −0.252340 | − | 0.967639i | \(-0.581200\pi\) | ||||
−0.252340 | + | 0.967639i | \(0.581200\pi\) | |||||||
\(308\) | 23.1924 | 1.32151 | ||||||||
\(309\) | −5.58186 | −0.317541 | ||||||||
\(310\) | 4.03053 | 0.228919 | ||||||||
\(311\) | 11.1415 | 0.631776 | 0.315888 | − | 0.948796i | \(-0.397698\pi\) | ||||
0.315888 | + | 0.948796i | \(0.397698\pi\) | |||||||
\(312\) | −11.5156 | −0.651945 | ||||||||
\(313\) | −17.4045 | −0.983760 | −0.491880 | − | 0.870663i | \(-0.663690\pi\) | ||||
−0.491880 | + | 0.870663i | \(0.663690\pi\) | |||||||
\(314\) | 0.980818 | 0.0553508 | ||||||||
\(315\) | −3.54685 | −0.199842 | ||||||||
\(316\) | 16.8484 | 0.947798 | ||||||||
\(317\) | 30.5137 | 1.71382 | 0.856910 | − | 0.515466i | \(-0.172381\pi\) | ||||
0.856910 | + | 0.515466i | \(0.172381\pi\) | |||||||
\(318\) | 2.12287 | 0.119045 | ||||||||
\(319\) | −47.6909 | −2.67018 | ||||||||
\(320\) | 6.75318 | 0.377514 | ||||||||
\(321\) | −8.77058 | −0.489526 | ||||||||
\(322\) | 22.3565 | 1.24588 | ||||||||
\(323\) | 2.59733 | 0.144519 | ||||||||
\(324\) | −1.03800 | −0.0576664 | ||||||||
\(325\) | −15.4249 | −0.855620 | ||||||||
\(326\) | 21.5706 | 1.19468 | ||||||||
\(327\) | −8.70332 | −0.481294 | ||||||||
\(328\) | −28.6463 | −1.58173 | ||||||||
\(329\) | 16.6374 | 0.917248 | ||||||||
\(330\) | 6.23267 | 0.343097 | ||||||||
\(331\) | 18.7043 | 1.02808 | 0.514040 | − | 0.857766i | \(-0.328148\pi\) | ||||
0.514040 | + | 0.857766i | \(0.328148\pi\) | |||||||
\(332\) | 8.35936 | 0.458780 | ||||||||
\(333\) | 6.50621 | 0.356538 | ||||||||
\(334\) | −0.0210034 | −0.00114926 | ||||||||
\(335\) | −6.64273 | −0.362931 | ||||||||
\(336\) | −2.98963 | −0.163098 | ||||||||
\(337\) | −18.1160 | −0.986842 | −0.493421 | − | 0.869791i | \(-0.664254\pi\) | ||||
−0.493421 | + | 0.869791i | \(0.664254\pi\) | |||||||
\(338\) | −1.89854 | −0.103267 | ||||||||
\(339\) | 8.93732 | 0.485409 | ||||||||
\(340\) | 1.04252 | 0.0565387 | ||||||||
\(341\) | −25.8870 | −1.40186 | ||||||||
\(342\) | 2.54751 | 0.137753 | ||||||||
\(343\) | 5.39900 | 0.291519 | ||||||||
\(344\) | 21.8670 | 1.17899 | ||||||||
\(345\) | −6.48262 | −0.349012 | ||||||||
\(346\) | −5.82159 | −0.312971 | ||||||||
\(347\) | −12.5427 | −0.673325 | −0.336663 | − | 0.941625i | \(-0.609298\pi\) | ||||
−0.336663 | + | 0.941625i | \(0.609298\pi\) | |||||||
\(348\) | −7.82411 | −0.419416 | ||||||||
\(349\) | −6.54338 | −0.350259 | −0.175129 | − | 0.984545i | \(-0.556034\pi\) | ||||
−0.175129 | + | 0.984545i | \(0.556034\pi\) | |||||||
\(350\) | −13.8246 | −0.738955 | ||||||||
\(351\) | −3.86467 | −0.206281 | ||||||||
\(352\) | −32.4518 | −1.72969 | ||||||||
\(353\) | 7.74439 | 0.412192 | 0.206096 | − | 0.978532i | \(-0.433924\pi\) | ||||
0.206096 | + | 0.978532i | \(0.433924\pi\) | |||||||
\(354\) | 3.57124 | 0.189809 | ||||||||
\(355\) | −11.6736 | −0.619571 | ||||||||
\(356\) | −2.24995 | −0.119247 | ||||||||
\(357\) | −3.53145 | −0.186904 | ||||||||
\(358\) | 14.4135 | 0.761776 | ||||||||
\(359\) | −5.80074 | −0.306151 | −0.153076 | − | 0.988214i | \(-0.548918\pi\) | ||||
−0.153076 | + | 0.988214i | \(0.548918\pi\) | |||||||
\(360\) | 2.99271 | 0.157730 | ||||||||
\(361\) | −12.2539 | −0.644941 | ||||||||
\(362\) | 4.03711 | 0.212186 | ||||||||
\(363\) | −29.0307 | −1.52371 | ||||||||
\(364\) | 14.1665 | 0.742525 | ||||||||
\(365\) | −10.8780 | −0.569383 | ||||||||
\(366\) | 7.13619 | 0.373014 | ||||||||
\(367\) | −9.02968 | −0.471345 | −0.235673 | − | 0.971832i | \(-0.575729\pi\) | ||||
−0.235673 | + | 0.971832i | \(0.575729\pi\) | |||||||
\(368\) | −5.46418 | −0.284840 | ||||||||
\(369\) | −9.61376 | −0.500472 | ||||||||
\(370\) | −6.40923 | −0.333200 | ||||||||
\(371\) | −7.64343 | −0.396827 | ||||||||
\(372\) | −4.24698 | −0.220196 | ||||||||
\(373\) | −1.15360 | −0.0597310 | −0.0298655 | − | 0.999554i | \(-0.509508\pi\) | ||||
−0.0298655 | + | 0.999554i | \(0.509508\pi\) | |||||||
\(374\) | 6.20562 | 0.320885 | ||||||||
\(375\) | 9.03046 | 0.466331 | ||||||||
\(376\) | −14.0380 | −0.723957 | ||||||||
\(377\) | −29.1307 | −1.50031 | ||||||||
\(378\) | −3.46371 | −0.178154 | ||||||||
\(379\) | 18.2491 | 0.937394 | 0.468697 | − | 0.883359i | \(-0.344724\pi\) | ||||
0.468697 | + | 0.883359i | \(0.344724\pi\) | |||||||
\(380\) | 2.70777 | 0.138906 | ||||||||
\(381\) | −7.22565 | −0.370181 | ||||||||
\(382\) | 7.33242 | 0.375159 | ||||||||
\(383\) | −23.5927 | −1.20553 | −0.602764 | − | 0.797919i | \(-0.705934\pi\) | ||||
−0.602764 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(384\) | −3.66333 | −0.186943 | ||||||||
\(385\) | −22.4408 | −1.14369 | ||||||||
\(386\) | −2.53126 | −0.128838 | ||||||||
\(387\) | 7.33861 | 0.373043 | ||||||||
\(388\) | −4.09238 | −0.207759 | ||||||||
\(389\) | 13.8726 | 0.703370 | 0.351685 | − | 0.936118i | \(-0.385609\pi\) | ||||
0.351685 | + | 0.936118i | \(0.385609\pi\) | |||||||
\(390\) | 3.80706 | 0.192778 | ||||||||
\(391\) | −6.45448 | −0.326417 | ||||||||
\(392\) | 16.3026 | 0.823403 | ||||||||
\(393\) | −15.2193 | −0.767710 | ||||||||
\(394\) | 20.2388 | 1.01962 | ||||||||
\(395\) | −16.3024 | −0.820265 | ||||||||
\(396\) | −6.56738 | −0.330023 | ||||||||
\(397\) | 19.8767 | 0.997581 | 0.498791 | − | 0.866722i | \(-0.333778\pi\) | ||||
0.498791 | + | 0.866722i | \(0.333778\pi\) | |||||||
\(398\) | 13.3555 | 0.669452 | ||||||||
\(399\) | −9.17235 | −0.459192 | ||||||||
\(400\) | 3.37889 | 0.168945 | ||||||||
\(401\) | −23.1378 | −1.15544 | −0.577722 | − | 0.816233i | \(-0.696058\pi\) | ||||
−0.577722 | + | 0.816233i | \(0.696058\pi\) | |||||||
\(402\) | −6.48703 | −0.323544 | ||||||||
\(403\) | −15.8124 | −0.787670 | ||||||||
\(404\) | 12.9503 | 0.644299 | ||||||||
\(405\) | 1.00436 | 0.0499070 | ||||||||
\(406\) | −26.1084 | −1.29574 | ||||||||
\(407\) | 41.1647 | 2.04046 | ||||||||
\(408\) | 2.97972 | 0.147518 | ||||||||
\(409\) | 30.7047 | 1.51825 | 0.759125 | − | 0.650945i | \(-0.225627\pi\) | ||||
0.759125 | + | 0.650945i | \(0.225627\pi\) | |||||||
\(410\) | 9.47046 | 0.467713 | ||||||||
\(411\) | −17.4584 | −0.861160 | ||||||||
\(412\) | −5.79394 | −0.285447 | ||||||||
\(413\) | −12.8583 | −0.632716 | ||||||||
\(414\) | −6.33067 | −0.311135 | ||||||||
\(415\) | −8.08848 | −0.397048 | ||||||||
\(416\) | −19.8223 | −0.971869 | ||||||||
\(417\) | −23.1304 | −1.13270 | ||||||||
\(418\) | 16.1180 | 0.788358 | ||||||||
\(419\) | 27.4810 | 1.34254 | 0.671268 | − | 0.741215i | \(-0.265750\pi\) | ||||
0.671268 | + | 0.741215i | \(0.265750\pi\) | |||||||
\(420\) | −3.68162 | −0.179644 | ||||||||
\(421\) | −32.6641 | −1.59195 | −0.795975 | − | 0.605329i | \(-0.793041\pi\) | ||||
−0.795975 | + | 0.605329i | \(0.793041\pi\) | |||||||
\(422\) | 21.5908 | 1.05103 | ||||||||
\(423\) | −4.71120 | −0.229066 | ||||||||
\(424\) | 6.44926 | 0.313204 | ||||||||
\(425\) | 3.99126 | 0.193605 | ||||||||
\(426\) | −11.4000 | −0.552331 | ||||||||
\(427\) | −25.6940 | −1.24342 | ||||||||
\(428\) | −9.10382 | −0.440050 | ||||||||
\(429\) | −24.4517 | −1.18054 | ||||||||
\(430\) | −7.22922 | −0.348624 | ||||||||
\(431\) | −0.416855 | −0.0200792 | −0.0100396 | − | 0.999950i | \(-0.503196\pi\) | ||||
−0.0100396 | + | 0.999950i | \(0.503196\pi\) | |||||||
\(432\) | 0.846572 | 0.0407307 | ||||||||
\(433\) | 6.04143 | 0.290332 | 0.145166 | − | 0.989407i | \(-0.453628\pi\) | ||||
0.145166 | + | 0.989407i | \(0.453628\pi\) | |||||||
\(434\) | −14.1718 | −0.680270 | ||||||||
\(435\) | 7.57056 | 0.362981 | ||||||||
\(436\) | −9.03401 | −0.432650 | ||||||||
\(437\) | −16.7644 | −0.801950 | ||||||||
\(438\) | −10.6231 | −0.507590 | ||||||||
\(439\) | −5.79669 | −0.276661 | −0.138330 | − | 0.990386i | \(-0.544174\pi\) | ||||
−0.138330 | + | 0.990386i | \(0.544174\pi\) | |||||||
\(440\) | 18.9348 | 0.902682 | ||||||||
\(441\) | 5.47117 | 0.260532 | ||||||||
\(442\) | 3.79054 | 0.180297 | ||||||||
\(443\) | −18.3239 | −0.870596 | −0.435298 | − | 0.900287i | \(-0.643357\pi\) | ||||
−0.435298 | + | 0.900287i | \(0.643357\pi\) | |||||||
\(444\) | 6.75342 | 0.320503 | ||||||||
\(445\) | 2.17704 | 0.103202 | ||||||||
\(446\) | −17.2677 | −0.817651 | ||||||||
\(447\) | −7.85577 | −0.371565 | ||||||||
\(448\) | −23.7450 | −1.12185 | ||||||||
\(449\) | −30.6524 | −1.44658 | −0.723289 | − | 0.690546i | \(-0.757370\pi\) | ||||
−0.723289 | + | 0.690546i | \(0.757370\pi\) | |||||||
\(450\) | 3.91470 | 0.184541 | ||||||||
\(451\) | −60.8261 | −2.86419 | ||||||||
\(452\) | 9.27691 | 0.436349 | ||||||||
\(453\) | 1.61453 | 0.0758570 | ||||||||
\(454\) | 20.7769 | 0.975109 | ||||||||
\(455\) | −13.7074 | −0.642613 | ||||||||
\(456\) | 7.73932 | 0.362427 | ||||||||
\(457\) | −40.9890 | −1.91739 | −0.958693 | − | 0.284444i | \(-0.908191\pi\) | ||||
−0.958693 | + | 0.284444i | \(0.908191\pi\) | |||||||
\(458\) | 18.3518 | 0.857524 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −6.72893 | −0.313738 | ||||||||
\(461\) | 29.9443 | 1.39465 | 0.697323 | − | 0.716757i | \(-0.254375\pi\) | ||||
0.697323 | + | 0.716757i | \(0.254375\pi\) | |||||||
\(462\) | −21.9148 | −1.01957 | ||||||||
\(463\) | −1.03311 | −0.0480129 | −0.0240065 | − | 0.999712i | \(-0.507642\pi\) | ||||
−0.0240065 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(464\) | 6.38121 | 0.296240 | ||||||||
\(465\) | 4.10936 | 0.190567 | ||||||||
\(466\) | 1.33154 | 0.0616822 | ||||||||
\(467\) | −29.8673 | −1.38209 | −0.691046 | − | 0.722811i | \(-0.742850\pi\) | ||||
−0.691046 | + | 0.722811i | \(0.742850\pi\) | |||||||
\(468\) | −4.01151 | −0.185432 | ||||||||
\(469\) | 23.3567 | 1.07851 | ||||||||
\(470\) | 4.64097 | 0.214072 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 10.8494 | 0.499384 | ||||||||
\(473\) | 46.4312 | 2.13491 | ||||||||
\(474\) | −15.9203 | −0.731245 | ||||||||
\(475\) | 10.3666 | 0.475653 | ||||||||
\(476\) | −3.66564 | −0.168014 | ||||||||
\(477\) | 2.16439 | 0.0991004 | ||||||||
\(478\) | −14.8309 | −0.678350 | ||||||||
\(479\) | 18.3559 | 0.838701 | 0.419350 | − | 0.907824i | \(-0.362258\pi\) | ||||
0.419350 | + | 0.907824i | \(0.362258\pi\) | |||||||
\(480\) | 5.15147 | 0.235131 | ||||||||
\(481\) | 25.1443 | 1.14648 | ||||||||
\(482\) | −16.1091 | −0.733751 | ||||||||
\(483\) | 22.7937 | 1.03715 | ||||||||
\(484\) | −30.1337 | −1.36971 | ||||||||
\(485\) | 3.95977 | 0.179804 | ||||||||
\(486\) | 0.980818 | 0.0444908 | ||||||||
\(487\) | 6.50618 | 0.294823 | 0.147412 | − | 0.989075i | \(-0.452906\pi\) | ||||
0.147412 | + | 0.989075i | \(0.452906\pi\) | |||||||
\(488\) | 21.6797 | 0.981394 | ||||||||
\(489\) | 21.9925 | 0.994533 | ||||||||
\(490\) | −5.38961 | −0.243478 | ||||||||
\(491\) | −34.8722 | −1.57376 | −0.786880 | − | 0.617106i | \(-0.788305\pi\) | ||||
−0.786880 | + | 0.617106i | \(0.788305\pi\) | |||||||
\(492\) | −9.97905 | −0.449890 | ||||||||
\(493\) | 7.53770 | 0.339481 | ||||||||
\(494\) | 9.84527 | 0.442960 | ||||||||
\(495\) | 6.35456 | 0.285616 | ||||||||
\(496\) | 3.46377 | 0.155528 | ||||||||
\(497\) | 41.0459 | 1.84116 | ||||||||
\(498\) | −7.89889 | −0.353958 | ||||||||
\(499\) | 31.2012 | 1.39676 | 0.698379 | − | 0.715728i | \(-0.253905\pi\) | ||||
0.698379 | + | 0.715728i | \(0.253905\pi\) | |||||||
\(500\) | 9.37358 | 0.419199 | ||||||||
\(501\) | −0.0214142 | −0.000956716 0 | ||||||||
\(502\) | −7.00306 | −0.312562 | ||||||||
\(503\) | 32.9316 | 1.46835 | 0.734173 | − | 0.678963i | \(-0.237570\pi\) | ||||
0.734173 | + | 0.678963i | \(0.237570\pi\) | |||||||
\(504\) | −10.5227 | −0.468720 | ||||||||
\(505\) | −12.5306 | −0.557604 | ||||||||
\(506\) | −40.0540 | −1.78062 | ||||||||
\(507\) | −1.93567 | −0.0859660 | ||||||||
\(508\) | −7.50020 | −0.332768 | ||||||||
\(509\) | 13.7677 | 0.610243 | 0.305121 | − | 0.952313i | \(-0.401303\pi\) | ||||
0.305121 | + | 0.952313i | \(0.401303\pi\) | |||||||
\(510\) | −0.985094 | −0.0436207 | ||||||||
\(511\) | 38.2486 | 1.69202 | ||||||||
\(512\) | 9.38726 | 0.414862 | ||||||||
\(513\) | 2.59733 | 0.114675 | ||||||||
\(514\) | 8.88319 | 0.391821 | ||||||||
\(515\) | 5.60619 | 0.247038 | ||||||||
\(516\) | 7.61745 | 0.335340 | ||||||||
\(517\) | −29.8076 | −1.31094 | ||||||||
\(518\) | 22.5356 | 0.990160 | ||||||||
\(519\) | −5.93545 | −0.260537 | ||||||||
\(520\) | 11.5658 | 0.507196 | ||||||||
\(521\) | 10.9548 | 0.479940 | 0.239970 | − | 0.970780i | \(-0.422862\pi\) | ||||
0.239970 | + | 0.970780i | \(0.422862\pi\) | |||||||
\(522\) | 7.39311 | 0.323588 | ||||||||
\(523\) | 28.5644 | 1.24903 | 0.624516 | − | 0.781012i | \(-0.285296\pi\) | ||||
0.624516 | + | 0.781012i | \(0.285296\pi\) | |||||||
\(524\) | −15.7975 | −0.690118 | ||||||||
\(525\) | −14.0950 | −0.615154 | ||||||||
\(526\) | −5.45155 | −0.237699 | ||||||||
\(527\) | 4.09152 | 0.178229 | ||||||||
\(528\) | 5.35624 | 0.233101 | ||||||||
\(529\) | 18.6603 | 0.811316 | ||||||||
\(530\) | −2.13212 | −0.0926135 | ||||||||
\(531\) | 3.64108 | 0.158009 | ||||||||
\(532\) | −9.52086 | −0.412782 | ||||||||
\(533\) | −37.1540 | −1.60932 | ||||||||
\(534\) | 2.12601 | 0.0920015 | ||||||||
\(535\) | 8.80881 | 0.380838 | ||||||||
\(536\) | −19.7076 | −0.851237 | ||||||||
\(537\) | 14.6954 | 0.634151 | ||||||||
\(538\) | −12.2818 | −0.529505 | ||||||||
\(539\) | 34.6160 | 1.49101 | ||||||||
\(540\) | 1.04252 | 0.0448630 | ||||||||
\(541\) | 3.26376 | 0.140320 | 0.0701599 | − | 0.997536i | \(-0.477649\pi\) | ||||
0.0701599 | + | 0.997536i | \(0.477649\pi\) | |||||||
\(542\) | −2.33051 | −0.100104 | ||||||||
\(543\) | 4.11606 | 0.176637 | ||||||||
\(544\) | 5.12911 | 0.219909 | ||||||||
\(545\) | 8.74126 | 0.374434 | ||||||||
\(546\) | −13.3861 | −0.572872 | ||||||||
\(547\) | −15.6784 | −0.670361 | −0.335180 | − | 0.942154i | \(-0.608797\pi\) | ||||
−0.335180 | + | 0.942154i | \(0.608797\pi\) | |||||||
\(548\) | −18.1218 | −0.774124 | ||||||||
\(549\) | 7.27575 | 0.310521 | ||||||||
\(550\) | 24.7682 | 1.05612 | ||||||||
\(551\) | 19.5779 | 0.834046 | ||||||||
\(552\) | −19.2325 | −0.818591 | ||||||||
\(553\) | 57.3214 | 2.43756 | ||||||||
\(554\) | 20.8481 | 0.885751 | ||||||||
\(555\) | −6.53457 | −0.277377 | ||||||||
\(556\) | −24.0092 | −1.01822 | ||||||||
\(557\) | −44.5967 | −1.88962 | −0.944811 | − | 0.327615i | \(-0.893755\pi\) | ||||
−0.944811 | + | 0.327615i | \(0.893755\pi\) | |||||||
\(558\) | 4.01303 | 0.169885 | ||||||||
\(559\) | 28.3613 | 1.19956 | ||||||||
\(560\) | 3.00266 | 0.126886 | ||||||||
\(561\) | 6.32698 | 0.267125 | ||||||||
\(562\) | 8.27041 | 0.348866 | ||||||||
\(563\) | 18.1585 | 0.765290 | 0.382645 | − | 0.923895i | \(-0.375013\pi\) | ||||
0.382645 | + | 0.923895i | \(0.375013\pi\) | |||||||
\(564\) | −4.89020 | −0.205915 | ||||||||
\(565\) | −8.97629 | −0.377635 | ||||||||
\(566\) | −5.69038 | −0.239184 | ||||||||
\(567\) | −3.53145 | −0.148307 | ||||||||
\(568\) | −34.6331 | −1.45317 | ||||||||
\(569\) | −17.4367 | −0.730984 | −0.365492 | − | 0.930814i | \(-0.619099\pi\) | ||||
−0.365492 | + | 0.930814i | \(0.619099\pi\) | |||||||
\(570\) | −2.55861 | −0.107169 | ||||||||
\(571\) | 20.6732 | 0.865147 | 0.432574 | − | 0.901599i | \(-0.357606\pi\) | ||||
0.432574 | + | 0.901599i | \(0.357606\pi\) | |||||||
\(572\) | −25.3807 | −1.06122 | ||||||||
\(573\) | 7.47583 | 0.312307 | ||||||||
\(574\) | −33.2993 | −1.38989 | ||||||||
\(575\) | −25.7615 | −1.07433 | ||||||||
\(576\) | 6.72387 | 0.280161 | ||||||||
\(577\) | −33.5049 | −1.39483 | −0.697413 | − | 0.716669i | \(-0.745666\pi\) | ||||
−0.697413 | + | 0.716669i | \(0.745666\pi\) | |||||||
\(578\) | −0.980818 | −0.0407967 | ||||||||
\(579\) | −2.58077 | −0.107253 | ||||||||
\(580\) | 7.85822 | 0.326295 | ||||||||
\(581\) | 28.4401 | 1.17989 | ||||||||
\(582\) | 3.86695 | 0.160290 | ||||||||
\(583\) | 13.6940 | 0.567148 | ||||||||
\(584\) | −32.2728 | −1.33546 | ||||||||
\(585\) | 3.88152 | 0.160481 | ||||||||
\(586\) | 24.8433 | 1.02627 | ||||||||
\(587\) | −14.9112 | −0.615452 | −0.307726 | − | 0.951475i | \(-0.599568\pi\) | ||||
−0.307726 | + | 0.951475i | \(0.599568\pi\) | |||||||
\(588\) | 5.67905 | 0.234200 | ||||||||
\(589\) | 10.6270 | 0.437879 | ||||||||
\(590\) | −3.58681 | −0.147666 | ||||||||
\(591\) | 20.6346 | 0.848796 | ||||||||
\(592\) | −5.50798 | −0.226376 | ||||||||
\(593\) | −22.1437 | −0.909332 | −0.454666 | − | 0.890662i | \(-0.650241\pi\) | ||||
−0.454666 | + | 0.890662i | \(0.650241\pi\) | |||||||
\(594\) | 6.20562 | 0.254619 | ||||||||
\(595\) | 3.54685 | 0.145407 | ||||||||
\(596\) | −8.15426 | −0.334011 | ||||||||
\(597\) | 13.6167 | 0.557295 | ||||||||
\(598\) | −24.4659 | −1.00049 | ||||||||
\(599\) | 11.8283 | 0.483289 | 0.241645 | − | 0.970365i | \(-0.422313\pi\) | ||||
0.241645 | + | 0.970365i | \(0.422313\pi\) | |||||||
\(600\) | 11.8928 | 0.485523 | ||||||||
\(601\) | −9.44203 | −0.385149 | −0.192574 | − | 0.981282i | \(-0.561684\pi\) | ||||
−0.192574 | + | 0.981282i | \(0.561684\pi\) | |||||||
\(602\) | 25.4189 | 1.03599 | ||||||||
\(603\) | −6.61390 | −0.269339 | ||||||||
\(604\) | 1.67587 | 0.0681902 | ||||||||
\(605\) | 29.1572 | 1.18541 | ||||||||
\(606\) | −12.2369 | −0.497090 | ||||||||
\(607\) | −22.1184 | −0.897756 | −0.448878 | − | 0.893593i | \(-0.648176\pi\) | ||||
−0.448878 | + | 0.893593i | \(0.648176\pi\) | |||||||
\(608\) | 13.3220 | 0.540278 | ||||||||
\(609\) | −26.6191 | −1.07866 | ||||||||
\(610\) | −7.16730 | −0.290195 | ||||||||
\(611\) | −18.2072 | −0.736585 | ||||||||
\(612\) | 1.03800 | 0.0419585 | ||||||||
\(613\) | −0.434638 | −0.0175549 | −0.00877744 | − | 0.999961i | \(-0.502794\pi\) | ||||
−0.00877744 | + | 0.999961i | \(0.502794\pi\) | |||||||
\(614\) | 8.67309 | 0.350017 | ||||||||
\(615\) | 9.65568 | 0.389354 | ||||||||
\(616\) | −66.5772 | −2.68247 | ||||||||
\(617\) | −13.4147 | −0.540056 | −0.270028 | − | 0.962853i | \(-0.587033\pi\) | ||||
−0.270028 | + | 0.962853i | \(0.587033\pi\) | |||||||
\(618\) | 5.47478 | 0.220228 | ||||||||
\(619\) | −38.8737 | −1.56246 | −0.781232 | − | 0.624241i | \(-0.785409\pi\) | ||||
−0.781232 | + | 0.624241i | \(0.785409\pi\) | |||||||
\(620\) | 4.26550 | 0.171306 | ||||||||
\(621\) | −6.45448 | −0.259009 | ||||||||
\(622\) | −10.9278 | −0.438164 | ||||||||
\(623\) | −7.65475 | −0.306681 | ||||||||
\(624\) | 3.27172 | 0.130974 | ||||||||
\(625\) | 10.8865 | 0.435459 | ||||||||
\(626\) | 17.0706 | 0.682280 | ||||||||
\(627\) | 16.4332 | 0.656281 | ||||||||
\(628\) | 1.03800 | 0.0414206 | ||||||||
\(629\) | −6.50621 | −0.259420 | ||||||||
\(630\) | 3.47881 | 0.138599 | ||||||||
\(631\) | −43.6469 | −1.73755 | −0.868777 | − | 0.495204i | \(-0.835093\pi\) | ||||
−0.868777 | + | 0.495204i | \(0.835093\pi\) | |||||||
\(632\) | −48.3659 | −1.92389 | ||||||||
\(633\) | 22.0131 | 0.874942 | ||||||||
\(634\) | −29.9284 | −1.18861 | ||||||||
\(635\) | 7.25716 | 0.287991 | ||||||||
\(636\) | 2.24662 | 0.0890844 | ||||||||
\(637\) | 21.1442 | 0.837766 | ||||||||
\(638\) | 46.7761 | 1.85188 | ||||||||
\(639\) | −11.6229 | −0.459796 | ||||||||
\(640\) | 3.67930 | 0.145437 | ||||||||
\(641\) | −7.34221 | −0.290000 | −0.145000 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.145000 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(642\) | 8.60234 | 0.339507 | ||||||||
\(643\) | 1.32896 | 0.0524089 | 0.0262044 | − | 0.999657i | \(-0.491658\pi\) | ||||
0.0262044 | + | 0.999657i | \(0.491658\pi\) | |||||||
\(644\) | 23.6598 | 0.932325 | ||||||||
\(645\) | −7.37061 | −0.290217 | ||||||||
\(646\) | −2.54751 | −0.100230 | ||||||||
\(647\) | −30.2272 | −1.18835 | −0.594177 | − | 0.804334i | \(-0.702522\pi\) | ||||
−0.594177 | + | 0.804334i | \(0.702522\pi\) | |||||||
\(648\) | 2.97972 | 0.117055 | ||||||||
\(649\) | 23.0370 | 0.904283 | ||||||||
\(650\) | 15.1290 | 0.593409 | ||||||||
\(651\) | −14.4490 | −0.566301 | ||||||||
\(652\) | 22.8281 | 0.894017 | ||||||||
\(653\) | −42.1752 | −1.65044 | −0.825222 | − | 0.564809i | \(-0.808950\pi\) | ||||
−0.825222 | + | 0.564809i | \(0.808950\pi\) | |||||||
\(654\) | 8.53637 | 0.333798 | ||||||||
\(655\) | 15.2856 | 0.597258 | ||||||||
\(656\) | 8.13874 | 0.317765 | ||||||||
\(657\) | −10.8308 | −0.422551 | ||||||||
\(658\) | −16.3182 | −0.636151 | ||||||||
\(659\) | 2.87875 | 0.112140 | 0.0560701 | − | 0.998427i | \(-0.482143\pi\) | ||||
0.0560701 | + | 0.998427i | \(0.482143\pi\) | |||||||
\(660\) | 6.59601 | 0.256749 | ||||||||
\(661\) | −4.30998 | −0.167639 | −0.0838193 | − | 0.996481i | \(-0.526712\pi\) | ||||
−0.0838193 | + | 0.996481i | \(0.526712\pi\) | |||||||
\(662\) | −18.3455 | −0.713017 | ||||||||
\(663\) | 3.86467 | 0.150091 | ||||||||
\(664\) | −23.9968 | −0.931256 | ||||||||
\(665\) | 9.21233 | 0.357239 | ||||||||
\(666\) | −6.38141 | −0.247275 | ||||||||
\(667\) | −48.6519 | −1.88381 | ||||||||
\(668\) | −0.0222279 | −0.000860022 0 | ||||||||
\(669\) | −17.6054 | −0.680666 | ||||||||
\(670\) | 6.51531 | 0.251708 | ||||||||
\(671\) | 46.0335 | 1.77710 | ||||||||
\(672\) | −18.1132 | −0.698732 | ||||||||
\(673\) | −36.1438 | −1.39324 | −0.696620 | − | 0.717440i | \(-0.745314\pi\) | ||||
−0.696620 | + | 0.717440i | \(0.745314\pi\) | |||||||
\(674\) | 17.7685 | 0.684417 | ||||||||
\(675\) | 3.99126 | 0.153624 | ||||||||
\(676\) | −2.00921 | −0.0772775 | ||||||||
\(677\) | 0.978831 | 0.0376195 | 0.0188098 | − | 0.999823i | \(-0.494012\pi\) | ||||
0.0188098 | + | 0.999823i | \(0.494012\pi\) | |||||||
\(678\) | −8.76589 | −0.336652 | ||||||||
\(679\) | −13.9230 | −0.534317 | ||||||||
\(680\) | −2.99271 | −0.114765 | ||||||||
\(681\) | 21.1832 | 0.811744 | ||||||||
\(682\) | 25.3904 | 0.972248 | ||||||||
\(683\) | −20.5167 | −0.785048 | −0.392524 | − | 0.919742i | \(-0.628398\pi\) | ||||
−0.392524 | + | 0.919742i | \(0.628398\pi\) | |||||||
\(684\) | 2.69602 | 0.103085 | ||||||||
\(685\) | 17.5345 | 0.669960 | ||||||||
\(686\) | −5.29544 | −0.202181 | ||||||||
\(687\) | 18.7107 | 0.713859 | ||||||||
\(688\) | −6.21266 | −0.236856 | ||||||||
\(689\) | 8.36463 | 0.318667 | ||||||||
\(690\) | 6.35827 | 0.242055 | ||||||||
\(691\) | 8.25164 | 0.313907 | 0.156954 | − | 0.987606i | \(-0.449833\pi\) | ||||
0.156954 | + | 0.987606i | \(0.449833\pi\) | |||||||
\(692\) | −6.16097 | −0.234205 | ||||||||
\(693\) | −22.3434 | −0.848757 | ||||||||
\(694\) | 12.3021 | 0.466980 | ||||||||
\(695\) | 23.2312 | 0.881210 | ||||||||
\(696\) | 22.4603 | 0.851354 | ||||||||
\(697\) | 9.61376 | 0.364147 | ||||||||
\(698\) | 6.41786 | 0.242920 | ||||||||
\(699\) | 1.35758 | 0.0513483 | ||||||||
\(700\) | −14.6305 | −0.552981 | ||||||||
\(701\) | −10.3876 | −0.392333 | −0.196166 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196166 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(702\) | 3.79054 | 0.143065 | ||||||||
\(703\) | −16.8988 | −0.637349 | ||||||||
\(704\) | 42.5418 | 1.60335 | ||||||||
\(705\) | 4.73173 | 0.178207 | ||||||||
\(706\) | −7.59584 | −0.285873 | ||||||||
\(707\) | 44.0592 | 1.65701 | ||||||||
\(708\) | 3.77943 | 0.142040 | ||||||||
\(709\) | −7.12066 | −0.267422 | −0.133711 | − | 0.991020i | \(-0.542689\pi\) | ||||
−0.133711 | + | 0.991020i | \(0.542689\pi\) | |||||||
\(710\) | 11.4497 | 0.429699 | ||||||||
\(711\) | −16.2317 | −0.608736 | ||||||||
\(712\) | 6.45882 | 0.242054 | ||||||||
\(713\) | −26.4086 | −0.989010 | ||||||||
\(714\) | 3.46371 | 0.129626 | ||||||||
\(715\) | 24.5583 | 0.918428 | ||||||||
\(716\) | 15.2537 | 0.570058 | ||||||||
\(717\) | −15.1210 | −0.564703 | ||||||||
\(718\) | 5.68947 | 0.212329 | ||||||||
\(719\) | 23.3538 | 0.870948 | 0.435474 | − | 0.900201i | \(-0.356581\pi\) | ||||
0.435474 | + | 0.900201i | \(0.356581\pi\) | |||||||
\(720\) | −0.850263 | −0.0316874 | ||||||||
\(721\) | −19.7121 | −0.734116 | ||||||||
\(722\) | 12.0188 | 0.447295 | ||||||||
\(723\) | −16.4242 | −0.610822 | ||||||||
\(724\) | 4.27246 | 0.158785 | ||||||||
\(725\) | 30.0849 | 1.11733 | ||||||||
\(726\) | 28.4738 | 1.05676 | ||||||||
\(727\) | 23.5558 | 0.873636 | 0.436818 | − | 0.899550i | \(-0.356105\pi\) | ||||
0.436818 | + | 0.899550i | \(0.356105\pi\) | |||||||
\(728\) | −40.6669 | −1.50722 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.6694 | 0.394891 | ||||||||
\(731\) | −7.33861 | −0.271428 | ||||||||
\(732\) | 7.55220 | 0.279137 | ||||||||
\(733\) | −17.3075 | −0.639266 | −0.319633 | − | 0.947541i | \(-0.603560\pi\) | ||||
−0.319633 | + | 0.947541i | \(0.603560\pi\) | |||||||
\(734\) | 8.85647 | 0.326898 | ||||||||
\(735\) | −5.49502 | −0.202687 | ||||||||
\(736\) | −33.1057 | −1.22029 | ||||||||
\(737\) | −41.8460 | −1.54142 | ||||||||
\(738\) | 9.42935 | 0.347099 | ||||||||
\(739\) | 35.2270 | 1.29584 | 0.647922 | − | 0.761706i | \(-0.275638\pi\) | ||||
0.647922 | + | 0.761706i | \(0.275638\pi\) | |||||||
\(740\) | −6.78286 | −0.249343 | ||||||||
\(741\) | 10.0378 | 0.368748 | ||||||||
\(742\) | 7.49681 | 0.275217 | ||||||||
\(743\) | 30.3847 | 1.11471 | 0.557353 | − | 0.830275i | \(-0.311817\pi\) | ||||
0.557353 | + | 0.830275i | \(0.311817\pi\) | |||||||
\(744\) | 12.1916 | 0.446965 | ||||||||
\(745\) | 7.89002 | 0.289068 | ||||||||
\(746\) | 1.13147 | 0.0414260 | ||||||||
\(747\) | −8.05337 | −0.294657 | ||||||||
\(748\) | 6.56738 | 0.240127 | ||||||||
\(749\) | −30.9729 | −1.13172 | ||||||||
\(750\) | −8.85724 | −0.323421 | ||||||||
\(751\) | −22.9662 | −0.838047 | −0.419024 | − | 0.907975i | \(-0.637628\pi\) | ||||
−0.419024 | + | 0.907975i | \(0.637628\pi\) | |||||||
\(752\) | 3.98837 | 0.145441 | ||||||||
\(753\) | −7.14002 | −0.260197 | ||||||||
\(754\) | 28.5719 | 1.04053 | ||||||||
\(755\) | −1.62156 | −0.0590148 | ||||||||
\(756\) | −3.66564 | −0.133318 | ||||||||
\(757\) | −52.4501 | −1.90633 | −0.953165 | − | 0.302451i | \(-0.902195\pi\) | ||||
−0.953165 | + | 0.302451i | \(0.902195\pi\) | |||||||
\(758\) | −17.8991 | −0.650123 | ||||||||
\(759\) | −40.8373 | −1.48230 | ||||||||
\(760\) | −7.77306 | −0.281958 | ||||||||
\(761\) | 21.3685 | 0.774609 | 0.387304 | − | 0.921952i | \(-0.373406\pi\) | ||||
0.387304 | + | 0.921952i | \(0.373406\pi\) | |||||||
\(762\) | 7.08705 | 0.256737 | ||||||||
\(763\) | −30.7354 | −1.11269 | ||||||||
\(764\) | 7.75988 | 0.280743 | ||||||||
\(765\) | −1.00436 | −0.0363127 | ||||||||
\(766\) | 23.1401 | 0.836086 | ||||||||
\(767\) | 14.0716 | 0.508095 | ||||||||
\(768\) | 17.0408 | 0.614907 | ||||||||
\(769\) | 6.12609 | 0.220913 | 0.110456 | − | 0.993881i | \(-0.464769\pi\) | ||||
0.110456 | + | 0.993881i | \(0.464769\pi\) | |||||||
\(770\) | 22.0104 | 0.793199 | ||||||||
\(771\) | 9.05691 | 0.326177 | ||||||||
\(772\) | −2.67883 | −0.0964131 | ||||||||
\(773\) | −6.32525 | −0.227504 | −0.113752 | − | 0.993509i | \(-0.536287\pi\) | ||||
−0.113752 | + | 0.993509i | \(0.536287\pi\) | |||||||
\(774\) | −7.19784 | −0.258721 | ||||||||
\(775\) | 16.3303 | 0.586602 | ||||||||
\(776\) | 11.7478 | 0.421721 | ||||||||
\(777\) | 22.9764 | 0.824273 | ||||||||
\(778\) | −13.6065 | −0.487818 | ||||||||
\(779\) | 24.9701 | 0.894647 | ||||||||
\(780\) | 4.02900 | 0.144261 | ||||||||
\(781\) | −73.5381 | −2.63140 | ||||||||
\(782\) | 6.33067 | 0.226384 | ||||||||
\(783\) | 7.53770 | 0.269376 | ||||||||
\(784\) | −4.63174 | −0.165419 | ||||||||
\(785\) | −1.00436 | −0.0358471 | ||||||||
\(786\) | 14.9273 | 0.532440 | ||||||||
\(787\) | 26.4440 | 0.942626 | 0.471313 | − | 0.881966i | \(-0.343780\pi\) | ||||
0.471313 | + | 0.881966i | \(0.343780\pi\) | |||||||
\(788\) | 21.4187 | 0.763009 | ||||||||
\(789\) | −5.55816 | −0.197876 | ||||||||
\(790\) | 15.9897 | 0.568889 | ||||||||
\(791\) | 31.5617 | 1.12221 | ||||||||
\(792\) | 18.8526 | 0.669899 | ||||||||
\(793\) | 28.1184 | 0.998512 | ||||||||
\(794\) | −19.4954 | −0.691866 | ||||||||
\(795\) | −2.17382 | −0.0770975 | ||||||||
\(796\) | 14.1341 | 0.500970 | ||||||||
\(797\) | −44.0474 | −1.56024 | −0.780119 | − | 0.625631i | \(-0.784841\pi\) | ||||
−0.780119 | + | 0.625631i | \(0.784841\pi\) | |||||||
\(798\) | 8.99640 | 0.318469 | ||||||||
\(799\) | 4.71120 | 0.166670 | ||||||||
\(800\) | 20.4716 | 0.723781 | ||||||||
\(801\) | 2.16759 | 0.0765881 | ||||||||
\(802\) | 22.6939 | 0.801351 | ||||||||
\(803\) | −68.5264 | −2.41824 | ||||||||
\(804\) | −6.86520 | −0.242117 | ||||||||
\(805\) | −22.8931 | −0.806874 | ||||||||
\(806\) | 15.5091 | 0.546283 | ||||||||
\(807\) | −12.5220 | −0.440794 | ||||||||
\(808\) | −37.1756 | −1.30783 | ||||||||
\(809\) | −2.28286 | −0.0802612 | −0.0401306 | − | 0.999194i | \(-0.512777\pi\) | ||||
−0.0401306 | + | 0.999194i | \(0.512777\pi\) | |||||||
\(810\) | −0.985094 | −0.0346127 | ||||||||
\(811\) | 30.9797 | 1.08784 | 0.543922 | − | 0.839136i | \(-0.316939\pi\) | ||||
0.543922 | + | 0.839136i | \(0.316939\pi\) | |||||||
\(812\) | −27.6305 | −0.969639 | ||||||||
\(813\) | −2.37609 | −0.0833332 | ||||||||
\(814\) | −40.3750 | −1.41514 | ||||||||
\(815\) | −22.0883 | −0.773721 | ||||||||
\(816\) | −0.846572 | −0.0296360 | ||||||||
\(817\) | −19.0608 | −0.666853 | ||||||||
\(818\) | −30.1157 | −1.05297 | ||||||||
\(819\) | −13.6479 | −0.476896 | ||||||||
\(820\) | 10.0226 | 0.350003 | ||||||||
\(821\) | 14.3457 | 0.500669 | 0.250334 | − | 0.968159i | \(-0.419459\pi\) | ||||
0.250334 | + | 0.968159i | \(0.419459\pi\) | |||||||
\(822\) | 17.1235 | 0.597252 | ||||||||
\(823\) | −17.0771 | −0.595272 | −0.297636 | − | 0.954679i | \(-0.596198\pi\) | ||||
−0.297636 | + | 0.954679i | \(0.596198\pi\) | |||||||
\(824\) | 16.6324 | 0.579416 | ||||||||
\(825\) | 25.2526 | 0.879184 | ||||||||
\(826\) | 12.6117 | 0.438816 | ||||||||
\(827\) | 17.7657 | 0.617774 | 0.308887 | − | 0.951099i | \(-0.400043\pi\) | ||||
0.308887 | + | 0.951099i | \(0.400043\pi\) | |||||||
\(828\) | −6.69972 | −0.232831 | ||||||||
\(829\) | 54.5361 | 1.89412 | 0.947058 | − | 0.321063i | \(-0.104040\pi\) | ||||
0.947058 | + | 0.321063i | \(0.104040\pi\) | |||||||
\(830\) | 7.93332 | 0.275370 | ||||||||
\(831\) | 21.2558 | 0.737356 | ||||||||
\(832\) | 25.9855 | 0.900886 | ||||||||
\(833\) | −5.47117 | −0.189565 | ||||||||
\(834\) | 22.6867 | 0.785576 | ||||||||
\(835\) | 0.0215076 | 0.000744300 0 | ||||||||
\(836\) | 17.0576 | 0.589951 | ||||||||
\(837\) | 4.09152 | 0.141424 | ||||||||
\(838\) | −26.9539 | −0.931106 | ||||||||
\(839\) | −8.42316 | −0.290800 | −0.145400 | − | 0.989373i | \(-0.546447\pi\) | ||||
−0.145400 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(840\) | 10.5686 | 0.364652 | ||||||||
\(841\) | 27.8170 | 0.959206 | ||||||||
\(842\) | 32.0375 | 1.10409 | ||||||||
\(843\) | 8.43216 | 0.290419 | ||||||||
\(844\) | 22.8495 | 0.786512 | ||||||||
\(845\) | 1.94411 | 0.0668793 | ||||||||
\(846\) | 4.62082 | 0.158867 | ||||||||
\(847\) | −102.520 | −3.52264 | ||||||||
\(848\) | −1.83231 | −0.0629217 | ||||||||
\(849\) | −5.80167 | −0.199113 | ||||||||
\(850\) | −3.91470 | −0.134273 | ||||||||
\(851\) | 41.9942 | 1.43954 | ||||||||
\(852\) | −12.0646 | −0.413325 | ||||||||
\(853\) | −26.0950 | −0.893476 | −0.446738 | − | 0.894665i | \(-0.647414\pi\) | ||||
−0.446738 | + | 0.894665i | \(0.647414\pi\) | |||||||
\(854\) | 25.2011 | 0.862364 | ||||||||
\(855\) | −2.60865 | −0.0892140 | ||||||||
\(856\) | 26.1339 | 0.893237 | ||||||||
\(857\) | −36.1183 | −1.23378 | −0.616889 | − | 0.787051i | \(-0.711607\pi\) | ||||
−0.616889 | + | 0.787051i | \(0.711607\pi\) | |||||||
\(858\) | 23.9826 | 0.818754 | ||||||||
\(859\) | −16.6305 | −0.567425 | −0.283712 | − | 0.958909i | \(-0.591566\pi\) | ||||
−0.283712 | + | 0.958909i | \(0.591566\pi\) | |||||||
\(860\) | −7.65066 | −0.260885 | ||||||||
\(861\) | −33.9506 | −1.15703 | ||||||||
\(862\) | 0.408859 | 0.0139258 | ||||||||
\(863\) | 25.9834 | 0.884485 | 0.442243 | − | 0.896895i | \(-0.354183\pi\) | ||||
0.442243 | + | 0.896895i | \(0.354183\pi\) | |||||||
\(864\) | 5.12911 | 0.174496 | ||||||||
\(865\) | 5.96132 | 0.202691 | ||||||||
\(866\) | −5.92554 | −0.201358 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −14.9980 | −0.509066 | ||||||||
\(869\) | −102.698 | −3.48377 | ||||||||
\(870\) | −7.42535 | −0.251743 | ||||||||
\(871\) | −25.5605 | −0.866085 | ||||||||
\(872\) | 25.9335 | 0.878218 | ||||||||
\(873\) | 3.94258 | 0.133436 | ||||||||
\(874\) | 16.4428 | 0.556187 | ||||||||
\(875\) | 31.8907 | 1.07810 | ||||||||
\(876\) | −11.2424 | −0.379844 | ||||||||
\(877\) | 3.16815 | 0.106981 | 0.0534904 | − | 0.998568i | \(-0.482965\pi\) | ||||
0.0534904 | + | 0.998568i | \(0.482965\pi\) | |||||||
\(878\) | 5.68550 | 0.191876 | ||||||||
\(879\) | 25.3292 | 0.854333 | ||||||||
\(880\) | −5.37960 | −0.181346 | ||||||||
\(881\) | −42.5202 | −1.43254 | −0.716271 | − | 0.697822i | \(-0.754153\pi\) | ||||
−0.716271 | + | 0.697822i | \(0.754153\pi\) | |||||||
\(882\) | −5.36622 | −0.180690 | ||||||||
\(883\) | −37.8272 | −1.27299 | −0.636493 | − | 0.771283i | \(-0.719616\pi\) | ||||
−0.636493 | + | 0.771283i | \(0.719616\pi\) | |||||||
\(884\) | 4.01151 | 0.134922 | ||||||||
\(885\) | −3.65695 | −0.122927 | ||||||||
\(886\) | 17.9724 | 0.603796 | ||||||||
\(887\) | 1.25871 | 0.0422633 | 0.0211317 | − | 0.999777i | \(-0.493273\pi\) | ||||
0.0211317 | + | 0.999777i | \(0.493273\pi\) | |||||||
\(888\) | −19.3867 | −0.650575 | ||||||||
\(889\) | −25.5171 | −0.855815 | ||||||||
\(890\) | −2.13528 | −0.0715748 | ||||||||
\(891\) | 6.32698 | 0.211962 | ||||||||
\(892\) | −18.2744 | −0.611872 | ||||||||
\(893\) | 12.2365 | 0.409480 | ||||||||
\(894\) | 7.70508 | 0.257696 | ||||||||
\(895\) | −14.7594 | −0.493353 | ||||||||
\(896\) | −12.9369 | −0.432191 | ||||||||
\(897\) | −24.9444 | −0.832870 | ||||||||
\(898\) | 30.0645 | 1.00326 | ||||||||
\(899\) | 30.8406 | 1.02859 | ||||||||
\(900\) | 4.14291 | 0.138097 | ||||||||
\(901\) | −2.16439 | −0.0721061 | ||||||||
\(902\) | 59.6593 | 1.98644 | ||||||||
\(903\) | 25.9160 | 0.862429 | ||||||||
\(904\) | −26.6307 | −0.885725 | ||||||||
\(905\) | −4.13401 | −0.137419 | ||||||||
\(906\) | −1.58356 | −0.0526101 | ||||||||
\(907\) | 0.600796 | 0.0199491 | 0.00997455 | − | 0.999950i | \(-0.496825\pi\) | ||||
0.00997455 | + | 0.999950i | \(0.496825\pi\) | |||||||
\(908\) | 21.9881 | 0.729702 | ||||||||
\(909\) | −12.4762 | −0.413810 | ||||||||
\(910\) | 13.4445 | 0.445680 | ||||||||
\(911\) | 45.7317 | 1.51516 | 0.757580 | − | 0.652743i | \(-0.226382\pi\) | ||||
0.757580 | + | 0.652743i | \(0.226382\pi\) | |||||||
\(912\) | −2.19883 | −0.0728104 | ||||||||
\(913\) | −50.9535 | −1.68631 | ||||||||
\(914\) | 40.2028 | 1.32979 | ||||||||
\(915\) | −7.30747 | −0.241577 | ||||||||
\(916\) | 19.4217 | 0.641710 | ||||||||
\(917\) | −53.7461 | −1.77485 | ||||||||
\(918\) | −0.980818 | −0.0323718 | ||||||||
\(919\) | 8.86669 | 0.292485 | 0.146243 | − | 0.989249i | \(-0.453282\pi\) | ||||
0.146243 | + | 0.989249i | \(0.453282\pi\) | |||||||
\(920\) | 19.3164 | 0.636842 | ||||||||
\(921\) | 8.84271 | 0.291377 | ||||||||
\(922\) | −29.3699 | −0.967246 | ||||||||
\(923\) | −44.9188 | −1.47852 | ||||||||
\(924\) | −23.1924 | −0.762974 | ||||||||
\(925\) | −25.9680 | −0.853822 | ||||||||
\(926\) | 1.01330 | 0.0332990 | ||||||||
\(927\) | 5.58186 | 0.183332 | ||||||||
\(928\) | 38.6617 | 1.26913 | ||||||||
\(929\) | 14.2950 | 0.469004 | 0.234502 | − | 0.972116i | \(-0.424654\pi\) | ||||
0.234502 | + | 0.972116i | \(0.424654\pi\) | |||||||
\(930\) | −4.03053 | −0.132166 | ||||||||
\(931\) | −14.2104 | −0.465728 | ||||||||
\(932\) | 1.40916 | 0.0461586 | ||||||||
\(933\) | −11.1415 | −0.364756 | ||||||||
\(934\) | 29.2944 | 0.958541 | ||||||||
\(935\) | −6.35456 | −0.207816 | ||||||||
\(936\) | 11.5156 | 0.376400 | ||||||||
\(937\) | 10.1695 | 0.332222 | 0.166111 | − | 0.986107i | \(-0.446879\pi\) | ||||
0.166111 | + | 0.986107i | \(0.446879\pi\) | |||||||
\(938\) | −22.9086 | −0.747994 | ||||||||
\(939\) | 17.4045 | 0.567974 | ||||||||
\(940\) | 4.91152 | 0.160196 | ||||||||
\(941\) | 53.2669 | 1.73645 | 0.868225 | − | 0.496170i | \(-0.165261\pi\) | ||||
0.868225 | + | 0.496170i | \(0.165261\pi\) | |||||||
\(942\) | −0.980818 | −0.0319568 | ||||||||
\(943\) | −62.0518 | −2.02068 | ||||||||
\(944\) | −3.08244 | −0.100325 | ||||||||
\(945\) | 3.54685 | 0.115379 | ||||||||
\(946\) | −45.5406 | −1.48065 | ||||||||
\(947\) | −6.12953 | −0.199183 | −0.0995915 | − | 0.995028i | \(-0.531754\pi\) | ||||
−0.0995915 | + | 0.995028i | \(0.531754\pi\) | |||||||
\(948\) | −16.8484 | −0.547211 | ||||||||
\(949\) | −41.8575 | −1.35875 | ||||||||
\(950\) | −10.1678 | −0.329886 | ||||||||
\(951\) | −30.5137 | −0.989474 | ||||||||
\(952\) | 10.5227 | 0.341044 | ||||||||
\(953\) | 20.2026 | 0.654426 | 0.327213 | − | 0.944951i | \(-0.393890\pi\) | ||||
0.327213 | + | 0.944951i | \(0.393890\pi\) | |||||||
\(954\) | −2.12287 | −0.0687304 | ||||||||
\(955\) | −7.50842 | −0.242967 | ||||||||
\(956\) | −15.6955 | −0.507629 | ||||||||
\(957\) | 47.6909 | 1.54163 | ||||||||
\(958\) | −18.0038 | −0.581675 | ||||||||
\(959\) | −61.6536 | −1.99090 | ||||||||
\(960\) | −6.75318 | −0.217958 | ||||||||
\(961\) | −14.2595 | −0.459983 | ||||||||
\(962\) | −24.6620 | −0.795136 | ||||||||
\(963\) | 8.77058 | 0.282628 | ||||||||
\(964\) | −17.0482 | −0.549087 | ||||||||
\(965\) | 2.59202 | 0.0834401 | ||||||||
\(966\) | −22.3565 | −0.719307 | ||||||||
\(967\) | 51.5095 | 1.65644 | 0.828218 | − | 0.560407i | \(-0.189355\pi\) | ||||
0.828218 | + | 0.560407i | \(0.189355\pi\) | |||||||
\(968\) | 86.5033 | 2.78032 | ||||||||
\(969\) | −2.59733 | −0.0834382 | ||||||||
\(970\) | −3.88381 | −0.124702 | ||||||||
\(971\) | 4.84236 | 0.155399 | 0.0776993 | − | 0.996977i | \(-0.475243\pi\) | ||||
0.0776993 | + | 0.996977i | \(0.475243\pi\) | |||||||
\(972\) | 1.03800 | 0.0332937 | ||||||||
\(973\) | −81.6839 | −2.61866 | ||||||||
\(974\) | −6.38138 | −0.204473 | ||||||||
\(975\) | 15.4249 | 0.493992 | ||||||||
\(976\) | −6.15945 | −0.197159 | ||||||||
\(977\) | 8.04118 | 0.257260 | 0.128630 | − | 0.991693i | \(-0.458942\pi\) | ||||
0.128630 | + | 0.991693i | \(0.458942\pi\) | |||||||
\(978\) | −21.5706 | −0.689752 | ||||||||
\(979\) | 13.7143 | 0.438311 | ||||||||
\(980\) | −5.70381 | −0.182201 | ||||||||
\(981\) | 8.70332 | 0.277875 | ||||||||
\(982\) | 34.2033 | 1.09147 | ||||||||
\(983\) | 58.1175 | 1.85366 | 0.926830 | − | 0.375481i | \(-0.122523\pi\) | ||||
0.926830 | + | 0.375481i | \(0.122523\pi\) | |||||||
\(984\) | 28.6463 | 0.913212 | ||||||||
\(985\) | −20.7246 | −0.660341 | ||||||||
\(986\) | −7.39311 | −0.235445 | ||||||||
\(987\) | −16.6374 | −0.529573 | ||||||||
\(988\) | 10.4192 | 0.331479 | ||||||||
\(989\) | 47.3669 | 1.50618 | ||||||||
\(990\) | −6.23267 | −0.198087 | ||||||||
\(991\) | −53.8212 | −1.70969 | −0.854843 | − | 0.518887i | \(-0.826347\pi\) | ||||
−0.854843 | + | 0.518887i | \(0.826347\pi\) | |||||||
\(992\) | 20.9858 | 0.666301 | ||||||||
\(993\) | −18.7043 | −0.593562 | ||||||||
\(994\) | −40.2585 | −1.27692 | ||||||||
\(995\) | −13.6761 | −0.433561 | ||||||||
\(996\) | −8.35936 | −0.264877 | ||||||||
\(997\) | −46.4864 | −1.47224 | −0.736119 | − | 0.676852i | \(-0.763344\pi\) | ||||
−0.736119 | + | 0.676852i | \(0.763344\pi\) | |||||||
\(998\) | −30.6027 | −0.968712 | ||||||||
\(999\) | −6.50621 | −0.205847 |
(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 | 8007.2.a.f.1.17 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.17 | ✓ | 48 | 1.1 | even | 1 | trivial |