Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26107 | −1.59882 | −0.799409 | − | 0.600787i | \(-0.794854\pi\) | ||||
−0.799409 | + | 0.600787i | \(0.794854\pi\) | |||||||
\(3\) | −2.17834 | −1.25766 | −0.628832 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628832 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(4\) | 3.11244 | 1.55622 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 4.92537 | 2.01078 | ||||||||
\(7\) | 1.01936 | 0.385283 | 0.192642 | − | 0.981269i | \(-0.438295\pi\) | ||||
0.192642 | + | 0.981269i | \(0.438295\pi\) | |||||||
\(8\) | −2.51531 | −0.889295 | ||||||||
\(9\) | 1.74515 | 0.581718 | ||||||||
\(10\) | −2.26107 | −0.715013 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −6.77995 | −1.95720 | ||||||||
\(13\) | −1.53471 | −0.425651 | −0.212825 | − | 0.977090i | \(-0.568267\pi\) | ||||
−0.212825 | + | 0.977090i | \(0.568267\pi\) | |||||||
\(14\) | −2.30485 | −0.615998 | ||||||||
\(15\) | −2.17834 | −0.562444 | ||||||||
\(16\) | −0.537594 | −0.134398 | ||||||||
\(17\) | 4.77394 | 1.15785 | 0.578925 | − | 0.815381i | \(-0.303472\pi\) | ||||
0.578925 | + | 0.815381i | \(0.303472\pi\) | |||||||
\(18\) | −3.94591 | −0.930061 | ||||||||
\(19\) | −3.44959 | −0.791391 | −0.395695 | − | 0.918382i | \(-0.629496\pi\) | ||||
−0.395695 | + | 0.918382i | \(0.629496\pi\) | |||||||
\(20\) | 3.11244 | 0.695963 | ||||||||
\(21\) | −2.22052 | −0.484557 | ||||||||
\(22\) | 2.26107 | 0.482062 | ||||||||
\(23\) | 0.771372 | 0.160842 | 0.0804211 | − | 0.996761i | \(-0.474374\pi\) | ||||
0.0804211 | + | 0.996761i | \(0.474374\pi\) | |||||||
\(24\) | 5.47919 | 1.11843 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.47008 | 0.680538 | ||||||||
\(27\) | 2.73348 | 0.526058 | ||||||||
\(28\) | 3.17271 | 0.599586 | ||||||||
\(29\) | 2.66217 | 0.494352 | 0.247176 | − | 0.968971i | \(-0.420497\pi\) | ||||
0.247176 | + | 0.968971i | \(0.420497\pi\) | |||||||
\(30\) | 4.92537 | 0.899246 | ||||||||
\(31\) | 0.126108 | 0.0226497 | 0.0113249 | − | 0.999936i | \(-0.496395\pi\) | ||||
0.0113249 | + | 0.999936i | \(0.496395\pi\) | |||||||
\(32\) | 6.24615 | 1.10417 | ||||||||
\(33\) | 2.17834 | 0.379200 | ||||||||
\(34\) | −10.7942 | −1.85119 | ||||||||
\(35\) | 1.01936 | 0.172304 | ||||||||
\(36\) | 5.43169 | 0.905281 | ||||||||
\(37\) | 7.53069 | 1.23804 | 0.619019 | − | 0.785376i | \(-0.287531\pi\) | ||||
0.619019 | + | 0.785376i | \(0.287531\pi\) | |||||||
\(38\) | 7.79977 | 1.26529 | ||||||||
\(39\) | 3.34311 | 0.535325 | ||||||||
\(40\) | −2.51531 | −0.397705 | ||||||||
\(41\) | −10.6052 | −1.65625 | −0.828127 | − | 0.560541i | \(-0.810593\pi\) | ||||
−0.828127 | + | 0.560541i | \(0.810593\pi\) | |||||||
\(42\) | 5.02075 | 0.774718 | ||||||||
\(43\) | −0.100944 | −0.0153938 | −0.00769689 | − | 0.999970i | \(-0.502450\pi\) | ||||
−0.00769689 | + | 0.999970i | \(0.502450\pi\) | |||||||
\(44\) | −3.11244 | −0.469218 | ||||||||
\(45\) | 1.74515 | 0.260152 | ||||||||
\(46\) | −1.74413 | −0.257157 | ||||||||
\(47\) | −3.79029 | −0.552871 | −0.276435 | − | 0.961033i | \(-0.589153\pi\) | ||||
−0.276435 | + | 0.961033i | \(0.589153\pi\) | |||||||
\(48\) | 1.17106 | 0.169028 | ||||||||
\(49\) | −5.96090 | −0.851557 | ||||||||
\(50\) | −2.26107 | −0.319764 | ||||||||
\(51\) | −10.3992 | −1.45619 | ||||||||
\(52\) | −4.77668 | −0.662406 | ||||||||
\(53\) | −12.5751 | −1.72732 | −0.863659 | − | 0.504076i | \(-0.831833\pi\) | ||||
−0.863659 | + | 0.504076i | \(0.831833\pi\) | |||||||
\(54\) | −6.18059 | −0.841072 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −2.56401 | −0.342631 | ||||||||
\(57\) | 7.51438 | 0.995303 | ||||||||
\(58\) | −6.01935 | −0.790379 | ||||||||
\(59\) | 3.22100 | 0.419338 | 0.209669 | − | 0.977772i | \(-0.432761\pi\) | ||||
0.209669 | + | 0.977772i | \(0.432761\pi\) | |||||||
\(60\) | −6.77995 | −0.875287 | ||||||||
\(61\) | −8.65632 | −1.10833 | −0.554164 | − | 0.832407i | \(-0.686962\pi\) | ||||
−0.554164 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(62\) | −0.285140 | −0.0362128 | ||||||||
\(63\) | 1.77895 | 0.224126 | ||||||||
\(64\) | −13.0478 | −1.63098 | ||||||||
\(65\) | −1.53471 | −0.190357 | ||||||||
\(66\) | −4.92537 | −0.606272 | ||||||||
\(67\) | 0.447815 | 0.0547093 | 0.0273547 | − | 0.999626i | \(-0.491292\pi\) | ||||
0.0273547 | + | 0.999626i | \(0.491292\pi\) | |||||||
\(68\) | 14.8586 | 1.80187 | ||||||||
\(69\) | −1.68031 | −0.202285 | ||||||||
\(70\) | −2.30485 | −0.275483 | ||||||||
\(71\) | 1.85434 | 0.220069 | 0.110035 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110035 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(72\) | −4.38960 | −0.517319 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −17.0274 | −1.97940 | ||||||||
\(75\) | −2.17834 | −0.251533 | ||||||||
\(76\) | −10.7367 | −1.23158 | ||||||||
\(77\) | −1.01936 | −0.116167 | ||||||||
\(78\) | −7.55900 | −0.855888 | ||||||||
\(79\) | 7.51741 | 0.845775 | 0.422887 | − | 0.906182i | \(-0.361017\pi\) | ||||
0.422887 | + | 0.906182i | \(0.361017\pi\) | |||||||
\(80\) | −0.537594 | −0.0601048 | ||||||||
\(81\) | −11.1899 | −1.24332 | ||||||||
\(82\) | 23.9791 | 2.64805 | ||||||||
\(83\) | 9.63959 | 1.05808 | 0.529041 | − | 0.848596i | \(-0.322552\pi\) | ||||
0.529041 | + | 0.848596i | \(0.322552\pi\) | |||||||
\(84\) | −6.91123 | −0.754077 | ||||||||
\(85\) | 4.77394 | 0.517806 | ||||||||
\(86\) | 0.228241 | 0.0246119 | ||||||||
\(87\) | −5.79910 | −0.621728 | ||||||||
\(88\) | 2.51531 | 0.268133 | ||||||||
\(89\) | −7.08347 | −0.750846 | −0.375423 | − | 0.926854i | \(-0.622503\pi\) | ||||
−0.375423 | + | 0.926854i | \(0.622503\pi\) | |||||||
\(90\) | −3.94591 | −0.415936 | ||||||||
\(91\) | −1.56442 | −0.163996 | ||||||||
\(92\) | 2.40085 | 0.250306 | ||||||||
\(93\) | −0.274707 | −0.0284858 | ||||||||
\(94\) | 8.57011 | 0.883940 | ||||||||
\(95\) | −3.44959 | −0.353921 | ||||||||
\(96\) | −13.6062 | −1.38868 | ||||||||
\(97\) | −2.72545 | −0.276728 | −0.138364 | − | 0.990381i | \(-0.544184\pi\) | ||||
−0.138364 | + | 0.990381i | \(0.544184\pi\) | |||||||
\(98\) | 13.4780 | 1.36148 | ||||||||
\(99\) | −1.74515 | −0.175394 | ||||||||
\(100\) | 3.11244 | 0.311244 | ||||||||
\(101\) | −1.50808 | −0.150060 | −0.0750298 | − | 0.997181i | \(-0.523905\pi\) | ||||
−0.0750298 | + | 0.997181i | \(0.523905\pi\) | |||||||
\(102\) | 23.5134 | 2.32818 | ||||||||
\(103\) | 18.2298 | 1.79623 | 0.898116 | − | 0.439759i | \(-0.144936\pi\) | ||||
0.898116 | + | 0.439759i | \(0.144936\pi\) | |||||||
\(104\) | 3.86026 | 0.378529 | ||||||||
\(105\) | −2.22052 | −0.216700 | ||||||||
\(106\) | 28.4331 | 2.76167 | ||||||||
\(107\) | 1.39080 | 0.134454 | 0.0672269 | − | 0.997738i | \(-0.478585\pi\) | ||||
0.0672269 | + | 0.997738i | \(0.478585\pi\) | |||||||
\(108\) | 8.50779 | 0.818663 | ||||||||
\(109\) | 12.9399 | 1.23942 | 0.619710 | − | 0.784831i | \(-0.287250\pi\) | ||||
0.619710 | + | 0.784831i | \(0.287250\pi\) | |||||||
\(110\) | 2.26107 | 0.215585 | ||||||||
\(111\) | −16.4044 | −1.55703 | ||||||||
\(112\) | −0.548004 | −0.0517815 | ||||||||
\(113\) | −8.97149 | −0.843967 | −0.421983 | − | 0.906604i | \(-0.638666\pi\) | ||||
−0.421983 | + | 0.906604i | \(0.638666\pi\) | |||||||
\(114\) | −16.9905 | −1.59131 | ||||||||
\(115\) | 0.771372 | 0.0719308 | ||||||||
\(116\) | 8.28584 | 0.769321 | ||||||||
\(117\) | −2.67830 | −0.247609 | ||||||||
\(118\) | −7.28291 | −0.670446 | ||||||||
\(119\) | 4.86638 | 0.446100 | ||||||||
\(120\) | 5.47919 | 0.500179 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 19.5725 | 1.77202 | ||||||||
\(123\) | 23.1017 | 2.08301 | ||||||||
\(124\) | 0.392505 | 0.0352480 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.02232 | −0.358337 | ||||||||
\(127\) | −7.68524 | −0.681955 | −0.340977 | − | 0.940071i | \(-0.610758\pi\) | ||||
−0.340977 | + | 0.940071i | \(0.610758\pi\) | |||||||
\(128\) | 17.0097 | 1.50346 | ||||||||
\(129\) | 0.219890 | 0.0193602 | ||||||||
\(130\) | 3.47008 | 0.304346 | ||||||||
\(131\) | 0.162327 | 0.0141826 | 0.00709131 | − | 0.999975i | \(-0.497743\pi\) | ||||
0.00709131 | + | 0.999975i | \(0.497743\pi\) | |||||||
\(132\) | 6.77995 | 0.590119 | ||||||||
\(133\) | −3.51639 | −0.304910 | ||||||||
\(134\) | −1.01254 | −0.0874703 | ||||||||
\(135\) | 2.73348 | 0.235260 | ||||||||
\(136\) | −12.0079 | −1.02967 | ||||||||
\(137\) | 9.34442 | 0.798348 | 0.399174 | − | 0.916875i | \(-0.369297\pi\) | ||||
0.399174 | + | 0.916875i | \(0.369297\pi\) | |||||||
\(138\) | 3.79930 | 0.323417 | ||||||||
\(139\) | 7.79712 | 0.661343 | 0.330672 | − | 0.943746i | \(-0.392725\pi\) | ||||
0.330672 | + | 0.943746i | \(0.392725\pi\) | |||||||
\(140\) | 3.17271 | 0.268143 | ||||||||
\(141\) | 8.25653 | 0.695325 | ||||||||
\(142\) | −4.19278 | −0.351851 | ||||||||
\(143\) | 1.53471 | 0.128339 | ||||||||
\(144\) | −0.938183 | −0.0781820 | ||||||||
\(145\) | 2.66217 | 0.221081 | ||||||||
\(146\) | −2.26107 | −0.187128 | ||||||||
\(147\) | 12.9848 | 1.07097 | ||||||||
\(148\) | 23.4388 | 1.92666 | ||||||||
\(149\) | −14.6093 | −1.19684 | −0.598421 | − | 0.801182i | \(-0.704205\pi\) | ||||
−0.598421 | + | 0.801182i | \(0.704205\pi\) | |||||||
\(150\) | 4.92537 | 0.402155 | ||||||||
\(151\) | 0.757490 | 0.0616437 | 0.0308218 | − | 0.999525i | \(-0.490188\pi\) | ||||
0.0308218 | + | 0.999525i | \(0.490188\pi\) | |||||||
\(152\) | 8.67678 | 0.703780 | ||||||||
\(153\) | 8.33125 | 0.673542 | ||||||||
\(154\) | 2.30485 | 0.185730 | ||||||||
\(155\) | 0.126108 | 0.0101293 | ||||||||
\(156\) | 10.4052 | 0.833084 | ||||||||
\(157\) | 3.32182 | 0.265110 | 0.132555 | − | 0.991176i | \(-0.457682\pi\) | ||||
0.132555 | + | 0.991176i | \(0.457682\pi\) | |||||||
\(158\) | −16.9974 | −1.35224 | ||||||||
\(159\) | 27.3927 | 2.17239 | ||||||||
\(160\) | 6.24615 | 0.493802 | ||||||||
\(161\) | 0.786308 | 0.0619698 | ||||||||
\(162\) | 25.3012 | 1.98785 | ||||||||
\(163\) | 11.0194 | 0.863104 | 0.431552 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431552 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(164\) | −33.0081 | −2.57750 | ||||||||
\(165\) | 2.17834 | 0.169583 | ||||||||
\(166\) | −21.7958 | −1.69168 | ||||||||
\(167\) | −19.4056 | −1.50165 | −0.750825 | − | 0.660502i | \(-0.770344\pi\) | ||||
−0.750825 | + | 0.660502i | \(0.770344\pi\) | |||||||
\(168\) | 5.58528 | 0.430914 | ||||||||
\(169\) | −10.6447 | −0.818821 | ||||||||
\(170\) | −10.7942 | −0.827878 | ||||||||
\(171\) | −6.02007 | −0.460366 | ||||||||
\(172\) | −0.314182 | −0.0239561 | ||||||||
\(173\) | −23.2231 | −1.76562 | −0.882808 | − | 0.469734i | \(-0.844350\pi\) | ||||
−0.882808 | + | 0.469734i | \(0.844350\pi\) | |||||||
\(174\) | 13.1122 | 0.994031 | ||||||||
\(175\) | 1.01936 | 0.0770566 | ||||||||
\(176\) | 0.537594 | 0.0405227 | ||||||||
\(177\) | −7.01642 | −0.527387 | ||||||||
\(178\) | 16.0162 | 1.20047 | ||||||||
\(179\) | −6.39292 | −0.477829 | −0.238915 | − | 0.971041i | \(-0.576792\pi\) | ||||
−0.238915 | + | 0.971041i | \(0.576792\pi\) | |||||||
\(180\) | 5.43169 | 0.404854 | ||||||||
\(181\) | 5.77136 | 0.428982 | 0.214491 | − | 0.976726i | \(-0.431191\pi\) | ||||
0.214491 | + | 0.976726i | \(0.431191\pi\) | |||||||
\(182\) | 3.53727 | 0.262200 | ||||||||
\(183\) | 18.8564 | 1.39390 | ||||||||
\(184\) | −1.94024 | −0.143036 | ||||||||
\(185\) | 7.53069 | 0.553667 | ||||||||
\(186\) | 0.621131 | 0.0455436 | ||||||||
\(187\) | −4.77394 | −0.349105 | ||||||||
\(188\) | −11.7971 | −0.860389 | ||||||||
\(189\) | 2.78641 | 0.202681 | ||||||||
\(190\) | 7.79977 | 0.565855 | ||||||||
\(191\) | 8.99854 | 0.651112 | 0.325556 | − | 0.945523i | \(-0.394449\pi\) | ||||
0.325556 | + | 0.945523i | \(0.394449\pi\) | |||||||
\(192\) | 28.4225 | 2.05122 | ||||||||
\(193\) | 4.60153 | 0.331226 | 0.165613 | − | 0.986191i | \(-0.447040\pi\) | ||||
0.165613 | + | 0.986191i | \(0.447040\pi\) | |||||||
\(194\) | 6.16244 | 0.442437 | ||||||||
\(195\) | 3.34311 | 0.239405 | ||||||||
\(196\) | −18.5529 | −1.32521 | ||||||||
\(197\) | 11.8571 | 0.844785 | 0.422393 | − | 0.906413i | \(-0.361190\pi\) | ||||
0.422393 | + | 0.906413i | \(0.361190\pi\) | |||||||
\(198\) | 3.94591 | 0.280424 | ||||||||
\(199\) | −5.74613 | −0.407332 | −0.203666 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203666 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(200\) | −2.51531 | −0.177859 | ||||||||
\(201\) | −0.975493 | −0.0688059 | ||||||||
\(202\) | 3.40988 | 0.239918 | ||||||||
\(203\) | 2.71372 | 0.190466 | ||||||||
\(204\) | −32.3670 | −2.26615 | ||||||||
\(205\) | −10.6052 | −0.740699 | ||||||||
\(206\) | −41.2188 | −2.87185 | ||||||||
\(207\) | 1.34616 | 0.0935647 | ||||||||
\(208\) | 0.825048 | 0.0572068 | ||||||||
\(209\) | 3.44959 | 0.238613 | ||||||||
\(210\) | 5.02075 | 0.346464 | ||||||||
\(211\) | 5.71879 | 0.393698 | 0.196849 | − | 0.980434i | \(-0.436929\pi\) | ||||
0.196849 | + | 0.980434i | \(0.436929\pi\) | |||||||
\(212\) | −39.1391 | −2.68809 | ||||||||
\(213\) | −4.03937 | −0.276773 | ||||||||
\(214\) | −3.14470 | −0.214967 | ||||||||
\(215\) | −0.100944 | −0.00688431 | ||||||||
\(216\) | −6.87554 | −0.467821 | ||||||||
\(217\) | 0.128550 | 0.00872657 | ||||||||
\(218\) | −29.2581 | −1.98161 | ||||||||
\(219\) | −2.17834 | −0.147198 | ||||||||
\(220\) | −3.11244 | −0.209841 | ||||||||
\(221\) | −7.32659 | −0.492840 | ||||||||
\(222\) | 37.0914 | 2.48941 | ||||||||
\(223\) | 14.3707 | 0.962330 | 0.481165 | − | 0.876630i | \(-0.340214\pi\) | ||||
0.481165 | + | 0.876630i | \(0.340214\pi\) | |||||||
\(224\) | 6.36710 | 0.425420 | ||||||||
\(225\) | 1.74515 | 0.116344 | ||||||||
\(226\) | 20.2852 | 1.34935 | ||||||||
\(227\) | 8.03332 | 0.533190 | 0.266595 | − | 0.963809i | \(-0.414101\pi\) | ||||
0.266595 | + | 0.963809i | \(0.414101\pi\) | |||||||
\(228\) | 23.3880 | 1.54891 | ||||||||
\(229\) | 18.7860 | 1.24141 | 0.620707 | − | 0.784042i | \(-0.286846\pi\) | ||||
0.620707 | + | 0.784042i | \(0.286846\pi\) | |||||||
\(230\) | −1.74413 | −0.115004 | ||||||||
\(231\) | 2.22052 | 0.146099 | ||||||||
\(232\) | −6.69617 | −0.439625 | ||||||||
\(233\) | 18.2338 | 1.19454 | 0.597268 | − | 0.802041i | \(-0.296253\pi\) | ||||
0.597268 | + | 0.802041i | \(0.296253\pi\) | |||||||
\(234\) | 6.05582 | 0.395881 | ||||||||
\(235\) | −3.79029 | −0.247251 | ||||||||
\(236\) | 10.0252 | 0.652583 | ||||||||
\(237\) | −16.3755 | −1.06370 | ||||||||
\(238\) | −11.0032 | −0.713233 | ||||||||
\(239\) | 4.27458 | 0.276499 | 0.138250 | − | 0.990397i | \(-0.455852\pi\) | ||||
0.138250 | + | 0.990397i | \(0.455852\pi\) | |||||||
\(240\) | 1.17106 | 0.0755916 | ||||||||
\(241\) | 9.04162 | 0.582422 | 0.291211 | − | 0.956659i | \(-0.405942\pi\) | ||||
0.291211 | + | 0.956659i | \(0.405942\pi\) | |||||||
\(242\) | −2.26107 | −0.145347 | ||||||||
\(243\) | 16.1749 | 1.03762 | ||||||||
\(244\) | −26.9423 | −1.72480 | ||||||||
\(245\) | −5.96090 | −0.380828 | ||||||||
\(246\) | −52.2346 | −3.33036 | ||||||||
\(247\) | 5.29411 | 0.336856 | ||||||||
\(248\) | −0.317202 | −0.0201423 | ||||||||
\(249\) | −20.9983 | −1.33071 | ||||||||
\(250\) | −2.26107 | −0.143003 | ||||||||
\(251\) | −5.28247 | −0.333427 | −0.166713 | − | 0.986005i | \(-0.553315\pi\) | ||||
−0.166713 | + | 0.986005i | \(0.553315\pi\) | |||||||
\(252\) | 5.53686 | 0.348790 | ||||||||
\(253\) | −0.771372 | −0.0484957 | ||||||||
\(254\) | 17.3769 | 1.09032 | ||||||||
\(255\) | −10.3992 | −0.651226 | ||||||||
\(256\) | −12.3645 | −0.772783 | ||||||||
\(257\) | −11.6631 | −0.727526 | −0.363763 | − | 0.931491i | \(-0.618508\pi\) | ||||
−0.363763 | + | 0.931491i | \(0.618508\pi\) | |||||||
\(258\) | −0.497186 | −0.0309535 | ||||||||
\(259\) | 7.67651 | 0.476995 | ||||||||
\(260\) | −4.77668 | −0.296237 | ||||||||
\(261\) | 4.64589 | 0.287573 | ||||||||
\(262\) | −0.367034 | −0.0226754 | ||||||||
\(263\) | −1.33569 | −0.0823625 | −0.0411812 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411812 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(264\) | −5.47919 | −0.337221 | ||||||||
\(265\) | −12.5751 | −0.772480 | ||||||||
\(266\) | 7.95080 | 0.487495 | ||||||||
\(267\) | 15.4302 | 0.944312 | ||||||||
\(268\) | 1.39380 | 0.0851398 | ||||||||
\(269\) | −12.3338 | −0.752004 | −0.376002 | − | 0.926619i | \(-0.622701\pi\) | ||||
−0.376002 | + | 0.926619i | \(0.622701\pi\) | |||||||
\(270\) | −6.18059 | −0.376139 | ||||||||
\(271\) | 6.89798 | 0.419023 | 0.209511 | − | 0.977806i | \(-0.432813\pi\) | ||||
0.209511 | + | 0.977806i | \(0.432813\pi\) | |||||||
\(272\) | −2.56644 | −0.155613 | ||||||||
\(273\) | 3.40784 | 0.206252 | ||||||||
\(274\) | −21.1284 | −1.27641 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −5.22986 | −0.314801 | ||||||||
\(277\) | 6.91692 | 0.415597 | 0.207799 | − | 0.978172i | \(-0.433370\pi\) | ||||
0.207799 | + | 0.978172i | \(0.433370\pi\) | |||||||
\(278\) | −17.6298 | −1.05737 | ||||||||
\(279\) | 0.220079 | 0.0131758 | ||||||||
\(280\) | −2.56401 | −0.153229 | ||||||||
\(281\) | −27.4989 | −1.64045 | −0.820223 | − | 0.572044i | \(-0.806151\pi\) | ||||
−0.820223 | + | 0.572044i | \(0.806151\pi\) | |||||||
\(282\) | −18.6686 | −1.11170 | ||||||||
\(283\) | −11.4651 | −0.681531 | −0.340765 | − | 0.940148i | \(-0.610686\pi\) | ||||
−0.340765 | + | 0.940148i | \(0.610686\pi\) | |||||||
\(284\) | 5.77151 | 0.342476 | ||||||||
\(285\) | 7.51438 | 0.445113 | ||||||||
\(286\) | −3.47008 | −0.205190 | ||||||||
\(287\) | −10.8106 | −0.638127 | ||||||||
\(288\) | 10.9005 | 0.642318 | ||||||||
\(289\) | 5.79049 | 0.340617 | ||||||||
\(290\) | −6.01935 | −0.353468 | ||||||||
\(291\) | 5.93695 | 0.348030 | ||||||||
\(292\) | 3.11244 | 0.182142 | ||||||||
\(293\) | −21.5489 | −1.25890 | −0.629451 | − | 0.777040i | \(-0.716720\pi\) | ||||
−0.629451 | + | 0.777040i | \(0.716720\pi\) | |||||||
\(294\) | −29.3597 | −1.71229 | ||||||||
\(295\) | 3.22100 | 0.187534 | ||||||||
\(296\) | −18.9420 | −1.10098 | ||||||||
\(297\) | −2.73348 | −0.158613 | ||||||||
\(298\) | 33.0327 | 1.91353 | ||||||||
\(299\) | −1.18383 | −0.0684626 | ||||||||
\(300\) | −6.77995 | −0.391440 | ||||||||
\(301\) | −0.102898 | −0.00593097 | ||||||||
\(302\) | −1.71274 | −0.0985570 | ||||||||
\(303\) | 3.28511 | 0.188725 | ||||||||
\(304\) | 1.85448 | 0.106362 | ||||||||
\(305\) | −8.65632 | −0.495659 | ||||||||
\(306\) | −18.8376 | −1.07687 | ||||||||
\(307\) | 2.33986 | 0.133543 | 0.0667713 | − | 0.997768i | \(-0.478730\pi\) | ||||
0.0667713 | + | 0.997768i | \(0.478730\pi\) | |||||||
\(308\) | −3.17271 | −0.180782 | ||||||||
\(309\) | −39.7106 | −2.25905 | ||||||||
\(310\) | −0.285140 | −0.0161949 | ||||||||
\(311\) | −22.8336 | −1.29478 | −0.647389 | − | 0.762160i | \(-0.724139\pi\) | ||||
−0.647389 | + | 0.762160i | \(0.724139\pi\) | |||||||
\(312\) | −8.40894 | −0.476062 | ||||||||
\(313\) | −10.2076 | −0.576967 | −0.288484 | − | 0.957485i | \(-0.593151\pi\) | ||||
−0.288484 | + | 0.957485i | \(0.593151\pi\) | |||||||
\(314\) | −7.51086 | −0.423863 | ||||||||
\(315\) | 1.77895 | 0.100232 | ||||||||
\(316\) | 23.3975 | 1.31621 | ||||||||
\(317\) | −22.3192 | −1.25357 | −0.626785 | − | 0.779192i | \(-0.715630\pi\) | ||||
−0.626785 | + | 0.779192i | \(0.715630\pi\) | |||||||
\(318\) | −61.9369 | −3.47325 | ||||||||
\(319\) | −2.66217 | −0.149053 | ||||||||
\(320\) | −13.0478 | −0.729394 | ||||||||
\(321\) | −3.02964 | −0.169098 | ||||||||
\(322\) | −1.77790 | −0.0990784 | ||||||||
\(323\) | −16.4681 | −0.916312 | ||||||||
\(324\) | −34.8279 | −1.93488 | ||||||||
\(325\) | −1.53471 | −0.0851301 | ||||||||
\(326\) | −24.9156 | −1.37995 | ||||||||
\(327\) | −28.1875 | −1.55877 | ||||||||
\(328\) | 26.6753 | 1.47290 | ||||||||
\(329\) | −3.86368 | −0.213012 | ||||||||
\(330\) | −4.92537 | −0.271133 | ||||||||
\(331\) | −17.8332 | −0.980204 | −0.490102 | − | 0.871665i | \(-0.663040\pi\) | ||||
−0.490102 | + | 0.871665i | \(0.663040\pi\) | |||||||
\(332\) | 30.0026 | 1.64661 | ||||||||
\(333\) | 13.1422 | 0.720188 | ||||||||
\(334\) | 43.8774 | 2.40086 | ||||||||
\(335\) | 0.447815 | 0.0244668 | ||||||||
\(336\) | 1.19374 | 0.0651237 | ||||||||
\(337\) | −2.60832 | −0.142084 | −0.0710420 | − | 0.997473i | \(-0.522632\pi\) | ||||
−0.0710420 | + | 0.997473i | \(0.522632\pi\) | |||||||
\(338\) | 24.0684 | 1.30915 | ||||||||
\(339\) | 19.5429 | 1.06143 | ||||||||
\(340\) | 14.8586 | 0.805821 | ||||||||
\(341\) | −0.126108 | −0.00682916 | ||||||||
\(342\) | 13.6118 | 0.736042 | ||||||||
\(343\) | −13.2119 | −0.713374 | ||||||||
\(344\) | 0.253905 | 0.0136896 | ||||||||
\(345\) | −1.68031 | −0.0904647 | ||||||||
\(346\) | 52.5090 | 2.82290 | ||||||||
\(347\) | 32.2905 | 1.73344 | 0.866721 | − | 0.498792i | \(-0.166223\pi\) | ||||
0.866721 | + | 0.498792i | \(0.166223\pi\) | |||||||
\(348\) | −18.0493 | −0.967547 | ||||||||
\(349\) | 22.4713 | 1.20286 | 0.601430 | − | 0.798925i | \(-0.294598\pi\) | ||||
0.601430 | + | 0.798925i | \(0.294598\pi\) | |||||||
\(350\) | −2.30485 | −0.123200 | ||||||||
\(351\) | −4.19509 | −0.223917 | ||||||||
\(352\) | −6.24615 | −0.332921 | ||||||||
\(353\) | 2.01085 | 0.107027 | 0.0535135 | − | 0.998567i | \(-0.482958\pi\) | ||||
0.0535135 | + | 0.998567i | \(0.482958\pi\) | |||||||
\(354\) | 15.8646 | 0.843195 | ||||||||
\(355\) | 1.85434 | 0.0984179 | ||||||||
\(356\) | −22.0469 | −1.16848 | ||||||||
\(357\) | −10.6006 | −0.561044 | ||||||||
\(358\) | 14.4548 | 0.763962 | ||||||||
\(359\) | 0.155016 | 0.00818144 | 0.00409072 | − | 0.999992i | \(-0.498698\pi\) | ||||
0.00409072 | + | 0.999992i | \(0.498698\pi\) | |||||||
\(360\) | −4.38960 | −0.231352 | ||||||||
\(361\) | −7.10031 | −0.373701 | ||||||||
\(362\) | −13.0495 | −0.685864 | ||||||||
\(363\) | −2.17834 | −0.114333 | ||||||||
\(364\) | −4.86917 | −0.255214 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −42.6356 | −2.22860 | ||||||||
\(367\) | −32.5646 | −1.69986 | −0.849929 | − | 0.526898i | \(-0.823355\pi\) | ||||
−0.849929 | + | 0.526898i | \(0.823355\pi\) | |||||||
\(368\) | −0.414685 | −0.0216169 | ||||||||
\(369\) | −18.5077 | −0.963472 | ||||||||
\(370\) | −17.0274 | −0.885213 | ||||||||
\(371\) | −12.8186 | −0.665507 | ||||||||
\(372\) | −0.855009 | −0.0443301 | ||||||||
\(373\) | −22.5314 | −1.16663 | −0.583317 | − | 0.812245i | \(-0.698245\pi\) | ||||
−0.583317 | + | 0.812245i | \(0.698245\pi\) | |||||||
\(374\) | 10.7942 | 0.558155 | ||||||||
\(375\) | −2.17834 | −0.112489 | ||||||||
\(376\) | 9.53374 | 0.491665 | ||||||||
\(377\) | −4.08564 | −0.210421 | ||||||||
\(378\) | −6.30027 | −0.324051 | ||||||||
\(379\) | −37.6303 | −1.93294 | −0.966469 | − | 0.256782i | \(-0.917338\pi\) | ||||
−0.966469 | + | 0.256782i | \(0.917338\pi\) | |||||||
\(380\) | −10.7367 | −0.550779 | ||||||||
\(381\) | 16.7410 | 0.857670 | ||||||||
\(382\) | −20.3463 | −1.04101 | ||||||||
\(383\) | −20.5106 | −1.04804 | −0.524022 | − | 0.851704i | \(-0.675569\pi\) | ||||
−0.524022 | + | 0.851704i | \(0.675569\pi\) | |||||||
\(384\) | −37.0529 | −1.89085 | ||||||||
\(385\) | −1.01936 | −0.0519516 | ||||||||
\(386\) | −10.4044 | −0.529570 | ||||||||
\(387\) | −0.176162 | −0.00895484 | ||||||||
\(388\) | −8.48281 | −0.430649 | ||||||||
\(389\) | 13.4390 | 0.681386 | 0.340693 | − | 0.940175i | \(-0.389338\pi\) | ||||
0.340693 | + | 0.940175i | \(0.389338\pi\) | |||||||
\(390\) | −7.55900 | −0.382765 | ||||||||
\(391\) | 3.68248 | 0.186231 | ||||||||
\(392\) | 14.9935 | 0.757286 | ||||||||
\(393\) | −0.353604 | −0.0178370 | ||||||||
\(394\) | −26.8098 | −1.35066 | ||||||||
\(395\) | 7.51741 | 0.378242 | ||||||||
\(396\) | −5.43169 | −0.272952 | ||||||||
\(397\) | −9.57942 | −0.480777 | −0.240389 | − | 0.970677i | \(-0.577275\pi\) | ||||
−0.240389 | + | 0.970677i | \(0.577275\pi\) | |||||||
\(398\) | 12.9924 | 0.651251 | ||||||||
\(399\) | 7.65988 | 0.383474 | ||||||||
\(400\) | −0.537594 | −0.0268797 | ||||||||
\(401\) | −14.9797 | −0.748048 | −0.374024 | − | 0.927419i | \(-0.622022\pi\) | ||||
−0.374024 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(402\) | 2.20566 | 0.110008 | ||||||||
\(403\) | −0.193539 | −0.00964088 | ||||||||
\(404\) | −4.69381 | −0.233526 | ||||||||
\(405\) | −11.1899 | −0.556031 | ||||||||
\(406\) | −6.13590 | −0.304520 | ||||||||
\(407\) | −7.53069 | −0.373282 | ||||||||
\(408\) | 26.1573 | 1.29498 | ||||||||
\(409\) | 33.4925 | 1.65610 | 0.828050 | − | 0.560655i | \(-0.189451\pi\) | ||||
0.828050 | + | 0.560655i | \(0.189451\pi\) | |||||||
\(410\) | 23.9791 | 1.18424 | ||||||||
\(411\) | −20.3553 | −1.00405 | ||||||||
\(412\) | 56.7390 | 2.79533 | ||||||||
\(413\) | 3.28337 | 0.161564 | ||||||||
\(414\) | −3.04377 | −0.149593 | ||||||||
\(415\) | 9.63959 | 0.473189 | ||||||||
\(416\) | −9.58600 | −0.469993 | ||||||||
\(417\) | −16.9848 | −0.831747 | ||||||||
\(418\) | −7.79977 | −0.381499 | ||||||||
\(419\) | −18.3882 | −0.898322 | −0.449161 | − | 0.893451i | \(-0.648277\pi\) | ||||
−0.449161 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(420\) | −6.91123 | −0.337233 | ||||||||
\(421\) | −12.4968 | −0.609058 | −0.304529 | − | 0.952503i | \(-0.598499\pi\) | ||||
−0.304529 | + | 0.952503i | \(0.598499\pi\) | |||||||
\(422\) | −12.9306 | −0.629452 | ||||||||
\(423\) | −6.61464 | −0.321615 | ||||||||
\(424\) | 31.6302 | 1.53610 | ||||||||
\(425\) | 4.77394 | 0.231570 | ||||||||
\(426\) | 9.13329 | 0.442510 | ||||||||
\(427\) | −8.82394 | −0.427020 | ||||||||
\(428\) | 4.32879 | 0.209240 | ||||||||
\(429\) | −3.34311 | −0.161407 | ||||||||
\(430\) | 0.228241 | 0.0110068 | ||||||||
\(431\) | 27.4430 | 1.32188 | 0.660941 | − | 0.750437i | \(-0.270157\pi\) | ||||
0.660941 | + | 0.750437i | \(0.270157\pi\) | |||||||
\(432\) | −1.46950 | −0.0707014 | ||||||||
\(433\) | 3.25015 | 0.156192 | 0.0780960 | − | 0.996946i | \(-0.475116\pi\) | ||||
0.0780960 | + | 0.996946i | \(0.475116\pi\) | |||||||
\(434\) | −0.290661 | −0.0139522 | ||||||||
\(435\) | −5.79910 | −0.278045 | ||||||||
\(436\) | 40.2748 | 1.92881 | ||||||||
\(437\) | −2.66092 | −0.127289 | ||||||||
\(438\) | 4.92537 | 0.235343 | ||||||||
\(439\) | 8.48640 | 0.405034 | 0.202517 | − | 0.979279i | \(-0.435088\pi\) | ||||
0.202517 | + | 0.979279i | \(0.435088\pi\) | |||||||
\(440\) | 2.51531 | 0.119913 | ||||||||
\(441\) | −10.4027 | −0.495366 | ||||||||
\(442\) | 16.5659 | 0.787961 | ||||||||
\(443\) | 31.9581 | 1.51838 | 0.759188 | − | 0.650872i | \(-0.225596\pi\) | ||||
0.759188 | + | 0.650872i | \(0.225596\pi\) | |||||||
\(444\) | −51.0576 | −2.42309 | ||||||||
\(445\) | −7.08347 | −0.335789 | ||||||||
\(446\) | −32.4931 | −1.53859 | ||||||||
\(447\) | 31.8240 | 1.50522 | ||||||||
\(448\) | −13.3005 | −0.628387 | ||||||||
\(449\) | 4.16081 | 0.196361 | 0.0981804 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981804 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(450\) | −3.94591 | −0.186012 | ||||||||
\(451\) | 10.6052 | 0.499379 | ||||||||
\(452\) | −27.9232 | −1.31340 | ||||||||
\(453\) | −1.65007 | −0.0775270 | ||||||||
\(454\) | −18.1639 | −0.852474 | ||||||||
\(455\) | −1.56442 | −0.0733413 | ||||||||
\(456\) | −18.9010 | −0.885119 | ||||||||
\(457\) | −36.0169 | −1.68480 | −0.842401 | − | 0.538852i | \(-0.818858\pi\) | ||||
−0.842401 | + | 0.538852i | \(0.818858\pi\) | |||||||
\(458\) | −42.4765 | −1.98480 | ||||||||
\(459\) | 13.0495 | 0.609097 | ||||||||
\(460\) | 2.40085 | 0.111940 | ||||||||
\(461\) | 24.9416 | 1.16165 | 0.580823 | − | 0.814030i | \(-0.302731\pi\) | ||||
0.580823 | + | 0.814030i | \(0.302731\pi\) | |||||||
\(462\) | −5.02075 | −0.233586 | ||||||||
\(463\) | 7.51867 | 0.349422 | 0.174711 | − | 0.984620i | \(-0.444101\pi\) | ||||
0.174711 | + | 0.984620i | \(0.444101\pi\) | |||||||
\(464\) | −1.43116 | −0.0664401 | ||||||||
\(465\) | −0.274707 | −0.0127392 | ||||||||
\(466\) | −41.2279 | −1.90985 | ||||||||
\(467\) | 2.89112 | 0.133785 | 0.0668926 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668926 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(468\) | −8.33604 | −0.385333 | ||||||||
\(469\) | 0.456487 | 0.0210786 | ||||||||
\(470\) | 8.57011 | 0.395310 | ||||||||
\(471\) | −7.23604 | −0.333419 | ||||||||
\(472\) | −8.10180 | −0.372916 | ||||||||
\(473\) | 0.100944 | 0.00464140 | ||||||||
\(474\) | 37.0261 | 1.70066 | ||||||||
\(475\) | −3.44959 | −0.158278 | ||||||||
\(476\) | 15.1463 | 0.694230 | ||||||||
\(477\) | −21.9454 | −1.00481 | ||||||||
\(478\) | −9.66512 | −0.442072 | ||||||||
\(479\) | −43.1382 | −1.97104 | −0.985518 | − | 0.169573i | \(-0.945761\pi\) | ||||
−0.985518 | + | 0.169573i | \(0.945761\pi\) | |||||||
\(480\) | −13.6062 | −0.621036 | ||||||||
\(481\) | −11.5574 | −0.526971 | ||||||||
\(482\) | −20.4437 | −0.931187 | ||||||||
\(483\) | −1.71284 | −0.0779371 | ||||||||
\(484\) | 3.11244 | 0.141475 | ||||||||
\(485\) | −2.72545 | −0.123756 | ||||||||
\(486\) | −36.5727 | −1.65897 | ||||||||
\(487\) | −5.67414 | −0.257120 | −0.128560 | − | 0.991702i | \(-0.541035\pi\) | ||||
−0.128560 | + | 0.991702i | \(0.541035\pi\) | |||||||
\(488\) | 21.7733 | 0.985631 | ||||||||
\(489\) | −24.0039 | −1.08549 | ||||||||
\(490\) | 13.4780 | 0.608875 | ||||||||
\(491\) | −33.5416 | −1.51371 | −0.756855 | − | 0.653582i | \(-0.773265\pi\) | ||||
−0.756855 | + | 0.653582i | \(0.773265\pi\) | |||||||
\(492\) | 71.9027 | 3.24162 | ||||||||
\(493\) | 12.7090 | 0.572386 | ||||||||
\(494\) | −11.9704 | −0.538572 | ||||||||
\(495\) | −1.74515 | −0.0784388 | ||||||||
\(496\) | −0.0677951 | −0.00304409 | ||||||||
\(497\) | 1.89024 | 0.0847889 | ||||||||
\(498\) | 47.4786 | 2.12757 | ||||||||
\(499\) | 11.3451 | 0.507877 | 0.253939 | − | 0.967220i | \(-0.418274\pi\) | ||||
0.253939 | + | 0.967220i | \(0.418274\pi\) | |||||||
\(500\) | 3.11244 | 0.139193 | ||||||||
\(501\) | 42.2719 | 1.88857 | ||||||||
\(502\) | 11.9440 | 0.533089 | ||||||||
\(503\) | −21.1105 | −0.941272 | −0.470636 | − | 0.882327i | \(-0.655976\pi\) | ||||
−0.470636 | + | 0.882327i | \(0.655976\pi\) | |||||||
\(504\) | −4.47459 | −0.199314 | ||||||||
\(505\) | −1.50808 | −0.0671087 | ||||||||
\(506\) | 1.74413 | 0.0775359 | ||||||||
\(507\) | 23.1877 | 1.02980 | ||||||||
\(508\) | −23.9199 | −1.06127 | ||||||||
\(509\) | −16.3206 | −0.723399 | −0.361700 | − | 0.932295i | \(-0.617803\pi\) | ||||
−0.361700 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(510\) | 23.5134 | 1.04119 | ||||||||
\(511\) | 1.01936 | 0.0450940 | ||||||||
\(512\) | −6.06232 | −0.267919 | ||||||||
\(513\) | −9.42939 | −0.416318 | ||||||||
\(514\) | 26.3712 | 1.16318 | ||||||||
\(515\) | 18.2298 | 0.803299 | ||||||||
\(516\) | 0.684394 | 0.0301287 | ||||||||
\(517\) | 3.79029 | 0.166697 | ||||||||
\(518\) | −17.3571 | −0.762628 | ||||||||
\(519\) | 50.5876 | 2.22055 | ||||||||
\(520\) | 3.86026 | 0.169283 | ||||||||
\(521\) | −40.6600 | −1.78135 | −0.890673 | − | 0.454644i | \(-0.849767\pi\) | ||||
−0.890673 | + | 0.454644i | \(0.849767\pi\) | |||||||
\(522\) | −10.5047 | −0.459777 | ||||||||
\(523\) | −6.33991 | −0.277225 | −0.138612 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138612 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(524\) | 0.505234 | 0.0220713 | ||||||||
\(525\) | −2.22052 | −0.0969113 | ||||||||
\(526\) | 3.02010 | 0.131683 | ||||||||
\(527\) | 0.602034 | 0.0262250 | ||||||||
\(528\) | −1.17106 | −0.0509639 | ||||||||
\(529\) | −22.4050 | −0.974130 | ||||||||
\(530\) | 28.4331 | 1.23506 | ||||||||
\(531\) | 5.62114 | 0.243937 | ||||||||
\(532\) | −10.9446 | −0.474506 | ||||||||
\(533\) | 16.2759 | 0.704986 | ||||||||
\(534\) | −34.8887 | −1.50978 | ||||||||
\(535\) | 1.39080 | 0.0601296 | ||||||||
\(536\) | −1.12639 | −0.0486528 | ||||||||
\(537\) | 13.9259 | 0.600949 | ||||||||
\(538\) | 27.8876 | 1.20232 | ||||||||
\(539\) | 5.96090 | 0.256754 | ||||||||
\(540\) | 8.50779 | 0.366117 | ||||||||
\(541\) | 7.24782 | 0.311608 | 0.155804 | − | 0.987788i | \(-0.450203\pi\) | ||||
0.155804 | + | 0.987788i | \(0.450203\pi\) | |||||||
\(542\) | −15.5968 | −0.669941 | ||||||||
\(543\) | −12.5720 | −0.539515 | ||||||||
\(544\) | 29.8187 | 1.27847 | ||||||||
\(545\) | 12.9399 | 0.554286 | ||||||||
\(546\) | −7.70537 | −0.329759 | ||||||||
\(547\) | 12.9456 | 0.553513 | 0.276756 | − | 0.960940i | \(-0.410740\pi\) | ||||
0.276756 | + | 0.960940i | \(0.410740\pi\) | |||||||
\(548\) | 29.0840 | 1.24241 | ||||||||
\(549\) | −15.1066 | −0.644734 | ||||||||
\(550\) | 2.26107 | 0.0964124 | ||||||||
\(551\) | −9.18339 | −0.391226 | ||||||||
\(552\) | 4.22649 | 0.179891 | ||||||||
\(553\) | 7.66297 | 0.325863 | ||||||||
\(554\) | −15.6396 | −0.664465 | ||||||||
\(555\) | −16.4044 | −0.696327 | ||||||||
\(556\) | 24.2681 | 1.02920 | ||||||||
\(557\) | −35.0209 | −1.48388 | −0.741942 | − | 0.670464i | \(-0.766095\pi\) | ||||
−0.741942 | + | 0.670464i | \(0.766095\pi\) | |||||||
\(558\) | −0.497613 | −0.0210656 | ||||||||
\(559\) | 0.154919 | 0.00655238 | ||||||||
\(560\) | −0.548004 | −0.0231574 | ||||||||
\(561\) | 10.3992 | 0.439057 | ||||||||
\(562\) | 62.1769 | 2.62278 | ||||||||
\(563\) | 1.43449 | 0.0604564 | 0.0302282 | − | 0.999543i | \(-0.490377\pi\) | ||||
0.0302282 | + | 0.999543i | \(0.490377\pi\) | |||||||
\(564\) | 25.6980 | 1.08208 | ||||||||
\(565\) | −8.97149 | −0.377433 | ||||||||
\(566\) | 25.9234 | 1.08964 | ||||||||
\(567\) | −11.4066 | −0.479031 | ||||||||
\(568\) | −4.66422 | −0.195706 | ||||||||
\(569\) | −15.8061 | −0.662628 | −0.331314 | − | 0.943521i | \(-0.607492\pi\) | ||||
−0.331314 | + | 0.943521i | \(0.607492\pi\) | |||||||
\(570\) | −16.9905 | −0.711655 | ||||||||
\(571\) | 15.4889 | 0.648190 | 0.324095 | − | 0.946025i | \(-0.394940\pi\) | ||||
0.324095 | + | 0.946025i | \(0.394940\pi\) | |||||||
\(572\) | 4.77668 | 0.199723 | ||||||||
\(573\) | −19.6019 | −0.818879 | ||||||||
\(574\) | 24.4434 | 1.02025 | ||||||||
\(575\) | 0.771372 | 0.0321684 | ||||||||
\(576\) | −22.7704 | −0.948767 | ||||||||
\(577\) | 1.69633 | 0.0706193 | 0.0353097 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353097 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(578\) | −13.0927 | −0.544585 | ||||||||
\(579\) | −10.0237 | −0.416570 | ||||||||
\(580\) | 8.28584 | 0.344051 | ||||||||
\(581\) | 9.82624 | 0.407661 | ||||||||
\(582\) | −13.4239 | −0.556437 | ||||||||
\(583\) | 12.5751 | 0.520806 | ||||||||
\(584\) | −2.51531 | −0.104084 | ||||||||
\(585\) | −2.67830 | −0.110734 | ||||||||
\(586\) | 48.7236 | 2.01276 | ||||||||
\(587\) | −16.8643 | −0.696066 | −0.348033 | − | 0.937482i | \(-0.613150\pi\) | ||||
−0.348033 | + | 0.937482i | \(0.613150\pi\) | |||||||
\(588\) | 40.4146 | 1.66667 | ||||||||
\(589\) | −0.435023 | −0.0179248 | ||||||||
\(590\) | −7.28291 | −0.299833 | ||||||||
\(591\) | −25.8288 | −1.06246 | ||||||||
\(592\) | −4.04845 | −0.166390 | ||||||||
\(593\) | 6.48817 | 0.266437 | 0.133219 | − | 0.991087i | \(-0.457469\pi\) | ||||
0.133219 | + | 0.991087i | \(0.457469\pi\) | |||||||
\(594\) | 6.18059 | 0.253593 | ||||||||
\(595\) | 4.86638 | 0.199502 | ||||||||
\(596\) | −45.4706 | −1.86255 | ||||||||
\(597\) | 12.5170 | 0.512287 | ||||||||
\(598\) | 2.67672 | 0.109459 | ||||||||
\(599\) | −38.7831 | −1.58463 | −0.792317 | − | 0.610110i | \(-0.791125\pi\) | ||||
−0.792317 | + | 0.610110i | \(0.791125\pi\) | |||||||
\(600\) | 5.47919 | 0.223687 | ||||||||
\(601\) | −22.2458 | −0.907424 | −0.453712 | − | 0.891148i | \(-0.649901\pi\) | ||||
−0.453712 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(602\) | 0.232661 | 0.00948254 | ||||||||
\(603\) | 0.781506 | 0.0318254 | ||||||||
\(604\) | 2.35764 | 0.0959311 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −7.42786 | −0.301736 | ||||||||
\(607\) | 28.4788 | 1.15592 | 0.577959 | − | 0.816066i | \(-0.303850\pi\) | ||||
0.577959 | + | 0.816066i | \(0.303850\pi\) | |||||||
\(608\) | −21.5467 | −0.873833 | ||||||||
\(609\) | −5.91139 | −0.239542 | ||||||||
\(610\) | 19.5725 | 0.792469 | ||||||||
\(611\) | 5.81698 | 0.235330 | ||||||||
\(612\) | 25.9305 | 1.04818 | ||||||||
\(613\) | 18.0424 | 0.728726 | 0.364363 | − | 0.931257i | \(-0.381287\pi\) | ||||
0.364363 | + | 0.931257i | \(0.381287\pi\) | |||||||
\(614\) | −5.29058 | −0.213510 | ||||||||
\(615\) | 23.1017 | 0.931550 | ||||||||
\(616\) | 2.56401 | 0.103307 | ||||||||
\(617\) | −33.9415 | −1.36643 | −0.683217 | − | 0.730215i | \(-0.739420\pi\) | ||||
−0.683217 | + | 0.730215i | \(0.739420\pi\) | |||||||
\(618\) | 89.7884 | 3.61182 | ||||||||
\(619\) | 8.71706 | 0.350368 | 0.175184 | − | 0.984536i | \(-0.443948\pi\) | ||||
0.175184 | + | 0.984536i | \(0.443948\pi\) | |||||||
\(620\) | 0.392505 | 0.0157634 | ||||||||
\(621\) | 2.10853 | 0.0846124 | ||||||||
\(622\) | 51.6285 | 2.07011 | ||||||||
\(623\) | −7.22063 | −0.289288 | ||||||||
\(624\) | −1.79723 | −0.0719469 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.0801 | 0.922466 | ||||||||
\(627\) | −7.51438 | −0.300095 | ||||||||
\(628\) | 10.3390 | 0.412569 | ||||||||
\(629\) | 35.9510 | 1.43346 | ||||||||
\(630\) | −4.02232 | −0.160253 | ||||||||
\(631\) | −39.2382 | −1.56205 | −0.781024 | − | 0.624501i | \(-0.785302\pi\) | ||||
−0.781024 | + | 0.624501i | \(0.785302\pi\) | |||||||
\(632\) | −18.9086 | −0.752143 | ||||||||
\(633\) | −12.4575 | −0.495140 | ||||||||
\(634\) | 50.4653 | 2.00423 | ||||||||
\(635\) | −7.68524 | −0.304980 | ||||||||
\(636\) | 85.2583 | 3.38071 | ||||||||
\(637\) | 9.14822 | 0.362466 | ||||||||
\(638\) | 6.01935 | 0.238308 | ||||||||
\(639\) | 3.23610 | 0.128018 | ||||||||
\(640\) | 17.0097 | 0.672368 | ||||||||
\(641\) | 16.9106 | 0.667927 | 0.333963 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333963 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(642\) | 6.85022 | 0.270357 | ||||||||
\(643\) | −23.8305 | −0.939782 | −0.469891 | − | 0.882725i | \(-0.655707\pi\) | ||||
−0.469891 | + | 0.882725i | \(0.655707\pi\) | |||||||
\(644\) | 2.44734 | 0.0964386 | ||||||||
\(645\) | 0.219890 | 0.00865815 | ||||||||
\(646\) | 37.2356 | 1.46502 | ||||||||
\(647\) | −22.7529 | −0.894510 | −0.447255 | − | 0.894407i | \(-0.647598\pi\) | ||||
−0.447255 | + | 0.894407i | \(0.647598\pi\) | |||||||
\(648\) | 28.1460 | 1.10568 | ||||||||
\(649\) | −3.22100 | −0.126435 | ||||||||
\(650\) | 3.47008 | 0.136108 | ||||||||
\(651\) | −0.280026 | −0.0109751 | ||||||||
\(652\) | 34.2972 | 1.34318 | ||||||||
\(653\) | 38.2483 | 1.49677 | 0.748386 | − | 0.663264i | \(-0.230829\pi\) | ||||
0.748386 | + | 0.663264i | \(0.230829\pi\) | |||||||
\(654\) | 63.7340 | 2.49220 | ||||||||
\(655\) | 0.162327 | 0.00634266 | ||||||||
\(656\) | 5.70129 | 0.222598 | ||||||||
\(657\) | 1.74515 | 0.0680849 | ||||||||
\(658\) | 8.73606 | 0.340567 | ||||||||
\(659\) | 15.0056 | 0.584537 | 0.292268 | − | 0.956336i | \(-0.405590\pi\) | ||||
0.292268 | + | 0.956336i | \(0.405590\pi\) | |||||||
\(660\) | 6.77995 | 0.263909 | ||||||||
\(661\) | −38.0233 | −1.47893 | −0.739467 | − | 0.673192i | \(-0.764923\pi\) | ||||
−0.739467 | + | 0.673192i | \(0.764923\pi\) | |||||||
\(662\) | 40.3222 | 1.56717 | ||||||||
\(663\) | 15.9598 | 0.619827 | ||||||||
\(664\) | −24.2465 | −0.940948 | ||||||||
\(665\) | −3.51639 | −0.136360 | ||||||||
\(666\) | −29.7154 | −1.15145 | ||||||||
\(667\) | 2.05352 | 0.0795126 | ||||||||
\(668\) | −60.3987 | −2.33690 | ||||||||
\(669\) | −31.3041 | −1.21029 | ||||||||
\(670\) | −1.01254 | −0.0391179 | ||||||||
\(671\) | 8.65632 | 0.334173 | ||||||||
\(672\) | −13.8697 | −0.535035 | ||||||||
\(673\) | 12.8520 | 0.495409 | 0.247705 | − | 0.968836i | \(-0.420324\pi\) | ||||
0.247705 | + | 0.968836i | \(0.420324\pi\) | |||||||
\(674\) | 5.89759 | 0.227167 | ||||||||
\(675\) | 2.73348 | 0.105212 | ||||||||
\(676\) | −33.1309 | −1.27427 | ||||||||
\(677\) | −14.4613 | −0.555792 | −0.277896 | − | 0.960611i | \(-0.589637\pi\) | ||||
−0.277896 | + | 0.960611i | \(0.589637\pi\) | |||||||
\(678\) | −44.1879 | −1.69703 | ||||||||
\(679\) | −2.77823 | −0.106619 | ||||||||
\(680\) | −12.0079 | −0.460483 | ||||||||
\(681\) | −17.4993 | −0.670574 | ||||||||
\(682\) | 0.285140 | 0.0109186 | ||||||||
\(683\) | 26.3011 | 1.00638 | 0.503192 | − | 0.864175i | \(-0.332159\pi\) | ||||
0.503192 | + | 0.864175i | \(0.332159\pi\) | |||||||
\(684\) | −18.7371 | −0.716431 | ||||||||
\(685\) | 9.34442 | 0.357032 | ||||||||
\(686\) | 29.8730 | 1.14056 | ||||||||
\(687\) | −40.9223 | −1.56128 | ||||||||
\(688\) | 0.0542668 | 0.00206890 | ||||||||
\(689\) | 19.2990 | 0.735234 | ||||||||
\(690\) | 3.79930 | 0.144637 | ||||||||
\(691\) | −16.6751 | −0.634350 | −0.317175 | − | 0.948367i | \(-0.602734\pi\) | ||||
−0.317175 | + | 0.948367i | \(0.602734\pi\) | |||||||
\(692\) | −72.2804 | −2.74769 | ||||||||
\(693\) | −1.77895 | −0.0675765 | ||||||||
\(694\) | −73.0110 | −2.77146 | ||||||||
\(695\) | 7.79712 | 0.295762 | ||||||||
\(696\) | 14.5865 | 0.552900 | ||||||||
\(697\) | −50.6286 | −1.91769 | ||||||||
\(698\) | −50.8092 | −1.92316 | ||||||||
\(699\) | −39.7194 | −1.50233 | ||||||||
\(700\) | 3.17271 | 0.119917 | ||||||||
\(701\) | 3.17852 | 0.120051 | 0.0600255 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600255 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(702\) | 9.48539 | 0.358003 | ||||||||
\(703\) | −25.9778 | −0.979771 | ||||||||
\(704\) | 13.0478 | 0.491758 | ||||||||
\(705\) | 8.25653 | 0.310959 | ||||||||
\(706\) | −4.54668 | −0.171117 | ||||||||
\(707\) | −1.53728 | −0.0578155 | ||||||||
\(708\) | −21.8382 | −0.820730 | ||||||||
\(709\) | 33.0245 | 1.24026 | 0.620132 | − | 0.784498i | \(-0.287079\pi\) | ||||
0.620132 | + | 0.784498i | \(0.287079\pi\) | |||||||
\(710\) | −4.19278 | −0.157352 | ||||||||
\(711\) | 13.1190 | 0.492002 | ||||||||
\(712\) | 17.8171 | 0.667724 | ||||||||
\(713\) | 0.0972765 | 0.00364303 | ||||||||
\(714\) | 23.9687 | 0.897008 | ||||||||
\(715\) | 1.53471 | 0.0573947 | ||||||||
\(716\) | −19.8976 | −0.743608 | ||||||||
\(717\) | −9.31147 | −0.347743 | ||||||||
\(718\) | −0.350502 | −0.0130806 | ||||||||
\(719\) | −3.22205 | −0.120162 | −0.0600810 | − | 0.998194i | \(-0.519136\pi\) | ||||
−0.0600810 | + | 0.998194i | \(0.519136\pi\) | |||||||
\(720\) | −0.938183 | −0.0349640 | ||||||||
\(721\) | 18.5827 | 0.692058 | ||||||||
\(722\) | 16.0543 | 0.597480 | ||||||||
\(723\) | −19.6957 | −0.732491 | ||||||||
\(724\) | 17.9630 | 0.667591 | ||||||||
\(725\) | 2.66217 | 0.0988704 | ||||||||
\(726\) | 4.92537 | 0.182798 | ||||||||
\(727\) | −35.4486 | −1.31471 | −0.657357 | − | 0.753579i | \(-0.728326\pi\) | ||||
−0.657357 | + | 0.753579i | \(0.728326\pi\) | |||||||
\(728\) | 3.93500 | 0.145841 | ||||||||
\(729\) | −1.66477 | −0.0616580 | ||||||||
\(730\) | −2.26107 | −0.0836860 | ||||||||
\(731\) | −0.481900 | −0.0178237 | ||||||||
\(732\) | 58.6894 | 2.16922 | ||||||||
\(733\) | −5.50396 | −0.203293 | −0.101647 | − | 0.994821i | \(-0.532411\pi\) | ||||
−0.101647 | + | 0.994821i | \(0.532411\pi\) | |||||||
\(734\) | 73.6308 | 2.71776 | ||||||||
\(735\) | 12.9848 | 0.478953 | ||||||||
\(736\) | 4.81811 | 0.177598 | ||||||||
\(737\) | −0.447815 | −0.0164955 | ||||||||
\(738\) | 41.8472 | 1.54042 | ||||||||
\(739\) | 49.2340 | 1.81110 | 0.905551 | − | 0.424238i | \(-0.139458\pi\) | ||||
0.905551 | + | 0.424238i | \(0.139458\pi\) | |||||||
\(740\) | 23.4388 | 0.861628 | ||||||||
\(741\) | −11.5324 | −0.423652 | ||||||||
\(742\) | 28.9837 | 1.06402 | ||||||||
\(743\) | 35.5739 | 1.30508 | 0.652540 | − | 0.757754i | \(-0.273703\pi\) | ||||
0.652540 | + | 0.757754i | \(0.273703\pi\) | |||||||
\(744\) | 0.690972 | 0.0253323 | ||||||||
\(745\) | −14.6093 | −0.535244 | ||||||||
\(746\) | 50.9452 | 1.86524 | ||||||||
\(747\) | 16.8226 | 0.615505 | ||||||||
\(748\) | −14.8586 | −0.543284 | ||||||||
\(749\) | 1.41773 | 0.0518028 | ||||||||
\(750\) | 4.92537 | 0.179849 | ||||||||
\(751\) | −24.3136 | −0.887216 | −0.443608 | − | 0.896221i | \(-0.646302\pi\) | ||||
−0.443608 | + | 0.896221i | \(0.646302\pi\) | |||||||
\(752\) | 2.03764 | 0.0743050 | ||||||||
\(753\) | 11.5070 | 0.419338 | ||||||||
\(754\) | 9.23793 | 0.336425 | ||||||||
\(755\) | 0.757490 | 0.0275679 | ||||||||
\(756\) | 8.67254 | 0.315417 | ||||||||
\(757\) | −16.0822 | −0.584519 | −0.292259 | − | 0.956339i | \(-0.594407\pi\) | ||||
−0.292259 | + | 0.956339i | \(0.594407\pi\) | |||||||
\(758\) | 85.0848 | 3.09042 | ||||||||
\(759\) | 1.68031 | 0.0609913 | ||||||||
\(760\) | 8.67678 | 0.314740 | ||||||||
\(761\) | −28.6409 | −1.03823 | −0.519115 | − | 0.854704i | \(-0.673739\pi\) | ||||
−0.519115 | + | 0.854704i | \(0.673739\pi\) | |||||||
\(762\) | −37.8527 | −1.37126 | ||||||||
\(763\) | 13.1905 | 0.477528 | ||||||||
\(764\) | 28.0074 | 1.01327 | ||||||||
\(765\) | 8.33125 | 0.301217 | ||||||||
\(766\) | 46.3760 | 1.67563 | ||||||||
\(767\) | −4.94328 | −0.178492 | ||||||||
\(768\) | 26.9341 | 0.971902 | ||||||||
\(769\) | −9.70738 | −0.350057 | −0.175028 | − | 0.984563i | \(-0.556002\pi\) | ||||
−0.175028 | + | 0.984563i | \(0.556002\pi\) | |||||||
\(770\) | 2.30485 | 0.0830611 | ||||||||
\(771\) | 25.4062 | 0.914983 | ||||||||
\(772\) | 14.3220 | 0.515460 | ||||||||
\(773\) | −38.9553 | −1.40113 | −0.700563 | − | 0.713591i | \(-0.747068\pi\) | ||||
−0.700563 | + | 0.713591i | \(0.747068\pi\) | |||||||
\(774\) | 0.398316 | 0.0143172 | ||||||||
\(775\) | 0.126108 | 0.00452995 | ||||||||
\(776\) | 6.85535 | 0.246093 | ||||||||
\(777\) | −16.7220 | −0.599899 | ||||||||
\(778\) | −30.3866 | −1.08941 | ||||||||
\(779\) | 36.5836 | 1.31074 | ||||||||
\(780\) | 10.4052 | 0.372567 | ||||||||
\(781\) | −1.85434 | −0.0663533 | ||||||||
\(782\) | −8.32635 | −0.297750 | ||||||||
\(783\) | 7.27698 | 0.260058 | ||||||||
\(784\) | 3.20454 | 0.114448 | ||||||||
\(785\) | 3.32182 | 0.118561 | ||||||||
\(786\) | 0.799523 | 0.0285181 | ||||||||
\(787\) | −27.2032 | −0.969689 | −0.484844 | − | 0.874600i | \(-0.661124\pi\) | ||||
−0.484844 | + | 0.874600i | \(0.661124\pi\) | |||||||
\(788\) | 36.9046 | 1.31467 | ||||||||
\(789\) | 2.90959 | 0.103584 | ||||||||
\(790\) | −16.9974 | −0.604740 | ||||||||
\(791\) | −9.14521 | −0.325166 | ||||||||
\(792\) | 4.38960 | 0.155978 | ||||||||
\(793\) | 13.2849 | 0.471761 | ||||||||
\(794\) | 21.6597 | 0.768676 | ||||||||
\(795\) | 27.3927 | 0.971520 | ||||||||
\(796\) | −17.8845 | −0.633899 | ||||||||
\(797\) | −19.6032 | −0.694380 | −0.347190 | − | 0.937795i | \(-0.612864\pi\) | ||||
−0.347190 | + | 0.937795i | \(0.612864\pi\) | |||||||
\(798\) | −17.3195 | −0.613105 | ||||||||
\(799\) | −18.0946 | −0.640141 | ||||||||
\(800\) | 6.24615 | 0.220835 | ||||||||
\(801\) | −12.3617 | −0.436780 | ||||||||
\(802\) | 33.8701 | 1.19599 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | −3.03616 | −0.107077 | ||||||||
\(805\) | 0.786308 | 0.0277137 | ||||||||
\(806\) | 0.437606 | 0.0154140 | ||||||||
\(807\) | 26.8671 | 0.945768 | ||||||||
\(808\) | 3.79329 | 0.133447 | ||||||||
\(809\) | 7.97624 | 0.280430 | 0.140215 | − | 0.990121i | \(-0.455221\pi\) | ||||
0.140215 | + | 0.990121i | \(0.455221\pi\) | |||||||
\(810\) | 25.3012 | 0.888992 | ||||||||
\(811\) | −35.0160 | −1.22958 | −0.614790 | − | 0.788691i | \(-0.710759\pi\) | ||||
−0.614790 | + | 0.788691i | \(0.710759\pi\) | |||||||
\(812\) | 8.44628 | 0.296406 | ||||||||
\(813\) | −15.0261 | −0.526990 | ||||||||
\(814\) | 17.0274 | 0.596810 | ||||||||
\(815\) | 11.0194 | 0.385992 | ||||||||
\(816\) | 5.59057 | 0.195709 | ||||||||
\(817\) | 0.348215 | 0.0121825 | ||||||||
\(818\) | −75.7290 | −2.64780 | ||||||||
\(819\) | −2.73016 | −0.0953994 | ||||||||
\(820\) | −33.0081 | −1.15269 | ||||||||
\(821\) | −16.0075 | −0.558664 | −0.279332 | − | 0.960195i | \(-0.590113\pi\) | ||||
−0.279332 | + | 0.960195i | \(0.590113\pi\) | |||||||
\(822\) | 46.0248 | 1.60530 | ||||||||
\(823\) | 15.1373 | 0.527654 | 0.263827 | − | 0.964570i | \(-0.415015\pi\) | ||||
0.263827 | + | 0.964570i | \(0.415015\pi\) | |||||||
\(824\) | −45.8534 | −1.59738 | ||||||||
\(825\) | 2.17834 | 0.0758400 | ||||||||
\(826\) | −7.42393 | −0.258312 | ||||||||
\(827\) | −31.1695 | −1.08387 | −0.541935 | − | 0.840420i | \(-0.682308\pi\) | ||||
−0.541935 | + | 0.840420i | \(0.682308\pi\) | |||||||
\(828\) | 4.18985 | 0.145607 | ||||||||
\(829\) | 34.1509 | 1.18611 | 0.593054 | − | 0.805163i | \(-0.297922\pi\) | ||||
0.593054 | + | 0.805163i | \(0.297922\pi\) | |||||||
\(830\) | −21.7958 | −0.756543 | ||||||||
\(831\) | −15.0674 | −0.522682 | ||||||||
\(832\) | 20.0245 | 0.694226 | ||||||||
\(833\) | −28.4570 | −0.985975 | ||||||||
\(834\) | 38.4037 | 1.32981 | ||||||||
\(835\) | −19.4056 | −0.671558 | ||||||||
\(836\) | 10.7367 | 0.371335 | ||||||||
\(837\) | 0.344715 | 0.0119151 | ||||||||
\(838\) | 41.5770 | 1.43625 | ||||||||
\(839\) | −22.7893 | −0.786774 | −0.393387 | − | 0.919373i | \(-0.628697\pi\) | ||||
−0.393387 | + | 0.919373i | \(0.628697\pi\) | |||||||
\(840\) | 5.58528 | 0.192711 | ||||||||
\(841\) | −21.9129 | −0.755616 | ||||||||
\(842\) | 28.2562 | 0.973774 | ||||||||
\(843\) | 59.9019 | 2.06313 | ||||||||
\(844\) | 17.7994 | 0.612681 | ||||||||
\(845\) | −10.6447 | −0.366188 | ||||||||
\(846\) | 14.9562 | 0.514203 | ||||||||
\(847\) | 1.01936 | 0.0350257 | ||||||||
\(848\) | 6.76028 | 0.232149 | ||||||||
\(849\) | 24.9749 | 0.857136 | ||||||||
\(850\) | −10.7942 | −0.370238 | ||||||||
\(851\) | 5.80896 | 0.199129 | ||||||||
\(852\) | −12.5723 | −0.430720 | ||||||||
\(853\) | 43.8953 | 1.50295 | 0.751474 | − | 0.659763i | \(-0.229343\pi\) | ||||
0.751474 | + | 0.659763i | \(0.229343\pi\) | |||||||
\(854\) | 19.9515 | 0.682728 | ||||||||
\(855\) | −6.02007 | −0.205882 | ||||||||
\(856\) | −3.49829 | −0.119569 | ||||||||
\(857\) | −29.4695 | −1.00666 | −0.503330 | − | 0.864094i | \(-0.667892\pi\) | ||||
−0.503330 | + | 0.864094i | \(0.667892\pi\) | |||||||
\(858\) | 7.55900 | 0.258060 | ||||||||
\(859\) | 44.8915 | 1.53168 | 0.765840 | − | 0.643031i | \(-0.222324\pi\) | ||||
0.765840 | + | 0.643031i | \(0.222324\pi\) | |||||||
\(860\) | −0.314182 | −0.0107135 | ||||||||
\(861\) | 23.5490 | 0.802549 | ||||||||
\(862\) | −62.0506 | −2.11345 | ||||||||
\(863\) | 21.8951 | 0.745317 | 0.372659 | − | 0.927969i | \(-0.378446\pi\) | ||||
0.372659 | + | 0.927969i | \(0.378446\pi\) | |||||||
\(864\) | 17.0737 | 0.580860 | ||||||||
\(865\) | −23.2231 | −0.789607 | ||||||||
\(866\) | −7.34881 | −0.249723 | ||||||||
\(867\) | −12.6136 | −0.428382 | ||||||||
\(868\) | 0.400105 | 0.0135805 | ||||||||
\(869\) | −7.51741 | −0.255011 | ||||||||
\(870\) | 13.1122 | 0.444544 | ||||||||
\(871\) | −0.687265 | −0.0232871 | ||||||||
\(872\) | −32.5479 | −1.10221 | ||||||||
\(873\) | −4.75633 | −0.160977 | ||||||||
\(874\) | 6.01652 | 0.203512 | ||||||||
\(875\) | 1.01936 | 0.0344608 | ||||||||
\(876\) | −6.77995 | −0.229073 | ||||||||
\(877\) | 12.6311 | 0.426523 | 0.213261 | − | 0.976995i | \(-0.431591\pi\) | ||||
0.213261 | + | 0.976995i | \(0.431591\pi\) | |||||||
\(878\) | −19.1884 | −0.647576 | ||||||||
\(879\) | 46.9408 | 1.58327 | ||||||||
\(880\) | 0.537594 | 0.0181223 | ||||||||
\(881\) | 46.6844 | 1.57284 | 0.786419 | − | 0.617694i | \(-0.211933\pi\) | ||||
0.786419 | + | 0.617694i | \(0.211933\pi\) | |||||||
\(882\) | 23.5212 | 0.792000 | ||||||||
\(883\) | −38.4042 | −1.29240 | −0.646202 | − | 0.763166i | \(-0.723644\pi\) | ||||
−0.646202 | + | 0.763166i | \(0.723644\pi\) | |||||||
\(884\) | −22.8036 | −0.766967 | ||||||||
\(885\) | −7.01642 | −0.235854 | ||||||||
\(886\) | −72.2595 | −2.42761 | ||||||||
\(887\) | 17.4443 | 0.585722 | 0.292861 | − | 0.956155i | \(-0.405393\pi\) | ||||
0.292861 | + | 0.956155i | \(0.405393\pi\) | |||||||
\(888\) | 41.2620 | 1.38466 | ||||||||
\(889\) | −7.83406 | −0.262746 | ||||||||
\(890\) | 16.0162 | 0.536865 | ||||||||
\(891\) | 11.1899 | 0.374876 | ||||||||
\(892\) | 44.7278 | 1.49760 | ||||||||
\(893\) | 13.0750 | 0.437537 | ||||||||
\(894\) | −71.9563 | −2.40658 | ||||||||
\(895\) | −6.39292 | −0.213692 | ||||||||
\(896\) | 17.3391 | 0.579258 | ||||||||
\(897\) | 2.57878 | 0.0861029 | ||||||||
\(898\) | −9.40789 | −0.313945 | ||||||||
\(899\) | 0.335722 | 0.0111969 | ||||||||
\(900\) | 5.43169 | 0.181056 | ||||||||
\(901\) | −60.0326 | −1.99998 | ||||||||
\(902\) | −23.9791 | −0.798417 | ||||||||
\(903\) | 0.224148 | 0.00745916 | ||||||||
\(904\) | 22.5660 | 0.750536 | ||||||||
\(905\) | 5.77136 | 0.191847 | ||||||||
\(906\) | 3.73092 | 0.123952 | ||||||||
\(907\) | −13.5165 | −0.448807 | −0.224404 | − | 0.974496i | \(-0.572043\pi\) | ||||
−0.224404 | + | 0.974496i | \(0.572043\pi\) | |||||||
\(908\) | 25.0032 | 0.829761 | ||||||||
\(909\) | −2.63183 | −0.0872924 | ||||||||
\(910\) | 3.53727 | 0.117259 | ||||||||
\(911\) | −36.2561 | −1.20122 | −0.600610 | − | 0.799542i | \(-0.705075\pi\) | ||||
−0.600610 | + | 0.799542i | \(0.705075\pi\) | |||||||
\(912\) | −4.03968 | −0.133767 | ||||||||
\(913\) | −9.63959 | −0.319024 | ||||||||
\(914\) | 81.4368 | 2.69369 | ||||||||
\(915\) | 18.8564 | 0.623373 | ||||||||
\(916\) | 58.4704 | 1.93191 | ||||||||
\(917\) | 0.165471 | 0.00546432 | ||||||||
\(918\) | −29.5058 | −0.973835 | ||||||||
\(919\) | 36.3161 | 1.19796 | 0.598979 | − | 0.800765i | \(-0.295573\pi\) | ||||
0.598979 | + | 0.800765i | \(0.295573\pi\) | |||||||
\(920\) | −1.94024 | −0.0639677 | ||||||||
\(921\) | −5.09700 | −0.167952 | ||||||||
\(922\) | −56.3948 | −1.85726 | ||||||||
\(923\) | −2.84586 | −0.0936726 | ||||||||
\(924\) | 6.91123 | 0.227363 | ||||||||
\(925\) | 7.53069 | 0.247607 | ||||||||
\(926\) | −17.0002 | −0.558663 | ||||||||
\(927\) | 31.8137 | 1.04490 | ||||||||
\(928\) | 16.6283 | 0.545851 | ||||||||
\(929\) | 28.0949 | 0.921763 | 0.460881 | − | 0.887462i | \(-0.347533\pi\) | ||||
0.460881 | + | 0.887462i | \(0.347533\pi\) | |||||||
\(930\) | 0.621131 | 0.0203677 | ||||||||
\(931\) | 20.5627 | 0.673914 | ||||||||
\(932\) | 56.7517 | 1.85896 | ||||||||
\(933\) | 49.7394 | 1.62839 | ||||||||
\(934\) | −6.53704 | −0.213898 | ||||||||
\(935\) | −4.77394 | −0.156124 | ||||||||
\(936\) | 6.73674 | 0.220197 | ||||||||
\(937\) | 5.82865 | 0.190414 | 0.0952068 | − | 0.995458i | \(-0.469649\pi\) | ||||
0.0952068 | + | 0.995458i | \(0.469649\pi\) | |||||||
\(938\) | −1.03215 | −0.0337008 | ||||||||
\(939\) | 22.2356 | 0.725631 | ||||||||
\(940\) | −11.7971 | −0.384777 | ||||||||
\(941\) | −26.6635 | −0.869205 | −0.434602 | − | 0.900622i | \(-0.643111\pi\) | ||||
−0.434602 | + | 0.900622i | \(0.643111\pi\) | |||||||
\(942\) | 16.3612 | 0.533076 | ||||||||
\(943\) | −8.18055 | −0.266395 | ||||||||
\(944\) | −1.73159 | −0.0563584 | ||||||||
\(945\) | 2.78641 | 0.0906419 | ||||||||
\(946\) | −0.228241 | −0.00742076 | ||||||||
\(947\) | 48.5378 | 1.57727 | 0.788634 | − | 0.614863i | \(-0.210789\pi\) | ||||
0.788634 | + | 0.614863i | \(0.210789\pi\) | |||||||
\(948\) | −50.9676 | −1.65535 | ||||||||
\(949\) | −1.53471 | −0.0498186 | ||||||||
\(950\) | 7.79977 | 0.253058 | ||||||||
\(951\) | 48.6187 | 1.57657 | ||||||||
\(952\) | −12.2404 | −0.396715 | ||||||||
\(953\) | −22.4157 | −0.726117 | −0.363059 | − | 0.931766i | \(-0.618268\pi\) | ||||
−0.363059 | + | 0.931766i | \(0.618268\pi\) | |||||||
\(954\) | 49.6201 | 1.60651 | ||||||||
\(955\) | 8.99854 | 0.291186 | ||||||||
\(956\) | 13.3044 | 0.430294 | ||||||||
\(957\) | 5.79910 | 0.187458 | ||||||||
\(958\) | 97.5386 | 3.15133 | ||||||||
\(959\) | 9.52536 | 0.307590 | ||||||||
\(960\) | 28.4225 | 0.917333 | ||||||||
\(961\) | −30.9841 | −0.999487 | ||||||||
\(962\) | 26.1321 | 0.842532 | ||||||||
\(963\) | 2.42716 | 0.0782142 | ||||||||
\(964\) | 28.1415 | 0.906377 | ||||||||
\(965\) | 4.60153 | 0.148129 | ||||||||
\(966\) | 3.87286 | 0.124607 | ||||||||
\(967\) | −35.1671 | −1.13090 | −0.565449 | − | 0.824783i | \(-0.691297\pi\) | ||||
−0.565449 | + | 0.824783i | \(0.691297\pi\) | |||||||
\(968\) | −2.51531 | −0.0808450 | ||||||||
\(969\) | 35.8732 | 1.15241 | ||||||||
\(970\) | 6.16244 | 0.197864 | ||||||||
\(971\) | 0.120404 | 0.00386395 | 0.00193197 | − | 0.999998i | \(-0.499385\pi\) | ||||
0.00193197 | + | 0.999998i | \(0.499385\pi\) | |||||||
\(972\) | 50.3435 | 1.61477 | ||||||||
\(973\) | 7.94810 | 0.254804 | ||||||||
\(974\) | 12.8296 | 0.411088 | ||||||||
\(975\) | 3.34311 | 0.107065 | ||||||||
\(976\) | 4.65358 | 0.148958 | ||||||||
\(977\) | −19.5697 | −0.626089 | −0.313044 | − | 0.949738i | \(-0.601349\pi\) | ||||
−0.313044 | + | 0.949738i | \(0.601349\pi\) | |||||||
\(978\) | 54.2746 | 1.73551 | ||||||||
\(979\) | 7.08347 | 0.226389 | ||||||||
\(980\) | −18.5529 | −0.592652 | ||||||||
\(981\) | 22.5822 | 0.720993 | ||||||||
\(982\) | 75.8399 | 2.42015 | ||||||||
\(983\) | 5.58741 | 0.178211 | 0.0891054 | − | 0.996022i | \(-0.471599\pi\) | ||||
0.0891054 | + | 0.996022i | \(0.471599\pi\) | |||||||
\(984\) | −58.1079 | −1.85241 | ||||||||
\(985\) | 11.8571 | 0.377799 | ||||||||
\(986\) | −28.7360 | −0.915141 | ||||||||
\(987\) | 8.41641 | 0.267897 | ||||||||
\(988\) | 16.4776 | 0.524222 | ||||||||
\(989\) | −0.0778652 | −0.00247597 | ||||||||
\(990\) | 3.94591 | 0.125409 | ||||||||
\(991\) | −19.7298 | −0.626739 | −0.313370 | − | 0.949631i | \(-0.601458\pi\) | ||||
−0.313370 | + | 0.949631i | \(0.601458\pi\) | |||||||
\(992\) | 0.787693 | 0.0250093 | ||||||||
\(993\) | 38.8468 | 1.23277 | ||||||||
\(994\) | −4.27397 | −0.135562 | ||||||||
\(995\) | −5.74613 | −0.182165 | ||||||||
\(996\) | −65.3559 | −2.07088 | ||||||||
\(997\) | 14.3506 | 0.454489 | 0.227245 | − | 0.973838i | \(-0.427028\pi\) | ||||
0.227245 | + | 0.973838i | \(0.427028\pi\) | |||||||
\(998\) | −25.6521 | −0.812004 | ||||||||
\(999\) | 20.5850 | 0.651280 |
(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 | 4015.2.a.c.1.3 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.c.1.3 | ✓ | 23 | 1.1 | even | 1 | trivial |