Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, 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("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1198728231\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} - 4865 x^{6} - 5483 x^{5} + 7607 x^{4} + 1210 x^{3} - 3153 x^{2} + 878 x - 54 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.13475\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.13475 | 0.655147 | 0.327573 | − | 0.944826i | \(-0.393769\pi\) | ||||
0.327573 | + | 0.944826i | \(0.393769\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.13475 | 0.463259 | ||||||||
\(7\) | −2.24922 | −0.850125 | −0.425062 | − | 0.905164i | \(-0.639748\pi\) | ||||
−0.425062 | + | 0.905164i | \(0.639748\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.71235 | −0.570783 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.13475 | 0.327573 | ||||||||
\(13\) | 0.202024 | 0.0560314 | 0.0280157 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280157 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(14\) | −2.24922 | −0.601129 | ||||||||
\(15\) | −1.13475 | −0.292991 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.27259 | 0.551185 | 0.275592 | − | 0.961275i | \(-0.411126\pi\) | ||||
0.275592 | + | 0.961275i | \(0.411126\pi\) | |||||||
\(18\) | −1.71235 | −0.403604 | ||||||||
\(19\) | 6.24810 | 1.43341 | 0.716706 | − | 0.697376i | \(-0.245649\pi\) | ||||
0.716706 | + | 0.697376i | \(0.245649\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.55229 | −0.556956 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.51752 | −0.524939 | −0.262470 | − | 0.964940i | \(-0.584537\pi\) | ||||
−0.262470 | + | 0.964940i | \(0.584537\pi\) | |||||||
\(24\) | 1.13475 | 0.231629 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.202024 | 0.0396201 | ||||||||
\(27\) | −5.34733 | −1.02909 | ||||||||
\(28\) | −2.24922 | −0.425062 | ||||||||
\(29\) | 3.26404 | 0.606116 | 0.303058 | − | 0.952972i | \(-0.401992\pi\) | ||||
0.303058 | + | 0.952972i | \(0.401992\pi\) | |||||||
\(30\) | −1.13475 | −0.207176 | ||||||||
\(31\) | 3.69060 | 0.662851 | 0.331426 | − | 0.943481i | \(-0.392470\pi\) | ||||
0.331426 | + | 0.943481i | \(0.392470\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.13475 | 0.197534 | ||||||||
\(34\) | 2.27259 | 0.389747 | ||||||||
\(35\) | 2.24922 | 0.380187 | ||||||||
\(36\) | −1.71235 | −0.285391 | ||||||||
\(37\) | −10.0765 | −1.65657 | −0.828285 | − | 0.560307i | \(-0.810683\pi\) | ||||
−0.828285 | + | 0.560307i | \(0.810683\pi\) | |||||||
\(38\) | 6.24810 | 1.01357 | ||||||||
\(39\) | 0.229246 | 0.0367088 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.61893 | 1.34605 | 0.673025 | − | 0.739620i | \(-0.264995\pi\) | ||||
0.673025 | + | 0.739620i | \(0.264995\pi\) | |||||||
\(42\) | −2.55229 | −0.393828 | ||||||||
\(43\) | −0.359773 | −0.0548649 | −0.0274324 | − | 0.999624i | \(-0.508733\pi\) | ||||
−0.0274324 | + | 0.999624i | \(0.508733\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.71235 | 0.255262 | ||||||||
\(46\) | −2.51752 | −0.371188 | ||||||||
\(47\) | −2.00249 | −0.292094 | −0.146047 | − | 0.989278i | \(-0.546655\pi\) | ||||
−0.146047 | + | 0.989278i | \(0.546655\pi\) | |||||||
\(48\) | 1.13475 | 0.163787 | ||||||||
\(49\) | −1.94102 | −0.277288 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.57882 | 0.361107 | ||||||||
\(52\) | 0.202024 | 0.0280157 | ||||||||
\(53\) | 3.20981 | 0.440902 | 0.220451 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220451 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(54\) | −5.34733 | −0.727679 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −2.24922 | −0.300564 | ||||||||
\(57\) | 7.09001 | 0.939095 | ||||||||
\(58\) | 3.26404 | 0.428589 | ||||||||
\(59\) | −2.01046 | −0.261740 | −0.130870 | − | 0.991400i | \(-0.541777\pi\) | ||||
−0.130870 | + | 0.991400i | \(0.541777\pi\) | |||||||
\(60\) | −1.13475 | −0.146495 | ||||||||
\(61\) | 1.59340 | 0.204014 | 0.102007 | − | 0.994784i | \(-0.467474\pi\) | ||||
0.102007 | + | 0.994784i | \(0.467474\pi\) | |||||||
\(62\) | 3.69060 | 0.468707 | ||||||||
\(63\) | 3.85144 | 0.485236 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.202024 | −0.0250580 | ||||||||
\(66\) | 1.13475 | 0.139678 | ||||||||
\(67\) | 10.9959 | 1.34336 | 0.671679 | − | 0.740842i | \(-0.265573\pi\) | ||||
0.671679 | + | 0.740842i | \(0.265573\pi\) | |||||||
\(68\) | 2.27259 | 0.275592 | ||||||||
\(69\) | −2.85675 | −0.343912 | ||||||||
\(70\) | 2.24922 | 0.268833 | ||||||||
\(71\) | 4.47296 | 0.530843 | 0.265422 | − | 0.964132i | \(-0.414489\pi\) | ||||
0.265422 | + | 0.964132i | \(0.414489\pi\) | |||||||
\(72\) | −1.71235 | −0.201802 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −10.0765 | −1.17137 | ||||||||
\(75\) | 1.13475 | 0.131029 | ||||||||
\(76\) | 6.24810 | 0.716706 | ||||||||
\(77\) | −2.24922 | −0.256322 | ||||||||
\(78\) | 0.229246 | 0.0259570 | ||||||||
\(79\) | 12.7687 | 1.43659 | 0.718295 | − | 0.695739i | \(-0.244923\pi\) | ||||
0.718295 | + | 0.695739i | \(0.244923\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −0.930819 | −0.103424 | ||||||||
\(82\) | 8.61893 | 0.951801 | ||||||||
\(83\) | −11.6129 | −1.27469 | −0.637343 | − | 0.770580i | \(-0.719967\pi\) | ||||
−0.637343 | + | 0.770580i | \(0.719967\pi\) | |||||||
\(84\) | −2.55229 | −0.278478 | ||||||||
\(85\) | −2.27259 | −0.246497 | ||||||||
\(86\) | −0.359773 | −0.0387953 | ||||||||
\(87\) | 3.70386 | 0.397095 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 9.86267 | 1.04544 | 0.522720 | − | 0.852504i | \(-0.324917\pi\) | ||||
0.522720 | + | 0.852504i | \(0.324917\pi\) | |||||||
\(90\) | 1.71235 | 0.180497 | ||||||||
\(91\) | −0.454396 | −0.0476336 | ||||||||
\(92\) | −2.51752 | −0.262470 | ||||||||
\(93\) | 4.18790 | 0.434265 | ||||||||
\(94\) | −2.00249 | −0.206541 | ||||||||
\(95\) | −6.24810 | −0.641041 | ||||||||
\(96\) | 1.13475 | 0.115815 | ||||||||
\(97\) | −10.1623 | −1.03182 | −0.515912 | − | 0.856641i | \(-0.672547\pi\) | ||||
−0.515912 | + | 0.856641i | \(0.672547\pi\) | |||||||
\(98\) | −1.94102 | −0.196072 | ||||||||
\(99\) | −1.71235 | −0.172097 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.1168 | 1.10616 | 0.553081 | − | 0.833127i | \(-0.313452\pi\) | ||||
0.553081 | + | 0.833127i | \(0.313452\pi\) | |||||||
\(102\) | 2.57882 | 0.255341 | ||||||||
\(103\) | 12.0478 | 1.18710 | 0.593550 | − | 0.804797i | \(-0.297726\pi\) | ||||
0.593550 | + | 0.804797i | \(0.297726\pi\) | |||||||
\(104\) | 0.202024 | 0.0198101 | ||||||||
\(105\) | 2.55229 | 0.249078 | ||||||||
\(106\) | 3.20981 | 0.311765 | ||||||||
\(107\) | −9.35618 | −0.904496 | −0.452248 | − | 0.891892i | \(-0.649378\pi\) | ||||
−0.452248 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(108\) | −5.34733 | −0.514547 | ||||||||
\(109\) | 15.2409 | 1.45981 | 0.729906 | − | 0.683548i | \(-0.239564\pi\) | ||||
0.729906 | + | 0.683548i | \(0.239564\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −11.4343 | −1.08530 | ||||||||
\(112\) | −2.24922 | −0.212531 | ||||||||
\(113\) | 3.51943 | 0.331080 | 0.165540 | − | 0.986203i | \(-0.447063\pi\) | ||||
0.165540 | + | 0.986203i | \(0.447063\pi\) | |||||||
\(114\) | 7.09001 | 0.664040 | ||||||||
\(115\) | 2.51752 | 0.234760 | ||||||||
\(116\) | 3.26404 | 0.303058 | ||||||||
\(117\) | −0.345935 | −0.0319817 | ||||||||
\(118\) | −2.01046 | −0.185078 | ||||||||
\(119\) | −5.11156 | −0.468576 | ||||||||
\(120\) | −1.13475 | −0.103588 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.59340 | 0.144260 | ||||||||
\(123\) | 9.78031 | 0.881860 | ||||||||
\(124\) | 3.69060 | 0.331426 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.85144 | 0.343114 | ||||||||
\(127\) | −0.831256 | −0.0737621 | −0.0368810 | − | 0.999320i | \(-0.511742\pi\) | ||||
−0.0368810 | + | 0.999320i | \(0.511742\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.408252 | −0.0359445 | ||||||||
\(130\) | −0.202024 | −0.0177187 | ||||||||
\(131\) | 5.24272 | 0.458058 | 0.229029 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229029 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(132\) | 1.13475 | 0.0987671 | ||||||||
\(133\) | −14.0533 | −1.21858 | ||||||||
\(134\) | 10.9959 | 0.949898 | ||||||||
\(135\) | 5.34733 | 0.460224 | ||||||||
\(136\) | 2.27259 | 0.194873 | ||||||||
\(137\) | −2.36028 | −0.201652 | −0.100826 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100826 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(138\) | −2.85675 | −0.243183 | ||||||||
\(139\) | 3.95726 | 0.335650 | 0.167825 | − | 0.985817i | \(-0.446326\pi\) | ||||
0.167825 | + | 0.985817i | \(0.446326\pi\) | |||||||
\(140\) | 2.24922 | 0.190094 | ||||||||
\(141\) | −2.27232 | −0.191364 | ||||||||
\(142\) | 4.47296 | 0.375363 | ||||||||
\(143\) | 0.202024 | 0.0168941 | ||||||||
\(144\) | −1.71235 | −0.142696 | ||||||||
\(145\) | −3.26404 | −0.271063 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | −2.20256 | −0.181664 | ||||||||
\(148\) | −10.0765 | −0.828285 | ||||||||
\(149\) | 9.40226 | 0.770263 | 0.385132 | − | 0.922862i | \(-0.374156\pi\) | ||||
0.385132 | + | 0.922862i | \(0.374156\pi\) | |||||||
\(150\) | 1.13475 | 0.0926517 | ||||||||
\(151\) | 10.4648 | 0.851615 | 0.425807 | − | 0.904814i | \(-0.359990\pi\) | ||||
0.425807 | + | 0.904814i | \(0.359990\pi\) | |||||||
\(152\) | 6.24810 | 0.506787 | ||||||||
\(153\) | −3.89147 | −0.314607 | ||||||||
\(154\) | −2.24922 | −0.181247 | ||||||||
\(155\) | −3.69060 | −0.296436 | ||||||||
\(156\) | 0.229246 | 0.0183544 | ||||||||
\(157\) | 21.7044 | 1.73220 | 0.866099 | − | 0.499872i | \(-0.166620\pi\) | ||||
0.866099 | + | 0.499872i | \(0.166620\pi\) | |||||||
\(158\) | 12.7687 | 1.01582 | ||||||||
\(159\) | 3.64233 | 0.288855 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.66245 | 0.446264 | ||||||||
\(162\) | −0.930819 | −0.0731320 | ||||||||
\(163\) | −2.25705 | −0.176786 | −0.0883930 | − | 0.996086i | \(-0.528173\pi\) | ||||
−0.0883930 | + | 0.996086i | \(0.528173\pi\) | |||||||
\(164\) | 8.61893 | 0.673025 | ||||||||
\(165\) | −1.13475 | −0.0883400 | ||||||||
\(166\) | −11.6129 | −0.901340 | ||||||||
\(167\) | 3.12464 | 0.241792 | 0.120896 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120896 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(168\) | −2.55229 | −0.196914 | ||||||||
\(169\) | −12.9592 | −0.996860 | ||||||||
\(170\) | −2.27259 | −0.174300 | ||||||||
\(171\) | −10.6989 | −0.818166 | ||||||||
\(172\) | −0.359773 | −0.0274324 | ||||||||
\(173\) | 19.7226 | 1.49948 | 0.749740 | − | 0.661733i | \(-0.230179\pi\) | ||||
0.749740 | + | 0.661733i | \(0.230179\pi\) | |||||||
\(174\) | 3.70386 | 0.280789 | ||||||||
\(175\) | −2.24922 | −0.170025 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −2.28136 | −0.171478 | ||||||||
\(178\) | 9.86267 | 0.739238 | ||||||||
\(179\) | 16.1286 | 1.20551 | 0.602755 | − | 0.797926i | \(-0.294069\pi\) | ||||
0.602755 | + | 0.797926i | \(0.294069\pi\) | |||||||
\(180\) | 1.71235 | 0.127631 | ||||||||
\(181\) | 0.309823 | 0.0230290 | 0.0115145 | − | 0.999934i | \(-0.496335\pi\) | ||||
0.0115145 | + | 0.999934i | \(0.496335\pi\) | |||||||
\(182\) | −0.454396 | −0.0336821 | ||||||||
\(183\) | 1.80811 | 0.133659 | ||||||||
\(184\) | −2.51752 | −0.185594 | ||||||||
\(185\) | 10.0765 | 0.740840 | ||||||||
\(186\) | 4.18790 | 0.307072 | ||||||||
\(187\) | 2.27259 | 0.166188 | ||||||||
\(188\) | −2.00249 | −0.146047 | ||||||||
\(189\) | 12.0273 | 0.874857 | ||||||||
\(190\) | −6.24810 | −0.453284 | ||||||||
\(191\) | 21.0739 | 1.52485 | 0.762426 | − | 0.647075i | \(-0.224008\pi\) | ||||
0.762426 | + | 0.647075i | \(0.224008\pi\) | |||||||
\(192\) | 1.13475 | 0.0818933 | ||||||||
\(193\) | −5.84784 | −0.420937 | −0.210468 | − | 0.977601i | \(-0.567499\pi\) | ||||
−0.210468 | + | 0.977601i | \(0.567499\pi\) | |||||||
\(194\) | −10.1623 | −0.729610 | ||||||||
\(195\) | −0.229246 | −0.0164167 | ||||||||
\(196\) | −1.94102 | −0.138644 | ||||||||
\(197\) | 4.39229 | 0.312938 | 0.156469 | − | 0.987683i | \(-0.449989\pi\) | ||||
0.156469 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(198\) | −1.71235 | −0.121691 | ||||||||
\(199\) | −18.1565 | −1.28708 | −0.643538 | − | 0.765414i | \(-0.722534\pi\) | ||||
−0.643538 | + | 0.765414i | \(0.722534\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 12.4775 | 0.880097 | ||||||||
\(202\) | 11.1168 | 0.782175 | ||||||||
\(203\) | −7.34153 | −0.515274 | ||||||||
\(204\) | 2.57882 | 0.180553 | ||||||||
\(205\) | −8.61893 | −0.601972 | ||||||||
\(206\) | 12.0478 | 0.839407 | ||||||||
\(207\) | 4.31087 | 0.299626 | ||||||||
\(208\) | 0.202024 | 0.0140078 | ||||||||
\(209\) | 6.24810 | 0.432190 | ||||||||
\(210\) | 2.55229 | 0.176125 | ||||||||
\(211\) | 13.2684 | 0.913435 | 0.456718 | − | 0.889612i | \(-0.349025\pi\) | ||||
0.456718 | + | 0.889612i | \(0.349025\pi\) | |||||||
\(212\) | 3.20981 | 0.220451 | ||||||||
\(213\) | 5.07569 | 0.347780 | ||||||||
\(214\) | −9.35618 | −0.639575 | ||||||||
\(215\) | 0.359773 | 0.0245363 | ||||||||
\(216\) | −5.34733 | −0.363839 | ||||||||
\(217\) | −8.30096 | −0.563506 | ||||||||
\(218\) | 15.2409 | 1.03224 | ||||||||
\(219\) | 1.13475 | 0.0766791 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 0.459118 | 0.0308836 | ||||||||
\(222\) | −11.4343 | −0.767420 | ||||||||
\(223\) | −10.7683 | −0.721101 | −0.360551 | − | 0.932740i | \(-0.617411\pi\) | ||||
−0.360551 | + | 0.932740i | \(0.617411\pi\) | |||||||
\(224\) | −2.24922 | −0.150282 | ||||||||
\(225\) | −1.71235 | −0.114157 | ||||||||
\(226\) | 3.51943 | 0.234109 | ||||||||
\(227\) | −7.05329 | −0.468143 | −0.234072 | − | 0.972219i | \(-0.575205\pi\) | ||||
−0.234072 | + | 0.972219i | \(0.575205\pi\) | |||||||
\(228\) | 7.09001 | 0.469547 | ||||||||
\(229\) | 3.70742 | 0.244993 | 0.122496 | − | 0.992469i | \(-0.460910\pi\) | ||||
0.122496 | + | 0.992469i | \(0.460910\pi\) | |||||||
\(230\) | 2.51752 | 0.166000 | ||||||||
\(231\) | −2.55229 | −0.167929 | ||||||||
\(232\) | 3.26404 | 0.214294 | ||||||||
\(233\) | 7.71390 | 0.505354 | 0.252677 | − | 0.967551i | \(-0.418689\pi\) | ||||
0.252677 | + | 0.967551i | \(0.418689\pi\) | |||||||
\(234\) | −0.345935 | −0.0226145 | ||||||||
\(235\) | 2.00249 | 0.130628 | ||||||||
\(236\) | −2.01046 | −0.130870 | ||||||||
\(237\) | 14.4892 | 0.941177 | ||||||||
\(238\) | −5.11156 | −0.331333 | ||||||||
\(239\) | 26.3200 | 1.70250 | 0.851249 | − | 0.524762i | \(-0.175846\pi\) | ||||
0.851249 | + | 0.524762i | \(0.175846\pi\) | |||||||
\(240\) | −1.13475 | −0.0732476 | ||||||||
\(241\) | −9.57433 | −0.616737 | −0.308368 | − | 0.951267i | \(-0.599783\pi\) | ||||
−0.308368 | + | 0.951267i | \(0.599783\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 14.9857 | 0.961335 | ||||||||
\(244\) | 1.59340 | 0.102007 | ||||||||
\(245\) | 1.94102 | 0.124007 | ||||||||
\(246\) | 9.78031 | 0.623569 | ||||||||
\(247\) | 1.26226 | 0.0803160 | ||||||||
\(248\) | 3.69060 | 0.234353 | ||||||||
\(249\) | −13.1778 | −0.835107 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.3728 | −0.780966 | −0.390483 | − | 0.920610i | \(-0.627692\pi\) | ||||
−0.390483 | + | 0.920610i | \(0.627692\pi\) | |||||||
\(252\) | 3.85144 | 0.242618 | ||||||||
\(253\) | −2.51752 | −0.158275 | ||||||||
\(254\) | −0.831256 | −0.0521577 | ||||||||
\(255\) | −2.57882 | −0.161492 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.8602 | −1.11409 | −0.557043 | − | 0.830483i | \(-0.688064\pi\) | ||||
−0.557043 | + | 0.830483i | \(0.688064\pi\) | |||||||
\(258\) | −0.408252 | −0.0254166 | ||||||||
\(259\) | 22.6643 | 1.40829 | ||||||||
\(260\) | −0.202024 | −0.0125290 | ||||||||
\(261\) | −5.58917 | −0.345961 | ||||||||
\(262\) | 5.24272 | 0.323896 | ||||||||
\(263\) | 3.26368 | 0.201247 | 0.100624 | − | 0.994925i | \(-0.467916\pi\) | ||||
0.100624 | + | 0.994925i | \(0.467916\pi\) | |||||||
\(264\) | 1.13475 | 0.0698389 | ||||||||
\(265\) | −3.20981 | −0.197177 | ||||||||
\(266\) | −14.0533 | −0.861665 | ||||||||
\(267\) | 11.1916 | 0.684917 | ||||||||
\(268\) | 10.9959 | 0.671679 | ||||||||
\(269\) | 0.313678 | 0.0191253 | 0.00956264 | − | 0.999954i | \(-0.496956\pi\) | ||||
0.00956264 | + | 0.999954i | \(0.496956\pi\) | |||||||
\(270\) | 5.34733 | 0.325428 | ||||||||
\(271\) | −1.47405 | −0.0895419 | −0.0447709 | − | 0.998997i | \(-0.514256\pi\) | ||||
−0.0447709 | + | 0.998997i | \(0.514256\pi\) | |||||||
\(272\) | 2.27259 | 0.137796 | ||||||||
\(273\) | −0.515625 | −0.0312070 | ||||||||
\(274\) | −2.36028 | −0.142589 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −2.85675 | −0.171956 | ||||||||
\(277\) | 23.4699 | 1.41017 | 0.705085 | − | 0.709122i | \(-0.250909\pi\) | ||||
0.705085 | + | 0.709122i | \(0.250909\pi\) | |||||||
\(278\) | 3.95726 | 0.237341 | ||||||||
\(279\) | −6.31959 | −0.378344 | ||||||||
\(280\) | 2.24922 | 0.134416 | ||||||||
\(281\) | −14.8057 | −0.883231 | −0.441616 | − | 0.897204i | \(-0.645594\pi\) | ||||
−0.441616 | + | 0.897204i | \(0.645594\pi\) | |||||||
\(282\) | −2.27232 | −0.135315 | ||||||||
\(283\) | 18.1441 | 1.07855 | 0.539277 | − | 0.842129i | \(-0.318698\pi\) | ||||
0.539277 | + | 0.842129i | \(0.318698\pi\) | |||||||
\(284\) | 4.47296 | 0.265422 | ||||||||
\(285\) | −7.09001 | −0.419976 | ||||||||
\(286\) | 0.202024 | 0.0119459 | ||||||||
\(287\) | −19.3858 | −1.14431 | ||||||||
\(288\) | −1.71235 | −0.100901 | ||||||||
\(289\) | −11.8353 | −0.696195 | ||||||||
\(290\) | −3.26404 | −0.191671 | ||||||||
\(291\) | −11.5316 | −0.675996 | ||||||||
\(292\) | 1.00000 | 0.0585206 | ||||||||
\(293\) | 14.5058 | 0.847439 | 0.423719 | − | 0.905794i | \(-0.360724\pi\) | ||||
0.423719 | + | 0.905794i | \(0.360724\pi\) | |||||||
\(294\) | −2.20256 | −0.128456 | ||||||||
\(295\) | 2.01046 | 0.117054 | ||||||||
\(296\) | −10.0765 | −0.585686 | ||||||||
\(297\) | −5.34733 | −0.310283 | ||||||||
\(298\) | 9.40226 | 0.544659 | ||||||||
\(299\) | −0.508599 | −0.0294131 | ||||||||
\(300\) | 1.13475 | 0.0655147 | ||||||||
\(301\) | 0.809208 | 0.0466420 | ||||||||
\(302\) | 10.4648 | 0.602183 | ||||||||
\(303\) | 12.6148 | 0.724699 | ||||||||
\(304\) | 6.24810 | 0.358353 | ||||||||
\(305\) | −1.59340 | −0.0912380 | ||||||||
\(306\) | −3.89147 | −0.222461 | ||||||||
\(307\) | −4.43968 | −0.253386 | −0.126693 | − | 0.991942i | \(-0.540436\pi\) | ||||
−0.126693 | + | 0.991942i | \(0.540436\pi\) | |||||||
\(308\) | −2.24922 | −0.128161 | ||||||||
\(309\) | 13.6712 | 0.777725 | ||||||||
\(310\) | −3.69060 | −0.209612 | ||||||||
\(311\) | −17.4668 | −0.990454 | −0.495227 | − | 0.868764i | \(-0.664915\pi\) | ||||
−0.495227 | + | 0.868764i | \(0.664915\pi\) | |||||||
\(312\) | 0.229246 | 0.0129785 | ||||||||
\(313\) | 18.3946 | 1.03972 | 0.519862 | − | 0.854250i | \(-0.325983\pi\) | ||||
0.519862 | + | 0.854250i | \(0.325983\pi\) | |||||||
\(314\) | 21.7044 | 1.22485 | ||||||||
\(315\) | −3.85144 | −0.217004 | ||||||||
\(316\) | 12.7687 | 0.718295 | ||||||||
\(317\) | −18.0011 | −1.01104 | −0.505521 | − | 0.862814i | \(-0.668700\pi\) | ||||
−0.505521 | + | 0.862814i | \(0.668700\pi\) | |||||||
\(318\) | 3.64233 | 0.204252 | ||||||||
\(319\) | 3.26404 | 0.182751 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −10.6169 | −0.592577 | ||||||||
\(322\) | 5.66245 | 0.315556 | ||||||||
\(323\) | 14.1994 | 0.790075 | ||||||||
\(324\) | −0.930819 | −0.0517121 | ||||||||
\(325\) | 0.202024 | 0.0112063 | ||||||||
\(326\) | −2.25705 | −0.125007 | ||||||||
\(327\) | 17.2945 | 0.956390 | ||||||||
\(328\) | 8.61893 | 0.475901 | ||||||||
\(329\) | 4.50404 | 0.248316 | ||||||||
\(330\) | −1.13475 | −0.0624658 | ||||||||
\(331\) | −5.15501 | −0.283345 | −0.141672 | − | 0.989914i | \(-0.545248\pi\) | ||||
−0.141672 | + | 0.989914i | \(0.545248\pi\) | |||||||
\(332\) | −11.6129 | −0.637343 | ||||||||
\(333\) | 17.2545 | 0.945541 | ||||||||
\(334\) | 3.12464 | 0.170973 | ||||||||
\(335\) | −10.9959 | −0.600768 | ||||||||
\(336\) | −2.55229 | −0.139239 | ||||||||
\(337\) | 0.0479947 | 0.00261444 | 0.00130722 | − | 0.999999i | \(-0.499584\pi\) | ||||
0.00130722 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(338\) | −12.9592 | −0.704887 | ||||||||
\(339\) | 3.99366 | 0.216906 | ||||||||
\(340\) | −2.27259 | −0.123249 | ||||||||
\(341\) | 3.69060 | 0.199857 | ||||||||
\(342\) | −10.6989 | −0.578531 | ||||||||
\(343\) | 20.1103 | 1.08585 | ||||||||
\(344\) | −0.359773 | −0.0193977 | ||||||||
\(345\) | 2.85675 | 0.153802 | ||||||||
\(346\) | 19.7226 | 1.06029 | ||||||||
\(347\) | −12.4765 | −0.669771 | −0.334886 | − | 0.942259i | \(-0.608698\pi\) | ||||
−0.334886 | + | 0.942259i | \(0.608698\pi\) | |||||||
\(348\) | 3.70386 | 0.198548 | ||||||||
\(349\) | −3.55815 | −0.190463 | −0.0952317 | − | 0.995455i | \(-0.530359\pi\) | ||||
−0.0952317 | + | 0.995455i | \(0.530359\pi\) | |||||||
\(350\) | −2.24922 | −0.120226 | ||||||||
\(351\) | −1.08029 | −0.0576615 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 4.93425 | 0.262623 | 0.131312 | − | 0.991341i | \(-0.458081\pi\) | ||||
0.131312 | + | 0.991341i | \(0.458081\pi\) | |||||||
\(354\) | −2.28136 | −0.121253 | ||||||||
\(355\) | −4.47296 | −0.237400 | ||||||||
\(356\) | 9.86267 | 0.522720 | ||||||||
\(357\) | −5.80033 | −0.306986 | ||||||||
\(358\) | 16.1286 | 0.852425 | ||||||||
\(359\) | 4.03340 | 0.212875 | 0.106437 | − | 0.994319i | \(-0.466056\pi\) | ||||
0.106437 | + | 0.994319i | \(0.466056\pi\) | |||||||
\(360\) | 1.71235 | 0.0902487 | ||||||||
\(361\) | 20.0387 | 1.05467 | ||||||||
\(362\) | 0.309823 | 0.0162839 | ||||||||
\(363\) | 1.13475 | 0.0595588 | ||||||||
\(364\) | −0.454396 | −0.0238168 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | 1.80811 | 0.0945114 | ||||||||
\(367\) | −15.6153 | −0.815111 | −0.407556 | − | 0.913180i | \(-0.633619\pi\) | ||||
−0.407556 | + | 0.913180i | \(0.633619\pi\) | |||||||
\(368\) | −2.51752 | −0.131235 | ||||||||
\(369\) | −14.7586 | −0.768302 | ||||||||
\(370\) | 10.0765 | 0.523853 | ||||||||
\(371\) | −7.21957 | −0.374821 | ||||||||
\(372\) | 4.18790 | 0.217132 | ||||||||
\(373\) | −5.60101 | −0.290009 | −0.145005 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145005 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(374\) | 2.27259 | 0.117513 | ||||||||
\(375\) | −1.13475 | −0.0585981 | ||||||||
\(376\) | −2.00249 | −0.103271 | ||||||||
\(377\) | 0.659413 | 0.0339615 | ||||||||
\(378\) | 12.0273 | 0.618618 | ||||||||
\(379\) | −23.3380 | −1.19879 | −0.599396 | − | 0.800453i | \(-0.704592\pi\) | ||||
−0.599396 | + | 0.800453i | \(0.704592\pi\) | |||||||
\(380\) | −6.24810 | −0.320521 | ||||||||
\(381\) | −0.943266 | −0.0483250 | ||||||||
\(382\) | 21.0739 | 1.07823 | ||||||||
\(383\) | −17.4899 | −0.893691 | −0.446846 | − | 0.894611i | \(-0.647453\pi\) | ||||
−0.446846 | + | 0.894611i | \(0.647453\pi\) | |||||||
\(384\) | 1.13475 | 0.0579073 | ||||||||
\(385\) | 2.24922 | 0.114631 | ||||||||
\(386\) | −5.84784 | −0.297647 | ||||||||
\(387\) | 0.616057 | 0.0313159 | ||||||||
\(388\) | −10.1623 | −0.515912 | ||||||||
\(389\) | 19.0646 | 0.966614 | 0.483307 | − | 0.875451i | \(-0.339435\pi\) | ||||
0.483307 | + | 0.875451i | \(0.339435\pi\) | |||||||
\(390\) | −0.229246 | −0.0116083 | ||||||||
\(391\) | −5.72130 | −0.289339 | ||||||||
\(392\) | −1.94102 | −0.0980362 | ||||||||
\(393\) | 5.94916 | 0.300095 | ||||||||
\(394\) | 4.39229 | 0.221280 | ||||||||
\(395\) | −12.7687 | −0.642462 | ||||||||
\(396\) | −1.71235 | −0.0860487 | ||||||||
\(397\) | 23.9517 | 1.20210 | 0.601051 | − | 0.799211i | \(-0.294749\pi\) | ||||
0.601051 | + | 0.799211i | \(0.294749\pi\) | |||||||
\(398\) | −18.1565 | −0.910101 | ||||||||
\(399\) | −15.9470 | −0.798348 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.28203 | 0.0640214 | 0.0320107 | − | 0.999488i | \(-0.489809\pi\) | ||||
0.0320107 | + | 0.999488i | \(0.489809\pi\) | |||||||
\(402\) | 12.4775 | 0.622323 | ||||||||
\(403\) | 0.745589 | 0.0371404 | ||||||||
\(404\) | 11.1168 | 0.553081 | ||||||||
\(405\) | 0.930819 | 0.0462528 | ||||||||
\(406\) | −7.34153 | −0.364354 | ||||||||
\(407\) | −10.0765 | −0.499474 | ||||||||
\(408\) | 2.57882 | 0.127671 | ||||||||
\(409\) | −30.7455 | −1.52027 | −0.760133 | − | 0.649768i | \(-0.774866\pi\) | ||||
−0.760133 | + | 0.649768i | \(0.774866\pi\) | |||||||
\(410\) | −8.61893 | −0.425658 | ||||||||
\(411\) | −2.67832 | −0.132112 | ||||||||
\(412\) | 12.0478 | 0.593550 | ||||||||
\(413\) | 4.52196 | 0.222511 | ||||||||
\(414\) | 4.31087 | 0.211868 | ||||||||
\(415\) | 11.6129 | 0.570057 | ||||||||
\(416\) | 0.202024 | 0.00990504 | ||||||||
\(417\) | 4.49049 | 0.219900 | ||||||||
\(418\) | 6.24810 | 0.305604 | ||||||||
\(419\) | −26.6982 | −1.30429 | −0.652146 | − | 0.758094i | \(-0.726131\pi\) | ||||
−0.652146 | + | 0.758094i | \(0.726131\pi\) | |||||||
\(420\) | 2.55229 | 0.124539 | ||||||||
\(421\) | −13.4999 | −0.657945 | −0.328973 | − | 0.944339i | \(-0.606702\pi\) | ||||
−0.328973 | + | 0.944339i | \(0.606702\pi\) | |||||||
\(422\) | 13.2684 | 0.645896 | ||||||||
\(423\) | 3.42897 | 0.166722 | ||||||||
\(424\) | 3.20981 | 0.155882 | ||||||||
\(425\) | 2.27259 | 0.110237 | ||||||||
\(426\) | 5.07569 | 0.245918 | ||||||||
\(427\) | −3.58391 | −0.173438 | ||||||||
\(428\) | −9.35618 | −0.452248 | ||||||||
\(429\) | 0.229246 | 0.0110681 | ||||||||
\(430\) | 0.359773 | 0.0173498 | ||||||||
\(431\) | 16.9683 | 0.817333 | 0.408666 | − | 0.912684i | \(-0.365994\pi\) | ||||
0.408666 | + | 0.912684i | \(0.365994\pi\) | |||||||
\(432\) | −5.34733 | −0.257273 | ||||||||
\(433\) | 14.5903 | 0.701165 | 0.350582 | − | 0.936532i | \(-0.385984\pi\) | ||||
0.350582 | + | 0.936532i | \(0.385984\pi\) | |||||||
\(434\) | −8.30096 | −0.398459 | ||||||||
\(435\) | −3.70386 | −0.177586 | ||||||||
\(436\) | 15.2409 | 0.729906 | ||||||||
\(437\) | −15.7297 | −0.752454 | ||||||||
\(438\) | 1.13475 | 0.0542203 | ||||||||
\(439\) | 12.9426 | 0.617718 | 0.308859 | − | 0.951108i | \(-0.400053\pi\) | ||||
0.308859 | + | 0.951108i | \(0.400053\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 3.32370 | 0.158271 | ||||||||
\(442\) | 0.459118 | 0.0218380 | ||||||||
\(443\) | −30.1339 | −1.43170 | −0.715852 | − | 0.698252i | \(-0.753961\pi\) | ||||
−0.715852 | + | 0.698252i | \(0.753961\pi\) | |||||||
\(444\) | −11.4343 | −0.542648 | ||||||||
\(445\) | −9.86267 | −0.467535 | ||||||||
\(446\) | −10.7683 | −0.509896 | ||||||||
\(447\) | 10.6692 | 0.504636 | ||||||||
\(448\) | −2.24922 | −0.106266 | ||||||||
\(449\) | −14.5155 | −0.685028 | −0.342514 | − | 0.939513i | \(-0.611278\pi\) | ||||
−0.342514 | + | 0.939513i | \(0.611278\pi\) | |||||||
\(450\) | −1.71235 | −0.0807209 | ||||||||
\(451\) | 8.61893 | 0.405849 | ||||||||
\(452\) | 3.51943 | 0.165540 | ||||||||
\(453\) | 11.8749 | 0.557933 | ||||||||
\(454\) | −7.05329 | −0.331027 | ||||||||
\(455\) | 0.454396 | 0.0213024 | ||||||||
\(456\) | 7.09001 | 0.332020 | ||||||||
\(457\) | −37.5708 | −1.75749 | −0.878745 | − | 0.477292i | \(-0.841619\pi\) | ||||
−0.878745 | + | 0.477292i | \(0.841619\pi\) | |||||||
\(458\) | 3.70742 | 0.173236 | ||||||||
\(459\) | −12.1523 | −0.567221 | ||||||||
\(460\) | 2.51752 | 0.117380 | ||||||||
\(461\) | −33.7192 | −1.57046 | −0.785230 | − | 0.619204i | \(-0.787455\pi\) | ||||
−0.785230 | + | 0.619204i | \(0.787455\pi\) | |||||||
\(462\) | −2.55229 | −0.118743 | ||||||||
\(463\) | 34.3995 | 1.59868 | 0.799341 | − | 0.600878i | \(-0.205182\pi\) | ||||
0.799341 | + | 0.600878i | \(0.205182\pi\) | |||||||
\(464\) | 3.26404 | 0.151529 | ||||||||
\(465\) | −4.18790 | −0.194209 | ||||||||
\(466\) | 7.71390 | 0.357340 | ||||||||
\(467\) | −22.3369 | −1.03363 | −0.516814 | − | 0.856098i | \(-0.672882\pi\) | ||||
−0.516814 | + | 0.856098i | \(0.672882\pi\) | |||||||
\(468\) | −0.345935 | −0.0159909 | ||||||||
\(469\) | −24.7321 | −1.14202 | ||||||||
\(470\) | 2.00249 | 0.0923681 | ||||||||
\(471\) | 24.6290 | 1.13484 | ||||||||
\(472\) | −2.01046 | −0.0925389 | ||||||||
\(473\) | −0.359773 | −0.0165424 | ||||||||
\(474\) | 14.4892 | 0.665512 | ||||||||
\(475\) | 6.24810 | 0.286682 | ||||||||
\(476\) | −5.11156 | −0.234288 | ||||||||
\(477\) | −5.49632 | −0.251659 | ||||||||
\(478\) | 26.3200 | 1.20385 | ||||||||
\(479\) | 3.41665 | 0.156111 | 0.0780553 | − | 0.996949i | \(-0.475129\pi\) | ||||
0.0780553 | + | 0.996949i | \(0.475129\pi\) | |||||||
\(480\) | −1.13475 | −0.0517939 | ||||||||
\(481\) | −2.03570 | −0.0928198 | ||||||||
\(482\) | −9.57433 | −0.436099 | ||||||||
\(483\) | 6.42545 | 0.292368 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.1623 | 0.461446 | ||||||||
\(486\) | 14.9857 | 0.679767 | ||||||||
\(487\) | −23.2454 | −1.05335 | −0.526675 | − | 0.850067i | \(-0.676562\pi\) | ||||
−0.526675 | + | 0.850067i | \(0.676562\pi\) | |||||||
\(488\) | 1.59340 | 0.0721300 | ||||||||
\(489\) | −2.56118 | −0.115821 | ||||||||
\(490\) | 1.94102 | 0.0876862 | ||||||||
\(491\) | −35.8534 | −1.61804 | −0.809021 | − | 0.587779i | \(-0.800002\pi\) | ||||
−0.809021 | + | 0.587779i | \(0.800002\pi\) | |||||||
\(492\) | 9.78031 | 0.440930 | ||||||||
\(493\) | 7.41783 | 0.334082 | ||||||||
\(494\) | 1.26226 | 0.0567920 | ||||||||
\(495\) | 1.71235 | 0.0769643 | ||||||||
\(496\) | 3.69060 | 0.165713 | ||||||||
\(497\) | −10.0607 | −0.451283 | ||||||||
\(498\) | −13.1778 | −0.590510 | ||||||||
\(499\) | 17.9926 | 0.805460 | 0.402730 | − | 0.915319i | \(-0.368061\pi\) | ||||
0.402730 | + | 0.915319i | \(0.368061\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 3.54568 | 0.158409 | ||||||||
\(502\) | −12.3728 | −0.552226 | ||||||||
\(503\) | −20.1316 | −0.897622 | −0.448811 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448811 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(504\) | 3.85144 | 0.171557 | ||||||||
\(505\) | −11.1168 | −0.494691 | ||||||||
\(506\) | −2.51752 | −0.111917 | ||||||||
\(507\) | −14.7054 | −0.653090 | ||||||||
\(508\) | −0.831256 | −0.0368810 | ||||||||
\(509\) | −5.76386 | −0.255479 | −0.127739 | − | 0.991808i | \(-0.540772\pi\) | ||||
−0.127739 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(510\) | −2.57882 | −0.114192 | ||||||||
\(511\) | −2.24922 | −0.0994996 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −33.4106 | −1.47511 | ||||||||
\(514\) | −17.8602 | −0.787778 | ||||||||
\(515\) | −12.0478 | −0.530887 | ||||||||
\(516\) | −0.408252 | −0.0179723 | ||||||||
\(517\) | −2.00249 | −0.0880695 | ||||||||
\(518\) | 22.6643 | 0.995812 | ||||||||
\(519\) | 22.3801 | 0.982379 | ||||||||
\(520\) | −0.202024 | −0.00885933 | ||||||||
\(521\) | 27.0492 | 1.18505 | 0.592524 | − | 0.805553i | \(-0.298131\pi\) | ||||
0.592524 | + | 0.805553i | \(0.298131\pi\) | |||||||
\(522\) | −5.58917 | −0.244631 | ||||||||
\(523\) | −38.9383 | −1.70265 | −0.851327 | − | 0.524635i | \(-0.824202\pi\) | ||||
−0.851327 | + | 0.524635i | \(0.824202\pi\) | |||||||
\(524\) | 5.24272 | 0.229029 | ||||||||
\(525\) | −2.55229 | −0.111391 | ||||||||
\(526\) | 3.26368 | 0.142303 | ||||||||
\(527\) | 8.38723 | 0.365353 | ||||||||
\(528\) | 1.13475 | 0.0493835 | ||||||||
\(529\) | −16.6621 | −0.724439 | ||||||||
\(530\) | −3.20981 | −0.139425 | ||||||||
\(531\) | 3.44261 | 0.149396 | ||||||||
\(532\) | −14.0533 | −0.609289 | ||||||||
\(533\) | 1.74123 | 0.0754210 | ||||||||
\(534\) | 11.1916 | 0.484309 | ||||||||
\(535\) | 9.35618 | 0.404503 | ||||||||
\(536\) | 10.9959 | 0.474949 | ||||||||
\(537\) | 18.3019 | 0.789787 | ||||||||
\(538\) | 0.313678 | 0.0135236 | ||||||||
\(539\) | −1.94102 | −0.0836055 | ||||||||
\(540\) | 5.34733 | 0.230112 | ||||||||
\(541\) | 27.1146 | 1.16575 | 0.582875 | − | 0.812562i | \(-0.301928\pi\) | ||||
0.582875 | + | 0.812562i | \(0.301928\pi\) | |||||||
\(542\) | −1.47405 | −0.0633157 | ||||||||
\(543\) | 0.351571 | 0.0150874 | ||||||||
\(544\) | 2.27259 | 0.0974366 | ||||||||
\(545\) | −15.2409 | −0.652847 | ||||||||
\(546\) | −0.515625 | −0.0220667 | ||||||||
\(547\) | −2.96129 | −0.126616 | −0.0633079 | − | 0.997994i | \(-0.520165\pi\) | ||||
−0.0633079 | + | 0.997994i | \(0.520165\pi\) | |||||||
\(548\) | −2.36028 | −0.100826 | ||||||||
\(549\) | −2.72846 | −0.116448 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 20.3940 | 0.868814 | ||||||||
\(552\) | −2.85675 | −0.121591 | ||||||||
\(553\) | −28.7196 | −1.22128 | ||||||||
\(554\) | 23.4699 | 0.997141 | ||||||||
\(555\) | 11.4343 | 0.485359 | ||||||||
\(556\) | 3.95726 | 0.167825 | ||||||||
\(557\) | −23.7930 | −1.00814 | −0.504071 | − | 0.863662i | \(-0.668165\pi\) | ||||
−0.504071 | + | 0.863662i | \(0.668165\pi\) | |||||||
\(558\) | −6.31959 | −0.267530 | ||||||||
\(559\) | −0.0726828 | −0.00307415 | ||||||||
\(560\) | 2.24922 | 0.0950468 | ||||||||
\(561\) | 2.57882 | 0.108878 | ||||||||
\(562\) | −14.8057 | −0.624539 | ||||||||
\(563\) | −5.10421 | −0.215117 | −0.107558 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107558 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(564\) | −2.27232 | −0.0956821 | ||||||||
\(565\) | −3.51943 | −0.148063 | ||||||||
\(566\) | 18.1441 | 0.762653 | ||||||||
\(567\) | 2.09361 | 0.0879235 | ||||||||
\(568\) | 4.47296 | 0.187681 | ||||||||
\(569\) | 16.6904 | 0.699697 | 0.349849 | − | 0.936806i | \(-0.386233\pi\) | ||||
0.349849 | + | 0.936806i | \(0.386233\pi\) | |||||||
\(570\) | −7.09001 | −0.296968 | ||||||||
\(571\) | −5.38893 | −0.225520 | −0.112760 | − | 0.993622i | \(-0.535969\pi\) | ||||
−0.112760 | + | 0.993622i | \(0.535969\pi\) | |||||||
\(572\) | 0.202024 | 0.00844704 | ||||||||
\(573\) | 23.9135 | 0.999002 | ||||||||
\(574\) | −19.3858 | −0.809150 | ||||||||
\(575\) | −2.51752 | −0.104988 | ||||||||
\(576\) | −1.71235 | −0.0713478 | ||||||||
\(577\) | −11.5172 | −0.479469 | −0.239734 | − | 0.970839i | \(-0.577060\pi\) | ||||
−0.239734 | + | 0.970839i | \(0.577060\pi\) | |||||||
\(578\) | −11.8353 | −0.492284 | ||||||||
\(579\) | −6.63582 | −0.275775 | ||||||||
\(580\) | −3.26404 | −0.135532 | ||||||||
\(581\) | 26.1201 | 1.08364 | ||||||||
\(582\) | −11.5316 | −0.478002 | ||||||||
\(583\) | 3.20981 | 0.132937 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0.345935 | 0.0143027 | ||||||||
\(586\) | 14.5058 | 0.599230 | ||||||||
\(587\) | −8.34988 | −0.344636 | −0.172318 | − | 0.985041i | \(-0.555126\pi\) | ||||
−0.172318 | + | 0.985041i | \(0.555126\pi\) | |||||||
\(588\) | −2.20256 | −0.0908322 | ||||||||
\(589\) | 23.0592 | 0.950138 | ||||||||
\(590\) | 2.01046 | 0.0827693 | ||||||||
\(591\) | 4.98414 | 0.205020 | ||||||||
\(592\) | −10.0765 | −0.414142 | ||||||||
\(593\) | 31.9432 | 1.31175 | 0.655875 | − | 0.754870i | \(-0.272300\pi\) | ||||
0.655875 | + | 0.754870i | \(0.272300\pi\) | |||||||
\(594\) | −5.34733 | −0.219403 | ||||||||
\(595\) | 5.11156 | 0.209553 | ||||||||
\(596\) | 9.40226 | 0.385132 | ||||||||
\(597\) | −20.6030 | −0.843224 | ||||||||
\(598\) | −0.508599 | −0.0207982 | ||||||||
\(599\) | −0.695079 | −0.0284001 | −0.0142001 | − | 0.999899i | \(-0.504520\pi\) | ||||
−0.0142001 | + | 0.999899i | \(0.504520\pi\) | |||||||
\(600\) | 1.13475 | 0.0463259 | ||||||||
\(601\) | −24.4761 | −0.998403 | −0.499201 | − | 0.866486i | \(-0.666373\pi\) | ||||
−0.499201 | + | 0.866486i | \(0.666373\pi\) | |||||||
\(602\) | 0.809208 | 0.0329809 | ||||||||
\(603\) | −18.8287 | −0.766766 | ||||||||
\(604\) | 10.4648 | 0.425807 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 12.6148 | 0.512440 | ||||||||
\(607\) | 2.61424 | 0.106109 | 0.0530543 | − | 0.998592i | \(-0.483104\pi\) | ||||
0.0530543 | + | 0.998592i | \(0.483104\pi\) | |||||||
\(608\) | 6.24810 | 0.253394 | ||||||||
\(609\) | −8.33078 | −0.337580 | ||||||||
\(610\) | −1.59340 | −0.0645150 | ||||||||
\(611\) | −0.404551 | −0.0163664 | ||||||||
\(612\) | −3.89147 | −0.157303 | ||||||||
\(613\) | −34.9165 | −1.41027 | −0.705133 | − | 0.709075i | \(-0.749113\pi\) | ||||
−0.705133 | + | 0.709075i | \(0.749113\pi\) | |||||||
\(614\) | −4.43968 | −0.179171 | ||||||||
\(615\) | −9.78031 | −0.394380 | ||||||||
\(616\) | −2.24922 | −0.0906236 | ||||||||
\(617\) | 13.0864 | 0.526837 | 0.263419 | − | 0.964682i | \(-0.415150\pi\) | ||||
0.263419 | + | 0.964682i | \(0.415150\pi\) | |||||||
\(618\) | 13.6712 | 0.549935 | ||||||||
\(619\) | 2.66239 | 0.107010 | 0.0535052 | − | 0.998568i | \(-0.482961\pi\) | ||||
0.0535052 | + | 0.998568i | \(0.482961\pi\) | |||||||
\(620\) | −3.69060 | −0.148218 | ||||||||
\(621\) | 13.4620 | 0.540212 | ||||||||
\(622\) | −17.4668 | −0.700357 | ||||||||
\(623\) | −22.1833 | −0.888755 | ||||||||
\(624\) | 0.229246 | 0.00917719 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.3946 | 0.735196 | ||||||||
\(627\) | 7.09001 | 0.283148 | ||||||||
\(628\) | 21.7044 | 0.866099 | ||||||||
\(629\) | −22.8998 | −0.913076 | ||||||||
\(630\) | −3.85144 | −0.153445 | ||||||||
\(631\) | 26.9788 | 1.07401 | 0.537005 | − | 0.843579i | \(-0.319556\pi\) | ||||
0.537005 | + | 0.843579i | \(0.319556\pi\) | |||||||
\(632\) | 12.7687 | 0.507911 | ||||||||
\(633\) | 15.0563 | 0.598434 | ||||||||
\(634\) | −18.0011 | −0.714915 | ||||||||
\(635\) | 0.831256 | 0.0329874 | ||||||||
\(636\) | 3.64233 | 0.144428 | ||||||||
\(637\) | −0.392132 | −0.0155368 | ||||||||
\(638\) | 3.26404 | 0.129224 | ||||||||
\(639\) | −7.65927 | −0.302996 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.91525 | 0.391629 | 0.195814 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195814 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(642\) | −10.6169 | −0.419016 | ||||||||
\(643\) | 15.6338 | 0.616535 | 0.308268 | − | 0.951300i | \(-0.400251\pi\) | ||||
0.308268 | + | 0.951300i | \(0.400251\pi\) | |||||||
\(644\) | 5.66245 | 0.223132 | ||||||||
\(645\) | 0.408252 | 0.0160749 | ||||||||
\(646\) | 14.1994 | 0.558667 | ||||||||
\(647\) | −11.9006 | −0.467859 | −0.233930 | − | 0.972254i | \(-0.575159\pi\) | ||||
−0.233930 | + | 0.972254i | \(0.575159\pi\) | |||||||
\(648\) | −0.930819 | −0.0365660 | ||||||||
\(649\) | −2.01046 | −0.0789175 | ||||||||
\(650\) | 0.202024 | 0.00792403 | ||||||||
\(651\) | −9.41950 | −0.369179 | ||||||||
\(652\) | −2.25705 | −0.0883930 | ||||||||
\(653\) | 8.13936 | 0.318518 | 0.159259 | − | 0.987237i | \(-0.449090\pi\) | ||||
0.159259 | + | 0.987237i | \(0.449090\pi\) | |||||||
\(654\) | 17.2945 | 0.676270 | ||||||||
\(655\) | −5.24272 | −0.204850 | ||||||||
\(656\) | 8.61893 | 0.336513 | ||||||||
\(657\) | −1.71235 | −0.0668051 | ||||||||
\(658\) | 4.50404 | 0.175586 | ||||||||
\(659\) | −23.4469 | −0.913362 | −0.456681 | − | 0.889631i | \(-0.650962\pi\) | ||||
−0.456681 | + | 0.889631i | \(0.650962\pi\) | |||||||
\(660\) | −1.13475 | −0.0441700 | ||||||||
\(661\) | −43.2799 | −1.68339 | −0.841697 | − | 0.539950i | \(-0.818443\pi\) | ||||
−0.841697 | + | 0.539950i | \(0.818443\pi\) | |||||||
\(662\) | −5.15501 | −0.200355 | ||||||||
\(663\) | 0.520983 | 0.0202333 | ||||||||
\(664\) | −11.6129 | −0.450670 | ||||||||
\(665\) | 14.0533 | 0.544965 | ||||||||
\(666\) | 17.2545 | 0.668599 | ||||||||
\(667\) | −8.21728 | −0.318174 | ||||||||
\(668\) | 3.12464 | 0.120896 | ||||||||
\(669\) | −12.2193 | −0.472427 | ||||||||
\(670\) | −10.9959 | −0.424807 | ||||||||
\(671\) | 1.59340 | 0.0615126 | ||||||||
\(672\) | −2.55229 | −0.0984569 | ||||||||
\(673\) | 20.4588 | 0.788628 | 0.394314 | − | 0.918976i | \(-0.370982\pi\) | ||||
0.394314 | + | 0.918976i | \(0.370982\pi\) | |||||||
\(674\) | 0.0479947 | 0.00184869 | ||||||||
\(675\) | −5.34733 | −0.205819 | ||||||||
\(676\) | −12.9592 | −0.498430 | ||||||||
\(677\) | 4.22663 | 0.162443 | 0.0812213 | − | 0.996696i | \(-0.474118\pi\) | ||||
0.0812213 | + | 0.996696i | \(0.474118\pi\) | |||||||
\(678\) | 3.99366 | 0.153376 | ||||||||
\(679\) | 22.8572 | 0.877179 | ||||||||
\(680\) | −2.27259 | −0.0871500 | ||||||||
\(681\) | −8.00370 | −0.306702 | ||||||||
\(682\) | 3.69060 | 0.141320 | ||||||||
\(683\) | −9.43617 | −0.361065 | −0.180532 | − | 0.983569i | \(-0.557782\pi\) | ||||
−0.180532 | + | 0.983569i | \(0.557782\pi\) | |||||||
\(684\) | −10.6989 | −0.409083 | ||||||||
\(685\) | 2.36028 | 0.0901815 | ||||||||
\(686\) | 20.1103 | 0.767815 | ||||||||
\(687\) | 4.20698 | 0.160506 | ||||||||
\(688\) | −0.359773 | −0.0137162 | ||||||||
\(689\) | 0.648459 | 0.0247043 | ||||||||
\(690\) | 2.85675 | 0.108755 | ||||||||
\(691\) | 18.3790 | 0.699171 | 0.349585 | − | 0.936904i | \(-0.386322\pi\) | ||||
0.349585 | + | 0.936904i | \(0.386322\pi\) | |||||||
\(692\) | 19.7226 | 0.749740 | ||||||||
\(693\) | 3.85144 | 0.146304 | ||||||||
\(694\) | −12.4765 | −0.473600 | ||||||||
\(695\) | −3.95726 | −0.150107 | ||||||||
\(696\) | 3.70386 | 0.140394 | ||||||||
\(697\) | 19.5873 | 0.741922 | ||||||||
\(698\) | −3.55815 | −0.134678 | ||||||||
\(699\) | 8.75333 | 0.331081 | ||||||||
\(700\) | −2.24922 | −0.0850125 | ||||||||
\(701\) | −13.6547 | −0.515731 | −0.257866 | − | 0.966181i | \(-0.583019\pi\) | ||||
−0.257866 | + | 0.966181i | \(0.583019\pi\) | |||||||
\(702\) | −1.08029 | −0.0407728 | ||||||||
\(703\) | −62.9591 | −2.37455 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 2.27232 | 0.0855807 | ||||||||
\(706\) | 4.93425 | 0.185703 | ||||||||
\(707\) | −25.0041 | −0.940376 | ||||||||
\(708\) | −2.28136 | −0.0857389 | ||||||||
\(709\) | −10.3750 | −0.389640 | −0.194820 | − | 0.980839i | \(-0.562412\pi\) | ||||
−0.194820 | + | 0.980839i | \(0.562412\pi\) | |||||||
\(710\) | −4.47296 | −0.167867 | ||||||||
\(711\) | −21.8644 | −0.819980 | ||||||||
\(712\) | 9.86267 | 0.369619 | ||||||||
\(713\) | −9.29116 | −0.347957 | ||||||||
\(714\) | −5.80033 | −0.217072 | ||||||||
\(715\) | −0.202024 | −0.00755527 | ||||||||
\(716\) | 16.1286 | 0.602755 | ||||||||
\(717\) | 29.8665 | 1.11539 | ||||||||
\(718\) | 4.03340 | 0.150525 | ||||||||
\(719\) | 32.2858 | 1.20406 | 0.602028 | − | 0.798475i | \(-0.294360\pi\) | ||||
0.602028 | + | 0.798475i | \(0.294360\pi\) | |||||||
\(720\) | 1.71235 | 0.0638155 | ||||||||
\(721\) | −27.0980 | −1.00918 | ||||||||
\(722\) | 20.0387 | 0.745763 | ||||||||
\(723\) | −10.8644 | −0.404053 | ||||||||
\(724\) | 0.309823 | 0.0115145 | ||||||||
\(725\) | 3.26404 | 0.121223 | ||||||||
\(726\) | 1.13475 | 0.0421144 | ||||||||
\(727\) | 12.0134 | 0.445553 | 0.222777 | − | 0.974870i | \(-0.428488\pi\) | ||||
0.222777 | + | 0.974870i | \(0.428488\pi\) | |||||||
\(728\) | −0.454396 | −0.0168410 | ||||||||
\(729\) | 19.7975 | 0.733240 | ||||||||
\(730\) | −1.00000 | −0.0370117 | ||||||||
\(731\) | −0.817618 | −0.0302407 | ||||||||
\(732\) | 1.80811 | 0.0668297 | ||||||||
\(733\) | −6.18587 | −0.228480 | −0.114240 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114240 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(734\) | −15.6153 | −0.576371 | ||||||||
\(735\) | 2.20256 | 0.0812428 | ||||||||
\(736\) | −2.51752 | −0.0927970 | ||||||||
\(737\) | 10.9959 | 0.405038 | ||||||||
\(738\) | −14.7586 | −0.543272 | ||||||||
\(739\) | 3.59211 | 0.132138 | 0.0660690 | − | 0.997815i | \(-0.478954\pi\) | ||||
0.0660690 | + | 0.997815i | \(0.478954\pi\) | |||||||
\(740\) | 10.0765 | 0.370420 | ||||||||
\(741\) | 1.43235 | 0.0526187 | ||||||||
\(742\) | −7.21957 | −0.265039 | ||||||||
\(743\) | −2.24031 | −0.0821890 | −0.0410945 | − | 0.999155i | \(-0.513084\pi\) | ||||
−0.0410945 | + | 0.999155i | \(0.513084\pi\) | |||||||
\(744\) | 4.18790 | 0.153536 | ||||||||
\(745\) | −9.40226 | −0.344472 | ||||||||
\(746\) | −5.60101 | −0.205068 | ||||||||
\(747\) | 19.8854 | 0.727569 | ||||||||
\(748\) | 2.27259 | 0.0830942 | ||||||||
\(749\) | 21.0441 | 0.768934 | ||||||||
\(750\) | −1.13475 | −0.0414351 | ||||||||
\(751\) | −7.59820 | −0.277262 | −0.138631 | − | 0.990344i | \(-0.544270\pi\) | ||||
−0.138631 | + | 0.990344i | \(0.544270\pi\) | |||||||
\(752\) | −2.00249 | −0.0730234 | ||||||||
\(753\) | −14.0400 | −0.511647 | ||||||||
\(754\) | 0.659413 | 0.0240144 | ||||||||
\(755\) | −10.4648 | −0.380854 | ||||||||
\(756\) | 12.0273 | 0.437429 | ||||||||
\(757\) | 16.7688 | 0.609473 | 0.304737 | − | 0.952437i | \(-0.401432\pi\) | ||||
0.304737 | + | 0.952437i | \(0.401432\pi\) | |||||||
\(758\) | −23.3380 | −0.847673 | ||||||||
\(759\) | −2.85675 | −0.103693 | ||||||||
\(760\) | −6.24810 | −0.226642 | ||||||||
\(761\) | −36.1062 | −1.30885 | −0.654425 | − | 0.756127i | \(-0.727089\pi\) | ||||
−0.654425 | + | 0.756127i | \(0.727089\pi\) | |||||||
\(762\) | −0.943266 | −0.0341709 | ||||||||
\(763\) | −34.2801 | −1.24102 | ||||||||
\(764\) | 21.0739 | 0.762426 | ||||||||
\(765\) | 3.89147 | 0.140696 | ||||||||
\(766\) | −17.4899 | −0.631935 | ||||||||
\(767\) | −0.406161 | −0.0146656 | ||||||||
\(768\) | 1.13475 | 0.0409467 | ||||||||
\(769\) | 52.3082 | 1.88628 | 0.943140 | − | 0.332395i | \(-0.107857\pi\) | ||||
0.943140 | + | 0.332395i | \(0.107857\pi\) | |||||||
\(770\) | 2.24922 | 0.0810562 | ||||||||
\(771\) | −20.2668 | −0.729890 | ||||||||
\(772\) | −5.84784 | −0.210468 | ||||||||
\(773\) | −14.1422 | −0.508659 | −0.254330 | − | 0.967118i | \(-0.581855\pi\) | ||||
−0.254330 | + | 0.967118i | \(0.581855\pi\) | |||||||
\(774\) | 0.616057 | 0.0221437 | ||||||||
\(775\) | 3.69060 | 0.132570 | ||||||||
\(776\) | −10.1623 | −0.364805 | ||||||||
\(777\) | 25.7182 | 0.922637 | ||||||||
\(778\) | 19.0646 | 0.683499 | ||||||||
\(779\) | 53.8519 | 1.92944 | ||||||||
\(780\) | −0.229246 | −0.00820833 | ||||||||
\(781\) | 4.47296 | 0.160055 | ||||||||
\(782\) | −5.72130 | −0.204593 | ||||||||
\(783\) | −17.4539 | −0.623750 | ||||||||
\(784\) | −1.94102 | −0.0693220 | ||||||||
\(785\) | −21.7044 | −0.774663 | ||||||||
\(786\) | 5.94916 | 0.212200 | ||||||||
\(787\) | 24.2345 | 0.863867 | 0.431933 | − | 0.901906i | \(-0.357832\pi\) | ||||
0.431933 | + | 0.901906i | \(0.357832\pi\) | |||||||
\(788\) | 4.39229 | 0.156469 | ||||||||
\(789\) | 3.70345 | 0.131846 | ||||||||
\(790\) | −12.7687 | −0.454289 | ||||||||
\(791\) | −7.91596 | −0.281459 | ||||||||
\(792\) | −1.71235 | −0.0608456 | ||||||||
\(793\) | 0.321905 | 0.0114312 | ||||||||
\(794\) | 23.9517 | 0.850014 | ||||||||
\(795\) | −3.64233 | −0.129180 | ||||||||
\(796\) | −18.1565 | −0.643538 | ||||||||
\(797\) | 2.00794 | 0.0711248 | 0.0355624 | − | 0.999367i | \(-0.488678\pi\) | ||||
0.0355624 | + | 0.999367i | \(0.488678\pi\) | |||||||
\(798\) | −15.9470 | −0.564517 | ||||||||
\(799\) | −4.55085 | −0.160998 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −16.8883 | −0.596719 | ||||||||
\(802\) | 1.28203 | 0.0452699 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 12.4775 | 0.440049 | ||||||||
\(805\) | −5.66245 | −0.199575 | ||||||||
\(806\) | 0.745589 | 0.0262623 | ||||||||
\(807\) | 0.355945 | 0.0125299 | ||||||||
\(808\) | 11.1168 | 0.391088 | ||||||||
\(809\) | −55.7732 | −1.96088 | −0.980441 | − | 0.196811i | \(-0.936941\pi\) | ||||
−0.980441 | + | 0.196811i | \(0.936941\pi\) | |||||||
\(810\) | 0.930819 | 0.0327056 | ||||||||
\(811\) | −12.3909 | −0.435103 | −0.217552 | − | 0.976049i | \(-0.569807\pi\) | ||||
−0.217552 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(812\) | −7.34153 | −0.257637 | ||||||||
\(813\) | −1.67267 | −0.0586631 | ||||||||
\(814\) | −10.0765 | −0.353182 | ||||||||
\(815\) | 2.25705 | 0.0790611 | ||||||||
\(816\) | 2.57882 | 0.0902767 | ||||||||
\(817\) | −2.24790 | −0.0786439 | ||||||||
\(818\) | −30.7455 | −1.07499 | ||||||||
\(819\) | 0.778084 | 0.0271885 | ||||||||
\(820\) | −8.61893 | −0.300986 | ||||||||
\(821\) | −12.9323 | −0.451340 | −0.225670 | − | 0.974204i | \(-0.572457\pi\) | ||||
−0.225670 | + | 0.974204i | \(0.572457\pi\) | |||||||
\(822\) | −2.67832 | −0.0934170 | ||||||||
\(823\) | 24.0588 | 0.838639 | 0.419319 | − | 0.907839i | \(-0.362269\pi\) | ||||
0.419319 | + | 0.907839i | \(0.362269\pi\) | |||||||
\(824\) | 12.0478 | 0.419703 | ||||||||
\(825\) | 1.13475 | 0.0395068 | ||||||||
\(826\) | 4.52196 | 0.157339 | ||||||||
\(827\) | −17.0786 | −0.593880 | −0.296940 | − | 0.954896i | \(-0.595966\pi\) | ||||
−0.296940 | + | 0.954896i | \(0.595966\pi\) | |||||||
\(828\) | 4.31087 | 0.149813 | ||||||||
\(829\) | −43.3214 | −1.50461 | −0.752307 | − | 0.658813i | \(-0.771059\pi\) | ||||
−0.752307 | + | 0.658813i | \(0.771059\pi\) | |||||||
\(830\) | 11.6129 | 0.403091 | ||||||||
\(831\) | 26.6324 | 0.923869 | ||||||||
\(832\) | 0.202024 | 0.00700392 | ||||||||
\(833\) | −4.41114 | −0.152837 | ||||||||
\(834\) | 4.49049 | 0.155493 | ||||||||
\(835\) | −3.12464 | −0.108133 | ||||||||
\(836\) | 6.24810 | 0.216095 | ||||||||
\(837\) | −19.7348 | −0.682136 | ||||||||
\(838\) | −26.6982 | −0.922273 | ||||||||
\(839\) | 25.5893 | 0.883439 | 0.441720 | − | 0.897153i | \(-0.354369\pi\) | ||||
0.441720 | + | 0.897153i | \(0.354369\pi\) | |||||||
\(840\) | 2.55229 | 0.0880625 | ||||||||
\(841\) | −18.3461 | −0.632623 | ||||||||
\(842\) | −13.4999 | −0.465238 | ||||||||
\(843\) | −16.8007 | −0.578646 | ||||||||
\(844\) | 13.2684 | 0.456718 | ||||||||
\(845\) | 12.9592 | 0.445810 | ||||||||
\(846\) | 3.42897 | 0.117890 | ||||||||
\(847\) | −2.24922 | −0.0772841 | ||||||||
\(848\) | 3.20981 | 0.110225 | ||||||||
\(849\) | 20.5890 | 0.706611 | ||||||||
\(850\) | 2.27259 | 0.0779493 | ||||||||
\(851\) | 25.3678 | 0.869599 | ||||||||
\(852\) | 5.07569 | 0.173890 | ||||||||
\(853\) | 24.7978 | 0.849060 | 0.424530 | − | 0.905414i | \(-0.360439\pi\) | ||||
0.424530 | + | 0.905414i | \(0.360439\pi\) | |||||||
\(854\) | −3.58391 | −0.122639 | ||||||||
\(855\) | 10.6989 | 0.365895 | ||||||||
\(856\) | −9.35618 | −0.319788 | ||||||||
\(857\) | −33.8755 | −1.15717 | −0.578583 | − | 0.815624i | \(-0.696394\pi\) | ||||
−0.578583 | + | 0.815624i | \(0.696394\pi\) | |||||||
\(858\) | 0.229246 | 0.00782633 | ||||||||
\(859\) | −19.8121 | −0.675980 | −0.337990 | − | 0.941150i | \(-0.609747\pi\) | ||||
−0.337990 | + | 0.941150i | \(0.609747\pi\) | |||||||
\(860\) | 0.359773 | 0.0122682 | ||||||||
\(861\) | −21.9980 | −0.749691 | ||||||||
\(862\) | 16.9683 | 0.577942 | ||||||||
\(863\) | 16.9471 | 0.576886 | 0.288443 | − | 0.957497i | \(-0.406862\pi\) | ||||
0.288443 | + | 0.957497i | \(0.406862\pi\) | |||||||
\(864\) | −5.34733 | −0.181920 | ||||||||
\(865\) | −19.7226 | −0.670588 | ||||||||
\(866\) | 14.5903 | 0.495798 | ||||||||
\(867\) | −13.4301 | −0.456110 | ||||||||
\(868\) | −8.30096 | −0.281753 | ||||||||
\(869\) | 12.7687 | 0.433148 | ||||||||
\(870\) | −3.70386 | −0.125572 | ||||||||
\(871\) | 2.22143 | 0.0752702 | ||||||||
\(872\) | 15.2409 | 0.516121 | ||||||||
\(873\) | 17.4014 | 0.588948 | ||||||||
\(874\) | −15.7297 | −0.532065 | ||||||||
\(875\) | 2.24922 | 0.0760375 | ||||||||
\(876\) | 1.13475 | 0.0383396 | ||||||||
\(877\) | 7.51955 | 0.253917 | 0.126959 | − | 0.991908i | \(-0.459478\pi\) | ||||
0.126959 | + | 0.991908i | \(0.459478\pi\) | |||||||
\(878\) | 12.9426 | 0.436792 | ||||||||
\(879\) | 16.4604 | 0.555197 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −9.79564 | −0.330023 | −0.165012 | − | 0.986292i | \(-0.552766\pi\) | ||||
−0.165012 | + | 0.986292i | \(0.552766\pi\) | |||||||
\(882\) | 3.32370 | 0.111915 | ||||||||
\(883\) | 21.2176 | 0.714029 | 0.357014 | − | 0.934099i | \(-0.383795\pi\) | ||||
0.357014 | + | 0.934099i | \(0.383795\pi\) | |||||||
\(884\) | 0.459118 | 0.0154418 | ||||||||
\(885\) | 2.28136 | 0.0766872 | ||||||||
\(886\) | −30.1339 | −1.01237 | ||||||||
\(887\) | 21.7273 | 0.729530 | 0.364765 | − | 0.931100i | \(-0.381149\pi\) | ||||
0.364765 | + | 0.931100i | \(0.381149\pi\) | |||||||
\(888\) | −11.4343 | −0.383710 | ||||||||
\(889\) | 1.86968 | 0.0627070 | ||||||||
\(890\) | −9.86267 | −0.330597 | ||||||||
\(891\) | −0.930819 | −0.0311836 | ||||||||
\(892\) | −10.7683 | −0.360551 | ||||||||
\(893\) | −12.5118 | −0.418690 | ||||||||
\(894\) | 10.6692 | 0.356831 | ||||||||
\(895\) | −16.1286 | −0.539121 | ||||||||
\(896\) | −2.24922 | −0.0751411 | ||||||||
\(897\) | −0.577132 | −0.0192699 | ||||||||
\(898\) | −14.5155 | −0.484388 | ||||||||
\(899\) | 12.0462 | 0.401765 | ||||||||
\(900\) | −1.71235 | −0.0570783 | ||||||||
\(901\) | 7.29460 | 0.243018 | ||||||||
\(902\) | 8.61893 | 0.286979 | ||||||||
\(903\) | 0.918247 | 0.0305573 | ||||||||
\(904\) | 3.51943 | 0.117054 | ||||||||
\(905\) | −0.309823 | −0.0102989 | ||||||||
\(906\) | 11.8749 | 0.394518 | ||||||||
\(907\) | 26.2924 | 0.873026 | 0.436513 | − | 0.899698i | \(-0.356213\pi\) | ||||
0.436513 | + | 0.899698i | \(0.356213\pi\) | |||||||
\(908\) | −7.05329 | −0.234072 | ||||||||
\(909\) | −19.0358 | −0.631379 | ||||||||
\(910\) | 0.454396 | 0.0150631 | ||||||||
\(911\) | −0.148527 | −0.00492093 | −0.00246047 | − | 0.999997i | \(-0.500783\pi\) | ||||
−0.00246047 | + | 0.999997i | \(0.500783\pi\) | |||||||
\(912\) | 7.09001 | 0.234774 | ||||||||
\(913\) | −11.6129 | −0.384332 | ||||||||
\(914\) | −37.5708 | −1.24273 | ||||||||
\(915\) | −1.80811 | −0.0597743 | ||||||||
\(916\) | 3.70742 | 0.122496 | ||||||||
\(917\) | −11.7920 | −0.389407 | ||||||||
\(918\) | −12.1523 | −0.401086 | ||||||||
\(919\) | 27.3087 | 0.900831 | 0.450416 | − | 0.892819i | \(-0.351276\pi\) | ||||
0.450416 | + | 0.892819i | \(0.351276\pi\) | |||||||
\(920\) | 2.51752 | 0.0830002 | ||||||||
\(921\) | −5.03792 | −0.166005 | ||||||||
\(922\) | −33.7192 | −1.11048 | ||||||||
\(923\) | 0.903646 | 0.0297439 | ||||||||
\(924\) | −2.55229 | −0.0839643 | ||||||||
\(925\) | −10.0765 | −0.331314 | ||||||||
\(926\) | 34.3995 | 1.13044 | ||||||||
\(927\) | −20.6300 | −0.677577 | ||||||||
\(928\) | 3.26404 | 0.107147 | ||||||||
\(929\) | 43.6002 | 1.43048 | 0.715238 | − | 0.698881i | \(-0.246318\pi\) | ||||
0.715238 | + | 0.698881i | \(0.246318\pi\) | |||||||
\(930\) | −4.18790 | −0.137327 | ||||||||
\(931\) | −12.1277 | −0.397468 | ||||||||
\(932\) | 7.71390 | 0.252677 | ||||||||
\(933\) | −19.8205 | −0.648893 | ||||||||
\(934\) | −22.3369 | −0.730885 | ||||||||
\(935\) | −2.27259 | −0.0743217 | ||||||||
\(936\) | −0.345935 | −0.0113072 | ||||||||
\(937\) | −14.2353 | −0.465047 | −0.232523 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232523 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(938\) | −24.7321 | −0.807532 | ||||||||
\(939\) | 20.8732 | 0.681172 | ||||||||
\(940\) | 2.00249 | 0.0653141 | ||||||||
\(941\) | −23.6631 | −0.771395 | −0.385697 | − | 0.922625i | \(-0.626039\pi\) | ||||
−0.385697 | + | 0.922625i | \(0.626039\pi\) | |||||||
\(942\) | 24.6290 | 0.802456 | ||||||||
\(943\) | −21.6983 | −0.706595 | ||||||||
\(944\) | −2.01046 | −0.0654349 | ||||||||
\(945\) | −12.0273 | −0.391248 | ||||||||
\(946\) | −0.359773 | −0.0116972 | ||||||||
\(947\) | 28.5512 | 0.927789 | 0.463894 | − | 0.885891i | \(-0.346452\pi\) | ||||
0.463894 | + | 0.885891i | \(0.346452\pi\) | |||||||
\(948\) | 14.4892 | 0.470588 | ||||||||
\(949\) | 0.202024 | 0.00655797 | ||||||||
\(950\) | 6.24810 | 0.202715 | ||||||||
\(951\) | −20.4267 | −0.662381 | ||||||||
\(952\) | −5.11156 | −0.165667 | ||||||||
\(953\) | 42.5823 | 1.37937 | 0.689687 | − | 0.724107i | \(-0.257748\pi\) | ||||
0.689687 | + | 0.724107i | \(0.257748\pi\) | |||||||
\(954\) | −5.49632 | −0.177950 | ||||||||
\(955\) | −21.0739 | −0.681935 | ||||||||
\(956\) | 26.3200 | 0.851249 | ||||||||
\(957\) | 3.70386 | 0.119729 | ||||||||
\(958\) | 3.41665 | 0.110387 | ||||||||
\(959\) | 5.30877 | 0.171429 | ||||||||
\(960\) | −1.13475 | −0.0366238 | ||||||||
\(961\) | −17.3795 | −0.560628 | ||||||||
\(962\) | −2.03570 | −0.0656335 | ||||||||
\(963\) | 16.0210 | 0.516271 | ||||||||
\(964\) | −9.57433 | −0.308368 | ||||||||
\(965\) | 5.84784 | 0.188249 | ||||||||
\(966\) | 6.42545 | 0.206736 | ||||||||
\(967\) | 34.8942 | 1.12212 | 0.561062 | − | 0.827774i | \(-0.310393\pi\) | ||||
0.561062 | + | 0.827774i | \(0.310393\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 16.1127 | 0.517615 | ||||||||
\(970\) | 10.1623 | 0.326292 | ||||||||
\(971\) | −3.98812 | −0.127985 | −0.0639924 | − | 0.997950i | \(-0.520383\pi\) | ||||
−0.0639924 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(972\) | 14.9857 | 0.480668 | ||||||||
\(973\) | −8.90074 | −0.285345 | ||||||||
\(974\) | −23.2454 | −0.744831 | ||||||||
\(975\) | 0.229246 | 0.00734175 | ||||||||
\(976\) | 1.59340 | 0.0510036 | ||||||||
\(977\) | −25.6626 | −0.821019 | −0.410510 | − | 0.911856i | \(-0.634649\pi\) | ||||
−0.410510 | + | 0.911856i | \(0.634649\pi\) | |||||||
\(978\) | −2.56118 | −0.0818976 | ||||||||
\(979\) | 9.86267 | 0.315212 | ||||||||
\(980\) | 1.94102 | 0.0620035 | ||||||||
\(981\) | −26.0977 | −0.833235 | ||||||||
\(982\) | −35.8534 | −1.14413 | ||||||||
\(983\) | 0.124549 | 0.00397248 | 0.00198624 | − | 0.999998i | \(-0.499368\pi\) | ||||
0.00198624 | + | 0.999998i | \(0.499368\pi\) | |||||||
\(984\) | 9.78031 | 0.311785 | ||||||||
\(985\) | −4.39229 | −0.139950 | ||||||||
\(986\) | 7.41783 | 0.236232 | ||||||||
\(987\) | 5.11095 | 0.162683 | ||||||||
\(988\) | 1.26226 | 0.0401580 | ||||||||
\(989\) | 0.905736 | 0.0288007 | ||||||||
\(990\) | 1.71235 | 0.0544220 | ||||||||
\(991\) | −41.6751 | −1.32385 | −0.661926 | − | 0.749569i | \(-0.730261\pi\) | ||||
−0.661926 | + | 0.749569i | \(0.730261\pi\) | |||||||
\(992\) | 3.69060 | 0.117177 | ||||||||
\(993\) | −5.84963 | −0.185632 | ||||||||
\(994\) | −10.0607 | −0.319105 | ||||||||
\(995\) | 18.1565 | 0.575598 | ||||||||
\(996\) | −13.1778 | −0.417553 | ||||||||
\(997\) | 9.64175 | 0.305357 | 0.152679 | − | 0.988276i | \(-0.451210\pi\) | ||||
0.152679 | + | 0.988276i | \(0.451210\pi\) | |||||||
\(998\) | 17.9926 | 0.569546 | ||||||||
\(999\) | 53.8824 | 1.70476 |
(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 | 8030.2.a.bd.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.bd.1.9 | ✓ | 14 | 1.1 | even | 1 | trivial |