Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(1,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, 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("429.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.571993 | −0.404460 | −0.202230 | − | 0.979338i | \(-0.564819\pi\) | ||||
−0.202230 | + | 0.979338i | \(0.564819\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.67282 | −0.836412 | ||||||||
\(5\) | −4.24482 | −1.89834 | −0.949170 | − | 0.314764i | \(-0.898075\pi\) | ||||
−0.949170 | + | 0.314764i | \(0.898075\pi\) | |||||||
\(6\) | 0.571993 | 0.233515 | ||||||||
\(7\) | −2.67282 | −1.01023 | −0.505116 | − | 0.863051i | \(-0.668550\pi\) | ||||
−0.505116 | + | 0.863051i | \(0.668550\pi\) | |||||||
\(8\) | 2.10083 | 0.742756 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.42801 | 0.767803 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.67282 | 0.482903 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.52884 | 0.408599 | ||||||||
\(15\) | 4.24482 | 1.09601 | ||||||||
\(16\) | 2.14399 | 0.535997 | ||||||||
\(17\) | −0.428007 | −0.103807 | −0.0519034 | − | 0.998652i | \(-0.516529\pi\) | ||||
−0.0519034 | + | 0.998652i | \(0.516529\pi\) | |||||||
\(18\) | −0.571993 | −0.134820 | ||||||||
\(19\) | 6.67282 | 1.53085 | 0.765425 | − | 0.643525i | \(-0.222529\pi\) | ||||
0.765425 | + | 0.643525i | \(0.222529\pi\) | |||||||
\(20\) | 7.10083 | 1.58779 | ||||||||
\(21\) | 2.67282 | 0.583258 | ||||||||
\(22\) | −0.571993 | −0.121949 | ||||||||
\(23\) | −7.81681 | −1.62992 | −0.814959 | − | 0.579519i | \(-0.803240\pi\) | ||||
−0.814959 | + | 0.579519i | \(0.803240\pi\) | |||||||
\(24\) | −2.10083 | −0.428830 | ||||||||
\(25\) | 13.0185 | 2.60369 | ||||||||
\(26\) | 0.571993 | 0.112177 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.47116 | 0.844970 | ||||||||
\(29\) | −2.91764 | −0.541792 | −0.270896 | − | 0.962609i | \(-0.587320\pi\) | ||||
−0.270896 | + | 0.962609i | \(0.587320\pi\) | |||||||
\(30\) | −2.42801 | −0.443291 | ||||||||
\(31\) | 1.75518 | 0.315240 | 0.157620 | − | 0.987500i | \(-0.449618\pi\) | ||||
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(32\) | −5.42801 | −0.959545 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.244817 | 0.0419858 | ||||||||
\(35\) | 11.3456 | 1.91776 | ||||||||
\(36\) | −1.67282 | −0.278804 | ||||||||
\(37\) | 7.63362 | 1.25496 | 0.627480 | − | 0.778633i | \(-0.284087\pi\) | ||||
0.627480 | + | 0.778633i | \(0.284087\pi\) | |||||||
\(38\) | −3.81681 | −0.619168 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −8.91764 | −1.41000 | ||||||||
\(41\) | −2.38485 | −0.372451 | −0.186226 | − | 0.982507i | \(-0.559626\pi\) | ||||
−0.186226 | + | 0.982507i | \(0.559626\pi\) | |||||||
\(42\) | −1.52884 | −0.235905 | ||||||||
\(43\) | −11.7737 | −1.79547 | −0.897733 | − | 0.440541i | \(-0.854787\pi\) | ||||
−0.897733 | + | 0.440541i | \(0.854787\pi\) | |||||||
\(44\) | −1.67282 | −0.252188 | ||||||||
\(45\) | −4.24482 | −0.632780 | ||||||||
\(46\) | 4.47116 | 0.659237 | ||||||||
\(47\) | 6.48963 | 0.946610 | 0.473305 | − | 0.880899i | \(-0.343061\pi\) | ||||
0.473305 | + | 0.880899i | \(0.343061\pi\) | |||||||
\(48\) | −2.14399 | −0.309458 | ||||||||
\(49\) | 0.143987 | 0.0205695 | ||||||||
\(50\) | −7.44648 | −1.05309 | ||||||||
\(51\) | 0.428007 | 0.0599329 | ||||||||
\(52\) | 1.67282 | 0.231979 | ||||||||
\(53\) | −2.85601 | −0.392304 | −0.196152 | − | 0.980574i | \(-0.562845\pi\) | ||||
−0.196152 | + | 0.980574i | \(0.562845\pi\) | |||||||
\(54\) | 0.571993 | 0.0778384 | ||||||||
\(55\) | −4.24482 | −0.572371 | ||||||||
\(56\) | −5.61515 | −0.750356 | ||||||||
\(57\) | −6.67282 | −0.883837 | ||||||||
\(58\) | 1.66887 | 0.219133 | ||||||||
\(59\) | 12.4896 | 1.62601 | 0.813006 | − | 0.582255i | \(-0.197830\pi\) | ||||
0.813006 | + | 0.582255i | \(0.197830\pi\) | |||||||
\(60\) | −7.10083 | −0.916713 | ||||||||
\(61\) | 3.14399 | 0.402546 | 0.201273 | − | 0.979535i | \(-0.435492\pi\) | ||||
0.201273 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(62\) | −1.00395 | −0.127502 | ||||||||
\(63\) | −2.67282 | −0.336744 | ||||||||
\(64\) | −1.18319 | −0.147899 | ||||||||
\(65\) | 4.24482 | 0.526505 | ||||||||
\(66\) | 0.571993 | 0.0704075 | ||||||||
\(67\) | 13.3888 | 1.63570 | 0.817851 | − | 0.575430i | \(-0.195165\pi\) | ||||
0.817851 | + | 0.575430i | \(0.195165\pi\) | |||||||
\(68\) | 0.715980 | 0.0868253 | ||||||||
\(69\) | 7.81681 | 0.941033 | ||||||||
\(70\) | −6.48963 | −0.775660 | ||||||||
\(71\) | −7.34565 | −0.871768 | −0.435884 | − | 0.900003i | \(-0.643564\pi\) | ||||
−0.435884 | + | 0.900003i | \(0.643564\pi\) | |||||||
\(72\) | 2.10083 | 0.247585 | ||||||||
\(73\) | 11.7305 | 1.37295 | 0.686475 | − | 0.727153i | \(-0.259157\pi\) | ||||
0.686475 | + | 0.727153i | \(0.259157\pi\) | |||||||
\(74\) | −4.36638 | −0.507581 | ||||||||
\(75\) | −13.0185 | −1.50324 | ||||||||
\(76\) | −11.1625 | −1.28042 | ||||||||
\(77\) | −2.67282 | −0.304597 | ||||||||
\(78\) | −0.571993 | −0.0647655 | ||||||||
\(79\) | 6.42801 | 0.723207 | 0.361604 | − | 0.932332i | \(-0.382229\pi\) | ||||
0.361604 | + | 0.932332i | \(0.382229\pi\) | |||||||
\(80\) | −9.10083 | −1.01750 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.36412 | 0.150642 | ||||||||
\(83\) | 1.79834 | 0.197393 | 0.0986967 | − | 0.995118i | \(-0.468533\pi\) | ||||
0.0986967 | + | 0.995118i | \(0.468533\pi\) | |||||||
\(84\) | −4.47116 | −0.487844 | ||||||||
\(85\) | 1.81681 | 0.197061 | ||||||||
\(86\) | 6.73445 | 0.726195 | ||||||||
\(87\) | 2.91764 | 0.312804 | ||||||||
\(88\) | 2.10083 | 0.223949 | ||||||||
\(89\) | 3.59046 | 0.380588 | 0.190294 | − | 0.981727i | \(-0.439056\pi\) | ||||
0.190294 | + | 0.981727i | \(0.439056\pi\) | |||||||
\(90\) | 2.42801 | 0.255934 | ||||||||
\(91\) | 2.67282 | 0.280188 | ||||||||
\(92\) | 13.0761 | 1.36328 | ||||||||
\(93\) | −1.75518 | −0.182004 | ||||||||
\(94\) | −3.71203 | −0.382866 | ||||||||
\(95\) | −28.3249 | −2.90607 | ||||||||
\(96\) | 5.42801 | 0.553994 | ||||||||
\(97\) | −11.6336 | −1.18122 | −0.590608 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590608 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(98\) | −0.0823593 | −0.00831955 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −21.7776 | −2.17776 | ||||||||
\(101\) | 7.48568 | 0.744853 | 0.372427 | − | 0.928062i | \(-0.378526\pi\) | ||||
0.372427 | + | 0.928062i | \(0.378526\pi\) | |||||||
\(102\) | −0.244817 | −0.0242405 | ||||||||
\(103\) | 1.71203 | 0.168691 | 0.0843455 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843455 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(104\) | −2.10083 | −0.206003 | ||||||||
\(105\) | −11.3456 | −1.10722 | ||||||||
\(106\) | 1.63362 | 0.158671 | ||||||||
\(107\) | 4.48963 | 0.434029 | 0.217015 | − | 0.976168i | \(-0.430368\pi\) | ||||
0.217015 | + | 0.976168i | \(0.430368\pi\) | |||||||
\(108\) | 1.67282 | 0.160968 | ||||||||
\(109\) | −10.0185 | −0.959595 | −0.479798 | − | 0.877379i | \(-0.659290\pi\) | ||||
−0.479798 | + | 0.877379i | \(0.659290\pi\) | |||||||
\(110\) | 2.42801 | 0.231501 | ||||||||
\(111\) | −7.63362 | −0.724551 | ||||||||
\(112\) | −5.73050 | −0.541481 | ||||||||
\(113\) | −10.4896 | −0.986782 | −0.493391 | − | 0.869808i | \(-0.664243\pi\) | ||||
−0.493391 | + | 0.869808i | \(0.664243\pi\) | |||||||
\(114\) | 3.81681 | 0.357477 | ||||||||
\(115\) | 33.1809 | 3.09414 | ||||||||
\(116\) | 4.88070 | 0.453161 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −7.14399 | −0.657657 | ||||||||
\(119\) | 1.14399 | 0.104869 | ||||||||
\(120\) | 8.91764 | 0.814065 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.79834 | −0.162814 | ||||||||
\(123\) | 2.38485 | 0.215035 | ||||||||
\(124\) | −2.93611 | −0.263671 | ||||||||
\(125\) | −34.0369 | −3.04436 | ||||||||
\(126\) | 1.52884 | 0.136200 | ||||||||
\(127\) | 10.6297 | 0.943230 | 0.471615 | − | 0.881804i | \(-0.343671\pi\) | ||||
0.471615 | + | 0.881804i | \(0.343671\pi\) | |||||||
\(128\) | 11.5328 | 1.01936 | ||||||||
\(129\) | 11.7737 | 1.03661 | ||||||||
\(130\) | −2.42801 | −0.212950 | ||||||||
\(131\) | 19.6336 | 1.71540 | 0.857699 | − | 0.514153i | \(-0.171894\pi\) | ||||
0.857699 | + | 0.514153i | \(0.171894\pi\) | |||||||
\(132\) | 1.67282 | 0.145601 | ||||||||
\(133\) | −17.8353 | −1.54652 | ||||||||
\(134\) | −7.65831 | −0.661577 | ||||||||
\(135\) | 4.24482 | 0.365336 | ||||||||
\(136\) | −0.899170 | −0.0771032 | ||||||||
\(137\) | −8.81286 | −0.752933 | −0.376467 | − | 0.926430i | \(-0.622861\pi\) | ||||
−0.376467 | + | 0.926430i | \(0.622861\pi\) | |||||||
\(138\) | −4.47116 | −0.380611 | ||||||||
\(139\) | −9.40727 | −0.797915 | −0.398957 | − | 0.916970i | \(-0.630628\pi\) | ||||
−0.398957 | + | 0.916970i | \(0.630628\pi\) | |||||||
\(140\) | −18.9793 | −1.60404 | ||||||||
\(141\) | −6.48963 | −0.546526 | ||||||||
\(142\) | 4.20166 | 0.352596 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 2.14399 | 0.178666 | ||||||||
\(145\) | 12.3849 | 1.02851 | ||||||||
\(146\) | −6.70977 | −0.555304 | ||||||||
\(147\) | −0.143987 | −0.0118758 | ||||||||
\(148\) | −12.7697 | −1.04966 | ||||||||
\(149\) | −4.67282 | −0.382813 | −0.191406 | − | 0.981511i | \(-0.561305\pi\) | ||||
−0.191406 | + | 0.981511i | \(0.561305\pi\) | |||||||
\(150\) | 7.44648 | 0.608002 | ||||||||
\(151\) | −5.73050 | −0.466341 | −0.233171 | − | 0.972436i | \(-0.574910\pi\) | ||||
−0.233171 | + | 0.972436i | \(0.574910\pi\) | |||||||
\(152\) | 14.0185 | 1.13705 | ||||||||
\(153\) | −0.428007 | −0.0346023 | ||||||||
\(154\) | 1.52884 | 0.123197 | ||||||||
\(155\) | −7.45043 | −0.598433 | ||||||||
\(156\) | −1.67282 | −0.133933 | ||||||||
\(157\) | 8.38485 | 0.669184 | 0.334592 | − | 0.942363i | \(-0.391402\pi\) | ||||
0.334592 | + | 0.942363i | \(0.391402\pi\) | |||||||
\(158\) | −3.67678 | −0.292509 | ||||||||
\(159\) | 2.85601 | 0.226497 | ||||||||
\(160\) | 23.0409 | 1.82154 | ||||||||
\(161\) | 20.8930 | 1.64660 | ||||||||
\(162\) | −0.571993 | −0.0449400 | ||||||||
\(163\) | −4.82076 | −0.377591 | −0.188796 | − | 0.982016i | \(-0.560458\pi\) | ||||
−0.188796 | + | 0.982016i | \(0.560458\pi\) | |||||||
\(164\) | 3.98943 | 0.311523 | ||||||||
\(165\) | 4.24482 | 0.330459 | ||||||||
\(166\) | −1.02864 | −0.0798378 | ||||||||
\(167\) | 19.6336 | 1.51930 | 0.759648 | − | 0.650335i | \(-0.225371\pi\) | ||||
0.759648 | + | 0.650335i | \(0.225371\pi\) | |||||||
\(168\) | 5.61515 | 0.433218 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.03920 | −0.0797032 | ||||||||
\(171\) | 6.67282 | 0.510284 | ||||||||
\(172\) | 19.6952 | 1.50175 | ||||||||
\(173\) | 4.42801 | 0.336655 | 0.168328 | − | 0.985731i | \(-0.446163\pi\) | ||||
0.168328 | + | 0.985731i | \(0.446163\pi\) | |||||||
\(174\) | −1.66887 | −0.126517 | ||||||||
\(175\) | −34.7961 | −2.63034 | ||||||||
\(176\) | 2.14399 | 0.161609 | ||||||||
\(177\) | −12.4896 | −0.938778 | ||||||||
\(178\) | −2.05372 | −0.153933 | ||||||||
\(179\) | 13.2488 | 0.990260 | 0.495130 | − | 0.868819i | \(-0.335121\pi\) | ||||
0.495130 | + | 0.868819i | \(0.335121\pi\) | |||||||
\(180\) | 7.10083 | 0.529265 | ||||||||
\(181\) | 11.4425 | 0.850516 | 0.425258 | − | 0.905072i | \(-0.360183\pi\) | ||||
0.425258 | + | 0.905072i | \(0.360183\pi\) | |||||||
\(182\) | −1.52884 | −0.113325 | ||||||||
\(183\) | −3.14399 | −0.232410 | ||||||||
\(184\) | −16.4218 | −1.21063 | ||||||||
\(185\) | −32.4033 | −2.38234 | ||||||||
\(186\) | 1.00395 | 0.0736134 | ||||||||
\(187\) | −0.428007 | −0.0312990 | ||||||||
\(188\) | −10.8560 | −0.791756 | ||||||||
\(189\) | 2.67282 | 0.194419 | ||||||||
\(190\) | 16.2017 | 1.17539 | ||||||||
\(191\) | 0.489634 | 0.0354287 | 0.0177143 | − | 0.999843i | \(-0.494361\pi\) | ||||
0.0177143 | + | 0.999843i | \(0.494361\pi\) | |||||||
\(192\) | 1.18319 | 0.0853894 | ||||||||
\(193\) | −1.03920 | −0.0748035 | −0.0374017 | − | 0.999300i | \(-0.511908\pi\) | ||||
−0.0374017 | + | 0.999300i | \(0.511908\pi\) | |||||||
\(194\) | 6.65435 | 0.477755 | ||||||||
\(195\) | −4.24482 | −0.303978 | ||||||||
\(196\) | −0.240864 | −0.0172046 | ||||||||
\(197\) | 9.16246 | 0.652798 | 0.326399 | − | 0.945232i | \(-0.394165\pi\) | ||||
0.326399 | + | 0.945232i | \(0.394165\pi\) | |||||||
\(198\) | −0.571993 | −0.0406498 | ||||||||
\(199\) | −8.40332 | −0.595696 | −0.297848 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297848 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(200\) | 27.3496 | 1.93391 | ||||||||
\(201\) | −13.3888 | −0.944373 | ||||||||
\(202\) | −4.28176 | −0.301264 | ||||||||
\(203\) | 7.79834 | 0.547336 | ||||||||
\(204\) | −0.715980 | −0.0501286 | ||||||||
\(205\) | 10.1233 | 0.707039 | ||||||||
\(206\) | −0.979268 | −0.0682288 | ||||||||
\(207\) | −7.81681 | −0.543306 | ||||||||
\(208\) | −2.14399 | −0.148659 | ||||||||
\(209\) | 6.67282 | 0.461569 | ||||||||
\(210\) | 6.48963 | 0.447827 | ||||||||
\(211\) | 14.4649 | 0.995808 | 0.497904 | − | 0.867232i | \(-0.334103\pi\) | ||||
0.497904 | + | 0.867232i | \(0.334103\pi\) | |||||||
\(212\) | 4.77761 | 0.328127 | ||||||||
\(213\) | 7.34565 | 0.503315 | ||||||||
\(214\) | −2.56804 | −0.175548 | ||||||||
\(215\) | 49.9770 | 3.40840 | ||||||||
\(216\) | −2.10083 | −0.142943 | ||||||||
\(217\) | −4.69129 | −0.318466 | ||||||||
\(218\) | 5.73050 | 0.388118 | ||||||||
\(219\) | −11.7305 | −0.792674 | ||||||||
\(220\) | 7.10083 | 0.478738 | ||||||||
\(221\) | 0.428007 | 0.0287908 | ||||||||
\(222\) | 4.36638 | 0.293052 | ||||||||
\(223\) | −2.73445 | −0.183112 | −0.0915562 | − | 0.995800i | \(-0.529184\pi\) | ||||
−0.0915562 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(224\) | 14.5081 | 0.969364 | ||||||||
\(225\) | 13.0185 | 0.867898 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 18.7961 | 1.24754 | 0.623770 | − | 0.781608i | \(-0.285600\pi\) | ||||
0.623770 | + | 0.781608i | \(0.285600\pi\) | |||||||
\(228\) | 11.1625 | 0.739252 | ||||||||
\(229\) | 4.48963 | 0.296683 | 0.148342 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148342 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(230\) | −18.9793 | −1.25146 | ||||||||
\(231\) | 2.67282 | 0.175859 | ||||||||
\(232\) | −6.12947 | −0.402419 | ||||||||
\(233\) | −11.0040 | −0.720893 | −0.360446 | − | 0.932780i | \(-0.617376\pi\) | ||||
−0.360446 | + | 0.932780i | \(0.617376\pi\) | |||||||
\(234\) | 0.571993 | 0.0373924 | ||||||||
\(235\) | −27.5473 | −1.79699 | ||||||||
\(236\) | −20.8930 | −1.36002 | ||||||||
\(237\) | −6.42801 | −0.417544 | ||||||||
\(238\) | −0.654353 | −0.0424154 | ||||||||
\(239\) | 25.2778 | 1.63509 | 0.817543 | − | 0.575868i | \(-0.195336\pi\) | ||||
0.817543 | + | 0.575868i | \(0.195336\pi\) | |||||||
\(240\) | 9.10083 | 0.587456 | ||||||||
\(241\) | 15.2593 | 0.982940 | 0.491470 | − | 0.870894i | \(-0.336460\pi\) | ||||
0.491470 | + | 0.870894i | \(0.336460\pi\) | |||||||
\(242\) | −0.571993 | −0.0367691 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.25934 | −0.336694 | ||||||||
\(245\) | −0.611196 | −0.0390479 | ||||||||
\(246\) | −1.36412 | −0.0869730 | ||||||||
\(247\) | −6.67282 | −0.424582 | ||||||||
\(248\) | 3.68734 | 0.234146 | ||||||||
\(249\) | −1.79834 | −0.113965 | ||||||||
\(250\) | 19.4689 | 1.23132 | ||||||||
\(251\) | 7.91369 | 0.499508 | 0.249754 | − | 0.968309i | \(-0.419650\pi\) | ||||
0.249754 | + | 0.968309i | \(0.419650\pi\) | |||||||
\(252\) | 4.47116 | 0.281657 | ||||||||
\(253\) | −7.81681 | −0.491439 | ||||||||
\(254\) | −6.08010 | −0.381499 | ||||||||
\(255\) | −1.81681 | −0.113773 | ||||||||
\(256\) | −4.23030 | −0.264394 | ||||||||
\(257\) | −15.3456 | −0.957235 | −0.478618 | − | 0.878023i | \(-0.658862\pi\) | ||||
−0.478618 | + | 0.878023i | \(0.658862\pi\) | |||||||
\(258\) | −6.73445 | −0.419269 | ||||||||
\(259\) | −20.4033 | −1.26780 | ||||||||
\(260\) | −7.10083 | −0.440375 | ||||||||
\(261\) | −2.91764 | −0.180597 | ||||||||
\(262\) | −11.2303 | −0.693810 | ||||||||
\(263\) | −26.7776 | −1.65118 | −0.825589 | − | 0.564272i | \(-0.809157\pi\) | ||||
−0.825589 | + | 0.564272i | \(0.809157\pi\) | |||||||
\(264\) | −2.10083 | −0.129297 | ||||||||
\(265\) | 12.1233 | 0.744726 | ||||||||
\(266\) | 10.2017 | 0.625504 | ||||||||
\(267\) | −3.59046 | −0.219733 | ||||||||
\(268\) | −22.3971 | −1.36812 | ||||||||
\(269\) | 6.85601 | 0.418019 | 0.209009 | − | 0.977914i | \(-0.432976\pi\) | ||||
0.209009 | + | 0.977914i | \(0.432976\pi\) | |||||||
\(270\) | −2.42801 | −0.147764 | ||||||||
\(271\) | −18.1832 | −1.10455 | −0.552275 | − | 0.833662i | \(-0.686240\pi\) | ||||
−0.552275 | + | 0.833662i | \(0.686240\pi\) | |||||||
\(272\) | −0.917641 | −0.0556401 | ||||||||
\(273\) | −2.67282 | −0.161767 | ||||||||
\(274\) | 5.04090 | 0.304532 | ||||||||
\(275\) | 13.0185 | 0.785043 | ||||||||
\(276\) | −13.0761 | −0.787091 | ||||||||
\(277\) | −23.7490 | −1.42694 | −0.713469 | − | 0.700687i | \(-0.752877\pi\) | ||||
−0.713469 | + | 0.700687i | \(0.752877\pi\) | |||||||
\(278\) | 5.38090 | 0.322725 | ||||||||
\(279\) | 1.75518 | 0.105080 | ||||||||
\(280\) | 23.8353 | 1.42443 | ||||||||
\(281\) | 23.6442 | 1.41049 | 0.705247 | − | 0.708962i | \(-0.250836\pi\) | ||||
0.705247 | + | 0.708962i | \(0.250836\pi\) | |||||||
\(282\) | 3.71203 | 0.221048 | ||||||||
\(283\) | 28.0616 | 1.66809 | 0.834045 | − | 0.551696i | \(-0.186019\pi\) | ||||
0.834045 | + | 0.551696i | \(0.186019\pi\) | |||||||
\(284\) | 12.2880 | 0.729157 | ||||||||
\(285\) | 28.3249 | 1.67782 | ||||||||
\(286\) | 0.571993 | 0.0338227 | ||||||||
\(287\) | 6.37429 | 0.376262 | ||||||||
\(288\) | −5.42801 | −0.319848 | ||||||||
\(289\) | −16.8168 | −0.989224 | ||||||||
\(290\) | −7.08405 | −0.415990 | ||||||||
\(291\) | 11.6336 | 0.681975 | ||||||||
\(292\) | −19.6231 | −1.14835 | ||||||||
\(293\) | −27.4874 | −1.60583 | −0.802915 | − | 0.596094i | \(-0.796719\pi\) | ||||
−0.802915 | + | 0.596094i | \(0.796719\pi\) | |||||||
\(294\) | 0.0823593 | 0.00480329 | ||||||||
\(295\) | −53.0162 | −3.08672 | ||||||||
\(296\) | 16.0369 | 0.932128 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 2.67282 | 0.154833 | ||||||||
\(299\) | 7.81681 | 0.452058 | ||||||||
\(300\) | 21.7776 | 1.25733 | ||||||||
\(301\) | 31.4689 | 1.81384 | ||||||||
\(302\) | 3.27781 | 0.188617 | ||||||||
\(303\) | −7.48568 | −0.430041 | ||||||||
\(304\) | 14.3064 | 0.820531 | ||||||||
\(305\) | −13.3456 | −0.764170 | ||||||||
\(306\) | 0.244817 | 0.0139953 | ||||||||
\(307\) | 9.15455 | 0.522478 | 0.261239 | − | 0.965274i | \(-0.415869\pi\) | ||||
0.261239 | + | 0.965274i | \(0.415869\pi\) | |||||||
\(308\) | 4.47116 | 0.254768 | ||||||||
\(309\) | −1.71203 | −0.0973938 | ||||||||
\(310\) | 4.26160 | 0.242042 | ||||||||
\(311\) | 15.2409 | 0.864230 | 0.432115 | − | 0.901818i | \(-0.357767\pi\) | ||||
0.432115 | + | 0.901818i | \(0.357767\pi\) | |||||||
\(312\) | 2.10083 | 0.118936 | ||||||||
\(313\) | −8.87448 | −0.501616 | −0.250808 | − | 0.968037i | \(-0.580696\pi\) | ||||
−0.250808 | + | 0.968037i | \(0.580696\pi\) | |||||||
\(314\) | −4.79608 | −0.270658 | ||||||||
\(315\) | 11.3456 | 0.639255 | ||||||||
\(316\) | −10.7529 | −0.604899 | ||||||||
\(317\) | 7.01452 | 0.393975 | 0.196987 | − | 0.980406i | \(-0.436884\pi\) | ||||
0.196987 | + | 0.980406i | \(0.436884\pi\) | |||||||
\(318\) | −1.63362 | −0.0916089 | ||||||||
\(319\) | −2.91764 | −0.163357 | ||||||||
\(320\) | 5.02242 | 0.280762 | ||||||||
\(321\) | −4.48963 | −0.250587 | ||||||||
\(322\) | −11.9506 | −0.665983 | ||||||||
\(323\) | −2.85601 | −0.158913 | ||||||||
\(324\) | −1.67282 | −0.0929347 | ||||||||
\(325\) | −13.0185 | −0.722135 | ||||||||
\(326\) | 2.75744 | 0.152721 | ||||||||
\(327\) | 10.0185 | 0.554023 | ||||||||
\(328\) | −5.01017 | −0.276640 | ||||||||
\(329\) | −17.3456 | −0.956296 | ||||||||
\(330\) | −2.42801 | −0.133657 | ||||||||
\(331\) | 24.3681 | 1.33939 | 0.669695 | − | 0.742636i | \(-0.266425\pi\) | ||||
0.669695 | + | 0.742636i | \(0.266425\pi\) | |||||||
\(332\) | −3.00830 | −0.165102 | ||||||||
\(333\) | 7.63362 | 0.418320 | ||||||||
\(334\) | −11.2303 | −0.614495 | ||||||||
\(335\) | −56.8330 | −3.10512 | ||||||||
\(336\) | 5.73050 | 0.312624 | ||||||||
\(337\) | −28.6050 | −1.55821 | −0.779106 | − | 0.626892i | \(-0.784327\pi\) | ||||
−0.779106 | + | 0.626892i | \(0.784327\pi\) | |||||||
\(338\) | −0.571993 | −0.0311123 | ||||||||
\(339\) | 10.4896 | 0.569719 | ||||||||
\(340\) | −3.03920 | −0.164824 | ||||||||
\(341\) | 1.75518 | 0.0950485 | ||||||||
\(342\) | −3.81681 | −0.206389 | ||||||||
\(343\) | 18.3249 | 0.989452 | ||||||||
\(344\) | −24.7345 | −1.33359 | ||||||||
\(345\) | −33.1809 | −1.78640 | ||||||||
\(346\) | −2.53279 | −0.136164 | ||||||||
\(347\) | −1.42405 | −0.0764472 | −0.0382236 | − | 0.999269i | \(-0.512170\pi\) | ||||
−0.0382236 | + | 0.999269i | \(0.512170\pi\) | |||||||
\(348\) | −4.88070 | −0.261633 | ||||||||
\(349\) | 18.1233 | 0.970116 | 0.485058 | − | 0.874482i | \(-0.338799\pi\) | ||||
0.485058 | + | 0.874482i | \(0.338799\pi\) | |||||||
\(350\) | 19.9031 | 1.06387 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −5.42801 | −0.289314 | ||||||||
\(353\) | −9.46721 | −0.503889 | −0.251944 | − | 0.967742i | \(-0.581070\pi\) | ||||
−0.251944 | + | 0.967742i | \(0.581070\pi\) | |||||||
\(354\) | 7.14399 | 0.379699 | ||||||||
\(355\) | 31.1809 | 1.65491 | ||||||||
\(356\) | −6.00621 | −0.318329 | ||||||||
\(357\) | −1.14399 | −0.0605462 | ||||||||
\(358\) | −7.57821 | −0.400521 | ||||||||
\(359\) | −5.04711 | −0.266376 | −0.133188 | − | 0.991091i | \(-0.542521\pi\) | ||||
−0.133188 | + | 0.991091i | \(0.542521\pi\) | |||||||
\(360\) | −8.91764 | −0.470001 | ||||||||
\(361\) | 25.5266 | 1.34350 | ||||||||
\(362\) | −6.54505 | −0.344000 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −4.47116 | −0.234353 | ||||||||
\(365\) | −49.7938 | −2.60633 | ||||||||
\(366\) | 1.79834 | 0.0940007 | ||||||||
\(367\) | 16.6992 | 0.871691 | 0.435846 | − | 0.900021i | \(-0.356449\pi\) | ||||
0.435846 | + | 0.900021i | \(0.356449\pi\) | |||||||
\(368\) | −16.7591 | −0.873630 | ||||||||
\(369\) | −2.38485 | −0.124150 | ||||||||
\(370\) | 18.5345 | 0.963562 | ||||||||
\(371\) | 7.63362 | 0.396318 | ||||||||
\(372\) | 2.93611 | 0.152230 | ||||||||
\(373\) | 28.6050 | 1.48111 | 0.740555 | − | 0.671996i | \(-0.234563\pi\) | ||||
0.740555 | + | 0.671996i | \(0.234563\pi\) | |||||||
\(374\) | 0.244817 | 0.0126592 | ||||||||
\(375\) | 34.0369 | 1.75766 | ||||||||
\(376\) | 13.6336 | 0.703100 | ||||||||
\(377\) | 2.91764 | 0.150266 | ||||||||
\(378\) | −1.52884 | −0.0786349 | ||||||||
\(379\) | −31.8291 | −1.63495 | −0.817475 | − | 0.575965i | \(-0.804627\pi\) | ||||
−0.817475 | + | 0.575965i | \(0.804627\pi\) | |||||||
\(380\) | 47.3826 | 2.43068 | ||||||||
\(381\) | −10.6297 | −0.544574 | ||||||||
\(382\) | −0.280067 | −0.0143295 | ||||||||
\(383\) | 1.83528 | 0.0937785 | 0.0468892 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468892 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(384\) | −11.5328 | −0.588530 | ||||||||
\(385\) | 11.3456 | 0.578228 | ||||||||
\(386\) | 0.594417 | 0.0302550 | ||||||||
\(387\) | −11.7737 | −0.598488 | ||||||||
\(388\) | 19.4610 | 0.987982 | ||||||||
\(389\) | 19.4689 | 0.987113 | 0.493556 | − | 0.869714i | \(-0.335697\pi\) | ||||
0.493556 | + | 0.869714i | \(0.335697\pi\) | |||||||
\(390\) | 2.42801 | 0.122947 | ||||||||
\(391\) | 3.34565 | 0.169197 | ||||||||
\(392\) | 0.302491 | 0.0152781 | ||||||||
\(393\) | −19.6336 | −0.990385 | ||||||||
\(394\) | −5.24086 | −0.264031 | ||||||||
\(395\) | −27.2857 | −1.37289 | ||||||||
\(396\) | −1.67282 | −0.0840626 | ||||||||
\(397\) | −21.0162 | −1.05477 | −0.527387 | − | 0.849625i | \(-0.676828\pi\) | ||||
−0.527387 | + | 0.849625i | \(0.676828\pi\) | |||||||
\(398\) | 4.80664 | 0.240935 | ||||||||
\(399\) | 17.8353 | 0.892881 | ||||||||
\(400\) | 27.9114 | 1.39557 | ||||||||
\(401\) | −35.2162 | −1.75861 | −0.879306 | − | 0.476257i | \(-0.841993\pi\) | ||||
−0.879306 | + | 0.476257i | \(0.841993\pi\) | |||||||
\(402\) | 7.65831 | 0.381962 | ||||||||
\(403\) | −1.75518 | −0.0874319 | ||||||||
\(404\) | −12.5222 | −0.623004 | ||||||||
\(405\) | −4.24482 | −0.210927 | ||||||||
\(406\) | −4.46060 | −0.221376 | ||||||||
\(407\) | 7.63362 | 0.378385 | ||||||||
\(408\) | 0.899170 | 0.0445155 | ||||||||
\(409\) | −6.96080 | −0.344189 | −0.172095 | − | 0.985080i | \(-0.555053\pi\) | ||||
−0.172095 | + | 0.985080i | \(0.555053\pi\) | |||||||
\(410\) | −5.79043 | −0.285969 | ||||||||
\(411\) | 8.81286 | 0.434706 | ||||||||
\(412\) | −2.86392 | −0.141095 | ||||||||
\(413\) | −33.3826 | −1.64265 | ||||||||
\(414\) | 4.47116 | 0.219746 | ||||||||
\(415\) | −7.63362 | −0.374720 | ||||||||
\(416\) | 5.42801 | 0.266130 | ||||||||
\(417\) | 9.40727 | 0.460676 | ||||||||
\(418\) | −3.81681 | −0.186686 | ||||||||
\(419\) | −18.5944 | −0.908397 | −0.454198 | − | 0.890901i | \(-0.650074\pi\) | ||||
−0.454198 | + | 0.890901i | \(0.650074\pi\) | |||||||
\(420\) | 18.9793 | 0.926093 | ||||||||
\(421\) | −30.6129 | −1.49198 | −0.745990 | − | 0.665957i | \(-0.768024\pi\) | ||||
−0.745990 | + | 0.665957i | \(0.768024\pi\) | |||||||
\(422\) | −8.27385 | −0.402765 | ||||||||
\(423\) | 6.48963 | 0.315537 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −5.57199 | −0.270281 | ||||||||
\(426\) | −4.20166 | −0.203571 | ||||||||
\(427\) | −8.40332 | −0.406665 | ||||||||
\(428\) | −7.51037 | −0.363027 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | −28.5865 | −1.37856 | ||||||||
\(431\) | −8.20957 | −0.395441 | −0.197720 | − | 0.980258i | \(-0.563354\pi\) | ||||
−0.197720 | + | 0.980258i | \(0.563354\pi\) | |||||||
\(432\) | −2.14399 | −0.103153 | ||||||||
\(433\) | −28.1153 | −1.35114 | −0.675569 | − | 0.737297i | \(-0.736102\pi\) | ||||
−0.675569 | + | 0.737297i | \(0.736102\pi\) | |||||||
\(434\) | 2.68339 | 0.128807 | ||||||||
\(435\) | −12.3849 | −0.593808 | ||||||||
\(436\) | 16.7591 | 0.802617 | ||||||||
\(437\) | −52.1602 | −2.49516 | ||||||||
\(438\) | 6.70977 | 0.320605 | ||||||||
\(439\) | −16.7529 | −0.799573 | −0.399787 | − | 0.916608i | \(-0.630916\pi\) | ||||
−0.399787 | + | 0.916608i | \(0.630916\pi\) | |||||||
\(440\) | −8.91764 | −0.425132 | ||||||||
\(441\) | 0.143987 | 0.00685650 | ||||||||
\(442\) | −0.244817 | −0.0116448 | ||||||||
\(443\) | 12.9793 | 0.616664 | 0.308332 | − | 0.951279i | \(-0.400229\pi\) | ||||
0.308332 | + | 0.951279i | \(0.400229\pi\) | |||||||
\(444\) | 12.7697 | 0.606023 | ||||||||
\(445\) | −15.2409 | −0.722486 | ||||||||
\(446\) | 1.56409 | 0.0740617 | ||||||||
\(447\) | 4.67282 | 0.221017 | ||||||||
\(448\) | 3.16246 | 0.149412 | ||||||||
\(449\) | 24.1954 | 1.14185 | 0.570927 | − | 0.821001i | \(-0.306584\pi\) | ||||
0.570927 | + | 0.821001i | \(0.306584\pi\) | |||||||
\(450\) | −7.44648 | −0.351030 | ||||||||
\(451\) | −2.38485 | −0.112298 | ||||||||
\(452\) | 17.5473 | 0.825356 | ||||||||
\(453\) | 5.73050 | 0.269242 | ||||||||
\(454\) | −10.7512 | −0.504580 | ||||||||
\(455\) | −11.3456 | −0.531892 | ||||||||
\(456\) | −14.0185 | −0.656475 | ||||||||
\(457\) | −4.32492 | −0.202311 | −0.101156 | − | 0.994871i | \(-0.532254\pi\) | ||||
−0.101156 | + | 0.994871i | \(0.532254\pi\) | |||||||
\(458\) | −2.56804 | −0.119997 | ||||||||
\(459\) | 0.428007 | 0.0199776 | ||||||||
\(460\) | −55.5058 | −2.58797 | ||||||||
\(461\) | −6.38485 | −0.297372 | −0.148686 | − | 0.988884i | \(-0.547504\pi\) | ||||
−0.148686 | + | 0.988884i | \(0.547504\pi\) | |||||||
\(462\) | −1.52884 | −0.0711279 | ||||||||
\(463\) | 30.6560 | 1.42471 | 0.712354 | − | 0.701821i | \(-0.247629\pi\) | ||||
0.712354 | + | 0.701821i | \(0.247629\pi\) | |||||||
\(464\) | −6.25538 | −0.290399 | ||||||||
\(465\) | 7.45043 | 0.345505 | ||||||||
\(466\) | 6.29419 | 0.291573 | ||||||||
\(467\) | 31.8538 | 1.47402 | 0.737008 | − | 0.675884i | \(-0.236238\pi\) | ||||
0.737008 | + | 0.675884i | \(0.236238\pi\) | |||||||
\(468\) | 1.67282 | 0.0773263 | ||||||||
\(469\) | −35.7859 | −1.65244 | ||||||||
\(470\) | 15.7569 | 0.726810 | ||||||||
\(471\) | −8.38485 | −0.386354 | ||||||||
\(472\) | 26.2386 | 1.20773 | ||||||||
\(473\) | −11.7737 | −0.541353 | ||||||||
\(474\) | 3.67678 | 0.168880 | ||||||||
\(475\) | 86.8700 | 3.98587 | ||||||||
\(476\) | −1.91369 | −0.0877137 | ||||||||
\(477\) | −2.85601 | −0.130768 | ||||||||
\(478\) | −14.4587 | −0.661327 | ||||||||
\(479\) | 29.8168 | 1.36236 | 0.681182 | − | 0.732114i | \(-0.261466\pi\) | ||||
0.681182 | + | 0.732114i | \(0.261466\pi\) | |||||||
\(480\) | −23.0409 | −1.05167 | ||||||||
\(481\) | −7.63362 | −0.348063 | ||||||||
\(482\) | −8.72824 | −0.397560 | ||||||||
\(483\) | −20.8930 | −0.950662 | ||||||||
\(484\) | −1.67282 | −0.0760374 | ||||||||
\(485\) | 49.3826 | 2.24235 | ||||||||
\(486\) | 0.571993 | 0.0259461 | ||||||||
\(487\) | −19.4257 | −0.880265 | −0.440132 | − | 0.897933i | \(-0.645068\pi\) | ||||
−0.440132 | + | 0.897933i | \(0.645068\pi\) | |||||||
\(488\) | 6.60498 | 0.298994 | ||||||||
\(489\) | 4.82076 | 0.218002 | ||||||||
\(490\) | 0.349600 | 0.0157933 | ||||||||
\(491\) | 16.7282 | 0.754935 | 0.377467 | − | 0.926023i | \(-0.376795\pi\) | ||||
0.377467 | + | 0.926023i | \(0.376795\pi\) | |||||||
\(492\) | −3.98943 | −0.179858 | ||||||||
\(493\) | 1.24877 | 0.0562418 | ||||||||
\(494\) | 3.81681 | 0.171726 | ||||||||
\(495\) | −4.24482 | −0.190790 | ||||||||
\(496\) | 3.76309 | 0.168968 | ||||||||
\(497\) | 19.6336 | 0.880688 | ||||||||
\(498\) | 1.02864 | 0.0460944 | ||||||||
\(499\) | 18.0017 | 0.805866 | 0.402933 | − | 0.915229i | \(-0.367991\pi\) | ||||
0.402933 | + | 0.915229i | \(0.367991\pi\) | |||||||
\(500\) | 56.9378 | 2.54634 | ||||||||
\(501\) | −19.6336 | −0.877165 | ||||||||
\(502\) | −4.52658 | −0.202031 | ||||||||
\(503\) | 30.0448 | 1.33963 | 0.669817 | − | 0.742526i | \(-0.266373\pi\) | ||||
0.669817 | + | 0.742526i | \(0.266373\pi\) | |||||||
\(504\) | −5.61515 | −0.250119 | ||||||||
\(505\) | −31.7753 | −1.41398 | ||||||||
\(506\) | 4.47116 | 0.198767 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −17.7816 | −0.788929 | ||||||||
\(509\) | 1.79213 | 0.0794346 | 0.0397173 | − | 0.999211i | \(-0.487354\pi\) | ||||
0.0397173 | + | 0.999211i | \(0.487354\pi\) | |||||||
\(510\) | 1.03920 | 0.0460167 | ||||||||
\(511\) | −31.3536 | −1.38700 | ||||||||
\(512\) | −20.6459 | −0.912428 | ||||||||
\(513\) | −6.67282 | −0.294612 | ||||||||
\(514\) | 8.77761 | 0.387164 | ||||||||
\(515\) | −7.26724 | −0.320233 | ||||||||
\(516\) | −19.6952 | −0.867035 | ||||||||
\(517\) | 6.48963 | 0.285414 | ||||||||
\(518\) | 11.6706 | 0.512775 | ||||||||
\(519\) | −4.42801 | −0.194368 | ||||||||
\(520\) | 8.91764 | 0.391064 | ||||||||
\(521\) | −29.0946 | −1.27466 | −0.637329 | − | 0.770592i | \(-0.719961\pi\) | ||||
−0.637329 | + | 0.770592i | \(0.719961\pi\) | |||||||
\(522\) | 1.66887 | 0.0730445 | ||||||||
\(523\) | −20.0695 | −0.877579 | −0.438790 | − | 0.898590i | \(-0.644593\pi\) | ||||
−0.438790 | + | 0.898590i | \(0.644593\pi\) | |||||||
\(524\) | −32.8436 | −1.43478 | ||||||||
\(525\) | 34.7961 | 1.51863 | ||||||||
\(526\) | 15.3166 | 0.667836 | ||||||||
\(527\) | −0.751230 | −0.0327241 | ||||||||
\(528\) | −2.14399 | −0.0933050 | ||||||||
\(529\) | 38.1025 | 1.65663 | ||||||||
\(530\) | −6.93442 | −0.301212 | ||||||||
\(531\) | 12.4896 | 0.542004 | ||||||||
\(532\) | 29.8353 | 1.29352 | ||||||||
\(533\) | 2.38485 | 0.103299 | ||||||||
\(534\) | 2.05372 | 0.0888732 | ||||||||
\(535\) | −19.0577 | −0.823935 | ||||||||
\(536\) | 28.1276 | 1.21493 | ||||||||
\(537\) | −13.2488 | −0.571727 | ||||||||
\(538\) | −3.92159 | −0.169072 | ||||||||
\(539\) | 0.143987 | 0.00620194 | ||||||||
\(540\) | −7.10083 | −0.305571 | ||||||||
\(541\) | 24.1153 | 1.03680 | 0.518400 | − | 0.855138i | \(-0.326528\pi\) | ||||
0.518400 | + | 0.855138i | \(0.326528\pi\) | |||||||
\(542\) | 10.4007 | 0.446747 | ||||||||
\(543\) | −11.4425 | −0.491046 | ||||||||
\(544\) | 2.32322 | 0.0996074 | ||||||||
\(545\) | 42.5266 | 1.82164 | ||||||||
\(546\) | 1.52884 | 0.0654282 | ||||||||
\(547\) | 32.5019 | 1.38968 | 0.694840 | − | 0.719164i | \(-0.255475\pi\) | ||||
0.694840 | + | 0.719164i | \(0.255475\pi\) | |||||||
\(548\) | 14.7424 | 0.629762 | ||||||||
\(549\) | 3.14399 | 0.134182 | ||||||||
\(550\) | −7.44648 | −0.317519 | ||||||||
\(551\) | −19.4689 | −0.829403 | ||||||||
\(552\) | 16.4218 | 0.698958 | ||||||||
\(553\) | −17.1809 | −0.730607 | ||||||||
\(554\) | 13.5843 | 0.577139 | ||||||||
\(555\) | 32.4033 | 1.37544 | ||||||||
\(556\) | 15.7367 | 0.667385 | ||||||||
\(557\) | 41.6890 | 1.76642 | 0.883211 | − | 0.468977i | \(-0.155377\pi\) | ||||
0.883211 | + | 0.468977i | \(0.155377\pi\) | |||||||
\(558\) | −1.00395 | −0.0425007 | ||||||||
\(559\) | 11.7737 | 0.497973 | ||||||||
\(560\) | 24.3249 | 1.02792 | ||||||||
\(561\) | 0.428007 | 0.0180705 | ||||||||
\(562\) | −13.5243 | −0.570489 | ||||||||
\(563\) | −5.74897 | −0.242290 | −0.121145 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121145 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(564\) | 10.8560 | 0.457121 | ||||||||
\(565\) | 44.5266 | 1.87325 | ||||||||
\(566\) | −16.0511 | −0.674676 | ||||||||
\(567\) | −2.67282 | −0.112248 | ||||||||
\(568\) | −15.4320 | −0.647511 | ||||||||
\(569\) | 15.8521 | 0.664553 | 0.332276 | − | 0.943182i | \(-0.392183\pi\) | ||||
0.332276 | + | 0.943182i | \(0.392183\pi\) | |||||||
\(570\) | −16.2017 | −0.678613 | ||||||||
\(571\) | −5.57199 | −0.233181 | −0.116590 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116590 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(572\) | 1.67282 | 0.0699443 | ||||||||
\(573\) | −0.489634 | −0.0204548 | ||||||||
\(574\) | −3.64605 | −0.152183 | ||||||||
\(575\) | −101.763 | −4.24381 | ||||||||
\(576\) | −1.18319 | −0.0492996 | ||||||||
\(577\) | −2.20957 | −0.0919855 | −0.0459927 | − | 0.998942i | \(-0.514645\pi\) | ||||
−0.0459927 | + | 0.998942i | \(0.514645\pi\) | |||||||
\(578\) | 9.61910 | 0.400102 | ||||||||
\(579\) | 1.03920 | 0.0431878 | ||||||||
\(580\) | −20.7177 | −0.860254 | ||||||||
\(581\) | −4.80664 | −0.199413 | ||||||||
\(582\) | −6.65435 | −0.275832 | ||||||||
\(583\) | −2.85601 | −0.118284 | ||||||||
\(584\) | 24.6438 | 1.01977 | ||||||||
\(585\) | 4.24482 | 0.175502 | ||||||||
\(586\) | 15.7226 | 0.649494 | ||||||||
\(587\) | −15.1809 | −0.626584 | −0.313292 | − | 0.949657i | \(-0.601432\pi\) | ||||
−0.313292 | + | 0.949657i | \(0.601432\pi\) | |||||||
\(588\) | 0.240864 | 0.00993307 | ||||||||
\(589\) | 11.7120 | 0.482586 | ||||||||
\(590\) | 30.3249 | 1.24846 | ||||||||
\(591\) | −9.16246 | −0.376893 | ||||||||
\(592\) | 16.3664 | 0.672654 | ||||||||
\(593\) | −7.81681 | −0.320998 | −0.160499 | − | 0.987036i | \(-0.551310\pi\) | ||||
−0.160499 | + | 0.987036i | \(0.551310\pi\) | |||||||
\(594\) | 0.571993 | 0.0234692 | ||||||||
\(595\) | −4.85601 | −0.199077 | ||||||||
\(596\) | 7.81681 | 0.320189 | ||||||||
\(597\) | 8.40332 | 0.343925 | ||||||||
\(598\) | −4.47116 | −0.182839 | ||||||||
\(599\) | −15.5104 | −0.633736 | −0.316868 | − | 0.948470i | \(-0.602631\pi\) | ||||
−0.316868 | + | 0.948470i | \(0.602631\pi\) | |||||||
\(600\) | −27.3496 | −1.11654 | ||||||||
\(601\) | −3.38259 | −0.137979 | −0.0689894 | − | 0.997617i | \(-0.521977\pi\) | ||||
−0.0689894 | + | 0.997617i | \(0.521977\pi\) | |||||||
\(602\) | −18.0000 | −0.733625 | ||||||||
\(603\) | 13.3888 | 0.545234 | ||||||||
\(604\) | 9.58611 | 0.390053 | ||||||||
\(605\) | −4.24482 | −0.172576 | ||||||||
\(606\) | 4.28176 | 0.173935 | ||||||||
\(607\) | −14.9097 | −0.605167 | −0.302584 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302584 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(608\) | −36.2201 | −1.46892 | ||||||||
\(609\) | −7.79834 | −0.316005 | ||||||||
\(610\) | 7.63362 | 0.309076 | ||||||||
\(611\) | −6.48963 | −0.262542 | ||||||||
\(612\) | 0.715980 | 0.0289418 | ||||||||
\(613\) | −5.82472 | −0.235258 | −0.117629 | − | 0.993058i | \(-0.537529\pi\) | ||||
−0.117629 | + | 0.993058i | \(0.537529\pi\) | |||||||
\(614\) | −5.23634 | −0.211322 | ||||||||
\(615\) | −10.1233 | −0.408209 | ||||||||
\(616\) | −5.61515 | −0.226241 | ||||||||
\(617\) | 35.6353 | 1.43462 | 0.717312 | − | 0.696752i | \(-0.245372\pi\) | ||||
0.717312 | + | 0.696752i | \(0.245372\pi\) | |||||||
\(618\) | 0.979268 | 0.0393919 | ||||||||
\(619\) | 26.5697 | 1.06793 | 0.533964 | − | 0.845507i | \(-0.320702\pi\) | ||||
0.533964 | + | 0.845507i | \(0.320702\pi\) | |||||||
\(620\) | 12.4633 | 0.500536 | ||||||||
\(621\) | 7.81681 | 0.313678 | ||||||||
\(622\) | −8.71767 | −0.349547 | ||||||||
\(623\) | −9.59668 | −0.384483 | ||||||||
\(624\) | 2.14399 | 0.0858282 | ||||||||
\(625\) | 79.3882 | 3.17553 | ||||||||
\(626\) | 5.07615 | 0.202884 | ||||||||
\(627\) | −6.67282 | −0.266487 | ||||||||
\(628\) | −14.0264 | −0.559713 | ||||||||
\(629\) | −3.26724 | −0.130273 | ||||||||
\(630\) | −6.48963 | −0.258553 | ||||||||
\(631\) | 14.4834 | 0.576576 | 0.288288 | − | 0.957544i | \(-0.406914\pi\) | ||||
0.288288 | + | 0.957544i | \(0.406914\pi\) | |||||||
\(632\) | 13.5042 | 0.537166 | ||||||||
\(633\) | −14.4649 | −0.574930 | ||||||||
\(634\) | −4.01226 | −0.159347 | ||||||||
\(635\) | −45.1210 | −1.79057 | ||||||||
\(636\) | −4.77761 | −0.189444 | ||||||||
\(637\) | −0.143987 | −0.00570495 | ||||||||
\(638\) | 1.66887 | 0.0660712 | ||||||||
\(639\) | −7.34565 | −0.290589 | ||||||||
\(640\) | −48.9546 | −1.93510 | ||||||||
\(641\) | 19.0162 | 0.751095 | 0.375548 | − | 0.926803i | \(-0.377455\pi\) | ||||
0.375548 | + | 0.926803i | \(0.377455\pi\) | |||||||
\(642\) | 2.56804 | 0.101352 | ||||||||
\(643\) | 11.5905 | 0.457083 | 0.228542 | − | 0.973534i | \(-0.426604\pi\) | ||||
0.228542 | + | 0.973534i | \(0.426604\pi\) | |||||||
\(644\) | −34.9502 | −1.37723 | ||||||||
\(645\) | −49.9770 | −1.96784 | ||||||||
\(646\) | 1.63362 | 0.0642739 | ||||||||
\(647\) | 9.22239 | 0.362570 | 0.181285 | − | 0.983431i | \(-0.441974\pi\) | ||||
0.181285 | + | 0.983431i | \(0.441974\pi\) | |||||||
\(648\) | 2.10083 | 0.0825284 | ||||||||
\(649\) | 12.4896 | 0.490261 | ||||||||
\(650\) | 7.44648 | 0.292075 | ||||||||
\(651\) | 4.69129 | 0.183866 | ||||||||
\(652\) | 8.06429 | 0.315822 | ||||||||
\(653\) | 35.0162 | 1.37029 | 0.685145 | − | 0.728407i | \(-0.259739\pi\) | ||||
0.685145 | + | 0.728407i | \(0.259739\pi\) | |||||||
\(654\) | −5.73050 | −0.224080 | ||||||||
\(655\) | −83.3411 | −3.25641 | ||||||||
\(656\) | −5.11309 | −0.199633 | ||||||||
\(657\) | 11.7305 | 0.457650 | ||||||||
\(658\) | 9.92159 | 0.386784 | ||||||||
\(659\) | −4.81455 | −0.187548 | −0.0937741 | − | 0.995593i | \(-0.529893\pi\) | ||||
−0.0937741 | + | 0.995593i | \(0.529893\pi\) | |||||||
\(660\) | −7.10083 | −0.276399 | ||||||||
\(661\) | 7.43196 | 0.289070 | 0.144535 | − | 0.989500i | \(-0.453831\pi\) | ||||
0.144535 | + | 0.989500i | \(0.453831\pi\) | |||||||
\(662\) | −13.9384 | −0.541730 | ||||||||
\(663\) | −0.428007 | −0.0166224 | ||||||||
\(664\) | 3.77801 | 0.146615 | ||||||||
\(665\) | 75.7075 | 2.93581 | ||||||||
\(666\) | −4.36638 | −0.169194 | ||||||||
\(667\) | 22.8066 | 0.883077 | ||||||||
\(668\) | −32.8436 | −1.27076 | ||||||||
\(669\) | 2.73445 | 0.105720 | ||||||||
\(670\) | 32.5081 | 1.25590 | ||||||||
\(671\) | 3.14399 | 0.121372 | ||||||||
\(672\) | −14.5081 | −0.559662 | ||||||||
\(673\) | −9.13608 | −0.352170 | −0.176085 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176085 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(674\) | 16.3619 | 0.630235 | ||||||||
\(675\) | −13.0185 | −0.501081 | ||||||||
\(676\) | −1.67282 | −0.0643394 | ||||||||
\(677\) | −8.50641 | −0.326928 | −0.163464 | − | 0.986549i | \(-0.552267\pi\) | ||||
−0.163464 | + | 0.986549i | \(0.552267\pi\) | |||||||
\(678\) | −6.00000 | −0.230429 | ||||||||
\(679\) | 31.0946 | 1.19330 | ||||||||
\(680\) | 3.81681 | 0.146368 | ||||||||
\(681\) | −18.7961 | −0.720267 | ||||||||
\(682\) | −1.00395 | −0.0384433 | ||||||||
\(683\) | −25.7075 | −0.983670 | −0.491835 | − | 0.870688i | \(-0.663674\pi\) | ||||
−0.491835 | + | 0.870688i | \(0.663674\pi\) | |||||||
\(684\) | −11.1625 | −0.426807 | ||||||||
\(685\) | 37.4090 | 1.42932 | ||||||||
\(686\) | −10.4817 | −0.400194 | ||||||||
\(687\) | −4.48963 | −0.171290 | ||||||||
\(688\) | −25.2426 | −0.962363 | ||||||||
\(689\) | 2.85601 | 0.108805 | ||||||||
\(690\) | 18.9793 | 0.722528 | ||||||||
\(691\) | −14.7424 | −0.560826 | −0.280413 | − | 0.959879i | \(-0.590471\pi\) | ||||
−0.280413 | + | 0.959879i | \(0.590471\pi\) | |||||||
\(692\) | −7.40727 | −0.281582 | ||||||||
\(693\) | −2.67282 | −0.101532 | ||||||||
\(694\) | 0.814549 | 0.0309199 | ||||||||
\(695\) | 39.9322 | 1.51471 | ||||||||
\(696\) | 6.12947 | 0.232337 | ||||||||
\(697\) | 1.02073 | 0.0386630 | ||||||||
\(698\) | −10.3664 | −0.392373 | ||||||||
\(699\) | 11.0040 | 0.416208 | ||||||||
\(700\) | 58.2077 | 2.20004 | ||||||||
\(701\) | −33.3210 | −1.25852 | −0.629258 | − | 0.777197i | \(-0.716641\pi\) | ||||
−0.629258 | + | 0.777197i | \(0.716641\pi\) | |||||||
\(702\) | −0.571993 | −0.0215885 | ||||||||
\(703\) | 50.9378 | 1.92116 | ||||||||
\(704\) | −1.18319 | −0.0445931 | ||||||||
\(705\) | 27.5473 | 1.03749 | ||||||||
\(706\) | 5.41518 | 0.203803 | ||||||||
\(707\) | −20.0079 | −0.752475 | ||||||||
\(708\) | 20.8930 | 0.785205 | ||||||||
\(709\) | 1.25934 | 0.0472953 | 0.0236477 | − | 0.999720i | \(-0.492472\pi\) | ||||
0.0236477 | + | 0.999720i | \(0.492472\pi\) | |||||||
\(710\) | −17.8353 | −0.669346 | ||||||||
\(711\) | 6.42801 | 0.241069 | ||||||||
\(712\) | 7.54296 | 0.282684 | ||||||||
\(713\) | −13.7199 | −0.513816 | ||||||||
\(714\) | 0.654353 | 0.0244885 | ||||||||
\(715\) | 4.24482 | 0.158747 | ||||||||
\(716\) | −22.1629 | −0.828265 | ||||||||
\(717\) | −25.2778 | −0.944017 | ||||||||
\(718\) | 2.88691 | 0.107739 | ||||||||
\(719\) | −15.2672 | −0.569372 | −0.284686 | − | 0.958621i | \(-0.591889\pi\) | ||||
−0.284686 | + | 0.958621i | \(0.591889\pi\) | |||||||
\(720\) | −9.10083 | −0.339168 | ||||||||
\(721\) | −4.57595 | −0.170417 | ||||||||
\(722\) | −14.6010 | −0.543394 | ||||||||
\(723\) | −15.2593 | −0.567501 | ||||||||
\(724\) | −19.1413 | −0.711382 | ||||||||
\(725\) | −37.9832 | −1.41066 | ||||||||
\(726\) | 0.571993 | 0.0212287 | ||||||||
\(727\) | −24.1233 | −0.894682 | −0.447341 | − | 0.894363i | \(-0.647629\pi\) | ||||
−0.447341 | + | 0.894363i | \(0.647629\pi\) | |||||||
\(728\) | 5.61515 | 0.208111 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 28.4817 | 1.05416 | ||||||||
\(731\) | 5.03920 | 0.186382 | ||||||||
\(732\) | 5.25934 | 0.194391 | ||||||||
\(733\) | 47.5737 | 1.75717 | 0.878587 | − | 0.477582i | \(-0.158487\pi\) | ||||
0.878587 | + | 0.477582i | \(0.158487\pi\) | |||||||
\(734\) | −9.55183 | −0.352564 | ||||||||
\(735\) | 0.611196 | 0.0225443 | ||||||||
\(736\) | 42.4297 | 1.56398 | ||||||||
\(737\) | 13.3888 | 0.493183 | ||||||||
\(738\) | 1.36412 | 0.0502139 | ||||||||
\(739\) | −17.7305 | −0.652227 | −0.326113 | − | 0.945331i | \(-0.605739\pi\) | ||||
−0.326113 | + | 0.945331i | \(0.605739\pi\) | |||||||
\(740\) | 54.2050 | 1.99262 | ||||||||
\(741\) | 6.67282 | 0.245132 | ||||||||
\(742\) | −4.36638 | −0.160295 | ||||||||
\(743\) | 5.99209 | 0.219829 | 0.109914 | − | 0.993941i | \(-0.464942\pi\) | ||||
0.109914 | + | 0.993941i | \(0.464942\pi\) | |||||||
\(744\) | −3.68734 | −0.135185 | ||||||||
\(745\) | 19.8353 | 0.726708 | ||||||||
\(746\) | −16.3619 | −0.599050 | ||||||||
\(747\) | 1.79834 | 0.0657978 | ||||||||
\(748\) | 0.715980 | 0.0261788 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | −19.4689 | −0.710904 | ||||||||
\(751\) | 45.5058 | 1.66053 | 0.830266 | − | 0.557367i | \(-0.188189\pi\) | ||||
0.830266 | + | 0.557367i | \(0.188189\pi\) | |||||||
\(752\) | 13.9137 | 0.507380 | ||||||||
\(753\) | −7.91369 | −0.288391 | ||||||||
\(754\) | −1.66887 | −0.0607767 | ||||||||
\(755\) | 24.3249 | 0.885274 | ||||||||
\(756\) | −4.47116 | −0.162615 | ||||||||
\(757\) | 46.1708 | 1.67810 | 0.839052 | − | 0.544051i | \(-0.183110\pi\) | ||||
0.839052 | + | 0.544051i | \(0.183110\pi\) | |||||||
\(758\) | 18.2060 | 0.661272 | ||||||||
\(759\) | 7.81681 | 0.283732 | ||||||||
\(760\) | −59.5058 | −2.15850 | ||||||||
\(761\) | −4.01057 | −0.145383 | −0.0726914 | − | 0.997354i | \(-0.523159\pi\) | ||||
−0.0726914 | + | 0.997354i | \(0.523159\pi\) | |||||||
\(762\) | 6.08010 | 0.220259 | ||||||||
\(763\) | 26.7776 | 0.969414 | ||||||||
\(764\) | −0.819071 | −0.0296330 | ||||||||
\(765\) | 1.81681 | 0.0656869 | ||||||||
\(766\) | −1.04977 | −0.0379297 | ||||||||
\(767\) | −12.4896 | −0.450975 | ||||||||
\(768\) | 4.23030 | 0.152648 | ||||||||
\(769\) | 41.8432 | 1.50890 | 0.754452 | − | 0.656355i | \(-0.227903\pi\) | ||||
0.754452 | + | 0.656355i | \(0.227903\pi\) | |||||||
\(770\) | −6.48963 | −0.233870 | ||||||||
\(771\) | 15.3456 | 0.552660 | ||||||||
\(772\) | 1.73840 | 0.0625665 | ||||||||
\(773\) | −26.9440 | −0.969109 | −0.484554 | − | 0.874761i | \(-0.661018\pi\) | ||||
−0.484554 | + | 0.874761i | \(0.661018\pi\) | |||||||
\(774\) | 6.73445 | 0.242065 | ||||||||
\(775\) | 22.8498 | 0.820789 | ||||||||
\(776\) | −24.4403 | −0.877354 | ||||||||
\(777\) | 20.4033 | 0.731965 | ||||||||
\(778\) | −11.1361 | −0.399248 | ||||||||
\(779\) | −15.9137 | −0.570167 | ||||||||
\(780\) | 7.10083 | 0.254251 | ||||||||
\(781\) | −7.34565 | −0.262848 | ||||||||
\(782\) | −1.91369 | −0.0684333 | ||||||||
\(783\) | 2.91764 | 0.104268 | ||||||||
\(784\) | 0.308705 | 0.0110252 | ||||||||
\(785\) | −35.5922 | −1.27034 | ||||||||
\(786\) | 11.2303 | 0.400571 | ||||||||
\(787\) | 5.53674 | 0.197364 | 0.0986818 | − | 0.995119i | \(-0.468537\pi\) | ||||
0.0986818 | + | 0.995119i | \(0.468537\pi\) | |||||||
\(788\) | −15.3272 | −0.546008 | ||||||||
\(789\) | 26.7776 | 0.953308 | ||||||||
\(790\) | 15.6072 | 0.555281 | ||||||||
\(791\) | 28.0369 | 0.996879 | ||||||||
\(792\) | 2.10083 | 0.0746498 | ||||||||
\(793\) | −3.14399 | −0.111646 | ||||||||
\(794\) | 12.0211 | 0.426614 | ||||||||
\(795\) | −12.1233 | −0.429968 | ||||||||
\(796\) | 14.0573 | 0.498247 | ||||||||
\(797\) | 14.2465 | 0.504637 | 0.252319 | − | 0.967644i | \(-0.418807\pi\) | ||||
0.252319 | + | 0.967644i | \(0.418807\pi\) | |||||||
\(798\) | −10.2017 | −0.361135 | ||||||||
\(799\) | −2.77761 | −0.0982647 | ||||||||
\(800\) | −70.6643 | −2.49836 | ||||||||
\(801\) | 3.59046 | 0.126863 | ||||||||
\(802\) | 20.1434 | 0.711289 | ||||||||
\(803\) | 11.7305 | 0.413960 | ||||||||
\(804\) | 22.3971 | 0.789885 | ||||||||
\(805\) | −88.6868 | −3.12580 | ||||||||
\(806\) | 1.00395 | 0.0353627 | ||||||||
\(807\) | −6.85601 | −0.241343 | ||||||||
\(808\) | 15.7261 | 0.553244 | ||||||||
\(809\) | 40.6745 | 1.43004 | 0.715020 | − | 0.699104i | \(-0.246418\pi\) | ||||
0.715020 | + | 0.699104i | \(0.246418\pi\) | |||||||
\(810\) | 2.42801 | 0.0853115 | ||||||||
\(811\) | 21.9031 | 0.769123 | 0.384561 | − | 0.923099i | \(-0.374353\pi\) | ||||
0.384561 | + | 0.923099i | \(0.374353\pi\) | |||||||
\(812\) | −13.0452 | −0.457798 | ||||||||
\(813\) | 18.1832 | 0.637712 | ||||||||
\(814\) | −4.36638 | −0.153042 | ||||||||
\(815\) | 20.4633 | 0.716797 | ||||||||
\(816\) | 0.917641 | 0.0321238 | ||||||||
\(817\) | −78.5635 | −2.74859 | ||||||||
\(818\) | 3.98153 | 0.139211 | ||||||||
\(819\) | 2.67282 | 0.0933960 | ||||||||
\(820\) | −16.9344 | −0.591376 | ||||||||
\(821\) | 16.2201 | 0.566087 | 0.283043 | − | 0.959107i | \(-0.408656\pi\) | ||||
0.283043 | + | 0.959107i | \(0.408656\pi\) | |||||||
\(822\) | −5.04090 | −0.175821 | ||||||||
\(823\) | −47.5473 | −1.65739 | −0.828697 | − | 0.559697i | \(-0.810918\pi\) | ||||
−0.828697 | + | 0.559697i | \(0.810918\pi\) | |||||||
\(824\) | 3.59668 | 0.125296 | ||||||||
\(825\) | −13.0185 | −0.453245 | ||||||||
\(826\) | 19.0946 | 0.664387 | ||||||||
\(827\) | −27.4090 | −0.953103 | −0.476552 | − | 0.879147i | \(-0.658113\pi\) | ||||
−0.476552 | + | 0.879147i | \(0.658113\pi\) | |||||||
\(828\) | 13.0761 | 0.454427 | ||||||||
\(829\) | 6.97927 | 0.242400 | 0.121200 | − | 0.992628i | \(-0.461326\pi\) | ||||
0.121200 | + | 0.992628i | \(0.461326\pi\) | |||||||
\(830\) | 4.36638 | 0.151559 | ||||||||
\(831\) | 23.7490 | 0.823843 | ||||||||
\(832\) | 1.18319 | 0.0410197 | ||||||||
\(833\) | −0.0616272 | −0.00213526 | ||||||||
\(834\) | −5.38090 | −0.186325 | ||||||||
\(835\) | −83.3411 | −2.88414 | ||||||||
\(836\) | −11.1625 | −0.386062 | ||||||||
\(837\) | −1.75518 | −0.0606680 | ||||||||
\(838\) | 10.6359 | 0.367410 | ||||||||
\(839\) | 33.1888 | 1.14581 | 0.572903 | − | 0.819623i | \(-0.305817\pi\) | ||||
0.572903 | + | 0.819623i | \(0.305817\pi\) | |||||||
\(840\) | −23.8353 | −0.822395 | ||||||||
\(841\) | −20.4874 | −0.706461 | ||||||||
\(842\) | 17.5104 | 0.603447 | ||||||||
\(843\) | −23.6442 | −0.814349 | ||||||||
\(844\) | −24.1973 | −0.832906 | ||||||||
\(845\) | −4.24482 | −0.146026 | ||||||||
\(846\) | −3.71203 | −0.127622 | ||||||||
\(847\) | −2.67282 | −0.0918393 | ||||||||
\(848\) | −6.12325 | −0.210273 | ||||||||
\(849\) | −28.0616 | −0.963073 | ||||||||
\(850\) | 3.18714 | 0.109318 | ||||||||
\(851\) | −59.6706 | −2.04548 | ||||||||
\(852\) | −12.2880 | −0.420979 | ||||||||
\(853\) | 6.61289 | 0.226421 | 0.113210 | − | 0.993571i | \(-0.463887\pi\) | ||||
0.113210 | + | 0.993571i | \(0.463887\pi\) | |||||||
\(854\) | 4.80664 | 0.164480 | ||||||||
\(855\) | −28.3249 | −0.968692 | ||||||||
\(856\) | 9.43196 | 0.322378 | ||||||||
\(857\) | 11.0409 | 0.377150 | 0.188575 | − | 0.982059i | \(-0.439613\pi\) | ||||
0.188575 | + | 0.982059i | \(0.439613\pi\) | |||||||
\(858\) | −0.571993 | −0.0195275 | ||||||||
\(859\) | −8.52658 | −0.290923 | −0.145462 | − | 0.989364i | \(-0.546467\pi\) | ||||
−0.145462 | + | 0.989364i | \(0.546467\pi\) | |||||||
\(860\) | −83.6027 | −2.85083 | ||||||||
\(861\) | −6.37429 | −0.217235 | ||||||||
\(862\) | 4.69582 | 0.159940 | ||||||||
\(863\) | −17.2593 | −0.587515 | −0.293757 | − | 0.955880i | \(-0.594906\pi\) | ||||
−0.293757 | + | 0.955880i | \(0.594906\pi\) | |||||||
\(864\) | 5.42801 | 0.184665 | ||||||||
\(865\) | −18.7961 | −0.639086 | ||||||||
\(866\) | 16.0818 | 0.546481 | ||||||||
\(867\) | 16.8168 | 0.571129 | ||||||||
\(868\) | 7.84771 | 0.266369 | ||||||||
\(869\) | 6.42801 | 0.218055 | ||||||||
\(870\) | 7.08405 | 0.240172 | ||||||||
\(871\) | −13.3888 | −0.453662 | ||||||||
\(872\) | −21.0471 | −0.712745 | ||||||||
\(873\) | −11.6336 | −0.393738 | ||||||||
\(874\) | 29.8353 | 1.00919 | ||||||||
\(875\) | 90.9747 | 3.07551 | ||||||||
\(876\) | 19.6231 | 0.663002 | ||||||||
\(877\) | 12.1647 | 0.410773 | 0.205387 | − | 0.978681i | \(-0.434155\pi\) | ||||
0.205387 | + | 0.978681i | \(0.434155\pi\) | |||||||
\(878\) | 9.58256 | 0.323396 | ||||||||
\(879\) | 27.4874 | 0.927126 | ||||||||
\(880\) | −9.10083 | −0.306789 | ||||||||
\(881\) | 1.09462 | 0.0368786 | 0.0184393 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184393 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(882\) | −0.0823593 | −0.00277318 | ||||||||
\(883\) | −40.9793 | −1.37906 | −0.689531 | − | 0.724256i | \(-0.742183\pi\) | ||||
−0.689531 | + | 0.724256i | \(0.742183\pi\) | |||||||
\(884\) | −0.715980 | −0.0240810 | ||||||||
\(885\) | 53.0162 | 1.78212 | ||||||||
\(886\) | −7.42405 | −0.249416 | ||||||||
\(887\) | 32.0818 | 1.07720 | 0.538601 | − | 0.842561i | \(-0.318953\pi\) | ||||
0.538601 | + | 0.842561i | \(0.318953\pi\) | |||||||
\(888\) | −16.0369 | −0.538165 | ||||||||
\(889\) | −28.4112 | −0.952882 | ||||||||
\(890\) | 8.71767 | 0.292217 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 4.57425 | 0.153157 | ||||||||
\(893\) | 43.3042 | 1.44912 | ||||||||
\(894\) | −2.67282 | −0.0893926 | ||||||||
\(895\) | −56.2386 | −1.87985 | ||||||||
\(896\) | −30.8251 | −1.02979 | ||||||||
\(897\) | −7.81681 | −0.260996 | ||||||||
\(898\) | −13.8396 | −0.461835 | ||||||||
\(899\) | −5.12099 | −0.170795 | ||||||||
\(900\) | −21.7776 | −0.725920 | ||||||||
\(901\) | 1.22239 | 0.0407238 | ||||||||
\(902\) | 1.36412 | 0.0454202 | ||||||||
\(903\) | −31.4689 | −1.04722 | ||||||||
\(904\) | −22.0369 | −0.732938 | ||||||||
\(905\) | −48.5714 | −1.61457 | ||||||||
\(906\) | −3.27781 | −0.108898 | ||||||||
\(907\) | −2.81455 | −0.0934556 | −0.0467278 | − | 0.998908i | \(-0.514879\pi\) | ||||
−0.0467278 | + | 0.998908i | \(0.514879\pi\) | |||||||
\(908\) | −31.4425 | −1.04346 | ||||||||
\(909\) | 7.48568 | 0.248284 | ||||||||
\(910\) | 6.48963 | 0.215129 | ||||||||
\(911\) | 7.18093 | 0.237915 | 0.118957 | − | 0.992899i | \(-0.462045\pi\) | ||||
0.118957 | + | 0.992899i | \(0.462045\pi\) | |||||||
\(912\) | −14.3064 | −0.473734 | ||||||||
\(913\) | 1.79834 | 0.0595163 | ||||||||
\(914\) | 2.47382 | 0.0818268 | ||||||||
\(915\) | 13.3456 | 0.441193 | ||||||||
\(916\) | −7.51037 | −0.248149 | ||||||||
\(917\) | −52.4772 | −1.73295 | ||||||||
\(918\) | −0.244817 | −0.00808016 | ||||||||
\(919\) | 24.0123 | 0.792091 | 0.396046 | − | 0.918231i | \(-0.370382\pi\) | ||||
0.396046 | + | 0.918231i | \(0.370382\pi\) | |||||||
\(920\) | 69.7075 | 2.29819 | ||||||||
\(921\) | −9.15455 | −0.301653 | ||||||||
\(922\) | 3.65209 | 0.120275 | ||||||||
\(923\) | 7.34565 | 0.241785 | ||||||||
\(924\) | −4.47116 | −0.147090 | ||||||||
\(925\) | 99.3781 | 3.26753 | ||||||||
\(926\) | −17.5351 | −0.576238 | ||||||||
\(927\) | 1.71203 | 0.0562303 | ||||||||
\(928\) | 15.8370 | 0.519874 | ||||||||
\(929\) | −22.0017 | −0.721852 | −0.360926 | − | 0.932594i | \(-0.617539\pi\) | ||||
−0.360926 | + | 0.932594i | \(0.617539\pi\) | |||||||
\(930\) | −4.26160 | −0.139743 | ||||||||
\(931\) | 0.960797 | 0.0314888 | ||||||||
\(932\) | 18.4077 | 0.602963 | ||||||||
\(933\) | −15.2409 | −0.498963 | ||||||||
\(934\) | −18.2201 | −0.596181 | ||||||||
\(935\) | 1.81681 | 0.0594160 | ||||||||
\(936\) | −2.10083 | −0.0686678 | ||||||||
\(937\) | −18.4975 | −0.604288 | −0.302144 | − | 0.953262i | \(-0.597702\pi\) | ||||
−0.302144 | + | 0.953262i | \(0.597702\pi\) | |||||||
\(938\) | 20.4693 | 0.668346 | ||||||||
\(939\) | 8.87448 | 0.289608 | ||||||||
\(940\) | 46.0818 | 1.50302 | ||||||||
\(941\) | 34.4218 | 1.12212 | 0.561059 | − | 0.827776i | \(-0.310394\pi\) | ||||
0.561059 | + | 0.827776i | \(0.310394\pi\) | |||||||
\(942\) | 4.79608 | 0.156265 | ||||||||
\(943\) | 18.6419 | 0.607065 | ||||||||
\(944\) | 26.7776 | 0.871537 | ||||||||
\(945\) | −11.3456 | −0.369074 | ||||||||
\(946\) | 6.73445 | 0.218956 | ||||||||
\(947\) | −41.5473 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(948\) | 10.7529 | 0.349239 | ||||||||
\(949\) | −11.7305 | −0.380788 | ||||||||
\(950\) | −49.6890 | −1.61213 | ||||||||
\(951\) | −7.01452 | −0.227461 | ||||||||
\(952\) | 2.40332 | 0.0778921 | ||||||||
\(953\) | −3.53053 | −0.114365 | −0.0571825 | − | 0.998364i | \(-0.518212\pi\) | ||||
−0.0571825 | + | 0.998364i | \(0.518212\pi\) | |||||||
\(954\) | 1.63362 | 0.0528904 | ||||||||
\(955\) | −2.07841 | −0.0672557 | ||||||||
\(956\) | −42.2853 | −1.36760 | ||||||||
\(957\) | 2.91764 | 0.0943139 | ||||||||
\(958\) | −17.0550 | −0.551023 | ||||||||
\(959\) | 23.5552 | 0.760638 | ||||||||
\(960\) | −5.02242 | −0.162098 | ||||||||
\(961\) | −27.9193 | −0.900624 | ||||||||
\(962\) | 4.36638 | 0.140778 | ||||||||
\(963\) | 4.48963 | 0.144676 | ||||||||
\(964\) | −25.5262 | −0.822143 | ||||||||
\(965\) | 4.41123 | 0.142002 | ||||||||
\(966\) | 11.9506 | 0.384505 | ||||||||
\(967\) | 44.5450 | 1.43247 | 0.716236 | − | 0.697858i | \(-0.245863\pi\) | ||||
0.716236 | + | 0.697858i | \(0.245863\pi\) | |||||||
\(968\) | 2.10083 | 0.0675232 | ||||||||
\(969\) | 2.85601 | 0.0917484 | ||||||||
\(970\) | −28.2465 | −0.906941 | ||||||||
\(971\) | −14.5450 | −0.466773 | −0.233386 | − | 0.972384i | \(-0.574981\pi\) | ||||
−0.233386 | + | 0.972384i | \(0.574981\pi\) | |||||||
\(972\) | 1.67282 | 0.0536558 | ||||||||
\(973\) | 25.1440 | 0.806079 | ||||||||
\(974\) | 11.1114 | 0.356032 | ||||||||
\(975\) | 13.0185 | 0.416925 | ||||||||
\(976\) | 6.74066 | 0.215763 | ||||||||
\(977\) | 38.3681 | 1.22750 | 0.613752 | − | 0.789499i | \(-0.289660\pi\) | ||||
0.613752 | + | 0.789499i | \(0.289660\pi\) | |||||||
\(978\) | −2.75744 | −0.0881733 | ||||||||
\(979\) | 3.59046 | 0.114752 | ||||||||
\(980\) | 1.02242 | 0.0326601 | ||||||||
\(981\) | −10.0185 | −0.319865 | ||||||||
\(982\) | −9.56844 | −0.305341 | ||||||||
\(983\) | −34.6544 | −1.10530 | −0.552651 | − | 0.833413i | \(-0.686384\pi\) | ||||
−0.552651 | + | 0.833413i | \(0.686384\pi\) | |||||||
\(984\) | 5.01017 | 0.159718 | ||||||||
\(985\) | −38.8930 | −1.23923 | ||||||||
\(986\) | −0.714288 | −0.0227476 | ||||||||
\(987\) | 17.3456 | 0.552118 | ||||||||
\(988\) | 11.1625 | 0.355125 | ||||||||
\(989\) | 92.0324 | 2.92646 | ||||||||
\(990\) | 2.42801 | 0.0771671 | ||||||||
\(991\) | −1.06558 | −0.0338493 | −0.0169246 | − | 0.999857i | \(-0.505388\pi\) | ||||
−0.0169246 | + | 0.999857i | \(0.505388\pi\) | |||||||
\(992\) | −9.52715 | −0.302487 | ||||||||
\(993\) | −24.3681 | −0.773297 | ||||||||
\(994\) | −11.2303 | −0.356203 | ||||||||
\(995\) | 35.6706 | 1.13083 | ||||||||
\(996\) | 3.00830 | 0.0953218 | ||||||||
\(997\) | −8.53110 | −0.270183 | −0.135091 | − | 0.990833i | \(-0.543133\pi\) | ||||
−0.135091 | + | 0.990833i | \(0.543133\pi\) | |||||||
\(998\) | −10.2968 | −0.325941 | ||||||||
\(999\) | −7.63362 | −0.241517 |
(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 | 429.2.a.e.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1287.2.a.j.1.2 | 3 | |||
4.3 | odd | 2 | 6864.2.a.bu.1.1 | 3 | |||
11.10 | odd | 2 | 4719.2.a.u.1.2 | 3 | |||
13.12 | even | 2 | 5577.2.a.l.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1287.2.a.j.1.2 | 3 | 3.2 | odd | 2 | |||
4719.2.a.u.1.2 | 3 | 11.10 | odd | 2 | |||
5577.2.a.l.1.2 | 3 | 13.12 | even | 2 | |||
6864.2.a.bu.1.1 | 3 | 4.3 | odd | 2 |