Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.822526\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.822526 | 0.581614 | 0.290807 | − | 0.956782i | \(-0.406076\pi\) | ||||
0.290807 | + | 0.956782i | \(0.406076\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.32345 | −0.661725 | ||||||||
\(5\) | 2.11599 | 0.946300 | 0.473150 | − | 0.880982i | \(-0.343117\pi\) | ||||
0.473150 | + | 0.880982i | \(0.343117\pi\) | |||||||
\(6\) | −0.822526 | −0.335795 | ||||||||
\(7\) | 0.404149 | 0.152754 | 0.0763769 | − | 0.997079i | \(-0.475665\pi\) | ||||
0.0763769 | + | 0.997079i | \(0.475665\pi\) | |||||||
\(8\) | −2.73363 | −0.966482 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.74046 | 0.550381 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.32345 | 0.382047 | ||||||||
\(13\) | 4.06066 | 1.12623 | 0.563113 | − | 0.826380i | \(-0.309604\pi\) | ||||
0.563113 | + | 0.826380i | \(0.309604\pi\) | |||||||
\(14\) | 0.332423 | 0.0888438 | ||||||||
\(15\) | −2.11599 | −0.546346 | ||||||||
\(16\) | 0.398423 | 0.0996058 | ||||||||
\(17\) | 0.0205369 | 0.00498093 | 0.00249047 | − | 0.999997i | \(-0.499207\pi\) | ||||
0.00249047 | + | 0.999997i | \(0.499207\pi\) | |||||||
\(18\) | 0.822526 | 0.193871 | ||||||||
\(19\) | 3.97586 | 0.912124 | 0.456062 | − | 0.889948i | \(-0.349259\pi\) | ||||
0.456062 | + | 0.889948i | \(0.349259\pi\) | |||||||
\(20\) | −2.80041 | −0.626191 | ||||||||
\(21\) | −0.404149 | −0.0881925 | ||||||||
\(22\) | 0.822526 | 0.175363 | ||||||||
\(23\) | −8.67841 | −1.80957 | −0.904787 | − | 0.425864i | \(-0.859970\pi\) | ||||
−0.904787 | + | 0.425864i | \(0.859970\pi\) | |||||||
\(24\) | 2.73363 | 0.557999 | ||||||||
\(25\) | −0.522583 | −0.104517 | ||||||||
\(26\) | 3.34000 | 0.655028 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.534871 | −0.101081 | ||||||||
\(29\) | −5.89217 | −1.09415 | −0.547075 | − | 0.837084i | \(-0.684259\pi\) | ||||
−0.547075 | + | 0.837084i | \(0.684259\pi\) | |||||||
\(30\) | −1.74046 | −0.317763 | ||||||||
\(31\) | 5.40170 | 0.970174 | 0.485087 | − | 0.874466i | \(-0.338788\pi\) | ||||
0.485087 | + | 0.874466i | \(0.338788\pi\) | |||||||
\(32\) | 5.79496 | 1.02441 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.0168922 | 0.00289698 | ||||||||
\(35\) | 0.855175 | 0.144551 | ||||||||
\(36\) | −1.32345 | −0.220575 | ||||||||
\(37\) | 1.99527 | 0.328020 | 0.164010 | − | 0.986459i | \(-0.447557\pi\) | ||||
0.164010 | + | 0.986459i | \(0.447557\pi\) | |||||||
\(38\) | 3.27025 | 0.530504 | ||||||||
\(39\) | −4.06066 | −0.650227 | ||||||||
\(40\) | −5.78433 | −0.914582 | ||||||||
\(41\) | 6.26962 | 0.979150 | 0.489575 | − | 0.871961i | \(-0.337152\pi\) | ||||
0.489575 | + | 0.871961i | \(0.337152\pi\) | |||||||
\(42\) | −0.332423 | −0.0512940 | ||||||||
\(43\) | 7.16134 | 1.09209 | 0.546047 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546047 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(44\) | −1.32345 | −0.199518 | ||||||||
\(45\) | 2.11599 | 0.315433 | ||||||||
\(46\) | −7.13822 | −1.05247 | ||||||||
\(47\) | 8.53737 | 1.24530 | 0.622652 | − | 0.782499i | \(-0.286055\pi\) | ||||
0.622652 | + | 0.782499i | \(0.286055\pi\) | |||||||
\(48\) | −0.398423 | −0.0575075 | ||||||||
\(49\) | −6.83666 | −0.976666 | ||||||||
\(50\) | −0.429838 | −0.0607883 | ||||||||
\(51\) | −0.0205369 | −0.00287574 | ||||||||
\(52\) | −5.37409 | −0.745252 | ||||||||
\(53\) | 5.18361 | 0.712024 | 0.356012 | − | 0.934481i | \(-0.384136\pi\) | ||||
0.356012 | + | 0.934481i | \(0.384136\pi\) | |||||||
\(54\) | −0.822526 | −0.111932 | ||||||||
\(55\) | 2.11599 | 0.285320 | ||||||||
\(56\) | −1.10479 | −0.147634 | ||||||||
\(57\) | −3.97586 | −0.526615 | ||||||||
\(58\) | −4.84647 | −0.636372 | ||||||||
\(59\) | −0.638698 | −0.0831514 | −0.0415757 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415757 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(60\) | 2.80041 | 0.361531 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 4.44304 | 0.564267 | ||||||||
\(63\) | 0.404149 | 0.0509180 | ||||||||
\(64\) | 3.96966 | 0.496208 | ||||||||
\(65\) | 8.59233 | 1.06575 | ||||||||
\(66\) | −0.822526 | −0.101246 | ||||||||
\(67\) | 15.2035 | 1.85740 | 0.928700 | − | 0.370831i | \(-0.120927\pi\) | ||||
0.928700 | + | 0.370831i | \(0.120927\pi\) | |||||||
\(68\) | −0.0271796 | −0.00329601 | ||||||||
\(69\) | 8.67841 | 1.04476 | ||||||||
\(70\) | 0.703404 | 0.0840729 | ||||||||
\(71\) | 11.4793 | 1.36234 | 0.681168 | − | 0.732127i | \(-0.261472\pi\) | ||||
0.681168 | + | 0.732127i | \(0.261472\pi\) | |||||||
\(72\) | −2.73363 | −0.322161 | ||||||||
\(73\) | −15.0344 | −1.75965 | −0.879823 | − | 0.475301i | \(-0.842339\pi\) | ||||
−0.879823 | + | 0.475301i | \(0.842339\pi\) | |||||||
\(74\) | 1.64116 | 0.190781 | ||||||||
\(75\) | 0.522583 | 0.0603427 | ||||||||
\(76\) | −5.26185 | −0.603576 | ||||||||
\(77\) | 0.404149 | 0.0460570 | ||||||||
\(78\) | −3.34000 | −0.378181 | ||||||||
\(79\) | 10.9481 | 1.23175 | 0.615877 | − | 0.787842i | \(-0.288802\pi\) | ||||
0.615877 | + | 0.787842i | \(0.288802\pi\) | |||||||
\(80\) | 0.843060 | 0.0942570 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.15693 | 0.569487 | ||||||||
\(83\) | 4.60944 | 0.505952 | 0.252976 | − | 0.967473i | \(-0.418591\pi\) | ||||
0.252976 | + | 0.967473i | \(0.418591\pi\) | |||||||
\(84\) | 0.534871 | 0.0583592 | ||||||||
\(85\) | 0.0434559 | 0.00471346 | ||||||||
\(86\) | 5.89039 | 0.635177 | ||||||||
\(87\) | 5.89217 | 0.631707 | ||||||||
\(88\) | −2.73363 | −0.291405 | ||||||||
\(89\) | 12.7830 | 1.35500 | 0.677500 | − | 0.735523i | \(-0.263063\pi\) | ||||
0.677500 | + | 0.735523i | \(0.263063\pi\) | |||||||
\(90\) | 1.74046 | 0.183460 | ||||||||
\(91\) | 1.64111 | 0.172035 | ||||||||
\(92\) | 11.4855 | 1.19744 | ||||||||
\(93\) | −5.40170 | −0.560130 | ||||||||
\(94\) | 7.02221 | 0.724286 | ||||||||
\(95\) | 8.41288 | 0.863143 | ||||||||
\(96\) | −5.79496 | −0.591446 | ||||||||
\(97\) | −0.603085 | −0.0612340 | −0.0306170 | − | 0.999531i | \(-0.509747\pi\) | ||||
−0.0306170 | + | 0.999531i | \(0.509747\pi\) | |||||||
\(98\) | −5.62333 | −0.568043 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0.691613 | 0.0691613 | ||||||||
\(101\) | −14.6545 | −1.45818 | −0.729088 | − | 0.684420i | \(-0.760056\pi\) | ||||
−0.729088 | + | 0.684420i | \(0.760056\pi\) | |||||||
\(102\) | −0.0168922 | −0.00167257 | ||||||||
\(103\) | 11.1666 | 1.10028 | 0.550138 | − | 0.835074i | \(-0.314575\pi\) | ||||
0.550138 | + | 0.835074i | \(0.314575\pi\) | |||||||
\(104\) | −11.1003 | −1.08848 | ||||||||
\(105\) | −0.855175 | −0.0834566 | ||||||||
\(106\) | 4.26366 | 0.414123 | ||||||||
\(107\) | −8.54990 | −0.826550 | −0.413275 | − | 0.910606i | \(-0.635615\pi\) | ||||
−0.413275 | + | 0.910606i | \(0.635615\pi\) | |||||||
\(108\) | 1.32345 | 0.127349 | ||||||||
\(109\) | 14.0443 | 1.34520 | 0.672598 | − | 0.740008i | \(-0.265178\pi\) | ||||
0.672598 | + | 0.740008i | \(0.265178\pi\) | |||||||
\(110\) | 1.74046 | 0.165946 | ||||||||
\(111\) | −1.99527 | −0.189383 | ||||||||
\(112\) | 0.161022 | 0.0152152 | ||||||||
\(113\) | 9.57510 | 0.900749 | 0.450375 | − | 0.892840i | \(-0.351290\pi\) | ||||
0.450375 | + | 0.892840i | \(0.351290\pi\) | |||||||
\(114\) | −3.27025 | −0.306287 | ||||||||
\(115\) | −18.3634 | −1.71240 | ||||||||
\(116\) | 7.79800 | 0.724026 | ||||||||
\(117\) | 4.06066 | 0.375409 | ||||||||
\(118\) | −0.525346 | −0.0483620 | ||||||||
\(119\) | 0.00829997 | 0.000760857 0 | ||||||||
\(120\) | 5.78433 | 0.528034 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.822526 | −0.0744680 | ||||||||
\(123\) | −6.26962 | −0.565313 | ||||||||
\(124\) | −7.14889 | −0.641989 | ||||||||
\(125\) | −11.6857 | −1.04520 | ||||||||
\(126\) | 0.332423 | 0.0296146 | ||||||||
\(127\) | 6.13941 | 0.544785 | 0.272392 | − | 0.962186i | \(-0.412185\pi\) | ||||
0.272392 | + | 0.962186i | \(0.412185\pi\) | |||||||
\(128\) | −8.32478 | −0.735813 | ||||||||
\(129\) | −7.16134 | −0.630521 | ||||||||
\(130\) | 7.06741 | 0.619853 | ||||||||
\(131\) | 5.50042 | 0.480574 | 0.240287 | − | 0.970702i | \(-0.422758\pi\) | ||||
0.240287 | + | 0.970702i | \(0.422758\pi\) | |||||||
\(132\) | 1.32345 | 0.115192 | ||||||||
\(133\) | 1.60684 | 0.139331 | ||||||||
\(134\) | 12.5053 | 1.08029 | ||||||||
\(135\) | −2.11599 | −0.182115 | ||||||||
\(136\) | −0.0561402 | −0.00481399 | ||||||||
\(137\) | −2.78969 | −0.238339 | −0.119170 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119170 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(138\) | 7.13822 | 0.607646 | ||||||||
\(139\) | −11.0724 | −0.939148 | −0.469574 | − | 0.882893i | \(-0.655592\pi\) | ||||
−0.469574 | + | 0.882893i | \(0.655592\pi\) | |||||||
\(140\) | −1.13178 | −0.0956531 | ||||||||
\(141\) | −8.53737 | −0.718976 | ||||||||
\(142\) | 9.44198 | 0.792354 | ||||||||
\(143\) | 4.06066 | 0.339570 | ||||||||
\(144\) | 0.398423 | 0.0332019 | ||||||||
\(145\) | −12.4678 | −1.03539 | ||||||||
\(146\) | −12.3662 | −1.02343 | ||||||||
\(147\) | 6.83666 | 0.563879 | ||||||||
\(148\) | −2.64064 | −0.217059 | ||||||||
\(149\) | 0.473710 | 0.0388079 | 0.0194039 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194039 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(150\) | 0.429838 | 0.0350961 | ||||||||
\(151\) | 13.2622 | 1.07927 | 0.539633 | − | 0.841900i | \(-0.318563\pi\) | ||||
0.539633 | + | 0.841900i | \(0.318563\pi\) | |||||||
\(152\) | −10.8685 | −0.881552 | ||||||||
\(153\) | 0.0205369 | 0.00166031 | ||||||||
\(154\) | 0.332423 | 0.0267874 | ||||||||
\(155\) | 11.4300 | 0.918076 | ||||||||
\(156\) | 5.37409 | 0.430271 | ||||||||
\(157\) | −12.7759 | −1.01963 | −0.509814 | − | 0.860285i | \(-0.670286\pi\) | ||||
−0.509814 | + | 0.860285i | \(0.670286\pi\) | |||||||
\(158\) | 9.00508 | 0.716405 | ||||||||
\(159\) | −5.18361 | −0.411087 | ||||||||
\(160\) | 12.2621 | 0.969403 | ||||||||
\(161\) | −3.50737 | −0.276419 | ||||||||
\(162\) | 0.822526 | 0.0646238 | ||||||||
\(163\) | 24.5359 | 1.92180 | 0.960900 | − | 0.276897i | \(-0.0893060\pi\) | ||||
0.960900 | + | 0.276897i | \(0.0893060\pi\) | |||||||
\(164\) | −8.29753 | −0.647928 | ||||||||
\(165\) | −2.11599 | −0.164730 | ||||||||
\(166\) | 3.79139 | 0.294269 | ||||||||
\(167\) | 3.95593 | 0.306119 | 0.153060 | − | 0.988217i | \(-0.451087\pi\) | ||||
0.153060 | + | 0.988217i | \(0.451087\pi\) | |||||||
\(168\) | 1.10479 | 0.0852365 | ||||||||
\(169\) | 3.48899 | 0.268384 | ||||||||
\(170\) | 0.0357436 | 0.00274141 | ||||||||
\(171\) | 3.97586 | 0.304041 | ||||||||
\(172\) | −9.47768 | −0.722666 | ||||||||
\(173\) | −21.5757 | −1.64037 | −0.820186 | − | 0.572097i | \(-0.806130\pi\) | ||||
−0.820186 | + | 0.572097i | \(0.806130\pi\) | |||||||
\(174\) | 4.84647 | 0.367410 | ||||||||
\(175\) | −0.211201 | −0.0159653 | ||||||||
\(176\) | 0.398423 | 0.0300323 | ||||||||
\(177\) | 0.638698 | 0.0480075 | ||||||||
\(178\) | 10.5144 | 0.788086 | ||||||||
\(179\) | −13.5654 | −1.01392 | −0.506962 | − | 0.861968i | \(-0.669232\pi\) | ||||
−0.506962 | + | 0.861968i | \(0.669232\pi\) | |||||||
\(180\) | −2.80041 | −0.208730 | ||||||||
\(181\) | −20.9000 | −1.55349 | −0.776744 | − | 0.629817i | \(-0.783130\pi\) | ||||
−0.776744 | + | 0.629817i | \(0.783130\pi\) | |||||||
\(182\) | 1.34986 | 0.100058 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 23.7235 | 1.74892 | ||||||||
\(185\) | 4.22197 | 0.310405 | ||||||||
\(186\) | −4.44304 | −0.325780 | ||||||||
\(187\) | 0.0205369 | 0.00150181 | ||||||||
\(188\) | −11.2988 | −0.824049 | ||||||||
\(189\) | −0.404149 | −0.0293975 | ||||||||
\(190\) | 6.91981 | 0.502016 | ||||||||
\(191\) | 2.45440 | 0.177594 | 0.0887971 | − | 0.996050i | \(-0.471698\pi\) | ||||
0.0887971 | + | 0.996050i | \(0.471698\pi\) | |||||||
\(192\) | −3.96966 | −0.286486 | ||||||||
\(193\) | −8.31456 | −0.598495 | −0.299248 | − | 0.954176i | \(-0.596736\pi\) | ||||
−0.299248 | + | 0.954176i | \(0.596736\pi\) | |||||||
\(194\) | −0.496053 | −0.0356146 | ||||||||
\(195\) | −8.59233 | −0.615309 | ||||||||
\(196\) | 9.04799 | 0.646285 | ||||||||
\(197\) | 18.8004 | 1.33947 | 0.669736 | − | 0.742599i | \(-0.266407\pi\) | ||||
0.669736 | + | 0.742599i | \(0.266407\pi\) | |||||||
\(198\) | 0.822526 | 0.0584544 | ||||||||
\(199\) | −7.84162 | −0.555877 | −0.277939 | − | 0.960599i | \(-0.589651\pi\) | ||||
−0.277939 | + | 0.960599i | \(0.589651\pi\) | |||||||
\(200\) | 1.42855 | 0.101013 | ||||||||
\(201\) | −15.2035 | −1.07237 | ||||||||
\(202\) | −12.0537 | −0.848096 | ||||||||
\(203\) | −2.38131 | −0.167136 | ||||||||
\(204\) | 0.0271796 | 0.00190295 | ||||||||
\(205\) | 13.2665 | 0.926569 | ||||||||
\(206\) | 9.18480 | 0.639935 | ||||||||
\(207\) | −8.67841 | −0.603191 | ||||||||
\(208\) | 1.61786 | 0.112179 | ||||||||
\(209\) | 3.97586 | 0.275016 | ||||||||
\(210\) | −0.703404 | −0.0485395 | ||||||||
\(211\) | −25.6632 | −1.76673 | −0.883364 | − | 0.468688i | \(-0.844727\pi\) | ||||
−0.883364 | + | 0.468688i | \(0.844727\pi\) | |||||||
\(212\) | −6.86025 | −0.471164 | ||||||||
\(213\) | −11.4793 | −0.786545 | ||||||||
\(214\) | −7.03252 | −0.480733 | ||||||||
\(215\) | 15.1533 | 1.03345 | ||||||||
\(216\) | 2.73363 | 0.186000 | ||||||||
\(217\) | 2.18309 | 0.148198 | ||||||||
\(218\) | 11.5518 | 0.782385 | ||||||||
\(219\) | 15.0344 | 1.01593 | ||||||||
\(220\) | −2.80041 | −0.188804 | ||||||||
\(221\) | 0.0833935 | 0.00560966 | ||||||||
\(222\) | −1.64116 | −0.110147 | ||||||||
\(223\) | 1.31581 | 0.0881130 | 0.0440565 | − | 0.999029i | \(-0.485972\pi\) | ||||
0.0440565 | + | 0.999029i | \(0.485972\pi\) | |||||||
\(224\) | 2.34203 | 0.156483 | ||||||||
\(225\) | −0.522583 | −0.0348389 | ||||||||
\(226\) | 7.87577 | 0.523888 | ||||||||
\(227\) | 7.33476 | 0.486825 | 0.243413 | − | 0.969923i | \(-0.421733\pi\) | ||||
0.243413 | + | 0.969923i | \(0.421733\pi\) | |||||||
\(228\) | 5.26185 | 0.348475 | ||||||||
\(229\) | −4.61757 | −0.305137 | −0.152569 | − | 0.988293i | \(-0.548755\pi\) | ||||
−0.152569 | + | 0.988293i | \(0.548755\pi\) | |||||||
\(230\) | −15.1044 | −0.995955 | ||||||||
\(231\) | −0.404149 | −0.0265910 | ||||||||
\(232\) | 16.1070 | 1.05748 | ||||||||
\(233\) | 29.1255 | 1.90807 | 0.954036 | − | 0.299692i | \(-0.0968839\pi\) | ||||
0.954036 | + | 0.299692i | \(0.0968839\pi\) | |||||||
\(234\) | 3.34000 | 0.218343 | ||||||||
\(235\) | 18.0650 | 1.17843 | ||||||||
\(236\) | 0.845285 | 0.0550234 | ||||||||
\(237\) | −10.9481 | −0.711154 | ||||||||
\(238\) | 0.00682694 | 0.000442525 0 | ||||||||
\(239\) | −30.6121 | −1.98013 | −0.990064 | − | 0.140614i | \(-0.955092\pi\) | ||||
−0.990064 | + | 0.140614i | \(0.955092\pi\) | |||||||
\(240\) | −0.843060 | −0.0544193 | ||||||||
\(241\) | 22.3844 | 1.44191 | 0.720954 | − | 0.692983i | \(-0.243704\pi\) | ||||
0.720954 | + | 0.692983i | \(0.243704\pi\) | |||||||
\(242\) | 0.822526 | 0.0528740 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.32345 | 0.0847253 | ||||||||
\(245\) | −14.4663 | −0.924219 | ||||||||
\(246\) | −5.15693 | −0.328794 | ||||||||
\(247\) | 16.1446 | 1.02726 | ||||||||
\(248\) | −14.7662 | −0.937656 | ||||||||
\(249\) | −4.60944 | −0.292112 | ||||||||
\(250\) | −9.61182 | −0.607905 | ||||||||
\(251\) | 21.4637 | 1.35478 | 0.677390 | − | 0.735624i | \(-0.263111\pi\) | ||||
0.677390 | + | 0.735624i | \(0.263111\pi\) | |||||||
\(252\) | −0.534871 | −0.0336937 | ||||||||
\(253\) | −8.67841 | −0.545607 | ||||||||
\(254\) | 5.04983 | 0.316854 | ||||||||
\(255\) | −0.0434559 | −0.00272132 | ||||||||
\(256\) | −14.7867 | −0.924167 | ||||||||
\(257\) | 4.42849 | 0.276242 | 0.138121 | − | 0.990415i | \(-0.455894\pi\) | ||||
0.138121 | + | 0.990415i | \(0.455894\pi\) | |||||||
\(258\) | −5.89039 | −0.366720 | ||||||||
\(259\) | 0.806385 | 0.0501064 | ||||||||
\(260\) | −11.3715 | −0.705232 | ||||||||
\(261\) | −5.89217 | −0.364716 | ||||||||
\(262\) | 4.52424 | 0.279509 | ||||||||
\(263\) | −26.2060 | −1.61593 | −0.807966 | − | 0.589230i | \(-0.799431\pi\) | ||||
−0.807966 | + | 0.589230i | \(0.799431\pi\) | |||||||
\(264\) | 2.73363 | 0.168243 | ||||||||
\(265\) | 10.9685 | 0.673788 | ||||||||
\(266\) | 1.32167 | 0.0810366 | ||||||||
\(267\) | −12.7830 | −0.782309 | ||||||||
\(268\) | −20.1211 | −1.22909 | ||||||||
\(269\) | −11.4188 | −0.696217 | −0.348109 | − | 0.937454i | \(-0.613176\pi\) | ||||
−0.348109 | + | 0.937454i | \(0.613176\pi\) | |||||||
\(270\) | −1.74046 | −0.105921 | ||||||||
\(271\) | 2.05980 | 0.125124 | 0.0625620 | − | 0.998041i | \(-0.480073\pi\) | ||||
0.0625620 | + | 0.998041i | \(0.480073\pi\) | |||||||
\(272\) | 0.00818239 | 0.000496130 0 | ||||||||
\(273\) | −1.64111 | −0.0993246 | ||||||||
\(274\) | −2.29459 | −0.138621 | ||||||||
\(275\) | −0.522583 | −0.0315129 | ||||||||
\(276\) | −11.4855 | −0.691343 | ||||||||
\(277\) | 27.0262 | 1.62385 | 0.811923 | − | 0.583765i | \(-0.198421\pi\) | ||||
0.811923 | + | 0.583765i | \(0.198421\pi\) | |||||||
\(278\) | −9.10733 | −0.546221 | ||||||||
\(279\) | 5.40170 | 0.323391 | ||||||||
\(280\) | −2.33773 | −0.139706 | ||||||||
\(281\) | 4.85590 | 0.289679 | 0.144839 | − | 0.989455i | \(-0.453733\pi\) | ||||
0.144839 | + | 0.989455i | \(0.453733\pi\) | |||||||
\(282\) | −7.02221 | −0.418167 | ||||||||
\(283\) | 15.0805 | 0.896442 | 0.448221 | − | 0.893923i | \(-0.352058\pi\) | ||||
0.448221 | + | 0.893923i | \(0.352058\pi\) | |||||||
\(284\) | −15.1922 | −0.901493 | ||||||||
\(285\) | −8.41288 | −0.498336 | ||||||||
\(286\) | 3.34000 | 0.197498 | ||||||||
\(287\) | 2.53386 | 0.149569 | ||||||||
\(288\) | 5.79496 | 0.341472 | ||||||||
\(289\) | −16.9996 | −0.999975 | ||||||||
\(290\) | −10.2551 | −0.602199 | ||||||||
\(291\) | 0.603085 | 0.0353535 | ||||||||
\(292\) | 19.8973 | 1.16440 | ||||||||
\(293\) | −19.5057 | −1.13954 | −0.569769 | − | 0.821805i | \(-0.692967\pi\) | ||||
−0.569769 | + | 0.821805i | \(0.692967\pi\) | |||||||
\(294\) | 5.62333 | 0.327960 | ||||||||
\(295\) | −1.35148 | −0.0786861 | ||||||||
\(296\) | −5.45432 | −0.317026 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0.389639 | 0.0225712 | ||||||||
\(299\) | −35.2401 | −2.03799 | ||||||||
\(300\) | −0.691613 | −0.0399303 | ||||||||
\(301\) | 2.89425 | 0.166822 | ||||||||
\(302\) | 10.9085 | 0.627716 | ||||||||
\(303\) | 14.6545 | 0.841879 | ||||||||
\(304\) | 1.58407 | 0.0908529 | ||||||||
\(305\) | −2.11599 | −0.121161 | ||||||||
\(306\) | 0.0168922 | 0.000965660 0 | ||||||||
\(307\) | 7.49773 | 0.427918 | 0.213959 | − | 0.976843i | \(-0.431364\pi\) | ||||
0.213959 | + | 0.976843i | \(0.431364\pi\) | |||||||
\(308\) | −0.534871 | −0.0304771 | ||||||||
\(309\) | −11.1666 | −0.635244 | ||||||||
\(310\) | 9.40143 | 0.533966 | ||||||||
\(311\) | 17.7437 | 1.00616 | 0.503078 | − | 0.864241i | \(-0.332201\pi\) | ||||
0.503078 | + | 0.864241i | \(0.332201\pi\) | |||||||
\(312\) | 11.1003 | 0.628433 | ||||||||
\(313\) | 13.3708 | 0.755763 | 0.377882 | − | 0.925854i | \(-0.376653\pi\) | ||||
0.377882 | + | 0.925854i | \(0.376653\pi\) | |||||||
\(314\) | −10.5085 | −0.593030 | ||||||||
\(315\) | 0.855175 | 0.0481837 | ||||||||
\(316\) | −14.4892 | −0.815083 | ||||||||
\(317\) | −10.5527 | −0.592699 | −0.296350 | − | 0.955079i | \(-0.595769\pi\) | ||||
−0.296350 | + | 0.955079i | \(0.595769\pi\) | |||||||
\(318\) | −4.26366 | −0.239094 | ||||||||
\(319\) | −5.89217 | −0.329898 | ||||||||
\(320\) | 8.39977 | 0.469561 | ||||||||
\(321\) | 8.54990 | 0.477209 | ||||||||
\(322\) | −2.88490 | −0.160769 | ||||||||
\(323\) | 0.0816519 | 0.00454323 | ||||||||
\(324\) | −1.32345 | −0.0735250 | ||||||||
\(325\) | −2.12203 | −0.117709 | ||||||||
\(326\) | 20.1814 | 1.11775 | ||||||||
\(327\) | −14.0443 | −0.776650 | ||||||||
\(328\) | −17.1388 | −0.946331 | ||||||||
\(329\) | 3.45037 | 0.190225 | ||||||||
\(330\) | −1.74046 | −0.0958090 | ||||||||
\(331\) | −5.63583 | −0.309773 | −0.154887 | − | 0.987932i | \(-0.549501\pi\) | ||||
−0.154887 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(332\) | −6.10037 | −0.334801 | ||||||||
\(333\) | 1.99527 | 0.109340 | ||||||||
\(334\) | 3.25386 | 0.178043 | ||||||||
\(335\) | 32.1704 | 1.75766 | ||||||||
\(336\) | −0.161022 | −0.00878449 | ||||||||
\(337\) | 21.1177 | 1.15036 | 0.575178 | − | 0.818028i | \(-0.304933\pi\) | ||||
0.575178 | + | 0.818028i | \(0.304933\pi\) | |||||||
\(338\) | 2.86979 | 0.156096 | ||||||||
\(339\) | −9.57510 | −0.520048 | ||||||||
\(340\) | −0.0575118 | −0.00311901 | ||||||||
\(341\) | 5.40170 | 0.292519 | ||||||||
\(342\) | 3.27025 | 0.176835 | ||||||||
\(343\) | −5.59207 | −0.301943 | ||||||||
\(344\) | −19.5764 | −1.05549 | ||||||||
\(345\) | 18.3634 | 0.988654 | ||||||||
\(346\) | −17.7466 | −0.954063 | ||||||||
\(347\) | −24.5687 | −1.31892 | −0.659458 | − | 0.751742i | \(-0.729214\pi\) | ||||
−0.659458 | + | 0.751742i | \(0.729214\pi\) | |||||||
\(348\) | −7.79800 | −0.418017 | ||||||||
\(349\) | 3.91197 | 0.209403 | 0.104701 | − | 0.994504i | \(-0.466611\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466611\pi\) | |||||||
\(350\) | −0.173719 | −0.00928565 | ||||||||
\(351\) | −4.06066 | −0.216742 | ||||||||
\(352\) | 5.79496 | 0.308873 | ||||||||
\(353\) | −28.5152 | −1.51771 | −0.758856 | − | 0.651259i | \(-0.774241\pi\) | ||||
−0.758856 | + | 0.651259i | \(0.774241\pi\) | |||||||
\(354\) | 0.525346 | 0.0279218 | ||||||||
\(355\) | 24.2900 | 1.28918 | ||||||||
\(356\) | −16.9177 | −0.896638 | ||||||||
\(357\) | −0.00829997 | −0.000439281 0 | ||||||||
\(358\) | −11.1579 | −0.589712 | ||||||||
\(359\) | −27.2384 | −1.43759 | −0.718793 | − | 0.695224i | \(-0.755305\pi\) | ||||
−0.718793 | + | 0.695224i | \(0.755305\pi\) | |||||||
\(360\) | −5.78433 | −0.304861 | ||||||||
\(361\) | −3.19255 | −0.168029 | ||||||||
\(362\) | −17.1908 | −0.903530 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −2.17193 | −0.113840 | ||||||||
\(365\) | −31.8127 | −1.66515 | ||||||||
\(366\) | 0.822526 | 0.0429941 | ||||||||
\(367\) | −37.7100 | −1.96845 | −0.984224 | − | 0.176927i | \(-0.943384\pi\) | ||||
−0.984224 | + | 0.176927i | \(0.943384\pi\) | |||||||
\(368\) | −3.45768 | −0.180244 | ||||||||
\(369\) | 6.26962 | 0.326383 | ||||||||
\(370\) | 3.47268 | 0.180536 | ||||||||
\(371\) | 2.09495 | 0.108764 | ||||||||
\(372\) | 7.14889 | 0.370653 | ||||||||
\(373\) | 4.83715 | 0.250458 | 0.125229 | − | 0.992128i | \(-0.460033\pi\) | ||||
0.125229 | + | 0.992128i | \(0.460033\pi\) | |||||||
\(374\) | 0.0168922 | 0.000873472 0 | ||||||||
\(375\) | 11.6857 | 0.603449 | ||||||||
\(376\) | −23.3380 | −1.20356 | ||||||||
\(377\) | −23.9261 | −1.23226 | ||||||||
\(378\) | −0.332423 | −0.0170980 | ||||||||
\(379\) | −35.2816 | −1.81229 | −0.906146 | − | 0.422965i | \(-0.860989\pi\) | ||||
−0.906146 | + | 0.422965i | \(0.860989\pi\) | |||||||
\(380\) | −11.1340 | −0.571164 | ||||||||
\(381\) | −6.13941 | −0.314532 | ||||||||
\(382\) | 2.01881 | 0.103291 | ||||||||
\(383\) | 18.3228 | 0.936253 | 0.468127 | − | 0.883661i | \(-0.344929\pi\) | ||||
0.468127 | + | 0.883661i | \(0.344929\pi\) | |||||||
\(384\) | 8.32478 | 0.424822 | ||||||||
\(385\) | 0.855175 | 0.0435838 | ||||||||
\(386\) | −6.83894 | −0.348093 | ||||||||
\(387\) | 7.16134 | 0.364031 | ||||||||
\(388\) | 0.798153 | 0.0405201 | ||||||||
\(389\) | −34.4388 | −1.74612 | −0.873059 | − | 0.487614i | \(-0.837867\pi\) | ||||
−0.873059 | + | 0.487614i | \(0.837867\pi\) | |||||||
\(390\) | −7.06741 | −0.357872 | ||||||||
\(391\) | −0.178228 | −0.00901337 | ||||||||
\(392\) | 18.6889 | 0.943931 | ||||||||
\(393\) | −5.50042 | −0.277460 | ||||||||
\(394\) | 15.4638 | 0.779056 | ||||||||
\(395\) | 23.1660 | 1.16561 | ||||||||
\(396\) | −1.32345 | −0.0665059 | ||||||||
\(397\) | −6.67209 | −0.334862 | −0.167431 | − | 0.985884i | \(-0.553547\pi\) | ||||
−0.167431 | + | 0.985884i | \(0.553547\pi\) | |||||||
\(398\) | −6.44993 | −0.323306 | ||||||||
\(399\) | −1.60684 | −0.0804425 | ||||||||
\(400\) | −0.208209 | −0.0104105 | ||||||||
\(401\) | −19.4145 | −0.969515 | −0.484757 | − | 0.874649i | \(-0.661092\pi\) | ||||
−0.484757 | + | 0.874649i | \(0.661092\pi\) | |||||||
\(402\) | −12.5053 | −0.623706 | ||||||||
\(403\) | 21.9345 | 1.09264 | ||||||||
\(404\) | 19.3945 | 0.964912 | ||||||||
\(405\) | 2.11599 | 0.105144 | ||||||||
\(406\) | −1.95869 | −0.0972083 | ||||||||
\(407\) | 1.99527 | 0.0989018 | ||||||||
\(408\) | 0.0561402 | 0.00277936 | ||||||||
\(409\) | 0.767851 | 0.0379678 | 0.0189839 | − | 0.999820i | \(-0.493957\pi\) | ||||
0.0189839 | + | 0.999820i | \(0.493957\pi\) | |||||||
\(410\) | 10.9120 | 0.538906 | ||||||||
\(411\) | 2.78969 | 0.137605 | ||||||||
\(412\) | −14.7784 | −0.728080 | ||||||||
\(413\) | −0.258129 | −0.0127017 | ||||||||
\(414\) | −7.13822 | −0.350824 | ||||||||
\(415\) | 9.75354 | 0.478782 | ||||||||
\(416\) | 23.5314 | 1.15372 | ||||||||
\(417\) | 11.0724 | 0.542217 | ||||||||
\(418\) | 3.27025 | 0.159953 | ||||||||
\(419\) | 17.3337 | 0.846806 | 0.423403 | − | 0.905941i | \(-0.360835\pi\) | ||||
0.423403 | + | 0.905941i | \(0.360835\pi\) | |||||||
\(420\) | 1.13178 | 0.0552253 | ||||||||
\(421\) | 12.0651 | 0.588016 | 0.294008 | − | 0.955803i | \(-0.405011\pi\) | ||||
0.294008 | + | 0.955803i | \(0.405011\pi\) | |||||||
\(422\) | −21.1087 | −1.02755 | ||||||||
\(423\) | 8.53737 | 0.415101 | ||||||||
\(424\) | −14.1700 | −0.688158 | ||||||||
\(425\) | −0.0107322 | −0.000520590 0 | ||||||||
\(426\) | −9.44198 | −0.457466 | ||||||||
\(427\) | −0.404149 | −0.0195581 | ||||||||
\(428\) | 11.3154 | 0.546949 | ||||||||
\(429\) | −4.06066 | −0.196051 | ||||||||
\(430\) | 12.4640 | 0.601068 | ||||||||
\(431\) | −29.2010 | −1.40656 | −0.703282 | − | 0.710911i | \(-0.748283\pi\) | ||||
−0.703282 | + | 0.710911i | \(0.748283\pi\) | |||||||
\(432\) | −0.398423 | −0.0191692 | ||||||||
\(433\) | −35.8038 | −1.72062 | −0.860311 | − | 0.509769i | \(-0.829731\pi\) | ||||
−0.860311 | + | 0.509769i | \(0.829731\pi\) | |||||||
\(434\) | 1.79565 | 0.0861939 | ||||||||
\(435\) | 12.4678 | 0.597785 | ||||||||
\(436\) | −18.5869 | −0.890151 | ||||||||
\(437\) | −34.5041 | −1.65056 | ||||||||
\(438\) | 12.3662 | 0.590880 | ||||||||
\(439\) | 40.8584 | 1.95006 | 0.975032 | − | 0.222063i | \(-0.0712791\pi\) | ||||
0.975032 | + | 0.222063i | \(0.0712791\pi\) | |||||||
\(440\) | −5.78433 | −0.275757 | ||||||||
\(441\) | −6.83666 | −0.325555 | ||||||||
\(442\) | 0.0685934 | 0.00326265 | ||||||||
\(443\) | −27.9834 | −1.32953 | −0.664767 | − | 0.747051i | \(-0.731469\pi\) | ||||
−0.664767 | + | 0.747051i | \(0.731469\pi\) | |||||||
\(444\) | 2.64064 | 0.125319 | ||||||||
\(445\) | 27.0488 | 1.28224 | ||||||||
\(446\) | 1.08229 | 0.0512477 | ||||||||
\(447\) | −0.473710 | −0.0224057 | ||||||||
\(448\) | 1.60433 | 0.0757977 | ||||||||
\(449\) | −25.0254 | −1.18102 | −0.590512 | − | 0.807029i | \(-0.701074\pi\) | ||||
−0.590512 | + | 0.807029i | \(0.701074\pi\) | |||||||
\(450\) | −0.429838 | −0.0202628 | ||||||||
\(451\) | 6.26962 | 0.295225 | ||||||||
\(452\) | −12.6722 | −0.596049 | ||||||||
\(453\) | −13.2622 | −0.623115 | ||||||||
\(454\) | 6.03303 | 0.283144 | ||||||||
\(455\) | 3.47258 | 0.162797 | ||||||||
\(456\) | 10.8685 | 0.508964 | ||||||||
\(457\) | 3.70365 | 0.173249 | 0.0866247 | − | 0.996241i | \(-0.472392\pi\) | ||||
0.0866247 | + | 0.996241i | \(0.472392\pi\) | |||||||
\(458\) | −3.79807 | −0.177472 | ||||||||
\(459\) | −0.0205369 | −0.000958581 0 | ||||||||
\(460\) | 24.3031 | 1.13314 | ||||||||
\(461\) | −15.8022 | −0.735982 | −0.367991 | − | 0.929829i | \(-0.619954\pi\) | ||||
−0.367991 | + | 0.929829i | \(0.619954\pi\) | |||||||
\(462\) | −0.332423 | −0.0154657 | ||||||||
\(463\) | −25.2470 | −1.17333 | −0.586665 | − | 0.809830i | \(-0.699559\pi\) | ||||
−0.586665 | + | 0.809830i | \(0.699559\pi\) | |||||||
\(464\) | −2.34758 | −0.108984 | ||||||||
\(465\) | −11.4300 | −0.530051 | ||||||||
\(466\) | 23.9564 | 1.10976 | ||||||||
\(467\) | −17.2785 | −0.799552 | −0.399776 | − | 0.916613i | \(-0.630912\pi\) | ||||
−0.399776 | + | 0.916613i | \(0.630912\pi\) | |||||||
\(468\) | −5.37409 | −0.248417 | ||||||||
\(469\) | 6.14447 | 0.283725 | ||||||||
\(470\) | 14.8589 | 0.685391 | ||||||||
\(471\) | 12.7759 | 0.588683 | ||||||||
\(472\) | 1.74596 | 0.0803643 | ||||||||
\(473\) | 7.16134 | 0.329279 | ||||||||
\(474\) | −9.00508 | −0.413617 | ||||||||
\(475\) | −2.07771 | −0.0953321 | ||||||||
\(476\) | −0.0109846 | −0.000503478 0 | ||||||||
\(477\) | 5.18361 | 0.237341 | ||||||||
\(478\) | −25.1792 | −1.15167 | ||||||||
\(479\) | 10.8839 | 0.497297 | 0.248648 | − | 0.968594i | \(-0.420014\pi\) | ||||
0.248648 | + | 0.968594i | \(0.420014\pi\) | |||||||
\(480\) | −12.2621 | −0.559685 | ||||||||
\(481\) | 8.10212 | 0.369425 | ||||||||
\(482\) | 18.4118 | 0.838634 | ||||||||
\(483\) | 3.50737 | 0.159591 | ||||||||
\(484\) | −1.32345 | −0.0601569 | ||||||||
\(485\) | −1.27612 | −0.0579457 | ||||||||
\(486\) | −0.822526 | −0.0373105 | ||||||||
\(487\) | 39.0162 | 1.76799 | 0.883997 | − | 0.467492i | \(-0.154842\pi\) | ||||
0.883997 | + | 0.467492i | \(0.154842\pi\) | |||||||
\(488\) | 2.73363 | 0.123745 | ||||||||
\(489\) | −24.5359 | −1.10955 | ||||||||
\(490\) | −11.8989 | −0.537539 | ||||||||
\(491\) | 30.0322 | 1.35533 | 0.677667 | − | 0.735369i | \(-0.262991\pi\) | ||||
0.677667 | + | 0.735369i | \(0.262991\pi\) | |||||||
\(492\) | 8.29753 | 0.374082 | ||||||||
\(493\) | −0.121007 | −0.00544989 | ||||||||
\(494\) | 13.2794 | 0.597467 | ||||||||
\(495\) | 2.11599 | 0.0951067 | ||||||||
\(496\) | 2.15216 | 0.0966350 | ||||||||
\(497\) | 4.63933 | 0.208102 | ||||||||
\(498\) | −3.79139 | −0.169896 | ||||||||
\(499\) | 25.6100 | 1.14646 | 0.573232 | − | 0.819393i | \(-0.305690\pi\) | ||||
0.573232 | + | 0.819393i | \(0.305690\pi\) | |||||||
\(500\) | 15.4655 | 0.691638 | ||||||||
\(501\) | −3.95593 | −0.176738 | ||||||||
\(502\) | 17.6545 | 0.787958 | ||||||||
\(503\) | −9.23707 | −0.411861 | −0.205930 | − | 0.978567i | \(-0.566022\pi\) | ||||
−0.205930 | + | 0.978567i | \(0.566022\pi\) | |||||||
\(504\) | −1.10479 | −0.0492113 | ||||||||
\(505\) | −31.0088 | −1.37987 | ||||||||
\(506\) | −7.13822 | −0.317333 | ||||||||
\(507\) | −3.48899 | −0.154952 | ||||||||
\(508\) | −8.12521 | −0.360498 | ||||||||
\(509\) | 32.4717 | 1.43928 | 0.719642 | − | 0.694345i | \(-0.244306\pi\) | ||||
0.719642 | + | 0.694345i | \(0.244306\pi\) | |||||||
\(510\) | −0.0357436 | −0.00158276 | ||||||||
\(511\) | −6.07615 | −0.268793 | ||||||||
\(512\) | 4.48713 | 0.198305 | ||||||||
\(513\) | −3.97586 | −0.175538 | ||||||||
\(514\) | 3.64255 | 0.160666 | ||||||||
\(515\) | 23.6284 | 1.04119 | ||||||||
\(516\) | 9.47768 | 0.417232 | ||||||||
\(517\) | 8.53737 | 0.375473 | ||||||||
\(518\) | 0.663273 | 0.0291425 | ||||||||
\(519\) | 21.5757 | 0.947069 | ||||||||
\(520\) | −23.4882 | −1.03003 | ||||||||
\(521\) | 12.2202 | 0.535375 | 0.267687 | − | 0.963506i | \(-0.413741\pi\) | ||||
0.267687 | + | 0.963506i | \(0.413741\pi\) | |||||||
\(522\) | −4.84647 | −0.212124 | ||||||||
\(523\) | −24.8557 | −1.08686 | −0.543432 | − | 0.839453i | \(-0.682876\pi\) | ||||
−0.543432 | + | 0.839453i | \(0.682876\pi\) | |||||||
\(524\) | −7.27954 | −0.318008 | ||||||||
\(525\) | 0.211201 | 0.00921758 | ||||||||
\(526\) | −21.5551 | −0.939848 | ||||||||
\(527\) | 0.110934 | 0.00483238 | ||||||||
\(528\) | −0.398423 | −0.0173392 | ||||||||
\(529\) | 52.3148 | 2.27456 | ||||||||
\(530\) | 9.02186 | 0.391884 | ||||||||
\(531\) | −0.638698 | −0.0277171 | ||||||||
\(532\) | −2.12657 | −0.0921986 | ||||||||
\(533\) | 25.4588 | 1.10274 | ||||||||
\(534\) | −10.5144 | −0.455002 | ||||||||
\(535\) | −18.0915 | −0.782164 | ||||||||
\(536\) | −41.5606 | −1.79515 | ||||||||
\(537\) | 13.5654 | 0.585389 | ||||||||
\(538\) | −9.39227 | −0.404930 | ||||||||
\(539\) | −6.83666 | −0.294476 | ||||||||
\(540\) | 2.80041 | 0.120510 | ||||||||
\(541\) | 6.76305 | 0.290766 | 0.145383 | − | 0.989375i | \(-0.453559\pi\) | ||||
0.145383 | + | 0.989375i | \(0.453559\pi\) | |||||||
\(542\) | 1.69424 | 0.0727739 | ||||||||
\(543\) | 20.9000 | 0.896906 | ||||||||
\(544\) | 0.119011 | 0.00510254 | ||||||||
\(545\) | 29.7175 | 1.27296 | ||||||||
\(546\) | −1.34986 | −0.0577686 | ||||||||
\(547\) | 22.0518 | 0.942865 | 0.471432 | − | 0.881902i | \(-0.343737\pi\) | ||||
0.471432 | + | 0.881902i | \(0.343737\pi\) | |||||||
\(548\) | 3.69202 | 0.157715 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −0.429838 | −0.0183284 | ||||||||
\(551\) | −23.4264 | −0.998000 | ||||||||
\(552\) | −23.7235 | −1.00974 | ||||||||
\(553\) | 4.42465 | 0.188155 | ||||||||
\(554\) | 22.2297 | 0.944451 | ||||||||
\(555\) | −4.22197 | −0.179213 | ||||||||
\(556\) | 14.6538 | 0.621458 | ||||||||
\(557\) | 14.7373 | 0.624438 | 0.312219 | − | 0.950010i | \(-0.398928\pi\) | ||||
0.312219 | + | 0.950010i | \(0.398928\pi\) | |||||||
\(558\) | 4.44304 | 0.188089 | ||||||||
\(559\) | 29.0798 | 1.22994 | ||||||||
\(560\) | 0.340722 | 0.0143981 | ||||||||
\(561\) | −0.0205369 | −0.000867069 0 | ||||||||
\(562\) | 3.99411 | 0.168481 | ||||||||
\(563\) | −6.78450 | −0.285933 | −0.142966 | − | 0.989728i | \(-0.545664\pi\) | ||||
−0.142966 | + | 0.989728i | \(0.545664\pi\) | |||||||
\(564\) | 11.2988 | 0.475765 | ||||||||
\(565\) | 20.2608 | 0.852379 | ||||||||
\(566\) | 12.4041 | 0.521383 | ||||||||
\(567\) | 0.404149 | 0.0169727 | ||||||||
\(568\) | −31.3800 | −1.31667 | ||||||||
\(569\) | 10.9922 | 0.460817 | 0.230409 | − | 0.973094i | \(-0.425994\pi\) | ||||
0.230409 | + | 0.973094i | \(0.425994\pi\) | |||||||
\(570\) | −6.91981 | −0.289839 | ||||||||
\(571\) | −41.9268 | −1.75458 | −0.877290 | − | 0.479961i | \(-0.840651\pi\) | ||||
−0.877290 | + | 0.479961i | \(0.840651\pi\) | |||||||
\(572\) | −5.37409 | −0.224702 | ||||||||
\(573\) | −2.45440 | −0.102534 | ||||||||
\(574\) | 2.08417 | 0.0869914 | ||||||||
\(575\) | 4.53519 | 0.189130 | ||||||||
\(576\) | 3.96966 | 0.165403 | ||||||||
\(577\) | 22.2721 | 0.927200 | 0.463600 | − | 0.886045i | \(-0.346558\pi\) | ||||
0.463600 | + | 0.886045i | \(0.346558\pi\) | |||||||
\(578\) | −13.9826 | −0.581599 | ||||||||
\(579\) | 8.31456 | 0.345541 | ||||||||
\(580\) | 16.5005 | 0.685146 | ||||||||
\(581\) | 1.86290 | 0.0772861 | ||||||||
\(582\) | 0.496053 | 0.0205621 | ||||||||
\(583\) | 5.18361 | 0.214683 | ||||||||
\(584\) | 41.0985 | 1.70067 | ||||||||
\(585\) | 8.59233 | 0.355249 | ||||||||
\(586\) | −16.0440 | −0.662771 | ||||||||
\(587\) | −37.4028 | −1.54378 | −0.771888 | − | 0.635758i | \(-0.780688\pi\) | ||||
−0.771888 | + | 0.635758i | \(0.780688\pi\) | |||||||
\(588\) | −9.04799 | −0.373133 | ||||||||
\(589\) | 21.4764 | 0.884920 | ||||||||
\(590\) | −1.11163 | −0.0457649 | ||||||||
\(591\) | −18.8004 | −0.773345 | ||||||||
\(592\) | 0.794962 | 0.0326727 | ||||||||
\(593\) | −39.4377 | −1.61951 | −0.809756 | − | 0.586767i | \(-0.800400\pi\) | ||||
−0.809756 | + | 0.586767i | \(0.800400\pi\) | |||||||
\(594\) | −0.822526 | −0.0337487 | ||||||||
\(595\) | 0.0175627 | 0.000719999 0 | ||||||||
\(596\) | −0.626932 | −0.0256801 | ||||||||
\(597\) | 7.84162 | 0.320936 | ||||||||
\(598\) | −28.9859 | −1.18532 | ||||||||
\(599\) | 20.8174 | 0.850578 | 0.425289 | − | 0.905058i | \(-0.360172\pi\) | ||||
0.425289 | + | 0.905058i | \(0.360172\pi\) | |||||||
\(600\) | −1.42855 | −0.0583201 | ||||||||
\(601\) | 5.46084 | 0.222752 | 0.111376 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111376 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(602\) | 2.38059 | 0.0970258 | ||||||||
\(603\) | 15.2035 | 0.619134 | ||||||||
\(604\) | −17.5519 | −0.714178 | ||||||||
\(605\) | 2.11599 | 0.0860273 | ||||||||
\(606\) | 12.0537 | 0.489648 | ||||||||
\(607\) | 0.731366 | 0.0296852 | 0.0148426 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148426 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(608\) | 23.0400 | 0.934394 | ||||||||
\(609\) | 2.38131 | 0.0964957 | ||||||||
\(610\) | −1.74046 | −0.0704691 | ||||||||
\(611\) | 34.6674 | 1.40249 | ||||||||
\(612\) | −0.0271796 | −0.00109867 | ||||||||
\(613\) | 5.30018 | 0.214072 | 0.107036 | − | 0.994255i | \(-0.465864\pi\) | ||||
0.107036 | + | 0.994255i | \(0.465864\pi\) | |||||||
\(614\) | 6.16708 | 0.248883 | ||||||||
\(615\) | −13.2665 | −0.534955 | ||||||||
\(616\) | −1.10479 | −0.0445133 | ||||||||
\(617\) | −16.1004 | −0.648176 | −0.324088 | − | 0.946027i | \(-0.605057\pi\) | ||||
−0.324088 | + | 0.946027i | \(0.605057\pi\) | |||||||
\(618\) | −9.18480 | −0.369467 | ||||||||
\(619\) | 16.9174 | 0.679968 | 0.339984 | − | 0.940431i | \(-0.389578\pi\) | ||||
0.339984 | + | 0.940431i | \(0.389578\pi\) | |||||||
\(620\) | −15.1270 | −0.607514 | ||||||||
\(621\) | 8.67841 | 0.348253 | ||||||||
\(622\) | 14.5947 | 0.585194 | ||||||||
\(623\) | 5.16625 | 0.206981 | ||||||||
\(624\) | −1.61786 | −0.0647664 | ||||||||
\(625\) | −22.1140 | −0.884560 | ||||||||
\(626\) | 10.9978 | 0.439562 | ||||||||
\(627\) | −3.97586 | −0.158780 | ||||||||
\(628\) | 16.9083 | 0.674714 | ||||||||
\(629\) | 0.0409767 | 0.00163385 | ||||||||
\(630\) | 0.703404 | 0.0280243 | ||||||||
\(631\) | −43.2520 | −1.72184 | −0.860918 | − | 0.508743i | \(-0.830110\pi\) | ||||
−0.860918 | + | 0.508743i | \(0.830110\pi\) | |||||||
\(632\) | −29.9279 | −1.19047 | ||||||||
\(633\) | 25.6632 | 1.02002 | ||||||||
\(634\) | −8.67988 | −0.344722 | ||||||||
\(635\) | 12.9909 | 0.515530 | ||||||||
\(636\) | 6.86025 | 0.272027 | ||||||||
\(637\) | −27.7614 | −1.09995 | ||||||||
\(638\) | −4.84647 | −0.191873 | ||||||||
\(639\) | 11.4793 | 0.454112 | ||||||||
\(640\) | −17.6152 | −0.696300 | ||||||||
\(641\) | 22.4987 | 0.888644 | 0.444322 | − | 0.895867i | \(-0.353445\pi\) | ||||
0.444322 | + | 0.895867i | \(0.353445\pi\) | |||||||
\(642\) | 7.03252 | 0.277551 | ||||||||
\(643\) | 16.3425 | 0.644487 | 0.322243 | − | 0.946657i | \(-0.395563\pi\) | ||||
0.322243 | + | 0.946657i | \(0.395563\pi\) | |||||||
\(644\) | 4.64183 | 0.182914 | ||||||||
\(645\) | −15.1533 | −0.596662 | ||||||||
\(646\) | 0.0671608 | 0.00264241 | ||||||||
\(647\) | −18.5358 | −0.728719 | −0.364360 | − | 0.931258i | \(-0.618712\pi\) | ||||
−0.364360 | + | 0.931258i | \(0.618712\pi\) | |||||||
\(648\) | −2.73363 | −0.107387 | ||||||||
\(649\) | −0.638698 | −0.0250711 | ||||||||
\(650\) | −1.74543 | −0.0684613 | ||||||||
\(651\) | −2.18309 | −0.0855621 | ||||||||
\(652\) | −32.4720 | −1.27170 | ||||||||
\(653\) | 38.4291 | 1.50385 | 0.751924 | − | 0.659249i | \(-0.229126\pi\) | ||||
0.751924 | + | 0.659249i | \(0.229126\pi\) | |||||||
\(654\) | −11.5518 | −0.451710 | ||||||||
\(655\) | 11.6388 | 0.454767 | ||||||||
\(656\) | 2.49796 | 0.0975291 | ||||||||
\(657\) | −15.0344 | −0.586549 | ||||||||
\(658\) | 2.83802 | 0.110637 | ||||||||
\(659\) | −13.0048 | −0.506594 | −0.253297 | − | 0.967389i | \(-0.581515\pi\) | ||||
−0.253297 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(660\) | 2.80041 | 0.109006 | ||||||||
\(661\) | 17.4699 | 0.679500 | 0.339750 | − | 0.940516i | \(-0.389658\pi\) | ||||
0.339750 | + | 0.940516i | \(0.389658\pi\) | |||||||
\(662\) | −4.63562 | −0.180168 | ||||||||
\(663\) | −0.0833935 | −0.00323874 | ||||||||
\(664\) | −12.6005 | −0.488994 | ||||||||
\(665\) | 3.40006 | 0.131848 | ||||||||
\(666\) | 1.64116 | 0.0635937 | ||||||||
\(667\) | 51.1347 | 1.97994 | ||||||||
\(668\) | −5.23548 | −0.202567 | ||||||||
\(669\) | −1.31581 | −0.0508721 | ||||||||
\(670\) | 26.4610 | 1.02228 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −2.34203 | −0.0903457 | ||||||||
\(673\) | −21.0297 | −0.810637 | −0.405319 | − | 0.914175i | \(-0.632839\pi\) | ||||
−0.405319 | + | 0.914175i | \(0.632839\pi\) | |||||||
\(674\) | 17.3699 | 0.669063 | ||||||||
\(675\) | 0.522583 | 0.0201142 | ||||||||
\(676\) | −4.61751 | −0.177596 | ||||||||
\(677\) | 38.9808 | 1.49816 | 0.749078 | − | 0.662482i | \(-0.230497\pi\) | ||||
0.749078 | + | 0.662482i | \(0.230497\pi\) | |||||||
\(678\) | −7.87577 | −0.302467 | ||||||||
\(679\) | −0.243736 | −0.00935373 | ||||||||
\(680\) | −0.118792 | −0.00455547 | ||||||||
\(681\) | −7.33476 | −0.281069 | ||||||||
\(682\) | 4.44304 | 0.170133 | ||||||||
\(683\) | −12.0413 | −0.460746 | −0.230373 | − | 0.973102i | \(-0.573995\pi\) | ||||
−0.230373 | + | 0.973102i | \(0.573995\pi\) | |||||||
\(684\) | −5.26185 | −0.201192 | ||||||||
\(685\) | −5.90296 | −0.225540 | ||||||||
\(686\) | −4.59962 | −0.175614 | ||||||||
\(687\) | 4.61757 | 0.176171 | ||||||||
\(688\) | 2.85325 | 0.108779 | ||||||||
\(689\) | 21.0489 | 0.801899 | ||||||||
\(690\) | 15.1044 | 0.575015 | ||||||||
\(691\) | 20.6612 | 0.785988 | 0.392994 | − | 0.919541i | \(-0.371439\pi\) | ||||
0.392994 | + | 0.919541i | \(0.371439\pi\) | |||||||
\(692\) | 28.5544 | 1.08548 | ||||||||
\(693\) | 0.404149 | 0.0153523 | ||||||||
\(694\) | −20.2084 | −0.767099 | ||||||||
\(695\) | −23.4291 | −0.888715 | ||||||||
\(696\) | −16.1070 | −0.610534 | ||||||||
\(697\) | 0.128759 | 0.00487708 | ||||||||
\(698\) | 3.21770 | 0.121792 | ||||||||
\(699\) | −29.1255 | −1.10163 | ||||||||
\(700\) | 0.279514 | 0.0105647 | ||||||||
\(701\) | −11.9387 | −0.450920 | −0.225460 | − | 0.974252i | \(-0.572388\pi\) | ||||
−0.225460 | + | 0.974252i | \(0.572388\pi\) | |||||||
\(702\) | −3.34000 | −0.126060 | ||||||||
\(703\) | 7.93291 | 0.299195 | ||||||||
\(704\) | 3.96966 | 0.149612 | ||||||||
\(705\) | −18.0650 | −0.680367 | ||||||||
\(706\) | −23.4545 | −0.882722 | ||||||||
\(707\) | −5.92260 | −0.222742 | ||||||||
\(708\) | −0.845285 | −0.0317678 | ||||||||
\(709\) | −15.3955 | −0.578189 | −0.289095 | − | 0.957300i | \(-0.593354\pi\) | ||||
−0.289095 | + | 0.957300i | \(0.593354\pi\) | |||||||
\(710\) | 19.9792 | 0.749804 | ||||||||
\(711\) | 10.9481 | 0.410585 | ||||||||
\(712\) | −34.9440 | −1.30958 | ||||||||
\(713\) | −46.8782 | −1.75560 | ||||||||
\(714\) | −0.00682694 | −0.000255492 0 | ||||||||
\(715\) | 8.59233 | 0.321335 | ||||||||
\(716\) | 17.9531 | 0.670939 | ||||||||
\(717\) | 30.6121 | 1.14323 | ||||||||
\(718\) | −22.4043 | −0.836120 | ||||||||
\(719\) | 18.8466 | 0.702859 | 0.351430 | − | 0.936214i | \(-0.385696\pi\) | ||||
0.351430 | + | 0.936214i | \(0.385696\pi\) | |||||||
\(720\) | 0.843060 | 0.0314190 | ||||||||
\(721\) | 4.51296 | 0.168071 | ||||||||
\(722\) | −2.62596 | −0.0977280 | ||||||||
\(723\) | −22.3844 | −0.832486 | ||||||||
\(724\) | 27.6602 | 1.02798 | ||||||||
\(725\) | 3.07915 | 0.114357 | ||||||||
\(726\) | −0.822526 | −0.0305268 | ||||||||
\(727\) | −34.5785 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(728\) | −4.48619 | −0.166269 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.1668 | −0.968476 | ||||||||
\(731\) | 0.147072 | 0.00543965 | ||||||||
\(732\) | −1.32345 | −0.0489161 | ||||||||
\(733\) | −18.9209 | −0.698859 | −0.349430 | − | 0.936963i | \(-0.613625\pi\) | ||||
−0.349430 | + | 0.936963i | \(0.613625\pi\) | |||||||
\(734\) | −31.0175 | −1.14488 | ||||||||
\(735\) | 14.4663 | 0.533598 | ||||||||
\(736\) | −50.2911 | −1.85375 | ||||||||
\(737\) | 15.2035 | 0.560027 | ||||||||
\(738\) | 5.15693 | 0.189829 | ||||||||
\(739\) | 15.6521 | 0.575773 | 0.287886 | − | 0.957665i | \(-0.407047\pi\) | ||||
0.287886 | + | 0.957665i | \(0.407047\pi\) | |||||||
\(740\) | −5.58757 | −0.205403 | ||||||||
\(741\) | −16.1446 | −0.593088 | ||||||||
\(742\) | 1.72315 | 0.0632589 | ||||||||
\(743\) | 12.8846 | 0.472691 | 0.236346 | − | 0.971669i | \(-0.424050\pi\) | ||||
0.236346 | + | 0.971669i | \(0.424050\pi\) | |||||||
\(744\) | 14.7662 | 0.541356 | ||||||||
\(745\) | 1.00237 | 0.0367239 | ||||||||
\(746\) | 3.97868 | 0.145670 | ||||||||
\(747\) | 4.60944 | 0.168651 | ||||||||
\(748\) | −0.0271796 | −0.000993785 0 | ||||||||
\(749\) | −3.45543 | −0.126259 | ||||||||
\(750\) | 9.61182 | 0.350974 | ||||||||
\(751\) | 4.34890 | 0.158693 | 0.0793467 | − | 0.996847i | \(-0.474717\pi\) | ||||
0.0793467 | + | 0.996847i | \(0.474717\pi\) | |||||||
\(752\) | 3.40149 | 0.124039 | ||||||||
\(753\) | −21.4637 | −0.782182 | ||||||||
\(754\) | −19.6799 | −0.716699 | ||||||||
\(755\) | 28.0628 | 1.02131 | ||||||||
\(756\) | 0.534871 | 0.0194531 | ||||||||
\(757\) | 39.4539 | 1.43398 | 0.716989 | − | 0.697085i | \(-0.245520\pi\) | ||||
0.716989 | + | 0.697085i | \(0.245520\pi\) | |||||||
\(758\) | −29.0200 | −1.05405 | ||||||||
\(759\) | 8.67841 | 0.315006 | ||||||||
\(760\) | −22.9977 | −0.834213 | ||||||||
\(761\) | −38.6312 | −1.40038 | −0.700190 | − | 0.713957i | \(-0.746901\pi\) | ||||
−0.700190 | + | 0.713957i | \(0.746901\pi\) | |||||||
\(762\) | −5.04983 | −0.182936 | ||||||||
\(763\) | 5.67597 | 0.205484 | ||||||||
\(764\) | −3.24828 | −0.117519 | ||||||||
\(765\) | 0.0434559 | 0.00157115 | ||||||||
\(766\) | 15.0710 | 0.544538 | ||||||||
\(767\) | −2.59354 | −0.0936472 | ||||||||
\(768\) | 14.7867 | 0.533568 | ||||||||
\(769\) | −29.2863 | −1.05609 | −0.528046 | − | 0.849216i | \(-0.677075\pi\) | ||||
−0.528046 | + | 0.849216i | \(0.677075\pi\) | |||||||
\(770\) | 0.703404 | 0.0253489 | ||||||||
\(771\) | −4.42849 | −0.159488 | ||||||||
\(772\) | 11.0039 | 0.396039 | ||||||||
\(773\) | 1.46255 | 0.0526041 | 0.0263020 | − | 0.999654i | \(-0.491627\pi\) | ||||
0.0263020 | + | 0.999654i | \(0.491627\pi\) | |||||||
\(774\) | 5.89039 | 0.211726 | ||||||||
\(775\) | −2.82284 | −0.101399 | ||||||||
\(776\) | 1.64861 | 0.0591816 | ||||||||
\(777\) | −0.806385 | −0.0289289 | ||||||||
\(778\) | −28.3268 | −1.01557 | ||||||||
\(779\) | 24.9271 | 0.893107 | ||||||||
\(780\) | 11.3715 | 0.407166 | ||||||||
\(781\) | 11.4793 | 0.410760 | ||||||||
\(782\) | −0.146597 | −0.00524230 | ||||||||
\(783\) | 5.89217 | 0.210569 | ||||||||
\(784\) | −2.72389 | −0.0972817 | ||||||||
\(785\) | −27.0337 | −0.964874 | ||||||||
\(786\) | −4.52424 | −0.161374 | ||||||||
\(787\) | 25.9663 | 0.925600 | 0.462800 | − | 0.886463i | \(-0.346845\pi\) | ||||
0.462800 | + | 0.886463i | \(0.346845\pi\) | |||||||
\(788\) | −24.8814 | −0.886363 | ||||||||
\(789\) | 26.2060 | 0.932958 | ||||||||
\(790\) | 19.0547 | 0.677934 | ||||||||
\(791\) | 3.86976 | 0.137593 | ||||||||
\(792\) | −2.73363 | −0.0971351 | ||||||||
\(793\) | −4.06066 | −0.144198 | ||||||||
\(794\) | −5.48797 | −0.194761 | ||||||||
\(795\) | −10.9685 | −0.389012 | ||||||||
\(796\) | 10.3780 | 0.367838 | ||||||||
\(797\) | −31.4932 | −1.11555 | −0.557773 | − | 0.829993i | \(-0.688344\pi\) | ||||
−0.557773 | + | 0.829993i | \(0.688344\pi\) | |||||||
\(798\) | −1.32167 | −0.0467865 | ||||||||
\(799\) | 0.175331 | 0.00620278 | ||||||||
\(800\) | −3.02835 | −0.107068 | ||||||||
\(801\) | 12.7830 | 0.451666 | ||||||||
\(802\) | −15.9689 | −0.563883 | ||||||||
\(803\) | −15.0344 | −0.530553 | ||||||||
\(804\) | 20.1211 | 0.709615 | ||||||||
\(805\) | −7.42156 | −0.261576 | ||||||||
\(806\) | 18.0417 | 0.635492 | ||||||||
\(807\) | 11.4188 | 0.401961 | ||||||||
\(808\) | 40.0599 | 1.40930 | ||||||||
\(809\) | 8.19184 | 0.288010 | 0.144005 | − | 0.989577i | \(-0.454002\pi\) | ||||
0.144005 | + | 0.989577i | \(0.454002\pi\) | |||||||
\(810\) | 1.74046 | 0.0611535 | ||||||||
\(811\) | 8.90734 | 0.312779 | 0.156389 | − | 0.987695i | \(-0.450015\pi\) | ||||
0.156389 | + | 0.987695i | \(0.450015\pi\) | |||||||
\(812\) | 3.15155 | 0.110598 | ||||||||
\(813\) | −2.05980 | −0.0722404 | ||||||||
\(814\) | 1.64116 | 0.0575227 | ||||||||
\(815\) | 51.9177 | 1.81860 | ||||||||
\(816\) | −0.00818239 | −0.000286441 0 | ||||||||
\(817\) | 28.4725 | 0.996126 | ||||||||
\(818\) | 0.631577 | 0.0220826 | ||||||||
\(819\) | 1.64111 | 0.0573451 | ||||||||
\(820\) | −17.5575 | −0.613135 | ||||||||
\(821\) | −25.1573 | −0.877995 | −0.438997 | − | 0.898488i | \(-0.644666\pi\) | ||||
−0.438997 | + | 0.898488i | \(0.644666\pi\) | |||||||
\(822\) | 2.29459 | 0.0800331 | ||||||||
\(823\) | 50.8751 | 1.77340 | 0.886698 | − | 0.462350i | \(-0.152994\pi\) | ||||
0.886698 | + | 0.462350i | \(0.152994\pi\) | |||||||
\(824\) | −30.5252 | −1.06340 | ||||||||
\(825\) | 0.522583 | 0.0181940 | ||||||||
\(826\) | −0.212318 | −0.00738748 | ||||||||
\(827\) | 43.4799 | 1.51195 | 0.755973 | − | 0.654603i | \(-0.227164\pi\) | ||||
0.755973 | + | 0.654603i | \(0.227164\pi\) | |||||||
\(828\) | 11.4855 | 0.399147 | ||||||||
\(829\) | −34.9915 | −1.21530 | −0.607652 | − | 0.794203i | \(-0.707889\pi\) | ||||
−0.607652 | + | 0.794203i | \(0.707889\pi\) | |||||||
\(830\) | 8.02254 | 0.278466 | ||||||||
\(831\) | −27.0262 | −0.937528 | ||||||||
\(832\) | 16.1195 | 0.558842 | ||||||||
\(833\) | −0.140404 | −0.00486471 | ||||||||
\(834\) | 9.10733 | 0.315361 | ||||||||
\(835\) | 8.37072 | 0.289681 | ||||||||
\(836\) | −5.26185 | −0.181985 | ||||||||
\(837\) | −5.40170 | −0.186710 | ||||||||
\(838\) | 14.2574 | 0.492514 | ||||||||
\(839\) | 31.5500 | 1.08923 | 0.544614 | − | 0.838687i | \(-0.316676\pi\) | ||||
0.544614 | + | 0.838687i | \(0.316676\pi\) | |||||||
\(840\) | 2.33773 | 0.0806593 | ||||||||
\(841\) | 5.71771 | 0.197162 | ||||||||
\(842\) | 9.92384 | 0.341998 | ||||||||
\(843\) | −4.85590 | −0.167246 | ||||||||
\(844\) | 33.9640 | 1.16909 | ||||||||
\(845\) | 7.38267 | 0.253972 | ||||||||
\(846\) | 7.02221 | 0.241429 | ||||||||
\(847\) | 0.404149 | 0.0138867 | ||||||||
\(848\) | 2.06527 | 0.0709217 | ||||||||
\(849\) | −15.0805 | −0.517561 | ||||||||
\(850\) | −0.00882755 | −0.000302782 0 | ||||||||
\(851\) | −17.3158 | −0.593577 | ||||||||
\(852\) | 15.1922 | 0.520477 | ||||||||
\(853\) | −4.60871 | −0.157799 | −0.0788997 | − | 0.996883i | \(-0.525141\pi\) | ||||
−0.0788997 | + | 0.996883i | \(0.525141\pi\) | |||||||
\(854\) | −0.332423 | −0.0113753 | ||||||||
\(855\) | 8.41288 | 0.287714 | ||||||||
\(856\) | 23.3722 | 0.798846 | ||||||||
\(857\) | 49.6081 | 1.69458 | 0.847290 | − | 0.531131i | \(-0.178233\pi\) | ||||
0.847290 | + | 0.531131i | \(0.178233\pi\) | |||||||
\(858\) | −3.34000 | −0.114026 | ||||||||
\(859\) | −57.5877 | −1.96487 | −0.982433 | − | 0.186617i | \(-0.940248\pi\) | ||||
−0.982433 | + | 0.186617i | \(0.940248\pi\) | |||||||
\(860\) | −20.0547 | −0.683859 | ||||||||
\(861\) | −2.53386 | −0.0863537 | ||||||||
\(862\) | −24.0186 | −0.818077 | ||||||||
\(863\) | −40.8905 | −1.39193 | −0.695964 | − | 0.718076i | \(-0.745023\pi\) | ||||
−0.695964 | + | 0.718076i | \(0.745023\pi\) | |||||||
\(864\) | −5.79496 | −0.197149 | ||||||||
\(865\) | −45.6540 | −1.55228 | ||||||||
\(866\) | −29.4496 | −1.00074 | ||||||||
\(867\) | 16.9996 | 0.577336 | ||||||||
\(868\) | −2.88921 | −0.0980663 | ||||||||
\(869\) | 10.9481 | 0.371388 | ||||||||
\(870\) | 10.2551 | 0.347680 | ||||||||
\(871\) | 61.7362 | 2.09185 | ||||||||
\(872\) | −38.3918 | −1.30011 | ||||||||
\(873\) | −0.603085 | −0.0204113 | ||||||||
\(874\) | −28.3806 | −0.959987 | ||||||||
\(875\) | −4.72278 | −0.159659 | ||||||||
\(876\) | −19.8973 | −0.672268 | ||||||||
\(877\) | −7.81665 | −0.263949 | −0.131975 | − | 0.991253i | \(-0.542132\pi\) | ||||
−0.131975 | + | 0.991253i | \(0.542132\pi\) | |||||||
\(878\) | 33.6071 | 1.13418 | ||||||||
\(879\) | 19.5057 | 0.657912 | ||||||||
\(880\) | 0.843060 | 0.0284196 | ||||||||
\(881\) | −16.7321 | −0.563719 | −0.281860 | − | 0.959456i | \(-0.590951\pi\) | ||||
−0.281860 | + | 0.959456i | \(0.590951\pi\) | |||||||
\(882\) | −5.62333 | −0.189348 | ||||||||
\(883\) | −18.3230 | −0.616617 | −0.308308 | − | 0.951286i | \(-0.599763\pi\) | ||||
−0.308308 | + | 0.951286i | \(0.599763\pi\) | |||||||
\(884\) | −0.110367 | −0.00371205 | ||||||||
\(885\) | 1.35148 | 0.0454295 | ||||||||
\(886\) | −23.0171 | −0.773275 | ||||||||
\(887\) | 36.8957 | 1.23884 | 0.619419 | − | 0.785061i | \(-0.287368\pi\) | ||||
0.619419 | + | 0.785061i | \(0.287368\pi\) | |||||||
\(888\) | 5.45432 | 0.183035 | ||||||||
\(889\) | 2.48124 | 0.0832180 | ||||||||
\(890\) | 22.2483 | 0.745766 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −1.74141 | −0.0583066 | ||||||||
\(893\) | 33.9434 | 1.13587 | ||||||||
\(894\) | −0.389639 | −0.0130315 | ||||||||
\(895\) | −28.7042 | −0.959476 | ||||||||
\(896\) | −3.36445 | −0.112398 | ||||||||
\(897\) | 35.2401 | 1.17663 | ||||||||
\(898\) | −20.5841 | −0.686900 | ||||||||
\(899\) | −31.8278 | −1.06152 | ||||||||
\(900\) | 0.691613 | 0.0230538 | ||||||||
\(901\) | 0.106455 | 0.00354654 | ||||||||
\(902\) | 5.15693 | 0.171707 | ||||||||
\(903\) | −2.89425 | −0.0963145 | ||||||||
\(904\) | −26.1747 | −0.870558 | ||||||||
\(905\) | −44.2243 | −1.47006 | ||||||||
\(906\) | −10.9085 | −0.362412 | ||||||||
\(907\) | −1.15826 | −0.0384593 | −0.0192297 | − | 0.999815i | \(-0.506121\pi\) | ||||
−0.0192297 | + | 0.999815i | \(0.506121\pi\) | |||||||
\(908\) | −9.70720 | −0.322145 | ||||||||
\(909\) | −14.6545 | −0.486059 | ||||||||
\(910\) | 2.85629 | 0.0946850 | ||||||||
\(911\) | −39.7016 | −1.31537 | −0.657686 | − | 0.753292i | \(-0.728465\pi\) | ||||
−0.657686 | + | 0.753292i | \(0.728465\pi\) | |||||||
\(912\) | −1.58407 | −0.0524540 | ||||||||
\(913\) | 4.60944 | 0.152550 | ||||||||
\(914\) | 3.04635 | 0.100764 | ||||||||
\(915\) | 2.11599 | 0.0699525 | ||||||||
\(916\) | 6.11112 | 0.201917 | ||||||||
\(917\) | 2.22299 | 0.0734096 | ||||||||
\(918\) | −0.0168922 | −0.000557524 0 | ||||||||
\(919\) | 34.7872 | 1.14752 | 0.573762 | − | 0.819022i | \(-0.305483\pi\) | ||||
0.573762 | + | 0.819022i | \(0.305483\pi\) | |||||||
\(920\) | 50.1988 | 1.65500 | ||||||||
\(921\) | −7.49773 | −0.247059 | ||||||||
\(922\) | −12.9977 | −0.428057 | ||||||||
\(923\) | 46.6134 | 1.53430 | ||||||||
\(924\) | 0.534871 | 0.0175960 | ||||||||
\(925\) | −1.04269 | −0.0342835 | ||||||||
\(926\) | −20.7663 | −0.682424 | ||||||||
\(927\) | 11.1666 | 0.366758 | ||||||||
\(928\) | −34.1449 | −1.12086 | ||||||||
\(929\) | −16.5877 | −0.544226 | −0.272113 | − | 0.962265i | \(-0.587722\pi\) | ||||
−0.272113 | + | 0.962265i | \(0.587722\pi\) | |||||||
\(930\) | −9.40143 | −0.308285 | ||||||||
\(931\) | −27.1816 | −0.890841 | ||||||||
\(932\) | −38.5461 | −1.26262 | ||||||||
\(933\) | −17.7437 | −0.580904 | ||||||||
\(934\) | −14.2120 | −0.465030 | ||||||||
\(935\) | 0.0434559 | 0.00142116 | ||||||||
\(936\) | −11.1003 | −0.362826 | ||||||||
\(937\) | 29.0025 | 0.947470 | 0.473735 | − | 0.880667i | \(-0.342905\pi\) | ||||
0.473735 | + | 0.880667i | \(0.342905\pi\) | |||||||
\(938\) | 5.05399 | 0.165018 | ||||||||
\(939\) | −13.3708 | −0.436340 | ||||||||
\(940\) | −23.9081 | −0.779797 | ||||||||
\(941\) | 41.2410 | 1.34442 | 0.672210 | − | 0.740361i | \(-0.265345\pi\) | ||||
0.672210 | + | 0.740361i | \(0.265345\pi\) | |||||||
\(942\) | 10.5085 | 0.342386 | ||||||||
\(943\) | −54.4103 | −1.77184 | ||||||||
\(944\) | −0.254472 | −0.00828236 | ||||||||
\(945\) | −0.855175 | −0.0278189 | ||||||||
\(946\) | 5.89039 | 0.191513 | ||||||||
\(947\) | −14.9009 | −0.484214 | −0.242107 | − | 0.970250i | \(-0.577839\pi\) | ||||
−0.242107 | + | 0.970250i | \(0.577839\pi\) | |||||||
\(948\) | 14.4892 | 0.470588 | ||||||||
\(949\) | −61.0497 | −1.98176 | ||||||||
\(950\) | −1.70897 | −0.0554465 | ||||||||
\(951\) | 10.5527 | 0.342195 | ||||||||
\(952\) | −0.0226890 | −0.000735355 0 | ||||||||
\(953\) | −29.4563 | −0.954185 | −0.477092 | − | 0.878853i | \(-0.658309\pi\) | ||||
−0.477092 | + | 0.878853i | \(0.658309\pi\) | |||||||
\(954\) | 4.26366 | 0.138041 | ||||||||
\(955\) | 5.19349 | 0.168057 | ||||||||
\(956\) | 40.5135 | 1.31030 | ||||||||
\(957\) | 5.89217 | 0.190467 | ||||||||
\(958\) | 8.95227 | 0.289235 | ||||||||
\(959\) | −1.12745 | −0.0364073 | ||||||||
\(960\) | −8.39977 | −0.271101 | ||||||||
\(961\) | −1.82161 | −0.0587617 | ||||||||
\(962\) | 6.66420 | 0.214862 | ||||||||
\(963\) | −8.54990 | −0.275517 | ||||||||
\(964\) | −29.6247 | −0.954147 | ||||||||
\(965\) | −17.5935 | −0.566356 | ||||||||
\(966\) | 2.88490 | 0.0928202 | ||||||||
\(967\) | 39.2447 | 1.26202 | 0.631012 | − | 0.775773i | \(-0.282640\pi\) | ||||
0.631012 | + | 0.775773i | \(0.282640\pi\) | |||||||
\(968\) | −2.73363 | −0.0878620 | ||||||||
\(969\) | −0.0816519 | −0.00262304 | ||||||||
\(970\) | −1.04964 | −0.0337020 | ||||||||
\(971\) | 19.0146 | 0.610207 | 0.305104 | − | 0.952319i | \(-0.401309\pi\) | ||||
0.305104 | + | 0.952319i | \(0.401309\pi\) | |||||||
\(972\) | 1.32345 | 0.0424497 | ||||||||
\(973\) | −4.47489 | −0.143458 | ||||||||
\(974\) | 32.0919 | 1.02829 | ||||||||
\(975\) | 2.12203 | 0.0679594 | ||||||||
\(976\) | −0.398423 | −0.0127532 | ||||||||
\(977\) | 15.7282 | 0.503188 | 0.251594 | − | 0.967833i | \(-0.419045\pi\) | ||||
0.251594 | + | 0.967833i | \(0.419045\pi\) | |||||||
\(978\) | −20.1814 | −0.645330 | ||||||||
\(979\) | 12.7830 | 0.408548 | ||||||||
\(980\) | 19.1455 | 0.611579 | ||||||||
\(981\) | 14.0443 | 0.448399 | ||||||||
\(982\) | 24.7023 | 0.788281 | ||||||||
\(983\) | −41.9230 | −1.33714 | −0.668568 | − | 0.743651i | \(-0.733092\pi\) | ||||
−0.668568 | + | 0.743651i | \(0.733092\pi\) | |||||||
\(984\) | 17.1388 | 0.546365 | ||||||||
\(985\) | 39.7815 | 1.26754 | ||||||||
\(986\) | −0.0995315 | −0.00316973 | ||||||||
\(987\) | −3.45037 | −0.109826 | ||||||||
\(988\) | −21.3666 | −0.679763 | ||||||||
\(989\) | −62.1491 | −1.97623 | ||||||||
\(990\) | 1.74046 | 0.0553154 | ||||||||
\(991\) | 17.5601 | 0.557816 | 0.278908 | − | 0.960318i | \(-0.410027\pi\) | ||||
0.278908 | + | 0.960318i | \(0.410027\pi\) | |||||||
\(992\) | 31.3027 | 0.993861 | ||||||||
\(993\) | 5.63583 | 0.178848 | ||||||||
\(994\) | 3.81597 | 0.121035 | ||||||||
\(995\) | −16.5928 | −0.526027 | ||||||||
\(996\) | 6.10037 | 0.193298 | ||||||||
\(997\) | −11.7778 | −0.373008 | −0.186504 | − | 0.982454i | \(-0.559716\pi\) | ||||
−0.186504 | + | 0.982454i | \(0.559716\pi\) | |||||||
\(998\) | 21.0649 | 0.666799 | ||||||||
\(999\) | −1.99527 | −0.0631275 |
(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 | 2013.2.a.e.1.8 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.6 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.8 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.6 | 13 | 3.2 | odd | 2 |